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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Numerical solution of the Navier-Stokes equations for laminar, transonic flows

An implicit finite difference solution of the Navier-Stokes equations yielded time histories of the transonic laminar flow development about a circular cylinder and NACA-0018 airfoil. Reynolds numbers ranged from those corresponding to purely laminar flow to those corresponding to significant turbulence in the boundary layer. Body thermal conditions of an adiabatic wall and a specified body temperature were considered. Versatility in treating arbitrary bodies was incorporated by using numerically generated, body-fitted coordinate transformations. Solution of the simultaneous difference equations for the dependent variables was obtained using an accelerated Gauss-Seidel iterative scheme. Computational results are presented in the form of velocity vector fields, Mach number contours, aerodynamic coefficients, heat transfer rates at the body surface, and body temperature distributions. Truncation analyses of first and second derivative difference approximations resulted in general criteria for numerically generated coordinates so that flow near a body is more accurately represented.

Turner, L., III↗
NASA NTRS1979

Application of a velocity-split Navier-Stokes solution technique to external flow problems

A method for solving the Navier-Stokes equations based on splitting the velocity vector into its rotational and irrotational parts has recently been applied successfully to internal flow computations. In this paper, the applicability of the method to external flows is examined by studying two model problems; laminar incompressible flow over semiinfinite and finite flat plates. For these problems the procedure accurately reproduces the known solutions and is computationally very efficient even at high Reynolds numbers. Computational aspects of the method are discussed along with the possibility of using the procedure to retrofit a viscous capability into existing transonic potential flow codes.

Dwoyer, D. L.↗
NASA NTRS1991

An implicit three-dimensional Navier-Stokes solver for compressible flow

A three-dimensional numerical method based on the lower-upper symmetric-Gauss-Seidel implicit scheme in conjunction with the flux-limited dissipation model is developed for solving the compressible Navier-Stokes equations. A new computer code which is based on this method requires only 9 microsec per grid-point per iteration on a single processor of a Cray YMP computer and executes at the sustained rate of 170 MFLOPS. A reduction of 4 orders of magnitude in the residual for a high Reynolds number flow using 230 K grid points is obtained in 24 minutes. The computational results compare well with available experimental data.

Yoon, Seokkwan↗
NASA NTRS1990

Preconditioned upwind methods to solve 3-D incompressible Navier-Stokes equations for viscous flows

A computational method for calculating low-speed viscous flowfields is developed. The method uses the implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. An extensive study of optimizing the preconditioned system is carried out for two viscous flow problems. Computed results are compared with analytical solutions and experimental data.

Hsu, C.-H.↗
NASA NTRS1993

Incompressible Navier-Stokes Calculations in Pump Flows

Flow through pump components, such as the SSME-HPFTP Impeller and an advanced rocket pump impeller, is efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved in steadily rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. The resulting computer code is applied to the flow analysis inside an 11-inch SSME High Pressure Fuel Turbopump impeller, and an advanced rocket pump impeller. Numerical results of SSME-HPFTP impeller flow are compared with experimental measurements. In the advanced pump impeller, the effects of exit and shroud cavities are investigated. Flow analyses at design conditions will be presented.

Kiris, Cetin↗
NASA NTRS1991

Verification of the proteus two-dimensional Navier-Stokes code for flat plate and pipe flows

The Proteus Navier-Stokes Code is evaluated for 2-D/axisymmetric, viscous, incompressible, internal, and external flows. The particular cases to be discussed are laminar and turbulent flows over a flat plate, laminar and turbulent developing pipe flows, and turbulent pipe flow with swirl. Results are compared with exact solutions, empirical correlations, and experimental data. A detailed description of the code set-up, including boundary conditions, initial conditions, grid size, and grid packing is given for each case.

