In this research, a 3-D Thin Layer Navier-Stokes (TLNS) code is developed. This code consists of several numerical algorithms for space and time discretization, together with appropriate turbulence modeling. The Roe method is used for the discretization of inviscid terms and the central scheme for viscous terms. The explicit time marching technique is applied, based on finite volume space discretization. This code can be employed in the range of laminar and TURBULENT FLOW. It is validated for a SUPERSONIC FLOW with Mach number 3 around a tangent-ogive with incidence angles of 6o and a secant-ogive with incidence angles of 10o. The circumferential pressure distribution is compared with experimental and Euler code results and the results of TLNS are acceptable. The cross-sectional Mach number contours are also presented. In addition to an outer shock, a cross-FLOW shock wave is captured in the case of a 10o angle of incidence.

In this work, unsteady laminar and TURBULENT SUPERSONIC FLOWs of a discharged projectile from a tube have been numerically simulated. The equations of axisymmetric viscous compressible FLOW has been computed by Van Leer flux vector splitting method, using time and space second order accuracy and moving boundary considerations.When a projectile is discharged from a tube, a complicated FLOW in its front and back is created which this FLOW includes expansion and shock waves. Complicated intractions between these waves make the analysis of this FLOW very difficult. The numerical simulation predicts expansion wave, bow shock wave in front of projectile, barrel shock wave, Mach disk, vortex ring, and shear layer. Results show that, there are not many differences between the laminar and TURBULENT FLOW arrangements, but the aerodynamic forces are different. The variation of acceleration and aerodynamic forces, when projectile is discharging from a tube, due to more intractions between the expansion and shock waves, is large and causes vibration of the projectile and change in its path. When projectile starts to discharge from a tube, the acceleration will be maximum, but when discharges entirely from tube, the resistant force are increased and the acceleration is decreased.

A TURBULENT SUPERSONIC FLOW over bodies of revolution, including the base FLOW, is investigated using multiblock grid to solve the thin layer Navier-Stokes (TLNS) equations. Patched method has been used near the interfaces. Our numerical scheme was implicit Beam-Warming central differencing, while Baldwin-Lomax turbulence modeling was used to close the Reynolds averaged Navier-Stokes equations. The results of this work have been compared with existing computational and experimental benchmark data and shows close agreements.

The effect of counter FLOW jet through an extended nozzle on reducing aerodynamic drag is analyzed by using a combined method. FLOW field is simulated around a hemispherical body in a free stream with Mach 4. The results are reached by providing a 3D solver and applying the complete form of Navier-Stokes and energy equations along with modified shear stress transport model. Appropriate numerical validation has been made by comparing the surface pressure distribution in the zero pressure ratio of jet to free-stream and drag on the nose at a pressure ratio of 0 to 3. Four nozzles were used to analyze the effect of extending. The results show that the nozzle extensions have a significant effect on the wave drag after changing the shape of the bow shock. In a given pressure ratio, the effect of injected jet from the extended nozzle over the reduction of the nose is higher than that of direct jet injection from the nose. The effect is visible in all pressure ratios. Furthermore, a limited increase in the pressure ratio over a fixed length of the extended nozzle has led to a further reduction of total drag. However, in the higher pressure ratios, the linear increase of the retro jet has led to an increase in the total drag on the nose. The results also show that increasing the nozzle length in a constant pressure ratio leads to an increase in the depth of jet penetration and a larger reduction of total drag.

The three-dimensional SUPERSONIC TURBULENT FLOWs over wrap-around fin missiles have been computed using the Thin Layer Navier-Stokes (TLNS) equations to reduce the computational efforts compared to those of the Full Navier-Stokes (FNS) equations. In this research, the missile configuration is divided into multi regions to enable fluid FLOW simulation using Personal Computers (PC). It also makes it possible to use a different number of nodes and distribution of grids in each region to enhance the accuracy. The Thin Layer Navier-Stokes equations in the generalized coordinate system were solved using an efficient, implicit, finite-difference factored algorithm of the Beam and Warming. For the TURBULENT FLOW field computations, the well-known isotropic two-layer algebraic eddy viscosity Baldwin-Lomax model was used. The computations were performed for SUPERSONIC TURBULENT FLOWs over wrap-around fin configurations for free stream Mach numbers, M_{\infty}=1.9-2.86. Predicted roll moment and longitudinal aerodynamic coefficients were compared with the experimental data at various angles of attack. The computational results are in good agreement with experimental data.

