Computation of transonic viscous airfoil, inlet, and wing flowfields

Agarwal, Ramesh K.; Deese, J.

doi:10.2514/6.1984-1551

Cited by 17 publications

(6 citation statements)

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“…is the reduced frequency, o is the frequency of the gust, and a is the characteristic length. We then arrive at, (V 2 + K 2 )<b = Q (3) with the boundary conditions, = _i e -'v/P 2 (4) dr\ p along the body, "%<£<% anc^> A<D = (A<D) (j , e~' v/p2 (5) along the wake, ^>^. V is the Laplacian operator computed in the (£,r|) domain, and AO represents the jump of $ across the wakeline.…”

Section: Classical Analysis Of the Aerodynamic Problemmentioning

confidence: 99%

Acoustic radiation due to gust-airfoil interaction in compressible flow

Agarwal

Huh

1996

Aeroacoustics Conference

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The problem of unsteady loading and acoustic radiation due to the interaction of an airfoil with a gust in compressible mean flow is considered numerically. The acoustic perturbation field is calculated by solving the acoustic equations derived from the unsteady Euler equations by linearizing about a steady mean flow and by assuming a single frequency disturbance. A computational code is developed which is validated by computing the unsteady loads on a flat plate due to a gust in incompressible flow (Sears problem), and unsteady loads and acoustic radiation due to a compact and noncompact gust in compressible flow. For these three cases the numerical results are compared with the exact analytical solutions and the asymptotic solutions. Excellent agreement is obtained. In a companion paper, the validated code is employed to perform parametric studies by varying the Mach number of the mean flow, the angle of attack, and the geometry (thickness and camber) of the airfoil. Conclusions are drawn about the magnitude and phase of acoustic radiation due to gust/airfoil interaction for various Mach numbers, angles of attack, and airfoil geometries. (Author) ABSTRACTThe problem of unsteady loading and acoustic radiation due to the interaction of an airfoil with a gust in compressible mean flow is considered numerically. The acoustic perturbation field is calculated by solving the acoustic equations derived from the unsteady Euler equations by linearizing about a steady mean flow and by assuming a single frequency disturbance. A computational code is developed which is validated by computing the unsteady loads on a flat plate due to a gust in incompressible flow (Sears problem), and unsteady loads and acoustic radiation due to a compact and noncompact gust in compressible flow. For these three cases the numerical results are compared with the exact analytical solutions and the asymptotic solutions. Excellent agreement is obtained. In a companion paper, the validated code is employed to perform parametric studies by varying the Mach number of the mean flow, the angle of attack and the geometry (thickness and camber) of the airfoil. Conclusions are drawn about the magnitude and phase of acoustic radiation due to gust/airfoil interaction for various Mach numbers, angles of attack, and airfoil geometries.

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Section: Classical Analysis Of the Aerodynamic Problemmentioning

confidence: 99%

Acoustic radiation due to gust-airfoil interaction in compressible flow

Agarwal

Huh

1996

Aeroacoustics Conference

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“….. J.M (5) where the coefficients /c (2) and /c (4) are set equal to \ and ^respec-tively. The quantities v t depend on the pressure-gradient parameter and are modified to produce a TVD variation of the shock-detection switch 19 in the following manner:…”

Section: Artificial Dissipation Modelmentioning

confidence: 99%

“…Solutions of the Euler (inviscid) equations for essentially complete aircraft configurations 1 " 4 and the solutions of the NavierStokes equations for high-Reynolds-number, viscous, transonic flows over aircraft components are now available in the open literature. 5 " 9 Most of the efficient numerical schemes for solving aerodynamic flows rely on multigrid acceleration techniques 2 ' 8 ' 9 to enhance the convergence rate. The multigrid-based schemes have the desirable property that the number of iterations required to achieve a steady-state solution is nearly independent of the mesh size for a given class of problems.…”

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confidence: 99%

Evaluation of a multigrid-based Navier-Stokes solver for aerothermodynamic computations

