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At least 397 records · Page 22

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NASA NTRS1987

Numerical solution of the Navier-Stokes equations with emphasis on rotorcraft applications

Recent advances in CFD are surveyed, with a focus on the applicability of codes based on the Navier-Stokes (NS) equations to helicopter aerodynamics. The developmental history of two- and three-dimensional NS codes is recalled; the formulations employed by codes of increasing complexity are outlined; and previous reviews are noted. Particular attention is given to Reynolds-averaged NS methods and their use in analyzing subsonic, transonic, and vortex-dominated flows. Typical numerical results are compared with experimental data in diagrams and graphs, and a number of outstanding problems are considered.

Holst, Terry L.↗

NASA NTRS1988

Explicit upwind algorithm for the parabolized Navier-Stokes equations

A new explicit upwind algorithm based on Roe's flux-difference splitting (FDS) method has been developed for the three-dimensional Parabolized Navier-Stokes (PNS) equations. For three-dimensional flows, FDS's are determined separately for the two nonmarching directions and modified to account for the calculated shock angle in the crossflow plane. Second-order FDS is applied to the pressure and convection terms with the streamwise pressure gradient limited in the subsonic region to maintain a hyperbolic inviscid equation set. Second-order central differencing is obtained in the two-step algorithm for the shear and heat flux terms. The new algorithm is demonstrated for three laminar flow test cases: supersonic flow over a flat plate, hypersonic flow over a 15 deg ramp, and hypersonic flow past a 10 deg cone at a 24 deg angle of attack. The computed results agree well with experimental measurements.

Korte, John J.↗

NASA NTRS2006

Simulation of Synthetic Jets in Quiescent Air Using Unsteady Reynolds Averaged Navier-Stokes Equations

We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for the simulation of a synthetic jet created by a single diaphragm piezoelectric actuator in quiescent air. This configuration was designated as Case 1 for the CFDVAL2004 workshop held at Williamsburg, Virginia, in March 2004. Time-averaged and instantaneous data for this case were obtained at NASA Langley Research Center, using multiple measurement techniques. Computational results for this case using one-equation Spalart-Allmaras and two-equation Menter's turbulence models are presented along with the experimental data. The effect of grid refinement, preconditioning and time-step variation are also examined in this paper.

Vatsa, Veer N.↗

NASA NTRS1992

Propulsion-related flowfields using the preconditioned Navier-Stokes equations

A previous time-derivative preconditioning procedure for solving the Navier-Stokes is extended to the chemical species equations. The scheme is implemented using both the implicit ADI and the explicit Runge-Kutta algorithms. A new definition for time-step is proposed to enable grid-independent convergence. Several examples of both reacting and non-reacting propulsion-related flowfields are considered. In all cases, convergence that is superior to conventional methods is demonstrated. Accuracy is verified using the example of a backward facing step. These results demonstrate that preconditioning can enhance the capability of density-based methods over a wide range of Mach and Reynolds numbers.

Venkateswaran, S.↗

NASA NTRS1998

Application of Aeroelastic Solvers Based on Navier-Stokes Equations

A pre-release version of the Navier-Stokes solver (TURBO) was obtained from MSU. Along with Dr. Milind Bakhle of the University of Toledo, subroutines for aeroelastic analysis were developed and added to the TURBO code to develop versions 1 and 2 of the TURBO-AE code. For specified mode shape, frequency and inter-blade phase angle the code calculates the work done by the fluid on the rotor for a prescribed sinusoidal motion. Positive work on the rotor indicates instability of the rotor. The version 1 of the code calculates the work for in-phase blade motions only. In version 2 of the code, the capability for analyzing all possible inter-blade phase angles, was added. The version 2 of TURBO-AE code was validated and delivered to NASA and the industry partners of the AST project. The capabilities and the features of the code are summarized in Refs. [1] & [2]. To release the version 2 of TURBO-AE, a workshop was organized at NASA Lewis, by Dr. Srivastava and Dr. M. A. Bakhle, both of the University of Toledo, in October of 1996 for the industry partners of NASA Lewis. The workshop provided the potential users of TURBO-AE, all the relevant information required in preparing the input data, executing the code, interpreting the results and bench marking the code on their computer systems. After the code was delivered to the industry partners, user support was also provided. A new version of the Navier-Stokes solver (TURBO) was later released by MSU. This version had significant changes and upgrades over the previous version. This new version was merged with the TURBO-AE code. Also, new boundary conditions for 3-D unsteady non-reflecting boundaries, were developed by researchers from UTRC, Ref. [3]. Time was spent on understanding, familiarizing, executing and implementing the new boundary conditions into the TURBO-AE code. Work was started on the phase lagged (time-shifted) boundary condition version (version 4) of the code. This will allow the users to calculate non-zero interblade phase angles using, only one blade passage for analysis.

Keith, Theo G., Jr.↗

NASA NTRS1993

Comparisons between DSMC and the Navier-Stokes equations for reentry flows

A detailed comparison is made between Navier-Stokes and DSMC calculations for flows near the continuum limit to assess the accuracy of the continuum equations in this regime. Meaningful comparisons require the use of similar physical models. This necessitates the inclusion of a separate rotational energy equation and use of slip boundary conditions. Inclusion of slip boundary conditions resulted in improved agreement between surface properties. Moreover, good agreement was obtained for the various temperatures in the nonequilibrium portion of the flow field that does not contain the shock region. Departures are noted in the shock region and in regions where thermal diffusion effects are important.

Olynick, David R.↗

NASA NTRS1995

Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions

One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.

