Pressure Loss in Unsteady Annular Channel Flow

E. Pasquini presented a methodology for calculating the pressure loss in unsteady flows through concentric annular channels. The momentum equation in axial direction is solved in the Laplace domain to obtain the unsteady radial velocity distribution. Based on the velocity profile, the relation between the Laplace transforms of pressure loss and area-averaged flow velocity is derived. A time domain representation of this equation is provided for oscillating flows. For arbitrary temporal distributions of the flow, the inverse Laplace transform of the relation between pressure loss and flow velocity has to be derived. Since finding the inverse Laplace transform of the exact weighting function for each possible radius ratio is cumbersome, the annular channel flow is approximated by a plane channel. An error analysis shows that this approximation introduces errors less than 1 % for channel geometries down to radius ratios of 0.45. The approximated weighting function is transformed into the time domain by using the residue theorem from complex analysis. The resulting convolution integral can be used in one-dimensional hydraulic system simulation software.

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