Mass-averaged Navier-Stokes Equations Research Articles

Optimization of artillery projectiles base drag reduction using hot base flow

The CFD numerical simulations were carried out to investigate the base drag characteristics of a projectile with base bleed unit with a central jet. Different base bleed grain types with different combustion temperatures were used. The goal was to find a way to effectively control the base flow for base drag reduction and optimisate the latter using an adequate CFD software. Axisymmetric, compressible, mass-averaged Navier-Stokes equations are solved using the k-? SST, transition k-kl-?, and RSM turbulence models. The various base flow characteristics are obtained by the change in the non-dimensionalized injection impulse. The results obtained through the present study show that there is an optimum bleed condition for all base bleed grains tested. That optimum is dependent on the temperature of the grain combustion products. The optimum reduces the total drag for 6,9% in the case of air injection at temperature of 300 K and reaches up to 28% in the case of propellant combustion products injection at almost 2500 K. Besides, the increasing of molecular weight has a role no less important than temperature of the combustion products in terms of base drag reduction.

Modelling the Flow in a Transonic Diffuser with One Reynolds-Stress and Two Eddy-Viscosity Models

Turbulence modeling combined with the mass averaged Navier-Stokes equations and detailed comparisons with experimental data are presented for a transonic flow in a converging diverging diffuser for two different inlet Mach numbers. Three low-Reynolds number turbulence models, which do not use the concept of the wall distance and wall normal vector calculation are adopted: a linear eddy-viscosity model, a cubic non-linear eddy-viscosity model and a non-linear Reynolds-stress model. The compressibility effects due to the mean density variations are incorporated in a subsonic pressure-based flow solver through minor modifications to the pressure velocity-coupling algorithm and by introducing the dilatation-dissipation of turbulence to the equations of the turbulent models. Grid dependency studies were conducted and detailed velocity and pressure coefficient distributions are presented in comparison with available experimental data providing also information for the boundary layer development on the diffuser walls in the region downstream the shock wave. The final results are very promising concerning the capability of the turbulence models to capture the compressibility effects in transonic flows when they are incorporated with appropriate modifications in a pressure-based flow solver.

Optimization of Mass Bleed for Base-Drag Reduction

Efficient mass-bleed conditions to minimize base drag are examined in consideration of various base-to-orifice-exit area ratios for a body of revolution in the Mach 2.47 freestream. Axisymmetric, compressible, mass-averaged Navier-Stokes equations are solved using the standard k-w turbulence model, a fully implicit finite volume scheme, and a second-order upwind scheme. Base flow characteristics are explained regarding the base configuration as well as the injection parameter, which is defined as the mass flow rate of the bleed jet nondimensionalized by the product of the base area and freestream mass flux. The results obtained through the present study show that for a smaller base area, the optimum mass-bleed condition leading to minimum base drag occurs at relatively larger mass bleed, and a larger orifice exit can offer better drag control.

Numerical simulation of axisymmetric afterbody flows with jet exhaust

A fifth-order accurate compact difference scheme was used to compute the flow over an axisymmetric afterbody with jet exhaust. The solution was based on the mass-averaged Navier-Stokes equations combined with a two-parameter differential model of turbulence. The computations were performed on a specially generated mesh such that the flow in the exterior and interior of the nozzle could be described simultaneously. Numerical results are presented for various external flow conditions and various chamber pressures.

Optimization of mass bleed control for base drag reduction of supersonic flight bodies

The minimization of base drag using mass bleed control is examined in consideration of various base to orifice exit area ratios for a body of revolution in the Mach 2.47 freestream. Axisymmetric, compressible, mass-averaged Navier-Stokes equations are solved using the standard k-θ turbulence model, a fully implicit finite volume scheme, and a second order upwind scheme. Base flow characteristics are explained regarding the base configuration as well as the injection parameter which is defined as the mass flow rate of bleed jet non-dimensionalized by the product of the base area and freestream mass flux. The results obtained through the present study show that for a smaller base area, the optimum mass bleed condition leading to minimum base drag occurs at relatively larger mass bleed, and a larger orifice exit can offer better drag control.

