One-Dimensional Unsteady Periodic Flow Model with Boundary Conditions Constrained by Differential Equations

This paper describes a modeling method for closed-loop unsteady fluid transport systems based on 1D unsteady Euler equations with nonlinear forced periodic boundary conditions. A significant feature of this model is the incorporation of dynamic constraints on the variables that control the transport process at the system boundaries as they often exist in many transport systems. These constraints result in a coupling of the Euler equations with a system of ordinary differential equations that model the dynamics of auxiliary processes connected to the transport system. Another important feature of the transport model is the use of a quasilinear form instead of the flux-conserved form. This form lends itself to modeling with measurable conserved fluid transport variables and represents an intermediate model between the primitive variable approach and the conserved variable approach. A wave-splitting finite-difference upwind method is presented as a numerical solution of the model. An iterative procedure is implemented to solve the nonlinear forced periodic boundary conditions prior to the time-marching procedure for the upwind method. A shock fitting method to handle transonic flow for the quasilinear form of the Euler equations is presented. A closed-loop wind tunnel is used for demonstration of the accuracy of this modeling method.