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NASA NTRS1993

Computation of unsteady shock-induced combustion using logarithmic species conservation equations

Numerical simulations are used to investigate periodic combustion instabilities observed in ballistic-range experiments of blunt bodies flying at supersonic speeds through hydrogen-air mixtures. The computations are validated by comparing experimental shadowgraphs with shadowgraphs created from the computed flowfields and by comparing the experimentally measured instability frequencies with computed frequencies. The numerical simulations use a logarithmic transformation of the species conservation equations as a way to reduce the grid requirements for computing shock-induced combustion. The transformation is applied to the Euler equations coupled to a detailed hydrogen-air chemical reaction mechanism with 13 species and 33 reactions. The resulting differential equations are solved using a finite volume formulation and a two-step predictor-corrector scheme to advance the solution in time. Results are presented and compared for both a flux-vector splitting scheme and an upwind TVD scheme. The computations add insight to the physical processes observed in the experiments and the numerical methods needed to simulate them. The usefulness of the ballistic-range experiments for the validation of numerical techniques and chemical kinetic models is also demonstrated.

Wilson, Gregory J.↗
NASA NTRS1993

Wing flutter boundary prediction using unsteady Euler aerodynamic method

Modifications to an existing 3D implicit upwind Euler/Navier-Stokes code for the aeroelastic analysis of wings are described. These modifications include the incorporation of a deforming mesh algorithm and the addition of the structural equations of motion for their simultaneous time-integration with the governing flow equations. The paper gives a brief description of these modifications and presents unsteady calculations which check the modifications to the code. Euler flutter results for an isolated 45 deg swept-back wing are compared with experimental data for seven freestream Mach numbers which define the flutter boundary over a range of Mach number from 0.499 to 1.14. These comparisons show good agreement in flutter characteristics for freestream Mach numbers below unity. For freestream Mach numbers above unity, the computed aeroelastic results predict a premature rise in the flutter boundary as compared with the experimental boundary. Steady and unsteady contours of surface Mach number and pressure are included to illustrate the basic flow characteristics of the time-marching flutter calculations and to aid in identifying possible causes for the premature rise in the computational flutter boundary.

Lee-Rausch, Elizabeth M.↗
NASA NTRS1991

Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver

A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.

Kim, S.-W.↗
NASA NTRS1993

Multiblock Navier-Stokes solutions about the F/A-18 wing-LEX-fuselage configuration

Three-dimensional thin-layer Navier-Stokes computations are presented for the F/A-18 configuration. The modeled configuration includes an accurate surface representation of the fuselage, leading-edge extension (LEX), and wing, both with and without leading-edge flap deflection. A multiblock structured grid strategy is employed to decompose the computational flowfield domain around the subject configuration. Steady-state solutions are obtained from an algorithm that solves the compressible Navier-Stokes equations with an upwind-biased, flux-difference splitting approach. The results presented are based on a fully turbulent flow assumption, simulating the high Reynolds number flow conditions that correspond to a recent FI A-18 flight experiment. Good agreements between the computations and the flight test results are obtained for both surface flow patterns as well as surface pressure distributions. Furthermore, a correlation between the computed LEX vortex-core and the flight test results, observed by way of smoke visualization, is also presented.

Aircraft configurations↗
NASA NTRS1993

A numerical treatment of geodynamic viscous flow problems involving the advection of material interfaces

Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Lenardic, A.↗
NASA NTRS1993

Application of the multigrid solution technique to hypersonic entry vehicles

A multigrid solution procedure has been incorporated in a version of the Langley Aerothermodynamic Upwind Relaxation Algorithm. The multigrid scheme is based on the Full Approximation Storage approach and uses Full Multigrid to obtain a well defined fine mesh starting solution. Predictions were obtained using standard transfer operators and a 'V-cycle' was used to control grid sequencing. Computed hypersonic flow solutions compared with experimental data for a 15 degree sphere cone, blended-wing body, and shuttle-like geometries are presented. It is shown that the algorithm accurately predicts heating rates, and when compared with the single grid algorithm computes solutions in one-third the computational time.

