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Optimization and verification of free flight separation similarity law in high-speed wind tunnel
CJA 1422 16 October 2019 Chinese Journal of Aeronautics, (2019), xxx(xx): xxx–xxx
No. of Pages 7
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Chinese Society of Aeronautics and Astronautics & Beihang University
Chinese Journal of Aeronautics [email protected] www.sciencedirect.com
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Optimization and verification of free flight separation similarity law in high-speed wind tunnel Fei XUE a,*, Xin JIN b, Peihua FENG c, Han QIN a, Zenghui JIANG a, Yuchao WANG a, Peng BAI a a
China Academy of Aerospace Aerodynamics, Beijing 100074, China AVIC Chengdu Aircraft Design & Research Institute, Chengdu 610091, China c Beijing Machinery and Electronics Engineering Institute, Beijing 100074, China b
Received 31 October 2018; revised 11 September 2019; accepted 12 September 2019
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KEYWORDS
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Carrier and missile interference; Ejection separation; Gravity separation; High-speed weapon delivery; Multi-body separation; Similarity law optimization
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Abstract Based on the similarity of separation time, a similarity law optimization method for high-speed weapon delivery test is derived. The typical separation state under wind load is simulated by the numerical method. The real separation data of aircraft, separation data of previous test methods, separation data of ideal wind tunnel test of previous methods, and simulation data of the proposed optimization method are obtained. A comparison of the data shows that the method proposed can improve the performance of tracking. Similarity law optimization starts with the development of motion equations and dynamic equations in the windless state to address the problems of mismatching between vertical and horizontal displacement, and to address the problems of separation trajectory distortion caused by insufficient gravity acceleration of the scaling model of existing light model. The ejection velocity of the model is taken as a factor/vector, and is adjusted reasonably to compensate the linear displacement insufficiency caused by the insufficient vertical acceleration of the light model method, so as to ensure the matching of the vertical and horizontal displacement of the projectile, and to improve the consistency between the test results of high-speed projection and the actual separation trajectory. The optimized similarity law is applicable to many existing free-throwing modes of high-speed wind tunnels. The optimized similarity law is not affected by the ejection velocity and hanging mode of the projectile. The optimized similarity law is suitable not only for the launching of the buried ammunition compartment and external stores, but also for the test design of projectile launching and gravity separation. 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
* Corresponding author. E-mail address: [email protected] (F. XUE). Peer review under responsibility of Editorial Committee of CJA.
Production and hosting by Elsevier
1. Introduction
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The wind tunnel test of free flight separation is mainly divided into two forms: separation from the internal weapons bay and separation from the airborne weapon hanger, and each of the
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https://doi.org/10.1016/j.cja.2019.09.027 1000-9361 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: XUE F et al. Optimization and verification of free flight separation similarity law in high-speed wind tunnel, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.027
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two forms can also be divided into ejection throwing separation and gravity throwing separation.1,2 The main purpose of wind tunnel free throwing is to check the influence of throwing factors on separation safety.3–5 The throwing factors include the Ma, flying height, mass characteristics, initial position of throwing objects, initial separation line velocity of throwing objects, and initial angular velocity of throwing objects.6–8 The wind tunnel test is to use high-speed photography to take pictures of the separation process, identify the separation trajectory, assess the safety boundaries of the influencing factors, and provide a reference for real aircraft and weapons delivery.9–12 In this regard, researchers have made a lot of explorations. In 1983, Stallings et al. used wind tunnel tests to study the effect of different sizes of embedded capsules on missile separation under the condition of Ma = 2.36.13 In 2004, Baker et al. carried out numerical simulation of the launch of F22’s inner and outer stores, and compared the simulation results with flight test data.14 In 2009, Purdon et al. carried out numerical simulation of F-35 buried weapon delivery, and conducted load test and flight test for different loads.15 In 2012, Flora built a test platform to simulate the embedded ballistic chamber, and carried out the free supersonic release test with zero initial release velocity of suspended objects under the condition of Ma = 2.94. The influence of the zigzag flow control device on the motion trajectory of wall shear layer and falling object was studied, and numerical simulation was performed to verify the experiment.16 Ryan and Rick validated the research of Captive Trajectory Simulation test (CTS) based on the flight test,17–20 and Sickles et al. carried out the research on CFD combined with flight test validation.21–24 Fr is a similar parameter to be simulated in free flight wind tunnel test. In the experiment on separation of external stores in the low wind speed wind tunnel, because the wind speed is low, according to the similarity of Fr number, it is easy to use the light model method to achieve the similarity between the test trajectory and the real release trajectory by adjusting the wind speed in the wind tunnel.25–29 However, in the high-speed wind tunnel test of the scale model, the flow is the compressible flow, and the Ma number is more important and needs to be simulated.30–32 In order to achieve the Fr number similarity, it is no longer easy to adjust the incoming wind speed. In this case, the Fr number can be simulated theoretically by increasing the gravitational acceleration of the projection model. However, the wind tunnel free flight test is an unsteady test method, and the most important feature of the test is that there is no support interference,22–24 so the wind tunnel free release acceleration of the scale model is the same as that of the real aircraft, with the same gravity acceleration (g = 9.8 m/s2). Therefore, it is impossible to satisfy the Fr number similarity for the high-speed wind tunnel test of the scale model under the premise of the same Ma. In this case, it is difficult to get the same trajectory as the real one in the free flight test of the scale model in the high-speed wind tunnel. In view of the above dilemma, previous studies have come up with two similarity laws for the high-speed wind tunnel test of the scale model: light model method and heavy model method. In terms of the free flight test of the scale model in the high-speed wind tunnel, the similarity laws of the two models have their own advantages and disadvantages. The light model method can ensure that the horizontal acceleration
