Hesong HUANG,Zhongxiang TONG,Shijie CHAI,Yu ZHANG

College of Aeronautics Engineering,Air Force Engineering University,Xi’an 710038,China

KEYWORDS Aerodynamic coefficients;Chaff;Computational fluid dynamics;Infrared decoy;Wind tunnel test

Abstract To solve the kinetic and diffusion problem of surface-type infrared decoy,multi-chaff kinetic models are established and chaff cloud holistic kinetic performance are analyzed under the impact of high speed air flow in this work.Chaffs rotate rapidly during the motion under the impact of high speed air flow.The rotation speed is correlated with lift,position of pressure center and aerodynamic damping.Computational Fluid Dynamics(CFD)is used to compute the aerodynamic coefficients of chaff.It is found that there exists serious aerodynamic interference which mainly relates to the overlapping area and distance among chaffs during the diffusion of chaff cloud.The chaff wind tunnel test and rocket sled experiment are carried out to verify the credibility of the models in this work.Then,the variation of chaff cloud expectation and extremum are analyzed to achieve the holistic kinetic and diffusing performance of chaff cloud.Simulation results demonstrate that the chaffs diffuse rapidly under the impact of high speed air flow and chaff cloud can be formed rapidly within 0.5 s.The shape of the chaff cloud is similar to cone that forms a certain angle with the horizontal plane and most chaffs focus on the second half.

1.Introduction

Surface-type infrared decoy is compressed by thousands of chaffs in the launch canister,and physical adhesion does not exist between chaffs.1–3Due to the impact of high speed air flow and aerodynamic interference among chaffs,the chaffs diffuse rapidly and finally coalesce into clouds to shield the aircraft.4–6The kinetic models of chaffs are complicated.

Much effort has been made to establish multi-chaff kinetic models and analyze chaff cloud holistic kinetic performance.Li and Wang7analyzed the holistic performance of the chaff cloud by making full use of the weighted technique of stochastic dynamics and statistical distribution theory.A new method is presented,which can simulate the holistic kinetic performance of the chaff cloud including space position,attitude and velocity.Denison and Hookham8established the model of dust entrainment under the impact of high-speed air flow,which divided the dusty boundary layer into two regions.As a validation of the model,the code is used to simulate a windtunnel dust lofting experiment.The result shows that the model reaches a good agreement with experiment.Wang et al.9established chaff kinetic models and a database including 220 kinds of aerodynamic conditions,which are based on the flow field numerical simulation of multi-body separation process.After simulating the diffusing process of thousands of chaffs,they achieved the holistic kinetic performance of chaff cloud.Zou et al.10divided the chaffs motion into light off phase and complete combustion phase and established two phases of surface-type infrared decoy models by calculating one chaff and two parallel chaffs aerodynamic coefficients.But the established models are not completed.Owing to the rotation speed of chaff is constant and the aerodynamic interference coefficients are unsolved for the light off phase,there exists a certain gap between the simulation and experiment results.In fact,there is serious interference among chaffs within the chaff cloud and the interference coefficients and rotation speed of chaffs can directly impact on the accuracy of simulation results.

Establishing the chaff cloud models as a whole to study its motion and diffusion regularity is the main research method at present. One method is approximate the chaff cloud to a fixed geometry,such as sphere or spheroid.They think that the space density of chaffs obey a certain statistical distribution.11,12In fact,the shape of chaff cloud is not regular and the models need large measured data to support the credibility. Now the test data are little at high speed,what makes the accuracy of the models isn’t high.The other method is establishing stochastic probability models of chaff cloud based on its diffusion regularity.The models can reflect the motion regularity of chaff cloud in certain conditions,but they cannot reflect the motion regularity of single chaff and their limitations are also obvious.

At present,the research of chaff cloud models based on the single chaff is quite rare.The aerodynamic interference among chaffs is studied in this work and aerodynamic interference models are applied to the single chaff models.Then thousands of chaffs motion models are solved simultaneously,so the chaff cloud diffusion regularity is obtained.The models take the aerodynamic interference among chaffs into consideration,which can reflect the real chaff motion process.Thus the chaff cloud obtained via simulation is quite accurate.Furthermore,the chaff wind tunnel test and rocket sled experiment are carried out to verify the credibility of the models.Moreover,the variation of chaff cloud shape and chaff cloud holistic kinetic performance are analyzed.

