A CLASS OF COMPACT UPWIND TVD DIFFERENCE SCHEMES

A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD （CTVD） schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.

Numerical simulation of quasi-streamwise hairpin-like vortex generation in turbulent boundary layer

A mechanism for generation of near wall quasi-streamwise hairpin-like vortex （QHV） and secondary quasi-streamwise vortices （SQV） is presented. The conceptual model of resonant triad in the theory of hydrodynamic instability and direct numerical simulation of a turbulent boundary layer were applied to reveal the formation of QHV and SQV. The generation procedures and the characteristics of the vortex structures are obtained, which share some similarities with previous numerical simulations. The research using resonant triad conceptual model and numerical simulation provides a possibility for investigating and controling the vortex structures, which play a dominant role in the evolution of coherent structures in the near-wall region.

Developing shock-capturing difference methods

A new shock-capturing method is proposed which is based on upwind schemes and flux-vector splittings. Firstly, original upwind schemes are projected along characteristic directions. Secondly, the amplitudes of the characteristic decompositions are carefully controlled by limiters to prevent non-physical oscillations. Lastly, the schemes are converted into conservative forms, and the oscillation-free shock-capturing schemes are acquired. Two explicit upwind schemes （2nd-order and 3rd-order） and three compact upwind schemes （3rd-order, 5th-order and 7th-order） are modified by the method for hyperbolic systems and the modified schemes are checked on several one-dimensional and two-dimensional test cases. Some numerical solutions of the schemes are compared with those of a WENO scheme and a MP scheme as well as a compact-WENO scheme. The results show that the method with high order accuracy and high resolutions can capture shock waves smoothly.

Three-Dimensional Waves in Tilt Thermal Boundary Layers

We numerically and theoretically study the stabilities of tilt thermal boundary layers immersed in stratified air. An interesting phenomenon is revealed： the stationary longitudinal-roll mode becomes unstable to some oscillating state even when the Grashof number is smaller than its corresponding critical value. By stability analysis, this phenomenon is explained in terms of a new three-dimensional wave mode. The effect of the tilt angle on the stability of the boundary flows is investigated. Since the new three-dimensional wave is found to be the most unstable mode when the title angle is between 30° and 64°, it is expected to play an important role in the transition to turbulence.

Gas-solid flow in a diffuser:Effect of inter-particle and particle-wall collisions

This article investigates the role of the specularity coefficient(φ,the extent of the energy dissipation due to particle-wall collisions),inter-particle restitution coefficient(e_(pp),the extent of the energy dissipation due to inter-particle collisions),and four combinations of these variables on the hydrodynamics,and the pressure recovery of the dilute gas-solid suspension in a diffuser.The investigation applies the two-fluid modeling approach along with the kinetic theory of the granular flow.The present investigation’s findings indicate that an increase inφor a reduction in e_(pp) reduces the pressure recovery by weakening the reverse momentum transfer phenomenon,which is recognized as the primary means for the pressure recovery.Besides,in a gas-solid flow system,a higherφor smaller e_(pp) enhances the particles’trapping in the recirculation zone.The recirculation zone’s strength and size increase asφincreases or e_(pp) reduces.Moreover,an increase in the wall-particle and inter-particle interactions strengthens the sidewise displacement of the particles.The effect of the wall-particle and inter-particle interactions are insignificant for extremely small solid loading.

Robust Conservative Level SetMethod for 3D Mixed-Element Meshes —Application to LES of Primary Liquid-Sheet Breakup

In this article we detail the methodology developed to construct an efficient interface description technique—the robust conservative level set(RCLS)—to simulate multiphase flows on mixed-element unstructured meshes while conserving mass to machine accuracy.The approach is tailored specifically for industry as the three-dimensional unstructured approach allows for the treatment of very complex geometries.In addition,special care has been taken to optimise the trade-off between accuracy and computational cost while maintaining the robustness of the numerical method.This was achieved by solving the transport equations for the liquid volume fraction using a WENO scheme for polyhedral meshes and by adding a flux-limiter algorithm.The performance of the resulting method has been compared against established multiphase numerical methods and its ability to capture the physics of multiphase flows is demonstrated on a range of relevant test cases.Finally,the RCLS method has been applied to the simulation of the primary breakup of a flat liquid sheet of kerosene in co-flowing high-pressure gas.This quasi-DNS/LES computation was performed at relevant aero-engine conditions on a three-dimensional mixed-element unstructured mesh.The numerical results have been validated qualitatively against theoretical predictions and experimental data.In particular,the expected breakup regime was observed in the simulation results.Finally,the computation reproduced faithfully the breakup length predicted by a correlation based on experimental data.This constitutes a first step towards a quantitative validation.

High Order Schemes on Three-Dimensional General Polyhedral Meshes—Application to the Level Set Method

In this article,we detail the methodology developed to construct arbitrarily high order schemes—linear and WENO—on 3D mixed-element unstructured meshes made up of general convex polyhedral elements.The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems.The construction of WENO schemes on 3D unstructured meshes is notoriously difficult,as it involves a much higher level of complexity than 2D approaches.This due to the multiplicity of geometrical considerations introduced by the extra dimension,especially on mixed-element meshes.Therefore,we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces.The contribution of this work concerns several areas of interest:the formulation of an improved methodology in 3D,the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations,the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.