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NASA NTRS1992

A hybrid multigrid technique for computing steady-state solutions to supersonic flows

Recently, Li and Sanders have introduced a class of finite difference schemes to approximate generally discontinuous solutions to hyperbolic systems of conservation laws. These equations have the form together with relevant boundary conditions. When modelling hypersonic spacecraft reentry, the differential equations above are frequently given by the compressible Euler equations coupled with a nonequilibrium chemistry model. For these applications, steady state solutions are often sought. Many tens (to hundreds) of super computer hours can be devoted to a single three space dimensional simulation. The primary difficulty is the inability to rapidly and reliably capture the steady state. In these notes, we demonstrate that a particular variant from the schemes presented can be combined with a particular multigrid approach to capture steady state solutions to the compressible Euler equations in one space dimension. We show that the rate of convergence to steady state coming from this multigrid implementation is vastly superior to the traditional approach of artificial time relaxation. Moreover, we demonstrate virtual grid independence. That is, the rate of convergence does not depend on the degree of spatial grid refinement.

Sanders, Richard↗

NASA NTRS1997

Rapid Decimation for Direct Volume Rendering

An approach for eliminating unnecessary portions of a volume when producing a direct volume rendering is described. This reduction in volume size sacrifices some image quality in the interest of rendering speed. Since volume visualization is often used as an exploratory visualization technique, it is important to reduce rendering times, so the user can effectively explore the volume. The methods presented can speed up rendering by factors of 2 to 3 with minor image degradation. A family of decimation algorithms to reduce the number of primitives in the volume without altering the volume's grid in any way is introduced. This allows the decimation to be computed rapidly, making it easier to change decimation levels on the fly. Further, because very little extra space is required, this method is suitable for the very large volumes that are becoming common. The method is also grid-independent, so it is suitable for multiple overlapping curvilinear and unstructured, as well as regular, grids. The decimation process can proceed automatically, or can be guided by the user so that important regions of the volume are decimated less than unimportant regions. A formal error measure is described based on a three-dimensional analog of the Radon transform. Decimation methods are evaluated based on this metric and on direct comparison with reference images.

Gibbs, Jonathan↗

NASA NTRS1996

A Pressure Based Multigrid Procedure for the Navier-Stokes Equations on Unstructured Grids

We present details and performance of a pressure based multigrid solution procedure for the Navier-Stokes equations discretized on triangular grids. The discretization uses a control volume methodology, with linear inter-nodal variation of the flow variables. The use of the multigrid technique provides rapid and grid-independent rates of convergence. Three model driven cavity flows are computed, and the performance of the method at several grid densities and Reynolds numbers is reported. Representative flow fields characterizing the viscous eddies are also presented.

Jyotsna, R.↗

NASA NTRS1991

Grid generation about complex three-dimensional aircraft configurations

The problem of obtaining three dimensional grids with sufficient resolution to resolve all the flow or other physical features of interest is addressed. The generation of a computational grid involves a series of compromises to resolve several conflicting requirements. On one hand, one would like the grid to be fine enough and not too skewed to reduce the numerical errors and to adequately resolve the pertinent physical features of the flow field about the aircraft. On the other hand, the capabilities of present or even future supercomputers are finite and the number of mesh points must be limited to a reasonable number: one which is usually much less than desired for numerical accuracy. One technique to overcome this limitation is the 'zonal' grid approach. In this method, the overall field is subdivided into smaller zones or blocks in each of which an independent grid is generated with enough grid density to resolve the flow features in that zone. The zonal boundaries or interfaces require special boundary conditions such that the conservation properties of the governing equations are observed. Much work was done in 3-D zonal approaches with nonconservative zonal interfaces. A 3-D zonal conservative interfacing method that is efficient and easy to implement was developed during the past year. During the course of the work, it became apparent that it would be much more feasible to do the conservative interfacing with cell-centered finite volume codes instead of the originally planned finite difference codes. Accordingly, the CNS code was converted to finite volume form. This new version of the code is named CNSFV. The original multi-zonal interfacing capability of the CNS code was enhanced by generalizing the procedure to allow for completely arbitrarily shaped zones with no mesh continuity between the zones. While this zoning capability works well for most flow situations, it is, however, still nonconservative. The conservative interface algorithm was also implemented but was not completely validated.

