Instability threshold of a negatively buoyant fountain

Experimental simulations were carried out to investigate the onset of instability in negatively buoyant fountains by injecting glycerin–water mixtures into silicon oil. The transition from a stable to an unstable fountain structure is primarily governed by the Richardson number, and to a lesser extent, Reynolds number, viscosity ratio, Weber number and vent geometry. Transition nominally occurs at a Ri = 1.0. For a fountain issuing from a cylindrical pipe, the major effect of the Reynolds number is in determining whether or not the fountain is laminar or turbulent. The Reynolds number effect can be largely accounted for by basing a corrected Richardson number on the root mean square of the mean velocity. Viscosity ratio deviating from unity has the effect of stabilizing the flow structure and thereby reducing the transition Richardson number. Similarly, interfacial tension stabilizes the flow pattern resulting in a trend of increasing transition Richardson number with increasing Weber number. The results are valid in rectangular vents if the Richardson number and Reynolds number are based on the hydraulic diameter.     

Numerical study of influence of different parameters on mixing in a coaxial jet mixer using LES

We present a comparative numerical study about the overall mixing process in a coaxial jet mixer. The two-stream mixing problem was investigated in non-reacting single phase gas and liquid mixtures using Large-Eddy Simulations with wall functions and subgrid scale models from eddy viscosity concepts. The influence of different parameters like Reynolds number, Schmidt number, Prandtl number, density ratio and flow rate ratio on the overall mixing process was investigated. Additionally two methods of control of mixing are shown to have a significant effect on the overall mixing in a coaxial jet mixer.     

Vortex reynolds number in turbulent boundary layers

The effects of vortex Reynolds number on the statistics of turbulence in a turbulent boundary layer have been investigated. Vortex Reynolds number is defined as the ratio of circulation around the vortex structure to the fluid viscosity. The vortex structure of the outer region was modeled and a full numerical simulation was then conducted using a high-order spectral method. A unit domain of the outer region of a turbulent boundary layer was assumed to be composed of essentially three elements: a wall, a Blasius mean shear, and an elliptic vortex inclined at 45° to the flow direction. The laminar base-flow Reynolds number is roughly in the same range as that of a turbulent boundary layer based on eddy viscosity, and the vortex-core diameter based on the boundary-layer thickness is nearly the same as the maximum mixing length in a turbulent boundary layer. The computational box size, namely, 500, 150, and 250 wall units in the streamwise, surface-normal, and spanwise directions, respectively, is approximately the same as the measured quasi-periodic spacings of the near-wall turbulence-producing events in a turbulent boundary layer. The effects of vortex Reynolds number and the signs of the circulation on the moments of turbulence were examined. The signs mimic the ejection and sweep types of organized motions of a turbulent boundary layer. A vortex Reynolds number of 200 describes the turbulence moments in the outer layer reasonably well.     

Effect of span length and temperature on the 3-D confined flow around a vortex promoter

This article presents a numerical study on the influence of span length and wall temperature on the 3-D flow pattern around a square section vortex promoter located inside a micro-channel in the low Reynolds number regime. The first objective of the work is to quantify the critical Reynolds number that defines the onset of vortex shedding and to identify the different regimes that appear as a function of the channel aspect ratio (span to height ratio). We found that the critical Reynolds number for the onset of the Karman street regime increases as the aspect ratio decreases. In particular, for the aspect ratio of 1/2 the critical Reynolds number is nearly six times the critical Reynolds number of the 2-D problem. An intermediate oscillating regime between the steady and the Karman street solutions was also found to exist within a rather wide range of Reynolds numbers for small channel aspect ratios. The second objective was to investigate the influence of the vortex promoter wall temperature on both vortex shedding and flow pattern. This has practical engineering implications because the working fluid considered in the article is water that has a viscosity that depends significantly on temperature and promotes a strong coupling between the momentum and energy equations that influences the system behaviour. Results indicate that high surface temperature on the prism promotes the onset of the Karman street, suggesting design guidelines for micro-channel based heat sinks that make use of vortex promoters.     

Numerical simulation of confined laminar jet flows

Two‐dimensional incompressible jet development inside a duct has been studied in the laminar flow regime, for cases with and without entrainment of ambient fluid. Results have been obtained for the flow structure and critical Reynolds number values for steady asymmetric jet development and for the onset of temporal oscillations, at various values of the duct‐to‐jet width ratio (aspect ratio). It is found that at low aspect ratios and Reynolds numbers, jet development inside the duct is symmetric. For larger aspect ratios and Reynolds numbers, the jet flow at steady state becomes asymmetric with respect to the midplane, and for still higher values, it becomes oscillatory with respect to time. When entrainment is present, the instabilities of asymmetric development and temporal oscillations occur at a much higher critical Reynolds number for a given aspect ratio, indicating that the stability of the jet flow is higher with entrainment. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of span length and temperature on the 3-D confined flow around a vortex promoter