F. XUE et al. meets the design requirements, but in the vertical direction, the requirements for acceleration similarity cannot be met, resulting in the vertical and horizontal displacement of the model, as well as inconsistency of angular displacement with the separation trajectory distortion, and thus low reliability of test results. Therefore, the original light model method is not suitable for the high-speed wind tunnel free flight test. To address the problem of proportional distortion between horizontal displacement and vertical displacement of the projectile in the light model method, the mass parameters of the high-speed wind tunnel free flight test model are considered by the heavy model method. In short, with the heavy model method, the mass of the wind tunnel model of the highspeed dropping object is increased to reduce the horizontal displacement of the model and ensure that the horizontal displacement is proportional to the vertical displacement, so as to match the vertical displacement with the horizontal displacement and the angular displacement of the model and thus improve the accuracy of test results. But in practice, it is found that the model designed by the heavy model method is often too heavy to match the desired mass value, even pure gold is difficult to match the desired mass value, and it is impossible to match the required centroid position and inertia characteristic value. Therefore, the heavy model method cannot be used in the high-speed wind tunnel free flight test. The model of heavy model method cannot be produced, and the trajectory of the separator of the light model method is distorted to result in the large test error. The two existing similarity laws are not suitable for the free flight test in the high-speed wind tunnel. Therefore, it is urgent to improve the similarity law of free floating in high-speed wind tunnels. To address the problem of the distorted trajectory caused by insufficient vertical acceleration in the light model method, this paper proposes motion equations and dynamic equations for the separated object in the windless state. The ejection velocity of the wind tunnel model is taken as a factor, and is adjusted reasonably. The optimized similarity law can make up for the shortcoming of the light model method by ensuring the correspondence between the vertical and the horizontal displacement, thus improving the precision of the high-speed test. The separation trajectory obtained with the optimized similarity law in the wind tunnel test in the windless state is consistent with the separation trajectory of real aircraft, and then the influence of the wind state on the separation trajectory is considered. A numerical example is given to analyze the separated data under wind load, and the validity of the optimal similarity law is verified. The optimized similarity law is applicable to many existing free-throwing modes of high-speed wind tunnels, which are not affected by ejection velocity and projectile hanging mode. The proposed law is not only suitable for the wind tunnel test of the submerged ammunition cabin and the external stores, but also for the wind tunnel test of ejection separation and gravity separation.
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2. Optimal similarity law
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State Explanation: Ss represents the data curve obtained by the real aircraft, and Sexp represents the data curve obtained by the ideal wind tunnel test of the previous methods. Ideal wind tunnel tests require a great increase in the acceleration of the sep-
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Please cite this article in press as: XUE F et al. Optimization and verification of free flight separation similarity law in high-speed wind tunnel, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.027
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aration. Therefore, Sexp is the data that the wind tunnel test aims to get but cannot get. Fr is a similar parameter to be simulated in free flight wind tunnel test. As shown in: Fr ¼
v2 gl
ð1Þ
From Eq. (1), we can see that ka = 1/(klkT). For the convenience of illustration, take kT 1, so ka 1/kl. Sfor represents the data curve obtained by the previous wind tunnel test. Because the ideal vertical acceleration cannot be obtained, the wind tunnel test data are obtained by using 1 g gravity acceleration. Sopt 1 represents the data curve obtained by the wind tunnel test with the improved method 1 (the time scale of the key point is equal), and Sopt 2 represents the data obtained from wind tunnel tests with the improved method 2 (least-squares). l0 is the reference length of the model. v0 is the initial separation speed of the real aircraft separation. v1 is the initial separation speed determined by the wind tunnel test based on energy similarity. v2 is the separation speed that ensure the time of improved method 1 reaches the reference length l0 is equal to that of Sexp. v3 is the separation speed to ensure improved method 2 reaches the reference length l0 position which the least square error of vertical displacement is the smallest. t0 is the time when the model reaches the l0 position. t0s is the time when the real separator reaches the real flight reference length l0s position. t0m is the time when the wind tunnel model reaches the wind tunnel reference length l0m position. Firstly, according to the real aircraft acceleration g = 9.8 m/s2, v0, wind tunnel flow field parameters and model parameters, the gravity acceleration a1 = ng is determined, n = 1/kl. And a1 is the vertical acceleration of Sexp curve to meet the similar Fr number wind tunnel test. Under the condition of no wind speed, we can know the trajectory of Sexp when we know v1 and a1. In the past, the wind tunnel test Sfor reached a1 = g, but failed to reach a1 = ng. In addition, there is often a safe separation distance to be considered in the test of release separation, which is usually twice the reference length l0 of the model. The vertical acceleration of Sopt 1 and Sopt 2 is g. The Sopt 1 and Sopt 2 curves can be obtained by knowing their initial velocities v2 and v3, respectively. Z t0s ySs ¼ ðgt þ v0 Þdt ð2Þ Z Z
t0m
ySfor ¼
1 gt þ v1 dt kl
ðgt þ v1 Þdt
Z ySopt 1 ¼
t0m
ðgt þ v3 Þdt
ð6Þ
0
Z ySopt 2 ¼
t0m
Coordinate system for similarity law verification.
