Numerical simulation of a compressible vortex–wall interaction

The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number \(M = 1.36\)) and shock-embedded \((M = 1.57)\) compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for \(M = 1.36\) and it reaches up to 60 % for \(M = 1.57\). The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.     

Ferrofluid magnetoviscous control of wall flow channeling in oorous media

We analyzed the phenomenon of ferrofiuid magnetoviscosity in high-permeability wall-region non-magnetic porous media of the Müller kind. After upscaling the pore-level ferrohydrodynamic model, we obtained a simplified volume-average zero-order axisymmetric model for non-Darcy non-turbulent flow of steady-state isothermal incompressible Newtonian ferrofluids through a porous medium experiencing external constant bulk-flow oriented gradient magnetic field, ferrofluid self-consistent demagnetizing field and induced magnetic field in the solid. The model was explored in contexts plagued by wall flow maldistribution due to low column-to-particle diameter ratios. It was shown that for proper magnetic field arrangement, wall channeling can be reduced by inflating wall flow resistance through magnetovisco-thickening and Kelvin body force density which reroute a fraction of wall flow towards bed core.     

An experimental study of circular sand–water wall jets

Laboratory experiments were carried out to study the effects of sand particles on circular sand–water wall jets. Mean and turbulence characteristics of sand particles in the sand–water wall jets were measured for different sand concentrations c_o ranging from 0.5% to 2.5%. Effects of sand particle size on the centerline sand velocity of the jets were evaluated for sand size ranging from 0.21 mm to 0.54 mm. Interesting results with the range of measurements are presented in this paper. It was found that the centerline sand velocity of the wall jets with larger particle size were 15% higher than the jets with smaller particle size. Concentration profiles in the vertical direction showed a peak value at x/d = 5 (where x is the longitudinal distance from the nozzle and d is the nozzle diameter) and the sand concentration decreased linearly for x/d > 5. Experimental results showed that the turbulence level enhanced from the nozzle to x/d = 10. For sand–water wall jets with a higher concentration (c_o = 1.5–2.5%), the turbulence intensity became smaller than the corresponding single-phase wall jets by 34% due to turbulent modulation. A modified logarithmic formulation was introduced to model the longitudinal turbulent intensity at the centerline and along the axis of the jet.     

Iterative control of Görtler vortices via local wall deformations

Görtler vortices develop along concave walls as a result of the imbalance between the centrifugal force and radial pressure gradient. In this study, we introduce a simple control strategy aimed at reducing the growth rate of Görtler vortices by locally modifying the surface geometry in spanwise and streamwise directions. Such wall deformations are accounted in the boundary region equations by using a Prandtl transform of dependent and independent variables. The vortex energy is then controlled via a classical proportional control algorithm for which either the wall-normal velocity or the wall shear stress serves as the control variable. Our numerical results indicate that the control algorithm is quite effective in minimizing the wall shear stress.     

Effect of wall conditions on DDT in hydrogen–oxygen mixtures

Detonation in ducts is usually studied assuming adiabatic walls because of the high kinetic energy due to the incoming flow being supersonic. In the present work, numerical simulations of deflagration-to-detonation transition (DDT) using a detailed chemical reaction model are performed under adiabatic and isothermal boundary conditions in a tube with no-slip walls. The results show a local explosion driving DDT, which occurs near the tube wall in the case of an adiabatic wall, but close to the flame front in the case of an isothermal wall. Furthermore, to examine the effects of a turbulent boundary layer, a simulation using the Baldwin–Lomax turbulence model is carried out. In the case of the isothermal wall, there is again a local explosion near the tube wall, which leads to detonation. In summary, the present study confirms that the boundary conditions affect the transition to detonation and that the boundary layer is a key component of DDT.     

