SHOCK IGNITION OF N-HEPTANE WITH SUPPLEMENTAL HYDROGEN

Transcription

1 SHOCK IGNITION OF N-HEPTANE WITH SUPPLEMENTAL HYDROGEN by JD MacLean A thesis submitted to the Department of Mechanical and Materials Engineering In conformity with the requirements for the degree of Master of Applied Science Queen s University Kingston, Ontario, Canada (August, 2014) Copyright JD MacLean, 2014

2 Abstract The objective of the study was to investigate the effect of adding molecular hydrogen to a mixture of n- heptane (surrogate for diesel fuel) and air on ignition delay time at prototypic post-compression diesel engine conditions. Ignition delay time data was measured using the reflected shock wave technique at a pressure of 20 bar (representative of part load engine conditions), for three fuel equivalence ratios (ϕ = 0.833, 1, 1.25) over a temperature range of 700 K to 1150 K. The ignition delay time data, obtained for all heptane-hydrogen fuel combinations and fuel-air equivalence ratios, is characterized by a negative temperature coefficient region between 800 K and 1000 K. This is shown to be consistent with known large hydrocarbon molecular kinetics at intermediate temperatures. For prototypic diesel postcompression temperatures of less than 1000 K the addition of hydrogen to n-heptane-air, for all three equivalence ratios, resulted in an increase in the measured ignition delay time. This increase was the result of hydrogen acting as a diluent due to the relatively slow dissociation compared to heptane. Therefore, although hydrogen addition to the diesel fuel is expected to reduce soot, it will have a negative impact on the cetane number. However, the impact is expected to be very small as 20% hydrogen addition on average only increases the ignition delay time by 8%. For temperatures above 1000 K, the fast decomposition of hydrogen provides free radicals that speed up the n-heptane abstraction process which results in a reduction in ignition delay time. The ignition delay time prediction using a constant volume model with the Lund reaction mechanism [1] was satisfactory. There was a negative 50 K temperature shift in the computed ignition delay time, compared to the measured data that can be attributed to the zero velocity approximation of the constant volume model. For all three equivalence ratios the constant volume model predicted the increase in ignition delay time with hydrogen addition for temperatures below 1000 K, and the decrease for temperatures above 1000 K. ii

3 Acknowledgements First and foremost, I would like to thank my supervisor, Dr. Gaby Ciccarelli, for his support. His continuous insight and guidance over the last two and a half years was essential to this project. I also must thank Mark Kellenberger for initially showing me how to operate my apparatus and the time he took to help me with any problems. Mitch Cross, Thomas Pinos and Andrew House were valuable colleagues and friends in the combustion lab. Their feedback and ideas were always appreciated. The constant construction of my apparatus would have been impossible without the help of the machine shop staff. Andy Bryson, Corey Fowler, Derek Hodgson and Paul Moreland always stepped up to meet the demanding deadlines I set and never hesitated to teach me how to use a machine. I must thank my former roommates for their support and distractions at home and within the department. Lastly, I must thank my parents, the rest of my family and my girlfriend, Kathryn, for their constant support, love and encouragement. iii

4 Table of Contents Abstract... ii Acknowledgements... iii List of Figures... vii List of Tables... x Nomenclature... xi Chapter 1 Introduction Objectives... 8 Chapter 2 Literature Review Ignition Delay Time Measurement of Ignition Delay Time Shock Tube Technique - Ignition Delay Time Diesel Surrogates Need for Surrogates Diesel Fuel Composition Targets for Diesel Surrogates Cetane Number N-Heptane as a Diesel Surrogate Benefits Drawbacks Measured n-heptane Ignition Delay Time n-heptane Reaction Mechanisms Effects of Supplemental Hydrogen Addition on Ignition Delay Time Chapter 3 Procedure and Apparatus Overview Shock Theory Normal Shock Relations Normal Shock Reflections Shock Tube Theory Shock Tube Tailoring Shock Tube Driver Double Diaphragm Holder iv

5 3.3.3 Transition Section Driven Section Control Panel Instrumentation Pressure Transducers Photodiode Ignition Delay Time Measurement Test Mixture Operating Procedure Chapter 4 Results and Discussion Effect of Driver Gas on Test Time Reflected Gas Temperature Ignition Delay Time Data Stoichiometric n-heptane-air Off-Stoichiometric n-heptane Air Data Repeatability Studies Stoichiometric n-heptane-air with Hydrogen Addition Off-Stoichiometric n-heptane-air with Hydrogen Addition Ignition Delay Time Predictions Constant Volume Reaction Model Solver Algorithm Mathematical Model Effects of Fuel Ratio Chapter 5 Summary and Conclusions References Appendix A Uncertainty Analysis Appendix B Shock Tube Theory B.1 Normal Shock Relations B.2 Normal Shock Reflections B.3 Shock Tube Theory B.4 Shock Tube Tailoring Appendix C Constant Volume Calculation C.1 Constant Volume Reaction C.1.1 Kinetic Models v

6 C.1.2 Equations of Motion C.1.3 Temperature Derivatives C.1.4 Physical Model C.1.5 Mathematical Model C.1.6 Solver Algorithm vi

7 List of Figures Figure 1.1: Top view of one fuel jet injected into a diesel engine cylinder [5]. 2 Figure 1.2: Top view of one fuel jet injected into a diesel engine cylinder with supplemental hydrogen premixed with air. 4 Figure 1.3: Unburned hydrocarbons in the exhaust of a diesel engine with increasing amounts of hydrogen in the fuel mixture [10]. 5 Figure 1.4: Exhaust NO x emissions with increasing amounts of hydrogen added to the fuel-air mixture under various load conditions [10]. 6 Figure 1.5: Exhaust gas NO x emissions with increasing amounts of hydrogen added to the fuel-air mixture [11]. 6 Figure 1.6: Soot formation with increasing amounts of diluents helium and hydrogen in propane fuel mixtures [12]. 7 Figure 2.1: Representation of molecules present in diesel fuel. C 16 isomers shown [24]. 15 Figure 2.2: Ignition delay times for stoichiometric n-heptane air mixtures scaled to a reflected shock pressure of 20 bar [31], [34]. 18 Figure 2.3: Ignition delay times for stoichiometric n-heptane air mixtures scaled to a reflected shock pressure of 40 bar [32], [33]. 19 Figure 2.4: Ignition delay times for stoichiometric n-heptane air mixtures calculated using the Lund mechanism [1] undergoing a constant volume reaction compared to shock tube data in the literature for a reflected shock pressure of 20 bar. 20 Figure 2.5: Ignition delay times for stoichiometric n-heptane air mixtures calculated using the Lund mechanism [1] undergoing a constant volume reaction compared to shock tube data in the literature for a reflected shock pressure of 40 bar. 21 Figure 2.6: Calculated ignition delay times for n-heptane-hydrogen-air mixtures for a pressure of 15 atm [38]. 22 Figure 3.1: Control volume for a normal shock wave 24 Figure 3.2: Reflection of a normal shock wave 25 Figure 3.3: Schematic of a shock tube after diaphragm rupture [40] 25 Figure 3.4: (a) An x-t diagram showing a position time history of the wave propagation; 26 Figure 3.5: Possible interactions between the reflected shock wave and the contact surface where (a) shows a shock wave propagating towards the end wall; and (b) shows an expansion fan propagating towards the end wall [41]. 28 vii

8 Figure 3.6: An x-t diagram of a tailored shock tube 30 Figure 3.7: Experimental shock tube apparatus 31 Figure 3.8: Double diaphragm holder with aluminum diaphragms 32 Figure 3.9: Schematic of double diaphragm operation 33 Figure 3.10: Diaphragm stamp method 34 Figure 3.11: a) Diaphragm stamp design, and b) fully opened burst aluminum diaphragm 34 Figure 3.12: Test showing planar shock wave downstream of the transition section [40] 35 Figure 3.13: Schematic of the apparatus 36 Figure 3.14: Responsivity of Edmund Optics s-series photodiode [43]. 39 Figure 3.15: Example of P3 pressure trace and CH emission showing the ignition delay time measurement technique 40 Figure 4.1 Available test time for a typical test with a helium driver and air as the test gas at an initial pressure of 67.6 kpa 44 Figure 4.2: Ignition delay time for a test under the same conditions as Figure Figure 4.3: Example of not enough test time after supplemental hydrogen addition with a helium driver 46 Figure 4.4: Pressure trace of the end wall pressure showing a tailored shock tube condition 47 Figure 4.5: Pressure trace of the end wall pressure showing a tailored shock tube condition with nitrogen in the driven section 48 Figure 4.6: Sensitivity of tailoring with varying driver gas mixture with air and nitrogen as the driven gas at an initial pressure of 68 kpa (absolute) 49 Figure 4.7: Comparison of different methods to calculate reflected temperature. CHOCFI temperature calculator (dotted) and normal shock relations assuming constant ratio of specific heats using Equation 3.12 (solid) for stoichiometric fuel-air ratio and 20 bar reflected pressure 51 Figure 4.8: Stoichiometric n-heptane-air data collected compared with data in the literature (Hartmann et al. [32], Fieweger et al. [33]) at 40 bar reflected pressure 53 Figure 4.9: Stoichiometric n-heptane-air data collected compared with data in the literature (Fieweger et al. [34], Davidson et al. [31]) at 20 bar reflected pressure 54 Figure 4.10: Ignition delay time of stoichiometric n-heptane-air with varying reflected pressure 55 Figure 4.11: Ignition delay times at 1000/T= Figure 4.12: Stoichiometric data at 20 bar plotted in terms of log (τ) 57 Figure 4.13: Ignition delay times for three different equivalence ratios (ϕ = 0.833, 1 and 1.25) at 20 bar reflected pressure and a fuel ratio of x = 1 58 Figure 4.14: Repeatability tests (points) compared to initial collected data (line) for ϕ = 1, x =1 and a reflected pressure of 20 bar 59 viii

9 Figure 4.15: Ignition delay times for stoichiometric n-heptane-hydrogen-air mixtures a 20 bar reflected pressure with a varying fuel ratio 61 Figure 4.16: Ignition delay times for ϕ = 1.25 n-heptane-hydrogen-air mixtures a 20 bar reflected pressure with a varying fuel ratio 62 Figure 4.17: Ignition delay times for ϕ = n-heptane-hydrogen-air mixtures a 20 bar reflected pressure with a varying fuel ratio 62 Figure 4.18: Ignition delay times for three different equivalence ratios (ϕ = 0.833, 1 and 1.25) at 20 bar reflected pressure and a fuel ratio of x = Figure 4.19: Stoichiometric n-heptane-hydrogen-air ignition delay times at 20 bar (dashed lines) compared to those predicted by the Lund mechanism (solid lines) 67 Figure 4.20: Rich (ϕ = 1.25) n-heptane-hydrogen-air ignition delay times (dashed lines) compared to those predicted by the Lund mechanism (solid lines) at 20 bar reflected pressure 68 Figure 4.21: Lean (ϕ = 0.833) n-heptane-hydrogen-air ignition delay times (dashed lines) compared to those predicted by the Lund mechanism (solid lines) at 20 bar reflected pressure 68 Figure 4.22: Comparison of different hydrogen mechanisms (Lund [8], Hong [11]) for x = 0, overlaid with various fuel ratios using the Lund mechanism for a stoichiometric fuel-air mixture and a reflected pressure of 20 bar 70 Figure A.1: Equations used in EES for uncertainty propagation 79 Figure A.2: Results of select properties and their uncertainty using EES 80 Figure B.1: Control volume for a normal shock wave 82 Figure B.2: Reflection of a normal shock wave 86 Figure B.3: Schematic of a shock tube after diaphragm rupture [40] 87 Figure B.4: (a) An x-t diagram showing a position time history of the wave propagation; 88 Figure B.5: Possible interactions between the reflected shock wave and the contact surface where (a) shows a shock wave propagating towards the end wall; and (b) shows an expansion fan propagating towards the end wall [41]. 90 Figure B.6: An x-t diagram of a tailored shock tube 92 Figure C.1: Path (red) between the frozen Hugoniot (solid) and equilibrium Hugoniot (dashed) curves for a constant volume explosion [18] 99 ix

10 List of Tables Table 2.1: Elementary reactions and their rate constants [17] 12 Table 2.2: Physical and chemical properties of North American diesel 14 Table 2.3: Standard operating conditions for a CFR engine [5] 17 Table 3.1: Diaphragm calibration 33 Table 3.2: Piezo-electric pressure transducer locations and properties 38 Table 4.1: Difference in ignition delay times at select reflected temperatures 59 Table 4.2: Difference in reflected temperature with repeat tests 60 Table A.1: Select properties for a test case with the associated uncertainty using EES error propagation 77 x

11 Nomenclature Abbreviations CFD CFR CN DAQ EES HHCI LLNL NTC TDC UHC CI computational fluid dynamics cooperative fuel research cetane number data acquisition Engineering Equation Solver homogeneous charge compression ignition Lawrence Livermore National Laboratory negative temperature coefficient top dead centre unburned hydrocarbon compression ignition Symbols A a Arrhenius pre-exponential constant [1/s] speed of sound [m/s] C molar concentration [mol/m 3 ] c e E a g h k specific heat capacity [J/K] specific internal energy [J/kg] activation energy [J/mol] Gibbs free energy [J/mol] specific enthalpy [J/kg] reaction rate constant [1/s] xi