Passive Control of Plume Interference on Slender Axisymmetric Bodies

The physics of the plume-induced shock and separation, particularly at high plume to exit pressure ratios with and without shock-turbulent boundary-layer control methods, were studied using computational techniques. Mass-averaged Navier-Stokes equations with a two-equation turbulence model were solved by using a fully implicit finite volume scheme and time.marching algorithm. The control methodologies for shock interactions included a porous tail and a porous extension attached at the nozzle exit or trailing edge. The porous tail produced a weaker shock and fixed the shock position on the control surface. The effect of the porous extension on shock interactions was mainly to restrain the plume from strongly underexpanding during a change in flight conditions. These techniques could give an additional dimension to the design and control of supersonic missiles.

Control of plume interference effects on axisymmetric afterbodies

Plume interference effects on the axisymmetric flowfields around powered missiles are investigated using computational techniques. The study is mainly to understand the physics of the plume-induced shock and separation particularly at high plume to exit pressure ratios with and without shock-turbulent boundary layer control methods. Mass-averaged Navier-Stokes equations with the RNG k-ε turbulence model are solved using a fully implicit finite volume scheme and time-marching algorithm. The shock position and extent of separation was found to be dependent on the freestream Mach number and plume pressure ratio. Rounding the tail or a groove on the surface near the tail moved the shockwave downstream of the tail fin which should enhance the control of the missile.

Pressure drop control using multiple orifice system in compressible pipe flows

In order to investigate the effectiveness of an orifice system in producing pressure drops and the effect of compressibility on the pressure drop, computations using the mass-averaged implicit Navier-Stokes equations were applied to the axisymmetric pipe flows with the operating pressure ratio from 1.5 to 20.0. The standard k- ɛ turbulence model was employed to close the governing equations. Numerical calculations were carried out for some combinations of the multiple orifice configurations. The present CFD data showed that the orifice systems, which have been applied to incompressible flow regime to date, could not be used for the high operating pressure ratio flows. The orifice interval did not strongly affect the total pressure drop, but the orifice area ratio more than 2.5 led to relatively high pressure drops. The total pressure drop rapidly increased in the range of the operating pressure ratio from 1.5 to 4.0, but it nearly did not increase when the operating pressure ratio was over 4.0. In the compressible pipe flows through double and triple orifice systems, the total pressure drop was largely due to shock losses.

Analysis of transitional flow and heat transfer over turbine blades: algebraic versus low-Reynolds-number turbulence model

AbstractThe numerical simulation of flow and heat transfer over turbine blades involving laminar-turbulent transition is presented. The predicted results are compared with the experimental surface heat transfer and pressure distributions for two transonic turbine blades over a wide range of flow conditions. The time-dependent, mass-averaged Navier-Stokes equations are solved by an explicit four-stage Runge-Kutta scheme in the finite volume formulation. Local time stepping, variable-coefficient implicit residual smoothing and a full multigrid method have been implemented to accelerate the steady state calculation. The turbulence is simulated by the algebraic Baldwin-Lomax model together with an explicitly imposed model for transition. For comparison, the low-Reynolds-number version of the two-equation (k-∊) model of Chien is also used. The modified Baldwin-Lomax model performs well in predicting the onset of laminar-turbulent transition, whereas the Chien model shows a tendency to mimic the transition early and over a shorter distance.

Analysis of transitional flow and heat transfer over turbine blades: Algebraic versus low-Reynolds-number turbulence model

The numerical simulation of flow and heat transfer over turbine blades involving laminar-turbulent transition is presented. The predicted results are compared with the experimental surface heat transfer and pressure distributions for two transonic turbine blades over a wide range of flow conditions. The time-dependent, mass-averaged Navier-Stokes equations are solved by an explicit four-stage Runge-Kutta scheme in the finite volume formulation. Local time stepping, variable-coefficient implicit residual smoothing and a full multigrid method have been implemented to accelerate the steady state calculation. The turbulence is simulated by the algebraic Baldwin-Lomax model together with an explicitly imposed model for transition. For comparison, the low-Reynolds-number version of the two-equation ( k-∊) model of Chien is also used. The modified Baldwin-Lomax model performs well in predicting the onset of laminar-turbulent transition, whereas the Chien model shows a tendency to mimic the transition early and over a shorter distance.