In some fluid dynamics problems, like FLOW stability and transition, accurate solution of mean FLOW is required. While such an accurate solution cannot be obtained by means of ordinary finite difference approximations, spectral approximations are able to surmount. Furthermore, the low inherent dissipation of spectral methods is not enough to stabilize the method in the presence of shocks. The spectral methods with shock-fitting have been shown to solve the in-viscid blunt body problem accurately and efficiently. In addition, errors decay exponentially fast with the increase in the grid points. In this study, the chebyshev spectral collocation method is used to solve Euler equations over cylinder and sphere in a SUPERSONIC FLOW fields. The axisymmetric and non-conservative form of Euler equations is considered as the governing equations. The sensitivity of spectral methods to boundary conditions, which can not be overstated, makes the boundary treatment the most difficult part of the solution. The Rankine-Hugoniot relations are used for shock boundary condition in accordance with a proper compatibility relation, which carry information from the FLOW field to the shock. The shock acceleration is derived similar to the method used by Kopriva but with different formulation to treat the shock boundary condition. Zero normal velocity along with compatibility relations in a matrix form is used as a boundary condition for solid body, which simplifies the implementation. Since the outFLOW is SUPERSONIC (all four characteristics are leaving the FLOW field), no explicit boundary conditions are necessary; therefore the governing equations are used to obtain the boundary variables. The solution is advanced in time using 4th order Runge-Kutta method.Finally, SUPERSONIC FLOWs over cylinder and sphere are solved to show the capability of the present approach. The body surface quantities and the shock shapes compare well with previous investigators. In addition, the accuracy of the spectral collocation method is demonstrated.

In this article, vibration and SUPERSONIC flutter analyses are studied for trapezoidal sandwich panels. Functionally graded trapezoidal panel as well as reinforced sandwich panel by graphene nano platelets are considered. It is assumed that the graphene platelet (GPL) nanofillers are distributed in the matrix either uniformly or non-uniformly in the direction of thickness. UD, FG-X, FG-V, FG-O and FG-A are the distribution patterns of GPLs. Based on the Kant higher-order theories, the dynamic equations of sandwich panels reinforced with graphene nanoplates are obtained using extended Hamilton’ s principle. Dynamic pressure is estimated according to the quasi-stable theory of SUPERSONIC piston. Then, using a transformation of coordinates, the governing equations and boundary conditions are converted from the original coordinates into new computational ones. Finally, the differential squares method (DQM) to obtain the natural frequencies, the shape of the modes, and the critical aerodynamic pressure is used. The effect of different porosity distribution, porosity coefficients, distribution of graphene nanoplates, weight fraction, geometry of graphene nanofillers and geometric dimensions on natural frequencies and system instability behavior are studied.

Aerodynamic simulation of APDS projectile with and without sabot has been conducted here. Due to less weight of APDS projectile in comparison with the projectile, with the same caliber, APDS projectile has higher muzzle velocity, longer range, high penetration capability, and higher impact velocity. Simulation of FLOW around the sabot walls has been carried out in two opening degrees of zero and 75 at SUPERSONIC regime, using the 3D Spalart-Allmaras turbulence model. Problem verification has been tested, using the wind tunnel drag coefficient experimental data at two opening degrees of zero and 75 and close agreements have been obtained. The drag coefficient has been used in the ballistic coefficient calculations, wherein 24 percent improvement has been attained.

This study investigates SUPERSONIC FLOW characteristics over circular and elliptic cones at various angles of attack. Simulations were conducted on the cones with the same base area and length-to-diameter ratio. The elliptic cones considered had axis ratios of 1. 5 and 3. The angle of attack varied from 0o to 50o, with two different Mach numbers (1. 97 and 2. 94) employed for the analysis. The numerical results were compared with the experimental and theoretical findings from existing literature. The results revealed that increasing the ellipticity ratio of the cones resulted in higher lift generation. The pressure distributions on the windward and leeward sides of the cones were also examined. The results demonstrated that elliptic cones outperformed circular cones in terms of lift production, and this advantage increased with higher ellipticity ratios. Specifically, when the ellipticity ratio was increased from 1 to 3, the maximum increase in lift coefficient was 96% and 100% at Mach numbers 2. 94 and 1. 97, respectively. Additionally, by changing the ellipticity ratio from 1 to 1. 5, the maximum gain in the lift-drag ratio was 16% and 22% at Mach numbers 1. 97 and 2. 94, respectively. Notably, an elliptic cone with an ellipticity ratio of 3 achieved a remarkable 46% gain in lift-to-drag ratio compared to a circular cone. However, as the angle of attack increased, a primary bow shock formed on the windward side of the cone, with an embedded shock appearing on the leeward side.