The effect of wall cooling on compressible Görtler vortices

It is known that in adiabatic boundary layer flow over a curved surface the detailed structure of the spanwise periodic Görtler vortex instability varies markedly over the range of spanwise wavelength. At short wavelengths the modes tend to be concentrated in a well-defined thin zone located within the boundary layer. As the vortex wavenumber diminishes so the region of vortex activity is first driven to the bounding wall but subsequently expands to cover the entire boundary layer at which stage the modes take on a principally inviscid form. At yet longer wavelengths the vortices are given by the solution of an interactive multi-deck structure which has some similarities with that for Tollmien–Schlichting waves.In this work we investigate how the application of wall cooling affects the above scenario. It is shown how cooling both restricts the range of mode types and gives rise to two new structures. The first, for moderate cooling and which relates to longer wavelengths, is interactive in nature. Here the viscous–inviscid interaction between an essentially inviscid Görtler problem, albeit for an effective basic flow which in its general form has a non-standard near-wall structure, and a viscous sublayer is provided by novel boundary conditions. Shorter wavelength vortices are largely unaffected by wall cooling unless this is quite severe. However when this degree of cooling is applied, the vortices take on a fully viscous form and are confined to a thin region next to the bounding wall wherein the basic flow assumes an analytic form. Numerical solutions are obtained and we provide evidence as to how the two new structures are related both to each other and to the previously known uncooled results.     

Control of Tollmien�CSchlichting instabilities by finite distributed wall actuation

Tollmien?CSchlichting waves are one of the key mechanisms triggering the laminar-turbulent transition in a flat-plate boundary-layer flow. By damping these waves and thus delaying transition, skin friction drag can be significantly decreased. In this simulation study, a wall segment is actuated according to a control scheme based on a POD-Galerkin model driven extended Kalman filter for state estimation and a model predictive controller to dampen TS waves by negative superposition based on this information. The setup of the simulation is chosen to resemble actuation with a driven compliant wall, such as a membrane actuator. Most importantly, a method is proposed to integrate such a localized wall actuation into a Galerkin model.     

Relation of entropy generation to wall ‘laws’ for turbulent flows

For non-dimensional pressure gradients sufficiently low and Reynolds numbers sufficiently high for the constant shear stress approximation to be valid at the first node of a turbulent wall layer computation, relationships for entropy generation rates are applied to popular wall ‘laws’. The resulting observations lead to a simple approach for evaluating the entropy generation rate per unit area in a computational fluid dynamics calculation for situations which satisfy this approximation.     

Variational principle of thermoelectroelasticity and its application to the problem of vibrations of a thin‐wall member

The dynamic behavior of thinwall members manufactured from materials with the pyroelectric effect was studied. A variational formulation of the problem is used, and a variational principle is formulated that differs from the wellknown one. Correct boundaryvalue problems describing the tension, compression, and bending of a thinwall pyroelectric member are constructed using the variational principle and a number of hypotheses on the distribution of the components of physical fields along the width of the member.     

The effect of sphere–wall interactions on particle motion in a viscoelastic suspension of FENE dumbbells

A new method for simulating the motion of particles in viscoelastic Boger fluids is extended to problems with bounded geometries. Viscoelasticity is incorporated into the Stokesian dynamics method by modeling a viscoelastic fluid as a suspension of finite-extension nonlinear-elastic (FENE) dumbbells. Wall–particle and wall–bead interactions are included by using the image system method of Blake; particle–particle and particle–bead interactions are also modified by the presence of the wall. The method of incorporating sphere–wall interactions is verified by doing calculations for several problems involving particle–wall interactions in Newtonian fluids. The method is then used to study particle–wall interactions in viscoelastic dumbbell suspensions by examining several problems of interest: the sedimentation of a spherical particle near vertical and tilted walls; the sedimentation of a nonspherical particle between two flat plates; and the migration of a neutrally buoyant sphere in plane Poiseuille flow. We find that a single sphere falling near a wall moves toward the wall and exhibits anomalous rotation. When the wall is tilted by an amount less than a few degrees, the sphere still moves toward the wall, but tilting the wall greater than an angle of approximately 1.5° results in the sphere falling away from the wall. A nonspherical particle settling in a channel exhibits an oscillatory motion, but ultimately becomes centered in the channel with its long axis parallel to gravity. Finally, it is shown that a neutrally buoyant sphere in plane Poiseuille flow migrates to the channel center in wide channels, but migrates to the walls when the sphere is sufficiently large relative to the channel width.     

