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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Spectral multi-domain for large-scale fluid dynamic simulations

A number of successful applications of a spectral collocation method extended by a multi-domain patching technique are shown. The multi-domain technique can be used to improve resolution for problems with widely disparate scales, and to reduce the ill-conditioning of the spectral operators for problems in which a large number of points are required for distributed resolution. A new nonreflecting outflow boundary treatment for unsteady transition-to-turbulence simulations is also presented, which relies on the multi-domain technique. The role of multi-domain in improving the efficiency of such calculations is discussed.

Streett, C. L.↗
NASA NTRS1992

A multi-domain method for subsonic viscous flows

We have developed a Schwarz type domain decomposition method for a pressure base, two- and three-dimensional Navier-Stokes solver. This technique allows one to partition a flow path, which can be characterized by complex geometry and/or complicated flow physics, into smaller sub-domains according to the local geometric simplicity or estimated flow scales. We can, then, sweep the sub-domains in some order and solve the Navier-Stokes equations using as boundary conditions, along the domain interfaces, the Dirichlet conditions which are taken from the most recent update of the solution in the adjacent neighboring domains. With this technique, one can minimize the adverse effects caused by grid skewness and the stiffness problem caused by disparate flow scales. Here, we report the results of a few fundamental flow cases to demonstrate that a judicious use of the multi-domain method can offer a significant convergence acceleration over the traditional one-domain method. This method can be extended to exploit the architecture of a parallel computer to further improve the speed.

Chan, Daniel C.↗
NASA NTRS1986

A spectral multi-domain technique with application to generalized curvilinear coordinates

Spectral collocation methods have proven to be efficient discretization schemes for many aerodynamic and fluid mechanic problems. The high order accuracy and resolution shown by these methods allows one to obtain engineering accuracy solutions on coarse meshes, or alternatively, to obtain solutions with very small error. One drawback to these techniques was the requirement that a complicated physical domain must map into a simple computational domain for discretization. This mapping must be smooth if the high order accuracy and expontential convergence rates associated with spectral methods are to be preserved. Additionally even smooth stretching transformations can decrease the accuracy of a spectral method, if the stretching is severe. A further difficulty with spectral methods was in their implementation on parallel processing computers, where efficient spectral algorithms were lacking. The above restrictions are overcome by splitting the domain into regions, each of which preserve the advantages of spectral collocation, and allow the ratio of the mesh spacing between regions to be several orders of magnitude higher than allowable in a single domain. Such stretchings would be required to resolve the thin viscous region in an external aerodynamic problem. Adjoining regions are interfaced by enforcing a global flux balance which preserves high-order continuity of the solution, regardless of the type of the equations being solved.

Macaraeg, M. G.↗
NASA NTRS1987

An analysis of artificial viscosity effects on reacting flows using a spectral multi-domain technique

Standard techniques used to model chemically-reacting flows require an artificial viscosity for stability in the presence of strong shocks. The resulting shock is smeared over at least three computational cells, so that the thickness of the shock is dictated by the structure of the overall mesh and not the shock physics. A gas passing through a strong shock is thrown into a nonequilibrium state and subsequently relaxes down over some finite distance to an equilibrium end state. The artificial smearing of the shock envelops this relaxation zone which causes the chemical kinetics of the flow to be altered. A method is presented which can investigate these issues by following the chemical kinetics and flow kinetics of a gas passing through a fully resolved shock wave at hypersonic Mach numbers. A nonequilibrium chemistry model for air is incorporated into a spectral multidomain Navier-Stokes solution method. Since no artificial viscosity is needed for stability of the multidomain technique, the precise effect of this artifice on the chemical kinetics and relevant flow features can be determined.

Macaraeg, M. G.↗
NASA NTRS1987

An analysis of artificial viscosity effects on reacting flows using a spectral multi-domain technique

Analytical and experimental techniques for modeling the aerothermodynamics of hypersonic flight are assessed, together with the problems which will be encountered in developing reusable hypersonic vehicles. Emphasis is placed on a numerical coupling between a nonequilibrium chemistry model and hypersonic flow kinematics. Finite difference and finite element descriptions of flow fields in which molecules encounter a shock wave and undergo various motion (and thereby energy) transformations are discussed. The effects of artificial smearing of the shock wave are considered in terms of the resulting effects on the distribution of the energies and chemical composition of the transition region. Results are provided from schlieren photographs of shock-tube experiments, Navier-Stokes calculations of axisymmetric flow over a conical body, and calculations using a spectral multidomain approach for chemically reacting flows.

