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NASA NTRS1989

Updated users' guide for TAWFIVE with multigrid

A program for the Transonic Analysis of a Wing and Fuselage with Interacted Viscous Effects (TAWFIVE) was improved by the incorporation of multigrid and a method to specify lift coefficient rather than angle-of-attack. A finite volume full potential multigrid method is used to model the outer inviscid flow field. First order viscous effects are modeled by a 3-D integral boundary layer method. Both turbulent and laminar boundary layers are treated. Wake thickness effects are modeled using a 2-D strip method. A brief discussion of the engineering aspects of the program is given. The input, output, and use of the program are covered in detail. Sample results are given showing the effects of boundary layer corrections and the capability of the lift specification method.

Melson, N. Duane↗

NASA NTRS1989

Calculation of reattaching shear layers in divergent channel with a multiple-time-scale turbulence model

Numerical calculations of turbulent reattaching shear layers in a divergent channel are presented. The turbulence is described by a multiple-time-scale turbulence model. The turbulent flow equations are solved by a control-volume based finite difference method. The computational results are compared with those obtained using k-epsilon turbulence models and algebraic Reynolds stress turbulence models. It is shown that the multiple-time-scale turbulence model yields significantly improved computational results than the other turbulence models in the region where the turbulence is in a strongly inequilibrium state.

Kim, S.-W.↗

NASA NTRS1989

Numerical investigation of an internal layer in turbulent flow over a curved hill

The development of an internal layer in a turbulent boundary layer flow over a curved hill is investigated numerically. The turbulence field of the boundary layer flow over the curved hill is compared with that of a turbulent flow over a symmetric airfoil (which has the same geometry as the curved hill except that the leading and trailing edge plates were removed) to study the influence of the strongly curved surface on the turbulence field. The turbulent flow equations are solved by a control-volume based finite difference method. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. Computational results for the mean flow field (pressure distributions on the walls, wall shearing stresses and mean velocity profiles), the turbulence structure (Reynolds stress and turbulent kinetic energy profiles), and the integral parameters (displacement and momentum thicknesses) compared favorably with the measured data. Computational results show that the internal layer is a strong turbulence field which is developed beneath the external boundary layer and is located very close to the wall. Development of the internal layer was more obviously observed in the Reynolds stress profiles and in the turbulent kinetic energy profiles than in the mean velocity profiles. In this regard, the internal layers is significantly different from wall-bounded simple shear layers in which the mean velocity profile characterizes the boundary layer most distinguishably. Development of such an internal layer, characterized by an intense turbulence field, is attributed to the enormous mean flow strain rate caused by the streamline curvature and the strong pressure gradient. In the turbulent flow over the curved hill, the internal layer begin to form near the forward corner of the hill, merges with the external boundary layer, and develops into a new fully turbulent boundary layer as the fluid flows in the downstream direction. For the flow over the symmetric airfoil, the boundary layer began to form from almost the same location as that of the curved hill, grew in its strength, and formed a fully turbulent boundary layer from mid-part of the airfoil and in the downstream region. Computational results also show that the detailed turbulence structure in the region very close to the wall of the curved hill is almost the same as that of the airfoil in most of the curved regions except near the leading edge. Thus the internal layer of the curved hill and the boundary layer of the airfoil were also almost the same. Development of the wall shearing stress and separation of the boundary layer at the rear end of the curved hill mostly depends on the internal layer and is only slightly influenced by the external boundary layer flow.

Kim, S-W.↗

NASA NTRS1990

Calculation of reattaching shear layers in divergent channel with a multiple-time-scale turbulence model

Kim, S.-W.↗

NASA NTRS1991

Viscous computations of cold air/air flow around scramjet nozzle afterbody

The flow field in and around the nozzle afterbody section of a hypersonic vehicle was computationally simulated. The compressible, Reynolds averaged, Navier Stokes equations were solved by an implicit, finite volume, characteristic based method. The computational grids were adapted to the flow as the solutions were developing in order to improve the accuracy. The exhaust gases were assumed to be cold. The computational results were obtained for the two dimensional longitudinal plane located at the half span of the internal portion of the nozzle for over expanded and under expanded conditions. Another set of results were obtained, where the three dimensional simulations were performed for a half span nozzle. The surface pressures were successfully compared with the data obtained from the wind tunnel tests. The results help in understanding this complex flow field and, in turn, should help the design of the nozzle afterbody section.