Numerical simulation of a 2-D jet-crossflow interaction related to film cooling applications: Effects of blowing rate, injection angle and free-stream turbulence

The aerodynamics of a coolant jet in a hot crossflow in an environment representative of the gas turbine practice, is numerically investigated for film cooling applications. The time-dependent, mass-averaged Navier-Stokes equations coupled with the compressible form of a two-equation low-Reynolds number (k-ɛ) model are solved based on an explicit finite volume formulation. The computed flow-field and surface temperature distributions along with the turbulence quantities are presented to illustrate the variation of flow-physics and heat transfer phenomena which occur in a jet-crossflow interaction with changing blowing rates, slot angles, and inlet free-stream turbulence levels.

Compressible cavity flow oscillation due to shear layer instabilities and pressure feedback

A computational analysis was performed on a compressible flow oscillation due to shear layer instabilities over a cavity and pressure feedback in a cavity of length-to-depth ratio 3 at Mach 1.5 and 2.5. The mass-averaged NavierStokes equations were solved. Turbulence closure was achieved using a k-u> model with compressibility corrections. Self-sustained oscillations were produced. Negative form drag coefficient was observed within an oscillatory cycle due to mass ejection from the cavity near the trailing edge and vortex production near the leading edge. The shock wave-expansion wave interaction patterns, modes of the oscillation, sound pressure level, and time-averaged surface pressure were compared with experimental results of previous investigations and good agreement was achieved, particularly the time-averaged pressure. The prediction showed a marked improvement over earlier analysis.

Numerical simulation of oblique shock-wave/vortex interaction

High Reynolds number supersonic flowfields were generated numerically by integration of the time-dependent three-dimensional compressible Euler and mass-averaged Navier-Stokes equations in order to simulate the interaction of a streamwise vortex with an oblique shock wave. The vortex develops at the tip of a vortex-generating fin which is suspended from the ceiling of a wind tunnel. Downstream, an oblique shock wave is produced by a wing surface which spans the width of the wind tunnel and has a two-dimensional sharp leading-edge wedge as its airfoil section. Grid resolution studies are provided in order to assess accuracy of the solutions. Resultant features of the numerical flowfields are discussed ,and comparison is made with experimental data in terms of static pressure distributions on the wing surface.

Navier-Stokes analysis of a circulation control airfoil

The two-dimensional, compressible, mass-averaged Navier-Stokes equations are used to investigate flows about a typical circulation control airfoil. The governing equations are solved using the implicit approximate-factorization algorithm of Beam-Warming with a modified algebraic eddy viscosity model. Results are compared with experimental data, and excellent agreement is obtained. The effects of different jet momentum coefficients and angles of attack on the flow are studied. The mechanism of genenating large lift by circulation control is discussed.

Numerical simulation of turbulent cylinder juncture flowfields

Steady high-Reynolds-number subsonic and supersonic flowfields about a circular cylinder mounted upright on a flat plate were simulated numerically by integration of the time-dependent three-dimensional compressible mass-averaged Navier-Stokes equations. Effects of turbulence were represented by a two-equation (k-e) closure model that included a generalized formulation and low-Reynolds-number terms. For the supersonic case, the turbulence equations incorporated a compressibility correction. Grid mesh step-size studies were performed to assess resolution requirements of the solutions. Comparison is made with experimental data in terms of static pressure and total pressure loss coefficients, velocity distributions, and surface limiting streamline patterns

Numerical study of mixing in supersonic combustors with hypermixing injectors

A numerical study was conducted to evaluate the performance of wall mounted fuel-injectors designed for potential Supersonic Combustion Ramjet (SCRAM-jet) engine applications. The focus of this investigation was to numerically simulate existing combustor designs for the purpose of validating the numerical technique and the physical models developed. Three different injector designs of varying complexity were studied to fully understand the computational implications involved in accurate predictions. A dual transverse injection system and two streamwise injector designs were studied. The streamwise injectors were designed with swept ramps to enhance fuel-air mixing and combustion characteristics at supersonic speeds without the large flow blockage and drag contribution of the transverse injection system. For this study, the Mass-Averaged Navier-Stokes equations and the chemical species continuity equations were solved. The computations were performed using a finite-volume implicit numerical technique and multiple block structured grid system. The interfaces of the multiple block structured grid systems were numerically resolved using the flux-conservative technique. Detailed comparisons between the computations and existing experimental data are presented. These comparisons show that numerical predictions are in agreement with the experimental data. These comparisons also show that a number of turbulence model improvements are needed for accurate combustor flowfield predictions.

