Turbulent Channel Flow with an Artificial Two-Dimensional Wall Layer

Turbulent flow of an incompressible fluid in a plane channel with parallel walls is considered. The three-dimensional time-dependent Navier-Stokes equations are solved numerically using the spectral finite-difference method. An artificial force which completely suppresses lateral oscillations of the velocity is introduced in the near-wall zone (10 % of the channel half-width in the neighborhood of each wall). Thus, the three-dimensional flow zone, in which turbulent oscillations can develop, is separated from the wall by a fluid layer. It is found that the elimination of three-dimensionality in the neighborhood of the walls leads to a significant reduction in the drag. However, complete laminarization does not occur. The flow in the stream core remains turbulent and can be interpreted as a turbulent flow in a channel with walls located on the boundary of the two-dimensional layer and traveling at the local mean-flow velocity. The oscillations developing inside the two-dimensional layer, which have significant amplitude, distort the flow only in the adjacent zone. Beyond this zone the distributions of the mean characteristics and the structure of instantaneous fields completely correspond to ordinary turbulent flow in a channel with rigid walls. The results obtained confirm the hypothesis of the unimportance of the no-slip boundary conditions for the fluctuating velocity component in the mechanism of onset and self-maintenance of turbulence in wall flows.     

Effect of heat flux on boundary layer flow under rotating conditions

The boundary layer flow behaviour in a smooth rotating channel with heated walls is measured by particle image velocimetry (PIV). To simulate the real operation environment of an internal coolant channel in a turbine blade, airflow is analysed in a rotating channel, whose four walls are uniformly heated by Indium Tin Oxide (ITO) glass. The flow is measured in the middle plane of the rotating channel with a Reynolds number equal to 10000 and rotation numbers ranging from 0 to 0.52. The results are presented for the boundary layer flow behaviour with and without heated thermal boundary conditions. The buoyancy force generated by the heated walls influences the flow behaviour under rotating conditions. Separated flow occurs, which substantially influences the turbulent flow behaviours. Sometimes, this buoyancy force can determine the flow behaviours. The results also showed that the displacement thickness and the momentum loss thickness present new changes at different radius positions due to the heated thermal boundary conditions. The displacement thicknesses of both the leading and trailing sides with heated walls are both thicker than those of the leading and trailing sides without heated walls. Then, the difference of the boundary layer thickness between these two cases increases with the increase of rotation number. For momentum loss thickness, a sharp drop happens when the rotation number increases to a certain value. At the large radius position, the drop in momentum loss thickness is much greater than that in the small radius position.     

PIV study on a shock-induced separation in a transonic flow

A transonic interaction between a steady shock wave and a turbulent boundary layer in a Mach 1.4 channel flow is experimentally investigated by means of particle image velocimetry (PIV). In the test section, the lower wall is equipped with a contour profile shaped as a bump allowing flow separation. The transonic interaction, characterized by the existence in the outer flow of a lambda shock pattern, causes the separation of the boundary layer, and a low-speed recirculating bubble is observed downstream of the shock foot. Two-component PIV velocity measurements have been performed using an iterative gradient-based cross-correlation algorithm, providing high-speed and flexible calculations, instead of the classic multi-pass processing with FFT-based cross-correlation. The experiments are performed discussing all the hypotheses linked to the experimental set-up and the technique of investigation such as the two-dimensionality assumption of the flow, the particle response assessment, the seeding system, and the PIV correlation uncertainty. Mean velocity fields are presented for the whole interaction with particular attention for the recirculating bubble downstream of the detachment, especially in the mixing layer zone where the effects of the shear stress are most relevant. Turbulence is discussed in details, the results are compared to previous study, and new results are given for the turbulent production term and the return to isotropy mechanism. Finally, using different camera lens, a zoom in the vicinity of the wall presents mean and turbulent velocity fields for the incoming boundary layer.     

Interaction of surface radiation with conjugate mixed convection from a vertical channel with multiple discrete heat sources

Important results of a numerical study performed on combined conduction–mixed convection–surface radiation from a vertical channel equipped with three identical flush-mounted discrete heat sources in its left wall are provided here. The channel has walls of identical height with the spacing varied by varying its aspect ratio (AR). The cooling medium is air that is considered to be radiatively transparent. The heat generated in the channel gets conducted along its walls before getting dissipated by mixed convection and radiation. The governing equations for fluid flow and heat transfer are considered without boundary layer approximations and are transformed into vorticity–stream function form and are later normalized. The resulting equations are solved, along with relevant boundary conditions, making use of the finite volume method. The computer code written for the purpose is validated both for fluid flow and heat transfer results with those available in the literature. Detailed parametric studies have been performed and the effects of modified Richardson number, surface emissivity, thermal conductivity and AR on various pertinent results have been looked into. The significance of radiation in various regimes of mixed convection has been elucidated. The relative contributions of mixed convection and radiation in carrying the mandated cooling load have been thoroughly explored.     

