Pressure distribution in a hydrostatic bearing of multi-wells
Pressure distribution in hydrostatic bearing of multi-wells obtained by use of Navier-Stokes equations
PRESSURE DISTRIBUTION↗
SEARCH · Engineering Papers
Results for “Stokes equations”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
A viscous model of the solar wind.
Viscous thermoconductive model of solar wind motion, using Navier-Stokes equations
MATHEMATICAL MODEL↗
A method for calculating laminar viscous, compressible flows with small pressure gradients
A method is presented for calculating laminar viscous, compressible flows in which pressure gradients are assumed to be neglibible in energy conservation and in developing property relations, but not in momentum conservation. The equations are developed from Navier-Stokes equations in a noninertial reference frame. The method is an extension of an approximate method developed for calculating combined forced and contained natural convection in a rotating tank. The restriction to small density and temperature variations in the previous method is removed. For illustration, a two-dimensional simulation of the rotating tank problem is formulated, and the numerical computation procedure to be used is indicated.
Martin, E. D.↗
Aerodynamic Analyses Requiring Advanced Computers, Part 1
Papers are presented which deal with results of theoretical research on aerodynamic flow problems requiring the use of advanced computers. Topics discussed include: viscous flows, boundary layer equations, turbulence modeling and Navier-Stokes equations, and internal flows.
Source record↗
Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence
The classical approach to the investigation of small-scale intermittency in turbulence is based on the higher-order derivative correlations such as skewness and flatness factors. In the study of the small scales, numerial simulations can provide more detail than experiments. In the present paper, a variety of velocity- and scalar-derivative correlations are calculated over a range of Reynolds numbers. Particular attention is given to third- and fourth-order correlations, taking into account also some fifth- and sixth-order correlations to allow comparisons with the phenomenological models. The governing equations are the incompresssible Navier-Stokes equation for the velocity and transport equation for a passive scalar. Two numerical codes are used for the simulations presented. Attention is given to details regarding the numerical method used, forcing, simulation parameters, spectra and skewnesses, and graphics.
Kerr, R. M.↗
Navier-Stokes Computations On Zonal Grids
Report describes numerical simulations of transonic flow of air about isolated wing and about wing and fuselage (not tail assembly) of F-16A aircraft. Fast, diagonalized Beam-Warming numerical-integration algorithm for solution of Euler and Navier-Stokes equations applied via Transonic Navier-Stokes computer program, using computational grids divided into zones of coarse and finer meshes.
Flores, Jolen↗
Numerical Modeling of a Vortex Stabilized Arcjet
Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.
Pawlas, Gary E.↗
A method for obtaining a statistically stationary turbulent free shear flow
The long-term goal of the current research is the study of Large-Eddy Simulation (LES) as a tool for aeroacoustics. New algorithms and developments in computer hardware are making possible a new generation of tools for aeroacoustic predictions, which rely on the physics of the flow rather than empirical knowledge. LES, in conjunction with an acoustic analogy, holds the promise of predicting the statistics of noise radiated to the far-field of a turbulent flow. LES's predictive ability will be tested through extensive comparison of acoustic predictions based on a Direct Numerical Simulation (DNS) and LES of the same flow, as well as a priori testing of DNS results. The method presented here is aimed at allowing simulation of a turbulent flow field that is both simple and amenable to acoustic predictions. A free shear flow is homogeneous in both the streamwise and spanwise directions and which is statistically stationary will be simulated using equations based on the Navier-Stokes equations with a small number of added terms. Studying a free shear flow eliminates the need to consider flow-surface interactions as an acoustic source. The homogeneous directions and the flow's statistically stationary nature greatly simplify the application of an acoustic analogy.
Timson, Stephen F.↗
Textbook Multigrid Efficiency for the Steady Euler Equations
A fast multigrid solver for the steady incompressible Euler equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.
Roberts, Thomas W.↗
Part 1 of a Computational Study of a Drop-Laden Mixing Layer
This first of three reports on a computational study of a drop-laden temporal mixing layer presents the results of direct numerical simulations (DNS) of well-resolved flow fields and the derivation of the large-eddy simulation (LES) equations that would govern the larger scales of a turbulent flow field. The mixing layer consisted of two counterflowing gas streams, one of which was initially laden with evaporating liquid drops. The gas phase was composed of two perfect gas species, the carrier gas and the vapor emanating from the drops, and was computed in an Eulerian reference frame, whereas each drop was tracked individually in a Lagrangian manner. The flow perturbations that were initially imposed on the layer caused mixing and eventual transition to turbulence. The DNS database obtained included transitional states for layers with various liquid mass loadings. For the DNS, the gas-phase equations were the compressible Navier-Stokes equations for conservation of momentum and additional conservation equations for total energy and species mass. These equations included source terms representing the effect of the drops on the mass, momentum, and energy of the gas phase. From the DNS equations, the expression for the irreversible entropy production (dissipation) was derived and used to determine the dissipation due to the source terms. The LES equations were derived by spatially filtering the DNS set and the magnitudes of the terms were computed at transitional states, leading to a hierarchy of terms to guide simplification of the LES equations. It was concluded that effort should be devoted to the accurate modeling of both the subgridscale fluxes and the filtered source terms, which were the dominant unclosed terms appearing in the LES equations.
