Optimization and verification of free flight separation similarity law in high-speed wind tunnel

Fei XUE, Xin JIN, Peihu FENG, Hn QIN, Zenghui JIANG,Yuho WANG, Peng BAI

a China Academy of Aerospace Aerodynamics, Beijing 100074, China

b AVIC Chengdu Aircraft Design & Research Institute, Chengdu 610091, China

c Beijing Machinery and Electronics Engineering Institute, Beijing 100074, China

KEYWORDS Carrier and missile interference;Ejection separation;Gravity separation;High-speed weapon delivery;Multi-body separation;Similarity law optimization

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.

1. Introduction

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 two forms can also be divided into ejection throwing separation and gravity throwing separation.1,2The main purpose of wind tunnel free throwing is to check the influence of throwing factors on separation safety.3-5The 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.6-8The 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=2.36.13In 2004, Baker et al. carried out numerical simulation of the launch of F-22’s inner and outer stores, and compared the simulation results with flight test data.14In 2009, Purdon et al. carried out numerical simulation of F-35 buried weapon delivery,and conducted load test and flight test for different loads.15In 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.16Ryan and Rick validated the research of Captive Trajectory Simulation test(CTS)based on the flight test,17-20and Sickles et al.carried out the research on CFD combined with flight test validation.21-24Fr 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.25-29However, 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.30-32In 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,22-24so 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 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.

2. Optimal similarity law

State Explanation:Ssrepresents the data curve obtained by the real aircraft,and Sexprepresents 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 separation. Therefore, Sexpis 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:

From Eq.(1),we can see that ka=1/(klkT).For the convenience of illustration, take kT≈1, so ka≈1/kl. Sforrepresents 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. Sopt1represents the data curve obtained by the wind tunnel test with the improved method 1 (the time scale of the key point is equal), and Sopt2represents the data obtained from wind tunnel tests with the improved method 2(least-squares). l0is the reference length of the model. v0is the initial separation speed of the real aircraft separation. v1is the initial separation speed determined by the wind tunnel test based on energy similarity. v2is the separation speed that ensure the time of improved method 1 reaches the reference length l0is equal to that of Sexp. v3is the separation speed to ensure improved method 2 reaches the reference length l0position which the least square error of vertical displacement is the smallest. t0is the time when the model reaches the l0position.t0sis the time when the real separator reaches the real flight reference length l0sposition.t0mis the time when the wind tunnel model reaches the wind tunnel reference length l0mposition.

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 a1is the vertical acceleration of Sexpcurve to meet the similar Fr number wind tunnel test.Under the condition of no wind speed,we can know the trajectory of Sexpwhen we know v1and a1. In the past, the wind tunnel test Sforreached 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 l0of the model. The vertical acceleration of Sopt1and Sopt2is g. The Sopt1and Sopt2curves can be obtained by knowing their initial velocities v2and v3, respectively.

Fig. 1 Coordinate system for similarity law verification.

Fig. 2 Comparison of optimized methods with previous methods.

Fig. 1 is the coordinate system used to verify the similarity law. According to the similarity theory, if the Sscurve is simulated in the wind tunnel test, the error of the test track is 0.Therefore, we should try to approach the Sscurve as far as possible to reduce the test error. The Sforcurve 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 Sexpcurve and Sforcurve. 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 Sopt1curve and the ideal Sexpcurve increases first and then decreases. In the l0separation 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 Sopt1curve and the ideal Sexpcurve 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 Sopt2distribute on both sides of the Sscurve.

3. Verification of optimal similarity law

In this paper, considering the difference of wind load, the improved similarity law is simulated, and the data obtained by various experimental methods are analyzed. The advantages of the improved similarity law are verified.

3.1. Model used in validation process

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.

3.2. State description

Fig. 3 Model used in validation process.

Table 1 Parameters of state and model.

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 α=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 kg·m2, Iy=488.1 kg·m2, and Iz=488.1 kg·m2.The mass of the wind tunnel test model is 595.9 g,and the inertia is Ix=7.916×10-5kg·m2, Iy=1.425×10-3kg·m2and Iz=1.425×10-3kg·m2. a indicates the vertical downward acceleration, v indicates the downward velocity of separation.