Klopfer, Goetz H.↗

NASA NTRS2005

Advanced Turbulence Modeling Concepts

The ZCET program developed at NASA Glenn Research Center is to study hydrogen/air injection concepts for aircraft gas turbine engines that meet conventional gas turbine performance levels and provide low levels of harmful NOx emissions. A CFD study for ZCET program has been successfully carried out. It uses the most recently enhanced National combustion code (NCC) to perform CFD simulations for two configurations of hydrogen fuel injectors (GRC- and Sandia-injector). The results can be used to assist experimental studies to provide quick mixing, low emission and high performance fuel injector designs. The work started with the configuration of the single-hole injector. The computational models were taken from the experimental designs. For example, the GRC single-hole injector consists of one air tube (0.78 inches long and 0.265 inches in diameter) and two hydrogen tubes (0.3 inches long and 0.0226 inches in diameter opposed at 180 degree). The hydrogen tubes are located 0.3 inches upstream from the exit of the air element (the inlet location for the combustor). To do the simulation, the single-hole injector is connected to a combustor model (8.16 inches long and 0.5 inches in diameter). The inlet conditions for air and hydrogen elements are defined according to actual experimental designs. Two crossing jets of hydrogen/air are simulated in detail in the injector. The cold flow, reacting flow, flame temperature, combustor pressure and possible flashback phenomena are studied. Two grid resolutions of the numerical model have been adopted. The first computational grid contains 0.52 million elements, the second one contains over 1.3 million elements. The CFD results have shown only about 5% difference between the two grid resolutions. Therefore, the CFD result obtained from the model of 1.3-million grid resolution can be considered as a grid independent numerical solution. Turbulence models built in NCC are consolidated and well tested. They can handle both coarse and fine grids near the wall. They can model the effect of anisotropy of turbulent stresses and the effect of swirling. The chemical reactions of Magnusson model and ILDM method were both used in this study.

Shih, Tsan-Hsing↗

NASA NTRS1993

A Realizable Reynolds Stress Algebraic Equation Model

The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

Shih, Tsan-Hsing↗

NASA NTRS1996

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

Eliasson, Peter↗

NASA NTRS1993

A multidimensional flux function with applications to the Euler and Navier-Stokes equations

In the present grid-independent approximate Riemann solver for 2D and 3D flows that are governed by the Euler or Navier-Stokes equations, fluxes on grid faces are obtained by wave decomposition; the assumption of information-propagation in the velocity-difference directions leads to a more accurate resolution of shear and shock waves, when these are are oblique to the grid. The model, which yields significantly greater accuracy in both supersonic and subsonic first-order spatially accurate computations, describes the difference in states at each grid interface by the action of five waves.

Rumsey, Christopher L.↗

NASA NTRS2024

Enabling Advanced Snow Physics within Land Surface Models Through an Interoperable Model-Physics Coupling Framework

Accurate estimation of snow accumulation and melt is a critical part of decision-making in snow-dominated watersheds. In this study, we demonstrate a flexible methodology to couple a detailed snow model, Crocus, separately to two different land surface models (LSMs), Noah-MP and Noah. The original LSMs and the coupled models (Noah-MP-Crocus and Noah-Crocus) are used to simulate snow depth, snow water equivalent, and other water and energy states and fluxes. The results of simulations are compared against a wide range of independent gridded and point scale reference datasets. Our results show that coupling the detailed snow model, Crocus, with the LSMs improves the snow depth and snow water equivalent relative to independent observations. Overall, larger improvements are obtained with coupling Crocus to the Noah LSM, with the coupled Noah-Crocus configuration reducing the RMSE and bias of snow depth from 2-12% and 57-75%, respectively, relative to Snow Data Assimilation System (SNODAS) and snow product from the University of Arizona. On the other hand, smaller improvements are obtained by coupling Crocus with Noah-MP. The Coupled Noah-MP-Crocus reduces the snow depth bias but slightly degrades the RMSE of snow depth and snow water equivalent. The corresponding impacts in other water budget terms such as evapotranspiration, soil moisture, and streamflow, however, are mixed, pointing to the significant need to improve the coupling assumptions of these processes within land models. Overall, the interoperable coupling framework demonstrated here offers the opportunity to include more detailed snow physics and processes, and to advance data assimilation systems through improved exploitation of information from snow remote sensing instruments.

Snow model↗

NASA NTRS2003

Information Power Grid (IPG) Tutorial 2003

For NASA and the general community today Grid middleware: a) provides tools to access/use data sources (databases, instruments, ...); b) provides tools to access computing (unique and generic); c) Is an enabler of large scale collaboration. Dynamically responding to needs is a key selling point of a grid. Independent resources can be joined as appropriate to solve a problem. Provide tools to enable the building of a frameworks for application. Provide value added service to the NASA user base for utilizing resources on the grid in new and more efficient ways. Provides tools for development of Frameworks.

Meyers, George↗

NASA NTRS1989

Study of hypersonic flow past sharp cones

Calculations using the direct simulation Monte Carlo (DSMC) method of Bird for flow past sharp cones in the near continuum to free molecule flow regime are presented and compared with experiment. It is found that results are sensitive to the grid and the interaction potential. Moreover, the time counter method was found to be as accurate as other methods when the solution is grid independent. Finally, the results show that the effects of the wake on the forebody surface properties are minimal.

