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NASA NTRS2004

Multidimensional Unstructured-Grid Liquid Rocket Engine Nozzle Performance and Heat Transfer Analysis

The objective of this study is to conduct a unified computational analysis for computing design parameters such as axial thrust, convective and radiative wall heat fluxes for regeneratively cooled liquid rocket engine nozzles, so as to develop a computational strategy for computing those parameters through parametric investigations. The computational methodology is based on a multidimensional, finite-volume, turbulent, chemically reacting, radiating, unstructured-grid, and pressure-based formulation, with grid refinement capabilities. Systematic parametric studies on effects of wall boundary conditions, combustion chemistry, radiation coupling, computational cell shape, and grid refinement were performed and assessed. Under the computational framework of this study, it is found that the computed axial thrust performance, flow features, and wall heat fluxes compared well with those of available data and calculations, using a strategy of structured-grid dominated mesh, finite-rate chemistry, and cooled wall boundary condition.

Wang, Ten-See↗

NASA NTRS1996

3D Feature Extraction for Unstructured Grids

Visualization techniques provide tools that help scientists identify observed phenomena in scientific simulation. To be useful, these tools must allow the user to extract regions, classify and visualize them, abstract them for simplified representations, and track their evolution. Object Segmentation provides a technique to extract and quantify regions of interest within these massive datasets. This article explores basic algorithms to extract coherent amorphous regions from two-dimensional and three-dimensional scalar unstructured grids. The techniques are applied to datasets from Computational Fluid Dynamics and those from Finite Element Analysis.

Silver, Deborah↗

NASA NTRS1993

Application of a two-equation turbulence model for high speed compressible flows using unstructured grids

Application of a two-equation compressible turbulence model for practical hypersonic flows 18 presented. The solution algorithm is based on solving all of the governing equations simultaneously. Application of the solution procedure to several test cases for compressible flows show good agreement with theoretical predictions and/or other computational results. The solution procedure is employed to investigate the effects of turbulence in Type III and Type IV shock-shock interactions in hypersonic flows in association with adaptive unstructured grids. Computational results for these cases are compared with available experimental data.

Vemaganti, Gururaja R.↗

NASA NTRS2021

Australian tidal currents – assessment of a barotropic model (COMPAS v1.3.0 rev6631) with an unstructured grid

While the variations of tidal range are large and fairly well known across Australia (less than 1 m near Perth but more than 14 m in King Sound), the properties of the tidal currents are not. We describe a new regional model of Australian tides and assess it against a validation dataset comprising tidal height and velocity constituents at 615 tide gauge sites and 95 current meter sites. The model is a barotropic implementation of COMPAS, an unstructured-grid primitive-equation model that is forced at the open boundaries by TPXO9v1. The mean absolute error (MAE) of the modelled M2 height amplitude is 8.8 cm, or 12 % of the 73 cm mean observed amplitude. The MAE of phase (10°), however, is significant, so the M2 mean magnitude of vector error (MMVE, 18.2 cm) is significantly greater. The root sum square over the eight major constituents is 26 % of the observed amplitude. We conclude that while the model has skill at height in all regions, there is definitely room for improvement (especially at some specific locations). For the M2 major axis velocity amplitude, the MAE across the 95 current meter sites, where the observed amplitude ranges from 0.1 to 156 cm s −1 , is 6.9 cm s −1 , or 22 % of the 31.7 cm s −1 observed mean. This nationwide average result is encouraging, but it conceals a very large regional variation. Relative errors of the tidal current amplitudes on the narrow shelves of New South Wales (NSW) and Western Australia exceed 100 %, but tidal currents are weak and negligible there compared to non-tidal currents, so the tidal errors are of little practical significance. Looking nationwide, we show that the model has predictive value for much of the 79 % of Australia's shelf seas where tides are a major component of the total velocity variability. In descending order this includes the Bass Strait, the Kimberley to Arnhem Land, and southern Great Barrier Reef regions. There is limited observational evidence to confirm that the model is also valuable for currents in other regions across northern Australia. We plan to commence publishing “unofficial” tidal current predictions for chosen regions in the near future based on both our COMPAS model and the validation dataset we have assembled.

