Veer N. Vatsa

Summary of the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control

Summary of the 2004 CFD ValidationWorkshop on Synthetic Jets and TurbulentSeparation Control C. L. Rumsey ∗, T. B. Gatski †, W. L. Sellers III ‡, V. N. Vatsa §, S. A. Viken ¶ NASA Langley Research Center, Hampton, VA 23681-2199, USA Submission to AIAA Journal A CFD validation workshop for synthetic jets and turbulent separation control (CFD-VAL2004) was held in Williamsburg, Virginia in March 2004. Three cases were inves-tigated: synthetic jet into quiescent air, synthetic jet into a turbulent boundary layercrossflow, and flow over a hump model with no-flow-control, steady suction, and oscilla-tory control. This paper is a summary of the CFD results from the workshop. Althoughsome detailed results are shown, mostly a broad viewpoint is taken, and the CFD state-of-the-art for predicting these types of flows is evaluated from a general point of view.Overall, for synthetic jets, CFD can only qualitatively predict the flow physics, but thereis some uncertainty regarding how to best model the unsteady boundary conditions fromthe experiment consistently. As a result, there is wide variation among CFD results. Forthe hump flow, CFD as a whole is capable of predicting many of the particulars of thisflow provided that tunnel blockage is accounted for, but the length of the separated regioncompared to experimental results is consistently overpredicted.

Effect of artificial viscosity on three-dimensional flow solutions

Artificial viscosity is added either implicitly or explicitly in practically every numerical scheme for suppressing spurious oscillations in the solution of fluid-dynamics equations. In the present central-difference scheme, artificial viscosity is added explicitly for suppressing high-frequency oscillations and achieving good convergence properties. The amount of artificial viscosity added is controlled through the use of preselected coefficients. In the standard scheme, scalar coefficients based on the spectral radii of the Jacobian of the convective fluxes are used. However, this can add too much viscosity to the slower waves. Hence, the use of matrix-valued coefficients, which give appropriate viscosity for each wave component, is suggested. With the matrix-valued coefficients, the central-difference scheme produces more accurate solutions on a given grid, particularly in the vicinity of shocks and boundary layers, while still maintaining good convergence properties.

development of a multigrid code for 3-D Navier-Stokes equations and its application to a grid-refinement study

Abstract A multigrid acceleration technique has been developed to solve the three-dimensional Navier-Stokes equations efficiently. An explicit multistage Runge-Kutta type-of time-stepping scheme is used as the basic algorithm in conjunction with the multigrid scheme. A grid-refinement study has been conducted to obtain grid converged solutions for transonic flow over a finite wing. Present solutions indicate that the number of multigrid cycles required to achieve a given level of convergence does not increase with the number of mesh points employed, making it a very attractive scheme for fine meshes.

Fourth-Order Runge---Kutta Schemes for Fluid Mechanics Applications

Multiple high-order time-integration schemes are used to solve stiff test problems related to the Navier–Stokes (NS) equations. The primary objective is to determine whether high-order schemes can displace currently used second-order schemes on stiff NS and Reynolds averaged NS (RANS) problems, for a meaningful portion of the work-precision spectrum. Implicit–Explicit (IMEX) schemes are used on separable problems that naturally partition into stiff and nonstiff components. Non-separable problems are solved with fully implicit schemes, oftentimes the implicit portion of an IMEX scheme. The convection–diffusion-reaction (CDR) equations allow a term by term stiff/nonstiff partition that is often well suited for IMEX methods. Major variables in CDR converge at near design-order rates with all formulations, including the fourth-order IMEX additive Runge–Kutta (ARK2) schemes that are susceptible to order reduction. The semi-implicit backward differentiation formulae and IMEX ARK2 schemes are of comparable efficiency. Laminar and turbulent aerodynamic applications require fully implicit schemes, as they are not profitably partitioned. All schemes achieve design-order convergence rates on the laminar problem. The fourth-order explicit singly diagonally implicit Runge–Kutta (ESDIRK4) scheme is more efficient than the popular second-order backward differentiation formulae (BDF2) method. The BDF2 and fourth-order modified extended backward differentiation formulae (MEBDF4) schemes are of comparable efficiency on the turbulent problem. High precision requirements slightly favor the MEBDF4 scheme (greater than three significant digits). Significant order reduction plagues the ESDIRK4 scheme in the turbulent case. The magnitude of the order reduction varies with Reynolds number. Poor performance of the high-order methods can partially be attributed to poor solver performance. Huge time steps allowed by high-order formulations challenge the capabilities of algebraic solver technology.

