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The study of pulsatile flow in stenosed vessels is of particular importance because of its significance in relation to blood flow in human pathophysiology. To date, however, there have been few comprehensive publications detailing systematic numerical simulations of turbulent pulsatile flow through stenotic tubes evaluated against comparable experiments. In this paper, two-equation turbulence modeling has been explored for sinusoidally pulsatile flow in 75% and 90% area reduction stenosed vessels, which undergoes a transition from laminar to turbulent flow as well as relaminarization. Wilcox's standard k-omega model and a transitional variant of the same model are employed for the numerical simulations. Steady flow through the stenosed tubes was considered first to establish the grid resolution and the correct inlet conditions on the basis of comprehensive comparisons of the detailed velocity and turbulence fields to experimental data. Inlet conditions based on Womersley flow were imposed at the inlet for all pulsatile cases and the results were compared to experimental data from the literature. In general, the transitional version of the k-omega model is shown to give a better overall representation of both steady and pulsatile flow. The standard model consistently over predicts turbulence at and downstream of the stenosis, which leads to premature recovery of the flow. While the transitional model often under-predicts the magnitude of the turbulence, the trends are well-described and the velocity field is superior to that predicted using the standard model. On the basis of this study, there appears to be some promise for simulating physiological pulsatile flows using a relatively simple two-equation turbulence model.

A unit-cube geometry model is proposed to characterize the internal structure of porous carbon foam. The unit-cube model is based on interconnected sphere-centered cubes, where the interconnected spheres represent the fluid or void phase. The unit-cube model is used to derive all of the geometric parameters required to calculate the heat transfer and flow through the porous foam. An expression for the effective thermal conductivity is derived based on the unit-cube geometry. Validations show that the conductivity model gives excellent predictions of the effective conductivity as a function of porosity. When combined with existing expressions for the pore-level Nusselt number, the proposed model also yields reasonable predictions of the internal convective heat transfer, but estimates could be improved if a Nusselt number expression for a spherical void phase material were available. Estimates of the fluid pressure drop are shown to be well-described using the Darcy-Forchhiemer law, however, further exploration is required to understand how the permeability and Forchhiemer coefficients vary as a function of porosity and pore diameter.

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A numerical and experimental investigation of free convection from vertical, isothermal, parallel-walled channels has been undertaken to explore the heat transfer enhancement obtained by adding adiabatic extensions of various sizes and shapes. Investigations were carried out for air (Pr= 0.7) over a wide range of wall heating conditions. In all cases, the adiabatic extensions were able to increase heat transfer. The increase varied from 2.5 at low Ra* to 1.5 at high Ra*. The experimental and numerical results are in excellent agreement. A single correlation accounting for the channel aspect ratio Lh/b, expansion ratio, B/b, modified Rayleigh number, Ra* and heated length ratio, Lh/L is presented.

SUMMARYThe equations governing the ow of a viscous uid in a two-dimensional channel with weakly modulated walls have been solved using a perturbation approach, coupled to a variable-step ÿnite-di erence scheme. The solution is assumed to be a superposition of a mean and perturbed ÿeld. The perturbation results were compared to similar results from a classical ÿnite-volume approach to quantify the error. The in uence of the wall geometry and ow Reynolds number have extensively been investigated. It was found that an explicit relation exists between the critical Reynolds number, at which the wall ow separates, and the dimensionless amplitude and wavelength of the wall modulation. Comparison of the ow shows that the perturbation method requires much less computational e ort without sacriÿcing accuracy. The di erences in predicted ow is kept well around the order of the square of the dimensionless amplitude, the order to which the regular perturbation expansion of the ow variables is carried out.

The flow inside channels with periodic, wavy walls of arbitrary shape is considered numerically. Solutions are obtained using either a perturbation approach, for weak modulation amplitude, or a finite volume technique, for strong amplitude. The flow is examined for sinusoidal, arched and triangular modulation over a wide range of amplitude, wavelength and Reynolds number in the steady laminar regime. For weak wall modulation (ε<0.3, α<2, where ε and α are the dimensionless half-wave height and wavelength, respectively), it is found that the flow behavior along the modulated wall is of the boundary-layer type. As such, the critical Reynolds number, Rec, for separation for each modulation shape can be expressed as an explicit function of ε and α, while the location of separation and pressure distribution along the modulated wall scale with ε, α, and Rec. For strong modulations, the boundary layer model is no longer satisfactory to predict the flow behavior and deviations from the trends found for weaker modulations are observed. It is also shown that the driving force required to sustain a given flow rate increases as ε increases. For all modulation amplitudes, the sinusoidal wave shape is found to require the largest pressure gradient to maintain a given flow rate through the channel and, consequently, yields the highest friction factor. Finally, the existence of a stable recirculating flow regime is discussed in the light of earlier stability analyses.

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