4. Simulation results and data analysis

4.1. Ejection separation

As can be seen from Fig. 4, the Sscurve is very vertical, with less horizontal displacement, but the error of Sexpcurve and Sforcurve is great,especially the Sforcurve,so the motion track is distorted and the test result is conservative. With the improved similarity law design method, Sopt1curve and Sopt2 curve have much smaller error, and is closer to Sscurve.Especially, with the optimized method, the Sopt1curve with the equal time scale is more accurate.

Fig. 4 Ejection separation trajectory.

Table 2 Trajectory error with ejection separation method.

Table 2 is the trajectory error with the ejection separation method. When y/l0=1, the errors are equal to the difference between the horizontal displacement value and the horizontal displacement value of the Sscurve,and the errors for 0.4 l0are the same.Thus,the error in the true flight state Ssis 0.As can be seen from the table, when the vertical displacement reaches 0.4 l0, the error with the Sexpmethod is about 1.06%, and the error with the Sformethod is about 2.27%,which is the biggest error of all test methods. The error with the Sopt1method is about 0.15%, which is the least error of all test methods; the error with the Sopt2method is about 0.78%, and the error is relatively small. When the vertical displacement reaches l0,the error with the Sexpmethod is about 10.57%,and that with the Sformethod is about 19.13%, which is the biggest error of all test methods. The optimum method error with the Sopt1is about 6.68%,which is the least error with all test methods;the error of the optimized method with the Sopt2is about 8.90%,and the error is relatively small.

Fig. 5 Comparison between vertical displacement and angular displacement of ejection objects.

Table 3 Ejection separation angular displacement error.

It can be seen from Fig. 5 that when the angle reference value α0=26°, the Sforerror is very large, the vertical displacement and angular displacement do not correspond, and the data distortion is obvious. The Sexpcurve is much more realistic than the Sfordata, but has a certain error in comparison with the Ss curve of the real flight state. The Sopt1curve and Sopt2curve 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 Sfordata is very large,meaning that the data are seriously distorted.

4.2. Gravity separation

As can be seen from Fig.6,the Sscurve of the real flight state is that the trajectory has also more vertical and less horizontal displacement. The Sexptrajectory curve has some errors. The error of the Sforcurve 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 Sscurve trajectory that this state is actually safe, so that it can be seen that the original test method Sforproduced the wrong test results. However, with the optimized similarity law design method, the error of the Sopt1curve and Sopt2curve is much smaller than that of the real flight state Sscurve.Especially when the vertical displacement appears before 0.4 l0,the Sopt2curve has higher accuracy.

Fig. 6 Gravity separation trajectory curves.

Table 4 Trajectory error with gravity separation methods.

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 Sexpcurve error is about 8.15%, and the Sforcurve 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 Sopt1curve is about -1.65%,and the error of Sopt2curve is relatively small. The error of Sopt2curve is about 1.13%, which is the least error of all test methods. When the vertical displacement reaches l0, the error of the Sexpcurve is about 27.9%, and the error of Sforcurve is infinite. Because the vertical displacement with the previous test methods cannot reach l0position, there is a misjudgment of safety. The Sforcurve obtained with the previous method has the most error of all test methods. The optimum error of Sopt1is about 0.70%, which is the least error of all test methods; the optimum error of Sopt2is about 12.66%.

Fig. 7 is the contrast curves of gravity projection line displacement and angular displacement. It can be seen from the figure that the Sforerror is very large: the data is completely distorted,and there is even a wrong movement trend.The Sexpcurve is much more real than the Sfordata. There are some errors between the Sopt1curve and the Sopt2curve 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 l0by different test methods has a slight difference. However, the error of the Sforcurve 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 Sscurve trajectory.

Fig. 7 Comparison between vertical displacement and angular displacement of gravity release.

Table 5 Gravitational separation angular displacement error.

Fig. 8 Vertical displacement versus time curves of gravity separation.

5. Conclusions

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.

Acknowledgement

This work was supported by the Advanced Research Fund for Weapons and Equipment Development of China.