ALBERT

Description: The objective of the present investigation is to assess the effect of the spatial order of accuracy used for the evaluation of the inviscid fluxes on the resolution of higher order quantitites, such as velocity gradients. The viscous terms are computed as second-order accurate with central difference formulas, even though for the explicit part of the algorithm higher order approximations may be used. A viscous/inviscid method is used, and the outer part of the flowfield is computed with the inviscid flow equations. The viscous boundary-layer type flow region close to the body surface is computed with an algebraic eddy viscosity model. Results obtained with the conservative and nonconservative formulations and the viscous/inviscid approach are compared with available experimental data. The effect of grid refinement on the accuracy of the solution is also presented.

Description: The structure of the vortical flowfield over delta wings at high angles of attack was investigated. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics, including leading-edge separation, secondary separation, and vortex breakdown. Flows over a 75- and a 63-deg sweep delta wing with sharp leading edges were investigated and compared with available experimental data. The effect of variation of circumferential grid resolution grid resolution in the vicinity of the wing leading edge on the accuracy of the solutions was addressed. Furthermore, the effect of turbulence modeling on the solutions was investigated. The effects of variation of angle of attack on the computed vortical flow structure for the 75-deg sweep delta wing were examined. At moderate angles of attack no vortex breakdown was observed. When a critical angle of attack was reached, bubble-type vortex breakdown was found. With further increase in angle of attack, a change from bubble-type breakdown to spiral-type vortex breakdown was predicted by the numerical solution. The effects of variation of sweep angle and freestream Mach number were addressed with the solutions on a 63-deg sweep delta wing.

Description: Experimental and computational investigations of the dynamic stall phenomenon continue to attract the attention of various research groups in the major aeronautical research laboratories. There are two reasons for this continued research interest. First, the occurrence of dynamic stall on the retreating blade of helicopters imposes a severe performance limitation and thus suggests to search for ways to delay the onset of dynamic stall. Second, the lift enhancement prior to dynamic stall presents an opportunity to achieve enhanced maneuverability of fighter aircraft. A description of the major parameters affecting dynamic stall and lift and an evaluation of research efforts prior to 1988 has been given by Carr. In this paper the authors' recent progress in the development of experimental and computational methods to analyze the dynamic stall phenomena occurring on NACA 0112 airfoils is reviewed. First, the major experimental and computational approaches and results are summarized. This is followed by an assessment of our results and an outlook toward the future.

Description: Two methods are described for calculating unsteady flows over rapidly pitching airfoils. The first method is based on an interactive scheme in which the inviscid flow is obtained by a panel method. The boundary layer flow is computed by an interactive method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier-Stokes equations. The solution of these equations is obtained with an approximately factorized numerical algorithm, and with single block or multiple grids which enable grid embedding to enhance the resolution at isolated flow regions. In addition, the attached flow region can be computed by the numerical solution of compressible boundary layer equations. Unsteady pressure distributions obtained with both methods are compared with available experimental data.

Description: Navier-Stokes solutions of subsonic vortical flow over a 75 deg sweep delta wing with a sharp leading edge are presented. The sensitivity of the solution to the numerical scheme is examined using both a partially upwind scheme and a scheme with central differencing in all directions. At moderate angles of attack, no vortex breakdown is observed, whereas the higher angle-of-attack cases exhibit breakdown. The effect of numerical grid density is investigated, and solutions that are obtained with various grid densities are compared with experimental data. An embedded grid approach is implemented to enable higher resolution in selected isolated flow regions, such as the leeward-side surface, the leading-edge vortical flow, and the vortex breakdown region.

Description: The effect of the order-of-accuracy, used for the spatial discretization, on the resolution of the leading edge vortices over sharp-edged delta wings is investigated. The flowfield is computed using a viscous/inviscid zonal approach. The viscous flow in the vicinity of the wing is computed using the conservative formulation of the compressible, thin-layer Navier-Stokes equations. The leeward-side vortical flowfield and the other flow regions away from the surface are computed as inviscid. The time integration is performed with both an explicit fourth-order Runge-Kutta scheme and an implicit, factorized, iterative scheme. High-order-accurate inviscid fluxes are computed using both a conservative and a non-conservative (primitive variable) formulation. The nonlinear, inviscid terms of the primitive variable form of the governing equations are evaluated with a finite-difference numerical scheme based on the sign of the eigenvalues. High-order, upwind-biased, finite difference formulas are used to evaluate the derivatives of the nonlinear convective terms. Computed results are compared with available experimental data, and comparisons of the flowfield in the vicinity of the vortex cores are presented.

Description: A unique comparison has been made between real time interferograms and full Navier-Stokes computations of the density field over an oscillating airfoil undergoing dynamic stall for compressible flow conditions. Good agreement was found until a dynamic stall vortex formed in the flow. Subsequent evolution of the flow field was found to be very different in the computations. The reasons for this difference have been explained in terms of the leading edge region flow physics and the refined flow modeling that needs to be used for the post-stall flow field.

Description: Unsteady flowfields of a two-dimensional oscillating wing are calculated using an implicit, finite-difference, Navier-Stokes numerical scheme using five widely used turbulence models. The objective of this study is to identify an appropriate turbulence model for accurate simulation of three-dimensional dynamic stall. Three unsteady flow conditions corresponding to attached flow, light-stall, and deep-stall of an oscillating wing experiment were chosen as test cases for computations. Results of unsteady airload hysteresis curves, harmonics of unsteady pressures, and instantaneous flow pictures are presented. Comparison of unsteady airloads with experiment show that all models are deficient in some sense and not a single model predicts all airloads consistently and in agreement with experiment for all flow conditions. For the attached flow condition, the Renormalization Group Theory (RNG), the Johnoson-King (J-K), and the Spalart-Allmaras (S-A) models have better performance. The Baldwin-Lomax (B-L) and the Baldwin-Barth (B-B) models fair poorly. At the light-stall condition, the results for the RNG, the J-K, and S-A models are in agreement with experiment for the upstroke but they all over predict the separation shown by the experiment and therefore have bigger hysteresis loops than experimental results. The B-B model results are also in good agreement for upstroke but have poor lift hysteresis for downstroke. It has superior drag and pitching-moment predictions. For deep-stall conditions, the airloads for the RNG, the B -B, and the S-A models have fair agreement with experiment, but the B-B model performed better at the extreme deep-stall condition. Overall, the RNG model provides significant improvement over the B-L model in all flow regimes with no additional computational cost. The Baldwin-Barth model is the most expensive of the models considered here, costing about 2.5 times that of the Baldwin-Lomax model. Finally, a brief discussion of the effects of grid density, time-step size, and numerical dissipation on the unsteady solutions are also presented.

Description: The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.

Description: In the present investigation of the vortical flowfield structure over delta wings at high angles of attack, three-dimensional Navier-Stokes numerical simulations were conducted to predict the complex leeward flowfield characteristics; these encompass leading-edge separation, secondary separation, and vortex breakdown. Attention is given to the effect on solution accuracy of circumferential grid-resolution variations in the vicinity of the wing leading edge, and well as to the effect of turbulence modeling on the solutions. When a critical angle-of-attack was reached, bubble-type vortex breakdown was found. With further angle-of-attack increase, a change from bubble-type to spiral-type vortex breakdown was predicted by the numerical solution.