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Register a new userHomogenized Flux-Body Force Treatment of Compressible Viscous Porous Wall Boundary Conditions
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A homogenization approach is proposed for the treatment of porous wall boundary conditions in the computation of compressible viscous flows. Like any other homogenization approach, it eliminates the need for pore-resolved fluid meshes and therefore enables practical flow simulations in computational fluid domains with porous wall boundaries. Unlike alternative approaches however, it does not require prescribing a mass flow rate and does not introduce in the computational model a heuristic discharge coefficient. Instead, it models the inviscid flux through a porous wall surrounded by the flow as a weighted average of the inviscid flux at an impermeable surface and that through pores. It also introduces a body force term in the governing equations to account for friction loss along the pore boundaries. The source term depends on the thickness of the porous wall and the concept of an equivalent single pore. The feasibility of the latter concept is demonstrated using low-speed permeability test data for the fabric of the Mars Science Laboratory parachute canopy. The overall homogenization approach is illustrated with a series of supersonic flow computations through the same fabric and verified using supersonic, pore-resolved numerical simulations.
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Understanding the generation mechanism of the heating flux is essential for the design of hypersonic vehicles. We proposed a novel formula to decompose the heat flux coefficient into the contributions of different terms by integrating the conservative equation of the total energy. The reliability of the formula is well demonstrated by the direct numerical simulation results of a hypersonic transitional boundary layer. Through this formula, the exact process of the energy transport in the boundary layer can be explained and the dominant contributors to the heat flux can be explored, which are beneficial for the prediction of the heat and design of the thermal protection devices
In a recent paper (El Omari and Le Guer, IJHMT, 53, 2010) we have investigated mixing and heat transfer enhancement in a mixer composed of two circular rods maintained vertically in a cylindrical tank. The rods and tank can rotate around their revolution axes while their surfaces were maintained at a constant temperature. In the present study we investigate the differences in the thermal mixing process arising from the utilization of a constant heat flux as a boundary condition. The study concerns a highly viscous fluid with a high Prandtl number $Pr = 10,000$ for which this chaotic mixer is suitable. Chaotic flows are obtained by imposing temporal modulations of the rotational velocities of the walls. By solving numerically the flow and energy equations, we studied the effects of different stirring protocols and flow configurations on the efficiency of mixing and heat transfer. For this purpose, we used different statistical indicators as tools to characterize the evolution of the fluid temperature and its homogenization. Fundamental differences have been reported between these two modes of heating or cooling: while the mixing with an imposed temperature results in a homogeneous temperature field, with a fixed heat flux we observe a constant difference between the maximal and minimal temperatures that establish in the fluid; the extent of this difference is governed by the efficiency of the mixing protocol.
Wall cooling has substantial effects on the development of instabilities and transition processes in hypersonic boundary layers (HBLs). A sequence of linear stability theory, two-dimensional and non-linear three-dimensional DNSs is used to analyze Mach~6 boundary layers, with wall temperatures ranging from near-adiabatic to highly cooled conditions, where the second-mode instability radiates energy. Fluid-thermodynamic analysis shows that this radiation comprises both acoustic as well as vortical waves. 2D simulations show that the conventional trapped nature of second-mode instability is ruptured. Although the energy efflux of both acoustic and vortical components increases with wall-cooling, the destabilization effect is much stronger and no significant abatement of pressure perturbations is realized. In the near-adiabatic HBL, the wavepacket remains trapped within the boundary layer and attenuates outside the region of linear instability. However, wavepackets in the cooled-wall HBLs amplify and display nonlinear distortion, and transition more rapidly. The structure of the wavepacket displays different behavior; moderately-cooled walls show bifurcation into a leading turbulent head region and a trailing harmonic region, while highly-cooled wall cases display lower convection speeds and significant wavepacket elongation, with intermittent spurts of turbulence in the wake of the head region. This elongation effect is associated with a weakening of the lateral jet mechanism due to the breakdown of spanwise coherent structures. In moderately cooled-walls, the spatially-localized wall loading is due to coherent structures in the leading turbulent head region. In highly-cooled walls, the elongated near-wall streaks in the wake region of the wavepacket result in more than twice as large levels of skin friction and heat transfer over a sustained period of time.
Transport of viscous fluid through porous media is a direct consequence of the pore structure. Here we investigate transport through a specific class of two-dimensional porous geometries, namely those formed by fluid-mechanical erosion. We investigate the tortuosity and dispersion by analyzing the first two statistical moments of tracer trajectories. For most initial configurations, tortuosity decreases in time as a result of erosion increasing the porosity. However, we find that tortuosity can also increase transiently in certain cases. The porosity-tortuosity relationships that result from our simulations are compared with models available in the literature. Asymptotic dispersion rates are also strongly affected by the erosion process, as well as by the number and distribution of the eroding bodies. Finally, we analyze the pore size distribution of an eroding geometry. The simulations are performed by combining a high-fidelity boundary integral equation solver for the fluid equations, a second-order stable time stepping method to simulate erosion, and new numerical methods to stably and accurately resolve nearly-touching eroded bodies and particle trajectories near the eroding bodies.
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