Uniform flows in rectangular lattice networks

Abstract

The general problem of describing the flow distribution in manifolds feeding parallel channels has been addressed in a number of earlier publications. Such systems are used for example as heat exchanger plates, as distributors for fuel cells, or as solar collectors. We address here the "inverse problem", i.e. of finding a design, which provides uniform flow distribution among the channels, for which much less literature is available. We approach that problem by considering the steady-state flow-rates in the branches of 2D rectangular lattice networks with a single inlet and a single outlet, of which the classical parallel channels (ladder) network can be viewed as a special case. The purpose of this paper is to show how to organize the flow resistances on the periphery of the lattice so as to achieve flow uniformity in all inside channels. This is done under the assumption of a resistive network, with linear flow/pressure behavior (pure viscous Stokes flow, neglecting the inertial terms, neglecting or linearizing the effect of branching singularities) allowing completely analytical solutions and comparison of different configurations. The compatibility of uniform flow distribution and uniform Residence-Time-Distribution is discussed. Examples of new conceptual designs of heat exchanger plates, of fluid distributors and of mixers are proposed, based on this possibility of uniform distribution.