A Dynamic Modeling Method of Unsteady Flows in Long Fluid Lines With Turbulent Bulk Velocities

Abstract

An analytical method is presented to solve the equations of unsteady gas flow in a long tube with turbulent bulk-flow velocity. The nonlinearity of the equations is overcome by judicious choice of integrating variables and by subsequent linearization, allowing integration as an ordinary matrix differential equation. The method yields, in operational form and in terms of pure time-delays, attenuations and other linear operators, a transfer matrix of the fluid line. This result can be directly implemented for line simulation or control applications; the integration process is not affected by changing end-conditions. Maximum accuracy of the resulting dynamic model is obtained for long lines (fl/D ≥ 2.2) and for small percent changes of the bulk-flow velocity along the tube. Adiabatic flow assumption and averaging of fluid properties over a cross section of tube restricts the analysis to turbulent flows and precludes the application of the model to small bulk flows.