Conley, Julianne M.↗
NASA NTRSDate not supplied

Simulation of Fluid Flow and Collection Efficiency at Low Stokes Number

Numerical simulations of fluid flow and collection efficiency for a Science Engineering Associates (SEA) Robust probe are presented. The cases cover a range of freestream velocity from 10-135 m/s, and particle sizes from 1-200 µm. This combination produces results for Stokes numbers in the range of 0.07-1092. A blended modified Stokes (defined in the paper) is introduced which covers a range of 0.07-146. Of particular interest is the collection efficiency of the sensing element (a forward-facing half-pipe), Etot, in the low Stokes number regime. It was observed that the collection efficiency of the sensing area approached one for large Stokes numbers (>100) as expected. As blended modified Stokes number approached one, the Etot dropped to approximately 0.5. By blended modified Stokes numbers of 0.3, the Etot has dropped to essentially zero. Plotting collection versus blended modified Stokes number, the different freestream velocities collapsed quite well on to a single curve. The paper presents a discussion on the flowfield and local collection efficiency, beta, in an effort to explain the predictions. Of particular interest is what is essentially a shadow zone in plain sight. As the Stokes number is reduced, the local beta along the centerline of the half-pipe goes to zero. This occurs at Stokes numbers where the overall collection, Etot, is still appreciable. An empirical relation was developed to allow for corrected collection values at low Stokes numbers. The correlation remains within 2% for blended modified Stokes numbers above 1, and within 6% for all cases.

Instrumentation↗
NASA NTRSDate not supplied

Simulation of Fluid Flow and Collection Efficiency at Low Stokes Number

Numerical simulations of fluid flow and collection efficiency for a Science Engineering Associates (SEA) Robust probe are presented. The cases cover a range of freestream velocity from 10-135 m/s, and particle sizes from 1-200 µm. This combination produces results for Stokes numbers in the range of 0.07-1092. A blended modified Stokes (defined in the paper) is introduced which covers a range of 0.07-146. Of particular interest is the collection efficiency of the sensing element (a forward-facing half-pipe), Etot, in the low Stokes number regime. It was observed that the collection efficiency of the sensing area approached one for large Stokes numbers (>100) as expected. As blended modified Stokes number approached one, the Etot dropped to approximately 0.5. By blended modified Stokes numbers of 0.3, the Etot has dropped to essentially zero. Plotting collection versus blended modified Stokes number, the different freestream velocities collapsed quite well on to a single curve. The paper presents a discussion on the flowfield and local collection efficiency, beta, in an effort to explain the predictions. Of particular interest is what is essentially a shadow zone in plain sight. As the Stokes number is reduced, the local beta along the centerline of the half-pipe goes to zero. This occurs at Stokes numbers where the overall collection, Etot, is still appreciable. An empirical relation was developed to allow for corrected collection values at low Stokes numbers. The correlation remains within 2% for blended modified Stokes numbers above 1, and within 6% for all cases.

Instrumentation↗
NASA NTRS1988

Navier Stokes computation of the flow field over delta wings with spanwise leading edge blowing

The concept of spanwise leading edge blowing, a means of controlling the position and strength of leading edge vortices, is analyzed by numerical solutions of the three-dimensional Thin-Layer Navier Stokes equations. The leading edge jet is simulated by defining a permeable boundary, corresponding to the jet slot, where suitable boundary conditions are implemented. Numerical results agree favorably with experimental measurements. It is found that the use of spanwise leading edge blowing not only magnifies the size and strength of the leading edge vortices, but also moves the vortex cores outboard and upward. As a result, the increase in lift comes primarily from the greater nonlinear vortex lift. The presence of the leading edge jet stream displaces the flow outboard, thereby increasing the effective aspect ratio of the delta wing. However, blowing causes earlier vortex breakdown, thus decreasing the stall angle.

Yeh, David T.↗
NASA NTRS1991

Verification of the Proteus two-dimensional Navier-Stokes code for flat plate and pipe flows

The Proteus Navier-Stokes Code is evaluated for two-dimensional/axisymmetric, viscous, incompressible, internal and external flows. The particular cases to be discussed are laminar and turbulent flows over a flat plate, laminar and turbulent dveloping pipe flows and turbulent pipe flow with swirl. Results are compared with exact solutions, empirical correlations and experimental data. A detailed description of the code set-up, including boundary conditions, intitial conditions, grid size and grid packing is given for each case.

Conley, Julianne M.↗
NASA NTRS1985

A comparison of Euler and Navier-Stokes solutions for supersonic flow over a conical delta wing

The flow around a thin elliptic cone at Mach number 2 and angle of attack 10 deg is simulated numerically, comparing the results obtained using a fine grid and the Navier-Stokes (NS) equations with those obtained using both coarse and fine grids and the Euler (E) equations. On the coarse grid, the E results are found to reproduce roughly the NS predictions of leading-edge separation and primary and secondary vortices on the leeward surface, but the E solution on the fine NS grid (showing no separation and a crossflow-shock-induced vorticity) reveals this agreement to be spurious. The fine-grid E prediction is shown to be a valid solution of the E equations, indicating their unsuitability as approximators of viscous flow. The imposition of a Kutta condition on the E computation is found to be ineffective in correcting this discrepancy.

