Author

# George S. Deiwert

Bio: George S. Deiwert is an academic researcher from Ames Research Center. The author has contributed to research in topics: Turbulence & Transonic. The author has an hindex of 12, co-authored 37 publications receiving 901 citations.

Topics: Turbulence, Transonic, Reynolds number, Grid, Flow (mathematics)

##### Papers

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TL;DR: In this paper, an experimental and theoretical study of transonic flow over a thick airfoil, prompted by a need for adequately documented experiments that could provide rigorous verification of viscous flow simulation computer codes, is reported.

Abstract: An experimental and theoretical study of transonic flow over a thick airfoil, prompted by a need for adequately documented experiments that could provide rigorous verification of viscous flow simulation computer codes, is reported. Special attention is given to the shock-induced separation phenomenon in the turbulent regime. Measurements presented include surface pressures, streamline and flow separation patterns, and shadowgraphs. For a limited range of free-stream Mach numbers the airfoil flow field is found to be unsteady. Dynamic pressure measurements and high-speed shadowgraph movies were taken to investigate this phenomenon. Comparisons of experimentally determined and numerically simulated steady flows using a new viscous-turbulent code are also included. The comparisons show the importance of including an accurate turbulence model. When the shock-boundary layer interaction is weak the turbulence model employed appears adequate, but when the interaction is strong, and extensive regions of separation are present, the model is inadequate and needs further development.

189 citations

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TL;DR: In this article, a self-adaptive-grid method is described for multidimensional steady and unsteady flow computations about airfoils in two dimensions, as well as a steady inviscid flow computation and a one-dimensional case.

Abstract: A self-adaptive-grid method is described that is suitable for multidimensional steady and unsteady computations. Based on variational principles, a spring analogy is used to redistribute grid points in an optimal sense to reduce the overall solution error. User-specified parameters, denoting both maximum and minimum permissible grid spacings, are used to define the all-important constants, thereby minimizing the empiricism and making the method self-adaptive. Operator splitting and one-sided controls for orthogonality and smoothness are used to make the method practical, robust, and efficient. Examples are included for both steady and unsteady viscous flow computations about airfoils in two dimensions, as well as for a steady inviscid flow computation and a one-dimensional case. These examples illustrate the precise control the user has with the self-adaptive method and demonstrate a significant improvement in accuracy and quality of the solutions.

122 citations

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TL;DR: In this article, a three-dimensional solution-adaptive grid scheme was proposed for complex fluid flows using tension and torsion spring analogies, which was previously developed and successfully applied for two-dimensional flows.

Abstract: A three-dimensional solution-adaptive-grid scheme is described which is suitable for complex fluid flows. This method, using tension and torsion spring analogies, was previously developed and successfully applied for two-dimensional flows. In the present work, a collection of three-dimensional flow fields are used to demonstrate the feasibility and versatility of this concept to include an added dimension. Flow fields considered include: (1) supersonic flow past an aerodynamic afterbody with a propulsive jet at incidence to the free stream, (2) supersonic flow past a blunt fin mounted on a solid wall, and (3) supersonic flow over a bump. In addition to generating three-dimensional solution-adapted grids, the method can also be used effectively as an initial grid generator. The utility of the method lies in: (1) optimum distribution of discrete grid points, (2) improvement of accuracy, (3) improved computational efficiency, (4) minimization of data base sizes, and (5) simplified three-dimensional grid generation.

92 citations

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TL;DR: In this article, four different algebraic eddy viscoisity models are tested for viability to achieve turbulence closure for the class of flows considered, ranging from an unmodified boundary-layer mixing-length model to a relaxation model incorporating special considerations for the separation bubble region.

