DISCUSSION. A NEW NUMERICAL METHOD APPLIED TO THE STUDY OF MASS OSCILLATIONS IN A PUMPED STORAGE HYDRO-ELECTRIC SCHEME.

Mr R . J. T. Casinader, Binnie and Partners Methods previously suggested for numerical or graphical solution of the problem of mass oscillations in hydraulic surge systems have, for all real cases, been in one form or another step-by-step integration procedures. The new method now proposed by the Authors breaks no new ground in this respect. While accepting that the governing equations can only be solved in closed analytical form for a limited number of cases, I still hope that a more elegant method will some day be devised for dealing with the problem. The refinement of the extrapolation technique proposed by the Authors is, however, a notable contribution to the subject. 52. The digital computer has, as the Authors mention, been used in conjunction with simple step-by-step integration methods, its main advantage being the facility of using smaller step sizes than would normally be used in hand or graphical computations. The limitation is of course the onset of instability as the step size is reduced, that is, instability in the computations rather than the actual surge. The Authors’ method is designed from the outset to avoid this instability at each step. However, it should be possible when using a digital computer with a simple step-bystep method, say the Heun method, to carry out successive runs using smaller and smaller step sizes until instability is induced. One or two such runs on any system should indicate the smallest step size that should be employed to obtain reasonable accuracy without inducing instability in the computations. The method is, in effect, to apply the equivalent of the Authors’ convergence, or accuracy, test and divergence test to the whole calculation rather than to each step. 53. The Authors’ views on the merits of this procedure relative to those of the method they propose would be of interest, bearing in mind the relative computational costs of each method. The simpler method should be suitable for the analysis of much more complicated surge systems than that analysed by the Authors. Would the Authors’ method be equally suitable for dealing with systems of, say, two or more surge tanks? 54. The new method has apparently been devised specifically for dealing with surges in pumped storage hydro-electric systems. Such systems have particular characteristics, which, although not exclusive to pumped storage schemes, have a bearing on the most suitable method of analysis. The schemes are generally high head with relatively short headrace and/or tailrace tunnels of large cross section. Friction losses are therefore relatively low. Surges in such systems have the following general characteristics: (a) amplitudes are low relative to total head on the system; (b) the period of the oscillations is short; (c) damping of the oscillations is poor.