Hydraulic and Pneumatic Systems
Amir Saidani; Ali Fourar; Fawaz Massouh
Abstract
< p>The paper investigates temperature effect on water hammer in an isothermal pressurized copper pipe rig, for single and two phase flow. The study concerns pressure wave’s intensity, celerity and attenuation. Also, the cavities volume created during low pressure periods is inspected. The mathematical ...
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< p>The paper investigates temperature effect on water hammer in an isothermal pressurized copper pipe rig, for single and two phase flow. The study concerns pressure wave’s intensity, celerity and attenuation. Also, the cavities volume created during low pressure periods is inspected. The mathematical model of hyperbolic equations is described by the dynamic and continuity equations, which have been transformed by the characteristics method (MOC) into ordinary differential equations. Water hammer solver was built considering two different models of cavitation and column separation, the discrete vapor cavity model (DVCM) and the discrete gas cavity model (DGCM). In addition of the quasi-steady friction model, two unsteady friction models were incorporated into the code, the convolution based model proposed by Vardy & Brown and the instantaneous acceleration model proposed by Brunone. The simulations concern temperature range within 4°C to 95°C. Although the single and the two phase water hammer don’t behave with the same manner, the results obtained with the different models, show a significant influence of the temperature.
Fluid Mechanics
F. Khalighi; A. Ahmadi; A. Keramat
Abstract
Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with ...
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Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), and with the results of Godunov''s scheme to verify the proposed numerical solution. The computations reveal that the proposed Lax-Friedrichs and Nessyahu-Tadmor schemes can predict the discontinuities in fluid pressure with an acceptable order of accuracy in cases of instantaneous and gradual closure. However, Lax-Wendroff and Lax-Wendroff with nonlinear filter schemes fail to predict the pressure discontinuities in instantaneous closure. The independency of time and space steps in these schemes are allowed to set different spatial grid size with a unique time step, thus increasing the efficiency with respect to the conventional MOC. In these schemes, no Riemann problems are solved; hence field-by-field decompositions are avoided. As provided in the results, this leads to reduced run times compared to the Godunov scheme.
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