Pattern analysis of viscous oscillation in a shear flow induced by an exothermic reaction

An investigation is made of oscillatory phenomenon induced by an exothermic reaction. This oscillatory phenomenon occurs in a very thin mixing layer between two miscible and reacting fluids. A qualitative model based on the interaction among reaction, molecular momentum transfer, molecular heat transfer, molecular mass transfer and forced convective transfer was proposed by Kuroda and Ogawa [1994. Nonlinear waves in a shear flow with a diffusive exothermic reaction and its qualitative reasoning. Chem. Eng. Sci. 49(16), 2699-2708]. It is experimentally shown in the present study that the oscillatory patterns change in the flow direction. In the upstream area where oscillatory patterns are nearly straight stripes, effects of viscosity on those stripes are investigated. In the downstream area where stripes are wavy and disordered, fractal analysis is introduced to investigate the relationship between the transition of oscillatory flow patterns and process factors, i.e. the viscosity ratio, the entire viscosity, flow rate and the flow rate ratio. Fractal analysis is also applied to temperature oscillation, and it is confirmed that the characteristic patterns of oscillation become obscure as the entire viscosity increases. The entire viscosity is an important factor for controlling both oscillatory patterns of flow and temperature in this reactive flow system.     

Wall pressure and shear stress measurements beneath an impinging jet

This paper presents comprehensive measurements of wall pressure and surface shear stress beneath a plane, two-dimensional, turbulent jet impinging normally onto a flat surface. The results cover a wider range of Reynolds number and ratio of impingement height (H) to nozzle gap (D) than do previous studies. The pressure distributions are nearly Gaussian, independent of Reynolds number, and closely balance the momentum flux from the jet nozzle as H/D varies. Particular attention was paid to probe size in measuring the wall shear stress because this has a significant effect on the results. A range of Preston tubes and Stanton probes were tested from which it was found that a 0.05-mm-high Stanton probe—the smallest that we could make—appeared to give accurate results. As expected, the shape of the wall shear stress distributions depended both on H/D and on Reynolds number. Furthermore, the relation between wall pressure and shear stress from Hiemenz's theoretical solution for stagnation flow is not in agreement with the results. It is postulated that the discrepancy is due to the relatively high free-stream turbulence level in the jet. Future papers will document the mean flow field and turbulence and the time dependence of the surface pressure.     

On the measurement of normal stress differences in steady shear flow

Summary Compared to the similar pressure-distribution cone-and-plate apparatus of Adams and Lodge (4), the new apparatus' improvements include: temperature control of the cone (as well as the plate); increased stiffening of the frame; four (not three) pressuremeasuring holes in the cone/plate region; inclusion of a pressure-measuring hole on the axis under the cone truncation; exclusive use of a vertical free liquid boundary at the cone rim (without a sea of liquid). Temperature control of the rotating cone and of the fixed plate leads to acceptable temperature uniformity in the test liquid for working temperatures within 10°C or 20°C of ambient; the corresponding interval is about 1°C if the cone temperature control is abandoned. Pressure gradients measured using a Newtonian liquid agree with those calculated using Walters' eq. (3). For a viscoelastic liquid, after subtracting inertial contributions, pressure distributions measured at a given shear rate in the cone/plate region do not change when the gap angle is changed from 2° to 3°, showing that the effects of secondary flow are negligible. Values ofN ₃ =N ₁ + 2N ₂ obtained from the gradients of these distributions are believed to be in error by not more than ±1 Pa, in favorable cases. The present most useful ranges are: 10 to 5000 Pa forN ₃; 0.1 to 200 sec^–1 for shear rate; up to 5 Pa s for viscosity; and 5 to 40°C for temperature. As an application, it is shown that adding 0.1% of a high molecular weight polyisobutylene to a 2% polyisobutylene solution doublesN ₃ and has no detectable effect on the viscosity measured at low shear rates with a Ferranti-Shirley viscometer.

