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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

An interaction algorithm for prediction of mean and fluctuating velocities in two-dimensional aerodynamic wake flows

A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.

Baker, A. J.↗
NASA NTRS1991

Acceleration of convergence by shifting the spectrum of implicit finite difference operators associated with the equations of gas dynamics

Eigensystem analysis techniques are applied to finite difference formulations of the Navier-Stokes equations in one dimension. Spectra of the resulting implicit difference operators are computed. The largest eigenvalues are calculated by using a combination of the Frechet derivative of the operators and Arnoldi's method. The accuracy of Arnoldi's method is tested by comparing the rate of convergence of the iterative method with the dominant eigenvalue of the original iteration matrix. On the basis of the pattern of eigenvalue distributions for various flow configurations, a shifting of the implicit operators in question is devised. This procedure has improved the rates of convergence of CFD codes by 20 - 50 percent.

Cheer, A.↗
DOE OSTI2020

A filtering strategy for the numerical convergence of radiation transport through purely absorbing particle clouds

Radiation transport through particle clouds plays a major role in many engineering applications. Here in this paper, we study this problem by means of solving the radiative transport equation (RTE) on a Eulerian continuous domain. The particle clouds are generated through direct numerical simulation of Navier-Stokes equations coupled with Lagrangian particle transport at different Stokes numbers. We confirm the earlier observation noted in the literature that the solution to the RTE on Eulerian mesh diverges when the Eulerian mesh size is of the order of the particle diameter. This observation is often called the homogenization error stemming from relegation of number density onto the Eulerian domain. In order to circumvent this divergence problem, we propose a filtering strategy that spreads the information of the particles to the neighboring cells in a way that the representation of the particles remains the same even when the mesh size is smaller than that of the particle size. We show through our simulations that our filtering strategy solves the issue of homogenization error for the cases where the Beer-Bouger law is valid.

42 ENGINEERING↗
NASA NTRS1978

Modeling of the Reynolds stresses

In their most general form, the Reynolds averaged conservation equations result from ensemble or time averages of the instantaneous Navier-Stokes equations or their compressible counterparts. For these averaging processes to be consistent, the averaging time period must exceed the periods identified with the largest time scales of the turbulence, and yet be shorter than the characteristic times of the flow field. With these equations long period variations in the flow fields are deterministic, provided initial conditions are known. The average dependent variables are sufficiently smooth to be resolvable by finite difference techniques consistent with the size and speed of modern computers.

Rubesin, M. W.↗
NASA NTRS1984

Physics on aircraft wakes

The roll-up of a vortex sheet is analyzed by two approaches. The first is based on exact compressible Euler equations while the second is based on the exact incompressible Navier-Stokes equations. The inviscid calculations for the two-dimensional problem do not indicate any roll-up of the sheet. On the other hand, the viscous calculations capture the dynamics of the roll-up rather well. This suggests that the generally held views regarding the roll-up process of aircraft wakes, namely, that it be treated as an inviscid process, may not be completely accurate.

Hassan, H. A.↗
NASA NTRS1986

Helmholtz decomposition revisited: Vorticity generation and trailing edge condition. I - Incompressible flows

Using the decomposition for the infinite-space, the issue of the nonuniqueness of the Helmholtz decomposition for the problem of the three-dimensional unsteady incompressible flow around a body is considered. A representation for the velocity that is valid for both the fluid region and the region inside the boundary surface is employed, and the motion of the boundary is described as the limiting case of a sequence of impulsive accelerations. At each instant of velocity discontinuity, vorticity is shown to be generated by the boundary condition on the normal component of the velocity, for both inviscid and viscous flows. In viscous flows, the vorticity is shown to diffuse into the surroundings, and the no-slip conditions are automatically satisfied. A trailing edge condition must be satisfied for the solution to the Euler equations to be the limit of the solution of the Navier-Stokes equations.