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Fig. 2 Comparison of optimized methods with previous methods.
0
Fig. 1
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In this paper, considering the difference of wind load, the improved similarity law is simulated, and the data obtained
ð4Þ ð5Þ
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ð3Þ
ðgt þ v2 Þdt
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3. Verification of optimal similarity law
0
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0
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t0m
ySexp ¼
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Fig. 1 is the coordinate system used to verify the similarity law. According to the similarity theory, if the Ss curve is simulated in the wind tunnel test, the error of the test track is 0. Therefore, we should try to approach the Ss curve as far as possible to reduce the test error. The Sfor curve in Fig. 2 is the data obtained with the previous test method that does not take into account gravity acceleration compensation. It can be seen from the diagram that there is a great difference between Sexp curve and Sfor curve. Because the difference between them increases with time, the linear displacement and angular displacement do not match, so the test error can be imagined. As can be seen from Fig. 2, when the separation length is less than l0, the error between the Sopt 1 curve and the ideal Sexp curve increases first and then decreases. In the l0 separation length where the key is considered, the time error of the two critical points is 0. Therefore, the problem that the horizontal displacement does not correspond to the vertical displacement of the test line can be reduced, and thus the test error can be greatly reduced. In addition, as mentioned earlier, the error between the Sopt 1 curve and the ideal Sexp curve increases first and then decreases, but the error is always positive. Therefore, in order to further reduce the error, the second optimization design method is proposed, which uses the least square method to make the optimization curve Sopt 2 distribute on both sides of the Ss curve.
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3
Fig. 3
Model used in validation process.
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F. XUE et al. Table 1
Parameters of state and model.
No.
State
Scale
a
v (m/s)
1 2 3 4 5 6 7 8 9 10
Ss Sexp Sfor Sopt 1 Sopt 2 Ss Sexp Sfor Sopt 1 Sopt 2
1/1 1/15 1/15 1/15 1/15 1/1 1/15 1/15 1/15 1/15
g 15 g g g g g 15 g g g g
2.5000 2.8208 2.8208 4.4455 3.6429 0 0 0 3.8040 2.5081
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by various experimental methods are analyzed. The advantages of the improved similarity law are verified.
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3.1. Model used in validation process
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To increase the universality of the numerical simulation results, the numerical simulation is validated using the international general release standard wing-store, as shown in Fig. 3.
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3.2. State description
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Table 1 illustrates the state parameters, State 1 to State 5 is the ejection separation state, and State 6 to State 10 is the gravity separation state with the ejection velocity being 0 m/s. Ejection separation refers to that the separation speed of the separator relative to the carrier aircraft is greater than 0 m/s, and gravity separation refers to that the separation speed of the separator relative to the carrier aircraft is equal to 0 m/s. The coming wind speed Ma = 0.8, angle of attack a = 0, the real aircraft scale 1:1, and the remaining wind tunnel state model scale kl = 1:15. The mass parameters of the model are designed according to the light model method, and the external objects are separated from the actual flight simulation of 10 km altitude. The wind tunnel parameters are analyzed by FD-12 wind tunnel data. The real aircraft mass is 907.2 kg, and the inertia is Ix = 27.11 kgm2, Iy = 488.1 kgm2, and Iz = 488.1 kgm2. The mass of the wind tunnel test model is 595.9 g, and the inertia is Ix = 7.916 105 kgm2, Iy = 1.425 103 kgm2 and Iz = 1.425 103 kgm2. a indicates the vertical downward acceleration, v indicates the downward velocity of separation.
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4. Simulation results and data analysis
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4.1. Ejection separation
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As can be seen from Fig. 4, the Ss curve is very vertical, with less horizontal displacement, but the error of Sexp curve and Sfor curve is great, especially the Sfor curve, so the motion track is distorted and the test result is conservative. With the improved similarity law design method, Sopt 1 curve and Sopt 2 curve have much smaller error, and is closer to Ss curve. Especially, with the optimized method, the Sopt 1 curve with the equal time scale is more accurate. Table 2 is the trajectory error with the ejection separation method. When y/l0 = 1, the errors are equal to the difference
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Fig. 4
Ejection separation trajectory.
between the horizontal displacement value and the horizontal displacement value of the Ss curve, and the errors for 0.4 l0 are the same. Thus, the error in the true flight state Ss is 0. As can be seen from the table, when the vertical displacement reaches 0.4 l0, the error with the Sexp method is about 1.06%, and the error with the Sfor method is about 2.27%, which is the biggest error of all test methods. The error with the Sopt 1 method is about 0.15%, which is the least error of all test methods; the error with the Sopt 2 method is about 0.78%, and the error is relatively small. When the vertical displacement reaches l0, the error with the Sexp method is about 10.57%, and that with the Sfor method is about 19.13%, which is the biggest error of all test methods. The optimum method error with the Sopt 1 is about 6.68%, which is the least error with all test methods; the error of the optimized method with the Sopt 2 is about 8.90%, and the error is relatively small. It can be seen from Fig. 5 that when the angle reference value a0 = 26, the Sfor error is very large, the vertical displacement and angular displacement do not correspond, and the data distortion is obvious. The Sexp curve is much more realistic than the Sfor data, but has a certain error in comparison with the Ss curve of the real flight state. The Sopt 1 curve and Sopt 2 curve obtained with the improved similarity law design method have higher consistency with the Ss curve in 0.4 l0. The data analysis is shown in Table 3. It can be seen from the table that the error of Sfor data is very large, meaning that the data are seriously distorted.
