Shock tube orifice design method for sparse wave elimination

Abstract

The invention relates to a design method of an explosion simulation device, in particular to a design method of a shock tube orifice for sparse wave elimination, and aims to solve the problem that the discharge area of a tube orifice cannot be determined according to shock wave parameters in the prior art. The method comprises the following steps: 1) determining a change relation of incident shock wave static pressure p2 at a shock tube opening along with time according to an experimental condition; 2) calculating the ratio pcr1 of the shock wave static pressure p2 to the environment pressure p1 when the airflow after the shock wave is at the sound velocity, and calculating the ratio pcr2 of the shock wave static pressure p2 to the environment pressure p1 when the shock wave outflow static pressure pj is equal to p1; 3) dividing into three intervals according to the following conditions: p2 / p1 > = Pcr1, pcr2 < p2 / p1 < = pcr1 and p2 / p1 < = pcr2; 4) respectively calculating the discharge area ratios Ae / Ac of the shock tube orifices in the three intervals; and 5) respectively mapping Ae / Ac in the three intervals into the change relation of the incident shock wave static pressure p2 along with the time to obtain the change relation of the discharge area ratio of the shock tube orifice along with the time, and then designing the shock tube orifice.

Description

Technical Field

[0001] The present invention relates to a design method for an explosion simulation device, and more particularly to a design method for the nozzle of a shock tube for eliminating rarefaction waves. Background Art

[0002] A shock tube is an important test platform for simulating explosion shock waves. It is widely used in many fields such as the evaluation of the anti-explosion shock performance of bridges, buildings, vehicles, and the study of biological blast injuries. The peak pressure and positive pressure action time of the shock wave generated by it are the key indicators for evaluating the simulation effect.

[0003] However, in experiments, when the shock wave passes through the nozzle of the shock tube, due to the higher air pressure inside the tube than the ambient pressure, the air flow accelerates and flows outwards, forming a rarefaction wave propagating in the reverse direction, resulting in a decrease in the static pressure inside the tube, an acceleration of the flow, and a shortening of the positive pressure time of the shock wave, seriously damaging the simulation environment in the test section of the shock tube. At present, usually two methods are adopted to avoid the influence of the nozzle rarefaction wave. One is to increase the length of the test section to 4 - 5 times the original length to delay the arrival time of the nozzle rarefaction wave at the test section. The other is to set a static baffle structure at the nozzle to reduce the actual outflow area of the pipe, thereby increasing the flow velocity at the nozzle and reducing the air pressure, and then weakening the intensity of the rarefaction wave. However, both of the above methods have relatively prominent problems. Increasing the length of the test section will significantly increase the construction cost and floor area of the shock tube, while the baffle structure can only be applied to shock waves within a certain overpressure range. For shock waves beyond this range, a relatively high peak reflux compression wave will be generated due to the excessive blocking area, introducing new interference factors in the experiment. Therefore, in order to achieve the real-time elimination of the entire process of the nozzle rarefaction wave of the shock tube during the positive pressure action time of the shock wave, a rarefaction wave real-time elimination device with a discharge area that can change with time needs to be installed at the nozzle. Thus, a design method that can determine the nozzle discharge area according to the shock wave parameters is required to guide the design of the shock tube rarefaction wave real-time elimination device. This method is of great significance for the construction cost control and simulation ability improvement of the shock tube device, especially large-scale shock tubes. At present, there is no reported method that can determine the nozzle discharge area according to the shock wave parameters. Summary of the Invention

[0004] The object of the present invention is to solve the problem that the prior art lacks a method for determining the nozzle discharge area according to shock wave parameters, and to provide a design method for the nozzle of a shock tube for eliminating rarefaction waves.

[0005] To achieve the above object, the technical solution provided by the present invention is as follows:

[0006] A design method for the nozzle of a shock tube for eliminating rarefaction waves is characterized by including the following steps:

[0007] Step 1: Set up the shock tube experimental environment and conduct experiments. Determine the relationship between the static pressure p2 of the incident shock wave at the shock tube nozzle and time according to the experimental conditions.

