Wall shape effects on multiphase flow in channels

Two-fluid flow is examined analytically and numerically for increased flow rates through a channel with surface roughness or branching or both. The viscosity and density ratios of the fluids are of order unity. There is much concern in terms of applications as well as fluid dynamical phenomena in configurations where one fluid is present only as a thin layer near an outer wall, leaving the other fluid occupying the channel core and part of a viscous wall layer. The interactive dynamics in both regions is studied and numerical and asymptotic analyses are performed. The major situations examined are: the flow to two symmetrically bifurcating daughters and the flow in a single channel over a rough wall, as well as a combination of the two situations. The principal phenomena of interest are conditions for flow reversal, the presence of upstream influence and the trajectories of the injected fluid as the density or viscosity ratio varies. Special relatively thin or thinning wall layers are produced when the core fluid viscosity increases or when the fluid travels downstream into a daughter vessel.     

Pulsatile flows and wall-shear stresses in models simulating normal and stenosed aortic arches

Pulsatile aqueous glycerol solution flows in the models simulating normal and stenosed human aortic arches are measured by means of particle image velocimetry. Three transparent models were used: normal, 25% stenosed, and 50% stenosed aortic arches. The Womersley parameter, Dean number, and time-averaged Reynolds number are 17.31, 725, and 1,081, respectively. The Reynolds numbers based on the peak velocities of the normal, 25% stenosed, and 50% stenosed aortic arches are 2,484, 3,456, and 3,931, respectively. The study presents the temporal/spatial evolution processes of the flow pattern, velocity distribution, and wall-shear stress during the systolic and diastolic phases. It is found that the flow pattern evolving in the central plane of normal and stenosed aortic arches exhibits (1) a separation bubble around the inner arch, (2) a recirculation vortex around the outer arch wall upstream of the junction of the brachiocephalic artery, (3) an accelerated main stream around the outer arch wall near the junctions of the left carotid and the left subclavian arteries, and (4) the vortices around the entrances of the three main branches. The study identifies and discusses the reasons for the flow physics’ contribution to the formation of these features. The oscillating wall-shear stress distributions are closely related to the featured flow structures. On the outer wall of normal and slightly stenosed aortas, large wall-shear stresses appear in the regions upstream of the junction of the brachiocephalic artery as well as the corner near the junctions of the left carotid artery and the left subclavian artery. On the inner wall, the largest wall-shear stress appears in the region where the boundary layer separates.     

The laminar boundary layer near a body corner point

A method is developed for calculating the characteristics of a laminar boundary layer near a body contour corner point, in the vicinity of which the outer supersonic stream passes through a rarefaction flow. In the study we use the asymptotic solution of the Navier-Stokes equations in the region with large longitudinal gradients of the flow functions for large values of the Reynolds number, the general form of which was used in [1].The pressure, heat flux, and friction distributions along the body surface are obtained. For small pressure differentials near the corner the solution of the corresponding equations for small disturbances is obtained in analytic form.The conventional method for studying viscous gas flow near body surfaces for large values of the Reynolds number is the use of the Prandtl boundary layer theory. Far from the body the asymptotic solution of the Navier-Stokes equations in the first approximation reduces to the solution of the Euler equations, while near the body it reduces to the solution of the Prandtl boundary layer equations. The characteristic feature of the boundary layer region is the small variation of the flow functions in the longitudinal direction in comparison with their variation in the transverse direction. However, in many cases this condition is violated.The necessity arises for constructing additional asymptotic expansions for the region in which the longitudinal and transverse variations of the flow functions are quantities of the same order. The general method for constructing asymptotic solutions for such flows with the use of the known method of outer and inner expansions is presented in [1].In the following we consider the flow in a laminar boundary layer for the case of a viscous supersonic gas stream in the vicinity of a body corner point. Behind the corner the flow separates from the body surface and flows around a stagnant zone, in which the pressure differs by a specified amount from the pressure in the undisturbed flow ahead of the point of separation. A pressure (rarefaction) disturbance propagates in the subsonic portion of the boundary layer upstream for a distance which in order of magnitude is equal to several boundary layer thicknesses. In the disturbed region of the boundary layer the longitudinal and transverse pressure and velocity disturbances are quantities of the same order. In this study we construct additional asymptotic expansions in the first approximation and calculate the distributions of the pressure, friction stress, and thermal flux along the body surface.     