12 M n N P q R s T u V W x x 4 y Mach number Arrhenius temperature power number of moles [mol] pressure [kpa, bar] total heat release [J] universal gas constant [J/mol K] entropy [J/mol K] temperature [K] flow velocity [m/s] shock wave speed [m/s] molecular weight [kg/mol] percentage of n-heptane with respect to the total fuel percentage of hydrogen with respect to the total driver mixture species fraction Greek Symbols γ η λ ratio of specific heats sonic parameter single progress variable ρ density [kg/m 3 ] thermicity [1/s] τ φ ignition delay time [s] equivalence ratio mass rate of production of species [kg/ m 3 s] molar rate of production of species [mol/m 3 s] xii

13 Chapter 1 Introduction With emission standards becoming ever-more strict, innovative internal combustion (IC) engine designs are required in order to meet these environmental restrictions. For example, particulate matter and oxides of nitrogen (NO x ) emissions have decreased for many years, with the latest taking effect in 2011 [2] in North America and 2014 in Europe [3]. The eventual regulation of carbon dioxide emissions in North America [4] is also having a strong influence on engine development. As a result of the impending carbon dioxide emission regulations, hydrogen has emerged as an important IC engine fuel. In a compression ignition engine, the fuel is injected directly into the cylinder via a nozzle. The nozzle typically has multiple holes producing radial fuel jets, a top view of which is shown in Figure 1.1where concentration contours of one of the jets is shown. As air is entrained, an inhomogeneous fuelair mixture is created surrounding the fuel jet. The mixture is fuel-rich at the center and lean around the edge of the jet. Ignition occurs somewhere in the premixed diesel-air region around stoichiometric conditions (ϕ = 1). At some point, the fuel becomes over-mixed and falls below the flammability limit, shaded area outside the ϕ L contour in Figure 1.1. Some of the fuel in this region does not take part in the reaction, which leads to emissions of unburned hydrocarbons (UHC). 1

14 Figure 1.1: Top view of one fuel jet injected into a diesel engine cylinder [5]. Historically diesel engines use high levels of exhaust gas recirculation (EGR) to dilute the cylinder fuel-air mixture to keep the combustion temperature down in order to control the production of NO x. More recently, high pressure common rail fuel injection was introduced to produce a very fine fuel spray to reduce the production of soot and unburned hydrocarbons. In the latest diesel engines, multiple fuel injections per cycle further reduce the amount of soot produced. In recent years, a new engine concept, referred to as homogeneous charge compression ignition (HCCI), has become possible because of advancements in fuel injector technology. HCCI can deliver diesel engine thermal efficiency at the same time as low NO x and particulate matter emissions. HCCI engines operate with the uniform combustion of a premixed fuel-air mixture, similar to a spark ignition engine, but ignition is via gas compression, similar to a compression ignition engine. In a HCCI engine the fuel is mixed with air before entering the cylinder via port injection. This avoids the fuel rich mixture zone inherent in direct injection engines. NO x emissions are very sensitive to combustion temperature, i.e., the higher the temperature the 2

15 more NOx that is produced. Therefore, NO x emissions can be reduced in a HCCI engine by running with lean mixture conditions that produce low temperature combustion. The main problems with current HCCI engine technology are the difficulties in controlling ignition timing and operating at full load where knock becomes an issue [6]. Dual fuel engines have also received quite a bit of attention lately. These engines, just like HCCI engines, operate by port injecting a primary fuel to produce a homogenous fuelair mixture, combustion is initiated by using a pilot fuel directly injected into the cylinder. The primary fuel is typically a gaseous fuel such as natural gas and the pilot fuel is typically diesel [7]. Syngas (mixture of methane, carbon monoxide and hydrogen) and hydrogen are being used in both HCCI and dual fuel engines to reduce the carbon to hydrogen ratio of the fuel in order to reduce the carbon dioxide produced [8], [9]. Mixing hydrogen with the inducted air in traditional diesel engines has also been used as an alternate method to reduce both particulate matter and UHC. A typical hydrogen addition method would be to premix the hydrogen with the air in the intake manifold [9], see Figure 1.2. As both components are gaseous under ambient conditions, mixing is easily accomplished in the intake system. The hydrogen-air mixture is entrained into the diesel jet forming a premixed diesel-hydrogen/air mixture region where ignition occurs. 3

16 Figure 1.2: Top view of one fuel jet injected into a diesel engine cylinder with supplemental hydrogen premixed with air. Engine studies by McWilliam [10] examine the effects of hydrogen induction with air on the UHC in the exhaust. It was found that in general, UHC is reduced as more hydrogen is added under various load conditions, as shown in Figure 1.3. The authors claim that this is due to the lower carbon number and more complete combustion because of the wide flammability limit of hydrogen, e.g., only 5% hydrogen by volume in air is required to propagate a flame. A drawback of this method is that hydrogen will be mixed with the air outside of the fuel jet, and as a result will not be consumed. 4

17 Figure 1.3: Unburned hydrocarbons in the exhaust of a diesel engine with increasing amounts of hydrogen in the fuel mixture [10]. In an engine, the highest temperature is achieved when the peak in heat release occurs near top dead centre because this corresponds to the point of maximum compression. Therefore, a second approach to reducing NO x is to delay the onset of combustion so that the peak heat release occurs well past top dead centre. This can be done by either delaying the start of fuel injection, or the so called ignition delay time relative to start of fuel injection. In engine studies performed by McWilliam [10] and Chun [11] it was determined that NO x emissions decreased with added hydrogen. The McWilliam data, shown in Figure 1.4, shows a decrease of NO x emissions up to a hydrogen addition of 4%, after which unstable combustion begins, leading to higher emissions. It was remarked that the pressure rise was slower under those conditions, leading to lower in-cylinder temperatures, caused by a delay in the ignition time due to the hydrogen addition. The Chun data, shown in Figure 1.5, shows decrease in exhaust NO x emissions for all hydrogen addition tested. 5

18 Figure 1.4: Exhaust NO x emissions with increasing amounts of hydrogen added to the fuel-air mixture under various load conditions [10]. 2% EGR Figure 1.5: Exhaust gas NO x emissions with increasing amounts of hydrogen added to the fuel-air mixture [11]. 6

19 The studies reported in [10] and [11] do not report on the effect of mixing hydrogen with the inducted air on soot production. It can be assumed that there is very little effect because the hydrogen does not penetrate the diesel rich zone where soot forms. Burner studies by Gulder [12] examined the effects of soot formation with varying amounts of hydrogen added to small alkanes, such as propane and butane. It was found that the soot reduction from hydrogen addition was similar to the soot reduction when the same fraction of inert helium was used instead of hydrogen, as shown in Figure 1.6. It was concluded that hydrogen reduces soot formation in small alkanes due to dilution effects, as there is less carbon in the fuel mixture and not chemical effects. Figure 1.6: Soot formation with increasing amounts of diluents helium and hydrogen in propane fuel mixtures [12]. Based on the Gulder burner study it can be imagined that if the hydrogen were added directly to the diesel fuel engine soot emissions could be reduced. This way the hydrogen molecule is in proximity to the carbon based fuel responsible for soot production. This should reduce the amount of soot produced at the same time as reducing the amount of over-mixing of the fuel because of the flammability limit widening by the presence of hydrogen in the over-mixed region. The challenge is coming up with a method to 7

20 premix the diesel and hydrogen, as they are in different states (liquid and vapour) under ambient conditions. Research is underway at University of Windsor to advance this technology of mixing hydrogen with diesel and implementing it on a diesel engine. The research reported in this thesis is part of the same project funded by the NSERC National Centre of Excellence Auto 21 program. 1.1 Objectives The engine technologies described above all involve ignition of hydrogen/diesel/air mixtures. There is plenty of ignition data for diesel, and diesel surrogates (to be discussed in the next chapter) air mixtures, in the literature but there is no experimental data available in the literature for diesel/hydrogen air mixtures. Chemical kinetic modellers make extensive use of ignition delay time data in the development and validation of combustion reaction mechanisms. The reaction mechanisms used to model IC engine combustion are tuned for the specific fuel. These mechanisms have not been validated when the hydrocarbon fuel is mixed with molecular hydrogen. Standard diesel engines operate with a compression ratio in the range of 13 to 15. Based on these values the in-cylinder post-compression temperature and pressure can be calculated assuming isentropic compression. For an initial temperature range of C, and a specific heat ratio of 1.4 the peak pressure ranges from bar and the peak temperature ranges from K. The objective of this project is to generate ignition delay time data that can be used to validate reaction mechanisms used for combustion modelling of engines that incorporate hydrogen in the fuel mix. 8

21 Chapter 2 Literature Review 2.1 Ignition Delay Time Ignition delay in a diesel engine is defined as the time that elapses between the start of fuel injection and the start of combustion. It consists of two parts that occur simultaneously: physical delay where mixing of the fuel air occurs and; chemical delay where pre-combustion reactions take place [13]. This is not a fundamental property of the fuel because during this time the pressure and temperature change as the fuel and air mix. However, if these parameters are held constant the ignition delay becomes an important parameter that can be used for developing and validating reaction mechanisms that can be used in modeling the transient phenomena that occur in a diesel engine Measurement of Ignition Delay Time Ignition delay time can be measured using many different methods that include rapid compression machines, jet stirred reactors and shock tubes. Rapid compression machines consist of a cylinder filled with an air-fuel mixture that undergoes a process much like the compression stroke of an IC engine. A piston quickly compresses the premixed gases to a final pressure and temperature at which point chemical reactions start. The process is considered isentropic, such that the temperature and pressure are related via the ideal gas isentropic relation. This technique can be used to determine whether a fuel-air mixture will auto-ignite for a given compression ratio and to measure the ignition delay time for a given post compression temperature and pressure. This technique is mainly used for low temperature, medium pressure conditions [14]. In a jet stirred reactor the reactants are injected into a spherical chamber with a high velocity through a perforated tube. The reactants burn and the products exit the chamber through outer ports. Because of the high inlet velocity and high levels of turbulence in the chamber, the reactants are thoroughly mixed with the products creating a homogeneous mixture within the chamber at a constant temperature. The overall reaction rate can be calculated by controlling the inlet flow rate and measuring 9

22 the chamber temperature and product concentrations. This technique is used for medium temperature, low pressure conditions [15]. Shock tubes are used to generate a shock wave of prescribed strength that instantaneously accelerates the test gas to a constant velocity, pressure and temperature. Ignition delay time can be measured at a location in the tube by measuring the time elapsed from the passage of the shock and start of chemical reaction. A more common approach to measure ignition delay time is to reflect the shock off the end wall. This creates a reflected shock wave that propagates in the direction opposite the incident shock wave generating a quiescent region of gas behind it. The stagnation of the post incident shock flow results in a step increase in pressure and temperature from the post incident shock condition. Measurements can be made on the tube sidewall, close to the end wall, or on the end wall itself. The ignition delay time is the time that elapses between the arrival of the reflected shock wave and the onset of reaction. The start of reaction is characterised by detection of chemiluminescence or a sudden rise in pressure. This technique is commonly used for high temperature, high pressure conditions [16] Shock Tube Technique - Ignition Delay Time Theoretically the conditions behind the reflected shock are zero flow and constant pressure and temperature. Ultimately there is a finite test time defined by the arrival of other gas dynamic waves that disrupt the constant pressure and temperature condition (this will be discussed in detail in the next chapter). A basic form of the energy equation is given by: ( ) 2.1 where the first term is the change in internal energy, the second term is the heat influx, the third term is the flow work, the fourth and fifth terms are the dissipation due to viscous forces, the sixth term is the heat input and the final term is the body-force work. Applying the energy equation to the zero flow condition behind the reflected shock, assuming adiabatic boundary condition, results in: 10

23 2.2 where is the mass rate of production of species i and is the enthalpy of formation at standard conditions, and N is the number of species considered. This is essentially First Law of Thermodynamics for a closed system undergoing an adiabatic process with no boundary work, and will be referred to as the constant volume model. The left hand side of the equation is the time rate of change of the sensible internal energy and the right hand side is the energy release rate from chemical reaction of the mixture. A reaction mechanism is required that defines the elementary reactions that describe the time evolution of the species concentration. The rate at which a species is produced or consumed (also referred to as the reaction rate) is given by in equation 1.1. This term follows the Law of Mass Action given by 2.3 where C i is the molar concentration of species i and ν i is the stoichiometric coefficient for species i. The reaction rate constant k takes the Arrhenius form given by: ( ) 2.4 where A, n and E a (activation energy) are empirical constants for the reaction, C i is the molar concentration of species i and ν i is the molar concentration coefficient for species i. The simplest and most developed reaction mechanism is for hydrogen and oxygen: 2.5 The key elementary reactions include: } 2.6 }

24 } 2.8 } 2.9 where M is any species present that acts as a collision partner. The first step is chain initiation where radicals are first formed. In chain propagation, there is no net change in the number of radicals. Chain branching has a net production of radicals which leads the reaction to occur rapidly. Chain termination recombines the radicals into the final products. Table 2.1 shows example chain reactions with their rate constants. Table 2.1: Elementary reactions and their rate constants [17] Reaction A n E a (cal/mol) Solving equations 1.2 and 1.3 with an appropriate reaction mechanism the mixture temperature time history can be obtained for a given initial mixture composition, pressure and temperature. Ideally the temperature remains constant, during which time free radicals form, and then suddenly increases as the radicals recombine to form the products. The ignition delay time is defined by the elapsed time to when the temperature gradient reaches its maximum [18]. Reaction mechanisms for hydrocarbons are considerably more complex than that of hydrogen. The most commonly used hydrocarbon fuel is methane (main component of natural gas) and as a result has the most developped reaction mechanism. Although methane only has a single carbon atom the mechanism consists of 53 species and 325 elementary reactions [17]. Mechanisms for larger hydrocarbons are significantly more complex than that for hydrogen and methane, both of which display single-stage ignition. The kinetics involved in the reaction of large straight-chain hydrocarbon fuels, such 12