Greene, Francis A.↗
NASA NTRS1993

Aerothermodynamics of a MESUR Martian entry

Computational fluid dynamics models for the thermodynamics and transport properties used in an equilibrium version of the Langley Aerothermodynamics Upwind Relaxation Algorithm (LAURA) for Martian Atmospheric entries are described. In addition, the physical models used in a nonequilibrium version of LAURA for Martian-entry flows are described. Uncertainties exist in defining constants used in the transport properties for the equilibrium model and in many of the physical models for the nonequilibrium version. Solutions from the two codes using the best available constants are examined at the Martian-entry conditions characteristic of the Mars Environmental Survey (MESUR) mission. While the flowfields are near thermal equilibrium, chemical nonequilibrium effects are present in the entry cases examined. Convective heating at the stagnation point for these flows (assuming fully catalytic wall boundary conditions) is approximately 100 W/sq cm. Radiative heating is negligible.

Mitcheltree, R. A.↗
NASA NTRS1991

Non equilibrium flow in an arc-jet

A method for simulating the flow of a nitrogen plasma in thermodynamic nonequilibrium is described. The method relies on the modeling of the relevant physical and chemical phenomena and on a fully coupled implicit finite volume upwind numerical approximation of the governing equations. The results agree with experimental data.

Rostand, P.↗
NASA NTRS1993

A multiblock analysis for shuttle orbiter re-entry heating from Mach 24 to Mach 12

A multiblock, laminar heating analysis for the shuttle orbiter at three trajectory points ranging from Mach 24.3 to Mach 12.86 on re-entry is described. The analysis is performed using the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) with both a seven species chemical nonequilibrium model and an equilibrium model. A finite-catalytic-wall model appropriate for shuttle tiles at a radiative equilibrium wall temperature is applied. Computed heating levels are generally in good agreement with the flight data though a few rather large discrepancies remain unexplained. The multiblock relaxation strategy partitions the flowfield into manageable blocks requiring a fraction of the computational resources (time and memory) required by a full domain approach. In hot, the computational cost for a solution at even a single trajectory point would be prohibitively expensive at the given resolution without the multiblock approach. Converged blocks are reassembled to enable a fully coupled converged solution over the entire vehicle, starting from a nearly converged initial condition.

Gnoffo, Peter A.↗
NASA NTRS1993

Two-dimensional CFD modeling of wave rotor flow dynamics

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. The Roe approximate Riemann solution scheme or the computationally less expensive Advection Upstream Splitting Method (AUSM) flux-splitting scheme are used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passage and the distribution of flow variables in the stationary inlet port region.

Welch, Gerard E.↗
NASA NTRS1993

Directionally adaptive finite element method for multidimensional Euler and Navier-Stokes equations

A directionally adaptive finite element method for multidimensional compressible flows is presented. Quadrilateral and hexahedral elements are used because they have several advantages over triangular and tetrahedral elements. Unlike traditional methods that use quadrilateral/hexahedral elements, our method allows an element to be divided in each of the three directions in 3D and two directions in 2D. Some restrictions on mesh structure are found to be necessary, especially in 3D. The refining and coarsening procedures, and the treatment of constraints are given. A new implementation of upwind schemes in the constrained finite element system is presented. Some example problems, including a Mach 10 shock interaction with the walls of a 2D channel, a 2D viscous compression corner flow, and inviscid and viscous 3D flows in square channels, are also shown.

Tan, Zhiqiang↗
NASA NTRS1993

Surface boundary conditions for the numerical solution of the Euler equations

We consider the implementation of boundary conditions at solid walls in inviscid Euler solutions by upwind, finite-volume methods. We review some current methods for the implementation of surface boundary conditions and examine their behavior for the problem of an oblique shock reflecting off a planar surface. We show the importance of characteristic boundary conditions for this problem and introduce a method of applying the classical flux-difference splitting of Roe as a characteristic boundary condition. Consideration of the equivalent problem of the intersection of two (equal and opposite) oblique shocks was very illuminating on the role of surface boundary conditions for an inviscid flow and led to the introduction of two new boundary-condition procedures, denoted as the symmetry technique and the curvature-corrected symmetry technique. Examples of the effects of the various surface boundary conditions considered are presented for the supersonic blunt body problem and the subcritical compressible flow over a circular cylinder. Dramatic advantages of the curvature-corrected symmetry technique over the other methods are shown, with regard to numerical entropy generation, total pressure loss, drag and grid convergence.

