# Navier-Stokes simulation of self-excited shock induced oscillations

19 Jun 1995-pp 381-388

TL;DR: Gillan et al. as discussed by the authors used an explicit cell-vertex-centred Navier-Stokes code in conjunction with a hyperbolic C-grid generator to predict self-excited shock induced oscillations on an 18% thick circular-arc airfoil.

Abstract: A numerical study investigating the ability of the full massaveraged Navier-Stokes equations to accurately predict selfexcited shock induced oscillations on an eighteen per cent thick circular-arc airfoil is presented. An explicit cell-vertex-centred Navier-Stokes code is employed in conjunction with a hyperbolic C-grid generator. Turbulence closure is accomplished using the zero equation algebraic Baldwin-Lomax model. The code accurately predicts the shock induced oscillation onset boundary, reduced frequencies and hysteresis region. Comparing these results with those obtained from a thin-layer version of the code highlights the limitations of the latter technique. Only by employing the full mass averaged Navier-Stokes equations, operating on a suitably fine grid, can the dynamic shear layers be adequately resolved. Introduction The need to accurately model the evolution of unsteady aerodynamic phenomena, such as buffet, flutter, limit cycle oscillations and buzz has thrust unsteady computational fluid dynamics to the forefront of modern research. The classical experiments performed by Tijdeman' on a NACA64A006 airfoil with a trailing-edge flap detected three types of shock motion. Tijdeman's results have proven equally valid for rigid airfoil studies and form the basis for the classification of self-excited shock induced oscillations, or SIO. Tijdeman type A SIO is were the shock wave remains distinct throughout the oscillation with a cyclic change in both the shock wave strength and location. In Tijdeman type B SIO the shock wave vanishes for part of the cycle, normally whilst the shock is propagating upstream. Finally, Tijdeman type C SIO describes the shock wave motion whereby the shock remains distinct as it propagates upstream past the leading-edge and into the on coming flow. Throughout the past two decades extensive experimental investigations into periodic flow over varying thickness circulararc airfoils have been p e r f ~ r m e d ~ ~ . These experiments, which were conducted over a wide range of free stream Mach and Reynolds numbers, have detected all three types of SIO. References 2 and 3 identified Tijdeman type C SIO, with a reduced frequency of, k = 0.49, for an 18 % thick circular-arc airfoil at zero incidence over a narrow range of Mach numbers, namely: 0.73 < M, < 0.78. Small regions of Tijdeman type A SIO were also detected in the extremities of the periodic flow band. Figure 1 indicates that the extent of this periodic band decreases considerably as the Reynolds number approaches 'ResearchTechnicalEngineer, Nacelle Systems, Member AIAA. Copyright " 1995 by Mark Gillan. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. 3 x 10'. A similar phenomenon was detected by Mabey et a1.' whereby the SIO vanished within the Reynolds number range of: 3 x lo6 < Re, < 5 x 10'. Furthermore, the region of flow hysteresis which McDevitt et al.' discovered was later verified by Seegmiller et aL4 and LevyS (fig.1). Finally, Gibbg, who conducted a comprehensive study of flow over a 14% thick circular-arc airfoil, detected strong Tijdeman type B SIO, with small regions of Tijdeman type A SIO, occurring within a narrow Mach number band, namely: 0.84 < M, < 0.88. Following various steady-state c~mputations~.'~-", Levy5 eventually produced the first unsteady Navier-Stokes computation over an 18 7% thick circular-arc airfoil that was capable of reproducing the intrinsically asymmetric periodic flow. Levy used a modified version of the code employed by DeiwertloaL' which included solid-wall test section inviscid boundary conditions. Despite employing an extremely coarse 78 X 35 grid and a 1 % chord nose radius (to alleviate numerical difficulties), the impulsively started computation produced SIO with a reduced frequency of, k=0.4, comparable to that produced experimentally by McDevitt et a1.I of, k=0.49. Furthermore, in an attempt to show that the periodic flow solution was the result of viscous effects alone and not due to spurious numerical inaccuracies, Levy ran the periodic test case for various different configurations. Both an inviscid test case and a viscous computation, with a 114 chord trailing-edge splitter plate, which effectively prevents pressure wave communication across the wake, produced steady flow solutions, thereby corroborating Levy's hypothesis. Seegmiller et aL4 developed Levy's research further by presenting an in-depth explanation regarding the exact nature of the periodic mechanism. Furthermore, they4 