Sijun Zhang

Generalized formulations for the Rhie-Chow interpolation

In this paper, generalized formulations for the Rhie-Chow interpolation for co-located-grid discretizations are derived. These generalized formulations eliminate the major known defects in the standard Rhie-Chow interpolation, including the following: dependence of the converged solution on the value of the under-relaxation factor, saw-tooth pressure oscillations in transient problems with small time steps, and incorrect or non-converged solutions for problems with discontinuities. The generalized formulations are also shown to be applicable to a wider range of flow conditions than the standard Rhie-Chow interpolation. The derivation of the Rhie-Chow interpolation is first recalled and its numerical errors are analyzed. Then, the generalized formulations are presented and explained, and the way in which they eliminate or counter some of the known defects of the standard Rhie-Chow interpolation are outlined. The generalized formulations are then verified and validated with numerical experiments, including experiments with flow in porous media and in a packed bed. It is then concluded that the generalized formulations presented in this work represent an advance over the standard Rhie-Chow interpolation with a negligible increase in computational cost.

Time Dependent Calculations for Incompressible Flows on Adaptive Unstructured Meshes

An adaptive unstructured method has been developed for simulating two-dimensional unsteady, viscous, incompressible flows. The pressure-based approach coupled with a mesh adaptation method is employed to better capture the details of flow physics for time dependent problems by optimizing computational cost with respect to accuracy. The mesh adaptation for locally refining and coarsening hybrid unstructured grid is based on hanging node approach. The time dependent calculations is further enhanced by virtue of parallel computing which is the most powerful for large scale intensive computation at the present time. The proposed method is validated by comparison with experimental results of low Reynolds number flow over a shedding circular cylinder.Copyright

Hypersonic Non-Equilibrium Computations for Ionizing Air

This paper presents a thermochemical non-equilibrium model for simulating the ionizing air flows. The fluid in the framework is considered as a reacting gas in chemical and thermal non-equilibrium. The non-equilibrium gas is dealt with by standard finite rate chemistry models and a two-temperature model, respectively. The chemical reactions take place with some degree of ionization depending on flow conditions, the atomic, molecular, or ionic species and electron are involved in the mixture. 7-reaction and 7-species (O, O2, N, N2, NO, NO + and e - ) are exploited to predict the non-equilibrium flows over re-entry vehicles. The results predicted by the present improvement are compared with that from LAURA.

Implicit Time-Accurate Method for Unsteady Computations

A dual time-stepping algorithm has been developed for the efficient computation of unsteady fluid dynamics. The algorithm is effective over a wide range of low Mach numbers and physical time scales, when working together with a preconditioning technique which offers a way to formulate the Euler and Navier-Stokes equations such that convergence can be made independent of Mach number. This enhancement is shown to provide more accurate solutions for unsteady subsonic and low-speed flows through several test cases. I. Introduction ime-accurate computations at all speeds are essential since many practical flows of engineering interest are inherently transient and may range from the incompressible limit to supersonic speeds. There are two popular methods for fluid flow simulations: pressure-based methods (1) for incompressible flows and density-based methods (2) for compressible flows. So far, flow problems at all speeds can be addressed by a well assessed flow solver employing a single solution algorithm. Two approaches are probably the most successful for the single solution algorithms. One is the extension of the pressure-based methods for high speed compressible flows using pressure- velocity-density correction algorithms. The other is based on low Mach number preconditioning technique for the density-based approach to equilibrate the eigenvalues, which are critical factors in the coupled system so that the stiffness is alleviated, which occurs when the flow speed is very small in comparison to acoustic speed. Both explicit and implicit algorithms are commonly used for unsteady computations. When applied as non- iterative, time-marching methods, these algorithms frequently lose temporal accuracy unless small physical time- step sizes are used. This is particularly true for complex flow fields involving strong non-linear behavior such as shock waves and chemical reaction. Furthermore, stability criteria impose further limitations on the physical time- step size, especially for explicit algorithms. Similar time-step restrictions also exist for implicit algorithms in multi- dimensions because of errors associated with the approximate-inversion methods that are typically used. In the presence of strong local grid-stretching or in low Mach numbers flows, such time-step restrictions may severely impair the usefulness of the algorithm. For these reasons, unsteady algorithms usually adopt some sort of an iterative procedure at each physical time-level that ensures temporal accuracy and, in the case of implicit schemes, also serves to eliminate the linearization and approximate-factorization errors introduced by the scheme. To achieve