2.Chaff kinetic models

2.1.Chaff kinetic equations

Chaff diffusing and kinematical equations are calculated in ground coordinate system and the kinetic equations are calculated in flight-path coordinate system.The relationship among flight-path coordinate system Oxhyhzh,ground coordinate system Oxgygzgand velocity coordinate system Oxayazaat initial time is illustrated in Fig.1.13

In Fig.1,ndis chaff axis,which is perpendicular to chaff plane,V is chaff velocity.Ground coordinate system fixed on the ground is inertial coordinate system,whose original are in the symmetry flow plane.The chaff kinetic equations in flight-path coordinate system are given by14point O is the projection of the coordinate on horizontal plane when chaffs are deployed.Oygaxis is vertical upward.Oxgand Ozgaxis are in the horizontal plane and constitute righthanded coordinate system with Oygaxis.Flight-path coordinate system is established whose original point O is the center of the chaff at time of deployment.Oxhaxis is the direction of chaff velocity and forward is positive.Oyhaxis is in the vertical plane which crosses Oxhaxis and is perpendicular to Oxhaxis.Upward is positive.Ozhaxis constitutes right-handed coordinate system with Oxhand Oyhaxis.Velocity coordinate system and flight-path coordinate system share the same original point O.Oxaaxis overlaps with Oxhaxis.Oyaaxis is in the plane which is composed by Oxaaxis and chaff axis and is perpendicular to Oxaaxis.Upward is positive.Ozaaxis constitutes right-handed coordinate system with Oxaand Oyaaxis.Owing to the symmetry of circular chaff,there is not any force in Ozaaxis.It can be observed in Fig.1 that the original point O of the three coordinate systems is in mutual coincidence at initial time.

Flight-path pitch angle θ is the angle between Oxhaxis and horizontal plane and flight direction upward is positive.Heading angle ψsis the angle between the projection of Oxhaxis on horizontal plane and Oxgygplane and left is positive.The angle between Oyaaxis and Oyhaxis is velocity roll angle γs,which is positive when velocity coordinate system leans to the right around Oxhaxis.

Chaff motion is unpowered movement and the diffusion process is only decided by aerodynamic force and gravity.The plane which is composed by chaff axis and velocity direction is air flow symmetry plane.10Then,both drag X and lift Y

where cxand cyare aerodynamic coefficients,ρ is atmospheric density,m is the mass of chaff,S is the area of chaff,g is the acceleration of gravity,t is the time.Because of the symmetry of circular chaff,the drag and lift coefficients are related to angle of attack(α)and velocity,which satisfy the following equations:

where c′xand c′yare drag and lift coefficients of chaff without aerodynamic interference,while a′xand a′yare aerodynamic interference impact factors,which can be obtained from Section 3.

Chaff kinematical equations are given by15,16

The velocity direction is described by the following equations:

where nVis the unit vector of velocity direction in ground coordinate system,while nVx,nVyand nVzare its three-axes components.ndx,ndyand ndzare the three-axes components of ndin ground coordinate system,which satisfy the following equations:

where ? and ψ are pitch angle and yaw angle.

Therefore,the unit vector of lift nYin ground coordinate system is described by the following equations:

Therefore,α and the velocity roll angle γsare given by

where nYx,nYyand nYzare the three-axes components of nY.

2.2.Chaff rotation equations

The position of chaff pressure center does not coincide with the center of chaff in the movement,therefore,there exists some moment.Chaffs rotate rapidly under the impact of the moment,which make α and the vector of chaff axis change continuously.So does the aerodynamic force of chaff.

2.2.1.Chaff rotation models

The moment of chaff is mainly generated by lift during rotation,which is described in velocity coordinate system by the following equations:17

where Yais lift of chaff in velocity coordinate system,while R is chaff radius,J is moment of inertia,ω is rotation speed,Mdis aerodynamic damping moment,xFis the distance between pressure center and chaff center.

The transfer matrix from ground coordinate system to velocity coordinate system is described by the following equation:

where Lagis the transfer matrix,while nYais the description of nYin velocity coordinate system,which satisfies the following equation:

Therefore,Yais given by

where nYayis the value of nYain Oyaaxis.