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4.2. Gravity separation
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As can be seen from Fig. 6, the Ss curve of the real flight state is that the trajectory has also more vertical and less horizontal displacement. The Sexp trajectory curve has some errors. The error of the Sfor curve is very large, showing trajectory is completely distorted. At the initial separation position, the vertical displacement of the projectile appears a short negative value, indicating that the projectile has an upward displacement. According to the previous test methods, gravity separation is obviously an unsafe separation method, but it can be seen from the Ss curve trajectory that this state is actually safe, so that it can be seen that the original test method Sfor produced
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Optimization and verification of free flight separation similarity law Table 2
Trajectory error with ejection separation method.
Error
Ss
Sexp
Sfor
Sopt
0.4 l0 error (%) l0 error (%)
0 0
1.06 10.57
2.27 19.13
0.15 6.86
Sopt
1
Table 4
2
0.78 8.90
Fig. 5 Comparison between vertical displacement and angular displacement of ejection objects.
Table 3 Error
Ss
0.4 l0 error (%) l0 error (%)
Fig. 6
0 0
Sexp 16.10 15.98
Sfor 58.82 1
Sopt
1
9.80 9.79
Gravity separation trajectory curves.
Sopt
Trajectory error with gravity separation methods.
Error
Ss
Sexp
Sfor
Sopt
0.4 l0 error (%) l0 error (%)
0 0
8.15 27.90
24.00 1
1.65 0.70
Sopt
2
1.13 12.66
Gravitational separation angular displacement error.
Error
Ss
Sexp
Sfor
Sopt
0.4 l0 error (%) l0 error (%)
0 0
29.06 15.32
1 1
24.49 17.20
2
13.74 12.10
1
Fig. 7 Comparison between vertical displacement and angular displacement of gravity release.
Table 5
Ejection separation angular displacement error.
5
1
Sopt
2
14.29 29.42
the wrong test results. However, with the optimized similarity law design method, the error of the Sopt 1 curve and Sopt 2 curve is much smaller than that of the real flight state Ss curve. Especially when the vertical displacement appears before 0.4 l0, the Sopt 2 curve has higher accuracy. Table 4 is error of the separation trajectory with the gravity separation method. As can be seen from Table 4, when the vertical displacement reaches 0.4 l0, the Sexp curve error is about 8.15%, and the Sfor curve error is about 24.0%. The previous wind tunnel test is one of the methods with the biggest error of all test methods. The error of Sopt 1 curve is about 1.65%, and the error of Sopt 2 curve is relatively small. The error of Sopt 2 curve is about 1.13%, which is the least error of all test methods. When the vertical displacement reaches l0, the error of the Sexp curve is about 27.9%, and the error of Sfor curve is infinite. Because the vertical displacement with the previous test methods cannot reach l0 position, there is a misjudgment of safety. The Sfor curve obtained with the previous method has the most error of all test methods. The optimum error of Sopt 1 is about 0.70%, which is the least error of all test methods; the optimum error of Sopt 2 is about 12.66%.
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Fig. 8 Vertical displacement versus time curves of gravity separation.
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Fig. 7 is the contrast curves of gravity projection line displacement and angular displacement. It can be seen from the figure that the Sfor error is very large: the data is completely distorted, and there is even a wrong movement trend. The Sexp curve is much more real than the Sfor data. There are some errors between the Sopt 1 curve and the Sopt 2 curve and the Ss curve of the real flight state. The quantitative analysis is shown in Table 5. Fig. 8 is the time curves of vertical displacement of the gravity projectile. It can be seen that the scaled time when the vertical displacement reaches l0 by different test methods has a slight difference. However, the error of the Sfor curve is very large, and the vertical displacement of the projectile is even negative for a long time, showing an upward movement trend. This is obviously an unsafe launch state, and is completely contrary to the real flight state of the Ss curve trajectory.
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5. Conclusion
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This paper proposes an optimization method for the free flight separation similarity law for the high-speed wind tunnel test. Motion equations and dynamic equations are developed for the windless state to address the problem that the vertical displacement does not match the horizontal displacement. Reasonable adjustment of ejection velocity can make up for the shortage of vertical linear displacement in the light model method. The matching of vertical displacement and horizontal displacement of the projectile can be ensured, the consistency between the test results of high-speed projection and the actual separation trajectory is improved, and the test error is thus reduced to improve the reliability of the test data. The validity of the improved similarity law is verified by analyzing the separated data under wind load by numerical simulation. The improved similarity law can be applied to many existing high-speed wind tunnel tests, and is not affected by the ejection speed and the way of hanging projectiles. Therefore, the optimized law is not only suitable for the separation of the internal capsule and the external storage wind tunnel tests, but also for the ejection separation and gravity separation wind tunnel tests.
