Tsan Hsing Shih

Bio: Tsan Hsing Shih is an academic researcher from Glenn Research Center. The author has contributed to research in topics: Turbulence & Reynolds stress equation model. The author has an hindex of 7, co-authored 7 publications receiving 4168 citations.

Modeling of Turbulent Swirling Flows

Abstract: Aircraft engine combustors generally involve turbulent swirling flows in order to enhance fuel-air mixing and flame stabilization. It has long been recognized that eddy viscosity turbulence models are unable to appropriately model swirling flows. Therefore, it has been suggested that, for the modeling of these flows, a second order closure scheme should be considered because of its ability in the modeling of rotational and curvature effects. However, this scheme will require solution of many complicated second moment transport equations (six Reynolds stresses plus other scalar fluxes and variances), which is a difficult task for any CFD implementations. Also, this scheme will require a large amount of computer resources for a general combustor swirling flow. This report is devoted to the development of a cubic Reynolds stress-strain model for turbulent swirling flows, and was inspired by the work of Launder's group at UMIST. Using this type of model, one only needs to solve two turbulence equations, one for the turbulent kinetic energy k and the other for the dissipation rate epsilon. The cubic model developed in this report is based on a general Reynolds stress-strain relationship. Two flows have been chosen for model evaluation. One is a fully developed rotating pipe flow, and the other is a more complex flow with swirl and recirculation.

Calculation of wall-bounded complex flows and free shear flows

Abstract: Various wall-bounded flows with complex geometries and free shear flows have been studied with a newly developed realizable Reynolds stress algebraic equation model. The model development is based on the invariant theory in continuum mechanics. This theory enables us to formulate a general constitutive relation for the Reynolds stresses. Pope (J. Fluid Mech., 72, 331–340 (1975)) was the first to introduce this kind of constitutive relation to turbulence modelling. In our study, realizability is imposed on the truncated constitutive relation to determine the coefficients so that, unlike the standard k–ϵ eddy viscosity model, the present model will not produce negative normal stresses in any situations of rapid distortion. The calculations based on the present model have shown encouraging success in modelling complex turbulent flows.

Transonic turbulent flow predictions with new two-equation turbulence models

Abstract: Solutions of the Favre-averaged Navier-Stokes equations for two well-documented transonic turbulent flows are compared in detail with existing experimental data. While the boundary layer in the first case remains attached, a region of extensive flow separation has been observed in the second case. Two recently developed k-epsilon, two-equation, eddy-viscosity models are used to model the turbulence field. These models satisfy the realizability constraints of the Reynolds stresses. Comparisons with the measurements are made for the wall pressure distribution, the mean streamwise velocity profiles, and turbulent quantities. Reasonably good agreement is obtained with the experimental data.

Error analysis and estimation for the finite volume method with applications to fluid flows

Abstract: The accuracy of numerical simulation algorithms is one of main concerns in modern Computational Fluid Dynamics. Development of new and more accurate mathematical models requires an insight into the problem of numerical errors. In order to construct an estimate of the solution error in Finite Volume calculations, it is first necessary to examine its sources. Discretisation errors can be divided into two groups: errors caused by the discretisation of the solution domain and equation discretisation errors. The first group includes insufficient mesh resolution, mesh skewness and non-orthogonality. In the case of the second order Finite Volume method, equation discretisation errors are represented through numerical diffusion. Numerical diffusion coefficients from the discretisation of the convection term and the temporal derivative are derived. In an attempt to reduce numerical diffusion from the convection term, a new stabilised and bounded second-order differencing scheme is proposed. Three new methods of error estimation are presented. The Direct Taylor Series Error estimate is based on the Taylor series truncation error analysis. It is set up to enable single-mesh single-run error estimation. The Moment Error estimate derives the solution error from the cell imbalance in higher moments of the solution. A suitable normalisation is used to estimate the error magnitude. The Residual Error estimate is based on the local inconsistency between face interpolation and volume integration. Extensions of the method to transient flows and the Local Residual Problem error estimate are also given. Finally, an automatic error-controlled adaptive mesh refinement algorithm is set up in order to automatically produce a solution of pre-determined accuracy. It uses mesh refinement and unrefinement to control the local error magnitude. The method is tested on several characteristic flow situations, ranging from incompressible to supersonic flows, for both steady-state and transient problems.

Computational Fluid Dynamics: Principles and Applications Ed. 3

Abstract: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques Will provide you with the knowledge required to develop and understand modern flow simulation codes Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

A numerical study of breaking waves in the surf zone

Abstract: This paper describes the development of a numerical model for studying the evolution of a wave train, shoaling and breaking in the surf zone. The model solves the Reynolds equations for the mean (ensemble average) flow field and the k–e equations for the turbulent kinetic energy, k, and the turbulence dissipation rate, e. A nonlinear Reynolds stress model (Shih, Zhu & Lumley 1996) is employed to relate the Reynolds stresses and the strain rates of the mean flow. To track free-surface movements, the volume of fluid (VOF) method is employed. To ensure the accuracy of each component of the numerical model, several steps have been taken to verify numerical solutions with either analytical solutions or experimental data. For non-breaking waves, very accurate results are obtained for a solitary wave propagating over a long distance in a constant depth. Good agreement between numerical results and experimental data has also been observed for shoaling and breaking cnoidal waves on a sloping beach in terms of free-surface profiles, mean velocities, and turbulent kinetic energy. Based on the numerical results, turbulence transport mechanisms under breaking waves are discussed.

Jet Impingement Heat Transfer: Physics, Correlations, and Numerical Modeling

Abstract: Publisher Summary This chapter presents a discussion on jet impingement heat transfer. The chapter describes the applications and physics of the flow and heat transfer phenomena, available empirical correlations and values they predict, and numerical simulation techniques and results of impinging jet devices for heat transfer. The relative strengths and drawbacks of the Reynolds stress model, algebraic stress models, shear stress transport, and v 2 f turbulence models for impinging jet flow and heat transfer are compared in the chapter. The chapter provides select model equations as well as quantitative assessments of model errors and judgments of model suitability. The review of recent impinging jet research publications identified a series of engineering research tasks that are important for improving the design and resulting performance of impinging jets: (1) clearly resolve the physical mechanisms by which multiple peaks occur in the transfer coefficient profiles, and clarify which mechanism(s) dominate in various geometries and Reynolds number regimes, (2) develop a turbulence model, and associated wall treatment if necessary, that reliably and efficiently provides time-averaged transfer coefficients, (3) develop alternate nozzle and installation geometries that provide higher efficiency, meaning improved Nu profiles at either a set flow or set blower power, and (4) further explore the effects of jet interference in jet array geometries, both experimentally and numerically. This includes improved design of exit pathways for spent flow in array installations.