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NASA NTRS1984

Numerical calculations of complex Mach reflection

Numerical simulations of the interaction of a planar blast wave with a compression ramp are presented. The split coefficient matrix (SCM) method in conjunction with boundary shock and floating discontinuity-fitting procedures was employed to obtain the time-asymptotic solutions of the two-dimensional, unsteady Euler equations. The solutions were computed for the complex Mach reflection (CMR) regime of the shock diffraction problem in an attempt to explore the basic physical process governing the evolution of an incipient second Mach stem and the associated topological changes. Numerical results were obtained for shock diffraction over a 40 degree ramp with varying incident shock Mach numbers. The validity of the present approach has been substantiated by experimental observations and earlier numerical calculations.

Yamamoto, O.↗

NASA NTRS1988

A comparative study and validation of upwind and central-difference Navier-Stokes codes for high-speed flows

A comparative study was made using 4 different computer codes for solving the compressible Navier-Stokes equations. Three different test problems were used, each of which has features typical of high speed internal flow problems of practical importance in the design and analysis of propulsion systems for advanced hypersonic vehicles. These problems are the supersonic flow between two walls, one of which contains a 10 deg compression ramp, the flow through a hypersonic inlet, and the flow in a 3-D corner formed by the intersection of two symmetric wedges. Three of the computer codes use similar recently developed implicit upwind differencing technology, while the fourth uses a well established explicit method. The computed results were compared with experimental data where available.

Rudy, David H.↗

NASA NTRS1989

Control-volume based Navier-Stokes equation solver valid at all flow velocities

A control-volume based finite difference method to solve the Reynolds averaged Navier-Stokes equations is presented. A pressure correction equation valid at all flow velocities and a pressure staggered grid layout are used in the method. Example problems presented herein include: a developing laminar channel flow, developing laminar pipe flow, a lid-driven square cavity flow, a laminar flow through a 90-degree bent channel, a laminar polar cavity flow, and a turbulent supersonic flow over a compression ramp. A k-epsilon turbulence model supplemented with a near-wall turbulence model was used to solve the turbulent flow. It is shown that the method yields accurate computational results even when highly skewed, unequally spaced, curved grids are used. It is also shown that the method is strongly convergent for high Reynolds number flows.

Kim, S.-W.↗

NASA NTRS1989

Supersonic flow computations by two-equation turbulence modeling

In the present work a solver for the Reynolds averaged compressible Navier-Stokes equations, to compute high speed turbulent flows characterized by interacting shock waves and viscous layers, is presented. A k-epsilon turbulence model that accounts for compressibility effects is developed. The numerical algorithm is based on a finite volume multistage Runge Kutta technique that is explicit for the solution of the mean flow variables, and implicit for the solution of the k-epsilon equations. The model is validated by extensive comparison with experimental results of flows over compression ramps characterized by interacting shock waves/boundary layers.

Grasso, Francesco↗

NASA NTRS1989

A validation study of four Navier-Stokes codes for high-speed flows

A code validation study has been conducted for four different codes for solving the compressible Navier-Stokes equations. Computations for a series of nominally two-dimensional high-speed laminar separated flows were compared with detailed experimental shock-tunnel results. The shock wave-boundary layer interactions considered were induced by a compression ramp in one case and by an externally-generated incident shock in the second case. In general, good agreement was reached between the grid-refined calculations and experiment for the incipient- and small-separation conditions. For the most highly separated flow, three-dimensional calculations which included the finite-span effects of the experiment were required in order to obtain agreement with the data. The finite-span effects were important in determining the extent of separation as well as the time required to establish the steady-flow interaction. The results presented provide a resolution of discrepancies with the experimental data encountered in several recent computational studies.

Rudy, David H.↗

NASA NTRS1990

An upwind-biased, point-implicit relaxation algorithm for viscous, compressible perfect-gas flows

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, compressible, perfect-gas flows is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. Viscous terms are discretized using central differences. The relaxation strategy is well suited for computers employing either vector or parallel architectures. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large, block tri-diagonal systems. Convergence rates and grid refinement studies are conducted for Mach 5 flow through an inlet with a 10 deg compression ramp and Mach 14 flow over a 15 deg ramp. Predictions for pressure distributions, surface heating, and aerodynamics coefficients compare well with experiment data for Mach 10 flow over a blunt body.

