Kinetic Stabilization¶of a Nonlinear Sonic Phase Boundary

We consider a system arising in the study of phase transitions in elastodynamics – a system of two conservation laws, in a single space dimension. The system has two hyperbolic regions with an elliptic zone in between. A phase boundary is a strong discontinuity in a solution, with left and right states belonging to different hyperbolic regions. We call such a solution a phase wave. We first address the Riemann problem for initial states close to a fixed sonic phase wave, in the genuinely nonlinear case. This problem is naturally underdetermined. We propose two essentially different types of Reimann problems: a sonic one, which is smooth, and a kinetic one, which is only Lipschitz-continuous. Both problems are well posed owing to a shared stability condition that is of a purely sonic nature. In the kinetic case we prove the global existence of solutions to the Cauchy problem for initial data having small variation and close to a sonic kinetic wave. The crucial issue is the interaction of the phase boundary with a small wave of the same mode. The introduction of a pertinent quantity, called here detonation potential, ensures a balance between ingoing and outgoing waves. The proof is based on a Glimm-type scheme; we define a potential, which includes the detonation potential, along the strong discontinuity, and this potential controls the outbreak of unusual shocks. Accepted: June 9, 1999     

Properties of the “Non-Free” Shock Wave/Boundary Layer Interaction on a Swept Plate

A comprehensive experimental investigation of the transition from the free to the non-free regime of interaction between a plane shock and a boundary layer in a conical flow and the non-free interaction properties has been carried out. A theoretical model is constructed and used to calculate the transition parameters and determine the range on which the non-free interaction can exist, together with its basic characteristics.     

Wall Effect on the Convective–Absolute Boundary for the Compressible Shear Layer

The linear stability of inviscid compressible shear layers is studied. When the layer develops at the vicinity of a wall, the two parallel flows can have a velocity of the same sign or of opposite signs. This situation is examined in order to obtain first hints on the stability of separated flows in the compressible regime. The shear layer is described by a hyperbolic tangent profile for the velocity component and the Crocco relation for the temperature profile. Gravity effects and the superficial tension are neglected. By examining the temporal growth rate at the saddle point in the wave-number space, the flow is characterized as being either absolutely unstable or convectively unstable. This study principally shows the effect of the wall on the convective–absolute transition in compressible shear flow. Results are presented, showing the amount of the backflow necessary to have this type of transition for a range of primary flow Mach numbers M ₁ up to 3.0. The boundary of the convective–absolute transition is defined as a function of the velocity ratio, the temperature ratio and the Mach number. Unstable solutions are calculated for both streamwise and oblique disturbances in the shear layer. Received 9 May 2001 and accepted 21 August 2001     

Experimental Investigation of Stability of a Hypersonic Boundary Layer on a Cone–Flare Model

Stability of a hypersonic flow in the regions of laminar separation of the boundary layer on a cone–flare model is experimentally studied for a Mach number M = 5.92. Development of natural disturbances and artificial wave packets in the boundary layer and separation region is examined. It is shown that highfrequency disturbances are predominantly amplified in the separation region; the most unstable waves are those propagating with an angle close to 60° to the freestream direction. It is found that separation and reattachment lines are generators of twodimensional disturbances.     

A Comment on “On Magneto Convection in a Mushy Layer” by D. N. Riahi

The impracticality of MHD convection in a porous medium is further clarified.     

Inertial and Darcy’s Terms Ratio in Boundary Layer at Fluid–Porous Medium Interface

The study considers the forced boundary-layer flow overlying the Darcy–Brinkman porous medium and gives a quantitative analysis of the nonlinear inertial terms in the Brinkman filtration equation. The inertial terms are shown to be larger than the Darcy’s drag near the porous medium interface. The applicability range of boundary-layer approach is determined. It is suitable in high-permeable media with moderate velocities of an external flow. If it is slow enough, the inertial terms can be omitted in spite of interface effect. On the other hand, fast external flow produces the filtration with large pore-scale Reynolds number; therefore, the Forchheimer’s drag should be taken into account. It is shown the Brinkman term as well as inertial terms have a significant role in boundary-layer formation within the porous medium.     

Interaction of Large‐Scale and Small‐Scale Oscillations During Separation of a Laminar Boundary Layer

The mutual influence of shortwave oscillations (instability waves of the separated boundary layer) and longwave disturbances at the frequency of shedding of periodic largescale vortices is experimentally studied in flow separation behind a step. The possibility of controlling the process of vortex formation by exciting amplifying disturbances in the shear layer is demonstrated.     

On the Propagation of Long‐Wave Perturbations in a Two‐Layer Free‐Boundary Rotational Fluid

A mathematical model for the propagation of longwave perturbations in a freeboundary shear flow of an ideal stratified twolayer fluid is considered. The characteristic equation defining the velocity of perturbation propagation in the fluid is obtained and studied. The necessary hyperbolicity conditions for the equations of motion are formulated for flows with a monotonic velocity profile over depth, and the characteristic form of the system is calculated. It is shown that the problem of deriving the sufficient hyperbolicity conditions is equivalent to solving a system of singular integral equations. The limiting cases of weak and strong stratification are studied. For these models, the necessary and sufficient hyperbolicity conditions are formulated, and the equations of motion are reduced to the Riemann integral invariants conserved along the characteristics.     