[0008] Step 2: Measure the ambient pressure p1 and ambient temperature T of the experimental environment. Calculate the ratio p of the static pressure p2 of the shock wave to the ambient pressure p1 when the post-shock wave flow is sonic according to the ambient temperature T, and the ratio p of the static pressure p2 of the shock wave to the ambient pressure p1 when the static pressure p cr1 at the shock wave outflow is equal to p1. p j < p cr2 ; cr2 cr1 ;

[0009] Step 3: According to the ratio p cr1 and the ratio p cr2 obtained in Step 2, divide the relationship between the static pressure p2 of the incident shock wave and time obtained in Step 1 into three intervals according to p2 / p1 ≥ P cr1 , p cr2 < p2 / p1 ≤ p cr1 and p2 / p1 ≤ p cr2 ;

[0010] Step 4: Calculate the discharge area ratio A e / A c at the shock tube nozzle in the three intervals in Step 3 respectively, where A c is the cross-sectional area inside the shock tube, and A e is the cross-sectional area at the shock tube outlet;

[0011] Step 5: Map the discharge area ratio A e / A c at the shock tube nozzle in the three intervals obtained in Step 4 into the relationship between the static pressure p2 of the incident shock wave and time respectively, to obtain the relationship between the discharge area ratio at the shock tube nozzle and time. Design the shock tube nozzle according to the relationship between the discharge area ratio at the shock tube nozzle and time, and then the full-process real-time elimination of the rarefaction wave can be achieved.

[0012] Further, Step 4 is specifically:

[0013] Calculate the discharge area ratio A e / A c at the shock tube nozzle in the three intervals in Step 3 respectively;

[0014] When p2 / p1 ≥ P cr1 , A e / A c = 100%;

[0015] When p cr2 < p2 / p1 ≤ p cr1 ​When, by adjusting the outflow area A at the orifice of the shock tube j , the outflow Mach number M j is always 1, and A j / A c is obtained. Then, using A j / A c to calculate the relief area ratio A e / A c ;

[0016] When p2 / p1 ≤ p cr2 , adjust the outflow area A at the orifice of the shock tube j so that the outflow pressure p j is always equal to the ambient pressure p1, and A j / A c is obtained. Then, using A j / A c to calculate the relief area ratio A e / A c .

[0017] Furthermore, in step 2, the p cr1 is calculated using the following formula:

[0018]

[0019] where M2 is the Mach number of the airflow behind the shock wave, and γ is the specific heat ratio of the ambient atmosphere. Furthermore, in step 2, the p cr2 is calculated using the following formula:

[0020]

[0021] where P is the total pressure of the airflow behind the shock wave.

[0022] Furthermore, in step 4, in step 4, using A j / A c to calculate A e / A c using the following formula:

[0023]

[0024] k2 = (γ - 1)M2 2 / (2 + (γ - 1)M2 2 ), k j = (γ - 1)M j 2 / (2 + (γ - 1)M j 2 )

[0025] m = 7kj +1 / (1 + 12k j ), A = (2m - 1)(1 - C0),

[0026] B = 2(1 - m)(1 - C0);

[0027] where C is the jet contraction ratio, and m, k2, k j , C0, A, and B are all intermediate variables.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0029] 1. The shock tube nozzle design method for rarefaction wave elimination provided by the present invention calculates the variation relationship of the discharge area ratio of the shock tube nozzle with time, and then designs the shock tube nozzle according to the variation relationship of the discharge area ratio of the shock tube nozzle with time, thereby realizing the real-time elimination of rarefaction waves throughout the process.

[0030] 2. The shock tube nozzle design method for rarefaction wave elimination provided by the present invention is not restricted by the driving mode, shape structure, etc. of the shock tube, and can be generally applied to the pipe-structured shock tube device with the end open to the atmosphere and requiring the flow field environment of the driven section to be stable within a certain period of time, and the method has strong practicability.

[0031] 3. For the shock tube nozzle design method for rarefaction wave elimination provided by the present invention, since the jet will contract when the air flow passes through the nozzle or slit structure, the discharge area directly given by theoretical calculation will be larger than the outflow area of the rarefaction wave elimination device in actual situations and cannot be accurately applied to the device design; the present invention gives the corresponding calculation relationship between the nozzle discharge area and the nozzle outflow area, and can guide the engineering design of various rarefaction wave elimination devices with the same principle through the corrected theoretical calculation conclusion. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flowchart of an embodiment of the shock tube nozzle design method for rarefaction wave elimination of the present invention;

