Parabolized Navier-Stokes Code Research Articles

Parabolized Navier-Stokes Algorithm for Solving Supersonic Flows with Upstream Influences

A new parabolized Navier ‐Stokes (PNS) algorithm has been developed to efe ciently compute supersonic e ows with embedded regions that produce upstream effects. Innovative techniques are used to automatically detect and measure the extent of the embedded regions. Within the embedded regions, the PNS equations are globally iterated to duplicate the results that would be obtained with the complete Navier ‐Stokes (NS) equations. Once an embedded region is computed, the algorithm returns to the standard space-marching PNS mode until the next embedded region is encountered. This procedure has been successfully incorporated into NASA’ s upwind PNS code and it has been validated by its application to several two-dimensional test cases. All of these test cases include embedded regions that produce signie cant upstream effects. The present numerical results arein excellent agreement with previous NS computations and experimental data. In addition, these calculations demonstrate the signie cant reduction in computer time and storage that can be achieved by the use of this approach.

Parabolized Navier--Stokes code for hypersonic flows in thermo-chemical equilibrium or nonequilibrium

A parabolized Navier–Stokes (PNS) code has been developed to efficiently compute three-dimensional flows in thermo-chemical equilibrium or nonequilibrium. The new code is an extension of NASA’s three-dimensional upwind PNS (UPS) code. The chemical, vibrational, and electronic nonequilibrium effects have been incorporated via a loosely-coupled approach. The new code has been used to compute air flows in thermo-chemical equilibrium and nonequilibrium through expanding hypersonic nozzles. The results are in good agreement with existing numerical and experimental results.

Joint computational/experimental aerodynamics research on hypersonicvehicle. II - Computational results

Parabolized and iterative Navier-Stokes codes are used to predict flowfield solutions around a hypersonic vehicle. Aerodynamic force and moment predictions from the codes are compared with experimental data from the Sandia National Laboratories Mach 8 wind tunnel. The comparisons are made on a spherically blunted cone with a slice parallel to the body axis. On the slice portion of the vehicle, a flap can be attached so that deflection angles of 10, 20, and 30 deg can be obtained. The Sandia parabolized Navier-Stokes code is used to generate solutions for the sliced vehicle with no flap. For the vehicle with a flap, axially separated flow occurs, and a time iterative Navier-Stokes code is used to provide comparisons with the data. Aerodynamic force and moment comparisons are made for laminar flow, and an ideal gas is assumed in the calculations. A detailed study of grid convergence is presented to determine the accuracy of the numerical solutions. Predictions obtained from the codes show very good agreement with the experimental data for force and moment coefficients, except for large flap deflections.

Aerodynamic characteristics of a family of cone-cylinder-flare projectiles

A systematic study of a number of flare-stabilized projectile geometries has been undertaken at the U.S. Army Ballistic Research Laboratory (BRL). Ten projectile configurations having identical forebodies and a variety of flares were tested in the BRL Aerodynamics Ballistic Range, and the results were compared to numerical computations based on two design codes and a parabolized Navier-Stokes (PNS) code. The design codes, in general, gave good results. The PNS code complimented these results by providing more details on the development of the aerodynamic forces. The results show the drag and stability tradeoffs involved for the different configurations. This information can be used to tailor the flare geometry to meet future mission requirements.

Development of a three-dimensional upwind parabolized Navier-Stokes code

Development of a three-dimensional upwind parabolized Navier-Stokes code

Calculation of internal flows using a single-pass, parabolized Navier-Stokes analysis

A single-pass, subsonic parabolized Navier-Stokes (PNS) procedure is developed to analyze three-dimensional viscous internal flows. Elliptic effects are incorporated by initializing the PNS code with the streamwise pressure gradient distribution obtained from a coarse grid Euler calculation. When the Euler code incorporates the transport of a «viscous-like» inlet vorticity profile, the rotational invisicid pressure distribution provides a good initialization for the single-pass PNS procedure

Upwind parabolized Navier-Stokes code for chemically reacting flows

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous, chemically reacting flow around two-dimensional or axisymmetric bodies. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence et al. (1986). The upwind algorithm is based on Roe's flux-difference splitting scheme which has been modified to account for real gas effects. The algorithm solves the gas dynamic and species continuity equations in a 'loosely' coupled manner. The new code has been validated by computing the laminar flow (at free stream Mach number 25) of chemically reacting air over a wedge and a cone. The results of these computations are compared with the results from a centrally-differenced, fully coupled, nonequilibrium PNS code. The agreement is excellent, except in the vicinity of the shock wave where the present code exhibits superior shock capturing capabilities.

