Low-speed Preconditioning Research Articles

Low-speed preconditioning for strongly coupled integration of Reynolds-averaged Navier–Stokes equations and two-equation turbulence models

Computational fluid dynamics codes using the density-based compressible flow formulation of the Navier–Stokes equations have proven to be very successful for the analysis of high-speed flows. However, solution accuracy degradation and, for explicit solvers, reduction of the residual convergence rates occur as the local Mach number decreases below the threshold of 0.1. This performance impairment worsens remarkably in the presence of flow reversals at wall boundaries and unbounded high-vorticity flow regions. These issues can be resolved using low-speed preconditioning, but there exists an outstanding problem regarding the use of this technology in the strongly coupled integration of the Reynolds-averaged Navier–Stokes equations and two-equation turbulence models, such as the k−ω shear stress transport model. It is not possible to precondition only the RANS equations without altering parts of the governing equations, and there did not exist an approach for preconditioning both the RANS and the SST equations. This study solves this problem by introducing a turbulent low-speed preconditioner of the RANS and SST equations that does not require any alteration of the governing equations. The approach has recently been shown to significantly improve convergence rates in the case of a one-equation turbulence model. The study focuses on the explicit multigrid integration of the governing equations, but most algorithms are applicable also to implicit integration methods. The paper provides all algorithms required for implementing the presented turbulent preconditioner in other computational fluid dynamics codes. The new method is applicable to all low- and mixed-speed aeronautical and propulsion flow problems, and is demonstrated by analyzing the flow field of a Darrieus wind turbine rotor section at two operating conditions, one of which is characterized by significant blade/vortex interaction. Verification and further validation of the new method is also based on the comparison of the results obtained with the developed density-based code and those obtained with a commercial pressure-based code.

Low-Speed Preconditioning for AUSM+-Up Scheme

Based on Navier-stokes equations, Weiss-Smith matrix preconditioning method is implemented within pseudo time derivative term. AUSM+-up family schemes and LU-SGS implicit iterative method were used to solve low speed flows and were compared with literature data and theoretical value. Through comparing calculation with the literature data and theoretical value, The results showed the preconditioning algorithm can be applied efficiently to the low speeds flow field, All these works built foundations for further application of chemical flows.

Analysis of Unsteady Flows Past Horizontal Axis Wind Turbine Airfoils Based on Harmonic Balance Compressible Navier-Stokes Equations With Low-Speed Preconditioning

This paper presents the numerical models underlying the implementation of a novel harmonic balance compressible Navier-Stokes solver with low-speed preconditioning for wind turbine unsteady aerodynamics. The numerical integration of the harmonic balance equations is based on a multigrid iteration, and, for the first time, a numerical instability associated with the use of such an explicit approach in this context is discussed and resolved. The harmonic balance solver with low-speed preconditioning is well suited for the analyses of several unsteady periodic low-speed flows, such as those encountered in horizontal axis wind turbines. The computational performance and the accuracy of the technology being developed are assessed by computing the flow field past two sections of a wind turbine blade in yawed wind with both the time-and frequency-domain solvers. Results highlight that the harmonic balance solver can compute these periodic flows more than 10 times faster than its time-domain counterpart, and with an accuracy comparable to that of the time-domain solver.

Compressible Navier–Stokes analysis of an oscillating wing in a power-extraction regime using efficient low-speed preconditioning

A wing that is simultaneously heaving and pitching may extract energy from an oncoming air flow, thus acting as a turbine. This paper analyzes the unsteady aerodynamics of such a device by means of time-dependent laminar flow simulations performed with a research compressible finite volume Navier–Stokes solver. The study confirms the findings of another independent report that the efficiency of the power extraction of this device can be of the order of 35%, and such an efficient operating condition is characterized by a strong dynamic stall. This study is part of a wider research programme aimed at developing a general-purpose computational framework for unsteady aerodynamic and aeroacoustic wind energy engineering. In view of aeroacoustic applications, the developed flow solver uses the compressible formulation of the Navier–Stokes equations with carefully optimized low-speed preconditioning. To demonstrate the modeling capabilities, the accuracy and the high computational performance of the developed low-speed preconditioning technology, the unsteady aerodynamics of the energy-extracting device is simulated by using a computationally challenging freestream Mach number of 0.001. A mixed preconditioning strategy that maintains both the nominal accuracy and the computational efficiency of the solver also for time-dependent low-speed problems is presented. The study also assesses the impact of a semi-implicit treatment of the unsteady source term associated with the discretization of the physical time-derivative of the governing equations on the numerical stability of the explicit multigrid integration.

Local preconditioners for steady and unsteady flow applications

Preconditioners for hyperbolic systems are numerical artifacts to accelerate the convergence to a steady state. In addition, the preconditioner should also be included in the artificial viscosity or upwinding terms to improve the accuracy of the steady state solution. For time dependent problems we use a dual time stepping approach. The preconditioner affects the convergence rate and the accuracy of the subiterations within each physical time step. We consider two types of local preconditioners: Jacob; and low speed preconditioning. We can express the algorithm in several sets of variables while using only the conservation variables for the flux terms. We compare the effect of these various variable sets on the efficiency and accuracy of the scheme.