25 as n-heptane, produces two-stage ignition at temperatures below 850 K. In two-stage ignition the fuel is initially partially oxidized via an isomerization reaction resulting in a small amount of heat release that produces a 5 to 10 K increase in temperature [19]. The isomerization process starts when a H is abstracted from the heptane, by for example a hydroxyl (OH) radical, to form an alkyl radical (original hydrocarbon molecule with an open C site, due to the vacated H) and a water molecule. The isomerization process is completed when the alkyl radical reacts with O 2 to form an alkylperoxy radical that has an unbonded O hanging from the chain. The O can then reach over and abstract a second H from the chain to expose another carbon that can act as the site for a second isomerization process. This new molecule can then react in a branching reaction to release three radicals, two OH radicals, and the hydrocarbon molecule with open O sites. This set of reactions which finally lead to the branching reaction producing two OH radicals and subsequent recombination to form water is responsible for the main ignition event where the temperature rises rapidly to the adiabatic flame temperature. In the intermediate temperature region, between 850 and 1000 K, the reaction proceeds by H abstraction by OH, as well as by the HO 2 radical. H abstraction by HO 2 produces the hydrogen peroxide (H 2 O 2 ) radical that is stable at temperatures below 1000 K. As the reaction proceeds the H 2 O 2 concentration increases and when the temperature reaches 1000 K the oxygen-oxygen bond readily breaks down to form two OH radicals [18]. The OH radicals then consume the fuel molecule resulting in rapid heat release causing an increase in temperature which further accelerates the breakdown of H 2 O 2. Once the temperature reaches 1200 K where hot ignition takes over through the branching reaction branching reaction, similar to that involved in hydrogen kinetics, see Equation 2.8. At temperatures below 1200 K, to around 850 K, this reaction is too slow. Due to the hydrogen peroxide branching reaction the intermediate and hot ignition temperatures of 1000 K and 1200 K are relatively independent of the fuel type. 13

26 2.2 Diesel Surrogates Need for Surrogates The complexity of the composition and the reaction kinetics of diesel fuel make it impossible to model directly diesel combustion. As a result there is a need to employ surrogate fuels. Surrogate fuels are simple representations that exhibit similar characteristics as the fuel in question. A surrogate can be multiple fuels of select species and concentrations blended together to better match the real fuel. To create a surrogate to match diesel fuel, both the physical and chemical properties must match. This would require numerous components. Most surrogate studies, especially those with multiple species, suffer from a lack of welldeveloped kinetic models. As a result, few dimensionally reduced kinetic models exist for the use in computation fluid dynamic (CFD) models Diesel Fuel Composition It is not necessary that a diesel surrogate contain components matching the molecules contained in diesel fuel in order for the behaviour to match, although, it is reasonable that a composition match may more likely yield a behaviour match. Commercial diesels are a blend of several hundred individual species [20]. Due to the varying refinement process from varying locations, there is great variability in the diesel properties. Some preliminary physical and chemical properties of North American diesel fuel are shown in Table 2.2 [21] [22] [23]. Table 2.2: Physical and chemical properties of North American diesel Property Value Cetane Number Carbon Range C 10 C 24 Boiling Range ( C) Vapour Pressure at 20 C (kpa) Composition: % normal, iso-paraffins % cyclo-paraffins % aromatics

27 A representation of normal paraffins, iso-paraffins, cyclo-paraffins and aromatics present in diesel fuel are shown in Figure 2.1. Only one isomer, C 16, is represented in Figure 2.1, whereas similar carbon chains will be present for all values of the carbon number shown in Table 2.2. Figure 2.1: Representation of molecules present in diesel fuel. C 16 isomers shown [24] Targets for Diesel Surrogates The surrogate fuel formulation depends on the application. The quantities used to compare a surrogate to real diesel are termed targets. Three different types of targets are: property targets, development targets and application targets [25]. Property targets refer to physical and chemical properties. Some property targets such as density or hydrogen carbon ratio can readily be matched by a single component surrogate. This however does not guarantee a match in combustion behaviour. Other properties such as phase behaviour or molecular transport properties can be matched by a surrogate with multiple species. Achieving matches for 15

28 properties such as chemical composition and viscosity can be difficult as many components could be needed, making the surrogate impractical for both experimental and CFD purposes. Developmental targets refer to important kinetic and fluid dynamic processes needed to validate surrogate behaviour. The processes are typically validated in systems more controlled than in engine tests. Some developmental targets include ignition delay, burn rate and emissions. These models can be validated in tests such as combustion bombs and shock tube ignition. It is likely that a few component surrogates would be needed to match multiple development targets. Application targets refer to results obtained from in-engine experiments. Some application targets include engine operating conditions such as heat release, combustion efficiency and emissions. Developing surrogates that match application targets is the ultimate goal but likely too many component surrogates will be required, thereby increasing the complexity of test mixtures for experiments and combustion models for CFD applications Cetane Number The cetane number is an important property of diesel that needs to be matched by the surrogate fuel. Cetane number is a function of the fuel density, boiling point and ignition delay. Congruence in cetane numbers suggests that property targets and developmental targets for a surrogate fuel match those of the real fuel. Higher cetane numbers mean the fuel has a shorter ignition delay. Accurate measurements of the cetane number can be obtained by burning the fuel in a variable compression Cooperative Fuel Research (CFR) engine, under standard test conditions, shown in Table 2.3. The fuel is injected 10 degrees CA before top dead center (TDC). The operator of the CFR engine increases the compression ratio (and therefore the peak pressure and temperature within the cylinder) of the engine until ignition occurs at 1 crank angle after TDC [26]. The resulting cetane number is then obtained by determining the mixture of n-cetane (CN = 100) and isocetane (CN = 15) that gives the same ignition delay at the compression ratio obtained with the test fuel using the following equation:

29 Table 2.3: Standard operating conditions for a CFR engine [5] Inlet temperature (ºC) 65.6 Speed (rpm) 900 Injection pressure (MPa) N-Heptane as a Diesel Surrogate Benefits Even though n-heptane is smaller (C7) than most diesel surrogates, it is widely used because the cetane number of n-heptane (55) falls in the cetane number range of diesel. This is a good indication that n- heptane meets some property and developmental targets. This suggests that n-heptane is a good diesel surrogate for experiments measuring ignition delay. There are vast amounts of experimental data and kinetic models for n-heptane. Diesel fuel is difficult to work with under standard conditions. The vapour pressure of diesel has a maximum value of 1.0 kpa and can be significantly lower at 20 C, as shown in Table 2.2. The vapour pressure of n-heptane at 20 C is 4.6 kpa [27]. This permits testing at higher initial pressure or richer mixtures at room temperature compared to diesel fuel when the test mixture is in a gaseous state Drawbacks Even though n-heptane is a widely used surrogate for diesel fuel, the combustion behaviour may differ from real diesel in some situations. The low temperature heat release of n-heptane and diesel exhibit a different dependence on temperature and pressure [25]. This is reflected by the absence of aromatics, cyclo-paraffins and iso-paraffins in the alkane n-heptane. The ability to reproduce mixing phenomena and pollutant formation cannot properly be obtained without the larger and more complex hydrocarbons present in real diesel. As n-heptane is a single component surrogate, it is not possible to achieve some property targets such as viscosity and chemical composition. It will always be more difficult for a single component surrogate to achieve as many surrogate targets than multiple component surrogates. 17

30 Ignition Delay Time (µs) Measured n-heptane Ignition Delay Time Numerous shock tube studies of stoichiometric n-heptane-air mixtures have been conducted in the literature covering a range of pressures and temperatures. Lower pressure data is available from Burcat et al. [28], Vermeer et al. [29] and Horning et al. [30]. This data is valuable for validating reaction mechanisms but it is not directly applicable to compression engine applications where the pressure during combustion is on the order of bar. Numerous shock tube studies of stoichiometric n-heptane air mixtures that focus on compression engine pressures have been reported in the literature. Experimentally measured ignition delay time as a function of the inverse of the reflected shock temperature at 20 and 40 bar from Davidson et al. [31], Hartmann et al. [32] and Fieweger et al. [33], [34] are provided in Figure 2.2 and Figure 2.3 respectively n-heptane Fieweger, 20 bar Davidson, 20 bar /T (1/K) Figure 2.2: Ignition delay times for stoichiometric n-heptane air mixtures scaled to a reflected shock pressure of 20 bar [31], [34]. 18

31 Ignition Delay Time (µs) n-heptane Hartmann (ASTM), 40 bar Hartmann (HPLC), 40 bar Fieweger, 40 bar /T (1/K) Figure 2.3: Ignition delay times for stoichiometric n-heptane air mixtures scaled to a reflected shock pressure of 40 bar [32], [33]. The data shown in Figure 2.2 and Figure 2.3 show good agreement for both reflected shock pressure conditions. Both collections of studies show the presence of a negative temperature coefficient (NTC), starting around 1000/T = 1.1 (910 K) for the 20 bar case; and 1.0 (1000 K) for the 40 bar case. Typically, as temperature increases, the reaction time decreases. The NTC is a temperature range where as the temperature increases, the reaction time also increases. This usually lasts over a period of K, after which normal behaviour continues. In this range a two stage reaction occurs, where the first stage is controlled by low temperature branching [35] and the second stage is controlled by degenerate branching from H 2 O 2 decomposition instead of RO 2 H [36], where R is a hydrocarbon chain n-heptane Reaction Mechanisms Several n-heptane reaction mechanisms have been developped in the literature. A comprehensive n- heptane mechanism was developed at Lawrence Livermore National Laboratory (LLNL) that contains 556 species and 2540 reactions [37]. A smaller mechanism from Lund University and Technology [1] 19

32 Ignition Delay Time (µs) contains 157 species and 1547 reactions. The Lund mechanism was developed from the LLNL mechanism and calibrated against the Fieweger et al. [33], [34] ignition delay time data shown in Figure 2.2 and Figure 2.3. The ignition delay time predicted by the constant volume model with the Lund mechanism is compared to the shock tube data in the literature in Figure 2.4 and Figure 2.5. The Lund mechanism agrees well with the experimental data in the literature over the entire temperature range for both 20 and 40 bar reflected shock pressures n-heptane Fieweger, 20 bar Davidson, 20 bar Lund mechanism, 20 bar /T (1/K) Figure 2.4: Ignition delay times for stoichiometric n-heptane air mixtures calculated using the Lund mechanism [1] undergoing a constant volume reaction compared to shock tube data in the literature for a reflected shock pressure of 20 bar. 20

33 Ignition Delay Time (µs) n-heptane Hartmann (ASTM), 40 bar Hartmann (HPLC), 40 bar Fieweger, 40 bar Lund mechanism, 40 bar /T (1/K) Figure 2.5: Ignition delay times for stoichiometric n-heptane air mixtures calculated using the Lund mechanism [1] undergoing a constant volume reaction compared to shock tube data in the literature for a reflected shock pressure of 40 bar Effects of Supplemental Hydrogen Addition on Ignition Delay Time In a numerical study Frolov et al. [38], using an in-house reaction mechanism, calculated the ignition delay times for various n-heptane-hydrogen-air mixtures, shown in Figure 2.6. At lower temperatures, pure n-heptane-air mixtures have shorter delay times than n-heptane-air mixtures with supplemental hydrogen. But at higher temperatures, the opposite occurs, where pure n-heptane-air mixture have longer delay times. It was concluded that in low temperature cases, hydrogen is involved in chain termination reactions, causing it to act as an ignition inhibitor. At high temperatures, oxidation of hydrogen occurs more rapidly than that of n-heptane, meaning hydrogen acts as an ignition promoter. The rapid oxidation of hydrogen creates radicals that can speed up the oxidation of n-heptane. 21

34 Figure 2.6: Calculated ignition delay times for n-heptane-hydrogen-air mixtures for a pressure of 15 atm [38]. There is no experimental ignition delay time data available in the literature to corroborate the numerical prediction of Frolov et al. The objective of the present study is to acquire such data and validate existing reaction models for mixtures of n-heptane/hydrogen in air. 22

35 Chapter 3 Procedure and Apparatus 3.1 Overview In this study, ignition delay times are measured in mixtures of n-heptane, hydrogen and air at prototypic diesel in-cylinder pressures over a range of temperatures. These conditions are generated at the end of a shock tube behind the reflected shock. Before describing the shock tube setup the basic theory required to select operating conditions are discussed as well as a description of the gas dynamics of a shock tube. 3.2 Shock Theory Normal Shock Relations A shock wave is a very thin region in space, typically a few mean free paths thick [39]. A normal shock wave is one where the flow is at right angles to the wave, as shown in Figure 1.1. Note the shock wave Mach number, M 1, is supersonic and thus greater than unity. The shock wave abruptly changes the thermodynamic properties and the flow velocity. The relative flow leaving the shock, u 2, is subsonic, i.e., the flow Mach number, M 2, defined as the ratio of the gas flow velocity to the speed of sound of the gas. 3.1 is less than unity. The speed of sound for a perfect gas, a, is defined by: 3.2 Where γ is the ratio of specific heats and is the specific gas constant. Using a control volume, an analysis of property changes across a normal shock wave can be performed. 23