Experimental Investigation of the Log-Law for an Adverse Pressure Gradient Turbulent Boundary Layer Flow at Re θ = 10000

We present an experimental investigation of a turbulent boundary layer flow at a significant adverse pressure gradient at Reynolds number Re _θ ?=?10000 using large field PIV. The testcase is designed to start from a zero pressure gradient flow at Re _θ ?=?8000 with a distinct log-law region following a slowly rising adverse pressure gradient. This allows to reveal a breakdown of the log-law under the effect of the adverse pressure gradient. The region described by the log-law is progressively reduced in terms of y ^?+? and then joins into a modified log-law which gives a good fit to the data up to at least y/δ ₉₉?≈?0.2. The scaling in the overlap region is demonstrated using the mean velocity slope diagnostic function, enabled due to the high quality of the PIV data. Locally, the velocity profile is measured down to the wall using long-range microscopic PIV with particle tracking velocimetry to determine the wall shear stress directly in the adverse pressure gradient region.     

The Solution to the Form of Poisson Equation by the Boundary Element Methods

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Numerical Modeling of Unsteady Radiative–Convective Heat Transfer on a Flat–Plate Boundary Layer in a Selectively Emitting and Scattering Medium

A conjugation problem for radiative–convective heat transfer in a turbulent flow of a high–temperature gas—particle medium around a thermally thin plate is considered. The plate experiences intense heating from an outside source that emits radiation in a restricted spectral range. Unsteady temperature fields and heat–flux distributions along the plate are calculated. The results permit prediction of the effect of the type and concentration of particles on the dynamics of the thermal state of both the medium in the boundary layer and the plate itself under conditions of its outside heating by a high–temperature source of radiation.     

An Experimental Study of the Modulation of the Bubble Motion by Gas–Liquid-Phase Interaction in Oscillating-Grid Decaying Turbulence

The purpose of the present research is to understand dynamic bubble–liquid interaction in a bubbly flow based on the experimental results of the modulation of the bubble motion in oscillating-grid decaying turbulence. By comparing the experimental results obtained from stagnant water and those from oscillating-grid decaying turbulence, we discussed and described detailed process of the modulation of the bubble motion in a water vessel. We discussed the enhancement of the transition of the bubble motion from 2D to 3D by combining the liquid-phase motion obtained through particle imaging velocimetry/laser-induced fluorescence (PIV/LIF) measurement and the bubble wake motion captured through the LIF/HPTS (8-hydroxypyrene-1, 3, 6-trisulfonic acid) method, under both conditions (in the stagnant water and in the oscillating-grid decaying turbulence) in which the initial bubble formation and the bubble motion (gravity-center motion and surface oscillation) were considered to be the same. In addition, by using PIV/LIF measurement along with an infrared shadow technique, we simultaneously obtained the bubble motion (2D zigzagging motion in stagnant water, and 3D motion in the decaying turbulence) and the standard deviation of the liquid-phase motion (the bubble Reynolds number: 775; the turbulent Reynolds number: 62.2). Taking all of the results together, the modulation of the bubble motion in the decaying turbulence, and the dynamic interaction between the bubble and the liquid-phase motion were experimentally and carefully investigated. Consequently, the enhancement and the modulation of the bubble wake motion were considered to be triggered by the collapse of the symmetric property of the bubble–liquid (i.e. ambient liquid-phase turbulence) interaction.     

Instability of the Benard–Marangoni Convection in a Porous Layer Affected by a Non-Vertical Magnetic Field

The onset of the Benard–Marangoni convection in a horizontal porous layer permeated by a magnetohydrodynamic fluid with a nonlinear magnetic permeability is examined. The porous layer is assumed to be governed by the Brinkman model; it is bounded by a rigid surface from below and by a non-deformable free surface from above and subjected to a non-vertical magnetic field. The critical effective Marangoni number and the critical Rayleigh number are obtained for different values of the effective Darcy number, Biot number, Chandrasekhar number, nonlinear magnetic parameter, and angle from the vertical axis for the cases of stationary convection and overstability. The related eigenvalue problem is solved by using the first-order Chebyshev polynomial method.     

Correction to: A New “λ2” Term for the Spalart–Allmaras Turbulence Model,Active in Axisymmetric Flows

Flow, Turbulence and Combustion -     

Stabilization of the passive walking dynamics of the compass-gait biped robot by developing the analytical expression of the controlled Poincaré map

Nonlinear Dynamics - The compass-gait biped robot is a two-DoF legged mechanical system that has been known by its passive dynamic walking. This kind of passive biped robot is modeled by an...     

On a Turbulent Mixing Layer Created Downstream of a “Λ” Notch Simulating One Wavelength of a Chevron Nozzle

Measurements were carried out in a turbulent mixing layer formed downstream of a splitter plate, that had a Λ-shaped trailing edge. The results revealed that the center of the mixing layer shifts toward the high-speed flow while its sides bend toward the low speed stream at larger distances from the splitter plate. This suggests the existence of a counter rotating streamwise eddies that dominate the flow and substantially increase its level of turbulence relative to the classical plane mixing layer. The change in the orientation of the vorticity, emanating from a chevron nozzle, decreases the susceptibility of the flow to spanwise uniform periodic excitation relative to a classical plane mixing layer.