Navier-Stokes computations of a prolate spheroid at angle of attack

Three-dimensional viscous flow calculations are made for a 6:1 prolate spheroid at conditions for which detailed experimental data are available. The computations are made with two finite-volume algorithms for the compressible Navier-Stokes equations, one using central differencing for the convective and pressure terms and the other using an upwind-biased flux-difference-splitting approach. The effects of artificial dissipation on the accuracy of the numerical results are included. Generally good agreement of the computations with the experimental results is obtained over a range of Reynolds numbers and angles of attack up to 30 deg, although the results at lower Reynolds numbers are sensitive to the assumed transition location.

Re-evaluation of an Optimized Second Order Backward Difference (BDF2OPT) Scheme for Unsteady Flow Applications

Recent experience in the application of an optimized, second-order, backward-difference (BDF2OPT) temporal scheme is reported. The primary focus of the work is on obtaining accurate solutions of the unsteady Reynolds-averaged Navier-Stokes equations over long periods of time for aerodynamic problems of interest. The baseline flow solver under consideration uses a particular BDF2OPT temporal scheme with a dual-timestepping algorithm for advancing the flow solutions in time. Numerical difficulties are encountered with this scheme when the flow code is run for a large number of time steps, a behavior not seen with the standard secondorder, backward-difference, temporal scheme. Based on a stability analysis, slight modifications to the BDF2OPT scheme are suggested. The performance and accuracy of this modified scheme is assessed by comparing the computational results with other numerical schemes and experimental data.

Simulation of Unsteady Flows Using an Unstructured Navier-Stokes Solver on Moving and Stationary Grids

We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for unstructured grids to time-dependent problems on both moving and stationary grids. Example problems considered are relevant to active flow control and stability and control. Computational results are presented using the Spalart-Allmaras turbulence model and are compared to experimental data. The effect of grid and time-step refinement are examined.

Numerical Simulation of Fluidic Actuators for Flow Control Applications

Active flow control technology is finding increasing use in aerospace applications to control flow separation and improve aerodynamic performance. In this paper we examine the characteristics of a class of fluidic actuators that are being considered for active flow control applications for a variety of practical problems. Based on recent experimental work, such actuators have been found to be more efficient for controlling flow separation in terms of mass flow requirements compared to constant blowing and suction or even synthetic jet actuators. The fluidic actuators produce spanwise oscillating jets, and therefore are also known as sweeping jets. The frequency and spanwise sweeping extent depend on the geometric parameters and mass flow rate entering the actuators through the inlet section. The flow physics associated with these actuators is quite complex and not fully understood at this time. The unsteady flow generated by such actuators is simulated using the lattice Boltzmann based solver PowerFLOW R . Computed mean and standard deviation of velocity profiles generated by a family of fluidic actuators in quiescent air are compared with experimental data. Simulated results replicate the experimentally observed trends with parametric variation of geometry and inflow conditions.

Development of an efficient multigrid code for 3-D Navier-Stokes equations

A multigrid acceleration technique has been developed to solve the three-dimensional Navier-Stokes equations efficiently. An explicit multistage Runge-Kutta type of time-stepping scheme is used as the basic algorithm in conjunction with the multigrid scheme. Solutions for flow over a finite wing have been obtained on extremely fine meshes in order to achieve grid convergence of the solutions. Present solutions indicate that the number of multigrid cycles required to achieve a given level of convergence does not increase with the number of mesh points employed, making it a very attractive scheme for fine meshes.

Time Integration Schemes for the Unsteady Navier-stokes Equations

The efficiency and accuracy of several time integration schemes are investigated for the unsteady Navier-Stokes equations. This study focuses on the efficiency of higher-order Runge-Kutta schemes in comparison with the popular Backward Differencing Formulations. For this comparison an unsteady two-dimensional laminar flow problem is chosen, i.e., flow around a circular cylinder at Re = 1200. It is concluded that for realistic error tolerances (smaller than 10(exp -1)) fourth-and fifth-order Runge-Kutta schemes are the most efficient. For reasons of robustness and computer storage, the fourth-order Runge-Kutta method is recommended. The efficiency of the fourth-order Runge-Kutta scheme exceeds that of second-order Backward Difference Formula by a factor of 2.5 at engineering error tolerance levels (10(exp -1) to 10(exp -2)). Efficiency gains are more dramatic at smaller tolerances.