36 Figure 3.1: Control volume for a normal shock wave Equations relating the downstream and upstream conditions as a function of the shock Mach number, assuming perfect gas and constant specific heat ratio across the shock, can be obtained from manipulating the steady mass, momentum and energy conservation equations: ( ( ) ( ) ) 3.3 [ ( )][ ( ) ] ( ) 3.4 ( ) 3.5 ( ) ( ) 3.6 The derivation of Equations 3.3 through 3.6 is provided in Appendix B. The downstream velocity can be calculated as a function of the shock strength (P 2 /P 1 ): ( ) ( ) ( ) ( )

37 3.2.2 Normal Shock Reflections When a normal shock wave reaches a closed end of a duct, it is reflected and travels back in the opposite direction, see Figure 1.2. As there can be no flow out of a closed duct, the gas at the end must be stationary. This means that the reflected shock must have sufficient strength to stagnate the gas flow generated by the incident shock wave. Figure 3.2: Reflection of a normal shock wave Shock Tube Theory A shock tube is designed to produce a shock wave of given strength. A shock tube consists of two sections: a driver (high pressure) and a driven (low pressure). The sections are separated by a diaphragm. A large pressure differential across the diaphragm causes it to rupture. The expansion of the driver gas produces a shock wave that propagates in the driven section, a schematic of which is shown in Figure 3.3. Figure 3.3: Schematic of a shock tube after diaphragm rupture [40] 25

38 Upon diaphragm rupture an expansion fan forms, centered at the diaphragm position, that travels back upstream into the driver accelerating the driver gas towards the driven end of the tube. The head of the expansion fan travels at the local speed of sound. The flow through the expansion is isentropic, whereas the flow through the shock is not. Following the shock wave is a contact surface which is the interface between the driven and driven gases. The pressure and velocity across the contact surface are constant; however the temperature is higher on the shock side due to the compression from the shock wave. An x-t diagram showing the trajectories of the different waves that form after the diaphragm is ruptured is shown in Figure 3.4a. To better visualize an x-t diagram, a horizontal line can be drawn across the diagram corresponding to a certain time, t 1, shown in Figure 3.4a. Figure 3.4b then shows how far each wave has travelled in the shock tube at that time. (a) (b) Figure 3.4: (a) An x-t diagram showing a position time history of the wave propagation; and (b) a visualization of wave propagation at a certain time [41].. 26

39 The shock wave travels to the end of the driven section reflecting off the end wall. The reflected shock wave stagnates the flow generated by the incident shock wave, such that a zone of high pressure and temperature gas between the reflected shock wave and the endplate is created, see zone (5) in Figure 3.4a. Auto-ignition occurs in this high temperature gas mixture after a period of time known as the ignition delay time. The reflected shock wave interacts with the contact surface producing an expansion fan or shock wave (depending on acoustic impedance across the contact surface) that propagates back towards the end wall. Since measurements are made near or at the end wall the available test time is the time interval from when the shock wave reaches the end wall to when the shock wave (generated by the reflected shock and contact surface interaction for the case shown in Figure 3.4a) reaches the end wall. This is called the available test time because it is the time in which the fuel-air mixture has to react uninterrupted. The flow across the expansion fan is isentropic meaning the pressure ratios across zones 3 and 4 are given by: ( ) 3.8 The initial pressure ratio, across zones 1 and 4 can be calculated by combining normal shock relations and the isentropic relations: [ ( )] [ ] 3.9 ( ) By applying normal shock relations over the reflected shock, the pressure ratio in terms of the incident Mach number can be found: ( ) ( ) ( )

40 By combining Equation 3.5 with Equation 3.10, the ratio of the reflected shock pressure, P 5, to the initial driven pressure, P 1, as a function of the incident Mach number can be found: [ ( ) ( ) ( ) ] [ ] 3.11 ( ) Similarly, the ratio of the reflected shock pressure, T 5, to the initial driven pressure, T 1, as a function of the incident Mach number can be found: [ ( ) ][( ) ( )] ( ) 3.12 The two possible interactions between the reflected shock wave and the contact surface result a shock wave or an expansion fan travelling back towards the end wall, shown in Figure 3.5 a and b respectively. (a) (b) Figure 3.5: Possible interactions between the reflected shock wave and the contact surface where (a) shows a shock wave propagating towards the end wall; and (b) shows an expansion fan propagating towards the end wall [41]. Velocity across the contact surface is constant making u 3 = u 2 and u 7 = u 8. With these assumptions, the flow velocity, u 7, can be found: 28

41 [( ) ] [ ] [ ( ) ] [ ( ) ] 3.13 When, a shock wave is obtained, meaning. When, an expansion fan is obtained, meaning Shock Tube Tailoring For a tailored shock tube, no wave reflects off the contact surface back towards the end wall. This means that in Equation 3.13, u 7 = 0 and P 5 = P 7. Noting that pressure is constant across the contact surface, P 8 = P 7 and P 3 = P 2, new pressure ratios can be found: : [( ) ] [ ] [ ( ) ] [ ( ) ] 3.14 When u 7 = 0, a new tailored x-t diagram can be made. This is shown in Figure 3.6. The reflected shock wave passes directly through the contact surface. This greatly increases the available test time with regards to Figure 3.4a. Test time is not unlimited as the expansion reflected off the end of the driver will eventually reach the end of the driven section. 29

42 Figure 3.6: An x-t diagram of a tailored shock tube Assuming that the driver gas is a mixture of two gases, an iterative process is needed to solve the equations to tailor a shock tube. Starting with a specified P 1, P 5, T 1, T 4, M 1 and γ 1 seven unknowns P 2, P 4, u 2, a 3, a 4, γ 4 and x 4 will be determined. Where x 4 is the percentage of one driver gas with respect to the total driver gas mixture. Since T 1 and γ 1 are specified, a 1 is known using Equation 3.2. P 2 can be obtained by using Equation 3.5. Next u 2 can be calculated using Equation 3.7. A value of x 4 must now be guessed. The unknowns a 4 and γ 4 can be found with x 4. A value for a 3 can now be determined using Equation After a 3 is found, and knowing P 3 = P 2, for gas across the contact surface, P 4 can be calculated using Equation 3.8. P 4 can also be calculated using Equation 3.9, after an initial guess of x 4 is made. Vary the guessed value x 4 until P 4 from Equations 3.8 and 3.9 are the same. 3.3 Shock Tube The shock tube used in this study consists of a round driver section, a round to square transition section and a square driven section as shown in Figure

43 All parts are machined from aluminum 6061-T6. All connections are sealed with rubber Buna-N O-rings. An Edwards RV3 vacuum pump is used to evacuate all elements of the shock tube, including plumbing before filling with desired gases. Figure 3.7: Experimental shock tube apparatus Driver The driver section is 1.96 m long with a 10 cm inner diameter. The wall thickness is 1.91 cm, allowing for a maximum driver pressure of 100 bar. Six clamps, fastened to one end of the driver, connect with the transition section, keeping the diaphragm holder in place. This allows for quick connections and disconnections needed to place the two diaphragms in place for each test. For most tests, a tailored mixture of hydrogen and nitrogen was used in the driver, where T i = 295 K, P i ~ 20 bar and the gas mixture varied from 60-80% H Double Diaphragm Holder The diaphragm holder separates the driver from the driven section. With an inner diameter of 10 cm and a thickness of 2.54 cm, the volume is 200 ml. The diaphragm holder can hold a diaphragm on either side. An image of the double diaphragm can be seen in Figure 3.8 with the driven-side diaphragm seen held in place by four pins. 31

44 Figure 3.8: Double diaphragm holder with aluminum diaphragms The double diaphragm design allows the desired shock wave Mach number to be accurately obtained. A schematic of the double diaphragm operation is shown in Figure 3.9. The design allows the intermediate volume to be filled to half of the driver pressure. This means each diaphragm withstands half of the total pressure difference and as a result thinner diaphragms can be used. Diaphragm rupture is triggered by evacuating the inter-diaphragm volume, exposing the first diaphragm to the full pressure difference. The double diaphragm technique allows for complete control over the driver pressure. 32

45 Figure 3.9: Schematic of double diaphragm operation After an extended period of diaphragm calibration two 1100-O aluminum thicknesses were found to cover the test reflected shock conditions. Tabulated in Table 3.1Table 3., are the press forces and burst pressures for both conditions. Table 3.1: Diaphragm calibration Thickness [mm] Press Force [kn] Burst Pressure [bar] Reflected Shock Pressure [bar] & 40 The diaphragms are stamped on a press using a load cell to accurately gauge the pressing force. An image showing the setup of the press is shown in Figure

46 Figure 3.10: Diaphragm stamp method The diaphragms are stamped with an X indentation to promote full diaphragm opening, see Figure 3.11a. The aluminum diaphragm is placed between multiple steel backing blocks. These blocks are used to ensure even force distribution which causes the groove in the diaphragm to have a uniform depth. The four circumferential grooves at the end of the radial grooves promote repeatable four petal opening. The stamp design was based on a design by Huang and adapted for this shock tube [42]. (a) (b) Figure 3.11: a) Diaphragm stamp design, and b) fully opened burst aluminum diaphragm 34

47 The four pin holes located just beyond the radial grooves, as seen in the sketch in Figure 3.11a and in the diaphragm in Figure 3.11b, keep the diaphragm aligned with the stamp. Once installed, pins through the holes prevent the diaphragm from being pulled radially inward as it stretches under the driver pressure. Tests have been conducted to determine the forces required to stamp the diaphragms to achieve different burst pressures. For example, a stamp force of 129 kn results in a single diaphragm that bursts at a pressure of 22.1 bar. Using the double diaphragm design, accurate triggering of the diaphragm rupture can be performed in a range of 22.1 to 44.2 bar across the diaphragms. In order to get optimal shock tube performance the petals need to open completely so as not to restrict the expanding driver gas, this was achieved as seen in Figure 3.11b Transition Section The transition section between the round driver and the square driven section is 0.75 m long. The gradual change in geometry maintains the planarity of the shock wave through the transition section. It is beneficial to have a round driver section because it is the cross-section that can withstand the highest pressure. Schlieren photography taken during an experiment performed with an optical section placed downstream from the transition section shows the shock wave produced is planar, shown in Figure 3.12 [40]. Very weak transverse waves can be seen behind the shock wave. Shock wave Transverse waves Figure 3.12: Test showing planar shock wave downstream of the transition section [40] 35

48 3.3.4 Driven Section The driven section is composed of two 1.91 m long, 7.6 cm square cross section channels, totaling 3.82 m of straight section. Added with the transition section, the total driven length is 4.57 m. The smallest wall thickness is 3.8 cm, allowing for a maximum pressure of 300 bar. Three pressure transducers record the shock event, located at 3.85, 4.15 and 4.46 m downstream of the diaphragm holder. An 11 cm long, 7.6 cm square block is inserted in the end of the driven section, essentially making the total length of the driven section 4.46 m. This allows the pressure transducer to be placed on the top of the driven section instead of directly on the end wall. This avoids a phenomenon called ringing, where the shock wave directly hits the pressure transducer causing it to oscillate, and producing undesirable results Control Panel Most of the valves and gauges needed to operate the shock tube are mounted on a control panel, constructed from 1/8 (3.2 mm) thick aluminum. Figure 3.13 shows a schematic of the entire apparatus, where the control panel is shown as a red box. The plumbing is constructed of ¼ (6.4 mm) stainless steel tubing, Swagelok fittings and valves as well as ½ (12.7 mm) brass tubing, Swagelok fittings and valves. Figure 3.13: Schematic of the apparatus Three needle valves (model 1RS4) are used to control the flow of compressed gases, valves 1-3 in Figure Valves 4 through 9 (model 45S8) are ball valves used to open or block flow to desired components. 36

49 Valve 10 (model 43S4) is used to fire the shock tube. Valves 11 and 12 (model 43S4) are used to protect the high pressure gauge (Omega Model PGT-60L-600 dial gauge, 0.25% of full scale accuracy) and the low pressure gauge (Omega Model PX G5V strain gauge, 1.5% relative accuracy) at the time of firing. The high pressure gauge has a measurement range of 0 to 600 psig. The medium pressure gauge has a measurement range of 0 to 60 psia. A more detailed description of the shock tube operation is given in Section Instrumentation National Instruments LabVIEW 11 was utilized in conjunction with a NI PCI-6133 DAQ card and a NI BNC-2110 terminal block. The PCI-6133 contains 8 simultaneously sampling analogue inputs at a resolution of 14 bits and a maximum sampling rate of 3 MHz for each channel. Input range was specified as -10 to 10 V for the pressure transducers to maximize accuracy. Tests were run at a sampling frequency of 2 MHz and a resolution of 14 bits. Three piezo-electric pressure transducers and a photodiode record the shock event and subsequent explosion. The data acquisition is triggered to start recording when the incident shock wave passes P Pressure Transducers All three pressure transducers are different as they require different functionalities depending on their location in the shock tube. These piezoelectric transducers measure gauge pressure with a very fast response time. Table 3.2 shows the locations of the transducers as well as some key features. All pressure transducers are from PCB Piezotronics. 37