Vatsa

1995

Journal of Spacecraft and Rockets

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A multigrid acceleration technique developed for solving the three-dimensional Navier-Stokes equations is used for computing high-Mach-number flows over configurations of practical interest. An explicit multistage RungeKutta time-stepping scheme is used as the basic algorithm. Solutions are presented for a spherically blunted cone at Mach 10 and a modified Shuttle orbiter at Mach 6. The computed surface heat-transfer distributions are shown to compare well with the experimental data. Effect of grid refinement on computed heat-transfer distributions is also examined to assess the numerical accuracy of the computed solutions. The rapid convergence rate associated with multigrid schemes in previous applications at transonic speeds is observed at the higher-Mach-number flows investigated here. NomenclatureCL = lift coefficient D = sum of dissipative and viscous fluxes d = artificial dissipation term E = energy per unit volume F, G, H = components of convective flux vector in stream, normal, and span directions G v = viscous flux component in normal direction i, j,k = coordinate indices in £, 77, and f directions / = Jacobian of transformation /, L = length of body, meters M = Mach number p = static pressure Q = sum of convective fluxes q = heat-transfer coefficient, W/cm 2 s = circumferential arc length, m £max = maximum arc length in circumferential direction, m TI , T 2 = parameters for shock detection switch t = time U = dependent-variable vector u,v,w = Cartesian velocity components, m/s W = a typical conserved variable x s = streamwise distance measured from apex of equivalent sharp cone, m a = angle of attack, deg 6 (2)= multiplicative coefficient for second-order dissipation 6 (4) = multiplicative coefficient for fourth-order dissipation /c (2) = scaling constant for second-order dissipation K (4) = scaling constant for fourth-order dissipation A.= eigenvalue used in dissipation scaling v = pressure-gradient parameter defined in Eq. (6) £, 77, ? = curvilinear coordinates along stream, normal, and span directions co = weight factor used in construction of shock detection switchPresented as Paper 92

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“…1 Although this approach as it is applied to three-dimensional flow over wings is new, a number of publications are now Presented as Paper 86-0508 at the AIAA 24th Aerospace Sciences Meeting, Reno, NV, Jan. [6][7][8][9]1986; received July 22, 1986; revision received Nov. 24,1986 appearing on the subject. The computation of the supersonic flow over a blunt delta wing by Vigneron et al, 9 the leadingedge separation vortex over a delta wing at high angle of attack by Fujii and Kutler, 10 the simulation of a tip vortex off a low-aspect-ratio wing at a transonic speed by Mansour,11 and the transonic wing solutions of Agarwal and Deese, 12 Vadyak, 13 Obayashi and Fujii, 14 and Hoist et al 15 In the present study, a computer program called transonic Navier-Stokes (TNS), which was developed by Hoist et al, 15 is used to compute the viscous flowfield around a low-aspectratio wing. The TNS program was chosen because of its speed, accuracy, and efficiency.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of transonic separated flows over low-aspect-ratio wings

Kaẏnak

Holst

Sorenson

et al. 1987

Journal of Aircraft

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Transonic flowfields about a low-aspect-ratio advanced technology wing have been computed using a viscous/inviscid zonal approach. The flowfield near the wing where viscous effects are important was solved using the "Reynolds-averaged Navier-Stokes equations" in "thin-layer" form. The Euler equations were used to determine the flowfield in regions away from the wing where viscous effects are insignificant. A zonal grid using an H-H topology was generated around the wing by first solving a set of Poisson's equations for the global grid. This grid was then subdivided into separate zones of viscous or inviscid flow as suggested by the flow physics. A series of flow cases were computed and compared with corresponding sets of experimental data. All cases showed good agreement with experiment in terms of the pressure field. Also, an encouraging correlation between computed separated surface flow and experimental oil flow was obtained.

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Computation of transonic viscous airfoil, inlet, and wing flowfields

Cited by 17 publications

References 0 publications

Acoustic radiation due to gust-airfoil interaction in compressible flow

Acoustic radiation due to gust-airfoil interaction in compressible flow

Evaluation of a multigrid-based Navier-Stokes solver for aerothermodynamic computations

Numerical simulation of transonic separated flows over low-aspect-ratio wings

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