2.2.2.Impact of aerodynamic damping on rotation speed

There will generate aerodynamic damping moment Md,which can resist the rotation of chaff during the process of high speed rotation.Chaff motion is decomposed into centroid displacement and rotation.Centroid displacement can be solved via chaff kinetic equations.Chaff is affected by moment M(M is the moment generated by lift)and aerodynamic damping moment Mdin the process of rotation,which is shown in Fig.2.

Moment analysis of the chaff is shown in Fig.3,dS is chaff surface source whose distance to chaff center is r.The drag dFdwhich is generated by dS in the process of rotation is described by the following equation:

Symmetry flow plane is vertical to chaff rotation speed and also overlaps with Oxayaplane in velocity coordinate system.Chaff axis is described in velocity coordinate system after Δt by the following equation:

where ndais the description of ndin velocity coordinate system.Hence,ndis described after Δt by the following equation:

3.Aerodynamic interference among chaffs

There exists serious aerodynamic interference among chaffs during the movement,which has great impact on the aerodynamic coefficients of section.In this chapter,the flow field of single chaff without aerodynamic interference and aerodynamic interference among chaffs are calculated via CFD.Then,the description of aerodynamic interference impact factors a′xand a′

yare achieved.

3.1.Chaff aerodynamic coefficients without aerodynamic interference

In this section,the chaff aerodynamic coefficients without aerodynamic interference are computed.Aerodynamic coefficients are computed via different turbulence models though CFD.Star-ccm+is used to compute the flow field of the chaff.Then comparing the results with the wind tunnel test to choose the most precise models,the aerodynamic coefficientsare obtained at different velocities and different angles of attack.Furthermore,the chaff aerodynamic coefficients databases are acquired.

3.1.1.Chaff wind tunnel test

Chaff aerodynamic coefficients are tested in low velocity wind tunnel of National Defense Key Laboratory.The length of wind tunnel is 2 m,whose cross section is rectangle.The inlet size is 1.2 m×1.2 m and outlet size is the same.The flow field quality of wind tunnel is quite well,and the turbulence intensity ε≤ 1%.The maximal usable Mach number Mamax=0.6 and the test Mach number Ma=0.6,the chord Reynolds number Re=6.8×105.The static pressure of inlet is 98.56 kPa,total pressure is 124.37 kPa and static temperature is 78.1°C.The chaff is mounted on six-degree-of-freedom strain-gauge internal balance,whose punctuality is 0.4%-0.5%and accuracy is 0.1%-0.2%.Baseline 0-Baseline 3 are the four times test results,which are shown in Fig.4.

The aerodynamic coefficient curves are quite smooth and obvious and the abnormal points cannot be found in Fig.4.Hence,the results tested via the strain-gauge internal balance are quite accurate.The four test results show that chaff aerodynamic coefficient curves overlap each other,which indicates that the stability of the force measuring system is quite well.Chaff aerodynamic coefficient curves show that the stalled angle of chaff is 25°and its maximal lift coefficient is 0.8649.

3.1.2.Comparison of wind tunnel test and numerical results

Navier-Stokes equations are used as control equations and the Pressure-Implicit with splitting of operators semi-implicit Method for Pressure-Linked Equations(PIM-PLE)algorithms are applied to solve Navier-Stokes equations in numerical results.Spatial discretization is based on finite volume method and second-order accuracy linear interpolation scheme.Time discretization is accomplished through second-order accuracy backward-difference scheme.The inlet and outlet of the computational domain are set as pressure far field.Pressure p=101325 Pa,temperature T=288.15 K and the incoming flow Mach number Ma=0.6.The surface of chaff is set as wall based on the no-slip wall boundary condition.Reynolds Stress turbulence Model(RSM),Shear Stress Transport(SST)turbulence model18and K-ε turbulence model19,20are applied as computational model,respectively.21Then their results are compared.

The diameter of the chaff is 50 mm,and computational region is the cube whose side length is 5000 mm.Chaff center coincides with the center of computational domain.The thickness of the first boundary layer is 10-6m and the amount of boundary layers is twelve.Polyhedral mesh is adopted for the calculation and the total number of meshes is 2.13 million,which are illustrated in Fig.5.The initial altitude is 0 km.The comparison results of wind tunnel test and numerical with different turbulence models are shown in Fig.6.

