Investigation on the f l ow control of micro-vanes on a supersonic spinning projectile

Jie MA*，Zhi-hua CHEN，Zhen-gui HUANG，Jian-guo GAO，Qiang ZHAO

Key Laboratory of Transient Physics，Nanjing University of Science and Technology，Nanjing 210094，China

Investigation on the f l ow control of micro-vanes on a supersonic spinning projectile

Jie MA*，Zhi-hua CHEN，Zhen-gui HUANG，Jian-guo GAO，Qiang ZHAO

Key Laboratory of Transient Physics，Nanjing University of Science and Technology，Nanjing 210094，China

Studies have shown that micro-wedge vortex generators （MVG）can effectively control the f l ow separation of supersonic boundary layer.In order to improve the f l ight stability of spinning projectile，the original standard 155 mm projectile was taken as an example，and the micro-vanes were mounted at the projectile shoulder to investigate the separation control on the aerodynamic characteristics of projectile.Numerical simulations were performed with the use of DES method for the f l ow f i elds of projectiles with and without micro-vanes，and the characteristics of the boundary layer structures and aerodynamic data were compared and discussed.Numerical results show that the micro-vanes can be used to inhibit separation of f l uid on projectile surface，and improve the f l ight stability and f i ring dispersion of projectile.

Spinning projectile；Micro-vane；Stability；Aerodynamic characteristics；Fluid control

1.Introduction

Precision strike is a general trend in modern warfare，and many countries in the world improve the fl ight stability and fi ring dispersion of projectile mainly through the development of guided munitions and transformation of conventional ammunition ［1］.Supersonic spinning projectiles are greatly in fl uenced by boundary layer separation in the process of fl ight［1，2］.The fl ight stability of a projectile is one of the basic requirements of the projectile design ［3］，which it means that its angle of attack between the axis of the projectile and velocity vector should be within a certain limit，and gradually decay［4-6］.

Micro-vanes are found to be able to suppress the separation of supersonic fl ow.In this paper，in order to further improve the fl ight stability of the standard 155 mm projectile ［7］，the microvanes were mounted at the projectile shoulder according to the Task Force fi ndings ［8-10］，so that the fl uid separation in the boundary layer of projectile can be suppressed，and the projectile has a stronger anti-interference ability during fl ight for improving its fl ight stability and fi ring accuracy.The supersonic fl ow structure around micro-vanes and the control mechanism of boundary layer separation were discussed in detail in Refs.［8-10］.

Numerical simulations were performed with the use of DES method for the f l ow f i elds of 155 mm standard projectiles for two cases with and without micro-vanes.The modif i cations of the boundary layer structures and aerodynamic data for two cases were compared and discussed.Numerical results show that the micro-vanes can be used to inhibit the f l uid separation of projectile surface，improve the projectile lift and pitching moment，and eliminate the shaking of lift and pitching moment，as a result of improving the f l ight stability and f i ring dispersion，which can provide guidance for the improvement of supersonic projectiles.

2.Investigation approach

The fl uid fi eld of supersonic spinning projectile was simulated based on DES simulation method.Realizablek-εturbulence model is used for the near wall region，and the large eddy simulation （LES）is used for external fl ow fi eld，in which the spatial discrete are discretized using the fi nite volume method，the convection term is approached with the second orderAUSM format，and a central difference scheme is used for the viscosity term.

The transport equations of turbulent kinetic energy and dissipation in realizablek-εturbulence model are

The control equations of LES model can be obtained by fi ltering Navier-Stokes equations in wave number space or irrational space.The fi ltration process is to remove the small vortexes which are shorter than fi lter width or a given unreasonable width.The resulting control equations of maelstrom are

whereτijis de fi ned as subgrid stress，τij=ρuiuj-ρuiuj.

A sliding mesh needs to be used in order to simulate the fl ight state of spinning projectile.Sliding grid technology requires an external f i xed area and inner motion area round the projectile，with a pair of interfaces being between two areas，and the points of the interface grid do not need to overlap；they only need to do numerical interpolation on the slip boundary to ensure the f l ux conservation between two regions，and the deformation of grid cell in motion，do not occur.Therefore the sliding grid technology occupies less memory of computer，calculates fast and has high precision.

Fig.1.M549 projectile ［7］.

Fig.2.Grid around the projectile.

155 mm M549 projectile，as shown in Fig.1（a），was used as an example in the present paper.The micro-vanes were mounted at the projectile shoulder to form a new physical model，as shown in Fig.1（b）.Fig.2 shows the computationaldomain of M549 projectile.Fig.2（a）shows the grid distribution of symmetric surface，and Fig.2（b）and （c）show the sliding grid near the projectile and the grid near a vane，respectively. The computational domain is divided into an external f i xed area and an internal sliding area.The grids within boundary layer were ref i ned along the normal direction，and the grids near the head，shoulder and tail of projectile were ref i ned along the f l ow direction.After repeated calculations and convergence tests，the grid number of the whole area is about 2 million.

