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NASA NTRS2007

RANS and URANS Application with CFL3D

This case was run using CFL3D, a multi-zone Reynolds-averaged Navier-Stokes code developed at NASA Langley [1]. It solves the thin-layer form of the Navier-Stokes equations in each of the (selected) coordinate directions. It can use 1-to-1, patched, or overset grids, and employs local time step scaling, grid sequencing, and multigrid to accelerate convergence to steady state. In time-accurate mode, CFL3D has the option to employ dual-time stepping with subiterations and multigrid, and it achieves second order temporal accuracy. CFL3D is a finite volume method. It uses third-order upwind-biased spatial differencing on the convective and pressure terms, and second-order differencing on the viscous terms; it is globally second-order spatially accurate. The flux difference-splitting (FDS) method of Roe is employed to obtain fluxes at the cell faces. It is advanced in time with an implicit three-factor approximate factorization method.

Rumsey, C. L.↗

NASA NTRS2009

Towards an "All Speed" Unstructured Upwind Scheme

In the authors previous studies [1], a time-accurate, upwind finite volume method (ETAU scheme) for computing compressible flows on unstructured grids was proposed. The scheme is second order accurate in space and time and yields high resolution in the presence of discontinuities. The scheme features a multidimensional limiter and multidimensional numerical dissipation. These help to stabilize the numerical process and to overcome the annoying pathological behaviors of upwind schemes. In the present paper, it will be further shown that such multidimensional treatments also lead to a nearly all-speed or Mach number insensitive upwind scheme. For flows at very high Mach number, e.g., 10, local numerical instabilities or the pathological behaviors are suppressed, while for flows at very low Mach number, e.g., 0.02, computation can be directly carried out without invoking preconditioning. For flows in different Mach number regimes, i.e., low, medium, and high Mach numbers, one only needs to adjust one or two parameters in the scheme. Several examples with low and high Mach numbers are demonstrated in this paper. Thus, the ETAU scheme is applicable to a broad spectrum of flow regimes ranging from high supersonic to low subsonic, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics).

Loh, Ching Y.↗

NASA NTRS2011

Network Flow Simulation of Fluid Transients in Rocket Propulsion Systems

Fluid transients, also known as water hammer, can have a significant impact on the design and operation of both spacecraft and launch vehicle propulsion systems. These transients often occur at system activation and shutdown. The pressure rise due to sudden opening and closing of valves of propulsion feed lines can cause serious damage during activation and shutdown of propulsion systems. During activation (valve opening) and shutdown (valve closing), pressure surges must be predicted accurately to ensure structural integrity of the propulsion system fluid network. In the current work, a network flow simulation software (Generalized Fluid System Simulation Program) based on Finite Volume Method has been used to predict the pressure surges in the feed line due to both valve closing and valve opening using two separate geometrical configurations. The valve opening pressure surge results are compared with experimental data available in the literature and the numerical results compared very well within reasonable accuracy (< 5%) for a wide range of inlet-to-initial pressure ratios. A Fast Fourier Transform is preformed on the pressure oscillations to predict the various modal frequencies of the pressure wave. The shutdown problem, i.e. valve closing problem, the simulation results are compared with the results of Method of Characteristics. Most rocket engines experience a longitudinal acceleration, known as "pogo" during the later stage of engine burn. In the shutdown example problem, an accumulator has been used in the feed system to demonstrate the "pogo" mitigation effects in the feed system of propellant. The simulation results using GFSSP compared very well with the results of Method of Characteristics.

Bandyopadhyay, Alak↗

NASA NTRS2013

Experimental Investigation of Shock-Shock Interactions Over a 2-D Wedge at M=6

The effects of fin-leading-edge radius and sweep angle on peak heating rates due to shock-shock interactions were investigated in the NASA Langley Research Center 20-inch Mach 6 Air Tunnel. The fin model leading edges, which represent cylindrical leading edges or struts on hypersonic vehicles, were varied from 0.25 inches to 0.75 inches in radius. A 9deg wedge generated a planar oblique shock at 16.7deg to the flow that intersected the fin bow shock, producing a shock-shock interaction that impinged on the fin leading edge. The fin angle of attack was varied from 0deg (normal to the free-stream) to 15deg and 25deg swept forward. Global temperature data was obtained from the surface of the fused silica fins through phosphor thermography. Metal oil flow models with the same geometries as the fused silica models were used to visualize the streamline patterns for each angle of attack. High-speed zoom-schlieren videos were recorded to show the features and temporal unsteadiness of the shock-shock interactions. The temperature data were analyzed using one-dimensional semi-infinite as well as one- and two-dimensional finite-volume methods to determine the proper heat transfer analysis approach to minimize errors from lateral heat conduction due to the presence of strong surface temperature gradients induced by the shock interactions. The general trends in the leading-edge heat transfer behavior were similar for the three shock-shock interactions, respectively, between the test articles with varying leading-edge radius. The dimensional peak heat transfer coefficient augmentation increased with decreasing leading-edge radius. The dimensional peak heat transfer output from the two-dimensional code was about 20% higher than the value from a standard, semi-infinite one-dimensional method.