Gnoffo, Peter A.↗

NASA NTRS1989

A comparative study of Navier-Stokes codes for high-speed flows

A comparative study was made with four different codes for solving the compressible Navier-Stokes equations using three different test problems. The first of these cases was hypersonic flow through the P8 inlet, which represents inlet configurations typical of a hypersonic airbreathing vehicle. The free-stream Mach number in this case was 7.4. This 2-D inlet was designed to provide an internal compression ratio of 8. Initial calculations were made using two state-of-the-art finite-volume upwind codes, CFL3D and USA-PG2, as well as NASCRIN, a code which uses the unsplit finite-difference technique of MacCormack. All of these codes used the same algebraic eddy-viscosity turbulence model. In the experiment, the cowl lip was slightly blunted; however, for the computations, a sharp cowl leading edge was used to simplify the construction of the grid. The second test problem was the supersonic (Mach 3.0) flow in a three-dimensional corner formed by the intersection of two wedges with equal wedge angles of 9.48 degrees. The flow in such a corner is representative of the flow in the corners of a scramjet inlet. Calculations were made for both laminar and turbulent flow and compared with experimental data. The three-dimensional versions of the three codes used for the inlet study (CFL3D, USA-PG3, and SCRAMIN, respectively) were used for this case. For the laminar corner flow, a fourth code, LAURA, which also uses recently-developed upwind technology, was also utilized. The final test case is the two-dimensional hypersonic flow over a compression ramp. The flow is laminar with a free-stream Mach number of 14.1. In the experiment, the ramp angle was varied to change the strength of the ramp shock and the extent of the viscous-inviscid interaction. Calculations were made for the 24-degree ramp configuration which produces a large separated-flow region that extends upstream of the corner.

Rudy, David H.↗

NASA NTRS1991

Radiative interactions in chemically reacting supersonic internal flows

The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with finite-rate chemistry and radiation for hydrogen-air systems. The chemistry source terms in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed flow in a channel with a ten-degree compression ramp. Three different chemistry models are used, accounting for increasing number of reactions and participating species. Two chemistry models assure nitrogen as inert, while the third model accounts for nitrogen reactions and NO(x) formation. The tangent slab approximation is used in the radiative flux formulation. A pseudo-gray model is used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interactions vary substantially, depending on reactions involving HO2 and NO species and that this can have a significant influence on the flowfield.

Tiwari, S. N.↗

NASA NTRS1991

Computation of laminar viscous-inviscid interactions in high-speed internal flows

A review is given of computations for a series of nominally 2-D laminar viscous-inviscid interactions. Comparisons were made with detailed experimental shock tunnel results. The shock wave boundary layer interactions considered were induced by a compression ramp in one case and by an externally generated incident shock in the second case. In general, good agreement was reached between the grid refined calculations and experiment for the incipient and small separation conditions. For the highly separated flow, 3-D calculations which included the finite span effects of the experiment were required in order to obtain agreement with the data.

Rudy, David H.↗

NASA NTRS1991

An effective multigrid method for high-speed flows

The use is considered of a multigrid method with central differencing to solve the Navier-Stokes equations for high speed flows. The time dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time stepping and variable coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for 2-D laminar flow over a circular cylinder and a 15 deg compression ramp.

Swanson, R. C.↗

NASA NTRS1991

Investigation of radiative interactions in supersonic internal flows

Analyses and numerical procedures are presented to study the radiative interactions of absorbing emitting species in chemically reacting supersonic flow in various ducts. The 2-D time dependent Navier-Stokes equations in conjunction with radiative flux equation are used to study supersonic flows undergoing finite rate chemical reaction in a hydrogen air system. The specific problem considered is the flow of premixed radiating gas between parallel plates. Specific attention was directed toward studying the radiative contribution of H2O, OH, and NO under realistic physical and flow conditions. Results are presented for the radiative flux obtained for different gases and for various combination of these gases. The problem of chemically reacting and radiating flows was solved for the flow of premixed hydrogen-air through a 10 deg compression ramp. Results demonstrate that the radiative interaction increases with an increase in pressure, temperature, amount of participating species, plate spacing, and Mach number. Most of the energy, however, is transferred by convection in the flow direction. In general the results indicate that radiation can have a significant effect on the entire flow field.

Tiwari, Surendra N.↗

NASA NTRS1991

Radiative interactions in a hydrogen-fueled supersonic combustor

The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with finite-rate chemistry and radiation, for hydrogen-air systems. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed flow in a channel with a 10-deg compression ramp. Three different chemistry models are used, accounting for increasing number of reactions and participating species. Two chemistry models assume nitrogen as inert, while the third model accounts for nitrogen reactions and NO(x) formation. The tangent slab approximation is used in the radiative flux formulation. A pseudogray model is used to represent the absorption-emission characteristics of the participating species. Results otained for specific conditions indicate that the radiative interactions vary substantially, depending on reactions involving HO2 and NO species, and that this can have a significant influence on the flowfield.