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Zusammenfassung Im Vergleich zu dem ähnlichen Kegel-Platte-Gerät von Adams und Lodge (4) zur Messung der Druckverteilung wurden an dem neuen Gerät die folgenden Verbesserungen vorgenommen: Temperaturregelung an Kegel und Platte, Versteifung des Rahmens, vier (anstatt drei) Druckmeßlöcher im Kegel-Platte-Bereich, ein zusätzliches Druckmeßloch auf der Achse unter der Kegelstumpf-Deckfläche, ausschließliche Verwendung einer vertikalen freien Grenzfläche der Flüssigkeit am Kegelrand (ohne umgebenden Flüssigkeitssee). Die Temperaturregelung des rotierenden Kegels und der festen Platte führt zu einer ausreichenden Temperaturgleichförmigkeit in der Testflüssigkeit für Betriebstemperaturen, die höchstens um 10–20°C von der Umgebungstemperatur abweichen. Dieses Intervall beträgt dagegen nur etwa 1°C, wenn auf die Temperaturregelung am Kegel verzichtet wird. Für newtonsche Flüssigkeiten entsprechen die gemessenen Druckgradienten den mittels der Gleichung von Walters (3) berechneten. Für viskoelastische Flüssigkeiten zeigen sich bei der Änderung des Spaltwinkels von 2° auf 3° nach Abzug der Trägheitsbeiträge keine Änderungen der bei einer bestimmten Schergeschwindigkeit gemessenen Druckverteilung. Dies zeigt, daß Sekundärströmungseffekte vernachlässigbar sind. Es darf angenommen werden, daß die Werte vonN ₃ =N ₁ + 2N ₂, die man aus den Gradienten dieser Verteilungen erhält, unter günstigen Umständen mit einem Fehler von nicht mehr als ±1 Pa behaftet sind. Gegenwärtig liegen die günstigsten Bereiche bei 10 bis 5000 Pa fürN ₃, 0,1 bis 200 s^–1 für die Schergeschwindigkeit, unterhalb von 5 Pa s für die Viskosität und 5 bis 40°C für die Temperatur. Als Anwendung wird gezeigt, daß ein Zusatz von 0,1% hochmolekularen Polyisobutylens zu einer 2%igen Polyisobutylenlösung den Wert vonN ₃ verdoppelt, aber keinen erkennbaren Einfluß auf die (bei geringen Schergeschwindigkeiten mit einem Ferranti-Shirley-Viskosimeter gemessen) Viskosität hat.

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udsf unidirectional shear flow - TCP truncated-cone and plate - N ₁,N ₂ 1st and 2nd normal stress differences in udsf - N ₃ N ₁ + 2N ₂ - : = A is defined by the equationA := B - P ^* hole pressurePw – Pm; Pw, Pm = pressures measured by flush transducer and by hole-mounted transducer - t time - , strain rate, shear rate - (P,t) covariant body metric tensor at particleP and timet - ⁱ , _i covariant and contravariant udsf body base vectors (i = 1, 2, 3) - ^–1 inverse of - R, plate radius, cone/plate gap angle - r ₀,h ₀ radius and height of cone truncation - r,, spherical polar coordinates; cone axis = 0; plate surface = /2 - physical components of stress; for a tensile component - cone angular velocity - p on the plate = /2 - ,T, density, absolute temperature, viscosity - P 0.15 ²(r ² –R ²) (inertial contribution) [2.7] - P _ve contribution [2.8] from flow perturbations of viscoelastic origin - r _i i = 1,2,3,4; values ofr at centers of holes in cone/plate region - P _i () pressure change recorded by transducerTi when cone angular velocity goes from zero to - 1/2 {P _i ()+ P _i (–)} (average for 2 senses of rotation) - rim pressure, from least-squares line through four points - Re Reynolds' number:R ²/ - (P,t)/t With 11 figures and 2 tables     

Wall shear stress modified by bubbles in a horizontal channel flow of silicone oil in the transition region