Thin shear boundary layers in flow of hot aluminium

The flow of hot aluminium in channels is investigated. The constitutive relation considered for the flow stress is the inverse hyperbolic sine function of the Zener–Hollomon parameter. Analytical solutions for the flow are derived. At high strain rates, an exponential velocity profile close to the channel walls is predicted indicating the existence of a thin shear boundary layer characterized by strong shear. The characteristic length scale for the exponential velocity profile is a function of material parameters in the constitutive relation and the inverse of the local pressure gradient. The analytical prediction of a thin shear boundary layer close to the channel walls for large strain rates is consistent with the observed microstructure in an extruded section.     

Rotational inviscid flow with circulation zones in a channel of variable cross section

The development of the theory of rotational motion of inviscid fluids for the purposes of describing channel flow encounters certain difficulties in connection with the appearance of viscosity effects near the walls. In the potential-rotational model [1], in which the vorticity is nonzero only in a closed circulation zone surrounded by potential flow, it is assumed that the separation and attachment points are known in advance. For example, for flow around a cavity these points coincide with the extreme corner points of the contour. The problem of determining the vorticity in a closed zone for the potential-rotational model has been investigated in a number of studies [2, 3], etc. In the case of an incompressible fluid the vorticity in the circulation zone is constant for two-dimensional flow and proportional to the distance from the axis for axisymmetric flow. The value of the constant is found from the steady-state condition for the adjoining viscous layers. If the channel walls have a smooth profile without corner points, then for determining the boundaries of the circulation zones additional conditions must be used. This study employs another scheme, in which the vorticity is formed outside the region of flow and in a particular problem is specified in the form of a boundary condition. An analytic solution describing the rotational flow of an inviscid fluid in a channel with a slightly varying cross section is obtained. Three types of entrance flow nonuniformity are considered: 1) uniform shear flow, 2) wake-type flow, and 3) potential flow with a narrow wall boundary layer. Streamline patterns with circulation zones are constructed for flows in diffuser channels with the above-mentioned types of entrance nonuniformity. A model of flow separation in a channel with a turbulent boundary layer on the walls is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 31–37, March–April, 1985.In conclusion the author wishes to thank E. Yu. Shal'man, A. N. Kraiko, and A. B. Vatazhin for useful discussions and advice.     

Numerical study of particulate suspension flow through wavy‐walled channels

The particulate suspension flow in a channel whose walls describe a travelling wave motion is examined numerically. A perturbation method is employed and the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first‐order perturbation quantities are numerically determined by solving the governing system of ordinary differential equations by shooting technique. The present approach does not impose any restriction on the Reynolds number of the flow and the wave number and frequency of the wavy‐walled channel, although it is limited by the linear analysis. The wall shear stress and the positions of flow separation and reattachment points are computed and the influence of the volume fraction density of the particles is examined. The variations of velocity and pressure of the particulate suspension flow with frequency of excitation are also presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Molecular dynamics simulation of liquid argon flow at platinum surfaces

The micro Poiseuille flow for liquid argon flowing in a nanoscale channel formed by two solid walls was studied in the present paper. The solid wall material was selected as platinum, which has well established interaction potential. We consider the intermolecular force not only among the liquid argon molecules, but also between the liquid argon atoms and the solid wall particles, therefore three regions, i.e. the liquid argon computation domain, the top and bottom solid wall regions are included for the force interaction. The present MD (Molecular Dynamics) simulation was performed without any assumptions at the wall surface. The objective of the study is to find how the flow and the slip boundaries at the wall surface are affected by the applied gravity force, or the shear rate. The MD simulations are performed in a nondimensional unit system, with the periodic boundary conditions applied except in the channel height direction. Once the steady state is reached, the macroscopic parameters are evaluated using the statistical mechanics approach. For all the cases tested numerically in the present paper, slip boundaries occur, and such slip velocity at the stationary wall surface increases with increasing the applied gravity force, or the shear rate. The slip length, which is defined as the distance that the liquid particles shall travel beyond the wall surfaces to reach the same velocity as the wall surface, sharply decreases at small shear rate, then slightly decreases with increasing the applied shear rate. We observe that the liquid viscosity remains nearly constant at small shear rates, and the Newtonian flow occurs. However, with increasing the shear rate, the viscosity increases and the non-Newtonian flow appears.     