Chandrasekhar, R.↗

NASA NTRS1991

Mach 6.5 air induction system design for the Beta II Two-Stage-to-Orbit booster vehicle

A preliminary, two-dimensional, mixed compression air induction system is designed for the Beta II Two-Stage-to-Orbit booster vehicle to minimize installation losses and efficiently deliver the required airflow. Design concepts, such as an external isentropic compression ramp and a bypass system, are developed and evaluated for performance benefits. The design is optimized by maximizing installed propulsion/vehicle system performance, and the resulting system design operating characteristics and performance are presented. The air induction system design has significantly lower transonic drag than similar designs, and only requires approximately 1/3 of the bleed extraction. In addition, the design efficiently provides the integrated system required airflow, while maintaining adequate levels of total pressure recovery. The excellent performance of this highly integrated air induction system is essential for the successful completion of the Beta II booster vehicle mission.

Midea, Anthony C.↗

NASA NTRS1991

Mach 6.5 air induction system design for the Beta 2 two-stage-to-orbit booster vehicle

A preliminary, two-dimensional, mixed compression air induction system is designed for the Beta II Two Stage to Orbit booster vehicle to minimize installation losses and efficiently deliver the required airflow. Design concepts, such as an external isentropic compression ramp and a bypass system were developed and evaluated for performance benefits. The design was optimized by maximizing installed propulsion/vehicle system performance. The resulting system design operating characteristics and performance are presented. The air induction system design has significantly lower transonic drag than similar designs and only requires about 1/3 of the bleed extraction. In addition, the design efficiently provides the integrated system required airflow, while maintaining adequate levels of total pressure recovery. The excellent performance of this highly integrated air induction system is essential for the successful completion of the Beta II booster vehicle mission.

Midea, Anthony C.↗

NASA NTRS1992

Comparison between computational and experimental data for a hypersonic laser propelled vehicle

A 3-D axisymmetric hypersonic engine inlet was investigated using PARC2D, an ideal gas Computational Fluid Dynamics code. The code was used to predict the results of tests conducted in the Rensselaer Polytechnic Institute Hypersonic Shock Tunnel which measured surface and pitot pressures, and shock positions (through Schlieren photography) at freestream Mach numbers of 10, 13, and 15. A strong viscous/shock interaction was observed in both the experiment and the CFD results, due to the model's parabolic compression ramp. Good agreement was found between the experimental results and the CFD solution both for surface pressures and shock positions. Agreement between pitot pressures was less reliable.

Messitt, D. G.↗

NASA NTRS1993

Supersonic boundary-layer flow turbulence modeling

Baldwin-Lomax and kappa-epsilon turbulence models were modified for use in Navier-Stokes numerical computations of Mach 2.9 supersonic turbulent boundary layer flows along compression ramps. The computational results of Reynolds shear stress profiles were compared with experimental data. The Baldwin-Lomax model was modified to account for the Reynolds shear stress amplification within the flow field. A hybrid kappa-epsilon model with viscous sublayer turbulence treatment was constructed to predict the Reynolds shear stress profiles within the entire flow field. These modified turbulence models were effective for the computations of the surface pressure and the skin friction factor variations along an 8 deg ramp surface. The hybrid kappa-epsilon model could improve the predictions of the Reynolds shear stress profile and the skin friction factor near the corner of a 16 deg ramp.

Wang, Chi-Rong↗

NASA NTRS1992

An effective multigrid method for high-speed flows

Swanson, R. C.↗

NASA NTRS1992

An implicit multigrid scheme for hypersonic strong-interaction flowfields

An implicit multigrid method for the compressible Navier-Stokes equations is applied to a series of two-dimensional, steady, laminar hypersonic flows over a compression ramp, including both attached and separated flow conditions. The algorithm uses upwind-biased differencing for the convective and pressure terms and central differencing for the shear-stress and heat-transfer terms. An implicit spatially factored scheme is used to advance the solution in terms on a given mesh, and a V-cycle multigrid strategy is used to accelerate convergence. The multigrid algorithm provided an order of magnitude decrease in the computational time required to obtain a converged position of the separation location and enabled a substantially grid-independent result to be obtained for each of the flows considered.

Thomas, James L.↗