[0033] Figure 2 is a flow field schematic diagram of the shock wave front in the shock tube;

[0034] Figure 3 is a flow field schematic diagram of the rarefaction wave front of the reflux in the shock tube;

[0035] Figure 4 is a flow field schematic diagram of the reflected wave front on the inner wall surface of the shock tube;

[0036] Figure 5 is a schematic diagram of the rarefaction wave elimination principle in the case of standing wave elimination;

[0037] Figure 6Schematic diagram of the principle of rarefaction wave elimination in the case of isobaric wave dissipation;

[0038] Figure 7 Schematic diagram of the jet contraction phenomenon at the orifice of a shock tube under ideal conditions;

[0039] Figure 8 Schematic diagram of the jet contraction phenomenon at the orifice of a shock tube under actual conditions;

[0040] Figure 9 Graph of the corresponding relationship between the incident shock wave intensity and the orifice area ratio. Specific implementation manner

[0041] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. Figures 2 to 4 The internal flow field of the shock tube is shown. When the post-wave air flow is subsonic and no rarefaction wave elimination measures are taken at the orifice, since the pressure of the post-wave air flow is higher than the ambient pressure, a reverse rarefaction wave will be generated after the shock wave passes through the orifice. The pressure in the tube in the area where the rarefaction wave passes drops from p2 to p', resulting in a significant short-term decrease in the pressure in the test section and a shortening of the positive pressure action time. For a shock wave with a specific pressure, by appropriately reducing the open area of the orifice, the influence of the rarefaction wave can be eliminated. After the rarefaction wave is eliminated, there is only one reverse compression wave formed by the reflection of the orifice wall in the test section, and the air flow pressure p3 behind the compression wave is equal to the pressure p2 of the undisturbed post-wave air flow. Reflected in the pressure history, this is manifested as only one pressure peak with an extremely short action time, minimizing the influence of the orifice outflow boundary on the internal flow field environment of the pipeline.

[0042] A design method for the orifice of a shock tube for rarefaction wave elimination, the flowchart of which is shown in Figure 1 , including the following steps:

[0043] Step 1: Set up the shock tube experimental environment and conduct experiments, and determine the variation relationship of the static pressure p2 of the incident shock wave at the orifice of the shock tube with time according to the experimental situation; this step is to determine the pressure history of the incident shock wave at the orifice according to the actual experimental situation, that is, the variation relationship of the static pressure of the shock wave with time; the acquisition methods include but are not limited to lengthening the driven section of the shock tube to carry out preliminary tests, conducting numerical simulations, directly using the equivalent replacement of the explosion shock wave history to be simulated, using the historical experimental data of shock tubes with similar structures for equivalent replacement, etc.

[0044] Step 2: Measure the ambient pressure p1 and ambient temperature T of the experimental environment, and calculate the ratio p of the static pressure p2 of the shock wave to the ambient pressure p1 when the post-wave air flow of the shock wave is sonic, and the ratio p of the static pressure p2 of the shock wave to the ambient pressure p1 when the outflow static pressure p of the shock wave is equal to p1, p cr1 , and when the outflow static pressure p of the shock wave j = p1, the ratio p of the static pressure p2 of the shock wave to the ambient pressure p1 cr2 , p cr2<p cr1 ; where p cr2 Determined by the ambient pressure p1 and the atmospheric specific heat ratio γ, when the ratio of static pressure to ambient pressure is p cr2 When the airflow behind the shock wave is accelerated to the local speed of sound, its outflow static pressure just drops to the ambient pressure;

[0045] Here we explain the critical pressure ratio p cr1 Since the shock tube mouth is connected to the external environment, the static pressure in the tube is consistent with the environmental pressure p1 when it is not disturbed by the shock wave. The Mach number of the airflow after the shock wave with a static pressure of p2 is given by the formula Given as follows, where γ is the specific heat ratio of the ambient atmosphere, which is usually taken as γ = 1.4. By setting the Mach number of the airflow to 1, the critical pressure ratio p that distinguishes supersonic flow from subsonic flow can be calculated. cr1 =p2 / p1(M2=1), when p2 / p1>p cr1 The airflow behind the wave is supersonic, and vice versa is subsonic.

