Hele-Shaw flow

About: Hele-Shaw flow is a research topic. Over the lifetime, 5451 publications have been published within this topic receiving 151320 citations.

Numerical simulation of immiscible two-phase flow in porous media

Abstract: Nonlinear evolution of viscous and gravitational instability in two-phase immiscible displacements is analyzed with a high-accuracy numerical method. We compare our results with linear stability theory and find good agreement at small times. The fundamental physical mechanisms of finger evolution and interaction are described in terms of the competing viscous, capillary, and gravitational forces. For the parameter range considered, immiscible viscous fingers are found to undergo considerably weak interaction as compared to miscible fingers. The wave number of nonlinear fingers decreases rapidly due to the shielding mechanism and scales uniformly as t−1 at long times. We have observed that even a small amount of density contrast can eliminate viscous fingers. The dominant feature for these flows is the gravity tongue, which develops a “ridge instability” when capillary and gravity effects are of similar magnitude.

Correction to the four-fifths law due to variations of the dissipation

Abstract: The full Kolmogorov equation is analyzed with respect to Galilean invariance. It is shown that the time-dependent term in typical applications as jets and wakes will cause rather large deviations from the four-fifths law, even at fairly large Reynolds numbers. With the use of the K−e-model an inertial range model expression is derived for the third-order structure function of freely decaying turbulence at finite Reynolds number. The expression is compared with results from previously reported experiments. It is argued that experiments to test intermittency corrections to the Kolmogorov 1941 theory should be made in flows which are both stationary and homogeneous in the mean flow direction, such as pipe and channel flows.