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NASA NTRS1993

Efficiency and reliability enhancements in propulsion flowfield modeling

The implementation of traditional CFD algorithms in practical propulsion related flowfields often leads to dramatic reductions in efficiency and/or robustness. The present research is directed at understanding the reasons for this deterioration and finding methods to circumvent it. Work to date has focussed on low Mach number regions, viscous dominated regions, and high grid aspect ratios. Time derivative preconditioning, improved definition of the local time stepping, and appropriate application of boundary conditions are employed to decrease the required time to obtain a solution, while maintaining accuracy. A number of cases having features typical of rocket engine flowfields are computed to demonstrate the improvement over conventional methods. These cases include laminar and turbulent high Reynolds number flat plate boundary layers, flow over a backward-facing step, a diffusion flame, and wall heat-flux calculations in a turbulent converging-diverging nozzle. Results from these cases show convergence that is virtually independent of the local Mach number and the grid aspect ratio, which translates to a convergence speed-up of up to several orders of magnitude over conventional algorithms. Current emphasis is in extending these results to three-dimensional flows with highly stretched grids.

Buelow, Philip E. O.↗

NASA NTRS1988

Incompressible and anelastic flow simulations on numerically generated grids

In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property of orthogonality has been preserved. Flow equations in general curvilinear coordinates maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible models, using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.

Sharman, R. D.↗

NASA NTRS1985

Embedded mesh solutions of the Euler equation using a multiple-grid method

New developments make it now possible to obtain solutions to Euler equations for many problems on the basis of acceptable computing times. The possibility of an extension of these methods to more difficult flows and increasingly complex geometries can depend on obtaining suitable grid structures. Thus, an attractive approach to complex geometries involves the recasting of the problem into the framework of a multiple-grid structure. The discrete equations represented on the grid are solved as a simultaneous system. In the present investigation, this is accomplished with the aid of Ni's multiple-grid algorithm. The multiple-grid structure provided in this study represents the first step towards a completely general modular approach to the solution of the complete compressible flow problem. In the presented cases, a fine mesh resolution is obtained within the embedded mesh regions, while preserving the global coarse mesh convergence rates.

Usab, W. J., Jr.↗

NASA NTRS1986

Efficient solutions of two-dimensional incompressible steady viscous flows

A simple, efficient, and robust numerical technique is provided for solving two dimensional incompressible steady viscous flows at moderate to high Reynolds numbers. The proposed approach employs an incremental multigrid method and an extrapolation procedure based on minimum residual concepts to accelerate the convergence rate of a robust block-line-Gauss-Seidel solver for the vorticity-stream function Navier-Stokes equations. Results are presented for the driven cavity flow problem using uniform and nonuniform grids and for the flow past a backward facing step in a channel. For this second problem, mesh refinement and Richardson extrapolation are used to obtain useful benchmark solutions in the full range of Reynolds numbers at which steady laminar flow is established.

Morrison, J. H.↗

NASA NTRS1988

Efficient solutions of two-dimensional incompressible steady viscous flows

Morrison, J. H.↗

NASA NTRS1989

Unsteady Euler algorithm with unstructured dynamic mesh for complex-aircraft aeroelastic analysis

A finite-volume unstructured-grid FEM scheme with multistage Runge-Kutta time stepping is applied to the three-dimensional time-dependent Euler equations for inviscid flows on complex aircraft configurations undergoing structural deformation. The derivation of the model, the solution procedure, and the computer implementation are described, and results are presented graphically for a NASA Langley supersonic fighter aircraft model in steady and unsteady (harmonic oscillation in complete-vehicle bending mode) flow regimes. Good agreement between FEM predictions and experimental data is demonstrated.

Batina, John T.↗

NASA NTRS1992

Finite element simulations involving simultaneous multiple interface fronts in phase change problems

The present paper describes the simulation of phase change problems involving simultaneous multiple interface fronts employing the finite element method. Much of the past investigations employing finite elements have been restricted to primarily a single phase change situation. The existence of more than one phase, that is, the presence of multiple phase fronts poses certain challenges and further complications. However, the results provide a very interesting thermal behavior for this class of problems. In this paper, attention is focused on fixed grid methods and the trapezoidal family of one-step methods using the enthalpy formulations. Illustrative examples which handle simultaneous multiple fronts in phase change problems are presented.