50 Table 3.2: Piezo-electric pressure transducer locations and properties Transducer number P1 P2 P3 Location downstream from diaphragm (m) Model number 113A26 113A24 113A22 Measurement range (kpa) Sensitivity (mv/kpa) Resolution (kpa) Rise time (µs) P3 must have a high measurement range as it is located at the end of the shock tube and directly measures the reflected shock pressure and the much higher explosion pressure caused by shock ignition. The main drawback of the high measurement range on P3 is that the resolution is lower. This can cause some inaccuracy in the measured pressure compared to that of P1 and P2. P1 has the lowest measurement range as it is the farthest from the end wall, meaning it does not see the high pressure that the end wall does. P2 is located between the other transducers, both in location and in properties. All three transducers have a rise time that is less than one microsecond Photodiode A photodiode (S-050-H, Edmund Optics) with a 430 ± 10 nm filter (FB430-10, Thorlabs) mounted on the end plate is used to detect emission from excited CH radicals following the start of reaction. The spectral response of the photodiode is shown in Figure Although the relative response of the photodiode is low at 430 nm, it was found to be more than adequate for the experiment. A 6 mm acrylic rod is held in a Swagelok fitting mounted to the endplate. The acrylic rod extends to the inner surface of the end plate and the photodiode is placed on the other end of the rod. 38

51 Figure 3.14: Responsivity of Edmund Optics s-series photodiode [43] Ignition Delay Time Measurement Ignition delay time in a shock tube is defined as the time between when the initial shock wave hits the end plate to the onset of auto ignition. The onset of ignition can be determined by a rise in the reflected shock pressure and the appearance of CH radicals as measured by a photodiode [44]. For strong ignition cases, the appearance of CH radicals happens very quickly, making the slope very steep. For weaker ignition cases, the slope of CH emission is less steep, especially at the start of reaction. A standard approach is adopted where a line is drawn tangential to the steepest slope of the CH emission curve. The point where the line intercepts the time axis is taken to be the onset of ignition [45]. An example P3 pressure trace and CH emission plot showing this technique is shown in Figure Note the ignition time obtained using the CH emission intercept technique matches the pressure excursion associated with reaction measured at P3 located near the end wall. 39

52 Figure 3.15: Example of P3 pressure trace and CH emission showing the ignition delay time measurement technique 3.5 Test Mixture The test gas is a mixture of n-heptane, hydrogen and air made in a mixing chamber shown in the blue box in Figure The test mixture composition is defined by the following global chemical balance equation: ( ) ( )[ ] ( ) ( )( ) 3.15 where x is the n-heptane fuel mole fraction (relative to the total fuel mixture consisting of n-heptane and hydrogen). When x = 1, the fuel mixture is all n-heptane and when x = 0, the fuel mixture is all hydrogen. This chemical balance gives the number of moles of stoichiometric air as a function of the fuel mixture, i.e., 2.88(21x+1). 40

53 The fuel air mixture is prepared in a heated mixing chamber by the method of partial pressures. The mixing chamber is first heated to 40ºC and evacuated to a pressure below 0.1 kpa. Then the n- heptane is added to the mixing chamber from a 500 ml sample bottle that is heated to raise the vapour pressure. This is followed by the hydrogen addition from a compressed gas cylinder controlled using a needle valve (model 1RS4). During these steps, the mixing chamber pressure is monitored using a vacuum gauge (Omega Model PGT-60L-30V dial vacuum gauge, 0.25% of full scale accuracy) which has a measurement range of 0 to kpa (absolute). The air is added last to the mixing chamber to a final pressure that is above atmospheric pressure so the low pressure gauge described in Section is used for this filling process. Once all constituents have been loaded into the mixing chamber, a Parr magnetic stirrer is operated for 20 minutes in order to obtain a homogeneous mixture. During the time that the mixture is being stirred the driven section and plumbing is evacuated. The test mixture is downloaded from the mixing camber into the driven section of the shock tube to the desired test initial pressure. In this study, four different fuel fractions and three different equivalence ratios were chosen. The fuel fractions tested are x = 1.0, 0.8, 0.5 and The x = 1 provides a baseline where the fuel consists of pure heptane. The equivalence ratios tested were ϕ = (fuel lean), 1.0 (stoichiometric) and 1.25 (fuel rich). These values were chosen to give some insight on the effects of lean and rich mixtures compared to stoichiometric mixtures. 3.6 Operating Procedure To initiate a test, first the diaphragms are loaded on each side of the diaphragm holder, then clamped shut. Then the test mixture is prepared in the mixing chamber. Referring to Figure 3.13, valves 4, 5, 7, 9, 10 and 12 are opened and the vacuum pump turned on to evacuate of components of the shock tube. Once vacuum is achieved in these sections, valves 4, 7, 9 and 10 are closed. Valve 8 is then opened to fill the driven section to the desired pressure from the mixing chamber. Valves 5 and 8 are then closed. Valve 4 is opened to evacuate the remaining test mixture from the control panel plumbing. Once a vacuum is achieved, valves 4 and 12 are closed and the vacuum pump is turned off. Valves 7, 9, 10 and 11 are then 41

54 opened. The opening of valve 3 starts the nitrogen fill process for the driver section, double-diaphragm cavity and vacuum volume. When the desired amount of nitrogen is reached, valve 3 is closed. Then valve 1 is opened to start filling the same components with hydrogen. When the final double-diaphragm cavity pressure is reached, valves 1, 7 and 10 are closed and valve 3 is opened to continue filling just the shock tube driver section with nitrogen. Once the desired nitrogen pressure is reached, valve 3 is closed and valve 1 is opened to continue filling with hydrogen. When the final driver pressure is reached, valves 1, 9 and 11 are closed. Next the vacuum pump is turned back on and valves 4 and 7 are opened, evacuating the 500 ml vacuum volume. Once evacuated, valves 4 and 7 are closed. The shock tube is ready to fire at this point. To fire the system, valve 10 is opened. This causes the gases in the doublediaphragm cavity to be sucked into the vacuum volume. The diaphragm on the driver side bursts immediately as it is unable to withstand the full pressure differential across it. Then the diaphragm on the driven-side bursts as it also cannot withstand the full pressure differential across it. The expansion of the driver gas results in a shock wave propagating through the test gas mixture in the driven section. 42

55 Chapter 4 Results and Discussion 4.1 Effect of Driver Gas on Test Time The available test time must be long enough for the test gas at the end wall to self-ignite without interference from a secondary wave, as discussed in Section Figure 4.1shows the end wall pressure trace (pressure transducer is actually mounted on the side wall <1 mm from the reflecting surface) obtained for a test using a nonreactive test gas. Using helium as the driver gas and air as the test gas, the time of arrival of the expansion wave generated by the interaction of the reflected shock wave with the contact surface can be measured without the complication of chemical reaction occurring. The sharp rise in pressure at 0.6 ms indicates that the incident shock wave has arrived at the end plate. The high frequency oscillations are caused by the vibration of the pressure transducer that is mounted directly onto the shock tube. The pressure then remains roughly constant for a period of time. The small pressure rise observed during the test time is due to the interaction of the reflected shock wave with the boundary layer produced by the incident shock wave, as discussed in Section 4.6. After this time, the pressure decreases, indicating the arrival of an expansion wave and the end of the available test time. The available test time for this test condition is 0.87 ms. 43

56 Figure 4.1 Available test time for a typical test with a helium driver and air as the test gas at an initial pressure of 67.6 kpa Performing a test under the same conditions, except with a stoichiometric n-heptane-air mixture instead of just air as the test gas, shows if there is enough test time for auto-ignition to occur uninterrupted. The pressure and CH emission signal time history obtained in a test with n-heptane and air is shown in Figure 4.2. A comparison of the results shows that there is just enough test time for this case, as auto-ignition occurs after 0.85 ms compared to the available test time of 0.87 ms. 44

57 Figure 4.2: Ignition delay time for a test under the same conditions as Figure 4.1 Based on the predictions from Frolov et al. [38], it is expected that the addition of hydrogen to the mixture will increase the auto-ignition time. Figure 4.3 shows a measurement of inadequate test time when hydrogen is added to the test gas. In Figure 4.3 the test gas is a stoichiometric mixture and a fuel fraction of 0.5 (half n-heptane and half hydrogen). The expansion wave arrives well before the start of reaction characterized by the start of CH emission. The expansion wave cools the reacting gas, delaying chemical reaction (inflection in CH emission profile) and as a result the explosion pressure does not achieve the same magnitude peak pressure as in Figure 4.2. Note the test time is significantly shorter when the test mixture contains hydrogen because the addition of hydrogen increases the speed of sound of the test gas, so shock waves that have a similar Mach number have a higher shock velocity and therefore the same distance is covered in a shorter time. 45

58 Figure 4.3: Example of not enough test time after supplemental hydrogen addition with a helium driver As discussed in Section the test time can be extended by tailoring the shock tube by using a mixture of gases for the driver. The tailoring driver gas mixture used in this study is composed of hydrogen and nitrogen, varying from 60 80% hydrogen depending on the test conditions. Figure 4.4 shows an end wall pressure trace under tailored shock tube conditions. The available test time in this case is over three times more than that obtained using helium, see Figure 4.1. The end of the test time in this case is denoted by the large rise in pressure at 4 ms. The increase in pressure is too large to be that from the reflected shock wave off the contact surface and returning towards the end wall. It is believed that this large pressure pulse is associated with an explosion from the contact between the hydrogen containing driver gas and the shock heated air test gas. The ignition is probably initiated when the reflected shock wave interacts with the contact surface rapidly mixing the hot test gas and the colder driver gas. 46

59 Figure 4.4: Pressure trace of the end wall pressure showing a tailored shock tube condition This theory was tested by using an inert driver gas, i.e., nitrogen. Figure 4.5 shows the end wall pressure trace under the same conditions as Figure 4.4 except with nitrogen in the driven section. The large pressure pulse observed with the hydrogen containing driver was used is no longer produced. The reflected pressure starts to drop slightly at around 3 ms due to the arrival of an expansion wave due to imperfect tailoring. The large deviation from constant pressure occurs at around 6 ms, denoted by a black line in Figure 4.5. This drop in pressure is associated with the expansion wave that reflects off the end of the driver then travels back towards the end wall as shown in Figure 3.6. The available test time in this case is 5.32 ms. However, as the test gas will always be composed primarily of air and the driver gas will always have a significant portion consisting of hydrogen, the test time associated with the arrival of the compression wave generated by the explosion as observed in Figure 4.4 (3.09 ms) will govern the maximum available test time. 47

60 Figure 4.5: Pressure trace of the end wall pressure showing a tailored shock tube condition with nitrogen in the driven section Sensitivity tests were done to see the effect that variations in the driver gas mixture would have on the available test time. The driven (test) gas conditions remained the same throughout the tests, while the driver pressure was changed to achieve the same reflected temperature (870 K) and pressure (20 bar) for each test. The tailored condition calls for a driver mixture that is 72% hydrogen. Values of 50%, 62% and 82% hydrogen were investigated for the off-tailored conditions. Figure 4.6 shows the results of available test time with varying amounts of hydrogen in the driver gas mixture. For both air and nitrogen in the driven section, the same pattern emerges: the available test time peaks at the tailored mixture and then falls to a relatively constant value for the off-tailored mixtures. This shows that tailoring the shock tube greatly increases the available test time and therefore it is very important to have the correct driver mixture to maximize the test time. 48

61 Available Test Time (ms) Air N Driver Mixture (%H2) Figure 4.6: Sensitivity of tailoring with varying driver gas mixture with air and nitrogen as the driven gas at an initial pressure of 68 kpa (absolute) 4.2 Reflected Gas Temperature The key independent parameter that governs the chemical reaction rate is temperature, which in a shock tube study corresponds to the reflected shock temperature. Since it is very difficult to measure temperature on such a short time-scale, the reflected temperature is deduced based on the incident shock Mach number and initial temperature. With the assumption of a perfect gas the reflected gas temperature can be calculated by Equation In the derivation of this equation it was assumed that the ratio of specific heats remains unchanged at the reflected temperature. The specific heat ratio for a diatomic gas (hydrogen, oxygen, and nitrogen) remains constant within 7% up to a temperature of about 1350 K, which 49

62 is above the reflected gas temperatures tested [46]. N-heptane is a large molecule and thus the specific heat ratio is greatly affected even at low temperatures. The reflected shock wave stagnates the flow induced behind the incident shock wave. The equilibrium reflected shock temperature can be obtained equating the total energy of the gas behind the incident shock with that behind the reflected shock (u 5 = 0): 4.1 Where h 5 is a function of the reflected gas temperature T 5 : 4.2 where c p the specific heat at constant pressure and n is the number of moles. T 5 can be obtained by Equations 4.1 and 4.2 iteratively. This calculation takes into account the change in specific heat ratio. The program CHOCFI, developed at the CNRS Orleans [47], is used to calculate the equilibrium reflected temperature. The inputs used are initial test gas temperature, initial pressure, the shock wave speed and the species mole fractions. The program outputs the thermodynamic properties of the test gas at the reflected shock condition, including temperature. In order to check the accuracy of using the constant specific heat ratio based Equation 3.12, a comparison of the calculated reflected gas temperature was made with the prediction of the CHOCFI. The reflected temperature was calculated for stoichiometric ( =1) n-heptane and air at a pressure of 20 bars for different shock Mach numbers. The results are presented in Figure 4.7. The two methods give results that differ by 60 K at low temperatures to 200 K at high temperatures. A temperature variation of 60K has a very large effect on the ignition time and therefore the assumption of constant specific heat ratio is not valid. The data will be reported using the temperature calculated using the CHOCFI program as it takes into account that the fact that the ratio of specific heats is a function of temperature. The use of the reflected gas temperature calculated by CHOCFI assumes that the mixture is at equilibrium. This assumption implies that the relaxation time of the molecular kinetic energy occurs on a 50

