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Abstract. This paper describes a generalized wall function for threedimensional turbulent boundary layer flows. Since the formulation is valid for various pressure gradients including those associated with zero skin friction, it can be applied to wall bounded complex flows with acceleration, deceleration and recirculation. This generalized wall function is extended to the whole surface layer (or inner layer), covering the viscous sublayer, buffer layer and inertial sublayer; therefore, it is a unified wall function. This 'unified' feature is particularly useful for computational fluid dynamics (CFD) to deal with flows with complex geometries, because it allows a flexible grid resolution near the wall to provide accurate wall boundary conditions. This paper also describes a systematic procedure for implementing the wall function in a general CFD code. Finally, a few examples of complex turbulent flows are presented to show the performance of the generalized wall function.

Abstract. This paper describes a generalized wall function for threedimensional turbulent boundary layer flows. Since the formulation is valid for various pressure gradients including those associated with zero skin friction, it can be applied to wall bounded complex flows with acceleration, deceleration and recirculation. This generalized wall function is extended to the whole surface layer (or inner layer), covering the viscous sublayer, buffer layer and inertial sublayer; therefore, it is a unified wall function. This 'unified' feature is particularly useful for computational fluid dynamics (CFD) to deal with flows with complex geometries, because it allows a flexible grid resolution near the wall to provide accurate wall boundary conditions. This paper also describes a systematic procedure for implementing the wall function in a general CFD code. Finally, a few examples of complex turbulent flows are presented to show the performance of the generalized wall function.

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The present paper reports the development of the Least‐Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. The conventional approach requires special treatments for low‐speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique, and finite element methods rely on the mixed method and the operator‐splitting method. In this paper, however, we show that such a difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive‐definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: driven cavity flows at various Reynolds numbers and buoyancy‐driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

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An unstructured and massively parallel Reynolds-Averaged Navier-Stokes (RANS) code is used to simulate 3-D, turbulent, non-reacting, and confined swirling flow field associated with a single-element and a nine-element Lean Direct Injection (LDI) combustor. In addition, the computed results are compared with the Large Eddy Simulation (LES) results and are also validated against the experimental data. The LDI combustors are a new generation of liquid fuel combustors developed to reduce aircraft NOx emission to 70% below the 1996 International Civil Aviation Organization (ICAO) standards and to maintain carbon monoxide and unburned hydrocarbons at their current low levels at low power conditions. The concern in the stratosphere is that NOx would react with the ozone and deplete the ozone layer. This paper investigates the non-reacting aerodynamics characteristics of the flow associated with these new combustors using a RANS computational method. For the single-element LDI combustor, the experimental model consists of a cylindrical air passage with air swirlers and a converging-diverging venturi section, extending to a confined 50.8-mm square flame tube. The air swirlers have helical, axial vanes with vane angles of 60 degree. The air is highly swirled as it passes through the 60 degree swirlers and enters the flame tube. The nine-element LDI combustor is comprised of 9 elements that are designed to fit within a 76 mm 76 mm flametube combustor. In the experimental work, the jet-A liquid fuel is supplied through a small diameter fuel injector tube and is atomized as it exits the tip and enters the flame tube. The swirling and mixing of the fuel and air induces recirculation zone that anchors the combustion process, which is maintained as long as a flammable mixture of fuel and air is supplied. It should be noted that in the numerical simulation reported in this paper, only the non-reacting flow is considered. The numerical model encompasses the whole experimental flow passage, including the flow development sections for the air swirlers, and the flame tube. A low Reynolds number K-e turbulence model is used to model turbulence. Several RANS calculations are performed to determine the effects of the grid resolution on the flow field. The grid is refined several times until no noticeable change in the computed flow field occurred; the final refined grid is used for the detailed computations. The results presented are for the final refined grid. The final grids are all hexahedron grids containing approximately 861,823 cells for the single-element and 1,567,296 cells for the nine-element configuration. Fine details of the complex flow structure such as helical-ring vortices, re-circulation zones and vortex cores are well captured by the simulation. Consistent with the non-reacting experimental results, the computation model predicts a major re-circulation zone in the central region, immediately downstream of the fuel nozzle, and a second, recirculation zone in the upstream corner of the combustion chamber. Further, the computed results predict the experimental data with reasonable accuracy.

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