Macaraeg, Michele G.↗
NASA NTRS1987

A spectral multi-domain technique for analysis of chemically reacting flows

A technique is presented which models the chemical kinetics and flow kinematics of a nonionized air mixture passing through a fully resolved shock wave, thus alleviating the need for artificial viscosity. The quasi-one-dimensional Navier-Stokes equations and the species conversation equation are the governing equations. The validity of the multidomain Navier-Stokes algorithm is demonstrated via comparison with experiment.

Macaraeg, Michele G.↗
NASA NTRS1988

A spectral multi-domain technique for viscous compressible reacting flows

The first application of a spectral multidomain method for viscous compressible flow is presented. The method imposes a global flux balance condition at the interface so that high-order continuity of the solution is preserved. The solution scheme can be adapted to the particular requirement in each subdomain. To illustrate these advantages, a Mach 11 shock calculation is presented to study the chemical kinetics initiated as air passes through a fully resolved shock wave.

Macaraeg, M. G.↗
NASA NTRS1989

A spectral multi-domain technique applied to high-speed chemically reacting flows

The first applications of a spectral multidomain method for viscous compressible flow is presented. The method imposes a global flux balance condition at the interface so that high-order continuity of the solution is preserved. The global flux balance is imposed in terms of a spectral integral of the discrete equations across adjoining domains. Since the discretized equations interior to each domain solved are uncoupled from each other, and since the interface relation has a block structure, the solution scheme can be adapted to the particular requirements of each subdomain. The spectral multidomain technique presented is well-suited for the multiple scales associated with the chemically reacting and transition flows in hypersonic research. A nonstaggered multidomain discretization is used for the chemically reacting flow calculation, and the first implementation of a staggered multidomain mesh is presented for accurately solving the stability equation for a viscous compressible fluid.

Macaraeg, Michele G.↗
NASA NTRS1989

A multi-domain spectral computation of three-dimensional laminar horseshoe vortex flow using incompressible Navier-Stokes equations

Multidomain spectral methods are presently used to numerically simulate a strut-wall intersection's laminar horseshoe vortex flow through direct solution of the three-dimensional, incompressible, time-dependent Navier-Stokes equations. Direct expansion in Chebyshev polynomials and spectral element method spatial discretization of flow dependence are used to achieve high-order accuracy, and minimal dispersion errors. Low and moderate Reynolds number results are presented to illustrate the method application.

Tan, C. S.↗
NASA NTRS1989

A spectral multi-domain technique applied to stability and transition of incompressible and compressible flows

Techniques for the numerical simulation of compressible and incompressible viscous flows are described and demonstrated. The focus is on a multidomain spectral method based on the flux-balance domain-interface scheme of Macaraeg and Streett (1986). The fundamental principles of the method are reviewed, and it is shown that the multidomain spectral approach facilitates the treatment of instability and the transition to turbulence. Typical numerical results for the Taylor-Couette problem and for bounded compressible high-speed mixing layers are presented in graphs and briefly characterized.

Macaraeg, Michele↗
NASA NTRS1991

Computational study of three dimensional viscous flow through a turbine cascade using a multi-domain spectral technique

The three dimensional viscous flow through a planar turbine cascade is numerically simulated by direct solution of the incompressible Navier-Stokes equations. Flow dependence in the spanwise direction is represented by direct expansion in Chebyshev polynomials, while the discretization on planes parallel to the endwalls is accomplished using the spectral element method. Elemental mapping from the physical to the computational space uses an algebraic mapping technique. A fractional time stepping method that consists of an explicit nonlinear convective step, an implicit pressure correction step, and an implicit viscous step is used to advance the Navier-Stokes equations forward in time. Results computed at moderate Reynolds numbers show a three dimensional endwall flow separation, a midspan separation of the blade suction surface boundary layer, and other three-dimensional features such as the presence of a saddle point flow in the endwall region. In addition, the computed skin friction lines are shown to be orthogonal to the surface vorticity lines, demonstrating the accuracy achievable in the present method.