Projectile surface is applied with the no-slip wall boundary condition，and the meshes of the interior layers are designed to move with the projectile.The interfaces of external f i xed grid area and internal sliding area are adopted with the sliding boundary conditions.The mach number of incoming f l ow is assumed to be 2.05.The initial pressure P0is set to 1.014 × 105Pa，and the initial temperature T0is 278K.The spin rate of the projectile is chosen to be Ω =1112 rad/s，which equals a maximal dimensionless spin rate，pD2U∞= 0. 154. The rotation is anti-clockwise viewing from the base of the projectile.

3.Results and discussion

Fig.3 shows the comparison of previous measured and simulated side force coeff i cients of a generic 6.37 diameter long tangential-ogive-cylinder type projectile.The simulated results of unsteady DES method are compatible with the previous simulated and experimental results.It verif i es that the credibility of the numerical simulation results in this paper.

Fig.4 shows the pressure distributions on the surfaces of the standard projectile and the projectile with micro vanes and around them with Ma of 2.05 and angle of attack （AOA）of 4°. The main shock wave structures are the same for both cases；there are oblique shock waves around the heads and expansion waves near the tails.But for the projectile with micro-vanes，the oblique shock wave also forms along the micro-vanes，and its strength is much weaker than that of head shock wave.In addition，the shock waves around micro-vanes are stronger at the area close to the windward side，which makes the surface pressure higher than that on the leeward side，and leads to a raise in the projectile lift.

3.1.Control mechanism of micro-vanes

Micro-vortex generator is considered to be one of the most applicable prospects in the f i eld of supersonic and hypersonic f l ow control.It can generate a strong vortex pair under the action of windward airf l ow.The vortex structures can inhale the high-speed gas of mainstream into the boundary layer，and push the original low speed gas of the boundary layer f l ow into the main f l ow，thus increasing the momentum boundary layer and turning an adverse pressure gradient of f l ow separation into a favorable pressure gradient.The f l ow separation of boundary layer can be suppressed ［10］.

A series of studies about tail vortexes of micro-vane had been carried ［10］.The basic structure of micro-vane is shown in Fig.5，and the structure parameters of micro-vane are h=2 mm，a=7.5 mm，b=1.25 mm，c=13.05 mm.

It can be seen from Fig.6 that the wake f l ow structures are simple；there is mainly a counter-rotating streamwise vortexpair which suggests the main mechanism of the boundary layer control.The streamwise vortex tube can also entrain high

Fig.3.Comparison of the measured Magnus coeff i cient and the simulated results of a tangential-ogive-cylinder type projectile for Ma=3 ［11，12］.

Fig.4.Pressure distributions of （a）the standard projectile and （b）the projectile with micro-vanes for Ma=2.05，

Ω=1112 rad/s

Fig.5.Computational model of micro-vane.

and AOA=4°. momentum gas from the free stream into the boundary layer and redistribute the pressure distribution on the boundary layer.

Fig.7 shows the vorticity distribution on the cross sections of the projectiles without and with micro-wedge for Ma=3，AOA=4°and spin rate Ω=157 rad/s.It can be seen from Fig.7 that the vorticity distribution behind vanes on the projectile with micro-vanes is different from that on the standard projectile.As shown in Fig.7（c），the counter-rotating streamwise vortex-pair attaches on the surface of projectile.Its effect is consistent with the details described in Ref. ［4］.The vortex structure can inhale the high-speed gas of mainstream into the boundary layer，and push the original low speed gas of the boundary layer into the outer main f l ow.So far，the energy exchange between them is completed，and the f l uid separation on the surface of projectile is inhibited.

Fig.8 shows the density isosurfaces of projectiles without and with vanes for Ma=2.05 and AOA=0°，and the colors of the isosurface represents pressure value.It can be seen from Fig.8 that the typical streamwise vortex pair behind the microvanes is distributed along the body of projectile，and the trailing vortexes distribute spirally due to the rotation of projectile.The leeward pressure of projectile is slightly decreased after adding the micro-vanes；therefore the projectile lift is enhanced.It can also be seen from Fig.8 that the counter-rotating streamwise vortex pairs form the buffering zones.It is conducive to weakenthe interference encountered during f l ight so as to improve its f l ight stability.

Fig.6.Vortex rings shown by iso-surface of λ2［10］.

Fig.7.The vorticity distributions on cross sections of the projectiles without and with micro-wedge for Ma=2.05，AOA=0°and spin rate，Ω=1112 rad/s.

Fig.8.Density isosurfaces （ρ=0. 9 5 kg/m3）of projectiles without and with vanes for Ma=2.05 and AOA=0°.

Fig.9.Comparison of aerodynamic coeff i cients of projectile with and without vanes for Ma=2.05 and AOA=4°.

