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It is shown that the inviscid equations governing steady axisymmetric flow with swirl, admit solutions with closed streamlines. Results are obtained using two different numerical algorithms. The first is based on a multigrid method for nonlinear eigenvalue problems, while the second is based on a least squares formulation.
The flowfield, surface pressure, and integrated forces and moments for a fighter-type forebody with sharp leading-edge strakes have been obtained by numerical solution of the Euler equations. The method is found to correctly predict the leading-edge vortices and embedded shocks which arise at higher angles of attack. Results are presented for the effects of crossflow grid density, artificial viscosity, angle of attack, streamwise station, and camber on the flow characteristics.
Significant research has been underway for several years in NASA Glenn Research Center's nozzle branch to develop advanced computational methods for simulating turbulent flows in exhaust nozzles. The primary efforts of this research have concentrated on improving our ability to calculate the turbulent mixing layers that dominate flows both in the exhaust systems of modern-day aircraft and in those of hypersonic vehicles under development. As part of these efforts, a hybrid numerical method was recently developed to simulate such turbulent mixing layers. The method developed here is intended for configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. Interest in Large Eddy Simulation (LES) methods have increased in recent years, but applying an LES method to calculate the wide range of turbulent scales from small eddies in the wall-bounded regions to large eddies in the mixing region is not yet possible with current computers. As a result, the hybrid method developed here uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall-bounded regions entering a mixing section and uses a LES procedure to calculate the mixing-dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. With this technique, closure for the RANS equations is obtained by using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The LES equations are closed using the Smagorinsky subgrid scale model. Although the function of the Cebeci-Smith model to replace all of the turbulent stresses is quite different from that of the Smagorinsky subgrid model, which only replaces the small subgrid turbulent stresses, both are eddy viscosity models and both are derived at least in part from mixing-length theory. The similar formulation of these two models enables the RANS and LES equations to be solved with a single solution scheme and computational grid. The hybrid RANS-LES method has been applied to a benchmark compressible mixing layer experiment in which two isolated supersonic streams, separated by a splitter plate, provide the flows to a constant-area mixing section. Although the configuration is largely two dimensional in nature, three-dimensional calculations were found to be necessary to enable disturbances to develop in three spatial directions and to transition to turbulence. The flow in the initial part of the mixing section consists of a periodic vortex shedding downstream of the splitter plate trailing edge. This organized vortex shedding then rapidly transitions to a turbulent structure, which is very similar to the flow development observed in the experiments. Although the qualitative nature of the large-scale turbulent development in the entire mixing section is captured well by the LES part of the current hybrid method, further efforts are planned to directly calculate a greater portion of the turbulence spectrum and to limit the subgrid scale modeling to only the very small scales. This will be accomplished by the use of higher accuracy solution schemes and more powerful computers, measured both in speed and memory capabilities.
An experimental investigation was conducted at Mach 6 to determine the hypersonic aerodynamic characteristics of an all-body, delta-planform, hypersonic research aircraft (HYFAC configuration). The aerodynamic characteristics were obtained at Reynolds numbers based on model length of 2.84 million and 10.5 million and over an angle-of-attack range from minus 4 deg to 20 deg. The experimental results show that the HYFAC configuration is longitudinally stable and can be trimmed over the range of test conditions. The configuration had a small degree of directional stability over the angle-of-attack range and positive effective dihedral at angles of attack greater than 2 deg. Addition of canards caused a decrease in longitudinal stability and an increase in directional stability. Oil-flow studies revealed extensive areas of separated and vortex flow on the fuselage lee surface. A limited comparison of wind-tunnel data with several hypersonic approximations indicated that, except for the directional stability, the tangent-cone method gave adequate agreement at control settings between 5 deg and minus 5 deg and positive lift coefficient. A limited comparison indicated that the HYFAC configuration had greater longitudinal stability than an elliptical-cross-section configuration, but a lower maximum lift-drag ratio.
A procedure has been developed to calculate the effects of blowing two jets over a swept tapered wing at low subsonic speeds. The algorithm used is based on a vortex lattice representation of the wing lifting surface and a line sink-source distribution to simulate the effects of the jet exhaust on the wing lift and drag. The method is limited to those cases where the jet exhaust does not intersect or wash the wing. The predictions of this relatively simple procedure are in remarkably good agreement with experimentally measured interference lift and interference induced drag.