DPIV, HPTV and visualization study of a vortex ring–moving wall interaction

This paper presents an experimental study of the interaction between a vortex ring and a moving wall. This type of flow can be considered as modeling, in a simplified way, the interaction between a "typical eddy" and the viscous sublayer of a turbulent boundary layer. In the present study, the vortex ring is considered as a three-dimensional (3D) perturbation of a viscous Stokes layer. The interaction was first characterized by visualization. To obtain quantitative information, digital particle image velocimetry (DPIV) and holographic particle-tracking velocimetry (HPTV) were used. These different techniques led to a precise and detailed characterization of the vortex ring alone and of an interaction in which a hairpin vortex is generated in the Stokes layer. The results obtained show a good similarity between the observed vortex ring and the Oseen model. They also validate the Stokes layer model and show that in the present conditions, the hairpin vorticity is comparable to that of the Stokes layer. The holographic study, which was undertaken to obtain full 3D three-component (3D3C) velocity maps, showed the present limitations of HPTV.     

Air–water flow in a vertical pipe: experimental study of air bubbles in the vicinity of the wall

This study deals with the influence of bubbles on a vertical air–water pipe flow, for gas-lift applications. The effect of changing the bubble size is of particular interest as it has been shown to affect the pressure drop over the pipe. Local measurements on the bubbles characteristics in the wall region were performed, using standard techniques, such as high-speed video recording and optical fibre probe, and more specific techniques, such as two-phase hot film anemometry for the wall shear stress and conductivity measurement for the thickness of the liquid film at the wall. The injection of macroscopic air bubbles in a pipe flow was shown to increase the wall shear stress. Bubbles travelling close to the wall create a periodic perturbation. The injection of small bubbles amplifies this effect, because they tend to move in the wall region; hence, more bubbles are travelling close to the wall. A simple analysis based on a two-fluid set of equations emphasised the importance of the local gas fraction fluctuations on the wall shear stress.     

The characteristics of gas–solid flow and wall heat transfer in a fluidized bed reactor

Numerical study using computational fluid dynamics has been carried out to investigate the heat transfer characteristics of a laboratory fluidized bed reactor. The fluidized bed reactor of vTI (Johann Heinrich von Thünen-Institute)-Institute of Wood Technology and Wood Biology is modeled. For the simulation of multiphase flow and thermal fields, an Eulerian–Eulerian approach is applied. The flow and thermal characteristics of the reactor are fully investigated for the wide range of superficial gas velocities and two different particle diameters. In particular, the contributions of the gas bubble and emulsion phase flows on the wall heat transfer are scrutinized. From the predicted results, it is fully elucidated that particular near-wall bubble motions mainly govern the wall heat transfer.     

Fluid–structure interaction of turbulent pulsatile flow within a flexible wall axisymmetric aortic aneurysm model

Pulsatile turbulent flow characteristics in an axisymmetric aortic aneurysm (AA) model were analyzed numerically using a simulated physiological waveform. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. A fully-coupled fluid–structure interaction (FSI) analysis was utilized in this work. We investigated the effects of turbulent flow characteristics on the distribution of wall stress and flow patterns in AA models. Wall stress distributions were calculated by computational solid stress (CSS) model, which ignores the effect of the blood flow, and the FSI model that takes into account flow and solid mechanics. Our results showed that peak wall stress and peak deformation were found to occur shortly after peak systolic flow in the FSI model and at the peak luminal pressure condition in the CSS model. Further, CSS model underestimated wall stress calculations when compared to the FSI model. There were also significant differences in the structure of flow fields between the flexible and rigid wall aneurysm models. Contour plots of kinetic energy dissipation and the application of the Kolmogorov microscale suggest that the conditions that result in red blood cell damage and platelet activation most likely occur in the near-wall region of AA during turbulent flow.     

What does an ideal wall look like?