As illustrated in Fig.6,the results computed via SST turbulence model exhibit a satisfactory agreement with the tests.22The maximal error is 6.9%computed via SST turbulence model,which is quite ideal.Table 1 is the results comparison of wind tunnel test and SST turbulence model.SST turbulence model is chosen to compute the aerodynamic coefficients of chaff at different α and velocities herein.22Then chaff aerodynamic coefficients library at non-aerodynamic interference is established via SST turbulence model,whose Mach number varies from 0.1 to 1.2 and α varies from 0°to 90°.Soandcan be achieved at different α and different velocities.

3.1.3.Grid independence behavior

The flow field of chaff at α =25°is computed via SST turbulence model and the grid quantity varies from 513 thousand to 3.24 million.Fig.7 is the variation of aerodynamic coefficients with grid quantity.The drag and lift coefficients decrease continuously with the increase of the grid quantity,but the decrease rate reduces gradually.The lift coefficient reduces from 1.03653 to 0.799567 and the drag coefficient from 0.59567 to 0.405953.The numerical curves become horizontal gradually at 2.13 million grids.Consequently,numerical results are independent with grid when the grid quantity is more than 2.13 million.

3.2.Impact of aerodynamic interference on aerodynamic coefficients of chaff

In the initial phase of chaffs diffusion,overlapping among chaffs is serious.Chaffs are fairly close to each other;therefore,the aerodynamic interference shouldn’t be ignored.It can be known from the comparison of wind tunnel test and numerical results in Section 3.1 that SST turbulence model is more suited to compute chaff flow field.SST turbulence model is chosen to compute multi-chaff flow field.Then,the impact factors of aerodynamic interference based on the numerical results are analyzed.Furthermore,the approximate description of aerodynamic interference impact factorsandare achieved.

Table 1 Comparison of results of wind tunnel test and SST turbulence model.

First of all,the impact of α on the aerodynamic interference among chaffs is computed.Chaffs 1,2 and 3 are the bottom,middle and top chaff,respectively,which are parallel with the same speed.The center line of the chaffs is parallel to Oygaxis and the distance between the center of chaffs is 0.5R.The α ranges from 0°to 90°with an increment of 10°.cx1,cy1,cx2,cy2,cx3and cy3are the aerodynamic coefficients of chaff 1,chaff 2 and chaff 3,respectively,which are illustrated in Table 2.

Aerodynamic coefficients of the bottom chaff are slightly larger than those without aerodynamic interference,while the impact of aerodynamic interference on the middle and top chaffs are fairly strong,and are directly proportional to the α which can be achieved via Table 2.Owing to the impact of middle chaff,boundary layer separation point of the bottom chaff is delayed.As the result,the aerodynamic coefficients of bottom chaff become larger than any single chaff.However,as for the middle and top chaffs,the negative pressure region of chaff in the frontage of in flow direction increases obviously,which makes the pressure difference decreases significantly.Consequently,the aerodynamic coefficients of Chaff 2 and Chaff 3 reduce rapidly comparing with Chaff 1 and such impact increases with the increase of α.

Then,the impact of distance between chaffs on aerodynamic interference is computed.The center line of chaffs is the same as in flow direction and distances between chaffs are 0.5R and R,respectively.Chaffs pressure distribution is illustrated in Fig.8 at α =30°.

It can be achieved from Fig.8 that the negative pressure region of the front of the middle and top chaffs expand with the distance decreasing.Consequently,the aerodynamic coefficients decrease with distance decreasing.

It is concluded from numerical results that the aerodynamic interference effect of the chaffs is inversely proportional to the distance and directly proportional to the overlapping area.Aerodynamic interference impact factorsshould satisfy the following equation:

where s is the overlapping area,alis the distance impact factor,f is proportionality coefficient.

3.2.1.Impact of overlapping area on aerodynamic interference

The chaff plane is projected based on its kinetic direction,thus a cylindroid region in space is formed(the region of dotted line in Fig.9).Only the other chaffs in this region,the aerodynamic characteristics of the chaff will be affected.

It can be illustrated in Fig.9 that the center coordinate of chaff j in ground coordinate system is(xj,yj,zj),whose velocity unit vector is nVjand nVjx,nVjy,nVjzare its three-axes components.Chaff axis unit vector is ndj.The chaff k is in the projection region of chaff j,whose center coordinate in ground coordinate system is(xk,yk,zk)and velocity unit vector is nVk.Chaff axis unit vector is ndk.

