Frontal collision of internal solitary waves of first mode

The dynamics and energetics of a frontal collision of internal solitary waves (ISW) of first mode in a fluid with two homogeneous layers separated by a thin interfacial layer are studied numerically within the framework of the Navier–Stokes equations for stratified fluid. It was shown that the head-on collision of internal solitary waves of small and moderate amplitude results in a small phase shift and in the generation of dispersive wave train travelling behind the transmitted solitary wave. The phase shift grows as amplitudes of the interacting waves increase. The maximum run-up amplitude during the wave collision reaches a value larger than the sum of the amplitudes of the incident solitary waves. The excess of the maximum run-up amplitude over the sum of the amplitudes of the colliding waves grows with the increasing amplitude of interacting waves of small and moderate amplitudes whereas it decreases for colliding waves of large amplitude. Unlike the waves of small and moderate amplitudes collision of ISWs of large amplitude was accompanied by shear instability and the formation of Kelvin–Helmholtz (KH) vortices in the interface layer, however, subsequently waves again become stable. The loss of energy due to the KH instability does not exceed 5%–6%. An interaction of large amplitude ISW with even small amplitude ISW can trigger instability of larger wave and development of KH billows in larger wave. When smaller wave amplitude increases the wave interaction was accompanied by KH instability of both waves.     

Instability of uniform flow

We consider uniform flow of a Newtonian fluid trasverse to a domain bounded by parallel planes. We investigate the possibility of introducing instabilities in this flow by the choice of inflow and outflow conditions. Some instabilities of this kind are found.     

Spiral and circular waves in the flow between a rotating and a stationary disk

 Circular and spiral waves are observed in the flow between a rotating and a stationary disk. These waves are generated by instabilities of the stationary disk boundary layer. This experimental work is devoted to their study by means of flow visualization and measurements of the associated velocity fields. In particular, instantaneous velocity profiles are measured by ultrasonic Doppler anemometry. The spatio-temporal characteristics of the waves are studied with the help of Fourier transforms of these velocity signals. Received: 21 April 1997/Accepted: 2 February 1998     

Studies of reactive triple shock collision

Experimental studies have been performed on two-dimensional reactive blast waves in a diverging nozzle. Both blast and reaction wave loci have been measured and the results compared with numerical calculations.With the inclusion of additional wedges into the channel reactive Mach reflections were generated and the subsequent interactions of these waves have been observed and modelled using a full chemistry scheme. The results are in excellent agreement and the technique shows great promise for the study of the coupling between chemistry and gas dynamics under conditions similar to those obtaining within a single cell of a gaseous detonation.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Instability of self-similar ideal gas flows with shock waves

The results of the numerical simulation of three problems of ideal gas flow with shock waves, which admit self-similar solutions, are presented. These problems are the double Mach-type reflection of a shock from a wedge, the breakdown of a combined discontinuity on a 90° sharp corner, and the outflow of a supersonic jet from an expanding slot. It is shown that for certain input data the self-similar solution may become unstable and is replaced by a fluctuating flow. The reasons for the generation of these fluctuations and their mechanism are discussed. Volgograd. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 166–175, July–August, 1998.     

Dynamic flow in a realistic model of the upper human lung airways

The objective of the study is an analysis of lung ventilation during breathing under rest conditions and for high frequency ventilation (HFV). The measurements include investigations of the flow using an endotracheal tube. A transparent model of the upper human lung airways down to the 6th generation was generated, and the oscillatory flow through the branching network was studied by DPIV. The method of refractive index matching of the fluid (water/glycerin) and the model (silicone) allows an unobstructed view into the internal flow network. The mass flow rate and the frequency were adapted to the characteristic flow parameters, the Reynolds- and the Womersley-number. The comparison of the results for normal breathing and HFV shows that a mass exchange occurs for higher frequencies known as Pendelluft, which could not be seen during normal breathing. This mass exchange between the daughter tubes is a consequence of the asymmetric impedance in the successive daughter branches. The lung topology determines the local pressure loss in the model and therefore the local mass flow direction of the Pendelluft. At higher frequencies we observed an increase in exchange between the daughter branches. The transformation of the velocity profiles between inspiration and expiration suggests a net mass flow which is created into the model along the centerline and the inner walls of the bifurcations. This flow is compensated with a net mass outflow to the trachea along the outer walls of the branches.     