We performed laboratory experiments on bubbly channel flows using silicone oil, which has a low surface tension and clean interface to bubbles, as a test fluid to evaluate the wall shear stress modification for different regimes of bubble migration status. The channel Reynolds numbers of the flow ranged from 1000 to 5000, covering laminar, transition and turbulent flow regimes. The bubble deformation and swarms were classified as packing, film, foam, dispersed, and stretched states based on visualization of bubbles as a bulk void fraction changed. In the dispersed and film states, the wall shear stress reduced by 9% from that in the single-phase condition; by contrast, the wall shear stress increased in the stretched, packing, and foam states. We carried out statistical analysis of the time-series of the wall shear stress in the transition and turbulent-flow regimes. Variations of the PDF of the shear stress and the higher order moments in the statistic indicated that the injection of bubbles generated pseudo-turbulence in the transition regime and suppressed drag-inducing events in the turbulent regime. Bubble images and measurements of shear stress revealed a correlated wave with a time lag, for which we discuss associated to the bubble dynamics and effective viscosity of the bubble mixture in wall proximity.     

A fluid flow model in the lacunar-canalicular system under the pressure gradient and electrical field driven loads

The lacunar-canalicular system (LCS) is acknowledged to directly participate in bone tissue remodeling. The fluid flow in the LCS is synergic driven by the pressure gradient and electric field loads due to the electro-mechanical properties of bone. In this paper, an idealized annulus Maxwell fluid flow model in bone canaliculus is established, and the analytical solutions of the fluid velocity, the fluid shear stress, and the fluid flow rate are obtained. The results of the fluid flow under pressure gradient driven (PGD), electric field driven (EFD), and pressure-electricity synergic driven (P-ESD) patterns are compared and discussed. The effects of the diameter of canaliculi and osteocyte processes are evaluated. The results show that the P-ESD pattern can combine the regulatory advantages of single PGD and EFD patterns, and the osteocyte process surface can feel a relatively uniform shear stress distribution. As the bone canalicular inner radius increases, the produced shear stress under the PGD or P-ESD pattern increases slightly but changes little under the EFD pattern. The increase in the viscosity makes the flow slow down but does not affect the fluid shear stress (FSS) on the canalicular inner wall and osteocyte process surface. The increase in the high-valent ions does not affect the flow velocity and the flow rate, but the FSS on the canalicular inner wall and osteocyte process surface increases linearly. In this study, the results show that the shear stress sensed by the osteocyte process under the P-ESD pattern can be regulated by changing the pressure gradient and the intensity of electric field, as well as the parameters of the annulus fluid and the canaliculus size, which is helpful for the osteocyte mechanical responses. The established model provides a basis for the study of the mechanisms of electro-mechanical signals stimulating bone tissue (cells) growth.

     

Mode transition and oscillation suppression in supersonic cavity flow

Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation(DNS). For an uncontrolled cavity, as the thickness of the boundary layer declines, transition of the dominant mode from the steady mode to the Rossiter Ⅱ mode and then to the Rossiter Ⅲ mode is observed due to the change of vortex-corner interactions. Meanwhile, a low frequency mode appears. However, the wake mode observed in a subsonic cavity flow is absent in the current simulation.The oscillation frequencies obtained from a global dynamic mode decomposition(DMD)approach are consistent with the local power spectral density(PSD) analysis. The dominant mode transition is clearly shown by the dynamic modes obtained from the DMD. A passive control technique of substituting the cavity trailing edge with a quarter-circle is studied. As the effective cavity length increases, the dominant mode transition from the Rossiter Ⅱ mode to the Rossiter Ⅲ mode occurs. With the control, the pressure oscillations are reduced significantly. The interaction of the shear layer and the recirculation zone is greatly weakened, combined with weaker shear layer instability, responsible for the suppression of pressure oscillations. Moreover, active control using steady subsonic mass injection upstream of a cavity leading edge can stabilize the flow.     