This article presents a numerical study on the influence of span length and wall temperature on the 3-D flow pattern around a square section vortex promoter located inside a micro-channel in the low Reynolds number regime. The first objective of the work is to quantify the critical Reynolds number that defines the onset of vortex shedding and to identify the different regimes that appear as a function of the channel aspect ratio (span to height ratio). We found that the critical Reynolds number for the onset of the Karman street regime increases as the aspect ratio decreases. In particular, for the aspect ratio of 1/2 the critical Reynolds number is nearly six times the critical Reynolds number of the 2-D problem. An intermediate oscillating regime between the steady and the Karman street solutions was also found to exist within a rather wide range of Reynolds numbers for small channel aspect ratios. The second objective was to investigate the influence of the vortex promoter wall temperature on both vortex shedding and flow pattern. This has practical engineering implications because the working fluid considered in the article is water that has a viscosity that depends significantly on temperature and promotes a strong coupling between the momentum and energy equations that influences the system behaviour. Results indicate that high surface temperature on the prism promotes the onset of the Karman street, suggesting design guidelines for micro-channel based heat sinks that make use of vortex promoters.     

Flow and mixing characteristics of pulsed confined opposed jets in turbulent flow regime

A numerical study is performed on a two-dimensional confined opposed-jet configuration to gain basic understanding of the flow and mixing characteristics of pulsed turbulent opposed-jet streams. The sinusoidal pulsating flows with different temperature are imposed at opposed-jet inlets, which are mixed with each other in a confined flow channel. The current mathematical model taking the effect of temperature-dependent thermo-physical properties of fluid into account can present a good prediction for opposed-jet streams compared with experimental data. The numerical results indicate that introduction of temperature difference between opposed jet flows can lead to an asymmetric flow field immediately after jet impact, and the sinusoidal flow pulsations can effectively enhance mixing rate of opposed jets. Parameter studies are conducted for optimization of pulsed opposed jets. The effect of Reynolds number and flow pulsation as well as the configuration geometry on the mixing performance are discussed in detail. Examination of the flow and thermal field shows that the mixing rate is highly dependent on the vortex-induced mixing and residence time of jet fluid in the exit channel.     

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.     

Perturbation solutions for asymmetric laminar flow in porous channel with expanding and contracting walls

The cases of large Reynolds number and small expansion ratio for the asym- metric laminar flow through a two-dimensional porous expanding channel are considered. The Navier-Stokes equations are reduced to a nonlinear fourth-order ordinary differential equation by introducing a time and space similar transformation. A singular perturbation method is used for the large suction Reynolds case to obtain an asymptotic solution by matching outer and inner solutions. For the case of small expansion ratios, we are able to obtain asymptotic solutions by double parameter expansion in either a small Reynolds number or a small asymmetric parameter. The asymptotic solutions indicate that the Reynolds number and expansion ratio play an important role in the flow behavior. Nu- merical methods are also designed to confirm the correctness of the present asymptotic solutions.     

Mixing of miscible liquids in gas-segmented serpentine channels

The chaotic mixing of miscible liquids in gas-segmented serpentine channels is studied computationally in a two-dimensional setting. Passive tracer particles are used to visualize and quantify the mixing. The molecular diffusion is ignored and only the mixing due to chaotic stirring is considered. Mixing is quantified using the entropy and intensity of segregation measures. The effects of various non-dimensional parameters on the quality of mixing are investigated and it is found that the relative bubble size, the capillary number and the non-dimensional channel corrugation length are the most important parameters influencing the mixing. The mixing is found to be weakly dependent on Reynolds number and nearly independent of viscosity ratio.     

Side‐wall effects on the bifurcation of the flow through a sudden expansion

Three‐dimensional computations have been performed to study the flow through a symmetric sudden expansion with an expansion ratio of 3 at low Reynolds numbers. The aspect ratio of the flow channel is allowed to vary within a wide range to examine its influence on the flow which bifurcates from a symmetric state to an asymmetric state. The results reveal that the critical Reynolds number of the symmetry‐breaking bifurcation increases while the aspect ratio is reduced. The flow behaviour near the side walls is illustrated by using limiting streamlines. The origin of the singular points identifiable on the side wall can be traced back to the recirculating flows and the relevant reattachment/separation points in the core of the channel. It is seen that the determination of the exact critical Reynolds number is not trivial because it depends on how to define asymmetric flow. Computations have also been conducted to show that a slight asymmetry in the channel geometry causes a smooth transition from symmetric to non‐symmetric states. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical simulation of non-Darcian flow through a porous medium

This work reports on fluid flow in a fluid-saturated porous medium, accounting for the boundary and inertial effects in the momentum equation. The flow is simulated by Brinkman-Forchheimer-extended Darcy formulation (DFB), using MAC (Marker And Cell) and Chorin pressure iteration method. The method is validated by comparison with analytic results. The effect of Reynolds number, Darcy number, porosity and viscosity ratio on velocity is investigated. As a result, it is found that Darcy number has a decisive influence on pressure as well as velocity, and the effect of viscosity ratio on velocity is very strong given the Darcy number. Additional key findings include unreasonable choice of effective viscosity can involve loss of important physical information.     

