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NASA NTRS1981

Numerical Prediction Methods (Reynolds-Averaged Navier-Stokes Simulations of Transonic Separated Flows)

During the past five years, numerous pioneering archival publications have appeared that have presented computer solutions of the mass-weighted, time-averaged Navier-Stokes equations for transonic problems pertinent to the aircraft industry. These solutions have been pathfinders of developments that could evolve into a major new technological capability, namely the computational Navier-Stokes technology, for the aircraft industry. So far these simulations have demonstrated that computational techniques, and computer capabilities have advanced to the point where it is possible to solve forms of the Navier-Stokes equations for transonic research problems. At present there are two major shortcomings of the technology: limited computer speed and memory, and difficulties in turbulence modelling and in computation of complex three-dimensional geometries. These limitations and difficulties are the pacing items of the continuing developments, although the one item that will most likely turn out to be the most crucial to the progress of this technology is turbulence modelling. The objective of this presentation is to discuss the state of the art of this technology and suggest possible future areas of research. We now discuss some of the flow conditions for which the Navier-Stokes equations appear to be required. On an airfoil there are four different types of interaction of a shock wave with a boundary layer: (1) shock-boundary-layer interaction with no separation, (2) shock-induced turbulent separation with immediate reattachment (we refer to this as a shock-induced separation bubble), (3) shock-induced turbulent separation without reattachment, and (4) shock-induced separation bubble with trailing edge separation.

Mehta, Unmeel↗
NASA NTRS1976

Recent computation of viscous effects in transonic flow

The paper describes some improvements to a method of solving the time-dependent Reynolds-averaged Navier-Stokes equations for two-dimensional compressible flows for describing the coupling between viscous and inviscid regions in transonic flows. Mesh patching is implemented at the sublayer-boundary layer interfaces and the boundary layer-inviscid flow interface. Mesh stretching is geometric and is small in regions of large gradients and large in regions of small gradients, thus preserving second-order accuracy. Mesh lines are arranged so as to accommodate MacCormack's rapid solver for hyperbolic systems and a wider class of turbulent transport models. Results of computations of transonic flows over lifting airfoils are compared with experimental data and other solutions.

Deiwert, G. S.↗
NASA NTRS1978

Viscous flow simulations in VTOL aerodynamics

The critical issues in viscous flow simulations, such as boundary-layer separation, entrainment, turbulence modeling, and compressibility, are discussed with regard to the ground effects problem for vertical-takeoff-and-landing (VTOL) aircraft. A simulation of the two-dimensional incompressible lift jet in ground proximity is based on solution of the Reynolds-averaged Navier-Stokes equations and a turbulence-model equation which are written in stream function-vorticity form and are solved using Hoffman's augmented-central-difference algorithm. The resulting equations and their shortcomings are discussed when the technique is extended to two-dimensional compressible and three-dimensional incompressible flows.

Bower, W. W.↗
NASA NTRS1979

Simulation of three-dimensional compressible viscous flow on the Illiac IV computer

Complicated three-dimensional viscous transonic flows about bodies at high angles of attack are solved on the Illiac IV computer. It is shown that certain approximate forms of the compressible Reynolds-averaged Navier-Stokes equations can be computed about realistic three-dimensional geometries with relative ease on the Illiac IV. The ease and efficiency with which this can be done depend on the approximations made in the basic equations, the choice of the numerical algorithm used for the solution, and the data-base system that controls the data management and identifies and manipulates the vectors. A pencil data-base system is found to be particularly suitable for the approximations and numerical method chosen to produce the results presented. In addition, some comparisons are made of computer predictions with experimental results for various lows about hemisphere-cylinders in both subsonic and supersonic free streams. The same viscous model and numerical model are used, showing good qualitative agreement in the location of separation lines and pressure distributions.