The overlapping length of chaff k in the projection region of chaff j is l.If l＞0 overlapping exists,otherwise,there is no overlapping.l′is the projection of l on the plane of chaff j.Assume that(x0,y0,z0)is the intersection point of the chaff j projection region center line and the plane crosses the center of chaff k and vertical to nVjis given by

Table 2 Variation of chaff aerodynamic coefficients with α.

where d is the intermediate variable.

Chaff j and chaff k are projected to the plane crossing the center of chaff k and vertical to nVjbased on the kinetic direction nVjand ellipse j and ellipse k are formed,which satisfies the following equations:is described by the following equation

where n is the unit vector from(x0,y0,z0)to(xk,yk,zk).Rjand Rkare radiuses of ellipse j and ellipse k in the direction of n,while φjis the angle between Rjand the major axis of the ellipse j,φkis the angle between Rkand the major axis of the ellipse k.

l′is described by the following equation:

The angle coefficient λ can be achieved by the following equations:

where tx,ty,tzand ndkx,ndky,ndkzare three-axes components of t and ndkin ground coordinate system.

3.2.2.Impact of chaff interval on aerodynamic interference

The top and bottom chaffs are parallel and the angle between the center line of the chaffs and horizontal plane is 30°.The top chaff is behind the bottom chaff.The velocity of both are the same with α =30°,which is illustrated in Fig.10.The bottom chaff is completely in the projection region of the top,hence,s= πR2/2.Therefore,is described,in light of Eq.(17),by the following equation:

Assume that e is the distance between the center of the two chaffs,which ranges from 0.1R to 10R and the flow fields are computed.The numerical results are shown in Fig.11.

It can be obtained from the computed results thatis close toTherefore,it is considered thatin this work,which means f=1.Then,the distance impact factor alis achieved by the curves in Fig.12,which satisfies the following equation:

4.Experiment and simulation analysis

4.1.Comparison of experiment and simulation results

4.1.1.Experiment results

Two SC7700MW infrared thermal imagers are used to test the holistic kinetic performance of chaff cloud.The work waveband of SC7700MW is 3–5 μm and the field of view is 11°× 8.8°.One thousand chaffs are compressed into the launch canister which is upward fixed in rocket sled and the initial deploying speed of the chaffs is 25 m/s.Pyrophoric activated metal magnesium is covered on the surface of chaff.There is no adhesion between chaffs.The chaff diffuses at once under the impact of aerodynamic force after launching and begins pyrophoricity in the air.The impact of reaction heat generated by activated metal combustion on the diffusion process of chaff can be ignored,so the chaff cloud diffusion process can be obtained via the gray level image in infrared thermal imager.Rocket sled is moving in horizontal track and the length of the track is 3 km.Infrared thermal imager is on the right side of the track,the distance of which is 300 m from track.The angles between the center lines of field of view of two infrared thermal imagers and sidewise of track are 53.1°and 33.7°,respectively.The rocket sled is moving on the left of the track.When it is moving to the center line of field of view of the first infrared thermal imager,one canister is launched.Rocket sled is 1100 m from the starting point,and the Mach number of which is 0.8.When it is moving to the center line of field of view of the second infrared thermal imager,two canisters are launched and the launch interval is 0.1 s.Rocket sled is 1300 m from the starting point,the Mach number of which is 0.7.The experiment schematic is shown in Fig.13.

The gray level images are shown as Figs.14 and 15.It’s found from the experiment results that the chaffs diffuse rapidly under the impact of high speed air flow,as the result of which the chaffs diffusing shape formed within 1 s.The diffusing shape is similar to cone which forms a certain angle with the horizontal plane.Most chaffs focus on the second half.

4.1.2.Simulation results

The aircraft flies horizontally on the sea level and the flight Mach number Ma=0.8.One thousand chaffs are compressed into the deploying tube and the initial deploying speed of the chaffs is 25 m/s upward.The chaffs diffuse rapidly after deployment.

Owing to the impact of the random factors,such as atmospheric disturbance,there exist gaps in the initial attitudes of one thousand chaffs.Initial pitch angle ?0is uniformly distributed on ［ 0，π/2］and initial yaw angle ψ0is uniformly distributed on[0,2π]by comparing with the test data,then the initial chaff axis vector is obtained by Eq.(5).As the initial velocity of chaff is known,the initial trajectory pitch angle θ and heading angle ψsare obtained by Eq.(4).

The specific chaff cloud simulation process is shown as follows:

(1)Assume that the axis vector nd,trajectory pitch angle θ,heading angle ψs,velocity and coordinate of one thousand chaffs are known at time t.