Convective and absolute instabilities in non-Boussinesq mixed convection

The problem of non-Boussinesq mixed convection in a vertical channel formed by two differentially heated infinite plates is investigated and the complete convective/absolute instability boundary is computed for a wide range of physical parameters. A physical insight into the mechanisms causing instabilities is given. In particular, it is shown that the appearance of absolute instability is always dictated by a flow reversal within a channel; however, existence of the flow reversal does not exclude the possibility of convective instability. It is also shown that fluid’s non-linear transport property variations have a dramatic effect on the structure and complexity of spatio-temporal instabilities of the co-existing buoyancy and shear modes as the temperature difference across the channel increases. The validity of the stability results obtained using the procedure described in Suslov (J Comp Phys 212, 188–217, 2006) is assessed using the method of steepest descent. This work was partially supported by a computing grant from the Australian Partnership for Advanced Computing, 2000–2003.     

Écoulement de Couette Taylor diphasiqueTwo phase Couette Taylor flow

This paper presents the study of mutual interactions between dispersed and continuous phase in Couette Taylor flow. The introduction of the dispersed phase is obtained by ventilation or by pressure drop in an airtight chamber. In the first instabilities, the dispersed phase generate a modification of the flow state, the cavitating flow being moreover characterised by an advance to the third instability. The dispersed phase first stands along each of the apparent azimuthal waves as a string of individual bubbles located near the core of the Taylor cells and then migrates to the outflow regions near the inner cylinder. To cite this article: H. Djéridi et al., C. R. Mecanique 330 (2002) 113–119.     

Immersed Boundaries in Large Eddy Simulation of Compressible Flows

Methods to immerse walls in a structured mesh are examined in the context of fully compressible solutions of the Navier–Stokes equations. The ghost cell approach is tested along with compressible conservative immersed boundaries in canonical flow configurations; the reflexion of pressure waves on walls arbitrarily inclined on a cartesian mesh is studied, and mass conservation issues examined in both a channel flow inclined at various angles and flow past a cylinder. Then, results from Large Eddy Simulation of a flow past a rectangular cylinder and a transonic cavity flow are compared against experiments, using either a multi-block mesh conforming to the wall or immersed boundaries. Different strategies to account for unresolved transport by velocity fluctuations in LES are also compared. It is found that immersed boundaries allow for reproducing most of the coupling between flow instabilities and pressure-signal properties observed in the transonic cavity flow. To conclude, the complex geometry of a trapped vortex combustor, including a cavity, is simulated and results compared against experiments.     

The impact of instability appearance on the quadratic law for flow through porous media

In the present paper, we attempt to explain the macroscopic flow law evolution in porous media according to the Reynolds number. A crenellated channel, considered as an element of such a medium, is used to perform numerical simulations in stationary and non-stationary cases. In the case of non-stationary laminar flows, we point out flow instabilities occurring in the channel at high Reynolds numbers and we focus on their influence on the macroscopic law. We qualitatively prove that they generate an additional quadratic contribution to Forchheimer’s law. We use two methods to study this contribution: first, a periodic disturbance, for which the instabilities appearing at the beginning of disturbance become regular oscillations; then a pulse disturbance of the entry velocity field which enables us to link the additional quadratic contribution to the existence of an accumulation of fluid at low velocity in the channel.     