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F. XUE et al. Acknowledgement
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This work was supported by the Advanced Research Fund for Weapons and Equipment Development of China.
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Chinese Society of Aeronautics and Astronautics & Beihang University
Chinese Journal of Aeronautics [email protected] www.sciencedirect.com
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Optimization and verification of free flight separation similarity law in high-speed wind tunnel Fei XUE a,*, Xin JIN b, Peihua FENG c, Han QIN a, Zenghui JIANG a, Yuchao WANG a, Peng BAI a a
China Academy of Aerospace Aerodynamics, Beijing 100074, China AVIC Chengdu Aircraft Design & Research Institute, Chengdu 610091, China c Beijing Machinery and Electronics Engineering Institute, Beijing 100074, China b
Received 31 October 2018; revised 11 September 2019; accepted 12 September 2019
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KEYWORDS
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Carrier and missile interference; Ejection separation; Gravity separation; High-speed weapon delivery; Multi-body separation; Similarity law optimization
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Abstract Based on the similarity of separation time, a similarity law optimization method for high-speed weapon delivery test is derived. The typical separation state under wind load is simulated by the numerical method. The real separation data of aircraft, separation data of previous test methods, separation data of ideal wind tunnel test of previous methods, and simulation data of the proposed optimization method are obtained. A comparison of the data shows that the method proposed can improve the performance of tracking. Similarity law optimization starts with the development of motion equations and dynamic equations in the windless state to address the problems of mismatching between vertical and horizontal displacement, and to address the problems of separation trajectory distortion caused by insufficient gravity acceleration of the scaling model of existing light model. The ejection velocity of the model is taken as a factor/vector, and is adjusted reasonably to compensate the linear displacement insufficiency caused by the insufficient vertical acceleration of the light model method, so as to ensure the matching of the vertical and horizontal displacement of the projectile, and to improve the consistency between the test results of high-speed projection and the actual separation trajectory. The optimized similarity law is applicable to many existing free-throwing modes of high-speed wind tunnels. The optimized similarity law is not affected by the ejection velocity and hanging mode of the projectile. The optimized similarity law is suitable not only for the launching of the buried ammunition compartment and external stores, but also for the test design of projectile launching and gravity separation. 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
* Corresponding author. E-mail address: [email protected] (F. XUE). Peer review under responsibility of Editorial Committee of CJA.
Production and hosting by Elsevier
1. Introduction
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The wind tunnel test of free flight separation is mainly divided into two forms: separation from the internal weapons bay and separation from the airborne weapon hanger, and each of the
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https://doi.org/10.1016/j.cja.2019.09.027 1000-9361 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: XUE F et al. Optimization and verification of free flight separation similarity law in high-speed wind tunnel, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.027
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two forms can also be divided into ejection throwing separation and gravity throwing separation.1,2 The main purpose of wind tunnel free throwing is to check the influence of throwing factors on separation safety.3–5 The throwing factors include the Ma, flying height, mass characteristics, initial position of throwing objects, initial separation line velocity of throwing objects, and initial angular velocity of throwing objects.6–8 The wind tunnel test is to use high-speed photography to take pictures of the separation process, identify the separation trajectory, assess the safety boundaries of the influencing factors, and provide a reference for real aircraft and weapons delivery.9–12 In this regard, researchers have made a lot of explorations. In 1983, Stallings et al. used wind tunnel tests to study the effect of different sizes of embedded capsules on missile separation under the condition of Ma = 2.36.13 In 2004, Baker et al. carried out numerical simulation of the launch of F22’s inner and outer stores, and compared the simulation results with flight test data.14 In 2009, Purdon et al. carried out numerical simulation of F-35 buried weapon delivery, and conducted load test and flight test for different loads.15 In 2012, Flora built a test platform to simulate the embedded ballistic chamber, and carried out the free supersonic release test with zero initial release velocity of suspended objects under the condition of Ma = 2.94. The influence of the zigzag flow control device on the motion trajectory of wall shear layer and falling object was studied, and numerical simulation was performed to verify the experiment.16 Ryan and Rick validated the research of Captive Trajectory Simulation test (CTS) based on the flight test,17–20 and Sickles et al. carried out the research on CFD combined with flight test validation.21–24 Fr is a similar parameter to be simulated in free flight wind tunnel test. In the experiment on separation of external stores in the low wind speed wind tunnel, because the wind speed is low, according to the similarity of Fr number, it is easy to use the light model method to achieve the similarity between the test trajectory and the real release trajectory by adjusting the wind speed in the wind tunnel.25–29 However, in the high-speed wind tunnel test of the scale model, the flow is the compressible flow, and the Ma number is more important and needs to be simulated.30–32 In order to achieve the Fr number similarity, it is no longer easy to adjust the incoming wind speed. In this case, the Fr number can be simulated theoretically by increasing the gravitational acceleration of the projection model. However, the wind tunnel free flight test is an unsteady test method, and the most important feature of the test is that there is no support interference,22–24 so the wind tunnel free release acceleration of the scale model is the same as that of the real aircraft, with the same gravity acceleration (g = 9.8 m/s2). Therefore, it is impossible to satisfy the Fr number similarity for the high-speed wind tunnel test of the scale model under the premise of the same Ma. In this case, it is difficult to get the same trajectory as the real one in the free flight test of the scale model in the high-speed wind tunnel. In view of the above dilemma, previous studies have come up with two similarity laws for the high-speed wind tunnel test of the scale model: light model method and heavy model method. In terms of the free flight test of the scale model in the high-speed wind tunnel, the similarity laws of the two models have their own advantages and disadvantages. The light model method can ensure that the horizontal acceleration
