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NASA NTRS1988

The turbulent heat flux in low Mach number flows with large density variations

A transport equation has been derived which is the difference between the volume- and mass-averaged velocities and is simply related to the turbulent heat flux phi sup h. Using this equation and an assumption analogous to the drift flux approximation of two-phase flow modeling, an algebraic closure relation for phi sup h that exibits fluxes due to directed transport proportional to -del anti p and due to gradient transport proportional to -del tau has been obtained.

Orourke, Peter J.↗

NASA NTRS1989

Navier-Stokes calculations of transonic flows past cavities

A computational investigation of subsonic and transonic flows past 3-D deep transitional cavities is presented. Computational simulations of these self-induced oscillatory flows were generated through time-accurate solutions of the Reynolds averaged full Navier-Stokes equations, using the explicit MacCormack scheme. The Reynolds stresses were included through the Baldwin-Lomax algebraic turbulence model with certain modifications. Two cases were computed to demonstrate the capability of the numerical scheme in modeling the complex 3-D flow features inside a cavity. The results from an experimental investigation were used not only to benchmark the computations, but also to widen the database used for the discussions and conclusions. The computational results include instantaneous and time averaged flow properties everywhere in the computational zone. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The features of deep and transitional cavity flows, and the effect of the sidewall on the cavity flow flowfield are illustrated through computational graphics.

Baysal, Oktay↗

NASA NTRS1989

Navier-Stokes solutions for vortical flows over a tangent-ogive cylinder

Reynolds number (Re) effects on low-speed vortical flows over a 3.5 caliber tangent-ogive cylinders at two angles of attack (alpha = 20 and alpha = 30 degrees) are computationally assessed for Re(D) = 0.2 -3.0 million (D: maximum diameter). The flow field results are steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in their thin-layer approximation. Using a properly modified algebraic turbulence model, the numerical results are in good to excellent agreement with experiments.

Hartwich, PETER-M.↗

NASA NTRS1990

Euler and Navier-Stokes computations for two-dimensional geometries using unstructured meshes

A general purpose unstructured mesh solver for steady-state two-dimensional inviscid and viscous flows is described. The efficiency and accuracy of the method are enhanced by the simultaneous use of adaptive meshing and an unstructured multigrid technique. A method for generating highly stretched triangulations in regions of viscous flow is outlined, and a procedure for implementing an algebraic turbulence model on unstructured meshes is described. Results are shown for external and internal inviscid flows and for turbulent viscous flow over a multi-element airfoil configuration.

Mavriplis, D. J.↗

NASA NTRS1990

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

Venkatakrishnan, V.↗

NASA NTRS1990

Time-accurate Navier-Stokes computations of self-excited two-dimensional unsteady cavity flows

Time-accurate Navier Stokes computations were performed to study self-excited oscillatory shear layer behavior over a two-dimensional rectangular cavity and to gain insight into the vortex-acoustic coupling that sustains these oscillations. Results were obtained solving the full, unsteady compressible Navier-Stokes equations for Reynolds-averaged turbulent air flow past a cavity with L/d = 2. Conditions duplicated test conditions in experiments by Rossiter at Mach numbers varied from 0.6 to 1.2. The computational scheme was the USA 2D series code developed by Rockwell's Science Center with an algebraic turbulence model for the shear layer and recirculating region. Two physical conditions were simulated: an isolated cavity situated (1) in an infinite plane wall and (2) in an infinite channel with an opposing parallel wall. Computed results for (1) showed excellent agreement with Rossiter's measured amplitudes and frequencies. A tuned acoustic duct resonance effect was observed in (2), demonstrating a controlled change in the acoustic feedback mechanism and resultant amplification in computed oscillations.

Dougherty, N. Sam↗

NASA NTRS1989

Euler and Navier-Stokes computations for airfoil geometries using unstructured meshes

Mavriplis, D. J.↗

NASA NTRS1990

Numerical study of vortical flow over a sideslipping delta wing

The three-dimensional vortical viscous flow past a sideslipping delta wing at a high angle of attack is numerically investigated. A computational method for calculating low-speed viscous flowfields is developed. The time-iterative method uses an implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. An algebraic turbulence model is implemented to account for the eddy viscosity. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. Computed results are compared with experimental data.