(2)The solution process of chaff i is shown as follows at time t+Δt:the aerodynamic interference coefficients a′xand a′ycan be obtained by Eq.(17),hence aerodynamic coefficients are known by Eq.(2).Then the coordinate,pitch angle θ and heading angle ψsof chaff i are obtained by Eqs.(1)and(3)at time t+Δt.Furthermore,the axis vector of chaff i is acquired by Eqs.(9)and(15)at time t+Δt.

(3)The solution process of chaff i+1 at time t+Δt is the same as chaff i.Then all the parameters of one thousand chaffs are known at time t+Δt,and the chaff cloud diffusion regularity is obtained.

MATLAB is used to compute the holistic kinetic performance of chaff cloud.The simulated results are shown as Fig.16.

Chaff cloud approximately forms conical distribution at 0.2 s,whose Oxgand Ozgaxis length is about 20 m and 2 m,respectively.At 0.5 s,the Oxgaxis length of chaff cloud is about 21.9 m and Ozgaxis length is about 2.8 m.Chaff cloud forms rapidly within 0.5 s after it starts sinking.In the period of sinking,the Oxgaxis length of chaff cloud is essentially constant and that of Ozgaxis diffuses continuously to 3.7 m until 1.4 s.

4.1.3.Results comparison and error analysis

In this chapter,the chaff cloud length,quantity distribution and variance are compared with the experimental results respectively to verify the credibility of the simulation.Chaff cloud length,quantity distribution and variance can reflect diffusion performance,shape characteristics and degree of dispersion.Consequently,the credibility of the models is verified by comparing the three parameters with experiment.

(1)The comparison of chaff cloud length

The average of the three groups of chaffs experiment data are compared with the simulation results at different time.The comparison results are shown in Table 3.

The final length of the chaff cloud in the direction of Oxgand Oygaxis is about 25.9 m and 5.9 m,whose simulation error is about 13.5%and 14.4%respectively.

Table 3 Comparison of different chaff clouds.

(2)Comparison of chaff cloud quantity distribution

Chaffs quantity distribution in three axes reflects not only the space position of chaffs,but also the variation of chaff cloud shape.Taking one meter as unit length,Oxgand Oygaxis are divided into different regions.Then the quantities of the chaffs in different regions at 0.2 s and 1.5 s are computed.Finally,the curve of chaffs quantity distribution is achieved.The comparison of experiment and simulation curve is shown as Fig.17.

It can be observed in Fig.17 that the simulation curve is similar to the experiment.The diffusion of the experiment results is more sufficient no matter in Oxgaxis or in Oygaxis,and the holistic displacement of experiment results is larger.Some chaffs have fallen onto the ground at 1.5 s,but the simulated chaffs can continue to decline,which made the simulation different from the experiment.

(3)Comparison of chaff cloud variance

The chaff cloud is divided into symmetrical subspaces according to the simulation results.The discrete chaff cloud expectation is given by

The discrete variance is given by

where q is discrete subspace,Q is the amount of subspace,wqis the average displacement of subspace q,Pqis the probability of the chaffs distributed in the subspace q and Pq=nq/N,nqis the quantity of chaffs distributed in the subspace q,N is the quantity of the chaffs.The comparison of variance is shown as Fig.18.

It can be observed that the diffusion of the experiment results is more sufficient no matter in Oxgaxis or in Oygaxis,but the holistic variation regularity of simulation is similar to the experiment.As the ground obstacles the diffusion of chaff cloud,the variance in Oygaxis begins to decrease after 1.4 s.

The reason of the error generation can be explained as follows:

(A)There exists error between the aerodynamic coefficients computed via SST turbulence model and the wind tunnel test.

(B)The aerodynamic interference impact factorsare only the approximated value,which may have some difference with the actual values.

(C)The impact of the ground on the diffusion of chaff cloud is not taken into consideration in the simulation,which brings some errors.

It can be achieved from Figs.14–18 that the simulation holistic kinetic performance of chaff cloud is consistent with the experiment,the shape of chaff cloud is consistent with the experiment,and the errors of chaff cloud length,quantity distribution and variance are quite small,which means the simulation is quite accurate.The error will be decreased in future researches.