63 Reflected Temperature (K) time-scale much shorter than the reaction time. For kinetics studies where the test mixture consists almost entirely of a monatomic gas (up to 97% argon is used to minimize the amount of energy release so that pressure remains constant during the induction time) this is a good assumption because the relaxation time for translational energy is very fast. The relaxation time of the rotational and vibrational energy is slower than that of the translational energy. For the present study where the mixture is primarily composed of diatomic molecules (nitrogen and oxygen in the air) the assumption of equilibrium is a little less certain. However, for fuel-oxygen mixtures that are not overly diluted (such as 97% argon dilution) and at high reflected temperatures and pressures, such as in this study, vibrational relaxation effects are typically short enough to use the equilibrium assumption to determine the reflected gas temperature [16] Eqn 3.12 γ = 1.39 CHOCFI Mach Number Figure 4.7: Comparison of different methods to calculate reflected temperature. CHOCFI temperature calculator (dotted) and normal shock relations assuming constant ratio of specific heats using Equation 3.12 (solid) for stoichiometric fuel-air ratio and 20 bar reflected pressure 51

64 4.3 Ignition Delay Time Data In this section experimentally measured ignition delay time data will be presented and compared to existing data in the literature Stoichiometric n-heptane-air A limited number of tests were carried out with stoichiometric heptane-air at 40 bar reflected pressure. This is a representative of cylinder pressure at peak load and experimental data exists in the literature, see Section Shown in Figure 4.8 is ignition delay time as a function of inverse temperature from this study compared with data collected in the literature at 40 bar reflected pressure. The data collected, shown in red, falls within the range of data in the literature, matching closest to that of Fieweger et al. The data shows that the ignition delay time stays constant throughout the temperature range tested ( K) and based on the Lund mechanism the data falls in the NTC region. After these tests were performed there was some damage to the shock tube caused by the high local pressure generated by the explosion at the end of the shock tube. In order to avoid permanent damage the reflected pressure was reduced to 30 and 20 bar for subsequent tests. 52

65 Ignition Delay Time (µs) Hartmann (ASTM), 40 bar Hartmann (HPLC), 40 bar Fieweger, 40 bar Queen's, 40 bar /T (1/K) Figure 4.8: Stoichiometric n-heptane-air data collected compared with data in the literature (Hartmann et al. [32], Fieweger et al. [33]) at 40 bar reflected pressure Figure 4.9 shows stoichiometric n-heptane-air data collected in this study compared to data in the literature at 20 bar reflected pressure. The data collected matches very closely to the data collected by Fieweger et al. and Davidson et al. The location of the NTC is very similar for all data sets, peaking at just less than 1000 K. 53

66 Ignition Delay Time (µs) Fieweger, 20 bar Davidson, 20 bar Queen's, 20 bar /T (1/K) Figure 4.9: Stoichiometric n-heptane-air data collected compared with data in the literature (Fieweger et al. [34], Davidson et al. [31]) at 20 bar reflected pressure Generally temperature is the key parameter for chemical kinetics because of the exponential relationship in the Arrhenius correlation. However, the pressure also effects the species concentration that has a lower order effect on the reaction rate and there are certain elementary reactions (three-body type) that are sensitive to pressure. Figure 4.10 shows ignition delay times of stoichiometric n-heptane-air mixtures at reflected pressures of 20, 30 and 40 bar. 54

67 Ignition Delay Time (µs) Queen's, 40 bar Queen's, 30 bar Queen's, 20 bar K/T (1/K) Figure 4.10: Ignition delay time of stoichiometric n-heptane-air with varying reflected pressure As the reflected pressure increases, the ignition delay time decreases. This is expected since as the pressure increases the concentration, and thus the reaction rate, also increases. The NTC region occurs over the same temperature range, K, where the ignition delay time drops slightly with increased temperature (see dotted lines in Figure 4.10) for all reflected pressures. The ignition delay time at 1000/T= 1.15 (870 K) is plotted as a function of reflected pressure in Figure A power law fit yields, 4.3 with R 2 = In comparison, the pressure exponent index was reported as 0.86 by Vermeer et al. [29] and by Horning et al. [30] for heavily argon diluted stoichiometric n-heptane at reflected pressures below 6 bar and in the high temperature region (T>1300 K). 55

68 Ignition Delay Time (µs) τ = 1.5x10 5 P R² = Reflected Pressure (bar) Figure 4.11: Ignition delay times at 1000/T=1.15 Based on the Arrhenius relation log ( ) ~ (E a /R)1/T, the natural logarithm of the ignition time delay should be linearly proportional to temperature and the slope is proportional to the activation energy. For n-heptane this only applies outside the NTC region. Figure 4.12 is the 20 bar stoichiometric heptane-air data plotted in terms of log ( ). The resulting activation energies on the high and low temperature sides of the NTC are 25,200 cal/mol and 10,800 cal/mol, respectively. 56

69 ln (Ignition Delay Time) Complete Temperature Range High Temperature Range Low Temperature Range /T (1/K) Figure 4.12: Stoichiometric data at 20 bar plotted in terms of log (τ) In comparison, the activation energy on the high temperature side has been reported as 46,350 cal/mol by Vermeer et al. [29] and as 45,000 cal/mol by Horning et al. [30]. The high temperature activation energy reported in this study differs from those reported in the literature. The reflected temperatures in the literature were over 1200 K, whereas the reflected temperatures in this study are below 1200 K. More tests are needed to be done to obtain data in this higher temperature region Off-Stoichiometric n-heptane Air Data In diesel engines ignition is not restricted to the location where the mixture is at stoichiometric composition. The ignition delay time measured for two off-stoichiometric conditions as a function of 1/T are shown in Figure The ignition delay time is the shortest for the rich mixture which is consistent with what is observed in cylinder diesel studies. 57

70 Ignition Delay Time (µs) ϕ = ϕ = 1 ϕ = /T (1/K) Figure 4.13: Ignition delay times for three different equivalence ratios (ϕ = 0.833, 1 and 1.25) at 20 bar reflected pressure and a fuel ratio of x = Repeatability Studies Select tests for ϕ = 1, x = 1, P 5 = 20 bar were repeated to observe the reproducibility of the tests. Figure 4.14 shows the data set from Figure 4.10 with a line and a number of repeat tests at various reflected temperatures. The repeat data points match well with the Figure 4.10 data set. Table 4.1 shows the differences between the initial test and the average of all tests done at the same condition. Most differences are within 4% of the initial test, showing the repeat tests were good matches. The largest differences come at the lowest reflected temperatures. 58

71 Ignition Delay Time (µs) T = 740 K T = 800 K T = 870 K T = 960 K T = 1110 K x = /T (1/K) Figure 4.14: Repeatability tests (points) compared to initial collected data (line) for ϕ = 1, x =1 and a reflected pressure of 20 bar Table 4.1: Difference in ignition delay times at select reflected temperatures Initial Reflected Temperature (K) Initial Delay Time (µs) Average Delay Time (µs) % Difference Table 4.2 shows the difference in reflected temperatures of the repeat tests compared to the initial set of tests. The difference in temperature is less than 1.5% for all cases. These small differences are caused by 59

72 a slightly different incident Mach number. This could be attributed how quickly the diaphragms open each test. Slight variations in how the diaphragms open could change the flow area, which could change the Mach number from the desired Mach number. Table 4.2: Difference in reflected temperature with repeat tests Initial Reflected Temperature (K) Average Reflected Temperature (K) % Difference Stoichiometric n-heptane-air with Hydrogen Addition As discussed in Section 2.2.8, the addition of hydrogen to hydrocarbons should increase the ignition delay time. Figure 4.15 shows ignition delay times for stoichiometric n-heptane-hydrogen-air mixtures at 20 bar reflected pressure with x values of 1, 0.8, 0.5 and 0.25 (recall x is the fraction of the fuel made up of n- heptane). The addition of hydrogen to the n-heptane has little effect on the shape of the ignition delay curve. The shape and location of the NTC remains the same for all four conditions. This is interesting because hydrogen does not display a NTC and even with 75% hydrogen (x = 0.25) the curve is similar in shape to the case with no hydrogen (x = 1). In general, as the hydrogen addition increases, the ignition delay time also increases over the entire temperature range. 60

73 Ignition Delay Time (µs) x = 1 x = 0.8 x = 0.5 x = /T (1/K) Figure 4.15: Ignition delay times for stoichiometric n-heptane-hydrogen-air mixtures a 20 bar reflected pressure with a varying fuel ratio Off-Stoichiometric n-heptane-air with Hydrogen Addition Ignition in a diesel engine can occur in off-stoichiometric regions of the cylinder. Hydrogen tests were performed under fuel rich and fuel lean conditions. Figure 4.16 and Figure 4.17 show ignition delay times for fuel rich (ϕ = 1.25) and fuel lean (ϕ = 0.833) for n-heptane-hydrogen-air mixtures at 20 bar reflected pressure with varying fuel ratios respectively. Note the in Figure 4.17 there is a data point missing for x = 0.25, T = 740 K as there was not enough test time for the reaction to occur uninterrupted. 61

74 Ignition Delay Time (µs) Ignition Delay Time (µs) x = 1 x = 0.8 x = 0.5 x = /T (1/K) Figure 4.16: Ignition delay times for ϕ = 1.25 n-heptane-hydrogen-air mixtures a 20 bar reflected pressure with a varying fuel ratio 1000 x = 1 x = 0.8 x = 0.5 x = /T (1/K) Figure 4.17: Ignition delay times for ϕ = n-heptane-hydrogen-air mixtures a 20 bar reflected pressure with a varying fuel ratio 62

75 Ignition Delay Time (µs) Figure 4.18 shows ignition delay times for three different equivalence ratios (ϕ = 0.833, 1 and 1.25) for a constant fuel ratio value of x = 0.8 (20% hydrogen addition). All three curves are similar in shape, with the peak of the high-temperature end of the NTC being at a similar location. In general, the leaner fuel-air mixtures have longer delay times as was the case for x = 1 plotted in Figure Results in Figure 4.18 are similar for the lower fuel ratios (x = 0.5 and 0.25) ϕ = ϕ = 1 ϕ = /T (1/K) Figure 4.18: Ignition delay times for three different equivalence ratios (ϕ = 0.833, 1 and 1.25) at 20 bar reflected pressure and a fuel ratio of x =

76 4.6 Ignition Delay Time Predictions Constant Volume Reaction Model An important component of any kinetics study is to compare the measured ignition delay time data with predictions from different reaction mechanisms. In order to make such a comparison a model is required to simulate the conditions of the test gas following shock reflection. As discussed above immediately following shock reflection the test gas is assumed to be at the equilibrium reflected shock conditions and zero velocity. The assumption of a stagnant condition allows the reaction of the end wall gas to be treated as a constant volume process. This modeling approach is very common practice but has its limitations, especially for small diameter shock tubes [16]. Ideal shock tube behaviour is that the test gas will have a uniform temperature and velocity across the cross-section behind the incident shock wave. In reality the reflected shock passes through a non-uniform temperature and velocity flow field associated with the boundary layer generated by the incident shock [48]. The test gas nearest to the end wall where reaction starts first experiences an increase in temperature and pressure due to the reflected shock boundary layer interaction. The increase in pressure is linear as seen in the end wall pressure in Figure 4.4 after the instantaneous pressure rise associated with the arrival of the reflected shock wave. The extent of the pressure rise is a measure of how important this effect is. In the present study the dp/dt is typically 2 bar/ms. The constant volume model will be used with the understanding that there is a small effect associated with the boundary layer interacting with the reflected shock wave Solver Algorithm An algorithm created by Shepherd et al. [18] is used to find the change in thermodynamic properties and species during a constant volume reaction. The executable program is available at no cost on Shepherd s web site: By defining initial conditions of pressure, temperature and species with a desired error tolerance, the program seeks pressure, temperature and species as a function of time. The program requires a suitable reaction mechanism in standard Chemkin format and thermodynamic properties (enthalpy and entropy) as a function of 64

77 temperature of the species considered in the mechanism again in standard Chemkin format. The program uses an ODE solver to iteratively solve Equations 4.7, 4.8 and 4.9. The program outputs arrays for pressure, temperature and species as a function of time as well as three values for the induction time: maximum temperature gradient; temperature gradient reaches 10% of its maximum and; temperature gradient reaches 90% of its maximum. The program also provides the equilibrium composition of the test gas at the end of chemical reaction Mathematical Model The constant volume constraint can be applied to the energy equation (Equation 2.2) showing the change in specific internal energy: 4.4 Using the constant volume constraint, the equations derived by Shepherd et al. [18] to find the change in density, velocity, pressure, species and temperature over time is summarized here. Note the program was primarily developed to simulate the reaction zone of a detonation wave and therefore the equations are developed in terms of a moving reference (Lagrangian) frame: where is the thermicity, is the species mole fraction and is the mole rate of production of species. Derivations of Equations 4.5 through 4.9 can be found in Appendix C. 65