Hsu, C.-H.↗

NASA NTRS1991

Calculations of steady and transient channel flows with a time-accurate L-U factorization scheme

Calculations of steady and unsteady, transonic, turbulent channel flows with a time accurate, lower-upper (L-U) factorization scheme are presented. The L-U factorization scheme is formally second-order accurate in time and space, and it is an extension of the steady state flow solver (RPLUS) used extensively to solve compressible flows. A time discretization method and the implementation of a consistent boundary condition specific to the L-U factorization scheme are also presented. The turbulence is described by the Baldwin-Lomax algebraic turbulence model. The present L-U scheme yields stable numerical results with the use of much smaller artificial dissipations than those used in the previous steady flow solver for steady and unsteady channel flows. The capability to solve time dependent flows is shown by solving very weakly excited and strongly excited, forced oscillatory, channel flows.

Kim, S.-W.↗

NASA NTRS1989

Prediction of transitional (laminar-turbulent) hypersonic flows using the parabolized Navier-Stokes equations

Hypersonic transitional flow predictions have been made using the parabolized Navier-Stokes equations with an algebraic transition/turbulence model by appropriately modulating the turbulent viscosity with the available intermittency functions for incompressible and compressible flows. A comparison between the predictions with and without a low Reynolds number correction has also been made. The predictions are compared with the available experimental data and with the theory over a range of Mach number. A simple Re(theta)/M(delta) criterion is shown to satisfactorily predict the meridional variation of the onset location of transition on a cone at a small angle of attack, whereas none of the correlations discussed can do that. Various available correlations are discussed vis-a-vis the predictions as to the locations of the onset and the end of transition.

Kaul, Upender K.↗

NASA NTRS1991

Navier-Stokes calculations of transonic flows past cavities

Presented in this paper is a computational investigation of subsonic and transonic flows past three-dimensional deep and transitional cavities. Simulations of these self-induced oscillatory flows have been generated through time-accurate solutions of the Reynolds averaged, full Navier-Stokes equations, using the explicit MacCormack scheme. The Reynolds stresses have been included through the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties. The results of an experimental investigation have been used not only to validate the time-averaged results, but also to investigate the effects of varying the Mach number and the incoming boundary-layer thickness. Time series analyses have been performed for the instantaneous pressure values on the cavity floor and compared with the results obtained by a predictive formula. While most of the comparisons have been favorable, some discrepancies have been observed, particularly on the rear face. The present results help understanding the three-dimensional and unsteady features of the separations, vortices, the shear layer, as well as some of the aeroacoustic phenomena of compressible cavity flows.

Baysal, O.↗

NASA NTRS1991

Computational study of the aerodynamics and control by blowing of asymmetric vortical flows over delta wings

Some of the work is described which was done in a study of the flow field produced by tangential leading edge blowing on a 60 deg. delta wing. The flow is studied computationally by solving the Thin Layer Navier-Stokes equations. Steady state flow fields are calculated for various angles of attack and yaw, with and without the presence of tangential leading edge blowing. The effectiveness of blowing as a rolling moment control mechanism to extend the envelope of controllability is illustrated at pre- and post-stall angles of attack. The numerical grid is generated using algebraic grid generation and various interpolation and blending techniques. The jet emanates from a slot with linearly varying thickness and is introduced into the flow field using the concept of an actuator plane, thereby not requiring resolution of the jet slot geometry. The Baldwin-Lomax algebraic turbulence model is used to provide turbulent closure. The computational results are compared with those of experiments.

