Water Hammer Simulations

Contents An old topic still not completely solved An old topic; Applications and problems; This book; The computer programs Compressible flow theory: basic concepts Instantaneous operations; Wave celerity; Velocity of operations; Non-negligible headlosses; Governing equations; Continuity equation; Momentum equation; The governing equations Simplified solutions The Allievi's method (1913); The non-elastic hypothesis; Governing equations; Comparisons; Graphical method Numerical solution of the governing equations: The method of characteristics Numerical solution; Initial and boundary conditions; Reservoir; Valve; Junction; The computer code; First simple application Numerical solution of the governing equations: finite difference methods The Courant - Friedrichs - Levy stability condition; The Lax - Wendroff method; Solving the governing equations; Boundary conditions; Asymmetrical schemes; Ghost cells; The computer code; Again the simple application Devices - Boundary conditions Surge tanks; Simple surge tanks; Different types of surge tanks; Air chambers; Relief valves and rupture disks; Centrifugal pumps; Other methods for controlling the pressures; The computer codes; The simple surge tank; The simple air chamber; Air chamber with headlosses; Air chamber and valve; Valve modelling: an example; Pumps Instabilities Vibrations; General remarks; Computer program for oscillating velocity; Transfer matrix method; General remarks; Application to hydraulic transients; Description of simple system: pipes; Description of simple system: valves and effluxes; Global matrix of a system; A simple application; Numerical instabilities; Changing CFL number; First order methods; Flux-limiters; Artificial dissipation Effects of air and cavitation Cavities; Formation of the cavities; Collapse of the cavities; Description of the motion in the presence of cavities; Changing of celerity; Water column separation; Additional resistance terms; Models; Parameters; Laboratory experiments; Experimental set-up; Experimental tests; Computer code Advanced models 2D models; Continuity equation; Momentum equation; Headlossess; Pezzinga's model; k - ε model; avitation; Release gaseous cavitation model; Second viscosity cavitation model;Numerical schemes; Further problems Case studies Simple pressure pipe for petroleum products in Djibouti; lant characteristics; Expected scenarios; Case 1; Case 2; Case 3; Conclusions; A more complex example for seawater treatment plant in Tanzania; Plant characteristics; Unsteady flow simulations: existing plant; Plant to be designed; No air chambers; Air chamber 3 m3 volume; Air chamber 5 m3 volume; Conclusions; A very complex example for seawater treatment plant in Algeria; The plant to be modelled; A peculiar device: energy recovery PX; Laboratory plant; Laboratory tests; Model of the seawater plant in Algeria; Conclusions; Final remarks References