Tidal currents↗

NASA NTRS1991

The computation of three-dimensional flows using unstructured grids

A general method is described for automatically discretizing, into unstructured assemblies of tetrahedra, the three-dimensional solution domains of complex shape which are of interest in practical computational aerodynamics. An algorithm for the solution of the compressible Euler equations which can be implemented on such general unstructured tetrahedral grids is described. This is an explicit cell-vertex scheme which follows a general Taylor-Galerkin philosophy. The approach is employed to compute a transonic inviscid flow over a standard wing and the results are shown to compare favorably with experimental observations. As a more practical demonstration, the method is then applied to the analysis of inviscid flow over a complete modern fighter configuration. The effect of using mesh adaptivity is illustrated when the method is applied to the solution of high speed flow in an engine inlet.

Morgan, K.↗

NASA NTRS1998

Current Status on the use of Parallel Computing in Turbulent Reacting Flow Computations Involving Sprays, Monte Carlo PDF and Unstructured Grids

The state of the art in multidimensional combustor modeling as evidenced by the level of sophistication employed in terms of modeling and numerical accuracy considerations, is also dictated by the available computer memory and turnaround times afforded by present-day computers. With the aim of advancing the current multi-dimensional computational tools used in the design of advanced technology combustors, a solution procedure is developed that combines the novelty of the coupled CFD/spray/scalar Monte Carlo PDF (Probability Density Function) computations on unstructured grids with the ability to run on parallel architectures. In this approach, the mean gas-phase velocity and turbulence fields are determined from a standard turbulence model, the joint composition of species and enthalpy from the solution of a modeled PDF transport equation, and a Lagrangian-based dilute spray model is used for the liquid-phase representation. The gas-turbine combustor flows are often characterized by a complex interaction between various physical processes associated with the interaction between the liquid and gas phases, droplet vaporization, turbulent mixing, heat release associated with chemical kinetics, radiative heat transfer associated with highly absorbing and radiating species, among others. The rate controlling processes often interact with each other at various disparate time 1 and length scales. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and liquid phase evaporation in many practical combustion devices.

Raju, M. S.↗

NASA NTRS2004

Propulsion Simulations Using Advanced Turbulence Models with the Unstructured Grid CFD Tool, TetrUSS

A computational investigation has been completed to assess the capability of TetrUSS for exhaust nozzle flows. Three configurations were chosen for this study (1) an axisymmetric supersonic jet, (2) a transonic axisymmetric boattail with solid sting operated at different Reynolds number and Mach number, and (3) an isolated non-axisymmetric nacelle with a supersonic cruise nozzle. These configurations were chosen because existing experimental data provided a means for measuring the ability of TetrUSS for simulating complex nozzle flows. The main objective of this paper is to validate the implementation of advanced two-equation turbulence models in the unstructured-grid CFD code USM3D for propulsion flow cases. USM3D is the flow solver of the TetrUSS system. Three different turbulence models, namely, Menter Shear Stress Transport (SST), basic k epsilon, and the Spalart-Allmaras (SA) are used in the present study. The results are generally in agreement with other implementations of these models in structured-grid CFD codes. Results indicate that USM3D provides accurate simulations for complex aerodynamic configurations with propulsion integration.

Abdol-Hamid, Khaled S.↗

NASA NTRS1998

EUPDF: Eulerian Monte Carlo Probability Density Function Solver for Applications With Parallel Computing, Unstructured Grids, and Sprays