Three-dimensional upwind parabolized Navier-Stokes code for real gasflows

A real gas, upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional hypersonic flow of equilibrium air around various body shapes. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence et al. (1986). The upwind algorithm is based on Roe's (1981) flux-difference splitting scheme which has been modified to account for real gas effects using the nearly exact approach of Vinokur and Liu (1988). Simplified curve fits are employed to obtain the thermodynamic and transport properties of equilibrium air. The new code has been validated by computing the M-infinity = 25 laminar flow of air over cones at various angles of attack. The results of these computations are compared with the results from a conventional centrally-differenced, real gas PNS code and the previous axisymmetric, upwind, real gas code. The agreement is excellent in all cases.

Hypersonic parabolized Navier-Stokes code validation on a sharp nosecone

Perfect gas computational results from a newly developed parabolized Navier-Stokes (PNS) solver based on an upwind/relaxation numerical scheme are compared with an existing set of experimental laminar results for a 10-deg half-angle circular cone at M f =1.95. Comparisons were performed with surface pressure and heat-transfer data, and with flowfield pitpt measurements. The PNS code predicted the surface quantities accurately up through 20-deg angle of attack including crossflow separation, and the code correctly defined the location of the bow shock and the edge of the viscous boundary region. The importance of cell Reynolds number and grid density to the accurate prediction of the flowfield is examined through numerical examples.

A new PNS code for chemical nonequilibrium flows

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic laminar flow of a multicomponent, chemically reacting mixture of thermally perfect gases over two-dimensional and axisymmetric bodies. The new PNS code solves the gas dynamic and species conservation equations in a coupled manner using a noniterative, implicit, space-marching finite-difference method. The conditions for well-posedness of the space-marching method have been derived from an eigenvalue analysis of the governing equations. The code has been used to compute hypersonic laminar flow of chemically reacting air over wedges and cones. The results of these computations are in good agreement with the results of reacting boundary-layer calculations.

Real gas flows over complex geometries at moderate angles of attack

N simulation of supersonic and hypersonic flows over arbitrary geometries at moderate angles of attack is presented in this paper. The different geometries considered for analysis include a sphere-cone-cylinder-flare, a blunt-nosed inlet, and a 7-deg half-angle spherically blunted cone. The three-dimensional flowfields over these geometries are analyzed by a parabolized Navier-Stokes code (HYTAC) and a new viscous shock-layer code (VSLET), and the results are compared. Both laminar and turbulent flowfield results for both perfect gas and equilibrium air are presented. In general the surface pressure distributions are in good agreement, whereas the heat-transfer results differ depending on the differencing scheme used in the calculation of gradients and turbulent modeling. Aerodynamic force and moment coefficients are presented for some typical cases.

Hypersonic viscous flows past general bodies at angle of attack and yaw

Computational results of hypersonic viscous flows over blunt-nosed complex re-entry bodies are presented. An implicit iterative numerical scheme at each marching step is used to solve the parabolized Navier-Stokes (PNS) equations. An existing PNS code has been extended to treat nonaxisymmetric bodies at angle of attack and yaw, multiconic bodies with spin, surface mass transfer, and adiabatic wall conditions. Boundary conditions take into account the periodic condition around the body due to the yaw or spin, and the mass-transfer and/or spin effects at the body surface. The computational results presented include surface-measurable quantities and aerodynamic force and moment coefficients for complex geometries; available data were used for comparison. Grid-size effects on the accuracy of the Magnus force components due to spin are also discussed.