Results for “Fluid equations” — Page 11

NASA NTRS1989

Dynamic grid deformation using Navier-displacement equation for deforming wings

For dynamic and aeroelastic applications of maneuvering wings, the solid boundaries undergo rigid-body motion and aeroelastic deformation. For rigid-body motion, the conservative fluid dynamics equation, in terms of the Eulerian description, is written in terms of a moving frame of reference, and the problem is solved on a time-independent body-conformed grid. For both rigid-body motion and aeroelastic deformation, the Navier-displacement equation, in terms of the Lagrangian coordinates, is modified for fluid-flow problems. It is used along with the Eulerian description of the conservative fluid dynamics equations to account for the grid deformation.

Kandil, Osama A.↗

NASA NTRS1992

Three-dimensional simulation of slender delta wing rock and divergence

Computational simulation of three-dimensional flows around a delta wing undergoing rock and roll-divergence motions is presented. The problem is a multidisciplinary one where fluid-dynamics equations and rigid-body-dynamics equations are sequentially solved. For the fluid-dynamics part, the unsteady Euler equations, which are written relative to a moving frame of reference, are solved using an implicit, approximately-factored, central-difference, finite-volume scheme. For the rigid-body dynamics part, the Euler equation of rigid-body rolling motion is solved using a four-stage Runge-Kutta scheme. Since the applications do not include deforming wings or relative-rigid-body motions, the computational-fluid-dynamics grid, which is fixed in the moving frame of reference, does not need to be updated once it is generated.

Kandil, Osama A.↗

DOE OSTI2022

Droplet formation simulation using mixed finite elements

Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate the size of a droplet but fails to approximate the shape of the droplet. This is due to a highly nonlinear flow description near the point where the first pinch-off happens. A one-dimensional axisymmetric mathematical model was first developed by Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] using asymptotic analysis. This asymptotic approach to the Navier–Stokes equations leads to a universal scaling explaining the self-similar nature of the solution. Numerical models for the one-dimensional model were developed using the finite difference [Eggers and Dupont, “Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and finite element method [Ambravaneswaran et al., “Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops,” Phys. Fluids 14, 2606–2621 (2002)]. The focus of this study is to provide a robust computational model for one-dimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation. The code is verified using the Method of Manufactured Solutions and validated using previous experimental studies done by Zhang and Basaran [“An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184–1203 (1995)]. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinch-off phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1980

A simple numerical orthogonal coordinate generator for fluid dynamic applications

An application of a simple numerical technique which allows for the rapid construction of orthogonal coordinate systems about two dimensional and axisymmetric bodies is presented. The technique is based on a predictor corrector numerical method. It can be used to generate orthogonal meshes which have unequally spaced points in two directions. These orthogonal meshes in their transformed computational plane are, however, equally spaced so that the differencing for the metric coefficients and the fluid dynamic equation terms can be easily determined using equally spaced central finite differences. Solutions to the Navier-Stokes equations for flow over blunt bodies with reverse curvature are presented. The coupling of the time dependent fluid dynamic equations and the coordinate generator worked well with no undesirable effects noted.

Graves, R. A., Jr.↗

NASA NTRS1982

Approximate solution to the Hopf Phi equation for isotropic homogeneous fluid turbulence

Consistent with the observed t to the -n decay laws for isotropic homogeneous turbulence and the form of the longitudinal correlation function f(r, t) for small r, the Hopf Phi equation is shown to be satisfied approximately by an asymptotic power series in t to the -n. This solution features a self-similar universal equilibrium functional which manifests Kolmogoroff-type scaling.

Rosen, G.↗

DOE OSTI2025

Optical neural engine for solving scientific partial differential equations

Abstract Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, their demonstration for solving PDEs is limited. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson’s equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell’s equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations.

Tang, Yingheng (ORCID:0009000153622546)↗

NASA NTRS1975

Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation

Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Mean-flow results are compared with those given in a previous paper where the same problem was attacked using a Prandtl mixing-length hypothesis. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow. They highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient.

Frost, W.↗

NASA NTRS1975

Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation with reference to aeronautical operating systems

Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, STOL vehicles, etc.). Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow and highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient. Discussion of the effects of the disturbed wind field in CTOL and STOL aircraft flight path and obstruction clearance standards is given. The results indicate that closer inspection of these presently recommended standards as influenced by wind over irregular terrains is required.