Morino, L.↗
NASA NTRS1986

Numerical simulation of a controlled boundary layer

The problem of interest is the boundary layer over a flat plate. The three standard laminar flow control (LFC) techniques are pressure gradient, suction, and heating. The parameters used to describe the amount of control in the context of the boundary layer equations are introduced. The numerical method required to find the mean flow, the linear eigenvalues of the Orr-Sommerfeld equation, and the full, nonlinear, 3-D solution of the Navier-Stokes equations are outlined. A secondary instability exists for the parallel boundary subject to uniform pressure gradient, suction, or heating. Selective control of the spanwise mode reduces the secondary instability in the parallel boundary layer at low Reynolds number.

Zang, Thomas A.↗
NASA NTRS1988

Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

Tezduyar, T. E.↗
NASA NTRS1991

Vortical flow computations on a flexible blended wing-body configuration

Flows over blended wing-body configurations are often dominated by vortices. The unsteady aerodynamic forces due to such flows can couple with the elastic forces of the wing and lead to aeroelastic oscillations. Such aeroelastic oscillations can impair the performance of an aircraft; it is necessary to account for structural properties of the configuration and solve the aerodynamic and aeroelastic equations of motion simultaneously. The flow is modeled using the Navier-Stokes equations coupled with the aeroelastic equations of motion. Computations are made for a blended wing-body configuration at flow conditions dominated by vortices and separation. The computed results are validated with the available experimental data. Sustained aeroelastic oscillations observed in the wind tunnel are successfully simulated for freestream Mach = 0.975, alpha of 8.0 deg, and a frequency of about 2 Hz.

Guruswamy, Guru P.↗
NASA NTRS1989

Numerical study of a delta planform with multiple jets in ground effect

The flow past a 60-deg delta wing equipped with two thrust-reverser jets near the inboard trailing edge has been analyzed by numerical solution of the 3D thin-layer Navier-Stokes equations. An implicit, partially flux-split, approximately-factored Navier-Stokes solver coupled with a multiple grid embedding scheme has been adapted to this problem. Studies of the impact of numerical parameters (e.g., grid refinement and dissipation levels), and flow-field parameters such as the height of the delta wing above the ground plane and the jet size on the solution, were performed. Results of these numerical studies indicate some challenges in the accurate resolution of complex 3D free shear layers and jets. Nevertheless, flow features such as jet deformation and ground vortex formation observed in experimental flow visualizations are captured. Further, comparisons with experimental data confirm the ability to simulate the loss of wing-borne lift, commonly referred to 'suckdown, as the delta planform flies at slow speeds in close proximity to the ground. Detailed analysis of the numerical results has also given additional insight into the structure of the ground vortex and the mechanisms of lift loss.

Chawla, K.↗
NASA NTRS1994

A dynamic localization model with stochastic backscatter

The modeling of subgrid scales in large-eddy simulation (LES) has been rationalized by the introduction of the dynamic localization procedure. This method allows one to compute rather than prescribe the unknown coefficients in the subgrid-scale model. Formally, the LES equations are supposed to be obtained by applying to the Navier-Stokes equations a 'grid filter' operation. Though the subgrid stress itself is unknown, an identity between subgrid stresses generated by different filters has been derived. Although preliminary tests of the Dynamic Localization Model (DLM) with k-equation have been satisfactory, the use of a negative eddy viscosity to describe backscatter is probably a crude representation of the physics of reverse transfer of energy. Indeed, the model is fully deterministic. Knowing the filtered velocity field and the subgrid-scale energy, the subgrid stress is automatically determined. We know that the LES equations cannot be fully deterministic since the small scales are not resolved. This stems from an important distinction between equilibrium hydrodynamics and turbulence. In equilibrium hydrodynamics, the molecular motions are also not resolved. However, there is a clear separation of scale between these unresolved motions and the relevant hydrodynamic scales. The result of molecular motions can then be separated into an average effect (the molecular viscosity) and some fluctuations. Due to the large number of molecules present in a box with size of the order of the hydrodynamic scale, the ratio between fluctuations and the average effect should be very small (as a result of the 'law of large numbers'). For that reason, the hydrodynamic balance equations are usually purely deterministic. In turbulence, however, there is no clear separation of scale between small and large eddies. In that case, the fluctuations around a deterministic eddy viscosity term could be significant. An eddy noise would then appear through a stochastic term in the subgrid-scale model and could be the source of backscatter.