CFD development for macro particle simulations

Numerous industrial operations involve fluid-particle systems, in which both phases display very complex behaviour. Some examples include fluidisation technology in catalytic reactors, pneumatic transportation of grain or powder materials, carbon nanotube alignment in the nano-devices and circuit integration and so on. In this paper, a macro particle method is developed to model the fluid-particle flows. The macro particle is formed by a collection of micro-sized particles so that the number of macro particles to be tracked is much less than the number of smaller particles. Unlike the calculations of instantaneous point variables of fluid phase with moving discrete boundaries of the smaller particles with direct numerical simulation, the boundary of each macro particle is just dealt with the blocked-off approach. On the other hand, the flow fields based on the present method is solved by original Navier–Stokes, rather than the modified ones based on the locally averaged theorem. The flow fields are solved on the length scale of computational cells, while the resolutions of solid particles are the size of macro particle, which is determined as needed in specific applications. The macro particle method is validated by several selected cases, which demonstrate that the macro particle method could accurately resolve fluid-particle systems in an efficient, robust and flexible fashion.

Computational Approach for Aeroheating with Thermally Coupled Fields

In this paper, a coupling methodology was proposed to solve simultaneously the external flowfield of a hypersonic reentry vehicle/capsule and the resultant heating on the vehicle’s structure and internal components with buoyancy-driven very low-speed flows resulting from conjugate heat transfer through the thermal protection system of the vehicle/capsule. Two flow solvers were employed to solve the hypersonic flowfield and the very low-speed flowfield, respectively. The coupling was done through the exchange of appropriate interface data between the two solvers. One of them was a density-based solver, and the other was a pressure-based solver. Validations of the individual solvers were done with two benchmark cases. The proposed coupling method was proved through simulating two conjugate heat transfer problems. Finally, an aerothermal–man–machine system exposed in a hypersonic flow was computed using the proposed coupling method.

Discrete Element Simulations of Granular Flow in a Pebble Bed Reactor

This paper presents discrete element simulations of granular flow in a rectangular hopper model of the pebble bed reactor (PBR). Two flow conditions with/without granular materials recycled back are considered in this work. For both flows, the simulations have been conducted under comparable conditions so that the similarity and difference between them can be examined. The distributions of the physical properties including flow patterns, velocity and flow structure are also investigated. Moreover, the mean velocity, diffusion and particle mixing, the effects of wall friction have been analyzed based on the simulation results. The implications for the reactor design and fundamental research on granular flow physics are discussed as well.Copyright

CFD Development for Macro Particle Simulations

In this paper, a macro particle method is developed to model the fluid-particle flows. The macro particle is formed by a collection of micro-sized particle so that the number of macro particle to be tracked is much less than the number of smaller particle. Unlike the calculations of instantaneous point variables of fluid phase with moving discrete boundaries of the smaller particles with direct numerical simulation, the boundary of each macro particle is just dealt with the blocked-off approach. On the other hand, the flow fields based on the present method is solved by original Navier-Stokes, rather than the modified ones based on the locally averaged theorem. The flow fields are solved on the length scale of computational cell, while the resolutions of solid particles are the size of macro particle, which is determined as needed in specific applications. The macro particle method is validated by several cases, which demonstrate the macro particle method could accurately resolve fluid-particle systems in an efficient, robust and flexible fashion.Copyright

Flow Simulations in a Pebble Bed Reactor by a Combined DEM-CFD Approach

Abstract This paper presents computational fluid dynamics (CFD) gas flow simulations within a segment of the pebble bed core. The realistic packing structure in an entire pebble bed reactor (PBR) is produced by a means of discrete element method. The packing structure in the segment of the PBR core is then obtained. The gas flow through the voids formed by the packed pebbles is computed by CFD. It is found that the packing structure of pebbles in the PBR is crucial to CFD simulation results. On the other hand, in our numerical simulations both large eddy simulation and Reynolds-Averaged Navier-Stokes models are employed to study the effects of different turbulence models on gas flow field and relevant heat transfer. The calculations indicate the complex flow structure within the voids among the pebbles, which play the key role in heat transfer predictions.

Development of Arbitrary Unstructured Chimera Grid

nsteady three-dimensional viscous flow represents an important class of problems for which accurate methods of prediction are often required in some specific areas. Such applications are always complicated geometrically, may also involve relative motion among component bodies. Experiments can offer very important and useful means for performance analyses, engineering designs and optimizations, but they are often impossible for scale-model and full-scale prototype testing due to large cost, model limitations, human safety factors, and time constraint. Over the last two decades two major techniques have evolved to handle such a kind of problems, they are dynamic mesh approaches 1-4 and overset grid methods. 5-16