Analytical modeling of microscale diaphragm compressors

This article presents a set of simple equations for determining the performance of microscale diaphragm compressors. Equations applicable to circular and square/rectangular microscale diaphragm compressors are provided. Using the model it is possible to determine the influence of material, geometric and operating parameters, under the constraint of constant stroke, on the pressure rise vs. flow rate relationship as well as temporal variation of chamber pressure and volume and actuation pressure. Material parameters considered include Young's modulus and Poisson's ratio of the compressor material and the ratio of the specific heats of the gas. Geometric parameters considered are shape, planar dimensions and depth of compression chamber and thickness of the oscillating diaphragm. For a specific stroke of the diaphragm the least clearance ratio possible for cylindrical microscale compressors is determined to be 2 and correspondingly the maximum pressure ratio, for most gases, is determined to be around 1.76 using the model. For square microscale compressors the least clearance ratio is 2.5 and the corresponding pressure ratio is 1.6. For rectangular microscale compressors, reduction in aspect ratio of the diaphragm below unity increases and decreases the clearance ratio and the pressure ratio, respectively. Moreover, the model predicts that the actuation pressure, for a specific operating condition, increases with increase in discharge pressure and flexural rigidity of the diaphragm. Thus it is best to realize microscale diaphragm compressors with materials of low Young's Modulus or thin diaphragms or a combination of both.