Numerical Investigation of Supersonic Nozzle Flow Separation

S EPARATION of supersonic flow in a convergent–divergent nozzle is a fundamental fluid phenomenon that affects a large variety of applications, from fuel systems to aircraft engine nozzles. When a supersonic nozzle is operated at pressure ratioswell below its design point, a shock forms inside the nozzle andflowdownstreamof the shock separates from the nozzle walls. Even though flow separation is typically viewed as an undesirable occurrence, it may have some interesting applications in the area of fluid mixing. Specifically, past work at the University of California, Irvine has shown that flow exiting a severely overexpanded nozzle exhibits a strong instability that enhances mixing of the flow itself and can also be used as afluidic actuator to enhancemixing of an adjacentflow [1– 3]. A large portion of the literature on nozzle flow separation focuses on prediction of the separation location in rocket nozzles. A review paper by Morrisette and Goldberg [4], based on a variety of experimental results, concludes that computational methods, like those proposed by Reshotoko and Tucker [5], give reasonable predictions of turbulent flow separation in a nozzle with a large divergence angle. However, generic methods for boundary-layer separation prediction cannot capture entire series of events inside a nozzle. Recently, a theoretical model proposed by Romine [6] helps fill this gap. For shocks with moderate Mach numbers (less than 2.25), Romine postulates that the jet flow emerging from the shock is above ambient pressure and adjusts to the ambient pressure via a gradual underexpansion. It is important to note that this argument applies only in the vicinity of the centerline of the nozzle, the shock of which is normal or close to normal, and not in regions nearer to the walls. On thewalls, there is general consensus that the flow adjusts to the ambient pressure via a gradual compression. Previous numerical studies of separated nozzle flows, such as studies by Hunter [7], Carlson [8], and Xiao et al. [9,10] show that there is excellent agreement with available experimental data. In the study of Hunter, which is a combined computational and experimental investigation, two distinct separation regimes were found in a planar nozzle with an area ratio of exit to the throat area Ae=At of 1.8. For NPR< 1:8, the flow shows three-dimensional separation with partial reattachment. Fully detached two-dimensional separation is found for NPR> 2:0. The underexpansion of flow after the main shock, postulated by Romine [6], is evident from Presented as Paper 4640 at the 35thAIAAFluidDynamics Conference and Exhibit, Toronto, Canada; received 14 September 2005; revision received 20 April 2006; accepted for publication 29 June 2006. Copyright © 2006 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this papermay bemade for personalorinternal use,onconditionthatthecopier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923;includethecode0001-1452/07$10.00incorrespondencewiththeCCC. ∗Research Scientist, Temasek Laboratories. Principal Research Scientist, Temasek Laboratories. Member AIAA. Professor, Department of Mechanical and Aerospace Engineering. Associate Fellow AIAA. AIAA JOURNAL Vol. 45, No. 3, March 2007