Turbulent boundary layer on a mildly curved convex surface

Extensive single point turbulence measurements made in the boundary layer on a mildly curved heated convex wall show that the turbulence heat fluxes and Stanton number are more sensitive to a change in wall curvature than the Reynolds stresses and skinfriction coefficient, and that downstream, as the flow adjusts to new curved conditions, the St/c _f ratio of Reynolds analogy is appreciably lower than in plane wall flow for the same conditions. Details of the turbulence structure in unheated flow have been documented in an earlier paper; temperature field measurements now described comprise mean temperature distributions, the streamwise variation of wall heat flux, profiles of the temperature variance, transverse and streamwise heat fluxes, and triple correlations. Turbulent diffusion of heat flux is drastically reduced even by mild curvature; changes in the heat fluxes are of the same order as changes in the shear stress, that is, an order of magnitude greater than the ratio of boundary layer thickness to wall radius of curvature. The data include plane flow measurements taken in a developed boundary layer upstream of a change in wall curvature.     

Skin Friction following BLADE manipulation in a turbulent pipe flow

This study attempts to analyze the measured wall shear stress distribution downstream of single and tandem BLADEs in fully developed pipe flow. Previous works have indicated the adverse effect of overall drag increase with the single BLADE in both channel and pipe flows, and an even larger drag increase with the tandem BLADES. This is contrary to that observed for external boundary layer flow. Extensive comparisons are then made to the wall shear stress distribution following BLADEs in boundary layer flow, leading to the conclusion of little or no potential in the application of BLADEs alone to pipe flow.     

Reynolds number effects on a turbulent boundary layer with separation,reattachment, and recovery

The present paper addresses experimental studies of Reynolds number effects on a turbulent boundary layer with separation, reattachment, and recovery. A momentum thickness Reynolds number varies from 1,100 to 20,100 with a wind tunnel enclosed in a pressure vessel by varying the air density and wind tunnel speed. A custom-built, high-resolution laser Doppler anemometer provides fully resolved turbulence measurements over the full Reynolds number range. The experiments show that the mean flow is at most a very weak function of Reynolds number while turbulence quantities strongly depend on Reynolds number. Roller vortices are generated in the separated shear layer caused by the Kelvin–Helmholtz instability. Empirical Reynolds number scalings for the mean velocity and Reynolds stresses are proposed for the upstream boundary layer, the separated region, and the recovery region. The inflectional instability plays a critical role in the scaling in the separated region. The near-wall flow recovers quickly downstream of reattachment even if the outer layer is far from an equilibrium state. As a result, a stress equilibrium layer where a flat-plate boundary layer scaling is valid develops in the recovery region and grows outward moving downstream.     

FLOW VISUALIZATION AROUND A CIRCULAR CYLINDER NEAR TO A PLANE WALL

Flow visualization, particle image velocimetry and hot-film anemometry have been employed to study the fluid flow around a circular cylinder near to a plane wall for Reynolds numbers, based on cylinder diameter, between 1200 and 4960. The effect of changing the gap between the cylinder and the wall, G, from G=0 (cylinder touching the wall) to G/D=2, was investigated. It is shown that the flow may be characterized by four distinct regions. (a) For very small gaps, G/D≤0·125, the gap flow is suppressed or extremely weak, and separation of the boundary layer occurs both upstream and downstream of the cylinder. Although there is no regular vortex shedding, there is a periodicity associated with the outer shear-layer. (b) In the “small gap ratio” region, 0·125<G/D<0·5, the flow is very similar to that for very small gaps, except that there is now a pronounced pairing between the inner shear-layer shed from the cylinder and the wall boundary layer. (c) Intermediate gap ratios, 0·5<G/D<0·75, are characterized by the onset of vortex shedding from the cylinder. (d) For the fourth region, characterized by the largest gap ratios considered, G/D>1·0, there is no separation of the wall boundary layer, either upstream or downstream of the cylinder.     