A procedure has been developed for calculating the effects of blowing two jets over a swept tapered wing at low subsonic speeds. The algorithm used is based on a vortex-lattice representation of the wing lifting surface and a line sink-source distribution to simulate the effects of the jet exhaust on the wing lift and drag. The method is limited to those cases in which the jet exhaust does not intersect or wash the wing. The predictions of this relatively simple procedure are in remarkably good agreement with experimentally measured interference lift and interference induced drag.
In this paper we present numerical solutions to several optimal control problems for an unsteady viscous flow. The main thrust of this work is devoted to simulation and control of an unsteady flow generated by a circular cylinder undergoing rotary motion. By treating the rotation rate as a control variable, we can formulate two optimal control problems and use a central difference/pseudospectral transform method to numerically compute the optimal control rates. Several types of rotations are considered as potential controls, and we show that a proper synchronization of forcing frequency with the natural vortex shedding frequency can greatly influence the flow. The results here indicate that using moving boundary controls for such systems may provide a feasible mechanism for flow control.
Results are presented for the numerical simulation of unsteady viscous incompressible flow past thick airfoils. Specifically, flow past a NACA 4424 at an angle of attack of 2.5 deg and Reynolds numbers in the range of 1700-4000 has been simulated using the spectral element method. At these conditions the flow is separatedd and an unsteady wake is formed. Application of the method of empirical eigenfunction reveals the structure of the most energetic components of the flow. These are found to occur in pairs that, through phase exchange, are responsible for the vortex shedding. A set of ordinary differential equations is obtained for the amplitudes of these eigenfunctions by a Galerkin projection of the Navier-Stokes equations. The solutions of the model system are compared with the full simulation. The work is of relevance to the transition process and observed routes to chaos in airfoil wakes.
Steady and unsteady measured pressures for a Clipped Delta Wing (CDW) undergoing pitching oscillations and trailing-edge control surface oscillations have been presented . From the several hundred compiled data points, 22 static cases, 12 pitching-oscillation cases, and 12 control-surface-oscillation cases have been proposed for Computational Test Cases to illustrate the trends with Mach number, reduced frequency, and angle of attack. The planform for this wing was derived by simplifying the planform of a proposed design for a supersonic transport which is described as the Boeing 2707-300. The strake was deleted, the resulting planform was approximated by a trapezoid with an unswept trailing edge, and the twist and camber were removed. In order to facilitate pressure instrumentation, the thickness was increased to 6 percent from the typical 2.5 to 3 percent for the supersonic transport. The airfoil is thus a symmetrical circular arc section with t/c = 0.06. A wing of similar planform but with a thinner airfoil of t/c = 0.03 was used in the flutter investigations, and the buffet and stall flutter investigation . Flutter results are also reported both for the 3 per cent thick simplified wing and for a more complex SST model. One of the consequences of the increased thickness of the clipped delta wing is that transonic effects are enhanced for Mach numbers near one. They are significantly stronger than would be the case for the thinner wing. Also, with the combination of high leading edge sweep of 50.5, and the sharp leading edge, a leading edge vortex forms on the wing at relatively low angles of attack, on the order of three degrees. The Appendix discusses some of the vortex flow effects. In addition, a shock develops over the aft portion of the wing at transonic speeds such that at some angles of attack, there is both a leading edge vortex and a shock wave on the wing. Such cases are a computational challenge. Some previous applications of this data set have been for the evaluation of an aerodynamic panel method and for evaluation of a Navier-Stokes capability. Linear theory and panel method results are also presented, which demonstrated the need for inclusion of transonic effects. Flutter calculations for the related wing with t/c=O.O3 are given. In this report several Test Cases are selected to illustrate trends for a variety of different conditions with emphasis on transonic flow effects. An overview of the model and tests are given, and the standard formulary for these data is listed. For each type of data, a sample table and a sample plot of the measured pressures are presented. A complete tabulation and plotting of the Test Cases is given. Only the static pressures and the 1st harmonic real and imaginary parts of the pressures are available. All of the data for the test are included in a microfiche document in the original report and are available in electronic file form. The Test Cases are also available as separate electronic files.