astutely recognised that the period of the SIO depended on the time taken for the flow to adjust to, and counteract, the airfoil's effective change in camber due to the asymmetry of the shock-induced separation. This reasoning is supported by the earlier experimentation of ~ i n k e ' ~ . Subsequent Navier-Stokes computations over circular-arc airfoils have been performed by Steger", Edwards and ThomasL4, Gerteisenl' and illa an^^^'^. Steger" computed periodic flow with a reduced frequency of, k=0.41, at a free stream Mach number of, M, =0.783. Edwards and tho ma^'^ employed anupwind-biased Navier-Stokes scheme and computed Tijdeman type B SIO with a reduced frequency of, k=0.406, at a free-stream Mach number comparable to Steger's, of M, =0.78. GerteisenLs failed to reproduce either Tijdeman type B, or type C, SIO. Gertesin believed that this was due to a combination of insufficient shock resolution, inadequate turbulence modelling and the existence of transitionally dominated flow. Gillan16 computed periodic flow over an 18 % thick circular-arc airfoil at 0' angle of attack and a free stream Mach number of M, =0.771 (see fig.2). This Mach number lies within the periodic region which was detected both experimentally and computationally by Levy5 as depicted in fig. 1. No attempt was made during the computational analysis to detect the hysteresis region depicted in this figure. A 320x64 cells was employed, with 256 cells placed on the airfoil's surface. A far-field boundary of 20 chord lengths was enforced, with the initial near-wall normal grid spacing corresponding to a value of y+ < 2 for the assigned Reynolds number of Re, = 1 1 X 10.~. Moreover, a 1 % leading-edge radius was introduced in an attempt to avoid any unnecessary computational difficulties. The computational test case, which was impulsively started from free stream conditions, produced an unsteady periodic Tijdeman type B motion with a reduced frequency of, k = 0.396. Although this reduced frequency is approximately 21 % lower than that obtained experimentally by McDevitt et aL2 it compares favourably with the computed values of 0.4 and 0.406 obtained by Levy5 and Edwards and Thomasr4 respectively. In an attempt to introduce some non-equilibrium history effects into periodic flow computations various pre-eminent researchers have temporally 'abandoned' the use of NavierStokes solvers. Le Balleur and Girodroux-La~igne'~'~ used a small-disturbance potential method with a two-equation integral viscous solver to compute SIO with a reduced frequency of, k=0.34, at a free-stream Mach number of, M ~ 0 . 7 6 . Although this frequency is significantly lower than previous results, it indicates the ability of a non-Navier-Stokes solver to qualitatively reproduce unsteady periodic flows. Finally, Edwards2" has recently employed a new lag-entrainment integral boundary layer method coupled with a transonic small disturbance potential code to compute periodic flow over a range of configurations. Edwards accurately modelled the SIO period for an 18% thick circular-arc airfoil, detecting a seduced frequency of, k=0.47, at a free-stream Mach number of, M, =0.76. Furthermore, he reproduced, for the first time, the hysteresis region which was initially discovered experimentally by McDevitt et al.'. The primary objective of this paper is to investigate the ability of the full mass-averaged Navier-Stokes equations, operating on a suitably fine grid, to accurately predict SIO on an 18% thick circular-arc airfoil. In order to perform this analysis a hyperbolic grid generation code and an explicit finite volume cell vertex-centred Navier-Stokes code have been employed. The following section briefly describes both the numerical model and the results. Numerical Model A recently developed explicit Navier-Stokes finite volume code (MGENS2D) has been used in conjunction with an orthogonal boundary conforming hyperbolic C-grid. A detailed description of both the Navier-Stokes scheme and the grid generation code (MGHYPR) is given in ref. 16. If Q represents an arbitrary control volume, with a domain boundary, an, and a unit outward normal, n, then, neglecting body forces and external heat addition, the integral form of the 2-0 non-dimensional mass-averaged Navier-Stokes equations may be written as: where W is the vector of the conserved quantities: with p,u,v and E denoting the density, the cartesian velocities and the specific total internal energy respectively. The flux tensor P is then split into a convective part, Few, and a viscous part, F,,,: P = PCMV Fam

##### Citations

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TL;DR: In this article, two vortex generators are mounted in front of the shock wave region on the upper surface of an OAT15A supercritical airfoil at Mach number of 0.73 and angle of attack of 3.5 degrees.