4.2.Chaff cloud holistic kinetic performance

Some characteristics of chaff cloud have been analyzed in Section 4.1.3.In this section,the chaff cloud holistic kinetic performance has been obtained by the comparison of chaff cloud displacement,velocity and diffusing rang.

4.2.1.Variation of chaff cloud displacement and velocity

The holistic displacement of chaff cloud can reflect the cloud motion direction and velocity,which can be obtained by Eq.(27).Because the initial chaff cloud velocity of Oxgaxis is identical with the flight velocity of the aircraft at the time of deployment,the chaff cloud displacement of Oxgaxis is the largest after deploying.The velocity of chaff cloud decreases sharply under the impact of drag after deployment,which is shown in Fig.19.

The displacement of chaff cloud in Oxgaxis is quite large within 0.2 s,while the displacement becomes very small at the time of 0.2 s to 1.8 s.The velocity of Oxgaxis is almost zero after 1.8 s.The chaff cloud rises firstly,then goes down gradually.The altitude of chaff cloud decreases almost to the same as the initial deploying altitude at 1.1 s.Chaff cloud holistic only decreases by 3 m within 1.8 s,which can hang for a long time in the air.But there is little holistic movement of chaff cloud in Ozgaxis.

4.2.2.Variation of chaff cloud diffusing range

It can be observed by Fig.20 that the diffusion of chaff cloud in Oxgaxis is quite large,which even reaches to 22.3 m.But the diffusions in Oygaxis and Ozgaxis are quite small.The diffusion in Ozgaxis is the least,which is only 3.8 m.The length of chaff cloud in Oxgaxis reaches 20.5 m within 0.2 s and the diffusion decreases after 0.2 s.Otherwise,the diffusing velocities of Oygaxis and Ozgaxis do not decrease so much as Oxgaxis.The chaff cloud continuously diffuses in Oygaxis and Ozgaxis after 1.8 s.

Chaff cloud rises firstly,then goes down gradually and the diffusion range and displacement of Oxgaxis are the largest,which can be obtained from the variation of holistic displacement,velocity and diffusing rang of chaff cloud.The diffusion of Ozgaxis is symmetric about the original point.The diffusion of chaff cloud in Ozgaxis is the least,no matter to displacement or diffusing range.The length of chaff cloud in Oxgaxis is about six times that of the Ozgaxis.

5.Conclusions

The multi-chaff kinetic performance under the impact of high speed air flow is analyzed in this work.The chaff kinetic and rotation models are established and the impact of aerodynamic damping on chaff rotation speed is studied.The description of aerodynamic interference impact factors are achieved by studying the aerodynamic interference among chaffs.The chaff cloud length,quantity distribution and variance are compared with the experimental results respectively to verify the credibility of the simulation.Then,chaff cloud holistic kinetic performance is analyzed.The main conclusions are shown as follows:

(1)Only the other chaff in the projection of the chaff based on its motion direction,the aerodynamic characteristics of the chaff will be affected.The aerodynamic interference can be ignored when the distance between chaffs is longer than 10R.

(2)The diffusion shape of chaff cloud is related to the initial deploying direction and speed.When the initial deploying direction is upward,chaff cloud approximately forms conical distribution which constitutes positive angle with horizontal plane.The diffusing length of chaff cloud in Oxgaxis is 22.3 m,in Oygaxis is 5.0 m and in Ozgis 3.8 m.

(3)Under the impact of high speed air flow,chaffs diffuse quickly within 0.5 s.The diffusion is almost static after 0.5 s.The chaff cloud is quite steady,which could hang long time with a uniform distribution.

(4)SST turbulence model is quite accurate to compute the aerodynamic coefficients of the chaff.The stalled angle of the chaff is 25°.

The aerodynamic interference among chaffs is quite complex in the motion.Aerodynamic interference impact factors are related to the distance and overlapping area between chaffs according to the results of CFD.But they are more complex in reality.There also exist some errors in the calculation of overlapping area.The established models of aerodynamic interference impact factors reflect the basic regularity of aerodynamic interference in the motion.But the models only consider the aerodynamic interference from the chaffs ahead of the studied chaff in the kinetic direction.However,the chaffs behind it may also impact the aerodynamic interference.In particular,for the chaffs behind it,if the chaffs are very close,the boundary layer separation of chaffs may be delayed and the aerodynamic coefficients will be increased.These problems will be studied in the future.

Acknowledgements

This study was supported by the National Natural Science Foundation of China(No.61471390).