F. XUE et al. meets the design requirements, but in the vertical direction, the requirements for acceleration similarity cannot be met, resulting in the vertical and horizontal displacement of the model, as well as inconsistency of angular displacement with the separation trajectory distortion, and thus low reliability of test results. Therefore, the original light model method is not suitable for the high-speed wind tunnel free flight test. To address the problem of proportional distortion between horizontal displacement and vertical displacement of the projectile in the light model method, the mass parameters of the high-speed wind tunnel free flight test model are considered by the heavy model method. In short, with the heavy model method, the mass of the wind tunnel model of the highspeed dropping object is increased to reduce the horizontal displacement of the model and ensure that the horizontal displacement is proportional to the vertical displacement, so as to match the vertical displacement with the horizontal displacement and the angular displacement of the model and thus improve the accuracy of test results. But in practice, it is found that the model designed by the heavy model method is often too heavy to match the desired mass value, even pure gold is difficult to match the desired mass value, and it is impossible to match the required centroid position and inertia characteristic value. Therefore, the heavy model method cannot be used in the high-speed wind tunnel free flight test. The model of heavy model method cannot be produced, and the trajectory of the separator of the light model method is distorted to result in the large test error. The two existing similarity laws are not suitable for the free flight test in the high-speed wind tunnel. Therefore, it is urgent to improve the similarity law of free floating in high-speed wind tunnels. To address the problem of the distorted trajectory caused by insufficient vertical acceleration in the light model method, this paper proposes motion equations and dynamic equations for the separated object in the windless state. The ejection velocity of the wind tunnel model is taken as a factor, and is adjusted reasonably. The optimized similarity law can make up for the shortcoming of the light model method by ensuring the correspondence between the vertical and the horizontal displacement, thus improving the precision of the high-speed test. The separation trajectory obtained with the optimized similarity law in the wind tunnel test in the windless state is consistent with the separation trajectory of real aircraft, and then the influence of the wind state on the separation trajectory is considered. A numerical example is given to analyze the separated data under wind load, and the validity of the optimal similarity law is verified. The optimized similarity law is applicable to many existing free-throwing modes of high-speed wind tunnels, which are not affected by ejection velocity and projectile hanging mode. The proposed law is not only suitable for the wind tunnel test of the submerged ammunition cabin and the external stores, but also for the wind tunnel test of ejection separation and gravity separation.
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2. Optimal similarity law
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State Explanation: Ss represents the data curve obtained by the real aircraft, and Sexp represents the data curve obtained by the ideal wind tunnel test of the previous methods. Ideal wind tunnel tests require a great increase in the acceleration of the sep-
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aration. Therefore, Sexp is the data that the wind tunnel test aims to get but cannot get. Fr is a similar parameter to be simulated in free flight wind tunnel test. As shown in: Fr ¼
v2 gl
ð1Þ
From Eq. (1), we can see that ka = 1/(klkT). For the convenience of illustration, take kT 1, so ka 1/kl. Sfor represents the data curve obtained by the previous wind tunnel test. Because the ideal vertical acceleration cannot be obtained, the wind tunnel test data are obtained by using 1 g gravity acceleration. Sopt 1 represents the data curve obtained by the wind tunnel test with the improved method 1 (the time scale of the key point is equal), and Sopt 2 represents the data obtained from wind tunnel tests with the improved method 2 (least-squares). l0 is the reference length of the model. v0 is the initial separation speed of the real aircraft separation. v1 is the initial separation speed determined by the wind tunnel test based on energy similarity. v2 is the separation speed that ensure the time of improved method 1 reaches the reference length l0 is equal to that of Sexp. v3 is the separation speed to ensure improved method 2 reaches the reference length l0 position which the least square error of vertical displacement is the smallest. t0 is the time when the model reaches the l0 position. t0s is the time when the real separator reaches the real flight reference length l0s position. t0m is the time when the wind tunnel model reaches the wind tunnel reference length l0m position. Firstly, according to the real aircraft acceleration g = 9.8 m/s2, v0, wind tunnel flow field parameters and model parameters, the gravity acceleration a1 = ng is determined, n = 1/kl. And a1 is the vertical acceleration of Sexp curve to meet the similar Fr number wind tunnel test. Under the condition of no wind speed, we can know the trajectory of Sexp when we know v1 and a1. In the past, the wind tunnel test Sfor reached a1 = g, but failed to reach a1 = ng. In addition, there is often a safe separation distance to be considered in the test of release separation, which is usually twice the reference length l0 of the model. The vertical acceleration of Sopt 1 and Sopt 2 is g. The Sopt 1 and Sopt 2 curves can be obtained by knowing their initial velocities v2 and v3, respectively. Z t0s ySs ¼ ðgt þ v0 Þdt ð2Þ Z Z
t0m
ySfor ¼
1 gt þ v1 dt kl
ðgt þ v1 Þdt
Z ySopt 1 ¼
t0m
ðgt þ v3 Þdt
ð6Þ
0
Z ySopt 2 ¼
t0m
Coordinate system for similarity law verification.