Particle-image velocimetry measurements of flow over interacting barchan dunes

Barchan dunes are crescentic planform-shaped dunes that are present in many natural environments, and may occur either in isolation or in groups. This study uses high-resolution particle-image velocimetry (PIV) experiments using fixed-bed models to examine the effects of barchan dune interaction upon the flow field structure. The barchan dune models were created from an idealized contour map, the shape and dimensions of which were based upon previous empirical studies of dune morphology. The experimental setup comprised two, co-axially aligned, barchan dune models that were spaced at different distances apart. In this paper, two volumetric ratios (V _r, upstream dune: downstream dune) of 1.0 and 0.175 were examined. Models were placed in a boundary-layer wind tunnel and flow quantification was achieved via PIV measurements of the mean and turbulent flow field in the streamwise–wall-normal plane, along the centerline of the barchan(s), at an average flow Reynolds number of 59,000. The presence of an upstream barchan dune induces a “sheltering effect” on the flow. Flow on the stoss side of the downstream dune is controlled by the developing internal boundary layer from the upstream dune, as well as by the turbulent flow structures shed from the free shear layer of the upstream dune leeside. At both volumetric ratios, enhanced turbulence is present over the downstream barchan dune leeside, which is proposed to be caused by the interaction of shear layers from the upstream and downstream dunes. Both the size and magnitude of the shear layer formed in the leeside of the upstream dune control this interaction, together with the proximity of this shear layer to the stoss side of the downstream dune. Proper orthogonal decomposition (POD) analysis shows that the distribution of turbulent kinetic energy is shifted to higher modes (i.e., smaller spatial scales) over interacting barchan dunes, which also reflects the role of the leeside free shear layer in dominating the flow field by generation, or redistribution, of TKE to smaller scales.     

弯曲动脉的血流动力学数值分析

利用计算流体力学的理论和方法对弯曲动脉中的血流动力学进行数值分析，是研究心血管疾病流体动力学机理的一种行之有效的方法。本文将升主动脉、主动脉弓和降主动脉联系起来作为弯曲动脉几何模型，给出了血液流动的边界条件以及计算条件。根据生理脉动流条件，对狗的弯曲动脉几何模型内发展中的血液流动进行了有限元数值模拟，并利用可视化方法对血液流动的轴向速度、二次流、壁面切应力等计算结果进行了分析。研究结果表明，在弯管内侧壁处，同时存在主流方向和二次流方向的回流，此处容易形成涡流。弯管内侧壁比外侧壁的壁面切应力具有更强的脉动性。     

Low Reynolds number axisymmetric turbulent boundary layer on a cylinder

In the present study, an axisymmetric turbulent boundary layer growing on a cylinder is investigated experimentally using hot wire anemometry. The combined effects of transverse curvature as well as low Reynolds number on the mean and turbulent flow quantities are studied. The measurements include the mean velocity, turbulence intensity, skewness and flatness factors in addition to wall shear stress. The results are presented separately for the near wall region and the outer region using dimensionless parameters suitable for each case. They are also compared with the results available in the open literature.The present investigation revealed that the mean velocity in near wall region is similar to other simple turbulent flows (flat plate boundary layer, pipe and channel flows); but it differs in the logarithmic and outer regions. Further, for dimensionless moments of higher orders, such as skewness and flatness factors, the main effects of the low Reynolds number and the transverse curvature are present in the near wall region as well as the outer region.     

A plane turbulent wall jet on a fully rough surface

The mean velocity field and skin friction characteristics of a plane turbulent wall jet on a smooth and a fully rough surface were studied using Particle Image Velocimetry. The Reynolds number based on the slot height and the exit velocity of the jet was Re = 13,400 and the nominal size of the roughness was k = 0.44 mm. For this Reynolds number and size of roughness element, the flow was in the fully rough regime. The surface roughness results in a distinct change in the shape of the mean velocity profile when scaled in outer coordinates, i.e. using the maximum velocity and outer half-width as the relevant velocity and length scales, respectively. Using inner coordinates, the mean velocity in the lower region of the inner layer was consistent with a logarithmic profile which characterizes the overlap region of a turbulent boundary layer; for the rough wall case, the velocity profile was shifted downward due to the enhanced wall shear stress. For the fully rough flow, the decay rate of the maximum velocity of the wall jet is increased, and the skin friction coefficient is much larger than for the smooth wall case. The inner layer is also thicker for the rough wall case. The effects of surface roughness were observed to penetrate into the outer layer and slightly enhance the spread rate for the outer half-width, which was not observed in most other studies of transitionally rough wall jet flows.     

