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1 Problem 1: An 8cyl 426 ci Hemi motor makes 426 HP at 5500 rpm on a compression ratio of 10.5:1. It is over square by 10% meaning that it s stroke is 10% less than it s bore. It s volumetric efficiency is 95% at this speed. It runs at an AFR of 13:1 1) What is the bore and stroke, in mm. 2) What is the volume of the combustion chamber? 3) What are the (P 1, T 1) pressures and temps at BDC assuming the air was at 27C and 101 kpa (T 0, P 0) atmospheric and the induction process is entirely adiabatic/isentropic? 4) What is the mass of air, fuel in one cylinder? 5) How much heat is released upon combustion? 6) What is the a. arbitrary overall efficiency, b. specific fuel consumption and c. BMEP d. Otto Efficiency 7) Without calculating temperatures, how much heat is wasted (Q 41) 8) Calculate a. V2,P2,T2 b. V3,P3,T3 c. V4,P4,T4 d. Q41 using temperature formula and compare to (7). This engine is turbocharged with NO intercooler and makes 1050 HP at the same RPM with a density ratio of 1.5. Assuming the pressure (P1) is the same as that in the intake manifold and the turbocharger is 65% efficient and the compression ratio is lowered to 9:1, while other parameters remain the same, determine the following. 1) Given the density ratio, what is the mass of air in a cylinder at BDC (m1) 2) If the boost is 1.0 bars, what is P1 3) What is actual T1 (temp after turbocharger) 4) Show that the density ratio is as stated 5) How much heat is released, per cycle per cylinder? 6) How much power does this represent, in Horsepower? 7) What is the arbitrary overall efficiency? 8) What are T2,P2? 9) What are T3,P3? 10) What is the otto efficiency 11) What percentage and actual amount of heat ( in HP) is actually wasted? Take the same engine and add an intercooler that is 90% efficient at this flow with a 1PSI pressure drop and perform the same calcuations. Assuming the same overall efficiency, how much HP does it make?
2 Problem 2: A 4 cycle SI engine is designed to make peak of 200KW of power (1 kw = 1.34 HP) at 6000 RPM at 10% richer than stoichiometric mixture (14.7*0.9). The engine is an 8cyl Compression ratio is 11:1 Displacement is 5 liters. Calorific value for fuel is 44MJ/kg. sfc is 0.10 kg/mj, R air=287 J/kgK, Atmospheric T = 27C, P=101KPa Heat Capacity products and reactants is the same, C v= 950 J/kgKC p=1330 J/kgK Assume both compression and expansion are reversible isentropic adiabatic A) What is the combustion chamber volume? B) What is the Otto Efficiency? C) What is the torque output? D) What is the BMEP (2)? E) What is the arbitrary overall efficiency? F) What is the mass fuel flow rate at peak power? G) What is the mass air flow rate at peak power? H) What is the volumetric efficiency? Focus on ONE cycle: I) What is the mass of air in the cylinder? J) What is the mass of fuel in the cylinder K) How much heat is released by combustion? L) What is the temperature after compression (state 2)? M) What is the temperature after combustion (state 3)? N) What is the temperature after expansion (state 4)? O) What is the pressure after compression (state 2)? P) What is the pressure after combustion (state 3)? Q) What is the pressure after expansion (state 4)? R) How much heat must be released to return to the initial state? S) What is the temperature in the final state?
3 1) Problem 3: Weibe Function: An engine burns 0.1 g fuel per cycle per cylinder. Combustion begins at = 15 degrees BTDC and is 99% done at 45 degrees ATDC. a=5, m=2 (show work) 0 Weibe x( ) 1 exp( a b m 1 a. What percentage of the fuel is burned up to 13 degrees ATDC? (2) ) b. How much fuel is burned between 13 and 14 degrees ATDC? (2) c. Draw a graph of fuel burned (Y) vs. (X) and properly label axes (2)
4 Problem 4) In 1968, exploiting a loophole in the regulations, Porsche developed what would become a 5 liter 12 cylinder normally aspirated power plant making 600 HP at 6000 RPM. It used a 70.4mm stroke (same as the 6 cylinder 2.4) Top speed at le Mans was approximately 235 MPH in long tail configuration. Assume standard atmospheric conditions and use only data supplied. The arbitrary overall efficiency of the normally aspirated motor is 75% of the Otto efficiency. R=287 J/KgK CV = 44 MJ/kg T amb=27 C 1HP=0.746KW P amb=1 bar=101 kpa; =14.7 psi Ratio of Specific heats 1.4 Specific Heat air, fuel and mixture C p = 1.33, C v=0.950 kj/kgk Stoichiometric AFR 14.7:1 Assuming a volumetric efficiency of 95% at 6000 RPM The engine runs 10% rich at this horsepower Express P in Pa and Bar. Express T in both C and K MAJOR HINT: Q 23 is ONLY dependent on mass flow as is T 23, do not calculate this any more times than you have to! A) Normally Aspirated (25) 1) What is the bore, in mm? 2) What is the mass flow of air per second?, what is the AFR and mass flow of fuel per second? 3) What is the arbitrary overall efficiency? 4) What is the specific fuel consumption? 5) What is the compression ratio, based on the Otto efficiency? 6) What is the volume of the combustion chamber, in ccs? 7) Calculate ideal temperatures and pressures for the four data points of the Otto cycle, Remember, you have no data to use the ideal gas law with the fuel added! Also be sure to account for volumetric efficiency! a. What are V1, T1 and P1 based on R v and V f? Note: calculate mass then calculate V 0, then expand isentropic/adiabatic b. What are V2 na, T2 na, P2 na after compression? c. How much heat is produced by combustion per cycle per cyl (Q 23)? d. What are V3 na, T3 na, P3 na after combustion (ideal, adiabatic) e. What are V4 na, T4 na, P4na t after expansion? f. How much heat must be released (wasted) to return to the final/initial condition (Q 41) g. Show that the otto efficiency calculated using the ratio of heats(q 23, Q 41) and that using temperatures is equal to that calculated by the compression ratio and specific heat ratio.
