Numerical Simulations in Obtaining Drag Reduction for Projectile with Base Bleed

An artillery projectile in flight produces a low pressure area immediately behind the projectile which creates a force called base drag which lessens the velocity of the projectile. It is known that theoretically this base resistance can be reduced or even eliminated by allowing a stream of hot gas to flow out of the base surface of the projectile in a suitable manner. The effect produced by this stream of hot gas is called base-bleed effect. The internal ballistic calculation of existing base bleed configuration is presented in the paper. A numerical simulation of axisymmetric body projectiles was obtained with the Reynolds Averaged Navier-Stokes (RANS) computational fluid dynamics software (CFD). Also, two turbulence models were tested and validated with the semi empirical prediction. The realizable k-ɛ turbulence model was chosen for calculation of aerodynamic drag of the projectile with and without base bleed effect. Computed result show a drag reduction with base bleed of about 12% in supersonic flow regime


Introduction
HE base drag as a component of the total drag arises from vortices and turbulence in the air.These vortices produce a lowering of the air pressure behind the projectile.In addition to this, aerodynamic bodies such as projectiles, missiles and rockets, generally, undergo a significant deterioration of flight performance by the drag.For these types of flight bodies the drag in the base region has the most significant contribution to total drag.At transonic speeds, for example, base drag constitutes a major portion up to 50% of the total drag for typical projectiles at the speed range of Mach 0.9 [1].Therefore the base drag should be considered separately from the other drag components.For this reason, the minimization of base drag has been an important issue to date, and considerable effort has been made to find suitable techniques for obtaining a low base drag shell design.
During a projectile flight the reverse flow directly behind the projectile base is shown in Figure 1.The large turning angle behind the base causes separation and formation of reverse flow known as the recirculation region or the separation bubble [2][3].The size of the recirculation determines the turning angle of the external flow and therefore the strength of the expansion waves.A smaller recirculation region causes the flow sharp turning, leading to a stronger expansion wave and lower pressures behind the base.Therefore, small separated region causes larger base drag than large regions.
In recirculation region the point along the axis of symmetry, where the stream wise velocity diminishes, is called a shear layer reattachment point.As the shear layer reattaches, the flow is forced to turn along the axis of symmetry, causing the formation of a reattachment shock.
Figure 2 shows that injecting small amounts of gas into the flow field behind the base of the projectile will split the originally large recirculation zone into two parts.One recirculation region remains at the symmetry axis and the other one is formed right behind the base corner [4][5][6][7].As the mass flow rate increases, the recirculation zone at the axis is pushed further out and the other one at the base corner becomes larger.If the mass flow rate is increased away, the recirculation region near the axis disappears and the base bleed follows a straight path.

Internal ballistic calculation
The gas generator for the 122 mm base bleed projectile housed in the afterbody is presented in this paper.The gas generator cross section is shown in Fig. 3.The gas generator contains two identical solid propellant grains.These two elements provide an internal combustion surface consisting of two cylindrical surfaces and four flat surfaces, which results in total decreasing burning surface area.
For the injection mass flow rate, the dimensionless injection parameter I is generally used.The parameter I is defined as the bleed mass flow rate, p m , normalized by the product of the base area, base A ,and the free stream mass flux, eq. ( 1) [9,10]: where ρ ∞ is free stream density, and V ∞ is free stream velocity.
Mass flow produced by the combustion of the gas generator (GG) is shown in Fig. 4. Experimentally obtained curve of chamber gauge pressure, p, vs. time, t, is shown in Fig. 5.According to the experimental curve several values of the absolute pressure denoted in Fig. 6 were chosen for the mass flow rate calculation.In Fig. 6, p c is chamber pressure.Flow out of the combustion products bleed through orifice is subsonic.In dependency on the thermo-chemical characteristics of propellant and using gas dynamics relations can be written as: ( ) ( ) where T 0 is total temperature, p 0 is total pressure, k is ratio of specific heats, T 2 is temperature at the section 2 (nozzle exit), p 2 is pressure at the section 2 and M 2 is the Mach number at nozzle exit.
The products mass flow rate as a function of the pressure in combustion chamber is obtained as: where , ρ 2 is density at the section 2 ( ) ( ) .
, and R is gas constant.
Required combustion products mass flow rate (Fig. 7) can be achieved by an appropriate internal ballistic design of GG.In dependency on projectiles trajectory altitude all influential functions can be expressed as a function of time (using altitude y(t) and speed M(t) parameters: air density ρ ∞ (y) = ρ ∞ (t) and temperature T(y) = T(t)).Finally, optimal mass flow rate change in time can be determined using eq.( 5):

