The Effect of Different Gas Mediums on the Reflected Shock Pressure and Temperature in Shock Tubes

Transcription

1 International Conference on Advanced Material Science and Environmental Engineering (AMSEE 016) The Effect of Different Gas Mediums on the Reflected Shock Pressure and Temerature in Shock Tubes Bin Xue and Jun Yang Changcheng Institute of Metrology & Measurement, Beijing 10009, China Abstract The choice of gas mediums will affect the reflected shock ressure and temerature during analyzing the shock tube. Different mediums in driver and driven section result in the Mach number disarity in the rocess of shock wave roagating, adversely affecting the reflected shock wave. Based on the ideal conditions, to study the higher or lower reflected shock ressure and temerature circumstance, this aer comared several kinds of gas mediums as driver and driven section. Combined with FLUENT simulation verification, it could be confirmed that roer cases of mediums would rovide meaningful direction for exeriment and roject need. II. THEORETICAL STUDY Keywords-gas medium; reflected shock wave; ressure I. INTRODUCTION Shock tubes, as traditional devices have been used to rovide a ressure change with a very fast rise time and calculable amlitude, also been tools for studying high seed aerodynamics and shock wave characteristics as well as the resonse of material to blast loading [1]. For traditional shock tubes, the designs are based on how the simulated blast wave is created: comression-driven []. This ressure could rovide the basis for the calibn of ressure transducers used in highly dynamic alications. Based on the Knudsen number, which indicates the rarefaction gas effect, Arun K.R. et al [3] erformed comutational studies to investigate the shock wave roagation under different ressure s, shock tube diameters with sli condition and no sli wall boundary conditions. For the roagating rocess of the shock wave, Park J.O et al [4] erformed an exerimental study to investigate shock wave roagation. Due to the ressure, Du Shuiyou et al [] analyze the dun of the by using ressure sensor. In order to obtain lower ressure, Lin Jianmin et al [6] exlore two methods which contain changing the area of driver and driven section and adding orifice lates downstream of the diahragm in shock tube. From another ersective, A. Hertzberg [7] studied the way to gain strong shock wave. Currently, most direct method for adjusting the strength of ressure and temerature is changing the area of sections. However, for material and secific alication, it is an inconvenient choice, and regulating gas mediums can solve more ractical issues. A) Theoretical Analysis A simle shock tube contains two straight tubes of the same circular cross section that are searated by a diahragm. One tube consists a low-ressure driven gas, and the other is filled with a driver gas. When the difference in ressure reaches a certain value leading to the diahragm ruture, the driver gas will generate a series of comression waves within the driven gas which coalesce to form a shock wave that roagates into the remaining undisturbed driven gas. As the shock wave gets to the end face of low-ressure driven gas section, it will reflect back with a higher ressure and temerature [8]. In the condition of inviscid, the relation between the driver ressure P4, the driven ressure P1 and the Mach number M S is given as follows [9]: 4 1 1M S 1 4 a1 a4 M S MS Where 10 is the of the secific heat at constant ressure to that at constant volume for the driven gas. Similarly, 4 = and 4 is the of the secific heat for driver gas a1 and a4 is the seed of sound in driven and driver section. It can be calculated by the formula a RT m where T is the measured initial temerature (in kelvin) of the gas, m is its molecular weight and R is the gas constant. When the initial state of these two arts and the of ressure are known, the Mach number of the advancing shock wave can be gotten. After the diahragm breaking u, the shock front is roagating into the driven gas with a constant ressure behind the shock, whose ressure can be exressed as: 016. The authors - Published by Atlantis Press 1 = and 1 4 ( 4 1) M S 1 1 1