The success of any solution methodology used in the study of gas-turbine combustor flows depends a great deal on how well it can model the various complex and rate controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as convective and radiative heat transfer and other phenomena. The phenomena to be modeled, which are controlled by these processes, often strongly interact with each other at different times and locations. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and evaporation in many practical combustion devices. The influence of turbulence in a diffusion flame manifests itself in several forms, ranging from the so-called wrinkled, or stretched, flamelets regime to the distributed combustion regime, depending upon how turbulence interacts with various flame scales. Conventional turbulence models have difficulty treating highly nonlinear reaction rates. A solution procedure based on the composition joint probability density function (PDF) approach holds the promise of modeling various important combustion phenomena relevant to practical combustion devices (such as extinction, blowoff limits, and emissions predictions) because it can account for nonlinear chemical reaction rates without making approximations. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on the PDF method to unstructured grids, parallel computing, and sprays. EUPDF, which was developed by M.S. Raju of Nyma, Inc., was designed to be massively parallel and could easily be coupled with any existing gas-phase and/or spray solvers. EUPDF can use an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements. The application of the PDF method showed favorable results when applied to several supersonic-diffusion flames and spray flames. The EUPDF source code will be available with the National Combustion Code (NCC) as a complete package.

Raju, M. S.↗

NASA NTRS2001

Baseline Validation of Unstructured Grid Reynolds-Averaged Navier-Stokes Toward Flow Control

The value of the use of the Reynolds-averaged Navier-Stokes methodology for active flow control applications is assessed. An experimental flow control database exists for a NACA0015 airfoil modified at the leading edge to implement a fluidic actuator; hence, this configuration is used. Computational results are documented for the baseline wing configuration (no control) with the experimental results and assumes two-dimensional flow. The baseline wing configuration has discontinuities at the leading edge, trailing edge, and aft of midchord on the upper surface. A limited number of active flow control applications have been tested in the laboratory and in flight. These applications include dynamic stall control using a deformable leading edge, separation control for takeoff and landing flight conditions using piezoelectric devices, pulsed vortex generators, zero-net-mass oscillations, and thrust vectoring with zero-net-mass piezoelectric-driven oscillatory actuation. As yet, there is no definitive comparison with experimental data that indicates current computational capabilities can quantitatively predict the large aerodynamic performance gains achieved with active flow control in the laboratory. However, one study using the Reynolds-averaged Navier-Stokes (RANS) methodology has shown good quantitative agreement with experimental results for an isolated zero-net-mass actuator. In addition, some recent studies have used RANS to demonstrate qualitative performance gains compared with the experimental data for separation control on an airfoil. Those quantitative comparisons for both baseline and flow control cases indicated that computational results were in poor quantitative agreement with the experiments. The current research thrust will investigate the potential use of an unstructured grid RANS approach to predict aerodynamic performance for active flow control applications building on the early studies. First the computational results must quantitatively match experiments for the no-control case before proceeding to the time-dependent flow control case. This paper documents the baseline (no-control) case using an unswept airfoil configuration. The next section describes the configurations used for the computations and the experimentals. The computational approach is then described followed by results and concluding remarks.

Joslin, Ronald D.↗

NASA NTRS2018

Generating a Grid for Unstructured RANS Simulations of Jet Flows

A study has been performed to determine best practices for generating unstructured grids for Reynolds-Averaged Navier-Stokes (RANS) simulations of jet flows. The Axisymmetric Near-Sonic Jet Case from the Turbulence Modeling Resource was used for this study: a Mach 0.985 flow through the 2-in. diameter Acoustic Reference Nozzle (ARN2). Simulations were run with FUN3D and used the Menter Shear Stress Transport (SST-V), Spalart-Allmaras (S-A), and k-kL turbulence models. The axial velocity and turbulent kinetic energy fields in the jet plume of the unstructured grid solutions were compared to those of the baseline structured grid solution provided by the Turbulence Modeling Resource. Only solutions using grids with structured-like elements in the jet plume showed good agreement with the baseline structured grid solution. Using the SST-V turbulence model, the fully unstructured grid solutions predicted the jet potential core to decay upstream of the baseline solution. With the S-A turbulence model, the unstructured grid solutions predicted the jet potential core to decay upstream of the baseline solution. The solutions using the k-kL turbulence model seemed less sensitive to grid topology. Nozzle massflow and thrust performance were also compared for all simulations. Based on the results of this study, it is currently recommended that structured-like grid elements are used in the plumes of jet flows; unstructured grid elements can be used elsewhere.

RANS Simulations; Unstructured Grids; Jet Flows↗

NASA NTRS1993

Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids

The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.