Flow field investigation in rotating rib-roughened channel by means of particle image velocimetry

The turbulent velocity field over the rib-roughened wall of an orthogonally rotating channel is investigated by means of two-dimensional particle image velocimetry (PIV). The flow direction is outward, with a bulk Reynolds number of 1.5 × 10⁴ and a rotation number ranging from 0.3 to 0.38. The measurements are obtained along the wall-normal/streamwise plane at mid-span. The PIV system rotates with the channel, allowing to measure directly the relative flow velocity with high spatial resolution. Coriolis forces affect the stability of the boundary layer and free shear layer. Due to the different levels of shear layer entrainment, the reattachment point is moved downstream (upstream) under stabilizing (destabilizing) rotation, with respect to the stationary case. Further increase in rotation number pushes further the reattachment point in stabilizing rotation, but does not change the recirculation length in destabilizing rotation. Turbulent activity is inhibited along the leading wall, both in the boundary layer and in the separated shear layer; the opposite is true along the trailing wall. Coriolis forces affect indirectly the production of turbulent kinetic energy via the Reynolds shear stresses and the mean shear. Two-point correlation is used to characterize the coherent motion of the separated shear layer. Destabilizing rotation is found to promote large-scale coherent motions and accordingly leads to larger integral length scales; on the other hand, the spanwise vortices created in the separating shear layer downstream of the rib are less organized and tend to be disrupted by the three-dimensional turbulence promoted by the rotation. The latter observation is consistent with the distributions of span-wise vortices detected in instantaneous flow realizations.     

A Two-Layer Mathematical Model of Blood Flow in Porous Constricted Blood Vessels

In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian fluid. The wall of porous constricted blood vessel configured as thin transition Brinkman layer over layered by Darcy region. The boundary of fluid layer is defined as stress jump condition of Ocha-Tapiya and Beavers–Joseph. In this paper, we obtained an analytic expression for velocity, flow rate, wall shear stress. The effect of permeability, plasma layer thickness, yield stress and shape of the constriction on velocity in core & peripheral region, wall shear stress and flow rate is discussed graphically. This is found throughout the discussion that permeability and plasma layer thickness have accountable effect on various flow parameters which gives an important observation for diseased blood vessels.     

Analysis of turbulent near-wake development behind an infinitely yawed flat plate

An asymptotic analysis of the turbulent near-wake flow behind an infinitely yawed flat plate with sharp trailing edge has been formulated. The feature that the near-wake which is dominated by mixing of oncoming turbulent boundary layers, retains to a large extent the memory of the turbulent structure of the upstream boundary layer has been exploited to develop the analysis. This analysis leads to three regions of wake flow (the inner near-wake, the outer near-wake and the far-wake) for which the governing equations are derived. The matching conditions amongst these regions lead to logarithmic variations for both the components (i.e. components perpendicular to and along the trailing edge) of velocity vector in both normal and downstream directions in the overlapping region surrounding the inner near-wake. These features are validated by the available experimental data. Similarity solutions for both the components of the velocity vector (which satisfy the required matching conditions) in the inner near-wake and outer near-wake regions have been obtained by making appropriate eddy-viscosity assumptions. Uniformly valid solutions for both the components of the velocity vector have been constructed for the near-wake. The solutions show good agreement with available experimental data.     