Aerodynamic drag coefficient
The total aerodynamic drag of projectile can be divided into three components consisting of the pressure drag Dp C , viscous drag Dv C , and base drag DB C .This dependence is shown by eq. ( 6): The mass flow from the gas generator reduces the base drag component.The base drag component can be expressed as a function of the base pressure B p , pressure free stream flow field p ∞ and the Mach number M .
( ) From eq. ( 7), the difference between the base drag component for a projectile without base bleed 0 DB C , and projectile with base bleed DBB C , can be written as: or where 0 B p is a base pressure of projectile without base bleed, BB p is a base pressure of projectile with base bleed.

Numerical solution
The aerodynamic CFD prediction simulation of 122 mm projectile model with base bleed, shown in Fig. 8, was done numerically using the software GAMBIT 2.4 and ANSYS FLUENT 14 [8].The mathematical model is based on the RANS including conservation of mass, momentum, energy and ideal gas equation of state.Basic assumptions of the mathematical model are given in the Equations (10-14) [12]: continuity: ( ) ( ) ( ) ideal gas: where p is mean pressure, ρ is mean density, μ is molecular viscosity, 0 h is total enthalpy, λ is thermal conductivity.
Reynolds stresses are given as, 2 3 where t μ is turbulent or eddy viscosity, k is turbulent kinetic energy.To correctly account for turbulence, Reynolds stresses are modeled in order to achieve closure of eq.n (11).The method of modeling employed utilizes the Boussinesq hypothesis to relate the Reynolds stresses to the mean velocity gradients within the flow.The numerical simulation was done with two-equation realizable k-ε turbulence model.Even the Spalart-Allmaras SA model was designed specifically for aerospace applications [13], we concluded that the realizable k-ε turbulence model shows very good agreement with two semi-empirical methods.The turbulent viscosity in the model is computed through the solution of two additional transport equations for the turbulent kinetic energy, and the turbulent specific dissipation rate, ε, [12].The second model of the numerical simulation was four-equation transitional SST turbulence model.
The numerical discretization of the computational domain around the model was done with hybrid mesh of tetrahedral and hexahedra cells.The ellipsoidal computational domain is created with the longitudinal axis of 40 referent model diameter and lateral axes of 25 referent diameter, Fig. 9.The spatial discretization schemes of the equation were the second order upwind.Computational domain was consisted of about 3 million of cells.The mesh resolution near the wall of the model applied in the numerical simulations is shown in Fig. 10. .Numerical steady state simulations with two turbulences model k-ε and SST were done for each Mach number on a higher processor computing resource.
Nine cases of elements trajectory of the projectile are investigated, for every case, point on trajectory, velocity of projectile, air ambient pressure and temperature are chosen.For example the first case corresponds to the beginning of the base bleed operation.In this case, the air ambient pressure is 101235 Pa and air temperature is 288 K.This parameter corresponds to zero altitude.At the moment when the base bleed starts to operate, the projectile velocity was 715.0 m/s and mass flow rate of bleeding combustion products was 0.05 kg/s.
For the other cases, projectile velocities, air pressure, mass flow rates of bleeding combustion products are shown in Table 1.

Results and discussion
The research of aerodynamic drag, presented in the paper, is consisted of two groups of aerodynamic predictions: the semiempirical aerodynamic predictions MTI and ADK0 [14,15] and numerical prediction with code of computational fluid dynamics CFD incorporated into ANSYS FLUENT software [8].The presented values of axial force coefficient show very good agreement to semi empirical data for the case the k-ε turbulence model is utilized.However, the four-equation SST was implemented with no significant differences noted with the semi-empirical data [14,15].
A turbulence k-ε realizable model was selected for simulation projectile with base bleed because of the best agreement with C DB .

