# Computation of Separated Transonic Turbulent Flows

01 Jun 1976-AIAA Journal (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 14, Iss: 6, pp 735-740

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-

##### 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: 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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01 Jun 1977TL;DR: In this article, 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 various known solutions.

170 citations

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TL;DR: In this paper, an experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described, and an operational computer code for solving the two-dimensional, compressible NavierStokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models.

Abstract: An experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described. An operational computer code for solving the two-dimensional, compressible NavierStokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models. Steady and unsteady fiowfieids about an 18% thick circular arc airfoil at Mach numbers of 0.720, 0.754, and 0.783 and a chord Reynolds number of 11 x 10 are predicted and compared with experiment. Results from comparisons with experimental pressure and skin-friction distributions show improved agreement when including test-section wall boundaries in the computations. Steady-flow results were in good quantitative agreement with experimental data for flow conditions which result in relatively small regions of separated flow. For flows with larger regions of separated flow, improvements in turbulence modeling are required before good agreement with experiment will be obtained. For the first time, computed results for unsteady turbulent flows with separation caused by a shock wave were obtained which qualitatively reproduce the time-dependent aspects of experiments. Features such as the intensity and reduced frequency of airfoil surface-pressure fluctuations, oscillatory regions of trailing-edge and shock-induced separation, and the Mach number range for unsteady flows were all qualitatively reproduced.

152 citations

01 Jun 1985

TL;DR: In this paper, the supercritical flows at high subsonic speeds over a NACA 0012 airfoil were studied to acquire aerodynamic data suitable for evaluating numerical flow codes.

Abstract: The supercritical flows at high subsonic speeds over a NACA 0012 airfoil were studied to acquire aerodynamic data suitable for evaluating numerical-flow codes. The measurements consisted primarily of static and dynamic pressures on the airfoil and test-channel walls. Shadowgraphs were also taken of the flow field near the airfoil. The tests were performed at free-stream Mach numbers from approximately 0.7 to 0.8, at angles of attack sufficient to include the onset of buffet, and at Reynolds numbers from 1 million to 14 million. A test action was designed specifically to obtain two-dimensional airfoil data with a minimum of wall interference effects. Boundary-layer suction panels were used to minimize sidewall interference effects. Flexible upper and lower walls allow test-channel area-ruling to nullify Mach number changes induced by the mass removal, to correct for longitudinal boundary-layer growth, and to provide contouring compatible with the streamlines of the model in free air.

132 citations

##### References

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TL;DR: In this paper, the authors defined the distance from wall pipe radius pipe diameter mean local velocity parallel to wall velocity fluctuations parallel and normal to flow mass density coefficient of viscosity shear stress velocity correlation coefficient mixing length universal constant in I = Ky modified universal constant eddy viscosities size of roughness friction factor = 8rw/p V 2

Abstract: y* h k* a* A* = = = = = = = = = = = = = = = = = = = = = = = = = = = = distance from wall pipe radius pipe diameter mean local velocity parallel to wall velocity fluctuations parallel and normal to flow mass density coefficient of viscosity shear stress velocity correlation coefficient mixing length universal constant in I = Ky modified universal constant eddy viscosity size of roughness friction factor = 8rw/p V 2

1,710 citations

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TL;DR: In this article, the authors examined the effect of roughness on boundary layer characteristics and showed that the wall is aerodynamically smooth for a turbulent boundary layer if the roughness elements are so small as to be buried in the laminar sublayer.

Abstract: Publisher Summary This chapter discusses the simple case of the turbulent boundary layer in a constant pressure field and considers the complex problem of the effects of pressure gradients, and variable wall roughness The concepts of boundary layer phenomena, in general, and turbulent boundary layers, in particular, have found application in a wide range of fields including aeronautics, guided missiles, marine engineering, hydraulics, meteorology, oceanography, chemical engineering, atomic reactors, and the flow of liquids and gases in the human body Many ideas for turbulent boundary layers involve assumptions other than those for turbulent shear stresses and in these cases, the validity of the results is examined first for laminar layers and then interpreted in the light of the possible shear stress patterns of turbulent layers The effect of roughness on boundary layer characteristics is examined in the chapter The wall is aerodynamically smooth for a turbulent boundary layer if the roughness elements are so small as to be buried in the laminar sublayer Pressure gradients, Reynolds number, or roughness does not affect the constants of proportionality The assumption of a constant outer viscosity has been investigated only for the case of equilibrium layers

1,367 citations

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484 citations

01 Aug 1973

TL;DR: A review of current knowledge, a discussion of methods of predicting curvature effects, and a presentation of principles for the guidance of future workers can be found in this article, along with a progress report.

Abstract: : Streamline curvature in the plane of the mean shear produces large changes in the turbulence structure of shear layers, usually an order of magnitude more important than normal pressure gradients and other terms in the mean-motion equations for curved flows. The effects on momentum and heat transfer in boundary layers are noticeable on typical wing sections and are very important on highly-cambered turbomachine blades: turbulence may be nearly eliminated on highly-convex surfaces, while on highly-concave surfaces momentum transfer by quasi-steady longitudinal vortices dominates the ordinary turbulence processes. The greatly enhanced mixing rates of swirling jets and the characteristic non-turbulent cores of trailing vortices are also consequences of the effects of streamline curvature on the turbulence structure. A progress report, comprises a review of current knowledge, a discussion of methods of predicting curvature effects, and a presentation of principles for the guidance of future workers.

431 citations

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01 Jan 1971TL;DR: In this paper, a modified Lax-Wendroff difference technique was used to detect shock wave interaction with laminar boundary layer on flat plate using modified Lazy Lazy Wasserstein difference technique.

Abstract: Shock wave interaction with laminar boundary layer on flat plate using modified Lax-Wendroff difference technique

409 citations