Numerical simulation of the transition from adhesion to slip with friction in generalized Newtonian Poiseuille flow

The axisymmetric Poiseuille flow of a purely viscous generalized Newtonian fluid under rate of flow controlled conditions is studied with a change in the boundary conditions at a transition point from an adhesive to a slip condition with friction at the wall. The friction law used originates from an experimental study by (J.M. Piau and N. El Kissi, J. Non-Newtonian Fluid Mech. 54 (1994) 121–142) using a capillary made of steel and a silicone fluid, and is based also on a molecular dynamics theory by (Yu. B. Chernyak, A.I. Leonov, Wear, 108 (1986) 105–138). It gives a non-linear multivalued dependance of the wall shear stress to the velocity at the wall. Moreover, wall shear stress values may become smaller than values obtained when adhesion prevails in the capillary. The shear stress must over-step some limiting stress level to trigger the wall slip. After checking slip boundary condition implementation for the case of Poiseuille flow with slip along the entire wall, the convergence and the validity of the computation was studied. Important morphologic changes of the flow field and the stress field appear around the transition point from adhesion to slip boundary condition. Slip at the wall allows the principal stress difference to be drastically reduced, except in the vicinity of the transition point where this difference is maximum. A peak in shear stress located upstream of the transition, and a peak in elongational stress located downstream of the transition, are observed at the wall. Fully developed near plug-like flows are obtained within about 1D only downstream of the transition point. It is concluded that the effect of slip on extrudates distorsion should appear clearly even when the exit slippery zone is reduced to 1D.     

The effects of wall roughness on the separated flow over a smoothly contoured ramp

Experimental measurements address the effects on a turbulent boundary layer of wall roughness on a flat plate and a ramp that produces a separation bubble over the ramp trailing edge. A fully rough flow condition is achieved on the upstream flat plate. The main effect of the wall roughness on the outer layer turbulence on a flat plate is to change the friction velocity. The separation region is substantially larger for the rough-wall case. The rough-wall boundary layer turbulence is less sensitive to the onset of an adverse pressure gradient over the ramp, producing substantially smaller Reynolds stress peaks in upstream flat-plate, wall-unit coordinates.     

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.     

Effect of a Thin Longitudinal Inviscid Vortex on a Two-Dimensional Pre-Separation Boundary Layer

For large Reynolds numbers, an asymptotic solution of the Navier-Stokes equations describing the effect of a thin longitudinal vortex with a constant circulation on the development of an incompressible steady two-dimensional laminar boundary layer on a flat plate is obtained. It is established that, in a narrow wall region extending along the vortex filament, the viscous flow is described by the 3-D boundary layer equations. A solution of these equations for small values of the vortex circulation is studied. It is found that the solution of the two-dimensional pre-separation boundary layer equations collapses. This is attributable to the singular behavior of the 3-D disturbances near the zero-longitudinal-friction points.     

An experimental-based model for prediction of flow noise with drag reducing polymers

The drag reduction characteristics of certain high molecular weight polymers have been studied by various investigators. Because of the polymer’s ability to reduce turbulent shear stress and dependence of the boundary layer wall pressure spectral amplitude on the shear stress, polymer has the potential to suppress noise and vibration caused by the boundary layer unsteady pressures. Compared to its effect on drag reduction, polymer additive effects on turbulent boundary layer (TBL) wall pressure fluctuations have received little attention. Kadykov and Lyamshev [Sov. Phys. Acoust. 16 (1970) 59], Greshilor et al. [Sov. Phys. Acoust. 21 (1975) 247] showed that drag reducing polymer additives do indeed reduce wall pressure fluctuations, but they have not established any scaling relationship which effectively collapse data. Some effort has been made by Timothy et al. [JASA 108 (1) (2000) 71] at Penn State University to develop a scaling relationship for TBL wall pressure fluctuations that are modified by adding drag reducing polymer to pure water flow. This paper presents a theoretical model based on the work of the Timothy et al. team at ARL, Penn State University. Through this model one can estimate, reduction in TBL flow induced noise and vibration for rigid smooth surfaces due to release of drag reducing polymers in boundary layer region. Using this theoretical model, flow noise as experienced by a typical flush mounted hydrophone has been estimated for a smooth wall plate as a function of polymer additive concentration. Effect of non-dimensionalisation of the wall pressure fluctuations frequency spectra with traditional outer, inner and mixed flow variables will also be addressed in the paper. The paper also covers a model based on molecular relaxation time in polymer additives which not only reduce drag but also flow induced noise up to certain polymer concentration.