78 4.7 Effects of Fuel Ratio Figure 4.19 shows the data collected in Figure 4.15 compared with the ignition delay times predicted by using the Lund mechanism undergoing a constant volume reaction. The shapes of the different curves are similar, where the NTC location is predicted by the mechanism matches that in the study. The drop off in ignition delay occurs at 1000 K, which coincides with the breakdown temperature of hydrogen peroxide and chain branching leads to hot ignition. For temperatures below roughly 1100 K an increase in hydrogen increases the ignition delay time. This is because the initiation reaction Equation 2.6 is very slow at these temperatures and therefore the H2 does not breakdown and acts as a diluent soaking up any heat produced. The more hydrogen that is added the more dilute the n-heptane becomes and as a result the ignition time increases. In the high temperature region (>1100 K), the Lund mechanism predicts that the mixtures with higher concentrations of hydrogen will have shorter delay times. In this temperature range the molecular hydrogen dissociates via reaction in Equation 2.6 quicker than the n-heptane dissociates so that the radicals formed by the reactions in Equations 2.6 to 2.8 quickly consumes the n-heptane via H abstraction. 66

79 Ignition Delay Time (µs) x = 1 x = 0.8 x = 0.5 x = /T (1/K) Figure 4.19: Stoichiometric n-heptane-hydrogen-air ignition delay times at 20 bar (dashed lines) compared to those predicted by the Lund mechanism (solid lines) Figure 4.20 and Figure 4.21 respectively show rich (ϕ = 1.25) and lean (ϕ = 0.833) n-heptane-hydrogenair mixtures compared to the Lund mechanism. Similarly to the discussion about Figure 4.19, the measured data matches the predictions using the Lund mechanism undergoing a constant volume reaction. 67

80 Ignition Delay Time (µs) Ignition Delay Time (µs) x = 1 x = 0.8 x = 0.5 x = /T (1/K) Figure 4.20: Rich (ϕ = 1.25) n-heptane-hydrogen-air ignition delay times (dashed lines) compared to those predicted by the Lund mechanism (solid lines) at 20 bar reflected pressure 1000 x = 1 x = 0.8 x = 0.5 x = /T (1/K) Figure 4.21: Lean (ϕ = 0.833) n-heptane-hydrogen-air ignition delay times (dashed lines) compared to those predicted by the Lund mechanism (solid lines) at 20 bar reflected pressure 68

81 Since there is no ignition delay time for pure hydrogen tests reported in this work (because of the potential for large pressures that can be generated with hydrogen explosion at the end wall) we can use the model to predict what this data would look like. Sometimes mechanisms that are intended for large hydrocarbon kinetics do not do a good job predicting hydrogen-only kinetics. Therefore, the latest mechanism reported by Hong et al. [49] specifically intended for hydrogen kinetics will also be considered. Figure 4.22 shows a comparison of the two mechanisms to predict the ignition delay time for a fuel ratio of x = 0. Note, the ignition delay times reported for the other x values are obtained using the Lund mechanism. The ignition delay times for pure hydrogen-air mixtures do not show a presence of an NTC over the temperature range, therefore the ignition delay time has a constant slope, similar to the high temperature region of the n-heptane mixtures. There is a significant difference between the x = 0 predictions from the Lund mechanism and the Hong et al. [49] mechanisms. As discussed above, at temperatures above 1200 K hydrogen has a shorter ignition delay time than n-heptane. However, clearly at lower temperatures (<1100 K) n-heptane has a significantly lower ignition delay time when compared to pure hydrogen due to the NTC. Since the post compression air temperature in a diesel engine is lower than 1100 K, this is the region of interest for this study. For the n-heptane-hydrogen mixtures there is a clear trend for temperatures below 1100 K that the ignition delay time increases with increasing amounts of hydrogen. However, the increase with 20% hydrogen addition (x = 0.8) is very small i.e. only an 8% increase in average ignition delay times for the x = 0.8 case compared to x = 1 for temperatures below 1100 K. 69

82 Ignition Delay Time (µs) x = 1 x = 0.8 x = 0.5 x = 0.25 x = 0 (Lund) x = 0 (Hong) /T (1/K) Figure 4.22: Comparison of different hydrogen mechanisms (Lund [8], Hong [11]) for x = 0, overlaid with various fuel ratios using the Lund mechanism for a stoichiometric fuel-air mixture and a reflected pressure of 20 bar 70

83 Chapter 5 Summary and Conclusions Reflected shock wave experiments were performed to obtain ignition delay times of n-heptane-hydrogenair mixtures useful for developing and evaluating kinetic models and to support engine development. The bulk of the tests were performed at a reflected shock pressure of 20 bar and temperature in the range of K, but some limited testing of stoichiometric n-heptane air was performed at 40 and 30 bar. The driver gas was a mixture of nitrogen and hydrogen to achieve a tailored shock tube, in order to maximize the duration of the available test time. The fuel-air mixture was premixed in a separate mixing chamber before loading into the evacuated driven section. The experimental data was compared with predictions using a constant volume model with available reaction mechanisms. Stoichiometric n-heptane air ignition delay time data obtained at 30 and 40 bar matched closest to that of Fieweger et al. [33] and was also comparable to data collected by Hartmann et al. [32]. A NTC region was observed over a similar temperature range for the 20 and 30 bar tests. A power law correlation for ignition delay as a function of reflected shock pressure was developed for the three reflected shock pressure conditions studied (20, 30 and 40 bar) at a temperature of 870 K in the NTC region. The fuel ratio was varied from x = 1 (all n-heptane) to increasing amounts of hydrogen in the fuel mixture (x = 0.8, 0.5, 0.25) for a stoichiometric equivalence ratio. The trend observed was at lower temperatures (< 1100 K) increasing amounts of hydrogen increase the ignition delay time. At higher temperatures (> 1100 K) the ignition delay times had similar values for all fuel ratios. Although the values of the ignition delay times changed slightly for different fuel ratios, the shape of the curve stayed similar over the temperature range observed. The NTC spanned the same temperature range for all x values. These same patterns were also evident when the equivalence ratio was varied to fuel rich and fuel lean (ϕ = 1.25 and 0.833). The Lund mechanism [1] was used to predict the ignition delay times with a varying fuel ratio. The results calculated using the Lund mechanism followed the same trend as measured data in this study, 71

84 where an increasing amount of hydrogen in the fuel mixture increased the ignition delay time at low temperatures (< 1100 K). At higher temperatures (> 1100 K), an increase in hydrogen decreased the ignition delay time. The shape of the curve predicted by the Lund mechanism is similar to the data collected in this study. However, the value of the ignition delay times predicted using the Lund mechanism are typically lower than the data collected in this study except for the peak of the NTC. This difference is due to a 50 K shift in the data that could be explained by the model approximation where the boundary layer reflected shock wave interaction was neglected. It was observed that generally the fuel rich mixtures (ϕ = 1.25) have shorter ignition delay times while the fuel lean mixtures (ϕ = 0.833) have longer ignition delay times. The curves for all three equivalence ratios followed a similar trend. In conclusion, the Lund reaction mechanism did a good job at predicting the ignition delay time data over the pressure and temperature range tested, including the extent of the NTC region. The ignition delay time shows that although hydrogen addition to the diesel fuel is expected to reduce engine soot emissions, it will have a negative impact on the cetane number. However, the impact is expected to be very small as 20% hydrogen addition on average only increases the ignition delay time by 8%. 72

85 References [1] S. Ahmed, E. Bluroch and F. Mauss, "Detailed Mechanism for n-heptane and iso-octane Relevant for HCCI Engine Calculations," in Scandinavian-Nordic and Italian Sections of the Combustion Institute, Ischia, Italy, [2] California Environmental Protection Agency, "Proposed Regulation to Implement the Low Carbon Fuel Standard," [3] European Parliament and the Council of the European Union, "Regulation (EC) No 715/2007 of the European Parliament and the Council of 20 June 2007 on Type Approval of Motor Vehicles with Respect to Emissions from Light Passenger and Commercial Vehicles (Euro 5 and Euro 6)," Strasbourg, [4] "Passenger Automobile and Light Truck Greenhouse Gas Emissions Regulations," Canada Minister of Justice, [5] G. Ciccarelli, Mech 435 Course Notes, [6] J. Dec, "Advanced Compression-Ignition Engines - Understanding the In-Cylinder Processes," Proceedings of the Combustion Institute, vol. 32, pp , [7] J. Brachetti, "Position Paper: Dual Fuel The Best Fuel in the Most Efficient Engine," NGVA Europe, Madrid, [8] M. Ibrahim and A. Ramesh, "Experimental Investigations on a Hydrogen Diesel Homogeneous Charge Compression Ignition Engine with Exhaust Gas Recirculation," International Journal of Hydrogen Energy, vol. 38, pp , [9] W. Santoso, R. Bakar and A. Nur, "Combustion Characteristics of Diesel-Hydrogen Dual Fuel Engine at Low Load," Energy Procedia, vol. 32, pp. 3-10, [10] L. McWilliam, "Combined Hydrogen Diesel Combustion: An Experimental Investigation into the Effects of Hydrogen Addition on Exhaust Gas Emissions, Particulate Matter Size Distribution and Chemical Composition," Brunel University, [11] K. Chun, B. Shin, Y. Cho, D. Han and S. Song, "Hydrogen Effects on NOx Emissions and Brake Thermal Efficiency in a Diesel Engine under Low-Temperature and Heavy-EGR Conditions," International Journal of Hydrogen Energy, vol. 36, pp , [12] O. Gulder, D. Snelling and R. Sawchuk, "Influence of Hydrogen Addition to Fuel on Temperature 73

86 Field and Soot Formation in Diffusion Flames," International Symposium on Combustion, vol. 26, pp , [13] P. Lakshminarayanan and Y. Aghav, "Ignition Delay in a Diesel Engine," in Modelling Diesel Combustion, Springer, 2010, pp [14] G. Mittal, V. Davies and B. Parajuli, "Autoignition of Ethanol in a Rapid Compression Machine," in U.S. National Combustion Meeting, Salt Lake City, [15] P. Veloo, P. Dagaut, C. Togbe, G. Dayma, S. Sarathy, C. Westbrook and F. Egolfopoulos, "Jet- Stirred Reactor and Flame Studies of Propanal Oxidation," Proceedings of the Combustion Institute, vol. 34, pp , [16] D. Davidson and R. Hanson, "Interpreting Shock Tube Ignition Data," in Western States Section/ Combustion Institute, Los Angeles, [17] G. Smith, D. Golden, M. Frenklach, N. Moriarty, B. Eiteneer, M. Goldenberg, C. Bowman, R. Hanson, S. Song, W. Gardiner, V. Lissianski and Z. Qin, "GRI-Mechanism 3.0," [Online]. Available: [18] S. Kao and J. Shepherd, "Numerical Solution Methods for Control Volume Explosions and ZND Detonation Structure," Pasadena, CA, [19] C. Westbrook, "Chemical Kinetics of Hydrocarbon Ignition in Practical Combustion Systems," Proceedings of the Combustion Institute, vol. 25, pp , [20] Y. Briker, Z. Ring, A. Iacchelli, N. McLean, P. Rahimi, C. Fairbridge, R. Malhotra, M. Coggiola and S. Young, "Diesel Fuel Analysis by GC-FIMS: Normal-Paraffins, Isoparaffins, and Cycloparaffins," Energy & Fuels, vol. 15, pp , [21] J. Guthrie, P. Fowler and R. Sabourin, "Gasoline and Diesel Fuel Survey," Environment Canada, Ottawa, [22] N. Grumman, "Diesel Fuel Oils, 2003," Report NGMS-232 PPS, [23] Petro-Canada, "Material Safety Data Sheet: Diesel Fuel," [24] S. Sato, Y. Sugimoto, K. S. I. Sakanishi and S. Yui, "Diesel Quality and Molecular Structure of Bitumen-Derived Middle Distillates," Fuel, vol. 83, pp , [25] J. Farrell, N. Cernansky, F. Dryer, C. Law, D. Friend, C. Hergart, R. McDavid, A. Patel, C. Mueller and H. Pitsch, "Development of an Experimental Database and Kinetic Models for Surrogate Diesel Fuels," SAE, [26] M. Murphy, J. Taylor and R. McCormick, "Compendium of Experimental Cetane Number Data," 74

87 National Renewable Energy Laboratory, [27] Fisher Scientific, "Material Safety Data Sheet: Heptane," [28] A. Burcat, R. Farmer and R. Matula, "Shock Initiated Ignition in Heptane-Oxygen-Argon Mixtures," Shock Tubes and Waves, vol. 13, pp , [29] D. Vermeer, J. Meyer and A. Oppenheim, "Auto-Ignition of Hydrocarbons Behind Relfected Shock Waves," Combustion and Flame, vol. 18, pp , [30] D. Horning, D. Davidson and R. Hanson, "Study of the High-Temperature Autoignition of n- Alkane/O2/Ar Mixtures," Journal of Propulsion and Power, vol. 18, pp , [31] D. Davidson, B. Gauthier and R. Hanson, "Shock Tube Determination of Ignition Delay Times in Full-Blend and Surrogate Fuel Mixtures," Combustion and Flame, vol. 139, pp , [32] M. Hartmann, M. Fikri, R. Starke and C. Schulz, "Shock-Tube Investigation of Ignition Delay Times of Model Fuels," in European Combustion Meeting, Chania, Crete, [33] K. Fieweger, R. Blumenthal and G. Adomeit, "Self-Ignition of S.I. Engine Model Fuels: A Shock Tube Investigation at High Pressure," Combustion and Flame, vol. 109, pp , [34] K. Fieweger, R. Blumenthal and G. Adomeit, "Shock-Tube Investigations on the Self-Ignition of Hydrocarbon-Air Mixtures at High Pressures," International Symposium on Combustion, vol. 25, pp , [35] S. Benson, "The Kinetics and Thermochemistry of Chemical Oxidation with Application to Combustion and Flames," Progress in Energy and Combustion Science, vol. 7, pp , [36] F. Battin-Leclerc, F. Buda, M. Fairweather, P. Glaude, J. Griffiths, K. Hughes, R. Porter and A. Tomlin, "A Numerical Study of the Kinetic Origins of Two-Stage Autoignition and the Dependence of Autoignition Temperature on Reactant Pressure in Lean Alkane-Air Mixtures," in European Combustion Meeting, Louvain-la-Neuve, Belgium, [37] M. Mehl, C. Pitz, C. Westbrook and H. Curran, "Kinetic Modeling of Gasoline Surrogate Components and Mixtures Under Engine Conditions," Proceddings of the Combustion Institute, vol. 33, pp , [38] S. Frolov, S. Medvedev, V. Basevich and F. Frolov, "Autoignition and Combustion of Hydrocarbon- Hydrogen-Air Homogeneous and Heterogeneous Ternary Mixtures," Russian Journal of Physical Chemistry B, vol. 7, no. 4, pp , [39] P. H. Oosthuzien and W. E. Carscallen, Introduction to Compressible Fluid Flow, Kingston, [40] M. Kellenberger, "Dense Particle Cloud Dispersion by a Shock Wave," Queen's University, 75