Frost, W.↗

NASA NTRS1992

Vibrational relaxation of anharmonic oscillators in expanding flows

Although the Landau-Teller vibrational model accurately predicts vibrational excitation process in post-shock and compressing flows, it under-predicts the rate of de-excitation in cooling and expanding flows. In the present paper, detailed calculations of the vibrational relaxation process of N2 and CO in cooling flows are conducted. A coupled set of vibrational transition rate equations and quasi-one-dimensional fluid dynamic equations is solved. Multiple quantum level transition rates are computed using SSH theory. The SSH transition rate results are compared with available experimental data and other theoretical models. Vibration-vibration exchange collisions are responsible for some vibrational relaxation acceleration in situations of high vibrational temperature and low translational temperature. The present results support the relaxation mechanisms proposed by Bray and by Treanor Rich and Rehm.

Ruffin, Stephen M.↗

NASA NTRS1994

Preconditioned conjugate gradient methods for the Navier-Stokes equations

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Ajmani, Kumud↗

NASA NTRS2012

Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology

This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.

Rallabhandi, Siriam K.↗

NASA NTRS2015

Results of Microgravity Fluid Dynamics Captured With the Spheres-Slosh Experiment

This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.

slosh↗

NASA NTRS2015

Results of Microgravity Fluid Dynamics Captured with the Spheres-Slosh Experiment

This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.

slosh↗

NASA NTRS2015

Result of Microgravity Fluid Dynamics Captured with the SPHERES-Slosh Experiment

This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.

slosh↗

NASA NTRS1987

Adaptive finite difference methods in fluid dynamics

An adaptive method to solve partial differential equations in fluid mechanics is presented. The approach requires internal boundary conditions that must be conservative, data structures for keeping track of several layers of fine grid patches, error estimation, and heuristics for automatic grid generation. In practical calculations gains in computer efficiency up to 10 over nonadaptive methods are observed. The whole procedure takes 3000 lines of FORTRAN code.

Berger, Marsha J.↗

NASA NTRS1988

Optical matrix-vector processing for computational fluid dynamics

An optical processor to solve partial differential equations for computational fluid dynamics applications is considered. This application is new and original for optical processors. The algorithms that are used are optical realizations of the Newton-Raphson method for nonlinear equations and a new optical LU direct decomposition and Gauss-Seidel iterative solution to the resultant linear algebraic equations. These algorithms are used to solve Burger's equation (a specific form of the momentum equation in fluid dynamics). The nonlinear equations provide 1-D velocity data at each time step. Simulation results of optical processing with these algorithms on computational fluid dynamics data is included.

Perlee, Caroline J.↗

NASA NTRS2005

Full Multigrid Flow Solver

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Mineck, Raymond E.↗

NASA NTRS1997

Compton Scattering by Static and Moving Media: The Transfer Equation and its Moments - Part 1

Compton scattering of photons by nonrelativistic particles is thought to play an important role in forming the radiation spectrum of many astrophysical systems. Here we derive the time-dependent photon kinetic equation that describes spontaneous and induced Compton scattering, as well as absorption and emission by static and moving media, the corresponding radiative transfer equation, and their zeroth and first angular moments, both in the system frame and in the frame comoving with the medium. We show that it is necessary to use the correct relativistic differential scattering cross section in order to obtain a photon kinetic equation that is correct to first order in Epsilon/m(sub e), T(sub e)/m(sub e), and V, where Epsilon is the photon energy, T(sub e) and m(sub e) are the electron temperature and rest mass, and V is the electron bulk velocity in units of the speed of light. We also demonstrate that the terms in the radiative transfer equation that are second order in V should usually be retained, because if the radiation energy density is sufficiently large, compared to the radiation flux, the effects of bulk Comptonization described by the terms that are second order in V can be as important as the effects described by the terms that are first order in V, even when V is small. The system- and fluid-frame equations that we derive are correct to first order in Epsilon/m(sub e). Our system-frame equations, which are correct to second order in V, may be used when V is not too large. Our fluid-frame equations, which are exact in V, may be used when V approaches 1. Both sets of equations are valid for systems of arbitrary optical depth and can therefore be used in both the free-streaming and diffusion regimes. We demonstrate that Comptonization by the electron bulk motion occurs whether or not the radiation field is isotropic or the bulk flow converges and that it is more important than thermal Comptonization if V(sup 2) is greater than 3T(sub e)/m(sub e).

Psaltis, Dimitrios↗