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Fig. 2 Comparison of optimized methods with previous methods.
0
Fig. 1
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In this paper, considering the difference of wind load, the improved similarity law is simulated, and the data obtained
ð4Þ ð5Þ
203
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ð3Þ
ðgt þ v2 Þdt
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3. Verification of optimal similarity law
0
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0
195 197
t0m
ySexp ¼
192 194
Fig. 1 is the coordinate system used to verify the similarity law. According to the similarity theory, if the Ss curve is simulated in the wind tunnel test, the error of the test track is 0. Therefore, we should try to approach the Ss curve as far as possible to reduce the test error. The Sfor curve in Fig. 2 is the data obtained with the previous test method that does not take into account gravity acceleration compensation. It can be seen from the diagram that there is a great difference between Sexp curve and Sfor curve. Because the difference between them increases with time, the linear displacement and angular displacement do not match, so the test error can be imagined. As can be seen from Fig. 2, when the separation length is less than l0, the error between the Sopt 1 curve and the ideal Sexp curve increases first and then decreases. In the l0 separation length where the key is considered, the time error of the two critical points is 0. Therefore, the problem that the horizontal displacement does not correspond to the vertical displacement of the test line can be reduced, and thus the test error can be greatly reduced. In addition, as mentioned earlier, the error between the Sopt 1 curve and the ideal Sexp curve increases first and then decreases, but the error is always positive. Therefore, in order to further reduce the error, the second optimization design method is proposed, which uses the least square method to make the optimization curve Sopt 2 distribute on both sides of the Ss curve.
0
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3
Fig. 3
Model used in validation process.
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F. XUE et al. Table 1
Parameters of state and model.
No.
State
Scale
a
v (m/s)
1 2 3 4 5 6 7 8 9 10
Ss Sexp Sfor Sopt 1 Sopt 2 Ss Sexp Sfor Sopt 1 Sopt 2
1/1 1/15 1/15 1/15 1/15 1/1 1/15 1/15 1/15 1/15
g 15 g g g g g 15 g g g g
2.5000 2.8208 2.8208 4.4455 3.6429 0 0 0 3.8040 2.5081
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by various experimental methods are analyzed. The advantages of the improved similarity law are verified.
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3.1. Model used in validation process
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To increase the universality of the numerical simulation results, the numerical simulation is validated using the international general release standard wing-store, as shown in Fig. 3.
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3.2. State description
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234
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Table 1 illustrates the state parameters, State 1 to State 5 is the ejection separation state, and State 6 to State 10 is the gravity separation state with the ejection velocity being 0 m/s. Ejection separation refers to that the separation speed of the separator relative to the carrier aircraft is greater than 0 m/s, and gravity separation refers to that the separation speed of the separator relative to the carrier aircraft is equal to 0 m/s. The coming wind speed Ma = 0.8, angle of attack a = 0, the real aircraft scale 1:1, and the remaining wind tunnel state model scale kl = 1:15. The mass parameters of the model are designed according to the light model method, and the external objects are separated from the actual flight simulation of 10 km altitude. The wind tunnel parameters are analyzed by FD-12 wind tunnel data. The real aircraft mass is 907.2 kg, and the inertia is Ix = 27.11 kgm2, Iy = 488.1 kgm2, and Iz = 488.1 kgm2. The mass of the wind tunnel test model is 595.9 g, and the inertia is Ix = 7.916 105 kgm2, Iy = 1.425 103 kgm2 and Iz = 1.425 103 kgm2. a indicates the vertical downward acceleration, v indicates the downward velocity of separation.
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4. Simulation results and data analysis
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4.1. Ejection separation
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As can be seen from Fig. 4, the Ss curve is very vertical, with less horizontal displacement, but the error of Sexp curve and Sfor curve is great, especially the Sfor curve, so the motion track is distorted and the test result is conservative. With the improved similarity law design method, Sopt 1 curve and Sopt 2 curve have much smaller error, and is closer to Ss curve. Especially, with the optimized method, the Sopt 1 curve with the equal time scale is more accurate. Table 2 is the trajectory error with the ejection separation method. When y/l0 = 1, the errors are equal to the difference
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Fig. 4
Ejection separation trajectory.
between the horizontal displacement value and the horizontal displacement value of the Ss curve, and the errors for 0.4 l0 are the same. Thus, the error in the true flight state Ss is 0. As can be seen from the table, when the vertical displacement reaches 0.4 l0, the error with the Sexp method is about 1.06%, and the error with the Sfor method is about 2.27%, which is the biggest error of all test methods. The error with the Sopt 1 method is about 0.15%, which is the least error of all test methods; the error with the Sopt 2 method is about 0.78%, and the error is relatively small. When the vertical displacement reaches l0, the error with the Sexp method is about 10.57%, and that with the Sfor method is about 19.13%, which is the biggest error of all test methods. The optimum method error with the Sopt 1 is about 6.68%, which is the least error with all test methods; the error of the optimized method with the Sopt 2 is about 8.90%, and the error is relatively small. It can be seen from Fig. 5 that when the angle reference value a0 = 26, the Sfor error is very large, the vertical displacement and angular displacement do not correspond, and the data distortion is obvious. The Sexp curve is much more realistic than the Sfor data, but has a certain error in comparison with the Ss curve of the real flight state. The Sopt 1 curve and Sopt 2 curve obtained with the improved similarity law design method have higher consistency with the Ss curve in 0.4 l0. The data analysis is shown in Table 3. It can be seen from the table that the error of Sfor data is very large, meaning that the data are seriously distorted.