Baysal, Oktay↗

NASA NTRS1992

Development of a 3-D upwind PNS code for chemically reacting hypersonic flowfields

Two new parabolized Navier-Stokes (PNS) codes were developed to compute the three-dimensional, viscous, chemically reacting flow of air around hypersonic vehicles such as the National Aero-Space Plane (NASP). The first code (TONIC) solves the gas dynamic and species conservation equations in a fully coupled manner using an implicit, approximately-factored, central-difference algorithm. This code was upgraded to include shock fitting and the capability of computing the flow around complex body shapes. The revised TONIC code was validated by computing the chemically-reacting (M(sub infinity) = 25.3) flow around a 10 deg half-angle cone at various angles of attack and the Ames All-Body model at 0 deg angle of attack. The results of these calculations were in good agreement with the results from the UPS code. One of the major drawbacks of the TONIC code is that the central-differencing of fluxes across interior flowfield discontinuities tends to introduce errors into the solution in the form of local flow property oscillations. The second code (UPS), originally developed for a perfect gas, has been extended to permit either perfect gas, equilibrium air, or nonequilibrium air computations. The code solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that was modified to account for real gas effects. The dissipation term associated with this algorithm is sufficiently adaptive to flow conditions that, even when attempting to capture very strong shock waves, no additional smoothing is required. For nonequilibrium calculations, the code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. This code was used to calculate the hypersonic, laminar flow of chemically reacting air over cones at various angles of attack. In addition, the flow around the McDonnel Douglas generic option blended-wing-body was computed and comparisons were made between the perfect gas, equilibrium air, and the nonequilibrium air results.

Tannehill, J. C.↗

NASA NTRS1992

Practical aspects of spatially high accurate methods

The computational qualities of high order spatially accurate methods for the finite volume solution of the Euler equations are presented. Two dimensional essentially non-oscillatory (ENO), k-exact, and 'dimension by dimension' ENO reconstruction operators are discussed and compared in terms of reconstruction and solution accuracy, computational cost and oscillatory behavior in supersonic flows with shocks. Inherent steady state convergence difficulties are demonstrated for adaptive stencil algorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computational intensity is reflected in operation counts. Standard MUSCL differencing is included for comparison. Numerical experiments presented include the Ringleb flow for numerical accuracy and a shock reflection problem. A vortex-shock interaction demonstrates the ability of the ENO scheme to excel in simulating unsteady high-frequency flow physics.

Godfrey, Andrew G.↗

NASA NTRS1992

A three-dimensional upwind PNS code for chemically reacting scramjet flowfields

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional (3D) chemically reacting flow in scramjet (supersonic combustion ramjet) engines. The code is a modification of the 3D upwind PNS (UPS) airflow code which has been extended in the present study to permit internal flow calculations with hydrogen-air chemistry. With these additions, the new code has the capability of computing aerodynamic and propulsive flowfields simultaneously. The algorithm solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that has been modified to account for 'real gas' effects. The fluid medium is assumed to be a chemically reacting mixture of thermally perfect (but calorically imperfect) gases in thermal equilibrium. The new code has been applied to two test cases. These include the Burrows-Kurkov supersonic combustion experiment and a generic 3D scramjet flowfield. The computed results compare favorably with the available experimental data.

Wadawadigi, Ganesh↗

NASA NTRS1993

Higher-order accurate Osher schemes with application to compressible boundary layer stability

Two fourth order accurate Osher schemes are presented which maintain higher order accuracy on nonuniform grids. They use either a conservative finite difference or finite volume discretization. Both methods are successfully used for direct numerical simulations of flat plate boundary layer instability at different Mach numbers. Results of growth rates of Tollmien-Schlichting waves compare well with direct simulations of incompressible flow and for compressible flow with results obtained by solving the parabolic stability equations.

Van Der Vegt, J. J. W.↗

NASA NTRS1993

A comparison of high resolution upwind solvers on 3-D inviscid hypersonic flows

A detailed comparison of numerical results obtained by solving the Euler equations for the inviscid flow over delta wings in reentry configurations is presented. The investigation involves a side-by-side comparison between independently developed upwind Euler solvers at VKI (M3D) and NASA Johnson Space Center (E3D) using identical grids. In both solvers the governing equations are integrated by means of time marching finite volume shock capturing methods, based on a cell centered upwind evaluation of the cell face fluxes and nonlinear limiters. High resolution schemes are obtained via MUSCL characteristic variable extrapolation to ensure total variation diminishing (TVD) properties and therefore monotonic discontinuity capturing. Further comparisons are made with several published results by other authors based on both upwind and central discretizations. The present results contribute in asserting the high resolution upwind TVD schemes as the most reliable numerical technique to handle the strong discontinuities typical of high speed flows. The performances of the two upwind solvers are satisfactory and the numerical results in good agreement. However, the important issue of reaching a grid converged solution for the present complex three-dimensional inviscid flow problems was not achieved.