Newsome, R. W.↗
NASA NTRS1991

Navier-Stokes Simulation Of Wind-Tunnel Flow

Report describes three-dimensional Navier-Stokes simulation of transonic flow past model wing in wind tunnel and in free air. Numerical integration performed by LU-ADI factorization algorithm. Simulation shows effects of walls of tunnel.

Obayashi, S.↗
NASA NTRS1980

Numerical solution of the Navier-Stokes equations for high Reynolds number incompressible turbulent flow

The full Navier-Stokes equations for incompressible turbulent flow must be solved to accurately represent all flow phenomena which occur in a high Reynolds number incompressible flow. A two layer algebraic eddy viscosity turbulence model is used to represent the Reynolds stress in the primitive variable formulation. The development of the boundary-fitted coordinate systems makes the numerical solution of these equations feasible for arbitrarily shaped bodies. The nondimensional time averaged Navier-Stokes equations, including the turbulence mode, are represented by finite difference approximations in the transformed plane. The resulting coupled system of nonlinear algebraic equations is solved using a point successive over relaxation iteration. The test case considered was a NACA 64A010 airfoil section at an angle of attack of two degrees and a Reynolds number of 2,000,000.

Thompson, D. S.↗
NASA NTRS1989

Upwind Navier-Stokes solutions for leading-edge vortex flows

An incompressible Navier-Stokes solver using an upwind finite-difference algorithm is employed to investigate low-speed, three-dimensional, laminar, leading-edge vortex flows over three round-edged low-aspect-ratio wings. The effects of grid density, Reynolds number, and wing planform on the flowfield structures and integral values are studied. Computed results show good qualitative and quantitative agreement with the available experimental data.

Hsu, C.-H.↗
NASA NTRS1988

Navier-Stokes solutions for transonic flow over a wing mounted in a tunnel

Three-dimensional viscous flow calculations are performed for a swept, NACA 0012 wing mounted inside a wind tunnel for which detailed experimental data is available. A Runge-Kutta time-stepping scheme is used for obtaining steady-state solutions to the thin-layer Navier-Stokes equations. Free-air comptuations are also performed to assess the wall-interference effects. The effects of grid density and artificial dissipation on the accuracy of numerical results are included. The effect of the wind-tunnel sidewall boundary layer on the flow pattern over the wing surface, particularly in the vicinity of the wing/wall juncture is found to be significant.

Vatsa, V. N.↗
NASA NTRS1986

The calculation of supersonic viscous flows using the parabolized Navier-Stokes equations

Solution of the parabolic Navier-Stokes (PNS) equations for supersonic flows is discussed, and compatibility of the PNS method with the triple-deck theory of Stewartson (1974) is demonstrated. Characteristic and stability analyses show that use of an appropriate filter on the pressure term in the x-momentum equation can suppress the departure solutions, giving the usual desired weak interaction solution. An Alternating Direction Explicit procedure, with minimal computer storage requirements compared to the full Navier-Stokes solvers, is proposed to calculate strongly interacting flows using a global iteration procedure for the PNS equations. The PNS equations are used to solve the hypersonic viscous interaction problem, and good agreement is found with experimental results.

Davis, R. T.↗
NASA NTRS1975

A rigorous solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers around oscillating airfoils

A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.

Bratanow, T.↗
NASA NTRS1991

A three-dimensional Navier-Stokes stage analysis of the flow through a compact radial turbine

A steady, three dimensional Navier-Stokes average passage computer code is used to analyze the flow through a compact radial turbine stage. The code is based upon the average passage set of equations for turbomachinery, whereby the flow fields for all passages in a given blade row are assumed to be identical while retaining their three-dimensionality. A stage solution is achieved by alternating between stator and rotor calculations, while coupling the two solutions by means of a set of axisymmetric body forces which model the absent blade row. Results from the stage calculation are compared with experimental data and with results from an isolated rotor solution having axisymmetric inlet flow quantities upstream of the vacated stator space. Although the mass-averaged loss through the rotor is comparable for both solutions, the details of the loss distribution differ due to stator effects. The stage calculation predicts smaller spanwise variations in efficiency, in closer agreement with the data. The results of the study indicate that stage analyses hold promise for improved prediction of loss mechanisms in multi-blade row turbomachinery, which could lead to improved designs through the reduction of these losses.

Heidmann, James D.↗