Numerical solutions of quasi-two-dimensional models for laminar water hammer problems

ABSTRACT: Numerical solutions of two quasi-two-dimensional models for water hammer problems under laminar flow conditions are proposed. The solutions are based on modified Chebyshev polynomial expansion of radial distribution of velocities. The collocation method is used to solve for the expansion coefficients. Spatial variation in the axial direction and time advancement are treated using the method of characteristics. One model includes the radial velocity components in the continuity equation while the other is focused on the cross-sectional mean velocity without the radial component. The effect of including the radial velocity component in the flow system is evaluated. The Chebyshev polynomials constitute an orthogonal basis for approximating numerical solutions and show suitable behaviour of the expansion coefficients.