The objective is to provide turbine-cooling technologies to meet Propulsion 21 goals related to engine fuel burn, emissions, safety, and reliability. Specifically, the GE Aviation (GEA) Advanced Turbine Cooling and Thermal Management program seeks to develop advanced cooling and flow distribution methods for HP turbines, while achieving a substantial reduction in total cooling flow and assuring acceptable turbine component safety and reliability. Enhanced cooling techniques, such as fluidic devices, controlled-vortex cooling, and directed impingement jets, offer the opportunity to incorporate both active and passive schemes. Coolant heat transfer enhancement also can be achieved from advanced designs that incorporate multi-disciplinary optimization of external film and internal cooling passage geometry.
A pressure-sensitive paint (PSP) technique was applied in a wind tunnel experiment in the NASA Langley Research Center 8-Foot Transonic Pressure Tunnel to quantify the vortex-induced surface static pressures on a slender, faceted missile model at subsonic and transonic speeds. Satisfactory global calibrations of the PSP were obtained at =0.70, 0.90, and 1.20, angles of attack from 10 degrees to 20 degrees, and angles of sideslip of 0 and 2.5 degrees using an in-situ method featuring the simultaneous acquisition of electronically-scanned pressures (ESP) at 57 discrete locations on the model. Both techniques clearly revealed the significant influence on the surface pressure distributions of the vortices shed from the sharp, chine-like leading edges. The mean error in the PSP measurements relative to the ESP data was approximately 0.6 percent at M infinity =0.70 and 2.6 percent at M infinity =0.90 and 1.20. The vortex surface pressure signatures obtained from the PSP and ESP techniques were correlated with the off-surface vortex cross-flow structures obtained using a laser vapor screen (LVS) flow visualization technique. The on-surface and off-surface techniques were complementary, since each provided details of the vortex-dominated flow that were not clear or apparent in the other.
Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.
Abstract Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.
An analysis method and computer program have been developed for the calculation of the viscosity dependent aerodynamic characteristics of multi-element infinite swept wings in incompressible flow. The wing configuration consisting at the most of a slat, a main element and double slotted flap is represented in the method by a large number of panels. The inviscid pressure distribution about a given configuration in the normal chord direction is determined using a two dimensional potential flow program employing a vortex lattice technique. The boundary layer development over each individual element of the high lift configuration is determined using either integral or finite difference boundary layer techniques. A source distribution is then determined as a function of the calculated boundary layer displacement thickness and pressure distributions. This source distribution is included in the second calculation of the potential flow about the configuration. Once the solution has converged (usually after 2-5 iterations between the potential flow and boundary layer calculations) lift, drag, and pitching moments can be determined as functions of Reynolds number.
A theoretical method was developed for determining the optimum span load distribution for minimum induced drag for subsonic nonplanar configurations. The undistorted wing wake is assumed to have piecewise linear variation of shed vortex sheet strength, resulting in a quadratic variation of bound circulation and span load. The optimum loading is obtained either through a direct technique, whereby derivatives of the drag expression are calculated analytically in terms of the unknown wake vortex sheet strengths. Both techniques agree well with each other and with available exact solutions for minimum induced drag.
A computer code has been developed to solve for the steady-state solution of the 3D incompressible Reynolds-averaged Navier-Stokes equations. The approach is based on the cell-center, central-difference, finite-volume formulation and an explicit one-step, multistage Runge-Kutta time-stepping scheme. The Baldwin-Lomax turbulence model is used. Techniques to accelerate the rate of convergence to a steady-state solution include the preconditioned method, the local time stepping, and the implicit residual smoothing. Improvements in computational efficiency have been demonstrated in several areas. This numerical procedure has been used to simulate the turbulent horseshoe vortex flow around an airfoil/flat-plate juncture.
The use of a fitted-shock multidomain spectral method for solving the time-dependent Euler equations of gasdynamics is described. The multidomain method allows short spatial scale features near the shock to be resolved throughout the calculation. Examples presented are of a shock-plane wave, shock-hot spot and shock-vortex street interaction.
The generation of an acoustic field by an unsteady viscous vortical flow is investigated analytically, with a focus on the case where the reference scale length of the flow is much smaller than that of the acoustic field. The expansion schemes, governing equations, and far-field behavior are described; the effect of pressure and density fluctuations on the next-order far-field solution is explored; and the method of matched asymptotics is applied to construct the leading-order solution of the induced acoustic field. Particular attention is given to the sound generated by turbulence and by slender vortex filaments.