[0046] Explain the critical pressure ratio p cr2 The calculation method of Figure 5 and Figure 6 As shown in Figure 1, the process of subsonic airflow passing through a shock tube with a reduced area is equivalent in principle to the process of subsonic airflow passing through a convergent nozzle. In this process, the airflow velocity increases, the static pressure decreases, and the total pressure remains unchanged. The total pressure can be calculated to give The outflow Mach number M is then given j Calculation method Assuming the outflow Mach number to be 1, the critical pressure p that distinguishes different rarefaction wave elimination methods can be obtained: cr2 =p2 / p1(M j =1,p j =p1). When p cr2 <p2 / p1≤p cr1 When the static pressure of the outlet flow drops to the ambient pressure, the outlet flow has already accelerated to the speed of sound. At this time, the outlet still generates rarefaction waves, but they cannot continue to propagate upstream of the pipeline, thus achieving standing wave elimination (see Figure 5 ). When p2 / p1≤p cr2 When the static pressure of the outlet flow drops to the ambient pressure, the outlet flow has not yet accelerated to the speed of sound. At this time, the pressure inside and outside the pipe is balanced and no rarefaction waves are generated, thus achieving isobaric wave elimination (see Figure 6 ).

[0047] Step 3: According to the ratio p obtained in step 2 cr1 and ratio p cr2 , the relationship between the static pressure p2 of the incident shock wave obtained in step 1 and its time is calculated according to p2 / p1≥P cr1 、p cr2 <p2 / p1≤pcr1 and p2 / p1 ≤ p cr2 It is divided into three intervals, and the shock wave processes within the three intervals may not be continuous in the time series;

[0048] Step 4: Calculate the discharge area ratio A of the shock tube nozzle within the three intervals in Step 3 e / A c , where A c is the cross-sectional area inside the shock tube, and A e is the cross-sectional area at the outlet of the shock tube;

[0049] When the shock wave pressure satisfies p2 / p1 ≥ P cr1 , the post-wave airflow is sonic or supersonic, and no reverse flow rarefaction wave will be generated after flowing out of the nozzle and contacting the external environment. At this time, the discharge area ratio of the shock tube nozzle can be kept at 100%. The above-mentioned nozzle discharge area ratio refers to the ratio of the actual open area of the shock tube nozzle to the cross-sectional area of the shock tube nozzle.

[0050] When the shock wave pressure satisfies p cr2 <p2 / p1 ≤ p cr1 , the post-wave airflow is subsonic, and it is applicable to the standing wave shock elimination method, that is, by adjusting the outlet flow area A j , so that the outlet Mach number M j is always 1, and combined with the calculation method of the post-wave airflow Mach number M2 described above, the corresponding relationship between the shock wave intensity p2 / p1 and the outlet area ratio A j / A c can be determined.

[0051] When the shock wave pressure satisfies p2 / p1 ≤ p cr2 , the post-wave airflow is subsonic, and it is applicable to the isobaric shock elimination method, that is, by adjusting the outlet flow area A j , so that the outlet pressure p j is always consistent with the external environment. At this time, p j = p1. Combined with the calculation methods of the post-wave airflow Mach number M2, the post-wave airflow total pressure P and the outlet Mach number M j , the corresponding relationship between the shock wave intensity p2 / p1 and the outlet area ratio A j / A c can be determined.

[0052] On the basis of determining the corresponding relationship between the shock wave intensity p2 / p1 and the nozzle outlet area ratio A j / A c in various situations, as shown in Figure 7 and Figure 8 , when the post-wave airflow flows out of the shock tube nozzle, a jet contraction phenomenon will occur, making the actual outlet area A j smaller than the nozzle discharge area Ae , namely A jj = CA ee (C ≤ 1), A ee / A cc = A jj / CA cc . The jet contraction ratio C is given by the following formula:

[0053]

[0054] In addition,

[0055] The following gives a general calculation formula:

[0056]

[0057] k2 = (γ - 1)M2 2 / (2 + (γ - 1)M2 2 ), k j = (γ - 1)M j 2 / (2 + (γ - 1)M j 2 )

[0058] m = 7k j + 1 / (1 + 12k j ), A = (2m - 1)(1 - C0),

[0059] B = 2(1 - m)(1 - C0);

[0060] where C is the jet contraction ratio, and m, k2, k j , C0, A, B are all intermediate variables;

[0061] Step 5. Map the shock tube nozzle discharge area ratio A e / A c obtained in Step 4 to the relationship between the static pressure p2 of the incident shock wave and time respectively, to obtain the relationship between the shock tube nozzle discharge area ratio and time. Design the shock tube nozzle according to the relationship between the shock tube nozzle discharge area ratio and time, and then the full - process real - time elimination of the rarefaction wave can be realized. Finally, the corresponding relationship between the shock wave intensity p2 / p1 and the discharge area ratio A e / A c is calculated and given, as shown in Figure 9 .