Tidriri, M. D.↗

NASA NTRS2018

Navier-Stokes Equations Based Aeroelasticity of Supersonic Transport Including Short Period Oscillations

There is renewed interest in developing new supersonic transports after the discontinuation of the Concorde supersonic jet, which was mostly limited for flights over trans-oceanic routes due to the severe noise of the sonic boom. In order to avoid the sonic boom, more slender configurations, such as the Low Boom Flight Demonstrator (LBFD) configuration, are being considered. The aeroelastic characteristics of these new supersonic transports can significantly differ from conventional aircraft. Both rigid and flexible body modes can play a significant role in aeroelastic stability. For unconventional configurations, such as aircraft with forward swept wings, the short period oscillation (SPO) has been found to significantly impact the aeroelastic response. SPO can occur due to unanticipated events such as gusts, abrupt maneuvering, etc. During the design of the Concorde, the effects of SPO was considered in detail, though its impact is not publically disclosed. Assuring stability of supersonic aircraft, particularly during descent from the supersonic Mach regime to the transonic regime, is critical. An aircraft can deviate from its normal descent trajectory due to coupling between flows and body motions. The effect of SPO needs to be considered in aeroelastic responses. Preliminary studies using quasi-steady aerodynamics show that the presence of SPO can lead to unstable response. The well-established Reynolds Averaged Navier-Stokes (RANS) equations, which are computationally feasible with current supercomputers, have been in use for aeroelastic computations for the last three decades. Recently, such efforts have begun to include trajectory motions; for instance, the effect of phugoid motion on stability is studied in Ref. 9 using the RANS equations. In this paper, the effect of SPO on aeroelastic responses of a typical supersonic transport is studied.

Guruswamy, Guru↗

NASA NTRS1992

A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

Edwards, Jack R.↗

NASA NTRS1982

Simulation of large turbulent structures with the parabolic Navier-Stokes equations

The theoretical basis for well posed marching of a Parabolic Navier-Stokes (PNS) computational technique for supersonic flow is discussed and examples given to verify the analysis. It is demonstrated that stable computations can be made even with very small steps in the marching direction. The method is applied to cones at large angle of attack in high Reynolds number, supersonic flow. Streamline trajectories generated from the numerical solutions demonstrate the development of vortex structures on the lee side of the cone.

Rakich, J. V.↗

NASA NTRS1982

Simulation of large turbulent vortex structures with the parabolic Navier-Stokes equations

Rakich, J. V.↗

NASA NTRS1991

Solution of three-dimensional afterbody flow using reduced Navier-Stokes equations

The flow over afterbody geometries was investigated using the reduced Navier-Stokes (RNS) approximation. Both pressure velocity flux-split and composites velocity primitive variable formulations were considered. Pressure or pseudopotential relaxation procedures are combined with sparse matrix or coupled strongly implicit algorithms to form a three-dimensional solver for general non-orthogonal coordinates. Three-dimensional subsonic and transonic viscous/inviscid interacting flows were evaluated. Solutions with and without regions of recirculation were obtained.

Almahroos, H. M. H.↗

NASA NTRS2004

Simulation of Synthetic Jets in Quiescent Air Using Unsteady Reynolds Averaged Navier-Stokes Equations

We report research experience in applying an Unsteady Reynolds-Averaged Navier-Stokes (URANS) solver for the prediction of time-dependent flows in the presence of an active flow control device. The configuration under consideration is a synthetic jet created by a single diaphragm piezoelectric actuator in quiescent air. Time-averaged and instantaneous data for this case were obtained at Langley Research Center, using multiple measurement techniques. Computational results for this case using one-equation Spalart-Allmaras and two-equation Menter s turbulence models are presented here along with comparisons with the experimental data. The effect of grid refinement, preconditioning and time-step variation are also examined.

Vatsa, Veer N.↗

NASA NTRS1991

An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations: High Reynolds number flows

An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.

Goodrich, John W.↗

NASA NTRS1991

An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations - High Reynolds number flows

Goodrich, John W.↗

NASA NTRS1992

An efficient and robust algorithm for time dependent viscous incompressible Navier-Stokes equations

A recently developed finite difference algorithm is presented for steady incompressible Navier-Stokes calculations. The algorithm is extremely robust with respect to Reynolds number, and has been used to directly compute incompressible flows with smoothly resolved streamfunction, kinetic energy and vorticity contours for Reynolds numbers as high as Re = 100,000 without requiring any subscale modelling. The algorithm is second order accurate in both time and space, with Crank-Nicolson differencing for the diffusion terms, with a lagged second order Adams-Basforth differencing for the convection terms, and with central differencing for all space derivatives. The algorithm is extremely efficient with respect to both computing time and physical memory. Solutions are shown for cavity and channel flows at various Reynolds numbers.

Goodrich, John W.↗

NASA NTRS1978

Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows

A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.

Warsi, Z. U. A.↗

NASA NTRS1980

On the solution of the unsteady Navier-Stokes equations for hypersonic flow about axially-symmetric blunt bodies

A formulation of the complete Navier-Stokes problem for a viscous hypersonic flow in general curvilinear coordinates is presented. This formulation is applicable to both the axially symmetric and three dimensional flows past bodies of revolution. The equations for the case of zero angle of attack were solved past a circular cylinder with hemispherical caps by point SOR finite difference approximation. The free stream Mach number and the Reynolds number for the test case are respectively 22.04 and 168883. The whole algorithm is presented in detail along with the preliminary results for pressure, temperature, density and velocity distributions along the stagnation line.

Warsi, Z. U. A.↗