Introduction E is an honor and challenge to present the Dryden Lecture ..i Research for 1979. Since my topic concerns a new trend in fluid mechanics, it should not be surprising that some aspects of this paper involve basic mechanics of turbulence, a field enriched by numerous contributions of Dr. Hugh L. Dryden. Having worked in related fields of fluid mechanics during past years, and long respected both his professional contributions and personal integrity, it is a special pleasure to present this Dryden lecture. The field of computational fluid dynamics during recent years has developed sufficiently to initiate some changes in traditional methods of aerodynamic design. Both computer power and numerical algorithm efficiency are simultaneously improving with time, while the energy resource for driving large wind tunnels is becoming progressively more valuable. Partly for these reasons it has been advocated that the impact of computational aerodynamics on future methods of aircraft design will be profound. ' Qualitatively, the changes taking place are not foreign to past experience in other fields of engineering. For example, trajectory mechanics and neutron transport mechanics already have been largely revolutionized by the computer. Computations rather than experiments now provide the principal source of detailed information in these fields. The amount of reactor experimentation required has been much reduced over former years; experiments now are performed mainly on clear, physically describable arrays of elements aimed at further confirmation of computational techniques; and better designs are achieved than with former experimental methods alone. Similar changes in the relative roles of experimental and computational aerodynamics are anticipated in the future. There are three compelling motivations for vigorously developing computational aerodynamics. One is to provide important new technological capabilities that cannot be provided by experimental facilities. Because of their fundamental limitations, wind tunnels have rarely been able to simulate, for example, Reynolds numbers of aircraft flight, flowfield temperatures around atmosphere entry vehicles, aerodynamics of probes entering planetary atmospheres, aeroelastic distortions present in flight, or the propulsiveexternal flow interaction in flight. In addition, transonic wind tunnels are notoriously limited by wall and support interference; and stream nonuniformities of wind tunnels severely affect laminar-turbulent transition. Moreover, the dynamic-aerodynamic interaction between vehicle motion in flight and transition-dependent separated flow also is inaccessible to wind-tunnel simulation. In still different ways ground facilities for turbomachinery experiments are limited in their ability, for example, to simulate flight inlet-flow nonuniformities feeding into a compressor stage, or to determine detailed flowfields between rotating blades. Numerical flow simulations, on the other hand, have none of these fundamental limitations, but have their own: computer speed and memory. These latter limitations are fewer, but previously have been much more restrictive overall because the full Navier-Stokes equations are of such great complexity that only highly truncated and approximate forms could be handled in the past. In recent years the Navier-Stokes equations have begun to yield under computational attack with the largest current computers. Since the fundamental limitations of computational speed and memory are rapidly decreasing with time, whereas the fundamental limitations of experimental facilities are not, numerical simulations offer the potential of mending many ills of wind-tunnel and turbomachinery experiments, and of providing thereby important new technical capabilities for the aerospace industry. A second compelling motivation concerns energy conservation. The large developmental wind tunnels require large amounts of energy, whereas computers require comparatively

Computational Aerodynamics Development and Outlook

The primary objective of this work is to provide accurate numerical solutions for selected flow fields and to compare and evaluate the performance of selected turbulence models with experimental results. Four popular turbulence models have been tested and validated against experimental data often turbulent flows. The models are: (1) the two-equation k-epsilon model of Wilcox, (2) the two-equation k-epsilon model of Launder and Sharma, (3) the two-equation k-omega/k-epsilon SST model of Menter, and (4) the one-equation model of Spalart and Allmaras. The flows investigated are five free shear flows consisting of a mixing layer, a round jet, a plane jet, a plane wake, and a compressible mixing layer; and five boundary layer flows consisting of an incompressible flat plate, a Mach 5 adiabatic flat plate, a separated boundary layer, an axisymmetric shock-wave/boundary layer interaction, and an RAE 2822 transonic airfoil. The experimental data for these flows are well established and have been extensively used in model developments. The results are shown in the following four sections: Part A describes the equations of motion and boundary conditions; Part B describes the model equations, constants, parameters, boundary conditions, and numerical implementation; and Parts C and D describe the experimental data and the performance of the models in the free-shear flows and the boundary layer flows, respectively.