Pulliam, T. H.↗
NASA NTRS1979

Effect of Mach number and Reynolds number on a normal shock-wave/turbulent boundary-layer interaction

Experimental values of wall pressure and skin friction have been obtained for Mach numbers from 1.32 to 1.48 and for Reynolds numbers from 8.5 x 10 to the 6th to 225 x 10 to the 6th. Increasing the Mach number reduces the wall shear and promotes incipient separation. Reynolds number variations have little effect except at the lowest value where the flow abruptly approaches separation. Comparisons are made with solutions to the time-dependent, Reynolds-averaged, Navier-Stokes equations incorporating a two-equation, Wilcox-Rubesin turbulence model. The computations are in agreement with the experimental results. Additional numerical results indicated that the wind-tunnel walls constrained the flow and suppressed the formation of a separation bubble at the shock wave.

Mateer, G. G.↗
NASA NTRS1981

A reattaching free shear layer in compressible turbulent flow - A comparison of numerical and experimental results

An investigation of a two-dimensional, free turbulent shear layer reattaching on an inclined surface at Mach 2.92 and at a high Reynolds number is described. The test geometry is specifically designed to isolate the reattachment process of a high-speed separated flow. A numerical solution of the time-dependent, Reynolds-averaged, Navier-Stokes equations for the entire flow field, employing a two-equation eddy viscosity turbulence model, is presented. Detailed comparisons of prediction and experiment are made in the free shear layer, at reattachment, and in the developing boundary layer downstream. These comparisons include mean surface quantities as well as mean and fluctuating flowfield quantities. Although the overall features of this complex flow field are predicted, there are several deficiencies in the numerical solution, particularly in the region downstream of reattachment. Modifications of the turbulence model to correct these deficiencies are discussed.

Horstman, C. C.↗
NASA NTRS1982

Topological analysis of computed three-dimensional viscous flow fields

Computed solutions of the time-dependent, Reynolds-averaged Navier-Stokes equations for three dimensional flows having thin shear layers are analyzed using topological concepts. Specific examples include the transonic flow over a body of revolution with conical afterbody at moderate angles of incidence to the free stream. Experimental flow-visualization techniques are simulated graphically to visualize the computed flow. Scalar and vector fluid dynamics properties such as pressure, shear stress, and vorticity on the body surface are presented as topological maps, and their relationship to one another in terms of orientation and singular points is discussed. The extrapolation from these surface topologies toward the understanding of external flow-field behavior is and demonstrated.

Deiwert, G. S.↗
NASA NTRS1981

A summary of jet-impingement studies at McDonnell Douglas Research Laboratories

It has been the primary objective of the considered studies to determine and describe, through calculation, measurement, and visualization of the flowfields, the basic character of isolated and interacting impinging jets. The secondary objective has been to provide computed and experimental flow properties which can be used in the development and verification of empirically based prediction methodologies for complete aircraft configurations. The studies have resulted in the solution of the Reynolds-averaged Navier-Stokes and Jones-Launder turbulence model equations for two- and three-dimensional configurations and in the acquisition of an extensive data base and flow-visualization photographs for these configurations.

Bower, W. W.↗
NASA NTRS1982

Turbulence modeling for computational aerodynamics

The status of turbulence modeling for external aerodynamic flows is reviewed, and closure concepts for the compressible form of the Reynolds-averaged Navier-Stokes equations are briefly outlined to establish a framework for comparison. The importance of experimental requirements for developing and verifying turbulence models is emphasized. Attention is then given to three important flow categories: attached flows, separating and reattaching flows, and trailing-edge flows. Examples of comparisons between experiments and computations for twoand three-dimensional flows are presented to illustrate the status of modeling. It is shown that, for most two-dimensional attached flows, eddy viscosity concepts will probably be adequate. For attached three-dimensional flows, however, eddy-viscosity and Reynolds-stress models are both deficient, failing to predict the proper surface shear-stress in rapidly skewing boundary layers, regardless of whether they are pressure driven or strain driven.

Marvin, J. G.↗
NASA NTRS1981

Trends and pacing items in computational aerodynamics

A perspective is presented of trends in computational aerodynamics, and of important technology development items that pace future advanced applications. From a survey of AIAA Journal papers published during the past two decades, the growth trends and the progressively increasing emphasis on code development for viscous, compressible, turbulent flow are illustrated. These trends are reflected in the chronology of introduction by the aerospace industry of new computational methods in aircraft design. Key pacing items outlined are: automatic grid generation for nonlinear inviscid computations; advanced computers, improved efficiency of numerical methods, and improved turbulence models for Reynolds-averaged Navier-Stokes computations; advanced computers, time-dependent three-dimensional law-of-the-wall, code development, improved efficiency of numerical methods, and improved subgrid-scale turbulence modeling for large eddy simulations.