Peristaltic motion of a power-law fluid in an asymmetric channel

The flow of a power-law fluid is investigated in an asymmetric channel caused by the movement of peristaltic waves with the same speed but with different amplitudes and phases on the flexible walls of the channel. The differential equation governing the flow is non-linear and can admit non-unique solutions. There exist two different physically meaningful solutions one satisfying the boundary conditions at the upper wall and the other at the lower wall. The effects of the power-law nature of the fluid on the pumping characteristics and axial velocity are studied in detail.     

Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field

The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is driven by the expanding or contracting walls with different permeability. The velocities of the asymmetric flow at the upper and lower walls are different in not only the magnitude but also the direction. The asymptotic solutions are well constructed with the method of boundary layer correction in two cases with large Reynolds numbers, i.e., both walls of the channel are with suction, and one of the walls is with injection while the other one is with suction. For small Reynolds number cases, the double perturbation method is used to construct the asymptotic solution. All the asymptotic results are finally verified by numerical results.     

Study of laminar separation in the vicinity of the point of piecewise-constant pressure distribution over the wall

A family of two-dimensional divergent channels with piecewise-constant velocity and pressure distributions over the wall is considered. The method of matched asymptotic expansions is applied to study the two-dimensional viscous incompressible flow at high but subcritical Reynolds numbers in the vicinity of a pressure jump point on the channel wall. It is shown that if the pressure difference is of the order O(Re^?1/4), then in the vicinity of this point a classical region of interaction between the viscous boundary layer on the wall and the outer inviscid flow occurs. The problem formulated for the interaction region is solved numerically. The asymptotic values of the pressure difference corresponding to separationless flow are determined and the separation flow patterns are constructed.     

Stability of two-layer fluid flow

The problem of two-layer convective flow of viscous incompressible fluids in a horizontal channel with solid walls in the presence of evaporation is considered in the Oberbeck–Boussinesq approximation assuming that the interface is an undeformable thermocapillary surface and taking into account the Dufour effect in the upper layer which is a mixture of gas and liquid vapor. The effects of longitudinal temperature gradients at the boundaries of the channel and the thicknesses of the layer on the flow pattern and the evaporation rate are studied under conditions of specified gas flow and the absence of vapor flow on the upper boundary of the channel. It is shown that the long-wavelength asymptotics for the decrement is determined from the flow characteristics, the longwavelength perturbations occurring in the system decay monotonically, and the thermal instability mechanism is not potentially the most dangerous.     

Laminar flow and heat transfer in a periodically converging-diverging channel

A finite difference solution for laminar viscous flow through a sinusoidally curved converging-diverging channel is presented. The physical wavy domain is transformed into a rectangular computational domain in order to simplify the application of boundary conditions on the channel walls. The discretized conservation equations for mass, momentum and energy are derived on a control volume basis. The pseudo-diffusive terms that arise from the co-ordinate transformation are treated as source terms, and the resulting system of equations is solved by a semi-implicit procedure based on line relaxation. Results are obtained for both the developing and the fully developed flow for a Prandtl number of 0.72, channel maximum width-to-pitch ratio of 1.0, Reynolds number ranging from 100 to 500 and wall amplitude-to-pitch ratio varying from 0.1 to 0.25. Results are presented here for constant fluid properties and for a prescribed wall enthalpy only.     

Effect of finite cavity width on flow oscillation in a low-Mach-number cavity flow

The current study is focused on examining the effect of the cavity width and side walls on the self-sustained oscillation in a low Mach number cavity flow with a turbulent boundary layer at separation. An axisymmetric cavity geometry is employed in order to provide a reference condition that is free from any side-wall influence, which is not possible to obtain with a rectangular cavity. The cavity could then be partially filled to form finite-width geometry. The unsteady surface pressure is measured using microphone arrays that are deployed on the cavity floor along the streamwise direction and on the downstream wall along the azimuthal direction. In addition, velocity measurements using two-component Laser Doppler Anemometer are performed simultaneously with the array measurements in different azimuthal planes. The compiled data sets are used to investigate the evolution of the coherent structures generating the pressure oscillation in the cavity using linear stochastic estimation of the velocity field based on the wall-pressure signature on the cavity end wall. The results lead to the discovery of pronounced harmonic pressure oscillations near the cavity’s side walls. These oscillations, which are absent in the axisymmetric cavity, are linked to the establishment of a secondary mean streamwise circulating flow pattern near the side walls and the interaction of this secondary flow with the shear layer above the cavity.     

