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NASA NTRS1981

Blade loss transient dynamics analysis, volume 2. Task 2: Theoretical and analytical development. Task 3: Experimental verification

The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described.

Gallardo, V. C.↗
NASA NTRS1998

Electromagnetics and Fluid Dynamics

Previous efforts focused on developing tools for design of low observables were sustained. The final product was the maturation of a high-order accurate finite-volume based code to solve Maxwell's equations. One of the primary achievements was the development and implementation of efficient filtering techniques which enhance the robustness of high-order and optimized schemes without significant adverse impact on accuracy. This has eliminated the stability barrier which restrains the common use of high-order schemes for conservative wave propagation phenomena on curvilinear meshes. A study was performed of crossing shock interactions under conditions of increasing interaction strength and asymmetry. In the first category, the observed computed topological bifurcations were correlated with the formation of various lines of coalescence and divergence evident in experimental and computed surf-ace oil maps. ne flow structure arising from asymmetric interactions was investigated with particular emphasis on: 1) vorticity dynamics, 2) shock-structure and 3) sidewall vortex loading. Several efforts of the prior year were successfully published in archival journals. The high-order algorithms developed for CEM have been implemented into the FDL3DI CFD code are presently undergoing extensive testing. Preliminary results are highly encouraging.

Gaitonde, Datta↗
NASA NTRS1981

Basic advances in the finite-volume method for transonic potential flow calculations

The finite-volume method of Jameson and Caughey provides a framework within which it is possible to calculate transonic potential flows about essentially arbitrary geometrical configurations. Improvements designed to increase the accuracy of the basic scheme and its consistency in the far field will be described. These include the incorporation of an artificial viscosity which maintains the formal second-order accuracy of the scheme in supersonic zones, and a modification of the flux balances to allow the free-stream conditions to satisfy the difference equations identically. Results of calculations illustrating the importance of these effects will be presented.

Caughey, D. A.↗
NASA NTRS2001

Computational Aeroacoustics by the Space-time CE/SE Method

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

Loh, Ching Y.↗
NASA NTRS1992

A composite structured/unstructured-mesh Euler method for complex airfoil shapes

A general two-dimensional Euler zonal method has been developed for computing flows about complex airfoil geometries such as multielement and iced airfoils. The method utilizes a composite structured and unstructured grid generated using conformal mapping and Delaunay triangulation, respectively. The finite-volume Euler method is then modified to couple solutions in the zones with structured and unstructured grids. Solutions about an iced airfoil and a multielement airfoil are given as examples of applications of the scheme.

Hefazi, H.↗
NASA NTRS1991

Application of program LAURA to thermochemical nonequilibrium flow through a nozzle

Program LAURA (Langley Aerothermodynamic Upwind Relaxation Algorithm) is an upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3D 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 a modified Roe's averaging and with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. The code has been applied to Problem 8.2 of this workshop for the case of thermochemical nonequilibrium flow through a nozzle. Chemical reaction rates are defined with the model of Park (1987). Thermal nonequilibrium is modeled using a two-temperature approximation in which the vibrational energies of all molecules are assumed to be in equilibrium at a single temperature which is generally different from the translational-rotational temperature. Two grids were used to define the flow for the original problem, with a stagnation temperature of 6500 K. A third case with a stagnation temperature of 10,000 K is also presented. The solution domain includes the converging nozzle, subsonic flow domain in which the gas is substantially in thermochemical equilibrium and the diverging nozzle, hypersonic flow domain in which the gas is substantially in thermochemical nonequilibrium.

Gnoffo, Peter A.↗
NASA NTRS2003

Influence of Ice-phase of Hydrometeors on Moist-Convection

Climate models often ignore the influence of ice-phase physics (IPP) of hydrometeors as a second order effect. This has also been true for McRAS (Microphysics of clouds with Relaxed Arakawa Schubert Scheme) developed by the authors. Recognizing that the temperature sounding is critical for moist-convection, and, that IPP would modify it, we investigated the influence of introducing IPP into McRAS coupled to FvGCM (finite volume General Circulation Model with NCAR physics). We analyzed three 3-yr long simulations; the first called Control Case, CC and had no IPP; the other two called Experiments El and E2 had IPP introduced with two different in-cloud freezing assumptions. Simulation El assumed that all hydrometeors remain liquid in the updraft and freeze upon detrainment. Simulation E2 invoked the in-cloud freezing of new condensate generated at subfreezing temperatures in the updraft while old cloud water continued to ascend as liquid. Upon detrainment, this cloud water also froze like in E1. With these assumptions, about 50% of hydrometeors froze in the tower and the rest froze in the anvil. However, in both El and E2, the frozen hydrometeors melted during fall at the first encounter of above freezing ambient temperature. Comparative analysis revealed that El simulated far more mid-level and far less deep clouds while E2 had modified deep and more mid-level clouds as compared to CC along with some major changes around the melt-level. We infer that IPP produced a more realistic response in E2. At the basic level, the results show that ice-phase processes influence convective detrainment at mid- and deep levels in accord with TOGAGOARE observations. The results suggest that IPP can help to mitigate less-than-observed mid-level and over-abundance of deep convective clouds in McRAS.

Sud, Y. C.↗
NASA NTRS2008

A New Concurrent Multiscale Methodology for Coupling Molecular Dynamics and Finite Element Analyses

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

Yamakov, Vesselin↗
NASA NTRS2008

An Embedded Statistical Method for Coupling Molecular Dynamics and Finite Element Analyses

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

Saether, E.↗
NASA NTRS1993

Application of an unstructured grid flow solver to planes, trains and automobiles

Rampant, an unstructured flow solver developed at Fluent Inc., is used to compute three-dimensional, viscous, turbulent, compressible flow fields within complex solution domains. Rampant is an explicit, finite-volume flow solver capable of computing flow fields using either triangular (2d) or tetrahedral (3d) unstructured grids. Local time stepping, implicit residual smoothing, and multigrid techniques are used to accelerate the convergence of the explicit scheme. The paper describes the Rampant flow solver and presents flow field solutions about a plane, train, and automobile.

