Averaged Reynolds Equation for Flows between （平均雷诺方程之间的流动）.pdfVIP

Averaged Reynolds Equation for Flows between Rough Surfaces in Sliding Motion M. PRAT, F. PLOURABOUÉ, and N. LETALLEUR Institut de Mécanique des Fluides, UMR CNRS no 5502, Allée du Pr C. Soula 31400 Toulouse, France Abstract. The flow between rough surfaces in sliding motion with contacts between these surfaces, is analyzed through the volume averaging method. Assuming a Reynolds (lubrication) approximation at the roughness scale, an average flow model is obtained combining spatial and time average. Time average, which is often omitted in previous works, is specially discussed. It is shown that the effective transport coefficients, traditionally termed ‘flow factors’ in the lubrication literature, that appear in the average equations can be obtained from the solution to two closure problems. This allows for the numerical determination of flow factors on firmer bases and sheds light on some arguments to the literature. Moreover, fluid flows through fractures form an important subset of problems embodied in the present analysis, for which macroscopisation is given. Key words: volume averaging, Reynolds equations, lubrication, rough surfaces, fracture flows. Nomenclature a local distance between surfaces. Asf is the boundary of the contact zones within Sf . Asf is the vertical projection of Asf in the Euclidean plane Oxy. b, ci , c closure vectors fields for the pressure with i = 1, 2. C macroscopic transport tensor. hi height of solid surface number i = 1, 2. h0i mean height of solid surface number i = 1, 2. hm h02 − h01 − mean distance between surfaces. h local aperture between surfaces. K local permeability field. K∗ macroscopic permeability tensor. nsf normal vector pointing out of a subscript sf domain. is the mean surface defined by h+ (x) = (h + h )/2.