Experimental study of the effects of spanwise rotation on the flow in a low aspect ratio diffuser for turbomachinery applications

Two dimensional time accurate PIV measurements of the flow between pressure and suction side at different spanwise positions of a rotating channel are presented. The Reynolds and Rotation numbers are representative for the flow in radial impellers of micro gas turbines. Superposition of the 2D results at the different spanwise positions provides a quasi-3D view of the flow and illustrates the impact of Coriolis forces on the 3D flow structure. It is shown that the inlet flow is little affected by rotation. An increasing/decreasing boundary layer thickness is reported on the suction/pressure side wall halfway between the channel inlet and outlet. The turbulence intensity moves away from the suction side wall and remains close to the pressure side wall. The instantaneous measurements at mid-height of the rotating channel reveal the presence of hairpin vortices in the pressure side boundary layer and symmetric vortices near the suction side. Hairpin vortices occur in rotation in the pressure and in the suction side, for the measurement plane close to the channel bottom wall.     

Apparent wall slip velocity measurements in free surface flow of concentrated suspensions

In this work we have experimentally measured the apparent wall slip velocity in open channel flow of neutrally buoyant suspension of non-colloidal particles. The free surface velocity profile was measured using the tool of particle imaging velocimetry (PIV) for two different channels made of plane and rough walls. The rough walled channel prevents wall slip, whereas the plane wall showed significant wall slip due to formation of slip layer. By comparing the velocity profiles from these two cases we were able to determine the apparent wall slip velocity. This method allows characterization of wall slip in suspension of large sized particles which cannot be performed in conventional rheometers. Experiments were carried out for concentrated suspensions of various particle volume concentrations and for two different sizes of particles. It was observed that wall slip velocity increases with particle size and concentration but decreases with increase in the viscosity of suspending fluid. The apparent wall slip velocity coefficients are in qualitative agreement with the earlier measurements. The effect of wall slip on free surface corrugation was also studied by analyzing the power spectral density (PSD) of the refracted light from the free surface. Our results indicate that free surface corrugation is a bulk flow response and it does not arise from boundary problem such as development of slip layer.     

Boundary layer interaction in three-dimensional flows

An approach known from the theory of matched asymptotic expansions involving the isolation of subregions with different scales is used to study flows which are assumed to be described by the boundary layer equations almost everywhere near the surface except for a fairly narrow zone in which the inflowing boundary layers interact. Two characteristic types of interaction are identified. An approximate theory describing the flow in the interaction zone, which makes it possible to locate the position of the interaction zone on the surface, is proposed. The interaction flow on the end wall of a vane channel is calculated subject to certain simplifications. The results of an experimental investigation of this flow are presented and it is shown that the theoretical model proposed describes the three-dimensional corner separation which occurs in the neighborhood of the line of intersection of the end wall and the convex edge of the vane.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 116–123, May–June, 1988.     

Effect of wall friction and vortex generation on the radial distribution of different phases

Arguments are presented to prove the existence of rolling vortices in single-phase and two-phase flow. In the liquid phase, they appear in a boundary layer near a wall while in the continuous vapor phase they occur near the interface with a liquid film. The intensity and size of these vortices depend on the local velocity gradients normal to the wall. The interaction between the rotational field associated with such vortices and bubbles in liquid flow or droplets in vapor flow is discussed. This interaction may be called the wall-vortex effect. It appears that several, apparently unrelated, phenomena observed in two-phase flow systems may be interpreted in terms of this mechanism. Among these are: (i) radial void peaking near the walls (ii) vapor velocities less than liquid velocity observed also in vertical upward flow (iii) reduced droplet diffusion near the liquid film and (iv) reduced vapor mixing between subchannels at low steam qualities. The cause of secondary flows in non-circular channels may also be explained in terms of rolling vortices near the walls. Finally, a comparison is made with the well known Magnus effect.     

Jeffrey-Hamel flow of Leslie-Ericksen nematic liquids

A similarity solution of the Leslie-Ericksen equations for nematic liquid crystals is obtained for flow between converging and diverging planar walls (Jeffrey-Hamel flow). There are three regions in the flow: extensional or compressional flow near the centerline, shear near the wall, and a wall boundary layer in which elastic stresses control the transition from the wall-induced orientation to the bulk behavior. The boundary layer thickness is obtained in closed form; the scaling with the Ericksen number depends on whether or not the boundary layer extends into the region of extensional flow. Imposition of a magnetic field with an azimuthal component in a converging flow can result in a Freedericksz-like transition from radial to transverse orientation at the center line at a critical field strength. This transition provides a new means to measure the irrotational viscosity λ₂.