Gedney, Stephen D.↗

NASA NTRS2017

JIGSAW-GEO (1.0): Locally Orthogonal Staggered Unstructured Grid Generation for General Circulation Modelling on the Sphere

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered VoronoiDelaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

geophysical fluid dynamics↗

NASA NTRS1993

Robust unstructured grid generation with VGRID

The objective of this work is to develop a robust, user-oriented, unstructured grid-generation technique for fast generation of Euler/viscous grids around complex 2D and 3D configurations. To do this, two different approaches are employed: the advancing-front method for generation of Euler grids; and the advancing-layers method for generation of viscous grids. A discussion of these topics is presented in viewgraph form.

Shahyar Pirzadeh↗

NASA NTRS1999

Solving Navier-Stokes Equations with Advanced Turbulence Models on Three-Dimensional Unstructured Grids

USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flows. We have implemented two modified versions of the original Jones and Launder k-epsilon two-equation turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for two flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those of empirical formulae, theoretical results and the existing Spalart-Allmaras one-equation model.

Wang, Qun-Zhen↗

DOE OSTI2013

Verification & Validation of High-Order Short-Characteristics-Based Deterministic Transport Methodology on Unstructured Grids

The research team has developed a practical, high-order, discrete-ordinates, short characteristics neutron transport code for three-dimensional configurations represented on unstructured tetrahedral grids that can be used for realistic reactor physics applications at both the assembly and core levels. This project will perform a comprehensive verification and validation of this new computational tool against both a continuous-energy Monte Carlo simulation (e.g. MCNP) and experimentally measured data, an essential prerequisite for its deployment in reactor core modeling. Verification is divided into three phases. The team will first conduct spatial mesh and expansion order refinement studies to monitor convergence of the numerical solution to reference solutions. This is quantified by convergence rates that are based on integral error norms computed from the cell-by-cell difference between the code’s numerical solution and its reference counterpart. The latter is either analytic or very fine- mesh numerical solutions from independent computational tools. For the second phase, the team will create a suite of code-independent benchmark configurations to enable testing the theoretical order of accuracy of any particular discretization of the discrete ordinates approximation of the transport equation. For each tested case (i.e. mesh and spatial approximation order), researchers will execute the code and compare the resulting numerical solution to the exact solution on a per cell basis to determine the distribution of the numerical error. The final activity comprises a comparison to continuous-energy Monte Carlo solutions for zero-power critical configuration measurements at Idaho National Laboratory’s Advanced Test Reactor (ATR). Results of this comparison will allow the investigators to distinguish between modeling errors and the above-listed discretization errors introduced by the deterministic method, and to separate the sources of uncertainty.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1999

Portable Parallel Programming for the Dynamic Load Balancing of Unstructured Grid Applications

The ability to dynamically adapt an unstructured -rid (or mesh) is a powerful tool for solving computational problems with evolving physical features; however, an efficient parallel implementation is rather difficult, particularly from the view point of portability on various multiprocessor platforms We address this problem by developing PLUM, tin automatic anti architecture-independent framework for adaptive numerical computations in a message-passing environment. Portability is demonstrated by comparing performance on an SP2, an Origin2000, and a T3E, without any code modifications. We also present a general-purpose load balancer that utilizes symmetric broadcast networks (SBN) as the underlying communication pattern, with a goal to providing a global view of system loads across processors. Experiments on, an SP2 and an Origin2000 demonstrate the portability of our approach which achieves superb load balance at the cost of minimal extra overhead.

Biswas, Rupak↗

NASA NTRS1990

A three-dimensional space marching algorithm for the solution of the Euler equations on unstructured grids

A three-dimensional space marching algorithm using an unstructured discretization is proposed. The governing equations and the spatial discretization of the domain and the interpolation from one arbitrary unstructured mesh to another are discussed, and the grid generation technique is described. Solutions for several different geometries are presented, and the results are compared with existing numerical techniques and experimental results.

Mcgrory, W. D.↗

NASA NTRS2002

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

Wang, Z. J.↗