Jones, Michelle L.↗

NASA NTRS2013

Thermographic Phosphor Measurements of Shock-Shock Interactions on a Swept Cylinder

The effects of fin leading-edge radius and sweep angle on peak heating rates due to shock-shock interactions were investigated in the NASA Langley Research Center 20-inch Mach 6 Air Tunnel. The fin model leading edges, which represent cylindrical leading edges or struts on hypersonic vehicles, were varied from 0.25 inches to 0.75 inches in radius. A 9deg wedge generated a planar oblique shock at 16.7deg to the flow that intersected the fin bow shock, producing a shock-shock interaction that impinged on the fin leading edge. The fin angle of attack was varied from 0deg (normal to the free-stream) to 15deg and 25deg swept forward. Global temperature data was obtained from the surface of the fused silica fins using phosphor thermography. Metal oil flow models with the same geometries as the fused silica models were used to visualize the streamline patterns for each angle of attack. High-speed zoom-schlieren videos were recorded to show the features and temporal unsteadiness of the shock-shock interactions. The temperature data were analyzed using one-dimensional semi-infinite as well as one- and two-dimensional finite-volume methods to determine the proper heat transfer analysis approach to minimize errors from lateral heat conduction due to the presence of strong surface temperature gradients induced by the shock interactions. The general trends in the leading-edge heat transfer behavior were similar for the three shock-shock interactions, respectively, between the test articles with varying leading-edge radius. The dimensional peak heat transfer coefficient augmentation increased with decreasing leading-edge radius. The dimensional peak heat transfer output from the two-dimensional code was about 20% higher than the value from a standard, semi-infinite onedimensional method.

Jones, Michelle L.↗

NASA NTRS2017

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗

NASA NTRS2020

Experimental Investigation of Shock-Shock Interactions Over a 2D Wedge at M = 6

The effects of fin-leading-edge radius and sweep angle on peak heating rates due to shock-shock interactions were investigated in the NASA Langley Research Center 20-Inch Mach 6 Air Tunnel. The fin model leading edges, which represent cylindrical leading edges or struts on hypersonic vehicles, were varied from 0.25 inches to 0.75 inches in radius. A 9° wedge generated a planar oblique shock at 16.7° to the flow that intersected the fin bow shock, producing a shock-shock interaction that impinged on the fin leading edge. The fin angle of attack was varied from 0° (normal to the free-stream) to 15° and 25° swept forward. Global temperature data were obtained from the surface of the fused silica fins through phosphor thermography. Metal oil flow models with the same geometries as the fused silica models were used to visualize the streamline patterns for each angle of attack. High-speed zoom-schlieren videos were recorded to show the features and temporal unsteadiness of the shock-shock interactions. The temperature data were analyzed using one-dimensional semi-infinite as well as one- and two-dimensional finite-volume methods to determine the proper heat transfer analysis approach to minimize errors from lateral heat conduction due to the presence of strong surface temperature gradients induced by the shock interactions. The general trends in the leading-edge heat transfer behavior were similar for the three shock-shock interactions, respectively, between the test articles with varying leading-edge radius. The dimensional peak heat transfer coefficient augmentation increased with decreasing leading-edge radius. The dimensional peak heat transfer output from the two-dimensional code was about 20% higher than the value from a standard, semi-infinite one-dimensional method.

shock-shock interaction↗

NASA NTRSDate not supplied

Predictions of the Azimuthal Variation of the Noise from Chevron Jets using an Acoustic Analogy

An existing acoustic analogy formulation is used to make predictions of the turbulent mixing noise from a series of chevron jets tested at NASA Glenn Research Center. Reynolds-averaged Navier-Stokes solutions are used as input to provide the mean flow and turbulence quantities needed to compute the Green’s function and parameterize the source model. The Green’s function for the non-axisymmetric mean flows generated by these nozzles is computed using a second-order finite volume method. A slightly modified version of an existing source model originally developed for round jets is used to assess its capability in these non-axisymmetric flows. Prediction results are compared with experimental data for a range of azimuthal orders of the nozzle geometry and flow speeds. The results show that the RANS-based acoustic analogy prediction method is able to capture the observed azimuthal variation of the sound field fairly well at relatively low jet exit velocities. At higher speeds, the prediction method still captures the observed trends in azimuthal directivity but not the absolute levels, particularly at higher frequencies. Areas for potential improvement of the method are suggested.