[0062] When designing the shock tube nozzle, the elimination of the rarefaction wave at the nozzle can be achieved by designing a small mechanical device assembled at the shock tube nozzle, which can greatly reduce the floor area and construction cost of the shock tube device.

Claims

1. A shock tube nozzle design method for rarefaction wave elimination, characterized in that, It includes the following steps: Step 1: Set up the shock tube experimental environment and conduct experiments, and determine the variation relationship of the static pressure p2 of the incident shock wave at the shock tube nozzle with time according to the experimental conditions; Step 2: Measure the environmental pressure p1 and environmental temperature T of the experimental environment. According to the environmental temperature T, calculate the ratio p of the shock wave static pressure p2 to the environmental pressure p1 when the post-shock wave airflow is sonic cr1 , and when the static pressure p j = p1 of the shock wave outflow, the ratio p of the shock wave static pressure p2 to the environmental pressure p1 cr2 , p cr2 < p cr1 ; Step 3: According to the ratio p cr1 and the ratio p cr2 , divide the relationship between the static pressure p2 of the incident shock wave obtained in Step 1 and time into three intervals according to p2 / p1≥P cr1 , p cr2 <p2 / p1≤p cr1 and p2 / p1≤p cr2 ; Step 4: Calculate the relief area ratios A e / A c at the shock tube nozzle in the three intervals in Step 3, where A c is the cross-sectional area inside the shock tube, and A e is the cross-sectional area at the shock tube outlet; Step 5: Map the shock tube nozzle discharge area ratio A e / A c in the three intervals obtained in Step 4 to the relationship between the static pressure p2 of the incident shock wave and time respectively, to obtain the relationship between the shock tube nozzle discharge area ratio and time. Design the shock tube nozzle according to the relationship between the shock tube nozzle discharge area ratio and time, and then the full-process real-time elimination of the rarefaction wave can be realized.

2. The shock tube nozzle design method for rarefaction wave elimination according to claim 1, wherein: Step 4 is specifically: Calculate the discharge area ratio A of the shock tube nozzle at the three intervals in step 3 respectively e / A c ; When p2 / p1 ≥ P cr1 then A e / A c = 100%; When p cr2 <p2 / p1≤p cr1 By adjusting the outlet area A of the shock tube nozzle j the outlet Mach number M j is always 1, and A j / A c is obtained. Then, using A j / A c calculate the discharge area ratio A e / A c ; When p2 / p1 ≤ p cr2 Adjust the outflow area A at the nozzle of the shock tube j such that the outflow pressure p j is always equal to the ambient pressure p1, and obtain A j / A c Then, use A j / A c to calculate the relief area ratio A e / A c .

3. The shock tube nozzle design method for rarefaction wave elimination according to claim 2, wherein: In step 2, the p cr1 is calculated using the following formula: where M2 is the Mach number of the airflow behind the shock wave, and γ is the specific heat ratio of the ambient atmosphere.

4. The shock tube nozzle design method for rarefaction wave elimination according to claim 3, wherein: In step 2, the p cr2 is calculated using the following formula: where P is the total pressure of the airflow behind the shock wave.

5. The shock tube nozzle design method for rarefaction wave elimination according to claim 4, wherein: In step 4, Utilize A j / A c Calculate A using the following formula e / A c : k2 = (γ - 1)M2 2 / (2 + (γ - 1)M2 2 ), k j = (γ - 1)M j 2 / (2 + (γ - 1)M j 2 ) C0 = π / [π + 2 + 2k j 2 / (1 - k j ) 2 + 5k j / (1 - k j )], m = 7k j + 1 / (1 + 12k j ), A = (2m - 1)(1 - C0), B = 2(1 - m)(1 - C0); Among them, C is the jet contraction ratio, and m, k2, k j , C0, A, and B are all intermediate variables.

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