Taylor, Jeff C.↗

NASA NTRS1990

Computation of solid/liquid phase change including free convection - Comparison with data

A computational model is presented for solid/liquid phase-change energy transport including free convection fluid flow in the liquid phase. The computational model considers the velocity components of all nonliquid control volumes to be zero but fully solves the coupled mass-momentum problem within the liquid. The thermal energy model includes the entire domain and employs an enthalpy-like model and a recently developed method for handling the phase-change interface nonlinearity. Convergence studies are performed and comparisons made with experimental data for two different problems. Grid independence is achieved, and the comparison with experimental data indicates excellent quantitative prediction of the melt fraction evolution. Qualitative data are also provided as velocity vector and isotherm plots. The computational costs incurred are quite low by comparison with other models.

Schneider, G. E.↗

NASA NTRS1990

Navier-Stokes analysis of transonic cascade flow

A new kind of C-type grid is proposed, this grid is non-periodic on the wake and allows minimum skewness for cascades with high turning and large camber. Reynolds-averaged Navier-Stokes equations are solved on this type of grid using a finite volume discretization and a full multigrid method which uses Runge-Kutta stepping as the driving scheme. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A detailed numerical study is proposed for a highly loaded transonic blade. A grid independence analysis is presented in terms of pressure distribution, exit flow angles, and loss coefficient. Comparison with experiments clearly demonstrates the capability of the proposed procedure.

Arnone, A.↗

NASA NTRS1991

A locally refined rectangular grid finite element method - Application to computational fluid dynamics and computational physics

The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.

Young, David P.↗

NASA NTRS1990

Numerical Formulation for the Prediction of Solid/Liquid Change of a Binary Alloy

A computational model is presented for the prediction of solid/liquid phase change energy transport including the influence of free convection fluid flow in the liquid phase region. The computational model considers the velocity components of all non-liquid phase change material control volumes to be zero but fully solves the coupled mass-momentum problem within the liquid region. The thermal energy model includes the entire domain and uses an enthalpy like model and a recently developed method for handling the phase change interface nonlinearity. Convergence studies are performed and comparisons made with experimental data for two different problem specifications. The convergence studies indicate that grid independence was achieved and the comparison with experimental data indicates excellent quantitative prediction of the melt fraction evolution. Qualitative data is also provided in the form of velocity vector diagrams and isotherm plots for selected times in the evolution of both problems. The computational costs incurred are quite low by comparison with previous efforts on solving these problems.

Schneider, G. E.↗

NASA NTRS1992

Navier-Stokes solution of transonic cascade flows using nonperiodic C-type grids

Arnone, Andrea↗

NASA NTRS1992

Semi-coupled flow and thermal analysis of the field joint during rapid pressurization of the redesigned solid rocket motor

A transient, semi-coupled, multi-dimensional thermal and flow analysis methodology was developed to predict the thermal/gas dynamic conditions in the field joint region of the Redesigned Solid Rocket Motor (RSRM). Transient temperature response, pressure history, and combustion gas flow rate (within the field joint region), were of principle interest, in the course of this study. The thermal environment in the field joint was modeled using SINDA, a finite difference based thermal network analyzer. The combustion gas flow boundary condition was generated using the FLAP code; this code performs a transient, lumped-parameter, control volume analysis to solve the mass, momentum, and energy conservation equations. The FLAP computer code was modified to account for erosion of the NBR insulation material, following ignition. An independent grid sensitivity study was conducted to determine an appropriate grid distribution near the wall. The predicted results, obtained using an optimum grid distribution and computer generated flow boundary condition, were compared with subscale test data.

Ghaffarian, Benny↗

NASA NTRS1992

Studies on fuel spray characteristics in high-pressure environment

The present study deals with several issues involving the improvement of physical submodels and the computational efficiency in modeling dense fuel sprays. To improve the computational efficiency, a parcel PDF approach is implemented which can account for turbulent dispersion within each computational parcel. The advantage of a parcel PDF tracking method is to reduce the number of computational parcels representing the spray dynamics as well as to obtain grid-independent solutions for two-phase flows. To account for the dense spray effects, an existing drop collision and coalescence model, two breakup models, and a Reitz's wave instability model were used. These models were incorporated into a state-of-the-art multiphase all-speed transient flow solution procedure. Comparative performance for two breakup models as well as the turbulence modulation effects are also studied. Validation cases include the nonevaporating and evaporating solid-cone dense sprays. The predictions show a reasonably good agreement with available experimental results in terms of spray penetration, drop sizes, gas and drop mean velocities, and gas and drop rms velocities. The numerical results indicate that the present parcel PDF model has the capability of accurately representing drop dispersion in dense sprays with manageable number of computational parcels.

Shang, H. M.↗