Bifurcation mechanism of interfacial electrohydrodynamic gravity-capillary waves near the minimum phase speed under a horizontal electric field

We investigate the evolution of interfacial gravity-capillary waves propagating along the interface between two dielectric fluids under the action of a horizontal electric field. There is a uniform background flow in each layer, and the relative motion tends to induce Kelvin–Helmholtz(KH) instability. The combined effects of gravity, surface tension and electrically induced forces are all taken into account. Under the short-wave assumption, the expansion and truncation method of Dirichlet-Neumann(DN) operators is applied to derive a reduced dynamical model. When KH instability is suppressed linearly by a considerably large electric field, our numerical results reveal that in certain regions of parameter space, nonlinear symmetric traveling wave solutions can be found near the minimum phase speed. Additionally, the detailed bifurcation structures are presented together with typical wave profiles.     

Role of Buoyancy on Instabilities and Structure of Transitional Gas Jet Diffusion Flames

Transitional jet diffusion flames provide the link between dynamics of laminar and turbulent flames. In this study, instabilities and their interaction with the flow structure are explored in a transitional jet diffusion flame, with focus on isolating buoyancy effects. Experiments are conducted in hydrogen flames with fuel jet Reynolds number of up to 2,200 and average jet velocity of up to 54 m/s. Since the fuel jet is laminar at the injector exit, the transition from laminar to turbulent flame occurs by the hydrodynamic instabilities in the shear layer of fuel jet. The instabilities and the flow structures are visualized and quantified by the rainbow schlieren deflectometry technique coupled with a high-speed imaging system. The schlieren images acquired at 2,000 frames per second allowed exposure time of 23 μs with spatial resolution of 0.4 mm. Results identify a hitherto unknown secondary instability in the flame surface, provide explanation for the observed intermittency in the breakpoint length, show coherent vortical structures downstream of the flame breakpoint, and illustrate gradual breakdown of coherent structures into small-scale random structures in the far field turbulent region.     

A numerical study of the frontal region of gravity currents propagating on a free-slip boundary

We investigate numerically the three-dimensional flow near the head of gravity currents propagating along a free-slip boundary. The simulations show that two states are possible: a high-mixing state, where the flow departs from the analytic inviscid solution 0.5 channel heights downstream of the front location, and with characteristics similar to the ones observed for purely two-dimensional simulations; and a low-mixing state, where billows are weaker and appear further downstream. To access the high-mixing state, it is necessary to add a source of perturbation upstream of the head in the form of turbulence. At high values of the Reynolds number, the intensity of rms turbulent fluctuations necessary to switch to the high-mixing state is small (0.5% of the speed of propagation) and may explain why the low-mixing state has so far eluded experimental detection. In the low-mixing state, the flow becomes three-dimensional near the front due to centrifugal instabilities caused by the curved streamlines. This instability of the outer flow is coupled to overturning instabilities that develop within the heavy fluid in the head, and suppresses the formation of billows. This complex behavior, which feeds on the interplay of streamline curvature and stratification, should be considered a good model to understand how instabilities occur in other types of strongly nonlinear stratified flows.      

Can crack front waves explain the roughness of cracks?

We review recent theoretical progress on the dynamics of brittle crack fronts and its relationship to the roughness of fracture surfaces. We discuss the possibility that the small scale roughness of cracks, which is characterized by a roughness exponent ?0.5, could be caused by the generation, during local instabilities by depinning, of diffusively broadened corrugation waves, which have recently been observed to propagate elastically along moving crack fronts. We find that the theory agrees plausibly with the orders of magnitude observed. Various consequences and limitations, as well as alternative explanations, are discussed. We argue that another mechanism, possibly related to damage cavity coalescence, is needed to account for the observed large scale roughness of cracks that is characterized by a roughness exponent ?0.8.     

Formation of a spall cavity in a dielectric during electrical explosion

The wave dynamics of the stress-strain state of a solid dielectric during electrical explosion near its surface is analyzed. A quantitative model of an electrical explosion is developed which describes the operation of a high-voltage generator, the expansion of the discharge channel, and the generation and distribution of shock-wave perturbations. Two mechanisms of formation of a spall cavity on the surface of the solid are considered: the less energetic mechanism implemented by means of the waves reflected from the surface, and the more energetic mechanism in which result from the action of a direct wave of compressive stresses. The effects of the reflection surface shape and the mode of energy input into the channel on the possible fracture pattern are estimated.     