Ouyang, Tianhong↗

NASA NTRS1993

Compressible turbulent flow simulation with a multigrid multiblock method

We describe a multigrid multiblock method for compressible turbulent flow simulations and present results obtained from calculations on a two-element airfoil. A vertex-based spatial discretization method and explicit multistage Runge-Kutta time-stepping are used. The slow convergence of a single grid method makes the multigrid method, which yields a speed factor of about 20, indispensable. The numerical predictions are in good agreement with experimental results. It is shown that the convergence of the multigrid process depends considerably on the ordering of the various loops. If the block loop is put inside the stage loop, the process converges more rapidly than if the block loop is situated outside the stage loop when a three-stage Runge-Kutta method is used. If a five-stage scheme is used, the process does not converge in the latter block ordering. Finally, the process based on the five-stage method is about 60 percent more efficient than with the three-stage method, if the block loop is inside the stage loop.

Kuerten, Hans↗

NASA NTRS1995

Sensitivity analysis for aeroacoustic and aeroelastic design of turbomachinery blades

A new method for computing the effect that small changes in the airfoil shape and cascade geometry have on the aeroacoustic and aeroelastic behavior of turbomachinery cascades is presented. The nonlinear unsteady flow is assumed to be composed of a nonlinear steady flow plus a small perturbation unsteady flow that is harmonic in time. First, the full potential equation is used to describe the behavior of the nonlinear mean (steady) flow through a two-dimensional cascade. The small disturbance unsteady flow through the cascade is described by the linearized Euler equations. Using rapid distortion theory, the unsteady velocity is split into a rotational part that contains the vorticity and an irrotational part described by a scalar potential. The unsteady vorticity transport is described analytically in terms of the drift and stream functions computed from the steady flow. Hence, the solution of the linearized Euler equations may be reduced to a single inhomogeneous equation for the unsteady potential. The steady flow and small disturbance unsteady flow equations are discretized using bilinear quadrilateral isoparametric finite elements. The nonlinear mean flow solution and streamline computational grid are computed simultaneously using Newton iteration. At each step of the Newton iteration, LU decomposition is used to solve the resulting set of linear equations. The unsteady flow problem is linear, and is also solved using LU decomposition. Next, a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the mean and unsteady flow fields. The sensitivity analysis makes use of the nominal steady and unsteady flow LU decompositions so that no additional matrices need to be factored. Hence, the present method is computationally very efficient. To demonstrate how the sensitivity analysis may be used to redesign cascades, a compressor is redesigned for improved aeroelastic stability and two different fan exit guide vanes are redesigned for reduced downstream radiated noise. In addition, a framework detailing how the two-dimensional version of the method may be used to redesign three-dimensional geometries is presented.

Lorence, Christopher B.↗

NASA NTRS1994

An experiment in hurricane track prediction using parallel computing methods

The barotropic model is used to explore the advantages of parallel processing in deterministic forecasting. We apply this model to the track forecasting of hurricane Elena (1985). In this particular application, solutions to systems of elliptic equations are the essence of the computational mechanics. One set of equations is associated with the decomposition of the wind into irrotational and nondivergent components - this determines the initial nondivergent state. Another set is associated with recovery of the streamfunction from the forecasted vorticity. We demonstrate that direct parallel methods based on accelerated block cyclic reduction (BCR) significantly reduce the computational time required to solve the elliptic equations germane to this decomposition and forecast problem. A 72-h track prediction was made using incremental time steps of 16 min on a network of 3000 grid points nominally separated by 100 km. The prediction took 30 sec on the 8-processor Alliant FX/8 computer. This was a speed-up of 3.7 when compared to the one-processor version. The 72-h prediction of Elena's track was made as the storm moved toward Florida's west coast. Approximately 200 km west of Tampa Bay, Elena executed a dramatic recurvature that ultimately changed its course toward the northwest. Although the barotropic track forecast was unable to capture the hurricane's tight cycloidal looping maneuver, the subsequent northwesterly movement was accurately forecasted as was the location and timing of landfall near Mobile Bay.

Song, Chang G.↗

NASA NTRS1999

Regional Climate Simulation Experiments with a Variable Resolution Stretched Grid GCM

The variable resolution stretched grid (SG) version of the Goddard Earth Observing System (GEOS) GCM has been recently developed and tested in a regional climate simulation mode. The SG-approach is an alternative to the widely used nested grid approach introduced a decade ago as a pioneering step to regional climate modeling. The region of interest with a uniform about 60 km resolution used in experiments is a rectangle over the U.S. The results of one annual as well as two-month simulations for the anomalous climate event of the U.S. drought of 1988, are validated against data analysis fields and diagnostics. The efficient regional down-scaling as well as the positive impact of fine regional resolution, are obtained. The SG-concept appeared to be a promising candidate for regional and subregional climate studies and applications.