Chapman, D. R.↗
NASA NTRS1982

Transonic aerodynamics; Transonic Perspective Symposium, Moffett Field, CA, February 18-20, 1981, Technical Papers

After an historical account of the development of transonic aerodynamics before 1940 and in the period 1945-1975, attention is given to the design for cruise performance efficiency of commercial transport aircraft, with emphasis on transonic wing design, the practical aerodynamic problems of military aircraft, with emphasis on store carriage and separation, experimental testing in transonic wind tunnels capable of Reynolds number simulation and aerodynamic flow visualization, and such mathematical techniques as potential equation methods for flow prediction and Reynolds-averaged Navier-Stokes computations of transonic flows. Also considered are transonic design using computational aerodynamics, the application of computation methods to transonic wing design, computational experience with advanced tactical aircraft, the evaluation of full potential flow methods, and the application of a shock-turbulent boundary layer interaction theory to transonic flowfield analysis.

Nixon, D.↗
NASA NTRS1982

Topological analysis of computed three-dimensional viscous flow fields

Computed solutions of the time-dependent, Reynolds-averaged Navier-Stokes equations for three-dimensional flows having thin shear layers are analyzed, using topological concepts. Specific examples include the transonic flow over a body of revolution with conical afterbody at moderate angles of incidence to the free stream. Experimental flow-visualization techniques are simulated graphically to visualize the computed flow. Scalar and vector fluid dynamic properties, such as pressure, shear stress, and vorticity on the body surface, are presented as topological maps, and their relationship to one another in terms of orientation and singular points is discussed. The extrapolation from these surface topologies toward the understanding of external flow-field behavior is discussed and demonstrated.

Deiwert, G. S.↗
NASA NTRS1981

A Reattaching Free Shear Layer in Compressible Turbulent Flow: A Comparison of Numerical and Experimental Results

An investigation of the two-dimensional, free turbulent shear layer reattaching on an inclined surface at Mach 2.92 and at a high Reynolds number is described. The test geometry is specifically designed to isolate the reattachment process of a high-speed separated flow. A numerical solution of the time-dependent, Reynolds-averaged, Navier-Stokes equations for the entire flow field, employing a two-equation eddy viscosity turbulence model, is presented. Detailed comparisons of prediction and experiment are made in the free shear layer, at reattachment, and in the developing boundary layer downstream. These comparisons include mean surface quantities as well as mean and fluctuating flow-field quantities. Although the overall features of this complex flow field are predicted, there are several deficiencies in the numerical solution, particularly in the region downstream of reattachment. Modifications of the turbulence model to correct these deficiencies are discussed.

Horstman, C. C.↗
NASA NTRSDate not supplied

The NASA Turbulent Heat Flux (THX) Experiments: Summary and Lessons Learned

The Turbulent Heat Flux (THX) experiments were conducted at NASA Glenn Research Center (GRC) in order to collect measurements of velocities and temperatures for computational fluid dynamics (CFD) validation of heated flows, with a focus on propulsion system components. The experiments spanned 5 phases; four of which were conducted in the GRC AeroAcoustic Propulsion Laboratory (AAPL) using the Small Hot Jet Flow Rig (SHJAR). In addition to making velocity measurements with Particle Image Velocimetry (PIV), the THX experiments introduced a new Raman-scattering based capability to measure temperatures. Computational studies were also conducted for each of the experimental configurations, in order to provide a baseline of expected CFD results and conduct an assessment of the capability of various CFD approaches for calculating flows where the turbulent transport of heat was important. Two of the collected sets of data were used for American Institute of Aeronautics and Astronautics (AIAA) Propulsion Aerodynamic Workshops (PAWs). The data set from the 5th phase, collected for heated supersonic jets, was also used to construct new validation cases for the NASA Turbulence Model Resource (TMR). This paper provides an overview of the experiments and associated computations for each of the 5 test phases. Key experimental findings are presented. Lessons learned are provided concerning the effect of computational modeling choice on accuracy of predicting turbulent flows where thermal transport is important. Emphasis is placed on comparing Reynolds-averaged Navier-Stokes approaches with large-eddy simulation approaches. The benefits of utilizing a conjugate heat transfer method in conjunction with CFD solver for film cooling is demonstrated.

