A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller （HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257-311 （2004））. By analyzing the distribution of the finite-time Lyapunov exponent （FTLE） along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.

Effect of pressure evolution on the formation enhancement in dual interacting vortex rings

In the biological locomotion,the ambit pressure is of particular importance to use as a means of propulsion.The multiple vortex rings have been proved to generate additional thrust by interaction,but the mechanism of this thrust enhancement is still unknown.This study examines the effect of ambit pressure on formation enhancement in interacting dual vortex rings.The vortex rings,which have the same formation time,are successively generated in a piston-cylinder apparatus.The finite-time Lyapunov exponent(FTLE)visualizes the flow fields as an indication of Lagrangian coherent structures(LCSs),and the pressure field is calculated based on the digital particle image velocity(DPIV).We extract the back pressure of the rear vortex in dual vortices and the back pressure circulationΓ_(b),which is defined as a form of overpressure circulationΓ_(p).TheΓ_(b)has a positive linear relationship withΓ_(p).A critical interval distance d*_(cr)in a range of0.32-0.42 is found whereΓbandΓp reach the maximum synchronously,leading to a full-interaction mode.Moreover,an over-interaction mode and an under-interaction mode are proposed when the dimensionless interval distance d*_(is)smaller or larger than d*_(cr).To conclude,the high back pressure caused by vortex interaction can enhance the formation of vortex rings and lead to high thrust.

Hidden flow structures in compressible mixing layer and a quantitative analysis of entrainment based on Lagrangian method

The compressible mixing layer is an important physical model to describe the mixing enhancement in scramjet combustors.The downstream coherent structures are normally regarded as the main contribution of the entrainment in the compressible mixing layer.In this study,three cases of the compressible mixing layer of convective Mach number Ma=0.4 are numerically simulated through the Lagrangian coherent structure(LCS)method to show that the entrainment process in the compressible mixing layer is closely related to the upstream hidden structures termed as the"cn train me nt fbnnation structures^^.The entrainment fbrmatio n structures consist of a series of inclined control bodies that are identical and nested to one another upstream the compressible mixing layer.In combination with the separation of the flow properties of coherent structures,the entrainment characteristics in the compressible mixing layer can be evaluated by the inclined control bodies of the upstream entrainment formation structures in the upper and lower fluids.Furthermore,with the quantitative analysis of the spatial position of the upstream coherent structure,the entrainment ratio is determined.The study of the entrainment formation and its characteristics helps the effective control of the entrainment performance in the compressible mixing layer.

Passive scalar mixing induced by the formation of compressible vortex rings

This study aims to determine the relationship between the physical features of a compressible vortex and the mixing process.Such relationship is of significant importance to design combustors that can achieve optimal or most effective mixing.The passive scalar mixing induced by the formation of a canonical compressible vortex ring(CVR)generated at the end of a shock tube is investigated by using numerical simulation.In addition,the method of finite-time Lyapunov exponent(FTLE)field are detected to identify the region of CVR,as well as to analyze the passive scalar mixing during the CVR formation.As the CVR rolls up,the ambient fluid outside the shock tube is entrained into the ring.The entrainment fraction(the mass of entrained fluid to the total mass of CVR)is found to strongly depend on two features of CVRs.One is the compressibility of CVRs,which is characterized by the Mach number of the incident shock denoted by Mach number(Ma).The other is pinch-off of CVRs,which happens at a certain timescale with narrow range of 2–4.As Ma increases,the entrainment fraction of the leading CVR decreases linearly due to smaller vortex core and weaker radial diffusion of vorticity generated by larger compressibility.After CVRs pinch off,trailing vortices appear and show less effective at entrainment than the leading CVRs do.Moreover,the tendency of the rate of entrainment is examined.The results indicate that increasing compressibility and total fluid flux are in favor of the rate of entrainment but restrain the entrainment fraction of total jet.

Evolution of the Lagrangian drift and vortex added-mass of a growing vortex ring

The vortex-based propulsive systems’ enhanced performance greatly contributes to the vortex added-mass effect, which was initially developed to explain the added drag when a solid body accelerates in fluids. However, the solution of the instantaneous vortex added-mass coefficient is still remaining a question because vortices always do not have a stable geometric shape like solid bodies. In this paper, the formation of a canonical vortex ring is performed to investigate the nature of vortex added-mass and explore a solution for estimating the vortex added-mass coefficient. The vortex ring is generated by a piston-cylinder apparatus, and the time-dependent flow fields are recorded by particle image velocimetry technique. The ridges of finite-time Lyapunov exponent are applied to identify the Lagrangian boundary of the vortex ring. It is found that a part of the ambient fluids is entrained by the vortex ring when it propagates downstream, resulting in the growth of the vortex ring. Besides, a significant drift of the ambient fluid is observed to bypass the Lagrangian boundary of the vortex ring and reveals the nature of the vortex added-mass. Thus, the added-mass coefficient of the vortex is redefined as the ratio of the volume of the Lagrangian drift fluids in finite time interval step to the vortex volume at that instant. By referring to McPhaden’s method to estimate the added-mass of a solid body, a method based on the multiple material lines with relative-timestep is developed to estimate the volume of Lagrangian drift fluids induced by the vortex added-mass. Then, an empirical criterion for determining the material line number and the finite time interval step is suggested for the vortex ring flow, and the eventual vortex added-mass coefficient calculated by the volume of Lagrangian drift fluids is found to well agree with the results of Brennen. Moreover, the method based on multiple material lines for calculating Lagrangian drift fluids’ volume suggests a potential solution for estimating the added-mass coefficient of arbitrary vortex structures.