Flow and heat transfer in a turbulent boundary layer through skewed and pitched jets

A study was carried out of longitudinal vortices in a low speed turbulent boundary layer due to small jets. The jet was pitched at 45 deg and skewed between 0 and 120 deg. The effects of jet velocity ratio (0≤λ j ≤3.0) and skew angle (0≤θ≤120 deg) were addressed. Mass-averaged Navier-Stokes equations were solved using computational fluid dynamics and heat transfer. Turbulence closure was achieved using k-e model. Three types of vortex production were noted at various jet velocity ratios

Transonic turbulent separated flow predictions using a two-layer turbulence model

ANAVIER-STOKES code with algebraic stress model/k-e two-layer turbulence model has been developed to compute the transonic turbulent flow over an axisymmetric secantogive-cylinder-boattail (SOCBT) projectile with a flat base and over an axisymmetric bump. The implicit upwind-biased algorithm with Harten's second-order upwind total variation diminishing discretization is extended to splve the higher order turbulent transport equations of the two-layer model for high accuracy and acceptable convergent rate. Computed results are compared with both the experimental data and the results using other turbulence models. It is found that improvement of the prediction and anisotropic turbulent natures, in the recirculating region downstream of the strong shock-wave/ boundary-layer interaction flow, can be obtained using the two-layer model of turbulence. Contents In the past several years, considerable advances have been made in predictions of transonic turbulent separated flow. For the present study, the mixture of Rodi's 1 algebraic stress model (ASM) and Chien's2 k-e turbulence model is formed as the present ASM/k-e two-layer model. The two models are matched at a preselected grid line and the number of node points in the inner layer corresponds to minimum y^^ = 40 in the boundary-layer type flow region. The extra equations of turbulent quantities of (k, e, u 'u ', v ' v ', u ' v ') or (k, e) must be solved with the mass-averaged Navier-Stokes equations if an ASM or k-e turbulent model is employed. The system of governing equations with these extra variables becomes not only larger but also stiffer and is difficult to solve. Harten's second-order upwind TVD scheme3 is a good choice to discretize the convection terms and it is extended to solve the turbulent transport equations of the present two-layer model. In the present work, the mean flow equations and turbulent equations of k and e can be decoupled, so that solving 4x4 (mean flowfield equations) and 2x2 (turbulent field equations) block tridiagonal matrices can be reduced to solving a 4x4 block tridiagonal matrix and two tridiagonal matrices (k and e equations). These modifications improve the stability of the numerical computation and the details are given in Ref. 4. The nonlinear algebraic equations of ASM are solved simultaneously by Newton's method. About 15.4% more of the CPU time per iteration for the present ASM/A:-e two-layer model is required if it is compared with that of the k-e turbulence model, which consumed a CPU time of 0.89 seconds per iteration on CRAY-XMP14. During the computation, the L2 residual can be reduced more than 4.5-5 orders lower after 7000-9000 iterations arid the results can be considered as converged results. Numerical computations have been made

Computations and experiments for a multiple normal shock/boundary-layer interaction

Results from a numerical investigation of a Mach 1.61 multiple normal shock wave/turbulent boundary-layer interaction are compared to wall static pressure and laser Doppler velocimeter measurements. The computations used the explicit, time-dependent, second-order accurate MacCormack scheme to solve the mass-averaged Navier-Stokes equations. Turbulence was modeled by means of the Baldwin-Lomax algebraic model and the Wilcox-Rubesin two-equation model. The computation with the Wilcox-Rubesin model was able to capture the major features of the normal shock train and accurately predicted the flow reacceleration mechanisms which occur between shocks. However, this computation failed to accurately predict the level of flow separation under the first shock. The Baldwin-Lomax computation displayed a more limited ability to capture the features of this shock train flow.

Numerical simulation of slot injection into a turbulent supersonic stream

Steady flowfields resulting from slot injection at the surface of a flat plate in a freestream with a Mach number of 3.7 and a unit Reynolds number of 5.83 x 10 6 /m were simulated numerically by integration of the time-dependent compressible mass-averaged Navier-Stokes equations. Effects of fine scale turbulence were represented by a two-equation (k-e) closure model that included a generalized formulation, low Reynolds number terms, and a compressibility correction