Abstract: In the present paper, extremely unsteady shock wave buffet induced by strong shock wave/boundary-layer interactions (SWBLI) on the upper surface of an OAT15A supercritical airfoil at Mach number of 0.73 and angle of attack of 3.5 degrees is first numerically simulated by IDDES, one of the most advanced RANS/LES hybrid methods. The results imply that conventional URANS methods are unable to effectively predict the buffet phenomenon on the wing surface; IDDES, which involves more flow physics, predicted buffet phenomenon. Some complex flow phenomena are predicted and demonstrated, such as periodical oscillations of shock wave in the streamwise direction, strong shear layer detached from the shock wave due to SWBLI and plenty of small scale structures broken down by the shear layer instability and in the wake. The root mean square (RMS) of fluctuating pressure coefficients and streamwise range of shock wave oscillation reasonably agree with experimental data. Then, two vortex generators (VG) both with an inclination angle of 30 degrees to the main flow directions are mounted in front of the shock wave region on the upper surface to suppress shock wave buffet. The results show that shock wave buffet can be significantly suppressed by VGs, the RMS level of pressure in the buffet region is effectively reduced, and averaged shock wave position is obviously pushed downstream, resulting in increased total lift.

54 citations

01 Feb 1998

TL;DR: In this article, the authors compared the performance of the interactive boundary layer and the thin-layer Navier-Stokes equations solved with recent upwind techniques using similar transport field equation turbulence models for standard steady test cases.

Abstract: Flow and turbulence models applied to the problem of shock buffet onset are studied. The accuracy of the interactive boundary layer and the thin-layer Navier-Stokes equations solved with recent upwind techniques using similar transport field equation turbulence models is assessed for standard steady test cases, including conditions having significant shock separation. The two methods are found to compare well in the shock buffet onset region of a supercritical airfoil that involves strong trailing-edge separation. A computational analysis using the interactiveboundary layer has revealed a Reynolds scaling effect in the shock buffet onset of the supercritical airfoil, which compares well with experiment. The methods are next applied to a conventional airfoil. Steady shock-separated computations of the conventional airfoil with the two methods compare well with experiment. Although the interactive boundary layer computations in the shock buffet region compare well with experiment for the conventional airfoil, the thin-layer Navier-Stokes computations do not. These findings are discussed in connection with possible mechanisms important in the onset of shock buffet and the constraints imposed by current numerical modeling techniques.

28 citations

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R. Bartels

^{1}•TL;DR: In this paper, a study of recent flow and turbulence models applied to the problem of shock buffet onset was conducted, and the accuracy of the interactive boundary layer and the thin layer Navier-Stokes equations solved with recent upwind techniques using similar transport field equation turbulence models was assessed for standard steady test cases, including conditions having significant shock separation.

Abstract: This is a study of recent flow and turbulence models applied to the problem of shock buffet onset. The accuracy of the interactive boundary layer and the thin layer Navier-Stokes equations solved with recent upwind techniques using similar transport field equation turbulence models is assessed for standard steady test cases, including conditions having significant shock separation. The two methods are then used a study of the shock buffet onset region of a supercritical airfoil, and airfoil having strong trailing edge separation, and found to compare well. A Reynolds scaling effect in the onset of the shock buffeting of the supercritical airfoil computed with the interactive boundary layer method is found to compare well with that observed experimentally. This is used to argue that the experimental data are of conditions very near shock buffet onset. The methods are next applied to a conventional airfoil. Steady shock separated computations are shown to compare well. Computations in the shock buffeting region using the two methods, however, do not. These findings are discussed in connection with possible mechanisms important in the. onset of shock buffet.

21 citations

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09 Jan 2012

TL;DR: In this paper, two vortex generators were mounted in front of the shock wave region to suppress buffet, which significantly suppressed the RMS level of pressure in the buffet region and the averaged shock wave position was obviously pushed downstream.

