Quasi-steady friction in transient polytropic flow

An accurate method of integrating quasi-steady friction in transient polytropic hows is introduced and is justified both physically and analytically, When applied to subsonic flows, it is found to be especially informative at higher Mach numbers where existing methods of integration can lead to serious errors in mass conservation. The method is used herein to assess the accuracy of widely used finite difference representations of quasi-steady friction, attention focusing principally on solutions obtained using the method of characteristics. The new method is exact in the special case of steady flews. Of the approximate methods considered, the popular approximation V-t\Vt-Delta t\Delta t is found to perform well. A modification introduced by Karney and McInnis (Journal of Hydology Engineering. ACSE, 1992, 118(7), 1014-1030 [1]) improves the correlation for downstream characteristic lines, but has the opposite effect for upstream characteristics. A simple cubic scheme, loosely related to a more complex one used successfully by Murray (Proceedings of the International Conference on Unsteady Flow and Fluid Transients, 29 September-1 October. Balkema, Amsterdam, 1992, pp. 143-157 [2]), illustrates difficulties in higher-order schemes. The new method is not exact in transient flows, but it gives good accuracy in slowly varying flows and it is plausible in rapidly varying flows. Using it as a benchmark, the approximation V-t\Vt-Delta t\Delta t is again shown to perform well. All of the schemes considered are unreliable when the flow is about to become choked within the region of integration. (C) 1997 Elsevier Science Ltd.