Takacs, Lawrence L.↗

NASA NTRS2001

Regional Climate Studies with Variable-Resolution Stretched-Grid GCMs

A variable resolution GCM using a global stretched grid with fine resolution over the area(s) of interest, is a viable new approach to regional and subregional climate studies and applications. It is an alternative to the widely used nested grid approach introduced a decade ago as a pioneering step in regional climate modeling. The first version of the SG-GCM based on the GEOS (Goddard Earth Observing System) GCM using a finite-difference approximation, has been developed and thoroughly tested during the last few years. Successful simulations have been performed with the SG-GCM for the anomalous regional climate events of the U.S. 1988 summer drought and 1993 summer flood. They have shown the practical feasibility of the SG-approach for regional climate modeling. The GEOS SG-DAS (Data Assimilation System) incorporating the SG-GCM has also been developed and tested. The assimilated regional fields and diagnostics are used for validating the SG-GCM regional simulations. Two new SG-GCMs are being developed. The first is the SG-version of the new NASANCAR FV-GCM (with the finite-volume (FV) dynamics), and the second is the SG-version of the new GCM with spectral-element dynamics. Both GCMs use the WAR CCM4 physics. Using these advanced numerics will provide increased computational efficiency for the new the SG-GCMs, and will allow us to employ more flexible stretching strategies beneficial for the efficient regional down-scaling. The major current developments are focused on: simulating the 1997-1999 (and beyond) ENSO cycle and related monsoonal circulations, with enhanced regional resolution; studying intraseasonal and interannual regional climate variability for the extended multiyear (AMIP-type) SG-GCM simulations; and studying the impact of ensemble integrations.

Fox-Rabinovitz, Michael↗

NASA NTRS2002

Computational Study of Near-limit Propagation of Detonation in Hydrogen-air Mixtures

A computational investigation of the near-limit propagation of detonation in lean and rich hydrogen-air mixtures is presented. The calculations were carried out over an equivalence ratio range of 0.4 to 5.0, pressures ranging from 0.2 bar to 1.0 bar and ambient initial temperature. The computations involved solution of the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing (TVD) scheme, and a point implicit, first-order-accurate, time marching algorithm. The hydrogen-air combustion was modeled with a 9-species, 19-step reaction mechanism. A multi-level, dynamically adaptive grid was utilized in order to resolve the structure of the detonation. The results of the computations indicate that when hydrogen concentrations are reduced below certain levels, the detonation wave switches from a high-frequency, low amplitude oscillation mode to a low frequency mode exhibiting large fluctuations in the detonation wave speed; that is, a 'galloping' propagation mode is established.

Yungster, S.↗

NASA NTRS2003

Structure and Stability of One-Dimensional Detonations in Ethylene-Air Mixtures

The propagation of one-dimensional detonations in ethylene-air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit, first-order-accurate, time marching algorithm. The ethylene-air combustion is modeled with a 20-species, 36-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies over an equivalence ratio range of 0.5 less than phi less than 3 for different initial pressures and degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel-air equivalence ratio. For equivalence ratios less than approximately 1.2 the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures (phi greater than 1.2) exhibit a low-frequency mode that includes large fluctuations in the detonation wave speed; that is, a galloping propagation mode is established. At high degrees of overdrive, stable detonation wave propagation is obtained. A modified McVey-Toong short-period wave-interaction theory is in excellent agreement with the numerical simulations.