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4.2. Gravity separation
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As can be seen from Fig. 6, the Ss curve of the real flight state is that the trajectory has also more vertical and less horizontal displacement. The Sexp trajectory curve has some errors. The error of the Sfor curve is very large, showing trajectory is completely distorted. At the initial separation position, the vertical displacement of the projectile appears a short negative value, indicating that the projectile has an upward displacement. According to the previous test methods, gravity separation is obviously an unsafe separation method, but it can be seen from the Ss curve trajectory that this state is actually safe, so that it can be seen that the original test method Sfor produced
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Optimization and verification of free flight separation similarity law Table 2
Trajectory error with ejection separation method.
Error
Ss
Sexp
Sfor
Sopt
0.4 l0 error (%) l0 error (%)
0 0
1.06 10.57
2.27 19.13
0.15 6.86
Sopt
1
Table 4
2
0.78 8.90
Fig. 5 Comparison between vertical displacement and angular displacement of ejection objects.
Table 3 Error
Ss
0.4 l0 error (%) l0 error (%)
Fig. 6
0 0
Sexp 16.10 15.98
Sfor 58.82 1
Sopt
1
9.80 9.79
Gravity separation trajectory curves.
Sopt
Trajectory error with gravity separation methods.
Error
Ss
Sexp
Sfor
Sopt
0.4 l0 error (%) l0 error (%)
0 0
8.15 27.90
24.00 1
1.65 0.70
Sopt
2
1.13 12.66
Gravitational separation angular displacement error.
Error
Ss
Sexp
Sfor
Sopt
0.4 l0 error (%) l0 error (%)
0 0
29.06 15.32
1 1
24.49 17.20
2
13.74 12.10
1
Fig. 7 Comparison between vertical displacement and angular displacement of gravity release.
Table 5
Ejection separation angular displacement error.
5
1
Sopt
2
14.29 29.42
the wrong test results. However, with the optimized similarity law design method, the error of the Sopt 1 curve and Sopt 2 curve is much smaller than that of the real flight state Ss curve. Especially when the vertical displacement appears before 0.4 l0, the Sopt 2 curve has higher accuracy. Table 4 is error of the separation trajectory with the gravity separation method. As can be seen from Table 4, when the vertical displacement reaches 0.4 l0, the Sexp curve error is about 8.15%, and the Sfor curve error is about 24.0%. The previous wind tunnel test is one of the methods with the biggest error of all test methods. The error of Sopt 1 curve is about 1.65%, and the error of Sopt 2 curve is relatively small. The error of Sopt 2 curve is about 1.13%, which is the least error of all test methods. When the vertical displacement reaches l0, the error of the Sexp curve is about 27.9%, and the error of Sfor curve is infinite. Because the vertical displacement with the previous test methods cannot reach l0 position, there is a misjudgment of safety. The Sfor curve obtained with the previous method has the most error of all test methods. The optimum error of Sopt 1 is about 0.70%, which is the least error of all test methods; the optimum error of Sopt 2 is about 12.66%.
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Fig. 8 Vertical displacement versus time curves of gravity separation.
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Fig. 7 is the contrast curves of gravity projection line displacement and angular displacement. It can be seen from the figure that the Sfor error is very large: the data is completely distorted, and there is even a wrong movement trend. The Sexp curve is much more real than the Sfor data. There are some errors between the Sopt 1 curve and the Sopt 2 curve and the Ss curve of the real flight state. The quantitative analysis is shown in Table 5. Fig. 8 is the time curves of vertical displacement of the gravity projectile. It can be seen that the scaled time when the vertical displacement reaches l0 by different test methods has a slight difference. However, the error of the Sfor curve is very large, and the vertical displacement of the projectile is even negative for a long time, showing an upward movement trend. This is obviously an unsafe launch state, and is completely contrary to the real flight state of the Ss curve trajectory.
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5. Conclusion
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This paper proposes an optimization method for the free flight separation similarity law for the high-speed wind tunnel test. Motion equations and dynamic equations are developed for the windless state to address the problem that the vertical displacement does not match the horizontal displacement. Reasonable adjustment of ejection velocity can make up for the shortage of vertical linear displacement in the light model method. The matching of vertical displacement and horizontal displacement of the projectile can be ensured, the consistency between the test results of high-speed projection and the actual separation trajectory is improved, and the test error is thus reduced to improve the reliability of the test data. The validity of the improved similarity law is verified by analyzing the separated data under wind load by numerical simulation. The improved similarity law can be applied to many existing high-speed wind tunnel tests, and is not affected by the ejection speed and the way of hanging projectiles. Therefore, the optimized law is not only suitable for the separation of the internal capsule and the external storage wind tunnel tests, but also for the ejection separation and gravity separation wind tunnel tests.
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F. XUE et al. Acknowledgement
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This work was supported by the Advanced Research Fund for Weapons and Equipment Development of China.
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Please cite this article in press as: XUE F et al. Optimization and verification of free flight separation similarity law in high-speed wind tunnel, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.027