Turbulence Modeling Validation, Testing, and Development

The performances of four turbulence models are evaluated against eight selected experimental flow fields. The four models are the two-equation k-e model of Launder and Sharma, the two-equation k-a> model of Wilcox, the twoequation k-03 SST model of Menter, and the one-equation eddy-viscosity model of Spalart and Allmaras. The eight turbulent flows of the validation are four fully-developed freeshear flows, an incompressibl e boundary layer, and three complex flows with flow separation. The free-shear layer flows comprise a mixing layer, a round jet, a plane jet, and a plane wake flow. The three complex flows are comprised of an adverse-pressure-gradient boundary layer, an axisymmetric shock-wave/boundary-layer interaction, and a transonic RAE 2822 airfoil flow. The experimental data for these flows is well established and has been extensively used in model developments. The numerical predictions include mean velocity profiles, spreading rates, surface pressure coefficients, skin friction, and shear-stress profiles. Most significantly, this research includes a sensitivity study on the accuracy of the solutions with respect to the effects of freestream turbulence, grid resolution, grid spacing near the wall, initial conditions, numerical methods and codes, and free stream Mach number effects on incompressible flows.

Turbulence modeling validation

Wall pressure fluctuations have been measured in a two-dimensional separated compression ramp-induced shock wave turbulent boundary-layer interaction The tests were made at a nominal freestream Mach number of 3 and at Reynolds numbers based on boundary-layer thickness of 78 X 10 and 14x 10 The wall temperature condition was approximately adiabatic Large-amplitude pressure fluctuations exist throughout the interaction, particularly near separation and reattachment In the upstream region of the flowfield, the unsteadiness of the separation shock wave structure generates an intermittent wall pressure signal Mean wall pressures in this region result from the superposition of the relatively low-frequency, large-amplitude, shock wave-induced fluctuations on the pressure signal of the undisturbed boundary layer This behavior is qualitatively similar to that observed in three-dimensional blunt fin-induced flows In these two flowfields, the length scale of the shock motion is a significant fraction of the distance from the interaction start to separation

Unsteadiness of the Separation Shock Wave Structure in a Supersonic Compression Ramp Flowfield

An experimental study has been carried out to detail the interaction of a compressible turbulent boundary layer with shock waves of varying strengths. The interaction was produced by two-dimension al compression corners of 8, 16, 20, and 24 deg angles. The incoming boundary layer had an edge Mach number of 2.85 and a Reynolds number of 1.7 million based on overall thickness. Detailed mean flow and surface measurements are presented for the four corner angles. The 8 deg corner flow was found to be fully attached, while the 16 deg case was near incipient separation. Both the 20 and 24 deg corners produced significant flow separation regions. In the discussion of these results, emphasis is placed on the development of flowfield properties from attached to separated conditions. Comparisons made with a computational solution of the Navier-Stokes equations show good agreement when the corner flow is not separated. Separated corner flows seem to require a more complex turbulence model in the computational solution.

Detailed Study of Attached and Separated Compression Corner Flowfields in High Reynolds Number Supersonic Flow

A new and improved wall function method for compressible turbulent flows has been developed and tested. This method is applicable to attached and separated flows, to both high- and low-Reynolds number flows, and to flows with adiabatic and nonadiabatic surfaces. This wall function method has been applied to the Launder-Spalding k-epsilon two-equation model of turbulence. The tests consist of comparisons of calculated and experimental results for: (1) an axisymmetrical transonic shock-wave/boundary-wave interaction flow at low Reynolds number in an adiabatic tube, (2) an axisymmetrical high-Reynolds number transonic flow over a nonadiabatic bump, and (3) a two-dimensional supersonic high-Reynolds number flow on a nonadiabatic deflected flap. Each of these experiments had significant regions of flow separation. The calculations are performed with an implicit algorithm that solves the Reynolds-averaged Navier-Stokes equations. It is shown that the results obtained agree very well with the data for the complex compressible flows tested.