Abstract: Unsteady shock wave buffet phenomenon is often induced on the upper surface of supercritical airfoils. An OAT15A airfoil at Mach number of 0.73 and angle of attack of 3.5 degrees is numerically predicted. IDDES method is used with dissipation-adaptive functions introduced into high-order TVD methods. Conventional URANS predictions are unable to effectively predict the buffet phenomenon while IDDES successfully captured buffet phenomenon. Periodical oscillations of shock waves in the streamwise direction and strong shear layers are captured and plenty of small scale structures broken down by the shear layer instability and in the wake are predicted. The distribution of pressure coefficients and starting point of shock wave oscillation reasonably match experimental data. Then, two vortex generators (VG) in one span of 0.26 chord length are mounted in front of the shock wave region to suppress buffet. VGs significantly suppressed the RMS level of pressure in the buffet region and the averaged shock wave position is obviously pushed downstream.

7 citations

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TL;DR: In this article, the authors applied Reynolds averaged Navier-Stokes equations with k-ω SST turbulence model to predict the buffet onset for the flow over a supercritical airfoil NASA SC(2) 0714.

Abstract: Transonic flow over a supercritical airfoil leads to the appearances of unsteady shock waves in theflow field. At certain flow conditions, the interaction of unsteady shock waves with boundary layer becomescomplex and generates self-excited shock oscillation, lift fluctuation and thus initiate the buffet. In the presentstudy, Reynolds averaged Navier-Stokes equations with k-ω SST turbulence model has been applied to predictthe shock induced buffet onset for the flow over a supercritical airfoil NASA SC(2) 0714. The free streamtransonic Mach number is kept in the range of 0.71 to 0.75 while the angle of attack is varied in a wide range.The onset of buffet is confirmed by the fluctuating aerodynamic properties such as lift-coefficient, pressurecoefficient, static pressure and so on. The self-excited shock oscillation and the corresponding buffet frequencyare numerically analyzed. DOI: http://dx.doi.org/10.3329/jme.v43i1.15782

4 citations

### Cites methods from "Navier-Stokes simulation of self-ex..."

...On the other hand, prominent features of the shock buffet of the 18-percent-thick circular-arc airfoil have been computed by Gillan (1995) and Rumsey et al. (1995) with Navier-Stokes and thin-layer Navier-Stokes codes, repectively....

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##### References

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Joseph L. Steger

^{1}•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

21 Dec 1977

TL;DR: In this paper, an experimental analysis of high-subsonic and transonic flow on a conventional airfoil with oscillating flap and a supercritical airframe oscillating in pitch is presented, where the interaction between the steady and unsteady flow fields, the periodical motion of the shock waves and their contribution to the overall unstrainy airloads are discussed.

Abstract: Exploratory wind-tunnel experiments in high-subsonic and transonic flow on a conventional airfoil with oscillating flap and a supercritical airfoil oscillating in pitch are described. In the analysis of the experimental results, emphasis is placed upon the typical aspects of transonic flow, namely the interaction between the steady and unsteady flow fields, the periodical motion of the shock waves and their contribution to the overall unsteady airloads. Special attention is paid to the behaviour of the supercritical airfoil in its "shock-free" design condition. Moreover, it is discussed to what extent linearization of the unsteady transonic flow problem is allowed if the unsteady field is considered as a small perturbation superimposed upon a given mean steady-flow field. Finally, the current status of unsteady transonic flow theory is reviewed and the present test data are used to evaluate some of the recently developed calculation methods.

199 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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Lionel L. Levy

^{1}•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

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01 Jan 1978

TL;DR: In this article, an investigation of the transonic flow over a circular arc airfoil was conducted to obtain basic information for turbulence modeling of shock-induced separated flows and to verify numerical computer codes which are being developed to simulate such flows.

Abstract: An investigation of the transonic flow over a circular arc airfoil was conducted to obtain basic information for turbulence modeling of shock-induced separated flows and to verify numerical computer codes which are being developed to simulate such flows. The investigation included the employment of a laser velocimeter to obtain data concerning the mean velocity, the shear stress, and the turbulent kinetic energy profiles in the flowfield downstream of the airfoil midchord where the flow features are more complex. Depending on the free-stream Mach number, the flowfield developed was either steady with shock-wave-induced separation extending from the foot of the shock wave to beyond the trailing edge or unsteady with a periodic motion also undergoing shock-induced separation. The experimental data were compared with the results of numerical simulations in which a computer code was employed that solved the time-dependent Reynolds' averaged compressible Navier-Stokes equations.

104 citations