Fig.10.Comparison of Magnus coeff i cients of projectiles with and without vanes at Ma=2.05 and AOA=4°.

3.2.The inf l uence of micro-vanes on aerodynamic coeff i cient Figs.9 and 10 show the comparison of aerodynamic coeff icients of the projectiles with and without vanes for Ma=2.05 and AOA=4°.The aerodynamic coeff i cients of projectile with micro-vanes increase slightly.However，the obvious slight cyclical f l uctuations can be observed from the curve of aerodynamic coeff i cient versus time，but the aerodynamic coeff i cient becomes stable after the addition of micro-vanes.And the normal coeff i cient of projectile with vanes increases and eliminates its oscillation so as to improve the stability，but decrease the lift-to-drag ratio.Generally，vibration of aerodynamic coeff i cients is mainly caused by f l uid separation on the projectile surface.Separation vortex shedding from the projectile surface will cause pressure pulsation on the projectile surface，leading to the vibration of the aerodynamic force coeff i cient.However，aerodynamic coeff i cient changed smoothly after adding the micro-vanes，and it also can illustrate that f l uid separation on the projectile surface has been suppressed.

Fig.11 shows the comparison of aerodynamic moment coeff i cients of projectiles with and without vanes for Ma=2.05 and AOA=4°.It can be found from Fig.11 that Magnus moment coeff i cient changes little after adding the micro-vanes.Meanwhile，the rolling moment coeff i cient of the projectile with micro-vanes increases，but the increase in rolling moment coeff i cient is very small and close to zero.Pitching moment of the projectile with micro-vanes increases and becomes stable，which means the projectile can return to the equilibrium state more quickly.Therefore，the addition of micro-vanes can improve the f l ight stability and f i re dispersion of spinning projectiles.

Fig.11.Comparison of aerodynamic moment coeff i cients of projectiles with and without vanes for Ma=2.05 and AOA=4°.

In order to give a much broader scope of Mach numbers for a complete analysis，the normal force coeff i cient and pitching moment coeff i cient which are the typical parameters for AOA=4°and Ma=1.2 and Ma=4 in the present paper are shown in Figs.12 and 13.However，the obvious cyclical f l uctuations cab be observed from the curves of aerodynamic coef fi cient versus time in Figs.12 and 13，but the aerodynamic coef fi cient becomes stable after the addition of micro-vanes.As can be seen from Fig.13，there is a smaller vibration about the aerodynamic coef fi cients of projectile for Ma=4.It can be found by comparing Figs.12，13 and 9 that the vibration amplitude of aerodynamic force coef fi cient decreases and the vibration frequency increases gradually with the increase in Mach number.However，the control of micro-vanes can inhibit the fl uid separation on the surface of projectile and improve its fl ight stability and fi ring dispersion.

The vibration of aerodynamic force and moment coeff i cients is mainly caused by the f l uid separation on the surface of projectile.The separation vortexes shed from the surface of projectile may cause the f l uctuation of pressure on the surface of projectile and the vibration of aerodynamic coeff i cients. However，the aerodynamic coeff i cients become smooth after mounting the micro-vanes on a projectile，and it illustrates that the f l uid separation on the surface of projectile is suppressed，which is benef i cial for improving the f l ight stability of spinning projectile.

Fig.12.Comparison of aerodynamic coeff i cients of projectiles with and without vanes for Ma=1.2 and AOA=4°.

Fig.13.Comparison of aerodynamic coeff i cients of projectiles with and without vanes for Ma=4 and AOA=4°.

4.Conclusion

Numerical simulations were performed with the use of DES method for the f l ow f i elds of 155 mm standard projectiles with and without micro vanes，and the modif i cations of the boundary layer structures and the aerodynamic data for two cases were compared and discussed.The numerical results show that a counter-rotating streamwise vortex pair behind each vane attaches on the surface of projectile and it can inhibit the f l ow separation along the body of projectile.In addition，Magnus force and roll moment increase slightly after adding the micro vanes，and have smaller impact on the f l ight stability of projectile than lift and pitching moment so that they can be neglected basically.Meanwhile，the normal force coeff i cient and pitching moment coeff i cient of the projectile become stable，obviously and virtually eliminating the f l uctuation term over time so that the projectile gains the ability of anti-interference，and the f l ight stability and f i re dispersion can be improved.

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Received 5 July 2015；revised 8 January 2016；accepted 21 January 2016 Available online 26 February 2016

Peer review under responsibility of China Ordnance Society.

*Corresponding author.

E-mail address:majie19910@163.com （J.MA）.

http://dx.doi.org/10.1016/j.dt.2016.01.008

2214-9147/? 2016 China Ordnance Society.Production and hosting by Elsevier B.V.All rights reserved.

? 2016 China Ordnance Society.Production and hosting by Elsevier B.V.All rights reserved.