On the use of wall functions as boundary conditions for two-dimensional separated compressible flows

Several multiequation eddy viscosity models of turbulence are used with the Navier-Stokes equations to compute three classes of experimentally documented shock-separated turbulent boundary-layer flows. The types of flow studied are: (1) a normal shock at transonic speeds in both a circular duct and a two-dimensional channel; (2) an incident oblique shock at supersonic speeds on a flat surface; and (3) a two-dimensional compression corner at supersonic speeds. Established zero-equation (algebraic), one-equation (kinetic energy), and two-equation (kinetic energy plus length scale) turbulence models are each utilized to describe the Reynolds shear stress for the three classes of flows. These models are assessed by comparing the calculated values of skin friction, wall pressure distribution, velocity, Mach number, and turbulent kinetic energy profiles with experimental measurements. Of the models tested the two-equation model results gave the best overall agreement with the data.

Comparison of Multiequation Turbulence Models for Several Shock Boundary-Layer Interaction Flows

Detailed pitot, static, and wall pressure measurements have been obtained for a transonic normal shockwave/turbulent boundary-layer interaction at freestream Mach numbers of 1.28, 1.37, and 1.48, and at a constant unit Reynolds number of 4.92xl0 6/m in an axisymmetric, internal flow. Measurements have also been obtained at a unit Reynolds number of 9.84xl0 6/m at a freestream Mach number of 1.29. The interaction depends very strongly on the Mach number. The effect of Reynolds number on the unseparated interaction is small. Flow blockage due to the wind tunnel wall boundary layer produces a weaker interaction and a much larger supersonic tongue than observed for planar flows. Comparisons are made with solutions to the timedependent, mass-averaged, Navier-Stokes equations incorporating a two-equation, Wilcox-Rubesin turbulence model. The computations are in agreement with the experimental results.

Transonic shock-wave/turbulent boundary-layer interactions in a circular duct

A detailed Investigation of a flow in which a three-dimensional shock wave separates a two-dimensional turbulent boundary layer is presented. The resulting flowfield is highly three dimensional with a significant portion of flow separation on the surface at the phi = 0 deg (windward) plane was well as a large zone of secondary surface flow off this plane. Mean and fluctuating experimental measurements were obtained throughout the entire flowfield. These measurements included mean pressures, flow angles and shear on the surface, as well as yaw angles, static pressures, turbulent shear stresses, and turbulent kinetic energies on selected planes throughout the flowfield. In addition, numerical predictions of this flow, obtained by solving the Navier-Stokes equations with an algebraic eddy viscosity turbulence model, are presented. These computations reasonably predict both the surface and flowfield quantities, despite the extremely complicated nature of the experimental flow.

Investigation of a Three-Dimensional Shock Wave Separated Turbulent Boundary Layer

Zero-equation (algebraic), one-equation (kinetic energy), and two-equation (kinetic energy plus length scale) turbulence eddy viscosity models were used in computing three basic types of shock-separated boundary-layer flows. The three basic types of shock boundary-layer interaction discussed are: (1) a normal shock wave at transonic speeds, (2) a compression corner shock at supersonic speeds, and (3) an incident oblique shock at hypersonic speeds. The models tested are simple, unmodified models used extensively for incompressible, unseparated flows. A comparison of computed and measured results for the compressible, separated flows described herein indicates that model performance is dependent on flow configuration with no distinct superiority of one model over the other for all three flow configurations.

J. R. Viegas

Papers

On the use of wall functions as boundary conditions for two-dimensional separated compressible flows

Comparison of Multiequation Turbulence Models for Several Shock Boundary-Layer Interaction Flows

Transonic shock-wave/turbulent boundary-layer interactions in a circular duct

Investigation of a Three-Dimensional Shock Wave Separated Turbulent Boundary Layer

Evaluation of turbulence models for three primary types of shock-separated boundary layers