Abstract: 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 tur- bulent flowfield over an airfoil. Four different algebraic eddy viscoisity 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 flowfield. each of these studies the time-dependent Reynolds averaged Navier-Stokes equations for two-dimensional compressive flow are used and tur- bulence closure is achieved by means of model equations for the Reynolds stresses. Wilcox1'2 used a first-order accurate numerical scheme and the two equation differential tur- bulence model of Saffman 12 to simulate the supersonic shock boundary-layer interaction experiment of Reda and Mur- phy 13 and the compression corner flow of Law.14 Good quan- titative agreement with the Reda and Murphy data was ob- tained, but only the qualitative features of the compression corner flow were well simulated. Using a more sophisticated second-order accurate numerical scheme, Baldwin3'4 con- sidered both the two equation differential model of Saffman and a simpler algebraic mixing-length model to simulate the hypersonic shock boundary-layer interaction experiment of Holden.15 He found the more elaborate model of Saffman to yield somewhat better results than the algebraic model, but at the cost of considerably more computing time. Good quan- titative agreement with experiment was not obtained with either model. Following Baldwin's approach all subsequent investigations have been performed using the more rigorous second-order accurate numerical scheme of Mac- Cormack.17'18 Deiwert5'6'11 considered an algebraic mixing- length model to simulate the transonic airfoil experiment of McDevitt et al. 16 while Horstman et al. 8 used a similar ap- proach to simulate their hypersonic shock boundary-layer ex- periment on an axisymmetric cylinder. In each of these studies, while qualitative features of the flows were described well, good quantitative agreement with experiment in the in- teraction regions was not obtained. Using a relaxing turbulence model Shang and Hankey7 simulated the compression corner flow of Law, and Baldwin and Rose10 simulated the flat plate flow of Reda and Murphy. In each of these studies the relaxing model was found to per- form significantly better than the simpler algebraic model and, according to Shang and Hankey, provided significantly better comparisons with measurements than were obtained by Wilcox using the two equation differential model of Saffman. In each of these studies it was essential that the full Navier- Stokes equations be considered to describe the viscous- inviscid interaction and the elliptic nature of separating-

90 citations

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TL;DR: In this paper, an explicit finite-difference method with time splitting is used to solve the time-dependent equations for compressible turbulent flow, and a nonorthogonal computational mesh of arbitrary configuration facilitates the description of the flow field.

Abstract: A code has been developed for simulating high Reynolds number transonic flow fields of arbitrary configuration. An explicit finite-difference method with time splitting is used to solve the time-dependent equations for compressible turbulent flow. A nonorthogonal computational mesh of arbitrary configuration facilitates the description of the flow field. The code is applied to simulate the flow over an 18 percent thick circular-arc biconvex airfoil at zero angle of attack and free-stream Mach number of 0.775. A simple mixing-length model is used to describe the turbulence and chord Reynolds numbers of 1, 2, 4, and 10 million are considered. The solution describes in sufficient detail both the shock-induced and trailing-edge separation regions, and provides the profile and friction drag.

81 citations

##### Cited by

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TL;DR: An extensive review of the literature in V&V in computational fluid dynamics (CFD) is presented, methods and procedures for assessing V &V are discussed, and a relatively new procedure for estimating experimental uncertainty is given that has proven more effective at estimating random and correlated bias errors in wind-tunnel experiments than traditional methods.

948 citations

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TL;DR: In this article, an implicit finite-difference procedure for unsteady 3D flow capable of handling arbitrary geometry through the use of general coordinate transformations is described, where viscous effects are optionally incorporated with a "thin-layer" approximation of the Navier-Stokes equations.

Abstract: An implicit finite-difference procedure for unsteady three-dimensional flow capable of handling arbitrary geometry through the use of general coordinate transformations is described. Viscous effects are optionally incorporated with a "thin-layer" approximation of the Navier-Stokes equations. An implicit approximate factorization technique is employed so that the small grid sizes required for spatial accuracy and viscous resolution do not impose stringent stability limitations. Results obtained from the program include transonic inviscid or viscous solutions about simple body configurations. Comparisons with existing theories and experiments are made. Numerical accuracy and the effect of three-dimensional coordinate singularities are also discussed.

769 citations

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TL;DR: In this paper, an automatic grid generation program is employed, and because an implicit finite-difference algorithm for the flow equations is used, time steps are not severely limited when grid points are finely distributed.

Abstract: Finite-difference procedures are used to solve either the Euler equations or the "thin-layer" Navier-Stokes equations subject to arbitrary boundary conditions. An automatic grid generation program is employed, and because an implicit finite-difference algorithm for the flow equations is used, time steps are not severely limited when grid points are finely distributed. Computational efficiency and compatibility to vectorized computer processors is maintained by use of approximate factorization techniques. Computed results for both inviscid and viscous flow about airfoils are described and compared to viscous known solutions.

691 citations

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TL;DR: The field of computational fluid dynamics during recent years has developed sufficiently to initiate some changes in traditional methods of aerodynamic design, and 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.

Abstract: 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

689 citations

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TL;DR: A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given in this article, along with a general mathematical framework and error analysis common to such coordinate systems.

542 citations