2 And the temerature which is accomanied by the change of satisfy the relationshi as follows: T T When the shock wave reaches the end of the shock tube, it will reflect with the ressure in the end section rising to with an associated temeraturet. The value of can be gotten though the formula below: While the exression of T is similar to T which is shown as follows: T T According to relationshi above, it can be judged that the reflected wave ressure and temerature vary with different gas mediums. So on the basis of fitting ressure size, the theory contains guiding significance. B) Theoretical Result When the gas mediums in driver and driven section are the same, the Eq. (1) could be simlified as: 4 1 ( 1) M S 1 M S MS Several kinds of gas mediums have been listed here to imrove the effect of medium on the ressure and temerature. It is not difficult to find that the diverse mediums leads to the Mach number varying with the roagating seed of shock wave directly. To analyze the influence of gas tyes only, the initial ressure in the driven section is setting to 0.1MPa in each condition, and the driver section ressure can be gotten by the given ressure. Also the initial temerature is 300K in both sections during the calculation. The secific results are shown as the following table, which reflect the relationshi among the different gas mediums. TABLE I. MACH NUMBER IN DIFFERENT GAS MEDIUMS AND PRESSURE RADIO PR Ms H He N Air Ar Note: stands for the gas medium in both driver section and driven section. M S is the Mach number which is roducing after diahragm crushing. PR means the initial ressure before diahragm ruture. It can be gotten that the Mach number is only relevant to the secific heat of gas, and nothing with the tye of gas medium. For most diatomic gas, such as hydrogen, nitrogen and air, the secific heat is 1.4. Due to the monatomic gas, such as helium and argon, the secific heat is /3 [10]. With the ressure growing, the Mach number will be higher. III. SIMULATION FLUENT has been a oular software which is alied to the flow field simulation. Two-dimensional model is set u to simulate the whole rocess of shock tube. The length of shock tube is 00mm and the width is mm.in the ideal situation, there is no heat exchange between the shock tube wall and external environment. Based on the fundamental equation of thermodynamics, the starting conditions of simulation can be defined regardless of the viscous. 11

3 A) The Proagating of Shock Wave Before the diahragm breaking u, it is considered that status of gas in driver and driven section kees still. At an instant moment, the diahragm crushes and forms a shock tube whose Mach number is higher than 1. The ressure and temerature in the driver section will decline, and on the contrary they would be ascended in the driven section. When the shock wave reaches the end of shock tube, the ressure and temerature in the local area will rise u sharly within millisecond or even sub-millisecond. The size of the shock tube has been set u before. In the ideal circumstance, it can be assure that the result is irrelevant to shae and size of the shock tube from the relationshi between ressure or temerature and gas medium. When the size of shock tube is known and the gas mediums in driver and driven section are given, the latform of ressure and temerature will be confirmed. The rocess of changing in ressure is shown as following figure from the diahragm ruture to reflected shock wave forming. (a) (d) FIGURE I. THE PROCESS OF SHOCK WAVE PROPAGATING (a) Before the diahragm ruture, the ressure shows in the driver and driven section. (b) After the diahragm ruture, the ressure in driver section declines and ascends in driven art. (c) Rarefaction wave reflects in the driver section, which leads to the ressure going down. (d) Reflected shock wave results in the ressure rising u. B) The Comarison between Theory and Simulation with the Same Medium When the gas medium in the driver and driven section are the same, the of seed of sound a1/a4 will equal 1. Mach number can be calculated as the initial film ressure is determined. Take the situation of initial value equaling 3 for examle and four kinds of gas mediums are listed here which contain hydrogen, helium, air and argon. Meanwhile, the initial temerature in both sections is 300K. The results of the theory value and simulation are shown as Figure. (b) FIGURE II. THE PRESSURE STEP OF THE THEORY VALUE AND SIMULATION (c) In the ideal theoretical circumstance, the ressure take lace on a moment. While the simulation is close to the ractical situation, of which rising time works in milliseconds. Though recording the time which takes lace at the moment of changing 1

4 from original value, the seed of shock wave can be gotten. Then the of shock wave seed and the seed of sound is Mach number that is used to calculate the ressure and temerature later. So the comarisons of ressure between the theoretical and emulation results are shown as following table: TABLE II. THE COMPARISON OF PRESSURE STEP BETWEEN Theoretical ressure Emulation ressure H 0.76MPa 0.77MPa 0.18% He 0.686MPa 0.68MPa 0.04% Air 0.76MPa 0.764MPa 0.07% Ar 0.686MPa 0.68MPa 0.04% Meanwhile the comarisons of temerature are shown as following table: TABLE III. THE COMPARISON OF TEMPERATURE STEP BETWEEN Theoretical temerature Emulation temerature H K K 0.18% He K K 0.16% Air K K 0.07% Ar K K 0.17% From the above figure, it is not difficult to find out that error between theory and simulation is nearly less than 0.%. So the software FLUENT can emulate the rocess of shock wave erfectly. With the density of mesh which is generated rising u, the accuracy will get better. C) The Comarison between Theory and Simulation with the Different Medium When the gas medium in the driver and driven section are different, the ressure and temerature will vary considerably among distinct circumstance. Different gas mediums ossess own molar mass and secific heat, which lead to the Mach number is diverse from each other. In order to make this comarison, four kinds of situation have been enumerated here. The first kind of situation is helium as driver gas and air as driven gas. The second is hydrogen as driver gas and argon as driven gas. The third is air as driver gas and helium is full of driven section. The last situation is that argon acts as driver gas and hydrogen is driven art. So the theoretical and emulation results are shown as following figure. FIGURE III. THE PRESSURE STEP OF THE THEORY VALUE AND SIMULATION According to the results above, the ressure s of the first two cases are higher than the last two status. The comarisons between the theoretical and emulation results are shown as following table: TABLE IV. THE COMPARISON OF PRESSURE STEP BETWEEN Theoretical ressure Emulation ressure He Air MPa MPa 0.1% H Ar 0.09MPa 0.06MPa 0.0% Air He MPa MPa 0.06% Ar H MPa MPa 0.08% TABLE V. THE COMPARISON OF TEMPERATURE STEP BETWEEN Theoretical temerature Emulation temerature He Air 469.3K 468.8K 0.1% H Ar 91.87K 91.7K 0.0% Air He 37.6K 37.43K 0.06% Ar H 333.K 333.K 0.08% Note: means gas medium. The left gas fills with the driver section and right is driven art. So, the above data rovides an obvious suort for the relationshi between the gas medium and ressure. By a reliminary insection, the gas which owns smaller molar mass as driver section and bigger molar mass gas as driven gas will roduce higher ressure or temerature. On the contrary, as the driver gas medium, bigger molar mass gas will generate lower. 13