RANS↗
NASA NTRSDate not supplied

Improvements to RANS Modeling for Aeroheating Predictions on Blunt Bodies

Accurate predictions of aeroheating are critical for designing thermal protection systems for planetary entry vehicles. For larger vehicles, turbulence in the boundary layer can substantially increase convective heating. This turbulence must be accurately modeled to ensure the thermal protection system is sufficient. The majority of hypersonic turbulence model development and validation focuses on boundary layers developing over flat-plates or sharp cones; these cases are substantially different than the boundary layer that develops over the heatshield of a blunt body traveling at hypersonic speeds. Planetary missions often use blunt body geometries, such as the 70-degree sphere-cone favored by Mars missions or the 45-degree sphere-cone planned for the upcoming DAVINCI mission. Due to smaller vehicle size and the lower velocities in the stagnation region, planetary entry vehicles have relatively low Reynolds numbers. Surface curvature and high enthalpy gradients create additional challenges. These difficulties must be addressed to obtain high accuracy needed for the ambitious planetary missions in the upcoming decade. This work focuses on both assessing and improving Reynolds-averaged Navier-Stokes (RANS) turbulence models for blunt-body geometries typical of planetary entry vehicles, with a focus on one-equation and two-equation formulations.

Mars2020↗
NASA NTRS1981

A PANSONIC Navier-Stokes solver

A finite-difference formulation of the full Navier-Stokes equations which demonstrates a capability to economically solve two-dimensional problems has been developed. The basic algorithm was derived from the full, Reynolds-averaged, conservative, Navier-Stokes equations expressed in curvilinear coordinates. Eddy viscosity was determined by the Baldwin and Lomax algebraic turbulence model. This non-iterative, second-order accurate, implicit, numerical algorithm is based on the approximate factorization finite-difference scheme of Beam and Warming. Results indicate a facility for solving subsonic, transonic, and supersonic (hence PANSONIC) flows about arbitrary airfoils for a wide range of Reynolds numbers, Mach numbers, and angles of attack. Current computations demonstrate that vectorized implementations of this algorithm can solve steady-state, two-dimensional problems in five to ten minutes of computer time.

Cooper, G. K.↗
NASA NTRS1975

Computation of separated transonic turbulent flows

The two-dimensional Reynolds-averaged compressible Navier-Stokes equations are solved using MacCormack's second-order-accurate explicit finite difference method to simulate the separated transonic turbulent flow field over an airfoil. Four different algebraic eddy viscosity models are tested for viability to achieve turbulence closure for the class of flows considered. These models range from an unmodified boundary-layer mixing-length model to a relaxation model incorporating special considerations for the separation bubble region. Results of this study indicate the necessity for special attention to the separated flow region and suggest limits of applicability of algebraic turbulence models to these separated flow fields.

Deiwert, G. S.↗
NASA NTRS1995

Effect of turbulence models on criticality conditions in swirling flows

The critical state of vortex cores downstream of vortex breakdown has been studied. Base vortical flows were computed using the Reynolds-averaged, axisymmetric Navier-Stokes equations. Standard K - epsilon, RNG and second-order Reynolds stress models were employed. Results indicate that the return to supercriticality is highly dependent on the turbulence model. The K - epsilon model predicted a rapid return of the vortex to supercritical conditions, the location of which showed little sensitivity to changes in the swirl ratio. The Reynolds stress model predicted that the vortex remains subcritical to the end of the domain for each of the swirl ratios employed, and provided results in qualitative agreement with experimental work. The RNG model produced intermediate results, with a downstream movement in the critical location with increasing swirl. Calculations for which area reductions were introduced at the exit in a subcritical flow were also performed using the Reynolds stress model. The structure of the resulting recirculation zone was altered significantly. However, when area reductions were employed within supercritical flows as predicted using the two-equation models, no significant influence on the recirculation zone was noted.

Gatski, Thomas B.↗