A mathematical model for ATP-mediated calcium dynamics in vascular endothelial cells induced by fluid shear stress

In consideration of the mechanism for shear-stress-induced Ca^2＋ influx via ATP（adenosine triphosphate）-gated ion channel P2X4 in vascular endothelial cells, a modified model is proposed to describe the shear-stress-induced Ca^2＋ influx. It is affected both by the Ca^2＋ gradient across the cell membrane and extracellular ATP concentration on the cell surface. Meanwhile, a new static ATP release model is constructed by using published experimental data. Combining the modified intracellular calcium dynamics model with the new ATP release model, we establish a nonlinear Ca^2＋ dynamic system in vascular endothelial cells. The ATP-mediated calcium response in vascular endothelial cells subjected to shear stresses is analyzed by solving the governing equations of the integrated dynamic system. Numerical results show that the shear-stress-induced calcium response predicted by the proposed model is more consistent with the experimental observations than that predicted by existing models.     

Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel

This paper is concerned with the flow of two immiscible fluids through a porous horizontal channel. The fluid in the upper region is the micropolar fluid/the Eringen fluid, and the fluid in the lower region is the Newtonian viscous fluid. The flow is driven by a constant pressure gradient. The presence of micropolar fluids introduces additional rotational parameters. Also, the porous material considered in both regions has two different permeabilities. A direct method is used to obtain the analytical solution of the concerned problem. In the present problem, the effects of the couple stress, the micropolarity parameter, the viscosity ratio, and the permeability on the velocity profile and the microrotational velocity are discussed. It is found that all the physical parameters play an important role in controlling the translational velocity profile and the microrotational velocity. In addition, numerical values of the different flow parameters are computed. The effects of the different flow parameters on the flow rate and the wall shear stress are also discussed graphically.     

An experimental study on the coherent structures and chaotic phenomena in the axisymmetric countercurrent shear flow

The coherent structures and the chaotic phenomena in the transition of the axisymmetric countercurrent mixing shear flow were investigated experimentally. Two kinds of self-excited oscillation modes could exist in the axisymmetric countercurrent mixing shear flow. One is the shear layer self-excited oscillation mode corresponding to the high Reynolds number regime and the other is the jet column self-excited oscillation mode corresponding to the low Reynolds number regime in the case of the velocity ratio ranging from 1 to 1.5. Analyzing the auto-power spectrum, self-correlation-function and three dimensional reconstructed phase trajectory, the route to chaos through three Hopf bifurcations intercepted by an intermittence of the dynamical system corresponding to the axisymmetric countercurrent mixing shear flow was discovered when the velocity ratio is equal to 1.32.     

Free circular viscoplastic fluid flow with a hydrolubricant layer in the gap between coaxial cylinders

Free circular viscoplastic fluid flow in the gap between coaxial cylinders with a hydrolubricant layer on the inner cylinder is investigated theoretically. Mathematical models of the velocities and shear stresses for the transported and lubricating fluids in the laminar flow regime are proposed.     

Numerical simulation of blood flow and interstitial fluid pressure in solid tumor microcirculation based on tumor-induced angiogenesis

A coupled intravascular–transvascular–interstitial fluid flow model is developed to study the distributions of blood flow and interstitial fluid pressure in solid tumor microcirculation based on a tumor-induced microvascular network. This is generated from a 2D nine-point discrete mathematical model of tumor angiogenesis and contains two parent vessels. Blood flow through the microvascular network and interstitial fluid flow in tumor tissues are performed by the extended Poiseuille’s law and Darcy’s law, respectively, transvascular flow is described by Starling’s law; effects of the vascular permeability and the interstitial hydraulic conductivity are also considered. The simulation results predict the heterogeneous blood supply, interstitial hypertension and low convection on the inside of the tumor, which are consistent with physiological observed facts. These results may provide beneficial information for anti-angiogenesis treatment of tumor and further clinical research. The project supported by the National Natural Science Foundation of China (10372026).     

