Extensive numerical experiments were carried out to study the effect of cylinder heating on the characteristics of the flow and heat transfer in a two-dimensional horizontal laminar flow of air past a heated circular cylinder for the range of Reynolds numbers 0.001⩽Re⩽170. The fluid was treated as incompressible (density is independent of the pressure) while the variation of the fluid properties with temperature was taken into account. By including the transient density term of the continuity equation, which was neglected in a previous study by Lange, Durst, and Breuer [Int. J. Heat Mass Transfer 41, 3409 (1998)], we were able to predict correctly the vortex shedding frequency at various overheat ratios using an incompressible flow solver. The effect of dynamic viscosity and density variations on the flow dynamics occurring with the cylinder heating was analyzed separately. Another emphasis of the work was to investigate the physical mechanism behind the “effective Reynolds number” concept widely applied in engineering correlations. Similarity was discovered for the distribution of the local dimensionless viscous force, the vorticity and the Nusselt number at the cylinder surface and the pressure force in the rear part of the cylinder. Two characteristic temperatures, Teff=T∞+0.28(TW−T∞) for the flow dynamics and Tf=T∞+0.5(TW−T∞) for the heat transfer, were identified.
The effect of fuel properties and fuel temperature on the behaviour of the internal nozzle flow, atomization and cyclic spray fluctuations is examined for a three-hole direct injection spark ignition injector by combining numerical simulation of the nozzle flow with macroscopic and microscopic spray visualization techniques. A dominant influence of the liquid fuel viscosity on the highly unsteady, cavitating nozzle flow and spray formation was observed. A reduced viscosity (or larger Reynolds number) increases the flow velocity, turbulence and cavitation in the nozzle and leads to a slim spray with a reduced width but increased spray penetration. Furthermore, the spray cone angle is larger for lower Reynolds numbers due to the changed internal nozzle flow profile as predicted by the numerical calculation. The shot-to-shot fluctuations of the sprays were found to have their origin in the highly unsteady, cavitating nozzle flow. Larger cyclic spray fluctuations were observed at low Reynolds numbers although the predicted vapour formation in the nozzle is weaker. This can be explained by flow instabilities at low Reynolds numbers leading to large fluctuations in the nozzle flow.
SUMMARYA combined analytical-numerical method based on a matching asymptotic algorithm is proposed for treating angular (sharp corner or wedge) singularities in the numerical solution of the Navier-Stokes equations. We adopt an asymptotic solution for the local ow around the angular points based on the Stokes ow approximation and a numerical solution for the global ow outside the singular regions using a ÿnite-volume method. The coe cients involved in the analytical solution are iteratively updated by matching both solutions in a small region where the Stokes ow approximation holds. Moreover, an error analysis is derived for this method, which serves as a guideline for the practical implementation. The present method is applied to treat the leading-edge singularity of a semi-inÿnite plate. The e ect of various in uencing factors related to the implementation are evaluated with the help of numerical experiments. The investigation showed that the accuracy of the numerical solution for the ow around the leading edge can be signiÿcantly improved with the present method. The results of the numerical experiments support the error analysis and show the desired properties of the new algorithm, i.e. accuracy, robustness and e ciency. Based on the numerical results for the leading-edge singularity, the validity of various classical approximate models for the ow, such as the Stokes approximation, the inviscid ow model and the boundary layer theory of varying orders are examined. Although the methodology proposed was evaluated for the leading-edge problem, it is generally applicable to all kinds of angular singularities and all kinds of ÿnite-discretization methods.
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