88 Kingston, [41] G. Ben-Dor, O. Igra and T. Elperin, Handbook of Shock Waves, San Diego: Academic Press, [42] S. Huang, "A Study of Flow in Shock Tubes," University of Texas at Arlington, Arlington, [43] Edmund Optics, "S-Series Photodiode/ Receiver". [44] A. Amadio, M. Crofton and E. Petersen, "Test-Time Extension Behind Reflected Shock Waves Using CO2-He and C3H8-He Driver Mixtures," Shock Waves, vol. 16, pp , [45] M. Oehlschlaeger, D. Davidson, J. Herbon and R. Hanson, "Shock Tube Measurements of Branched Alkane Ignition Times and OH Concentration Time Histories," International Journal of Chemical Kinetics, vol. 36, pp , [46] M. Moran, H. Shapiro, D. Boettner and M. Bailey, Fundamentals of Engineering Thermodynamics, 7th Edition, Wiley, [47] C. Paillard, S. Youssefi and G. Dupre, "Dynamics of Reactive Systems Modeling and Heterogeneous Combustion," Progr Astronaut Aeronaut, vol. 105, p. 394, [48] J. Michael and J. Sutherland, "The Thermodynamic State of the Hot Gas behind Reflected Shock Waves: Implication to Chemical Kinetics," International Journal of Chemical Kinetics, vol. 18, pp , [49] Z. Hong and D. H. R. Davidson, "An Improved H2/O2 Mechanism Based on Recent Shock Tube/ Laser Absorption Measurements," Combustion and Flame, vol. 158, pp , [50] B. Taylor and C. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results," [51] D. Davidson and R. Hanson, "Interpreting Shock Tube Ignition Data," in Western States Section/ Combustion Institute Fall Meeting, Los Angeles,

89 Appendix A Uncertainty Analysis The uncertainty associated with the reported numerical values will be discussed in this section. The uncertainties are propagated from the uncertainties in the fill pressures. The vacuum pressure gauge, used to fill hydrogen and n-heptane for the fuel-air mixture, has a reported error of 0.25% of the full scale. The range of the vacuum gauge is kpa (absolute); this means there is an error of ±0.25 kpa associated with these fill pressures. The low pressure gauge, used to fill the air for the fuel-air mixture and used to fill the fuel-air mixture into the driven section, has a relative error of 1.5%. The high pressure gauge, used to fill hydrogen and nitrogen for the driver, has a reported error of 0.25% of the full scale. The range of the high pressure gauge is kpa (gauge); this means there is an error of ±10.3 kpa associated with these fill pressures. Using Engineering Equation Solver (EES) the uncertainties of the Mach number, M, equivalence ratio, ϕ, reflected shock pressure, P 5, fuel ratio, x, and driver gas ratio, x 4, were propagated based on the fill pressures. The method EES uses for determining uncertainty propagation is described in NIST Technical Note 1297 [50]. Table A.1 shows the results of a test case with the associated uncertainty using EES to propagate the error. The equations and results of the EES program can be found in Figure A.1 and Figure A.2. Table A.1: Select properties for a test case with the associated uncertainty using EES error propagation Property Value Uncertainty M 2.34 ±0.01 ϕ 1.00 ±0.04 P kpa ±7 kpa x 0.50 ±0.01 x ±

90 The velocity of the incident shock wave was measured by the time of arrival recorded by each pressure transducer and their separation distance. The time of arrival was dependent on the response time of the transducer and the DAQ system sample rate. The pressure transducers are specified to have a response time of less than 1 µs and the DAQ card sampling rate was 2 MHz for all tests. Uncertainty introduced by manual selection of the time of arrival from graphed data is estimated to be ±5 µs. This gives a total measurement error of ±5 µs for the time of arrival. The uncertainty in the distance between the transducers is taken as the tolerance during the machining process. That tolerance is ±0.13 mm. This results in an uncertainty of the velocity of the incident shock wave to be ±14 m/s. The CHOCFI program created at CNRS Orleans [47] is used to calculate the reflected shock temperature. The program uses incident shock wave velocity, initial driven section pressure and the partial pressures of the driven section components as the inputs to calculate the reflected shock temperature. By varying the inputs to their minimum and maximum values, the uncertainty of the reflected shock temperature, T 5, was found to be ±21 K. The constant volume program created by Shepherd et al. [18] is used to calculate the ignition delay time using the Lund [1] mechanism. The program uses reflected shock temperature, reflected shock pressure and partial pressures of the driven section components as inputs to calculate the ignition delay time. By varying these inputs to their minimum and maximum values the uncertainty of the predicted ignition delay time was found to be ±64 µs. The uncertainty associated with the measured ignition delay time depends on the manual selection of the maximum slope of the CH emission. The uncertainty introduced by this manual selection is estimated to be ±50 µs. 78

91 EES was used to propagate uncertainty from the fill pressures for select properties: Mach number, M, equivalence ratio, ϕ, reflected pressure, P 5, fuel ratio, x, and driver gas ratio, x 4. Figure A.1 shows the equations input into EES. Figure A.1: Equations used in EES for uncertainty propagation Figure A.1 shows the results of select properties and their uncertainties using EES. The results also show what percentage of the uncertainty is caused by which fill pressure. 79

92 Figure A.2: Results of select properties and their uncertainty using EES 80

93 Appendix B Shock Tube Theory The following section is an expansion upon Section 3.2 with a focus on the equation derivations. B.1 Normal Shock Relations Compressibility effects become significant in a gas flow as the flow velocity becomes high. Gases are typically highly compressible, although compressibility effects can be assumed to be negligible if the Mach number is small enough for the density changes in the flow to be small. As a general rule, it can be assumed that if M > 0.5 compressibility effects should be taken into account [39]. The dimensionless quantity Mach number, M, is defined as the ratio of the gas flow velocity to the speed of sound of the gas. B.1 Where a, the speed of sound, is defined by: B.2 Where γ is the ratio of specific heats and is the specific gas constant. This equation describes the speed of sound in a perfect gas, which only depends on temperature. When M < 1, the flow is said to be subsonic. When M > 1, the flow is supersonic. Supersonic flow is required for an almost spontaneous change in flow, called a shock wave to occur. Velocity decreases, while temperature, pressure and density sharply increase across the shock wave. A shock wave is very thin, typically a few mean free paths thick [39]. A normal shock wave is a shock wave where the flow is at right angles to the wave. Using a control volume, an analysis of property changes across a normal shock wave can be performed. 81

94 Figure B.1: Control volume for a normal shock wave Conservation of mass, momentum and energy apply across the control volume in Figure B.1, which are shown in Equations B.3, B.4 and B.5 respectively. B.3 ( ) B.4 B.5 Using ideal gas law: And assuming perfect gas, enthalpy, h, can be calculated: B.6 ( ) B.7 Combining all conservation equations, the perfect gas assumption, and assuming a constant specific heat ratio,, across the shock wave, the pressure ratio can be found: 82

95 ( ) ( ) B.8 The pressure ratio is an indication of the shock strength and therefore it is desirable to obtain density, velocity and temperature ratios as a function of the pressure ratio. Rearranging Equation B.8 gives: ( ) ( ) B.9 Rearranging the continuity equation in B.3 in combination with Equation B.9 gives: ( ) ( ) B.10 Using the ideal gas law for both states 1 and 2 in combination Equation B.9 gives: ( ) ( ) B.11 The ratios of density, velocity and temperature as a function of the pressure ratio are termed the Rankine- Hugoniot shock wave relations. Combining the shock jump relations gives the equations for the Hugoniot curve: ( ) B.12 ( ) B.13 Combining Equations B.3 and B.4 give the Rayleigh equation: ( ) ( ) B.14 Solving for the initial velocity, u 1, gives: 83

96 ( ) ( ) B.15 Two conditions satisfy u 1 to be a real number: case 1 where and, an expansion shock; or case 2 where and, a compression shock. Rearranging Equation B.14 gives: ( ) ( ) B.16 It is useful to determine flow property changes across a normal shock wave in term of the upstream Mach number, M 1. By combining Equations B.1 and B.3 the conversation of mass in terms of the Mach number can be rewritten as: B.17 Similarly combining Equations B.1 and B.4 the conservation of momentum in terms of the Mach number can be found: ( ) ( ) B.18 Next combining Equations B.1 and B.5 the conservation of energy as a function of the Mach number can be found: ( ) ( ( ) ( ) ) B.19 Combining Equations B.17, B.18 and B.19 gives the downstream Mach number, M 2, as a function of the upstream Mach number: ( ( ) ( ) ) B.20 84

97 Combining Equations B.19 and 3.3 gives the temperature ratio as a function of the upstream Mach number: [ ( )][ ( ) ] ( ) B.21 Using Equations B.17, 3.3, 3.4 and the ideal gas law at both states, gives the pressure ratio in terms of the upstream Mach number: ( ) B.22 Combining Equations 3.4 and 3.5 with ideal gas law at both states, the density ratio as a function of the upstream Mach number can be found: ( ) ( ) B.23 Results for Equations 3.3 through 3.6 are often tabulated for given M 1, and γ values. Combining Equations B.1, B.10 and 3.5 give u 2 as a function of the pressure ratio: ( ) ( ) ( ) ( ) B.24 B.2 Normal Shock Reflections When a normal shock wave reaches a closed end of a duct, it is reflected and travels back in the opposite direction. As there can be no flow out of a closed duct, the gas at the end must always have a velocity of zero. This means that the reflected shock must have sufficient shock strength to stagnate the gas flow generated by the incident shock wave. A diagram of this wave propagation is shown in Figure

98 Figure B.2: Reflection of a normal shock wave The upstream and downstream flow Mach numbers relative to the reflected shock wave, M up and M down are given by: B.25 B.26 Equating for V R in Equations B.25 and B.26 gives the downstream Mach number as a function of the upstream Mach number and the temperature ratio across the reflected shock wave: ( ) ( ) B.27 For a given induced velocity, u, and temperature in that zone, T 2, (needed to find a 2 using Equation B.2), an iterative approach can be used to find the downstream Mach number. By guessing a value for M up, normal shock relation Equations 3.3 and 3.4 can be used to calculate the downstream Mach number and the temperature ratio respectively. Then putting the upstream Mach number and the temperature ratio back into Equation B.27 will also give a value for the downstream Mach number. This process should be repeated until both values of M down are the same. 86

99 B.3 Shock Tube Theory A shock tube is designed to produce shock wave of given strength. A shock tube consists of two sections: a driver (high pressure) and a driven (low pressure). The sections are separated by a diaphragm. A large pressure differential across the diaphragm causes it to rupture. The expansion of the driver gas produces a shock wave that propagates in the driven section, a schematic of which is shown in Figure 3.3. Figure B.3: Schematic of a shock tube after diaphragm rupture [40] Upon diaphragm rupture there is an expansion fan formed that travels back upstream into the driver accelerating the driver gas towards the driven end of the tube. The head of the expansion fan travels at the speed of sound. The flow through the expansion is isentropic, whereas the flow through the shock is not. Following the shock wave is a contact surface which is the interface between the driven and driver gases. The pressure and velocity across the contact surface are constant. An x-t diagram showing the different waves formed after the diaphragm is ruptured is shown in Figure 3.4a. 87

100 (a) (b) Figure B.4: (a) An x-t diagram showing a position time history of the wave propagation; and (b) a visualization of wave propagation at a certain time [41]. To better visualize an x-t diagram, a horizontal line can be drawn across the diagram at a certain time, t 1, shown in Figure 3.4a. Figure 3.4b then shows how far each wave has travelled in the shock tube. The shock wave travels to the end of the driven section reflecting off the end wall. The reflected shock wave stagnates the flow generated by the incident shock wave, such that a zone of high pressure and temperature gas between the reflected shock wave and the endplate is created, see zone (5) in Figure 3.4a. Auto-ignition occurs in this high temperature gas mixture after a period of time known as the ignition delay time. The reflected shock wave interacts with the contact surface producing an expansion fan or shock wave (depending on acoustic impedance across the contact surface) that propagates back towards the end wall. The available test time is the time from when the shock wave reaches the end wall to when the contact surface, for the case shown in Figure 3.4a, reaches the end wall. This is called the available test time because it is the time in which the fuel-air mixture has to react uninterrupted. 88