Mathematical modelling of couple stresses on fluid flow in constricted tapered artery in presence of slip velocity-effects of catheter

This paper explores the mathematical model for couple stress fluid flow through an annular region. The above model is used for studying the blood flow be-tween the clogged （stenotic） artery and the catheter. The asymmetric nature of the stenosis is considered. The closed form expressions for the physiological parameters such as impedance and shear stress at the wall are obtained. The effects of various geomet-ric parameters and the parameters arising out of the fluid considered are discussed by considering the slip velocity and tapering angle. The study of the above model is very significant as it has direct applications in the treatment of cardiovascular diseases.     

Performance modeling and analysis of blood flow in elastic arteries

Nomenclature　　τ　　wallshearstressγshearrateτy yieldstressηc Cassonviscosityktheconsistencyindexnnon_Newtonianindexτp shearstressofthepthelementωangularvelocityRvessel’sradiusCwavespeedM　　magneticparameter (Hartmannnumber)u,w　velocitycomponentinther_andz_directions,respectivelyP　　pressureα　　unsteadinessparameter k , R meanparametersTp relaxationtimeofthepthelementρ densityIntroductionTheimportancetoatherogenesisofarterialflowphenomenasuchasflowseparation ,recirculationands…     

非牛顿流体在渐变管中压力和剪切应力的二次摄动解

本文利用双摄动方法求解缓慢变化管道中Johnson-Segalman(J-S)流体流动的渐近解．将管道的扩张（或收缩）角度和粘弹性参数分别作为双摄动的参数,由流函数和涡量函数的形式,推导出压力和壁面剪切应力的渐近解．在此基础上,分析了管道角度,粘弹性参数和雷诺数等参数对压力以及剪切力影响．主要结论如下：(1) 管道扩张角度增加时,流向同一位置处径向压力以及壁面剪切应力随扩张角度减小;(2) 在同一扩张管道中,径向压力随着流向位移减小,收缩管与之相反;(3) 扩张角度与雷诺数对流场起主导作用,粘弹性系数起次要作用．     

压剪联合冲击下K9玻璃中的失效波

对K9玻璃进行了冲击速度为150~400 m/s,倾斜角为10、15的纵剖试样斜撞击实验。结果表明,在加载剪切横波(S+)和卸载纵波(P-)之间有波速超过了纵波波速的波阵面存在,此波的存在对卸载纵波和卸载横波的幅值有一定的影响。由于失效波的产生与材料的表面性质密切相关,为消除纵剖试样中间界面的影响,模拟VISAR的实验条件,进行了冲击速度为70~300 m/s、倾斜角为10的横剖试样斜撞击实验。可以确定在此冲击范围失效波的波速在0.98~1.4 km/s,产生失效波的临界状态为：压应力0.86~1.01 GPa,对应剪应力0.053~0.071 GPa。表明剪应力的存在极大降低了失效波产生的阈值。在此基础上初步分析了撞击面的动摩擦因数和相对滑移速度。     

Effects of shear thinning on migration of neutrally buoyant particles in pressure driven flow of Newtonian and viscoelastic fluids

The pattern of cross stream migration of neutrally buoyant particles in a pressure driven flow depends strongly on the properties of the suspending fluid. These migration effects have been studied by direct numerical simulation in planar flow. Shear thinning has a large effect when the inertia or elasticity is large, but only a small effect when they are small. At moderate Reynolds numbers, shear thinning causes particles to migrate away from the centerline, creating a particle-free zone in the core of the channel, which increases with the amount of shear thinning. In a viscoelastic fluid with shear thinning, particles migrate either toward the centerline or toward the walls, creating an annular particle-free zone at intermediate radii. The simulations also give rise to precise determination of slip velocity distributions in the various cases studied.     