This paper deals with the interface between a solid and an ideal gas. The surface of the solid is considered to be an ideal wall, if the flux of entropy is continuous, i.e., if the interaction between wall and gas is non-dissipative. The concept of an ideal wall is discussed within the framework of kinetic theory. In particular it is shown that a non-dissipative wall must be adiabatic and does not exerts shear stresses to the gas, if the interaction of a gas atom with the wall is not influenced by the presence of other gas atoms. It follows that temperature jumps and slip will be observed at virtually all walls, although they will be negligibly small in the hydrodynamic regime (i.e., for small Knudsen numbers).     

Combined phosphor and CARS thermometry at the wall–gas interface of impinging flame and jet systems

For the determination of surface normal temperature gradients, a generic system was built up consisting of two opposed, vertical nozzles impinging onto a flat, horizontal copper plate. From below, the plate was heated by non-reacting, turbulent air jets (Re = 5,000) and by a laminar flame (λ = 0.7, Re = 350), respectively. For well-defined boundary conditions, the plate was cooled by a turbulent cold jet from above in both cases. Wall temperature as well as gas temperature distributions within and outside of the thermal boundary layer of the hot side of the system were determined. The radial surface temperature profile of the plate was measured by coating it with thermographic phosphors (TP), materials whose phosphorescence decay time is dependent on their temperature. The TP was excited electronically by a frequency-tripled Nd:YAG laser (355 nm). The temporal decay of the phosphorescence intensity was measured pointwise by a photomultiplier tube. In this case, the 659 nm emission line of Mg₄FGeO₆:Mn was monitored. Non-intrusive point measurements of the gas temperature close to the surface were performed by rovibrational coherent anti-Stokes Raman spectroscopy (CARS) of diatomic nitrogen. Beams from a seeded, frequency-doubled Nd:YAG laser (532 nm) and from a modeless broadband dye laser (607 nm) were phase-matched into a surface-parallel, planar-boxcars configuration. The temperature data could be collected as close as 300 μm to the surface. Thermographic phosphors as well as CARS proved to be consistent for wall temperature and boundary layer measurements in all test cases. The results and challenges of this approach are discussed.     

The onset of Görtler vortices in laminar boundary layer flow over a slightly concave wall

The onset of convective instability in the laminar boundary layer over the slightly curved wall is analyzed theoretically and compared with the existing experimental data. A new set of stability equations are derived by the propagation theory considering the relative instability under the linear stability theory. In this analysis the disturbances are assumed to have the form of longitudinal vortices and also to grow themselves in streamwise direction. The critical position to mark the onset of Görtler instability is obtained as a function of the Görtler number, where disturbances at the critical state are mainly confined to the hydrodynamic boundary layer. Comparing the theoretical predictions with available experimental and other theoretical results, the present predictions follow experimental trends fairly well with slightly higher critical Görtler numbers than those from the local stability theory. The propagation theory commanding the local eigenvalue analysis is successful to obtain stability conditions reasonably in Görtler vortex problems, relaxing the limitations by the conventional analyses.     

Turbulent Couette–Poiseuille flow with zero wall shear

A particular pressure-driven flow in a plane channel is considered, in which one of the walls moves with a constant speed that makes the mean shear rate and the friction at the moving wall vanish. The Reynolds number considered based on the friction velocity at the stationary wall (u_τ,S) and half the channel height (h) is Re_τ,S = 180. The resulting mean velocity increases monotonically from the stationary to the moving wall and exhibits a substantial logarithmic region. Conventional near-wall streaks are observed only near the stationary wall, whereas the turbulence in the vicinity of the shear-free moving wall is qualitatively different from typical near-wall turbulence. Large-scale-structures (LSS) dominate in the center region and their spanwise spacing increases almost linearly from about 2.3 to 4.2 channel half-heights at this Re_τ,S. The presence of LSS adds to the transport of turbulent kinetic energy from the core region towards the moving wall where the energy production is negligible. Energy is supplied to this particular flow only by the driving pressure gradient and the wall motion enhances this energy input from the mean flow. About half of the supplied mechanical energy is directly lost by viscous dissipation whereas the other half is first converted from mean-flow energy to turbulent kinetic energy and thereafter dissipated.