# Transonic Flow about a Thick Circular-Arc Airfoil

01 May 1976-AIAA Journal (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 14, Iss: 5, pp 606-613

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.

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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 article, a review of the physical mechanisms of the periodic shock motion on airfoils at transonic flow conditions are associated with the phenomenon of buffeting, and various modes of shock wave motion for different flow conditions and airfoil configurations are described.

333 citations

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TL;DR: Using DMR without multigriding, between 30% and 10% of the total computational efforts were saved in the subsonic compressible flow calculations, which seems to be especially suitable for stiff systems of equations.

Abstract: rest of the equations in the system. The DMR method computes a separate sequence of optimal acceleration factors to be used for each component of the general solution vector. The acceleration scheme was applied to the system of time-dependent Euler equations of inviscid gasdynamics in conjunction with the finite-volume, Runge-Kutta, explicit, time-stepping algorithm. Using DMR without multigriding, between 30% and 10% of the total computational efforts were saved in the subsonic compressible flow calculations. The DMR method seems to be especially suitable for stiff systems of equations and can be applied to other systems of differential equations and other numerical algorithms.

169 citations

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TL;DR: In this article, the accuracy and efficiency of two types of subiterations in both explicit and implicit Navier-Stokes codes are explored for unsteady laminar circular-cylinder flow and unsteby turbulent flow over an 18-percent-thick circular-arc (biconvex) airfoil.

167 citations

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TL;DR: In this article, the authors present a review of recent investigations in the field of transonic shock buffet and highlight the importance of these experiments for the development of physical models stressed with a particular emphasis on the emergence of frequency synchronisation phenomenon.

155 citations

##### References

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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 article, the velocity and streamline maps of the turbulent transonic separated flow generated on the rear portion of a two-dimensional circular-arc model mounted on the floor of a transonic duct are presented.

Abstract: Experimental details are presented of the turbulent transonic separated flow generated on the rear portion of a two-dimensional circular-arc model mounted on the floor of a transonic duct (M, ^ 0.7). Two interaction modes were studied and are characterized by their peak Mach numbers: case A, that of pressure-gradient induced separation (Mp 1.32). Separation criteria are determined for both modes which are based on the velocity field of the viscous layer at separation. The measured reverse-flow velocity profiles are shown to compare favorably with theoretical similarity solutions based on the turbulent energy equation, and are employed to construct a velocity and streamline map of the flowfield. Using an approximate inviscid streamline shape for the separated flow, a time dependent finite-difference solution has been obtained for the inviscid transonic pressure distribution which shows reasonable agreement with measured wall pressures throughout the entire field.

48 citations