Renaud, Earl W.↗
NASA NTRS1993

A strategy for the efficient simulation of viscous compressible flows using a multi-domain pseudospectral method

The viscous compressible flow in a quasi-1D nozzle is presently simulated by means of a novel multidomain pseudospectral method in which interface-point flow variables are advanced in time on the basis of the second-order time-marching scheme used for the interior points. A spectrally accurate modification of Van Leer's (1982) flux-vector flux-splitting method is used to evaluate the spatial derivatives of the inviscid flux vector; these derivatives are alternately evaluated from neighboring subdomains, and the scheme is found to be spectrally accurate and to resolve shock waves without oscillations.

Hanley, Patrick↗
NASA NTRS1983

Low frequency dielectric relaxation in boracites

In order to elucidate the nature of the imperfections which adversely affect pyroelectric processes in boracites, the thermal and dispersive characteristics of the low frequency dielectric response in iron-iodide boracite (Fe3B7O13I) and copper-chloride boracite (Cu3B7O13Cl) have been investigated. These characteristics were measured as a function of crystallographic orientation and applied field in both the ferroelectric and paraelectric states. The low frequency dielectric relaxation of 100 line oriented multi-domain copper-chloride boracite clearly indicates the dipole nature of the lattice imperfections. The activation energies calculated from a noninteracting Debye model, are 0.53 eV in the ferroelectric phase and 0.10 eV in the paraelectric phase.

Kim, Q.↗
NASA NTRS1988

A spectral collocation solution to the compressible stability eigenvalue problem

A newly developed spectral compressible linear stability code (SPECLS) (staggered pressure mesh) is presented for analysis of shear flow stability, and applied to high speed boundary layers and free shear flows. The formulation utilizes the first application of a staggered mesh for a compressible flow analysis by a spectral technique. An order of magnitude less number of points is needed for equivalent accuracy of growth rates compared to those calculated by a finite difference formulation. Supersonic disturbances which are found to have oscillatory structures were resolved by a spectral multi-domain discretization, which requires a factor of three fewer points than the single domain spectral stability code. It is indicated, as expected, that stability of mixing layers is enhanced by viscosity and increasing Mach number. The mean flow involves a jet being injected into a quiescent gas. Higher temperatures of the injected gas is also found to enhance stability characteristics of the free shear layer.

Macaraeg, Michele G.↗
NASA NTRS1989

Conservation equations and physical models for hypersonic air flows over the aeroassist flight experiment vehicle

The code development and application program for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA), with emphasis directed toward support of the Aeroassist Flight Experiment (AFE) in the near term and Aeroassisted Space Transfer Vehicle (ASTV) design in the long term is reviewed. LAURA is an upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3-D, viscous, hypersonic flows in chemical and thermal nonequilibrium. 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. 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. A single relaxation step depends only on information from nearest neighbors. Predictions for pressure distributions, surface heating, and aerodynamic coefficients compare well with experimental data for Mach 10 flow over an AFE wind tunnel model. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium over the full scale AFE configuration obtained on a multi-domain grid are discussed.

Gnoffo, Peter A.↗
NASA NTRS1991

Non-linear interaction of a detonation/vorticity wave

The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multi-domain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient encounter with a disturbance, the effects of exothermicity are more pronounced than predicted by linear theory. Finally, it is found that linear theory correctly determines the critical angle.

Lasseigne, D. G.↗
NASA NTRS1991

Nonlinear interaction of a detonation/vorticity wave

The interaction of an oblique, over driven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multi-domain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient encounter with a disturbance, the effects of exothermicity are more pronounced than predicted by linear theory. Finally, it is found that linear theory correctly determines the critical angle.

Lasseigne, D. G.↗
NASA NTRS1993

Integrated CFD modeling of gas turbine combustors

3D, curvilinear, multi-domain CFD analysis is becoming a valuable tool in gas turbine combustor design. Used as a supplement to experimental testing. CFD analysis can provide improved understanding of combustor aerodynamics and used to qualitatively assess new combustor designs. This paper discusses recent advancements in CFD combustor methodology, including the timely integration of the design (i.e. CAD) and analysis (i.e. CFD) processes. Allied Signal's F124 combustor was analyzed at maximum power conditions. The assumption of turbulence levels at the nozzle/swirler inlet was shown to be very important in the prediction of combustor exit temperatures. Predicted exit temperatures were compared to experimental rake data, and good overall agreement was seen. Exit radial temperature profiles were well predicted, while the predicted pattern factor was 25 percent higher than the harmonic-averaged experimental pattern factor.

Fuller, E. J.↗