Okong'o, Nora A.↗
Transonic Navier-Stokes solutions about a generic hypersonic configuration
Three-dimensional transonic viscous flow computations are presented for a generic high-speed accelerator model that includes wing, body, fillets, and a no-flow-through engine nacelle. Solutions are obtained from an algorithm for the compressible Navier-Stokes equations that incorporates an upwind-biased, flux-vector-splitting approach along with longitudinally patched grids. Results are presented for fully turbulent flow assumptions and include correlations with wind-tunnel data. A good quantitative agreement for the forebody surface pressure distribution is achieved between computations and the available wind-tunnel measurements at M∞ = 0.9. Furthermore, it is demonstrated that the flow is stagnating around the boattail region due to separation from the aft-engine cowl lip.
Hypersonic flows↗
A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows
This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.
Duque, Earl P. N.↗
Laminar flow past a sphere at high Mach number.
Laminar hypersonic flow past sphere based on constant-density approximation, solving Navier- Stokes equations and comparing with values of shock Reynolds number
LAMINAR FLOW↗
Modeling the Effects of a Backward-Facing Step on Boundary-Layer Transition
We model transition to turbulence in a two-dimensional boundary layer downstream of a backward-facing step (BFS) along a flat plate. With the goal of evaluating the available engineering models for predicting the effects of step excrescences on the transition characteristics, two separate methodologies are used to monitor the streamwise shift in the transition onset location as the step height and the flow speed are varied across the range of a previously reported experiment involving step-height-to-local-displacement-thickness ratios of 0 < h/δ* < 1.6. Unlike the variable N -factor method from the previous literature, both of these methods are general in scope and do not involve any empirical correlations that are specific to step excrescences. The first of these techniques involves an N -factor method that directly accounts for the change in boundary-layer instability characteristics due to the step. Stability computations using the harmonic linearized Navier-Stokes equations (HLNSE), which fully account for the nonparallel-mean-flow effects close to the BFS, indicate that the measured transition locations at nearly all test conditions ( h/δ* < 1.3) correlate well with a computed N -factor of N tr = 7.6, demonstrating a successful stability-based transition criterion related to step excrescences. Linear stability theory, which does not account for nonparallel effects, demonstrates reasonable agreement with the HLNSE results, yielding good predictions for the overall trends, but predicts a somewhat earlier onset of transition than HLNSE. The other methodology used in this work involves transport-equation-based transition models. We first show that the Langtry-Menter y - Re θt transition model cannot accurately predict the location of transition onset for moderate BFS heights because it is unable to accurately account for the flow history effects. Along with the Langtry-Menter transition model, we also show the amplification factor transport model does not produce accurate transition locations for subsonic flow over steps even though it accounts for some flow history effects.
Transition↗
Calculation of two-dimensional turbulent flow fields
Navier-Stokes equation solutions for two- dimensional turbulent flow fields of compressible viscous fluid
TWO-DIMENSIONAL FLOW↗
Analytical investigation of fluid amplifier dynamic characteristics, volume 1
Fluid amplifier dynamic characteristics and Fortran program for numerical solution of time- dependent two-dimensional Navier-Stokes equation for viscous jet in arbitrary flow field
COMPUTER PROGRAM↗
On the stability of Poiseuille flow in a pipe
Poiseuille pipe flow stability from finite difference equations approximation to nonlinear axisymmetric Navier-Stokes equations under stream function perturbation
Crowder, H. J.↗
Laminar separation on a blunted cone at high angles of attack
A new technique is reported for calculating the entire flow field on spherically blunted cones at high angles of attack and high laminar Reynolds numbers. An approximate system of parabolic equations obtained from the steady Navier-Stokes equations by assuming the viscous, streamwise derivative terms are small compared to the viscous normal and circumferential derivatives is the basis of the calculations. These equations are valid for both the inviscid and viscous regions, including the circumferential separation zone that develops on the leeward side at high angles of attack. Two different methods are used to obtain the initial conditions for these equations at the sphere cone tangency plane. For small nose Reynolds numbers, an axisymmetric merged layer solution around a sphere is rotated to provide a three-dimensional initial plane of data. For large nose Reynolds numbers, the nose region is solved using an inviscid, three dimensional time dependent solution combined with a boundary layer solution for the viscous flow. The computed flowfield including the leeward separation region is described and compared with data for a 7 deg half angle cone at 10 deg angle of attack, and a blunt 15 deg half angle cone at 15 deg angle of attack.
Lubard, S. C.↗