Lakshmi N. Sankar

Computational Study of Horizontal Axis Wind Turbines

A hybrid Navier-Stokes potential flow methodology for modeling three-dimensional unsteady viscous flow over horizontal axis wind turbine configurations is presented. In this approach, the costly viscous flow equations are solved only in a small viscous flow region surrounding the rotor. The rest of the flow field is modeled using a potential flow methodology. The tip vortices are modeled using a free wake approach, which allows the vortices to deform and interact with each other. Sample results are presented for two rotor configurations tested by the National Renewable Energy Laboratory. Comparisons with experimental data, full Navier-Stokes simulations and blade element momentum theory are given to establish the efficiency and accuracy of the present scheme.

Toward the direct calculation of noise - Fluid/acoustic coupled simulation

A numerical technique for the direct calculation of flow generated noise is developed in this paper and applied to the prediction of supersonic jet noise. In this approach, each flow parameter is decomposed into a time-averaged mean and a time-dependent fluctuating part. The mean flow is established with the solution of the three-dimensional compressible Navier-Stokes equations in the first step. Flow perturbations based on the description of the large-scale structures as a linear superposition of normal mode instability waves are introduced at the nozzle exit plane. Their propagation in time and space are studied through solution of the Euler equations for the perturbations in the second step. Such an approach ensures that the fluctuation variables, which may be several orders of magnitude smaller than the mean values, are computed accurately without numerical round-off errors. Some dynamic features of the jet flow are presented. Predictions of radiated noise for a few test cases and qualitative comparisons with experiments are made. Effects of jet temperature on the peak directivity of the radiated sound are examined.

Numerical Simulation of the Aerodynamics of Horizontal Axis Wind Turbines under Yawed Flow Conditions

The aerodynamic performance of the National Renewable Energy Laboratory (NREL) Phase VI horizontal axis wind turbine (HAWT) under yawed flow conditions is studied using a three-dimensional unsteady viscous flow analysis. Simulations have been performed for upwind cases at several wind speeds and yaw angles. Results presented include radial distribution of the normal and tangential forces, shaft torque, root flap moment, and surface pressure distributions at selected radial locations. The results are compared with the experimental data for the NREL Phase VI rotor. At low wind speeds (-7 m/s) where the flow is fully attached, even an algebraic turbulence model based simulation gives good agreement with measurements. When the flow is massively separated (wind speed of 20 m/s or above), many of the computed quantities become insensitive to turbulence and transition model effects, and the calculations show overall agreement with experiments. When the flow is partially separated at wind speed above 15 m/s, encouraging results were obtained with a combination of the Spalart-Allmaras turbulence model and Eppler s transition model only at high enough wind speeds.

EVALUATION OF TURBULENCE MODELS FOR THE PREDICTION OF WIND TURBINE AERODYNAMICS

The performance of the NREL Phase VI horizontal axis wind turbine has been studied with a 3-D unsteady Navier-Stokes solver. This solver is third order accurate in space and second order accurate in time, and uses an implicit time marching scheme. Calculations were done for a range of wind conditions from 7 m/s to 25 m/s where the flow conditions ranged from attached flow to massively separated flow. A variety of turbulence models were studied: Baldwin-Lomax Model, Spalart-Allmaras one-equation model, and k-e two equations model with and without wall corrections. It was found all the models predicted the normal forces and associated bending moments well, but most of them had difficulties in modeling the chord wise forces, power generation, and pitching moments. It was found that the k-e model with near wall corrections did the best job of predicting most the quantities with acceptable levels of accuracy. Additional studies aimed at transition model development, and grid sensitivity studies in the tip region are deemed necessary to improve the correlation with experiments.Copyright

Airfoil design method using the Navier-Stokes equations

An airfoil design procedure is described that has been incorporated into an existing two-dimensional Navier-Stokes airfoil analysis method. The resulting design method, an iterative procedure based on a residual-correction algorithm, permits the automated design of airfoil sections with prescribed surface pressure distributions. The paper describes the inverse design method and the technique used to specify target pressure distributions. It presents several example problems to demonstrate application of the design procedure. These examples illustrate that the inverse design method can be used to develop useful airfoil configurations with a reasonable expenditure of computer resources.