5 B) Turbocharging: In turbocharged form, without the aid of an intercooler, the engine was able to make 1200HP at 7500 RPM using twin turbos and mechanical fuel injection with no intercooler.. That engine had a compression ratio of exactly ½ of its normally aspirated brother. Unless specified otherwise, all other data is the same (AFR, Cv,etc) Assuming the ratio of to arbitrary overall efficiency to Otto efficiency to is decreased to 70%: 1) What is the Otto efficiency? otto 2) What is the overall arb. efficiency? arb 3) What is the mass fuel flow rate per second? 4) What is the mass air flow rate per second? 5) What is the mass fuel flow rate per cycle for one cylinder? 6) What is the mass air flow rate per cycle for one cylinder? 7) What volume of air at ambient temp/pressure is required per cycle (V 0)? 8) What is the effective Volumetric Efficiency (note, you must calculate air volume inducted at ambient pressure/temp)? 9) What volume will this air occupy at bottom dead center (V 1)? 10) Assuming the pressure at BDC is the same as it is when it leaves the turbocharger, what is the volume ratio (V 0/V 1) across the turbocharger (CAREFUL, this is NOT V f!)? 11) a. If you assume the turbocharger is 100% efficient, i.e. an isentropic adiabatic compression, what is the temperature AND pressure at bottom dead center (T 1*, P 1*) HINT: This is the same as any compression, pv k =const. b. If that the turbocharger is really only 70% efficient, what are the actual temperature after the turbocharger (T 1t)? (hint: assume that the increase in T is due to an influx of heat, output pressure is fixed by the wastegate, P 1*=P 1) c. What would a boost gauge read in Bar, reading gauge pressure, not absolute 12) Calculate T2 t, T3 t, T4 t and P2 t, P3 t, P4 t. Calculate Q23 t and Q41 t 13) Calculate Otto efficiency using temperatures, heats, compare to 1.
6 C) Intercooling: An intercooler is introduced into the system. It is 95% efficient ( i) and causes 1.47psi pressure drop. 1) Assume boost pressure is 2.1 bars absolute, and the turbocharger is 70% efficient, and P1 in the cylinder is same as boost. a. what are T 1t* and T 1t after the turbo, before the intercooler? b. What is T 1i, P 1i after the intercooler? c. If we seek a temperatures (T2 = 866K), what compression ratio can we run? d. What is the new Otto efficiency? e. What is V1i based on the new compression ratio f. What is the mass of air in the cylinder? g. How does this compare to the NA scenario? h. If the ratio of arbitrary overall efficiency to otto cycle remains the same, what is the new horsepower? (i.e. how much horsepower did we get for free ) i. Compare this to (B), Is this better or worse than and why discuss in depth? j. Bonus (3) What compression ratio would we need to run to make the same power as (B), 1200 HP assuming the only change were to the Otto Efficiency? k. If you need to make 1200 HP, which is the best way to do it and why (consider C.j vs B). Be specific!
7 Problem 5) Turbocharging: a) IN general we specify a pressure ratio in advance, i.e.. boost. Can we specify a Density ration (T0/T1*P1/P0) in advance and determine the Boost if we know the compressor efficiency? b) Example: We have a 65% efficient intercooler and desire a density ratio of 2. What boost pressure is needed to achieve this? Show all work and derivation. Show that it works. c) Assume that a turbocharger is in fact adiabatic and isentropic, and that you can then determine theoretical output temperature by knowing the pressures before and after the turbo and the ambient temperature. What formular relates pressure and temperature without need to know volumes or compression ratiors? Show derivation. d) Building on c: We know that turbochargers are far from adiabatic and isentropic output temperature is based on efficiency. What single formula relates temperature before the turbo, pressure ratio and true temperature after the turbo. Show derivation. e) Using d) If temp before the turbo is 300K and the pressure ratio is 2.5, with a compressor efficiency of 75%, show that the two step process (calculate ideal temp first then actual temp) is equal to the result from equation d).
8 A 4 cylinder SI engine uses a single overhead cam with two valves per cylinder. Cam opens and closes with simple harmonic motion, equations below. SHOW ALL WORK ON A SEPARATE SHEET Components are as follows: Data: Valve Weight: 150g, Spring Weight 90g, Retainer/Keeper Weight 40g Lifter: 60g Maximum Valve Lift 12mm Valve Spring: Free Length 50 mm o Installed height 45 mm, Fully Compressed Height 25.4 mm Crank speed of 7200 RPM and cam speed of ½ of that. Duration of this cam is 310 degrees CRANK ANGLE, with opening starting at 60 degrees BTDC and closing at degrees ABDC. a. What is the effective mass of the valve train? b. At this RPM what is the total length of time it takes for the cam to open and close the valve? c. What value should be used for in the equation below (specify units)? d. What is the velocity at TDC? (HINT: You must use speed of the engine and crank degrees duration or cam speed and cam degrees duration, do not mix them!, Also below refers to the duration to OPEN the valve, not open and close it) e. Valve float is most likely to occur with acceleration at it s most negative value, at what crank position is this? (Express as degrees ATDC) f. What is the value of the acceleration at this point? g. What spring force is needed to prevent float? h. Given the parameters above, what spring RATE is needed to prevent float at the specified crank speed? i. What is the installed height seat pressure (i.e. spring force with the valve closed) (2) NOW: Try the same questions with modified harmonic and eight degree polynomial. Where is the float??
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