Dadone, A.↗
NASA NTRS1993

Effects of spatial order of accuracy on the computation of vortical flowfields

The effect of the order-of-accuracy, used for the spatial discretization, on the resolution of the leading edge vortices over sharp-edged delta wings is investigated. The flowfield is computed using a viscous/inviscid zonal approach. The viscous flow in the vicinity of the wing is computed using the conservative formulation of the compressible, thin-layer Navier-Stokes equations. The leeward-side vortical flowfield and the other flow regions away from the surface are computed as inviscid. The time integration is performed with both an explicit fourth-order Runge-Kutta scheme and an implicit, factorized, iterative scheme. High-order-accurate inviscid fluxes are computed using both a conservative and a non-conservative (primitive variable) formulation. The nonlinear, inviscid terms of the primitive variable form of the governing equations are evaluated with a finite-difference numerical scheme based on the sign of the eigenvalues. High-order, upwind-biased, finite difference formulas are used to evaluate the derivatives of the nonlinear convective terms. Computed results are compared with available experimental data, and comparisons of the flowfield in the vicinity of the vortex cores are presented.

Ekaterinaris, J. A.↗
NASA NTRS1993

Extension of state-vector splitting to the Navier-Stokes equations

A multi-dimensional upwind scheme for solving the Euler equations has been extended to solve the Navier-Stokes equations. These methods share the property of not requiring body-fitted computational grids. A time advance scheme which is second-order accurate in time and space has been developed for use in conjunction with state-vector splitting to accurately resolve regions with significant gradients in flow quantities. The scheme has been tested on several simple viscous flow problems for which analytic solutions are known; the agreement of computation with theory is excellent.

Gooch, Carl F.↗
NASA NTRS1993

A multidomain spectral method for viscous compressible flows

We present a new multidomain spectral method for the solution of the compressible Navier-Stokes equations. In the subdomain interiors, Chebyshev spectral collocation is used. At interfaces, the advective terms are upwinded and the viscous terms are treated by a penalty method. The method is applied to the solution of a viscous hypersonic flow over a blunt body.

Kopriva, David A.↗
NASA NTRS1993

Time-accurate simulation of a self-excited oscillatory supersonic external flow with a multi-block solution-adaptive mesh algorithm

Results are presented of an investigation of the time-accurate simulation of supersonic unsteady flow oscillations over spike-tipped bodies using the multistage Runge-Kutta scheme coupled with a dynamic solution-adaptive grid algorithm modified for multiblock capabilities. The inviscid fluxes are described by a modified advective upwind split method to obviate the need for artificial dissipation. If a time-varying, solution-adaptive mesh algorithm is incorporated, resolution of the details of the unsteady spike-tipped body flow is improved. The adaptive algorithm is also shown to resolve multiple and diverse features of the flow simultaneously, with the adapted regions in the mesh convecting with these features as they translate.

Ingram, Clint L.↗
NASA NTRS1993

A new flux splitting scheme

A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of Roe's solver in the Euler and Navier-Stokes solutions performed in this study. The scheme is robust and converges as fast as the Roe splitting. An approximately defined cell-face advection Mach number is proposed using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as Advection Upstream Splitting Method (AUSM). A new pressure splitting is introduced which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids.

Liou, Meng-Sing↗
NASA NTRS1993

Supersonic vortex breakdown over a delta wing in transonic flow

The effects of freestream Mach number and angle of attack on the leading-edge vortex breakdown due to the terminating shock on a 65-degree, sharp-edged, cropped delta wing are investigated computationally, using the time-accurate solution of the laminar unsteady compressible full Navier-Stokes equations with the implicit upwind flux-difference splitting, finite-volume scheme. A fine O-H grid consisting of 125 x 85 x 84 points in the wrap-around, normal, and axial directions, respectively, is used for all the flow cases. Keeping the Reynolds number fixed at 3.23 x 10 exp 6, the Mach number is varied from 0.85 to 0.9 and the angle of attack is varied from 20 to 24 deg. The results show that, at 20-deg angle of attack, the increase of the Mach number from 0.85 to 0.9 results in moving the location of the terminating shock downstream. The results also show that, at 0.85 Mach number, the increase of the angle of attack from 20 to 24 deg results in moving the location of the terminating shock upstream. The results are in good agreement with the experimental data.

Kandil, Hamdy A.↗