Effect of yield stress on the flow of a Casson fluid in a homogeneous porous medium bounded by a circular tube

The effect of yield stress on the flow characteristics of a Casson fluid in a homogeneous porous medium bounded by a circular tube is investigated by employing the Brinkman model to account for the Darcy resistance offered by the porous medium. The non-linear coupled implicit system of differential equations governing the flow is first transformed into suitable integral equations and are solved numerically. Analytical solution is obtained for a Newtonian fluid in the case of constant permeability, and the numerical solution is verified with that of the analytic solution. The effect of yield stress of the fluid and permeability of the porous medium on shear stress and velocity distributions, plug flow radius and flow rate are examined. The minimum pressure gradient required to start the flow is found to be independent of the permeability of the porous medium and is equal to the yield stress of the fluid.     

Time dependent flow in equimolar micellar solutions: transient behaviour of the shear stress and first normal stress difference in shear induced structures coupled with flow instabilities

Recently we studied time dependent structural changes that are coupled with flow instabilities (Fischer 1998; Wheeler 1998; Fischer 2000). Within a stability analysis, a classification scheme for the feedback circuit of coupled shear-induced structure and flow instabilities was derived by Schmitt et al. (1995) and applied to our samples. Here, inhomogeneous flow layers of different concentration and viscosity are generated by shear-induced diffusion (spinodal demixing) and, as consequence, one no longer observes a homogeneous solution but a type of shear banding that is seen here for the first time. In this paper we present the behaviour of the first normal stress difference observed in the critical shear-rate regime where transient shear-induced structure is coupled with flow instability. Similar to the oscillations of the shear stresses (strain-controlled rheometer) one observes oscillations in the first normal stress difference. This behaviour indicates that elastic structures are built up and destroyed while the shear-induced structures occur and that the induced phase is more elastic than the initial one. Oscillations of shear stress and first normal stress difference are in phase and indicate that both phenomena are caused by the same mechanism. Received: 30 June 1999/Accepted: 14 December 1999     

Calculation of turbulent fluid flow and heat transfer in ducts by a full Reynolds stress model

A computational method has been developed to predict the turbulent Reynolds stresses and turbulent heat fluxes in ducts by different turbulence models. The turbulent Reynolds stresses and other turbulent flow quantities are predicted with a full Reynolds stress model (RSM). The turbulent heat fluxes are modelled by a SED concept, the GGDH and the WET methods. Two wall functions are used, one for the velocity field and one for the temperature field. All the models are implemented for an arbitrary three‐dimensional channel. Fully developed condition is achieved by imposing cyclic boundary conditions in the main flow direction. The numerical approach is based on the finite volume technique with a non‐staggered grid arrangement. The pressure–velocity coupling is handled by using the SIMPLEC‐algorithm. The convective terms are treated by the van Leer scheme while the diffusive terms are handled by the central‐difference scheme. The hybrid scheme is used for solving the ε equation. The secondary flow generation using the RSM model is compared with a non‐linear k–ε model (non‐linear eddy viscosity model). The overall comparison between the models is presented in terms of the friction factor and Nusselt number. Copyright © 2003 John Wiley & Sons, Ltd.     

Vortices and wall shear stresses in asymmetric and symmetric channels with sinusoidal wavy walls for pulsatile flow at low Reynolds numbers

Numerical simulation and flow visualization were performed to study the dynamical behavior of vortices generated in channels with two different geometries, i.e., a periodically converging–diverging channel and serpentine channel, both having sinusoidal wavy walls. This system for pulsatile flow is used to enhance heat and mass transfer in very viscous liquids. The numerical results predict well the dynamical behavior of vortices and agree with the flow visualizations. For both channels, the vortex expands in each furrow of the channel walls during the deceleration phase and shrinks during the acceleration phase, which leads to fluid exchange between the vortex and the mainstream. The time-averaged vortex strength and wall shear stresses increase, as the frequency of fluid oscillation increases under a fixed oscillatory fraction of the flow rate. However, above a certain value of the frequency, they reversely decrease due to viscous effects. This frequency for the serpentine channel is smaller than that for the converging–diverging channel. The channel geometries are found to have an important effect of the flow characteristics.