Jet Noise↗

NASA NTRSDate not supplied

Predictions of the Azimuthal Variation of the Noise from Chevron Jets using an Acoustic Analogy

Jet Noise↗

NASA NTRS1994

New Computer Simulations of Macular Neural Functioning

We use high performance graphics workstations and supercomputers to study the functional significance of the three-dimensional (3-D) organization of gravity sensors. These sensors have a prototypic architecture foreshadowing more complex systems. Scaled-down simulations run on a Silicon Graphics workstation and scaled-up, 3-D versions run on a Cray Y-MP supercomputer. A semi-automated method of reconstruction of neural tissue from serial sections studied in a transmission electron microscope has been developed to eliminate tedious conventional photography. The reconstructions use a mesh as a step in generating a neural surface for visualization. Two meshes are required to model calyx surfaces. The meshes are connected and the resulting prisms represent the cytoplasm and the bounding membranes. A finite volume analysis method is employed to simulate voltage changes along the calyx in response to synapse activation on the calyx or on calyceal processes. The finite volume method insures that charge is conserved at the calyx-process junction. These and other models indicate that efferent processes act as voltage followers, and that the morphology of some afferent processes affects their functioning. In a final application, morphological information is symbolically represented in three dimensions in a computer. The possible functioning of the connectivities is tested using mathematical interpretations of physiological parameters taken from the literature. Symbolic, 3-D simulations are in progress to probe the functional significance of the connectivities. This research is expected to advance computer-based studies of macular functioning and of synaptic plasticity.

Ross, Muriel D.↗

NASA NTRS1986

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

Nicholson, S.↗

NASA NTRS1976

The Relation of Finite Element and Finite Difference Methods

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Vinokur, M.↗

NASA NTRS1993

Numerical investigation of complex, transitional, and chemically reacting flows

This document is divided into two parts. Part A, on turbulent transport of chemical species in compressible reacting flows, includes the following topics: mixing of chemical species in reacting flows; chemically reacting turbulent flows; turbulent mixing of chemical species in reacting flows, which includes large eddy mixing, turbulent mixing, and molecular mixing; multiple time scale turbulence equations; species conservation equations for reacting flows; and a finite volume numerical method. Part B, on unsteady transitional flows over forced oscillatory surfaces, discusses unsteady transitional flow equations with moving boundaries and the application of the finite volume numerical solution method.

Kim, S.-W.↗

NASA NTRS1986

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

The finite volume explicit time marching method was refined and improved. Previously, extension had been made to the finite volume method to improve the accuracy of the calculation of total pressure in inviscid flow, extend the method to allow the calculation of laminar and turbulent boundary layers in internal flows, and improve the shock capturing properties of the method by introducing a Mach number dependent interpolation scheme for the pressure used in the calculating the density. The current work extends these developments by using the new pressure interpolation scheme in two dimensional viscous calculations, including a more complete description of the viscous stresses, introducing a criteria for the transverse upwind differencing which is a function of the ratio of transverse and streamwise mass fluxes, and allowing the calculation of internal flow where boundary layers are present on both walls of the duct. The manner in which the viscous stresses are evaluated in the nonorthogonal, nonuniform grid is detailed. The convergence is investigated and results for calculations of laminar flow in a converging duct are presented. Results for calculations of transonic flow in a converging-diverging nozzle are presented and the results are compared with Sajben's measurements and calculations by others.

Nicholson, S.↗

NASA NTRS1998

Unstructured Finite Volume Computational Thermo-Fluid Dynamic Method for Multi-Disciplinary Analysis and Design Optimization

This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational Fluid Dynamic(CFD) methods and therefore has the potential for implementation in Multi-Disciplinary analysis and design optimization in fluid and thermal systems. The paper also describes an algorithm of design optimization based on Newton-Raphson method which has been recently tested in a turbomachinery application.

Majumdar, Alok↗

DOE OSTI2024

Generalized boost transformations in finite volumes and application to Hamiltonian methods

The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian. In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological ππ scattering example.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2004

Demonstration Of Ultra HI-FI (UHF) Methods

Computational aero-acoustics (CAA) requires efficient, high-resolution simulation tools. Most current techniques utilize finite-difference approaches because high order accuracy is considered too difficult or expensive to achieve with finite volume or finite element methods. However, a novel finite volume approach (Ultra HI-FI or UHF) which utilizes Hermite fluxes is presented which can achieve both arbitrary accuracy and fidelity in space and time. The technique can be applied to unstructured grids with some loss of fidelity or with multi-block structured grids for maximum efficiency and resolution. In either paradigm, it is possible to resolve ultra-short waves (less than 2 PPW). This is demonstrated here by solving the 4th CAA workshop Category 1 Problem 1.

Dyson, Rodger W.↗

NASA NTRS1990

An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

Baysal, Oktay↗