Numerical investigation of a jet from a blunt body opposing a supersonic flow

Abstract

Numerical investigation of a sonic jet from a blunt body opposing a supersonic flow with a free stream Mach number M ∞ = 2.5 was carried out using large-eddy simulation for two total pressure ratios of the jet to the free stream, i.e. P = 0.816 and 1.633. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the flow phenomena, including shock/jet interaction, shock/shear-layer interaction, turbulent shear-layer evolution and coherent structures, have been studied systematically. Based on the analysis of the flow structures and features, two typical flow states, i.e. unstable and stable states corresponding to the two values of P, are identified and the behaviours relevant to the flow states are discussed. Small-scale vortical structures mainly occur in the jet column, and largescale vortices develop gradually in a recirculation region when the jet terminates through a Mach disk and reverses its orientation as a conical free shear layer. The turbulent fluctuations are enhanced by the rapid deviation of the shear layer and the interaction with shock waves. Moreover, the coherent structures of the flow motion are analysed using the proper orthogonal decomposition technique. It is found that the dominant mode in the cross-section plane exhibits an antisymmetric character for the unstable state and an axisymmetric one for the stable state, while statistical analysis of unsteady loads indicates that the side loads can be seen as a rotating vector uniformly distributed in the azimuthal direction. Further, we clarify a feedback mechanism whereby the unsteady motion is sustained by the upstream-propagating disturbance to the Mach disk through the recirculation subsonic region and downstream propagation in the conical shear layer. Feedback models are then proposed which can reasonably well predict the dominant frequencies of the two flow states. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the opposing jet/supersonic flow interaction.

Large-eddy simulation of highly underexpanded transient gas jets

“…The dissipative elements in their study were: (1) the CC-hyperviscosity for shock capturing, (2) explicit Smagorinsky model for turbulence closure, (3) upwind biased discretization of the convective terms, and (4) usage of tetrahedral mesh for the simulations. The observations 5,33 motivate further developments and application of FVM for compressible jet flows.…”

“…As mentioned by Pirozzoli,31 further studies on supersonic flows with unstructured FVM-codes are required. Recently, FVM was used in LES of a blunt body opposing a supersonic jet by Chen et al 33 The dissipative elements in their simulations were: (1) central/upwind scheme for shock capturing and (2) explicit closure model for turbulence. LES of an impinging supersonic jet was carried out by Dauptain et al 5 using a third order accurate FVM code.…”

Numerical investigation of the flow dynamics past a three-element aerofoil

“…The deviatoric part of the SGS stresses are given by −u i u j d = ν t (∂u i /∂x j + ∂u j /∂x i ) where u i is the resolved field. DES97 or delayed detached eddy simulation (DDES) (Spalart et al 2006) are well adapted to simulate massively separated flows characterized by a large-scale unsteadiness dominating the time-averaged solution (Chen, Xu & Lu 2010;Chen, Wang & Lu 2011). Nevertheless, it has been recognized by these authors (Shur, Spalart & Strelets 2005;Spalart 2009;Deck 2012b) and observed by others (Kok & Van der Ven 2012;Uzun & Hussaini 2012) that DDES may present a delay in the formation of instabilities in thin shear layer flows which can have dramatic sequels on the pressure (and, thus, acoustic) field (Deck 2012a).…”

Fourier mode decomposition of PIV data

“…Among these modes, the most energetic ones may correspond to the dominant spatial structures, which can be used to obtain the low-dimensional approximate descriptions for the high-dimensional field. The POD method has been used to analyze various flow phenomena such as turbulent flow [5,6], jet [7][8][9], flow control for circular cylinder [10][11][12][13], engine flow [14][15][16], backward-facing step flow [17], flow around a vibrating cantilever plate [18] and high-speed train model [19]. These studies indicate that the POD is an effective method for identifying dominant features and events in both experimental and numerical data.…”