5 In order to rove the above conclusion, more kinds of situation have been given as follows. Though these cases, it can be assure that higher ressure between the two sections will lead to higher Mach number. At the same time, the ressure and temerature get more. ressure (MPa) 0 The effect of gas mediums on ressure IV. CONCLUSION The aer analyze the effect of gas mediums on the ressure and temerature, which is used the method of combining the theoretical analysis with FLUENT simulation. It can be concluded that the s are influenced by the gas molar mass and secific heat directly in the ideal situation. On the one hand, in the case of same medium in the driver and driven section, the gas molar mass is irrelevant to the final result, yet only affect the time of arriving at the end of shock tube for shock wave. While the secific heat is the determining factor. In the case of different gas medium, aiming to gain higher, lower molar mass gas should be considered firstly. To the contrary, higher molar mass gas will result in the lower. On the other hand, the ressure kees ace with the temerature. The temerature varies with the ressure changing. So, in accordance with the content of this aer, roer gas medium can be chosen for the need of concrete exeriment or roject, which is taken advantage of the ressure or temerature. In the future, an exerimental study will be erformed to validate the resent theoretical conclusions and numerical results ressure of driver and driven section Air-Air He-Air H-H N-Air FIGURE IV. THE EFFECT OF GAS MEDIUMS ON PRESSURE STEP Ar-Air Air-He Air-Ar Ar-He [3] Arun. K. R. and Kim H. D, Comutational Study of the Unsteady Flow Characteristics of a Micro Shock Tube, Journal of Mechanical Science and Technology, vol. 7 (), 01, [4] Park. J. O., Kim G. W. and Kim. H. D, Exerimental Study of the Shock Wave Dynamics in Micro Shock Tube, Journal of the Korean Society of Proulsion Engineers, vol. 17 (), 014, [] Du Shuiyou, Qiu Guohong and Fu Chuanwei, The Study of Pressure Ste Dun on the Shock Tube, Journal of China Institute of Metrology, No.1 June [6] Lin Jianmin, Wei Yijia, Zhang Dayou, The Method of Obtaining Lower Strength Shock Wave in Shock Tube, Journal of Exeriments in Fluid Mechanic, vol. 0 No., June 006. [7] A. Hertzberg, W. Smith, A Method for Generating Strong Shock Wave, J, Al. Phys, No [8] I. I. Glass, Theory and Performance of Simle Shock Tube, International Shock Tube Symosium 10th, 197. [9] Stehen Downes, Andy Knott and Ian Robinson, Towards a Shock Tube Method for the Dynamic Calibn of Pressure Sensors, Philosohical Transactions of the Royal Society, Phil. Trans. R. Soc. A , , ublished 8 July 014. [10] Chen Qiang, The Theory and Exeriment Technology of Shock Tube Flow, University of Science and Technology of China, REFERENCES [1] Segars RA, Carboni MG. A shock tube for down selecting material concet for blasting rotecting art I: descrition of the shock tube and comarison of flush mounted and recess mounted ressure sensors; 008. Technical Reort. Natick/TR-09/010. [] Henshall BD. On some asects of the use of shock tube in aerodynamic research, HM Stationery Office,