Figure12. Effect of base bleed on drag coefficient
The values of predicted axial aerodynamic coefficient, C DB0 and values of axial aerodynamic coefficient with reduction using the gas generator unit, C DBB , vs. the Mach number are presented in Fig. 12.It is shown that there is an average reduction for all flow regimes, especially in supersonic, which is within the range of 4% to almost 12% as shown in Table 2. Reducing the base drag accomplished by the fill up the wake zone behind the projectile and thus increased the base pressure.Increased base pressure reduces the base drag and gives increased shooting distance for the projectile.The parameters of flow behind the projectile before and after injection of the hot gas produced by the gas generator are shown in Figures 13 -15  .Mass flow rate and corresponding impulse were chosen from internal ballistic calculation based on the static tests of gas generator propellant.
The influence of the base bleed flow effects on the drag coefficient was calculated.The computed drag coefficient of the projectile with and without base bleed showed a drag reduction with base bleed of about 12%.This investigation will be continued through studying the effect of base bleed on drag coefficient at different angles of attack, the influence of the base bleed effects on the lateral aero-dynamic coefficients, and especially dynamic derivatives and stability parameter.

Figure 1 .Figure 2 .
Figure 1.Streamlines near the base of projectile without base bleed (plane of symmetry of the projectile)[8]

Figure 3 .
Figure 3. Scheme of the gas generator unit and propellant grain

Figure 4 .
Figure 4. Mass flow produced by combustion of GG Designed GG is tested in the Military Technical Institute (MTI) laboratory ''Technicum'' in Baric (Belgrade).Experimentally obtained curve of chamber gauge pressure, p, vs. time, t, is shown in Fig.5.According to the experimental curve several values of the absolute pressure denoted in Fig.6were chosen for the mass flow rate calculation.In Fig.6, p c is chamber pressure.

Figure 5 .Figure 6 .
Figure 5. Experimental chamber gauge pressure vs. time for gas generator 122 mm

Figure 7 .
Figure 7. Mass flow rate change vs. time.

Figure 8 .
Figure 8. Model of a projectile with base bleed[11]

Figure 9 .
Figure 9. Mesh of a numerical domain for the 122 mm projectile with base bleed The criteria of convergence were constant values of aerodynamic coefficients of axial force and residuals less than 5•10 -4 .The mesh resolution near the wall of the model applied in the numerical simulations is shown in Fig.10.

Figure 10 .
Figure 10.Mesh resolution near the wall of the 122 mm projectile with base bleed The axial aerodynamic predictions are done for Mach number at different flight regimes 0.99 2.1 M ≤ ≤.Numerical steady state simulations with two turbulences model k-ε and SST were done for each Mach number on a higher processor computing resource.Nine cases of elements trajectory of the projectile are investigated, for every case, point on trajectory, velocity of projectile, air ambient pressure and temperature are chosen.For example the first case corresponds to the beginning of the base bleed operation.In this case, the air ambient pressure is 101235 Pa and air temperature is 288 K.This parameter corresponds to zero altitude.At the moment when the base bleed starts to operate, the projectile velocity was 715.0 m/s and mass flow rate of bleeding combustion products was 0.05 kg/s.For the other cases, projectile velocities, air pressure, mass flow rates of bleeding combustion products are shown in Table1.

Figure 11 .
Figure 11.Aerodynamic coefficient vs. the Mach number for the 122 mm projectile The compared results of the axial force coefficient C DB obtained by aerodynamic semi-empirical predictions and two sets of numerical simulations k-ε and SST are shown in Fig.11.The presented values of axial force coefficient show very good agreement to semi empirical data for the case the k-ε turbulence model is utilized.However, the four-equation SST was implemented with no significant differences noted with the semi-empirical data[14,15].A turbulence k-ε realizable model was selected for simulation projectile with base bleed because of the best agreement with C DB . .

Figure 13 . 15 .
Velocity magnitude contours of projectile before and after injection for M=2.1 a) Before injection b) After injection Figure 14.Dynamic pressure contours of projectile before and after injection for M=1.16 a) Before injection b) After injection Figure Dynamic pressure contours of projectile before and after injection for M=0.99ConclusionThe 3D numerical computation was performed for the122 mm projectile with and without base bleed at different values of the Mach number.A series of calculation drag coefficient was run for the 122 mm projectile with and without base bleed.The simulations were performed for the zero of attack and Mach number range 0.99 2.1 M ≤ ≤

Table 1 :
Elements of the projectile 122 mm trajectory in the shooting at maximum range during the base bleed operation.

Table 2 :
Drag coefficient reduction expressed in percentages