Craig, Ken↗

NASA NTRS1991

Viscous three-dimensional calculations of transonic fan performance

A 3-D flow analysis code was used to compute the design speed operating line of a transonic fan rotor, and the results were compared with experimental data. The code is an explicit finite difference code with an algebraic turbulence model. The transonic fan, called rotor 67, was tested experimentally at NASA-Lewis with conventional aerodynamic probes and with user anemometry and was included as one of the AGARD test cases for the computation of internal flows. The experimental data are described. Maps of total pressure ratio and adiabatic efficiency versus mass flow were computed and are compared with the experimental maps, with good agreement. Detailed comparisons between calculations and experiment are made at two operating points, one near peak efficiency and the other near stall. Blade-to-blade contour plots are used to show the shock structure. Comparisons of circumferentially integrated flow quantities downstream of the rotor show spanwise distributions of several aerodynamic parameters. Calculated Mach number distributions are compared with laser anemometer data within the blade row and the wake to quantify the accuracy of the calculations. Particle traces are used to show the nature of secondary flow.

Chima, Rodrick V.↗

NASA NTRS1992

Viscous three-dimensional calculations of transonic fan performance

A 3-D flow analysis code was used to compute the design speed operating line of a transonic fan rotor, and the results were compared with experimental data. The code is an explicit finite difference code with an algebraic turbulence model. The transonic fan, called Rotor 67, was tested experimentally at NASA Lewis conventional aerodynamic probes and with user anemometry and was included as one of the AGARD test cases for the computation of internal flows. The experimental data are described. Maps of total pressure ratio and adiabatic efficiency vs mass flow were computed and are compared with the experimental maps, with good agreement. Detailed comparisons between calculations and experiment are made at two operating points, one near peak efficiency and the other near stall. Blade-to-blade contour plots are used to show the shock structure. Comparisons of circumferentially integrated flow quantities downstream of the rotor show spanwise distributions of several aerodynamic parameters. Calculated Mach number distributions are compared with laser anemometer data within the blade row and the wake to quantify the accuracy of the calculations. Particle traces are used to show the nature of secondary flow.

Chima, Rodrick V.↗

NASA NTRS1992

CFD applications in pump flows

The objective of the proposed paper is to develop a computational procedure that solves incompressible Navier-Stokes equations for pump flows. 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. As a benchmark problem, the flow through the Rocketdyne inducer is numerically simulated. A coarse grid solution is obtained with a single zone by using an algebraic turbulence model. In multi-zone fine grid computation, a one-equation Baldwin-Barth turbulence model is utilized. Numerical results are compared with experimental measurements and a good agreement is found between the two. The resulting computer code is then applied to the flow analysis inside a two-stage fuel pump impeller operating at 80 percent, 100 percent, and 120 percent of design flow.

Kiris, Cetin↗

NASA NTRS1992

Bleed-boundary conditions for numerically simulated mixed-compression supersonic inlet flow

A numerical study was performed to investigate boundary conditions for bleed openings that are needed in the numerical simulation of critical flow through turbojet inlets with bleed. Nine different boundary conditions (BCs) were devised and examined. Of the BCs examined, three were able to stabilize the terminal shock near the inlet's throat. This numerical study was based on the ensemble-averaged, unsteady, three-dimensional, compressible Navier-Stokes equations closed by the Baldwin-Lomax algebraic turbulence model. Solutions to the Navier-Stokes equations were obtained by using a hybrid implicit-explicit method (Beam and Warming/MacCormack). The multiblock grid system used in the solution procedure was generated by solving a set of elliptic partial differential equations. Solutions obtained were compared with available experimental data.

Chyu, W. J.↗

NASA NTRS1992

Fluid flow and heat convection studies for actively cooled airframes

The work done during the progress report period from May-October 1992 is summarized. The effect of wall thermal boundary conditions on flows over a step or rib when repeated rib roughness is used for heating augmentation is examined. In numerical investigations of various such laminar and turbulent flows, the local heat transfer coefficients on a forward-facing step or on a rib were found to be very sensitive to the wall thermal boundary condition. For the computation of constant property laminar flow, the wall thermal boundary conditions were either a uniform heat flux or a uniform temperature. Results (Nusselt number and isotherms) of the studies are included. The second part of the work consisted of using PHOENICS to solve the conjugate heat transfer problem of flow over a rib in channel. Finally, the algebraic stress model in the TEAM (Turbulent Elliptic Algorithm-Manchester) code was tested for jet impingement flow, but there needs to be an addition of the energy equation to the code.

Mills, A. F.↗

NASA NTRS1992

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

Cannizzaro, Frank E.↗