Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow

Abstract

SUMMARYHere we describe analytical and numerical modiÿcations that extend the Di erential Reduced Ejector= mixer Analysis (DREA), a combined analytical=numerical, multiple species ejector=mixing code developed for preliminary design applications, to apply to periodic unsteady ow. An unsteady periodic ow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental uid dynamic unsteadiness, e.g. fan instability=vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing ows and that have greatly in uenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical-numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet ows with excitation shows reasonable agreement with the simulation. Other ow ÿelds are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic e ects can be included within the simple, e cient, coarse grid DREA implementation that has been the original intent of the DREA development e ort, namely, to provide a viable tool where more complex and expensive models are inappropriate.