Carati, Daniele↗
NASA NTRS2010

Conservational PDF Equations of Turbulence

Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

Shih, Tsan-Hsing↗
NASA NTRS1983

Nonparametric solution of the Euler equations for steady flow

A theory is presented for formulating well-posed boundary value problems for the Euler equations for steady rotational flow. It is shown that the Euler equations of motion are equivalent to a variational principle, which is used to define a finite difference scheme for numerically solving the Euler equations. The principle is extended to MHD problems in terms of a potential energy of a perfectly conducting plasma having a minimum number of stable configurations. The flow around a cylinder is considered, noting that time-independent solutions of the Euler equations can be used to provide limits to solutions of the Navier-Stokes equations. A sample is worked out in terms of the motion of vortices inside a circle.

Garabedian, P. R.↗
NASA NTRS1989

Computation of hypersonic flow fields

The present discussion of the theory, solution methods, and development status of chemically reactive flow CFD codes pertaining to the flow field around a hypersonic vehicle encompasses the formulation of multicomponent viscous equations, grid-generation techniques, and finite-difference algorithms. The Navier-Stokes equations presented focus on such particularities of high speed vehicles as their aerodynamic configuration, lee and wake flow, bow shock, and chemistry and low density effects. Issues for which further development is desirable encompass boundary treatments, grid quality, shock capturing, and the decoupling of chemistry from flow variables.

Li, Chien-Peng↗
NASA NTRS1991

Diagonal implicit multigrid solution of compressible turbulent flows

The Caughey (1988) multigrid diagonal implicit algorithm for Euler equations is extended to solve the two-dimensional thin layer Navier-Stokes equations for turbulent transonic flows. To further accelerate convergence to a steady state, the implicit scheme is used within the multigrid method. Results are presented for transonic flows past airfoils, and the flow-field results are compared with other computational data and experiments demonstrating the accuracy of the method.

Varma, R. R.↗
NASA NTRS1992

Computational fluid dynamics application to hypersonic flow over a Martian entry vehicle (MEV) - A correlation with experiment

A class of vehicles for a mission to Mars are analyzed for aerodynamic characteristics using advanced Computational Fluid Dynamics (CFD). The general configuration is a modified cone-conical-frustum geometry where the nose radius has a large influence on the flowfield. Inviscid-compressible flow using the Euler equations and viscous-compressible flow using the thin-layer Navier-Stokes equations is applied to the configuration. The surface modeling, grid generation and application of state-of-the-art CFD software are described. The effects of nose radius, angle of attack, and hypersonic velocity on the flight characteristics of the vehicle are discussed. The numerical simulations demonstrate the merits of the inviscid and viscous software. Results are compared with wind tunnel experiments.

Stewart, John E.↗
NASA NTRS1992

A new method for transonic static aeroelasticity problems

A new method has been developed to calculate the steady flow and structural deformations for fluid/structure interaction problems. The discretized fluid dynamic and structural equations are regarded as a single set of coupled, nonlinear, algebraic equations. The equilibrium solution is directly obtained using Newton's method. The governing equations used for the fluid flow are the two-dimensional Navier-Stokes equations, and a finite-element model is used to represent the structure. This paper describes the analytical method and presents sample calculations demonstrating the technique. The results show rapid convergence and good agreement with experimental data.

Felker, Fort F.↗
NASA NTRS1993

One-Equation Algebraic Model Of Turbulence

One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.

Baldwin, B. S.↗