Spragle, Gregory S.↗
NASA NTRS2001

Distributed Relaxation for Conservative Discretizations

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Diskin, Boris↗
NASA NTRS2008

A Goddard Multi-Scale Modeling System with Unified Physics

A multi-scale modeling system with unified physics has been developed at NASA Goddard Space Flight Center (GSFC). The system consists of an MMF, the coupled NASA Goddard finite-volume GCM (fvGCM) and Goddard Cumulus Ensemble model (GCE, a CRM); the state-of-the-art Weather Research and Forecasting model (WRF) and the stand alone GCE. These models can share the same microphysical schemes, radiation (including explicitly calculated cloud optical properties), and surface models that have been developed, improved and tested for different environments. The following is presented in this report: (1) a brief review of the GCE model and its applications on the impact of aerosols on deep precipitation processes, (2) the Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) a discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗
NASA NTRS2010

A Goddard Multi-Scale Modeling System with Unified Physics

A multi-scale modeling system with unified physics has been developed at NASA Goddard Space Flight Center (GSFC). The system consists of an MMF, the coupled NASA Goddard finite-volume GCM (fvGCM) and Goddard Cumulus Ensemble model (GCE, a CRM); the state-of-the-art Weather Research and Forecasting model (WRF) and the stand alone GCE. These models can share the same microphysical schemes, radiation (including explicitly calculated cloud optical properties), and surface models that have been developed, improved and tested for different environments. In this talk, I will present: (1) A brief review on GCE model and its applications on the impact of the aerosol on deep precipitation processes, (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications). We are also performing the inline tracer calculation to comprehend the physical processes (i.e., boundary layer and each quadrant in the boundary layer) related to the development and structure of hurricanes and mesoscale convective systems. In addition, high - resolution (spatial. 2km, and temporal, I minute) visualization showing the model results will be presented.

Tao, Wei-Kuo↗
NASA NTRS2010

A Goddard Multi-Scale Modeling System with Unified Physics

A multi-scale modeling system with unified physics has been developed at NASA Goddard Space Flight Center (GSFC). The system consists of an MMF, the coupled NASA Goddard finite-volume GCM (fvGCM) and Goddard Cumulus Ensemble model (GCE, a CRM); the state-of-the-art Weather Research and Forecasting model (WRF) and the stand alone GCE. These models can share the same microphysical schemes, radiation (including explicitly calculated cloud optical properties), and surface models that have been developed, improved and tested for different environments. In this talk, I will present: (1) A brief review on GCE model and its applications on the impact of the aerosol on deep precipitation processes, (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications). We are also performing the inline tracer calculation to comprehend the ph ysical processes (i.e., boundary layer and each quadrant in the boundary layer) related to the development and structure of hurricanes and mesoscale convective systems.

Tao, Wei-Kuo↗
NASA NTRS1984

Numerical study of two-dimensional non-plane MHD wave propagation in a supersonic, superalfvenic magnetohydrodynamic flow

The features of a 2.5-dimensional time-dependent MHD numerical code used to simulate the propagation of finite amplitude MHD waves through an inhomogeneous, supersonic superalfvenic medium are described. Basic equations for conservation of mass, momentum, and free energy in a unit volume plasma gas and for magnetic induction are defined. Initial conditions are functions of the radial coordinates and disturbances are introduced at the lower boundary. A set of finite difference equations based on a Lax-Wendroff scheme is used for the simulation. The model is applied to analyzing a solar flare shock wave in steady-state and global transient conditions while propagating at 1 AU heliolongitude.

Han, S. M.↗
NASA NTRS1987

Computational and experimental investigation of cavity flowfields

This paper presents a computational and experimental investigation of supersonic flow past a cavity in a flat plate. The source of the particular interest in this problem is the ongoing study of the aerodynamic interference effects between a separating store and its bay in the parent body. An upwind relaxation scheme, utilizing flux vector splitting and line-Gauss-Seidel iterations, is used to solve Reynolds-averaged Navier-Stokes equations. Spatial discretizations of this two-dimensional analysis are based on implicit and finite-volume methods. Turbulence is modeled and shocks are captured. The flowfield of the symmetry plane at the half-width is computationally visualized and all flow properties are computed. Experimental tests are conducted in the Langley Unitary Plan Wind Tunnel to measure wall pressures and to capture schlieren photographs. Qualitative as well as quantitative data of computations and experiments agree very well. These two vehicles of investigation are merged to show open, closed and transitional cavity flow behaviors.

Baysal, O.↗
NASA NTRS1990

An upwind-biased, point-implicit relaxation algorithm for viscous, compressible perfect-gas flows

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, compressible, perfect-gas flows is described. 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. Viscous terms are discretized using central differences. The relaxation strategy is well suited for computers employing either vector or parallel architectures. It is also well suited to the numerical solution of the governing equations on unstructured grids. 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. Convergence rates and grid refinement studies are conducted for Mach 5 flow through an inlet with a 10 deg compression ramp and Mach 14 flow over a 15 deg ramp. Predictions for pressure distributions, surface heating, and aerodynamics coefficients compare well with experiment data for Mach 10 flow over a blunt body.

Gnoffo, Peter A.↗
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.↗