Low-Dispersion Finite Volume Scheme for Aeroacoustic Applications

The development ofa low-dispersion numerical scheme is described in the context of a finite volume discretization of the governing fluid dynamic equations. Although low-dispersion finite difference schemes have been developed recently for uniform Cartesian meshes, current finite volume methods do not possess low-dispersion characteristics. A low-dispersion finite volume scheme is presented and applied to some common acoustics problems. The two-dimensional unsteady Euler equations linearized about a mean flow are solved using a finite volume formulation. The surface integrals are computed using flow properties at cell faces, interpolated from cell nodes. The interpolation process is chosen such that it accurately represents sinusoidal waves of short wavelengths at the cell faces. A number of classical acoustics problems are solved, and where possible, comparisons with other numerical and exact solutions are given. This scheme has low dispersion and may be retrofitted easily into existing finite volume codes. The resulting numerical method combines the flexibility and versatility of the finite volume method while minimizing numerical dispersion errors in a manner similar to that of the classical dispersion-relation-preserving scheme.

Euler solutions for transonic flow past a fighter wing

A procedure for the numerical solution of steady and unsteady transonic flows past a fighter wing is described. This procedure solves the three-dimensional, unsteady Euler equations in a body-fitted coordinate system. A finite-difference procedure of second-order spatial accuracy and first-order temporal accuracy is used to discretize the governing equations and a hybrid time-marching scheme is used to advance the solution from one time level to the next. In unsteady transonic flow applications involving oscillating wing surfaces, the surface motion is imposed on the solution as a transpiration boundary condition. A number of steady and unsteady calculations are presented for the F-5 fighter wing at transonic Mach numbers and detailed comparison with experiments are given.

Inverse aerodynamic design method for aircraft components

N existing, semi-inverse, aerodynamic design algorithm is ified to permit the unrestricted geometric design of aircraft components with prescribed aerodynamic surface pressures. A brief description of the present design procedure is given and computed results are presented for both a twodimensional airfoil and a three-dimensional nacelle configuration.

Computational Evaluation of the Steady and Pulsed Jet Effects on the Performance of a Circulation Control Wing Section

Circulation Control Wing (CCW) technology is a very effective way of achieving very high lift coefficients needed by aircraft during take-off and landing. This technology can also be used to directly control the flow field over the wing. Compared to a conventional high-lift system, a Circulation Control Wing (CCW) can generate the required values of lift coefficient C(sub L,max) during take-off/landing with fewer or no moving parts and much less complexity. Earlier designs of CCW configurations used airfoils with a large radius rounded trailing edge to maximize the lift benefit. However, these designs also produced very high drag. These high drag levels associated with the blunt, large radius trailing edge can be prohibitive under cruise conditions when Circulation Control is no longer necessary. To overcome this difficulty, an advanced CCW section, i.e., a circulation hinged flap was developed to replace the original rounded trailing edge CC airfoil. This concept developed by Englar is shown. The upper surface of the CCW flap is a large-radius arc surface, but the lower surface of the flap is flat. The flap could be deflected from 0 degrees to 90 degrees. When an aircraft takes-off or lands, the flap is deflected as in a conventional high lift system. Then this large radius on the upper surface produces a large jet turning angle, leading to high lift. When the aircraft is in cruise, the flap is retracted and a conventional sharp trailing edge shape results, greatly reducing the drag. This kind of flap does have some moving elements that increase the weight and complexity over an earlier CCW design. But overall, the hinged flap design still maintains most of the Circulation Control high lift advantages, while greatly reducing the drag in cruising condition associated with the rounded trailing edge CCW design. In the present work, an unsteady three-dimensional Navier-Stokes analysis procedure has been developed and applied to this advanced CCW configuration. The solver can be used in both a 2-D and a 3-D mode, and can thus model airfoils as well as finite wings. The jet slot location, slot height, and the flap angle can all be varied easily and individually in the grid generator and the flow solver. Steady jets, pulsed jets, the leading edge and trailing edge blowing can all be studied with this solver.

Computational Analysis of Stall and Separation Control in Centrifugal Compressors

A three-dimensional compressibleNavier ‐Stokes code has been used to model thesteady and unsteady e owe eld within a low-speed centrifugal compressor cone guration tested at NASA Lewis Research Center. Near-design conditions, the performance map, pressure e eld, and the velocity e eld were in good agreement with measured data. At off-design conditions, the calculations show that e ow reversal e rst occurs near the blade leading edge. If leftunchecked,thereversed-e owregiongrowsspatiallyandtemporally.Injectionofairupstreamofthecompressor face was found to modify the local e ow near the blade leading edge and to suppress rotating stall and surge. Even a moderate amount of air, typically around 5% of the total mass e ow rate, was sufe cient to extend the useful operating range of the compressor.