Manna, M.↗

NASA NTRS1993

Higher-order accurate Osher schemes with application to compressible boundary layer stability

Vandervegt, J. J. W.↗

NASA NTRS1995

Resolution of the buoyancy in the 8-foot high temperature tunnel combustor

Currently, the 8-Foot High Temperature Tunnel (8-Ft. HTT) combustor produces a good profile at only one point (2000 psia and 3650 R with oxygen enrichment). Air is enriched with oxygen (liquid) so that the combustor product gas will contain the volumetric amount of oxygen normally found in air. The oxygen enriched air has a large fraction that is not reacted and flows through the outer periphery of the fuel injector. This ring of cold air in addition to the relatively cold walls of the combustor set up buoyancy forces that produce a segregation of relatively cool gases at the bottom of the combustor exit. The basic problem is to produce a test gas that has uniform properties at all combustor conditions. The combustor temperature may be as high as 3700 R or as low as 2000 R. Combustor pressures can be as high as 3500 psia (no oxygen enrichment) and as low as 600 psia. The segregation is most severe with oxygen enriched air, since its temperature is lower and its density is high. The combustor is lined with nickel 201 and can be operated at about 1600 R maximum. A global mixing process is desired that produces an acceptable profile of temperature, species, and velocity at the exit of the combustor. The ultimate goal is a temperature profile with about 100 R variance and about 2 percent variance in oxygen. The exit total temperature must not be lowered significantly by the mixing apparatus or mechanisms employed. If immersed bodies are used, they must also be kept very hot. All combustor wall modifications must be able to survive the heat and structural conditions of the varied operating conditions. Our approach to resolving this issue is being conducted in three stages: (1) Consider mixing exclusively, (2) Resolve the heat transfer concerns resulting from the chosen mixing strategy, and (3) Solve the material and structural problems resulting from stages (1) and (2). Since the 8-Ft. HTT is unavailable for experimentation, the study is conducted exclusively with computational fluid dynamic (CPD) codes (Fluent/Uns and Rampant 3.1) using unstructured grid through body fitted coordinates. Both CFD codes are general purpose Navier-Stokes solution packages that can solve integral conservation equations for conservation of mass, momentum and energy. The governing equations are discretized using a control-volume finite-element method on unstructured triangular 2-D grids. In the interest of time, a 3-D tetrahedral grid was used to check the 2-D results on one mixing strategy and the 2-D results were confirmed. Preliminary results indicate that excellent mixing can be achieved with a body placed in the center of the flowing hot fluid with a minor modification to the combustor wall similar to a model positioned in the test section of a wind tunnel. The concept here, is to create longitudinal vortices strong enough to bring both fluids into intimate contact with each other near the wall where the cold fluid resides. However, there may be a trade-off in the choice of mixing strategy, heat transfer and structural requirements. Currently, we are examining the more promising geometries for heat transfer concerns and developing strategies for the material of construction of the center body.

Loney, Norman W.↗

NASA NTRS2003

Combustion Of Moving Droplets And Of Droplets Suspended Within A Convective Environment: Transient Numerical Results

The problem considered is that of a single-component liquid fuel (n-heptane) droplet undergoing evaporation and combustion in a hot, convective, low pressure, zero-gravity environment of infinite expanse. For a moving droplet, the relative velocity (U(sub infinity)) between the droplet and freestream is subject to change due to the influence of the drag force on the droplet. For a suspended droplet, the relative velocity is kept constant. The governing equations for the gas-phase and the liquid-phase consist of the unsteady, axisymmetric equations of mass, momentum, species (gas-phase only) and energy conservation. Interfacial conservation equations are employed to couple the two phases. Variable properties are used in the gas- and liquid-phase. Multicomponent diffusion in the gas-phase is accounted for by solving the Stefan-Maxwell equations for the species diffusion velocities. A one-step overall reaction is used to model the combustion. The governing equations are discretized using the finite volume and SIMPLEC methods. A colocated grid is adopted. Hyperbolic tangent stretching functions are used to concentrate grid points near the fore and aft lines of symmetry and at the droplet surface in both the gas- and liquid-phase. The discretization equations are solved using the ADI method with the TDMA used on each line of the two alternating directions. Iterations are performed within each time-step until convergence is achieved. The grid spacing, size of the computational domain and time-step were tested to ensure that all solutions are independent of these parameters. A detailed discussion of the numerical model is given.