Yungster, S.↗

NASA NTRS2016

The Impact of ARM on Climate Modeling

Climate models are among humanity's most ambitious and elaborate creations. They are designed to simulate the interactions of the atmosphere, ocean, land surface, and cryosphere on time scales far beyond the limits of deterministic predictability, and including the effects of time-dependent external forcings. The processes involved include radiative transfer, fluid dynamics, microphysics, and some aspects of geochemistry, biology, and ecology. The models explicitly simulate processes on spatial scales ranging from the circumference of the Earth down to one hundred kilometers or smaller, and implicitly include the effects of processes on even smaller scales down to a micron or so. The atmospheric component of a climate model can be called an atmospheric global circulation model (AGCM). In an AGCM, calculations are done on a three-dimensional grid, which in some of today's climate models consists of several million grid cells. For each grid cell, about a dozen variables are time-stepped as the model integrates forward from its initial conditions. These so-called prognostic variables have special importance because they are the only things that a model remembers from one time step to the next; everything else is recreated on each time step by starting from the prognostic variables and the boundary conditions. The prognostic variables typically include information about the mass of dry air, the temperature, the wind components, water vapor, various condensed-water species, and at least a few chemical species such as ozone. A good way to understand how climate models work is to consider the lengthy and complex process used to develop one. Lets imagine that a new AGCM is to be created, starting from a blank piece of paper. The model may be intended for a particular class of applications, e.g., high-resolution simulations on time scales of a few decades. Before a single line of code is written, the conceptual foundation of the model must be designed through a creative envisioning that starts from the intended application and is based on current understanding of how the atmosphere works and the inventory of mathematical methods available.

atmospheric circulation↗

NASA NTRS2016

Optimal Reorganization of NASA Earth Science Data for Enhanced Accessibility and Usability for the Hydrology Community

A long-standing "Digital Divide" in data representation exists between the preferred way of data access by the hydrology community and the common way of data archival by earth science data centers. Typically, in hydrology, earth surface features are expressed as discrete spatial objects (e.g., watersheds), and time-varying data are contained in associated time series. Data in earth science archives, although stored as discrete values (of satellite swath pixels or geographical grids), represent continuous spatial fields, one file per time step. This Divide has been an obstacle, specifically, between the Consortium of Universities for the Advancement of Hydrologic Science, Inc. and NASA earth science data systems. In essence, the way data are archived is conceptually orthogonal to the desired method of access. Our recent work has shown an optimal method of bridging the Divide, by enabling operational access to long-time series (e.g., 36 years of hourly data) of selected NASA datasets. These time series, which we have termed "data rods," are pre-generated or generated on-the-fly. This optimal solution was arrived at after extensive investigations of various approaches, including one based on "data curtains." The on-the-fly generation of data rods uses "data cubes," NASA Giovanni, and parallel processing. The optimal reorganization of NASA earth science data has significantly enhanced the access to and use of the data for the hydrology user community.

data rods↗

NASA NTRS2018

A Physics-Based Approach to Urban Air Mobility

High-fidelity Computational Fluid Dynamics (CFD) simulations for multi-rotor vehicles have been carried out. The three-dimensional unsteady Navier-Stokes equations are solved on overset grids employing high order accurate schemes, dual-time stepping, and a hybrid turbulence model using NASA's CFD code Over- flow. The vehicles studied consist of small to medium sized drones, and bigger vehicles for future Urban Air Mobility (UAM) applications. The performances for different configurations and rotor mounting are calculated in hover and in forward flight. Understanding the complex flows and the interactions between rotors and with other elements will help design the future multi-rotor vehicles to be quieter, safer, and more efficient.

Urban↗

NASA NTRSDate not supplied

Evaluation of Transport-Equations-Based Transition Models for High-Speed Boundary Layers Using OVERFLOW

Accurate modeling of laminar-turbulent transition is crucial for the design of hypersonic flight systems. However, the current transition models used in production CFD codes are insufficient for high-speed flows. Many extensions to low-speed models have been suggested; however, a thorough verification and validation effort is needed before these models can be used in design settings. Challenges include potentially missing details of the model implementation requirements and/or a complete specification of the input parameters needed to replicate the test findings. A meaningful assessment of the generalization capability of these models is also hindered by a lack of information regarding the specific flow configurations and associated grids employed for model calibration. As a key first step toward model verification, we present an independent assessment of two recently proposed models for high-speed transition, namely, a model within the SST-𝛾 framework and a model based on the SST-𝛾 – 𝜈 𝐿 equations. These models are implemented in the NASA OVERFLOW 2.3e solver and their performance in predicting first mode, second mode, and crossflow transition has been evaluated for several test cases in the supersonic and hypersonic regimes. Besides the test cases employed by the model developers, which could have also been used for model calibration, the present assessment includes supplementary configurations that contribute to an unbiased assessment of the models. The outcomes presented in this study indicate the potential for the models to be applied to high-speed flight configurations. Key steps toward future improvements to these models are also outlined.

CFD↗