Modeling of fluid dynamics interacting with ductile fraction propagation in high pressure pipeline

This paper presents a computational model for the fluid dynamics in a fractured ductile pipe under high pressure. The pressure profile in front of the crack tip, which is the driving source of crack propagation, is computed using a nonlinear wave equation. The solution is coupled with a one dimensional choked flow analysis behind the crack. The simulation utilizes a high order optimized prefactored compact-finite volume method in space, and low dispersion and dissipation Runge-Kutta in time. As the pipe fractures the rapid depressurization take place inside the pipe and the propagation of the crack-induced waves strongly influences the outflow dynamics. Consistent with the experimental observation, the model predicts the expansion wave inside the pipe, and the reflection and outflow of the wave. The model also helps characterize the propagation of the crack dynamics and fluid flows around the tip of the crack.     

Solving for unsteady airflow in a glottal model with immersed moving boundaries

This work builds on previous efforts to characterize the dynamic development of the airflow in the glottis from a fluid mechanical point of view. A multigrid finite-difference method with immersed boundaries is implemented to solve the Navier–Stokes equations in a channel constricted by a vibrating rigid structure with a shape conforming to the human vocal folds. For the dynamically evolving boundaries we apply a forced oscillation glottal model. The large scale deformations of the boundaries are handled without regridding and tracheal input velocity is either set to a constant value or synchronized with wall motion. Particular attention is paid to the mobility of the point where the airflow detaches from the flapping walls. Results illustrate the relevance and the diversity of flow separation dynamics within the constriction standing for the glottis, while flow instabilities past the constriction are not found to affect flow behavior between the moving walls significantly. A comparison between static and dynamic numerical experiments show that mobility of the flow separation point is nontrivial in general and only rarely quasi-static.     

On trailing vortices: A short review

This paper reviews some mechanisms involved in the dynamics of vortices in fluid flows. The topic is first introduced by pointing out its importance in aerodynamics. Several basic notions useful to appraise experimental observations are then surveyed, namely: centrifugal instabilities, inertial waves, cooperative instabilities, vortex merger, vortex breakdown and turbulence in vortices. Each topic is illustrated with experimental or numerical results.     

Time-resolved and volumetric PIV measurements of a transitional separation bubble on an SD7003 airfoil

To comprehensively understand the effects of Kelvin–Helmholtz instabilities on a transitional separation bubble on the suction side of an airfoil regarding as to flapping of the bubble and its impact on the airfoil performance, the temporal and spatial structure of the vortices occurring at the downstream end of the separation bubble is investigated. Since the bubble variation leads to a change of the pressure distribution, the investigation of the instantaneous velocity field is essential to understand the details of the overall airfoil performance. This vortex formation in the reattachment region on the upper surface of an SD7003 airfoil is analyzed in detail at different angles of attack. At a Reynolds number Re _c < 100,000 the laminar boundary layer separates at angles of attack >4°. Due to transition processes, turbulent reattachment of the separated shear layer occurs enclosing a locally confined recirculation region. To identify the location of the separation bubble and to describe the dynamics of the reattachment, a time-resolved PIV measurement in a single light-sheet is performed. To elucidate the spatial structure of the flow patterns in the reattachment region in time and space, a stereo scanning PIV set-up is applied. The flow field is recorded in at least ten successive light-sheet planes with two high-speed cameras enclosing a viewing angle of 65° to detect all three velocity components within a light-sheet leading to a time-resolved volumetric measurement due to a high scanning speed. The measurements evidence the development of quasi-periodic vortex structures. The temporal dynamics of the vortex roll-up, initialized by the Kelvin–Helmholtz (KH) instability, is shown as well as the spatial development of the vortex roll-up process. Based on these measurements a model for the evolving vortex structure consisting of the formation of c-shape vortices and their transformation into screwdriver vortices is introduced.