Gogos, George↗

NASA NTRS2015

A Radiation Solver for the National Combustion Code

A methodology is given that converts an existing finite volume radiative transfer method that requires input of local absorption coefficients to one that can treat a mixture of combustion gases and compute the coefficients on the fly from the local mixture properties. The Full-spectrum k-distribution method is used to transform the radiative transfer equation (RTE) to an alternate wave number variable, g . The coefficients in the transformed equation are calculated at discrete temperatures and participating species mole fractions that span the values of the problem for each value of g. These results are stored in a table and interpolation is used to find the coefficients at every cell in the field. Finally, the transformed RTE is solved for each g and Gaussian quadrature is used to find the radiant heat flux throughout the field. The present implementation is in an existing cartesian/cylindrical grid radiative transfer code and the local mixture properties are given by a solution of the National Combustion Code (NCC) on the same grid. Based on this work the intention is to apply this method to an existing unstructured grid radiation code which can then be coupled directly to NCC.

National Combustion Code↗

NASA NTRSDate not supplied

Axisymmetric Two-Dimensional Modeling of No Vent Filling of a Cryogenic Tank using Generalized Fluid System Simulation Program

This paper presents preliminary analysis using a finite volume based computational method for network flow analysis for the simulation of chill and fill of a cryogenic tank. An axisymmetric two-dimensional model of a spherical tank was developed using a nodal approach. No Vent Filling (NVF) was accomplished using a Thermodynamic Vent System assisted injector where the injector was cooled by the cold gas generated by Joule-Thompson expansion of the liquid propellant. The numerical model accounts for a) different regimes of pool boiling heat transfer, b) condensation of vapor around spray droplets, and c) condensation of vapor at the interface of the cooled injector and ullage. The numerical predictions of tank pressure, filling rate, and wall temperatures were compared with the test data and one-dimensional (1D) model predictions. It was demonstrated that the axisymmetric 2D model provided a more realistic prediction than the 1D model.

Cryogenics↗

NASA NTRS1991

A new technique for simulating composite material

This project dealt with the development on new methodologies and algorithms for the multi-spectrum electromagnetic characterization of large scale nonmetallic airborne vehicles and structures. A robust, low memory, and accurate methodology was developed which is particularly suited for modern machine architectures. This is a hybrid finite element method that combines two well known numerical solution approaches. That of the finite element method for modeling volumes and the boundary integral method which yields exact boundary conditions for terminating the finite element mesh. In addition, a variety of high frequency results were generated (such as diffraction coefficients for impedance surfaces and material layers) and a class of boundary conditions were developed which hold promise for more efficient simulations. During the course of this project, nearly 25 detailed research reports were generated along with an equal number of journal papers. The reports, papers, and journal articles are listed in the appendices along with their abstracts.

Volakis, John L.↗

NASA NTRS1989

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 2: User's manual

The user options available for running the MHOST finite element analysis package is described. MHOST is a solid and structural analysis program based on the mixed finite element technology, and is specifically designed for 3-D inelastic analysis. A family of 2- and 3-D continuum elements along with beam and shell structural elements can be utilized, many options are available in the constitutive equation library, the solution algorithms and the analysis capabilities. The outline of solution algorithms is discussed along with the data input and output, analysis options including the user subroutines and the definition of the finite elements implemented in the program package.

Nakazawa, Shohei↗

NASA NTRS1988

Computational structural mechanics and fluid dynamics: Advances and trends; Proceedings of the Symposium, Washington, DC, Oct. 17-19, 1988

Recent advances in computational structural and fluid dynamics are discussed in reviews and reports. Topics addressed include fluid-structure interaction and aeroelasticity, CFD techniques for reacting flows, micromechanics, stability and eigenproblems, probabilistic methods and chaotic dynamics, and perturbation and spectral methods. Consideration is given to finite-element, finite-volume, and boundary-element methods; adaptive methods; parallel processing machines and applications; and visualization, mesh generation, and AI interfaces.

Noor, Ahmed K.↗