A compact, low-pressure manifold with uniform flow at low Reynolds number

Abstract

Manifolds that distribute fluid into or that collect fluid from a multiplicity of streams are ubiquitous. We introduce a new theory for manifold design to produce uniform flow among their streams. By constructing a tapered header region that feeds uniformly spaced diffuser channels (constraint A), flow uniformity can be achieved with less than a quarter of the footprint of bifurcating manifolds, provided that diffuser channels are arrayed in triangular form (constraint B) with a design-specific angle that satisfies a compatibility condition between its header and diffuser (constraint C). The associated theory harnesses creeping-flow hydraulics to induce a constant header pressure-gradient, in contrast with past theory that relied on the interplay between kinetic energy, pressure, and viscous losses to uniformize header pressure at finite Reynolds number. Experiments using dye-based flow visualization from manifolds incorporating these three design constraints are shown to produce uniform flows, while designs that violate any of the three constraints produce flow that is biased toward the manifold's ends or its center. Our experiments and three-dimensional simulations of such uniformizing manifolds show maximum deviations from uniformity of ∼10% for Reynolds number as high as ∼10. As expected from creeping-flow theory, simulations confirm that such flow uniformity is facilitated by a uniform header-pressure gradient. Finally, the associated uniformizing manifold is shown to produce lower hydraulic resistance than a rectangular manifold circumscribed around it. In addition to the theory's embodiment in the specific form tested here, it is readily applicable to a variety of header and diffuser-channel cross-sectional types.