Experimental study of flow structures in a large range downstream the spacer grid in a 5 × 5 rod bundle using TR-PIV

In this paper, the time-resolved particle image velocimetry (TR-PIV) and match index refractive (MIR) techniques were used to study the flow field in a large range (0 – 22 D_h) downstream a spacer grid (SG) in a 5 × 5 rod bundle channel at different Reynolds number. The sodium chloride solution (1%) is used as the working fluid to reduce the refractive index error of fluorinated ethylene propylene (FEP) and water. The proper orthogonal decomposition (POD) background removal technique was used to minimize the FEP reflection. These methods greatly reduced the interference of background noise and improved the accuracy of cross-correlation calculation. For TR-PIV velocity fields downstream of the mixing vanes, time-averaged, statistical, spectral, and cross-correlation analysis were performed for the instantaneous full-field experimental data. The transport characteristics of coherent structures in different subchannels of rod bundles are calculated and discussed. The results show that the SG caused a relatively large transverse velocity and reduces the axial velocity. With the increase of the Reynolds number, the SG promotes the generation of transverse flow and has a great resistance to the axial flow. There is relatively large turbulence intensity downstream of the SG due to the mixing effect. The attenuation of transverse turbulence intensity component is slower than the axial component. Moreover, spectrum analysis shows that cross-arranged mixing vanes will generate periodic vortices but single mixing vane will not. These periodic vortices gradually propagate downstream along the inner subchannel and dissipate in the gap subchannel due to the effect of viscosity. The cross-correlation analysis shows that the mixing effect of the SG will reduce the scale of the coherent structure, and increase the convection velocity. The results of current research are helpful for understanding the strong anisotropic turbulence in the rod bundle channel with SG. Finally, the experimental results can be utilized to benchmark the applicability of turbulence models under different Reynolds number and the performance of partially averaged Naiver–Stokes or multiple RANS algorithms downstream of the SG.     

The instability of water-mud interface in viscous two-layer flow with large viscosity contrast

The temporal instability of parallel viscous two-phase mixing layers is extended to current-fluid mud by considering a composite error function velocity profile. The influence of viscosity ratio, Reynolds number, and Froude number on the instability of the system are discussed and a new phenomenon never discussed is investigated based on our numerical results. It is shown that viscosity can enlarge the unstable wave number range, cause new instability modes, and certainly reduce the growth rate of Kelvin—Helmholtz (K—H) instability.     

Direct numerical simulations of two-layer viscosity-stratified flow

Two-dimensional simulations of flow instability at the interface of a two-layer, density-matched, viscosity-stratified Poiseuille flow are performed using a front-tracking/finite difference method. We present results for the small-amplitude (linear) growth rate of the instability at small to medium Reynolds number for varying thickness ratio n, viscosity ratio m, and wavenumber. We also present results for large-amplitude non-linear evolution of the interface for varying viscosity ratio and interfacial tension. For the linear case, the interfacial mode is neutrally stable for as predicted by analysis. The growth rate is proportional to Reynolds number for small Re, and increases with viscosity ratio. The growth rate also increases when the thickness of the more viscous layer is reduced. Strong non-linear behavior is observed for relatively large initial perturbation amplitude. The higher viscosity fluid is drawn out as a finger that penetrates into the lower viscosity layer. The simulated interface shape compares well with previously reported experiments. Increasing interfacial tension retards the growth rate of the interface as expected, whereas increasing the viscosity ratio enhances it. Drop formation at the small Reynolds number considered in this study is precluded by the two-dimensional nature of the calculations.     

Numerical study of electroosmotic micromixing of non-Newtonian fluids

Biofluids which exhibit non-Newtonian behavior are widely used in microfluidic devices which involve fluid mixing in microscales. In order to study the effects of shear depending viscosity of non-Newtonian fluids on characteristics of electroosmotic micromixing, a numerical investigation of flow of power-law fluid in a two-dimensional microchannel with nonuniform zeta potential distributions along the channel walls was carried out via finite volume scheme. The simulation results confirmed that the shear depending viscosity has a significant effect on the degree of mixing efficiency. It was shown as the fluid behavior index of power-law fluid, n, decreases, more homogeneous solution can be achieved at the microchannel outlet. Hence, electroosmotic micromixing was found more practical and efficient in microscale mixing of pseudoplastic fluids rather than those Newtonian and dilatant ones. Furthermore, it was found that increase in Reynolds number results in lower mixing efficiency while electroosmotic forces are kept constant.     

Influence of adverse pressure gradient on rough-wall turbulent flows

This paper presents an experimental investigation of adverse pressure gradient turbulent flow over two rough surfaces and a reference smooth surface. The adverse pressure gradient was produced in an asymmetric diffuser whose opening angle was 3°. The rough surfaces comprised sand grains and gravels of nominal mean diameters of 1.55 mm and 4.22 mm, respectively. The tests were conducted at an approach flow velocity of 0.5 m/s and the momentum thickness Reynolds number varied from 900 to 3000. A particle image velocimetry technique was used for the velocity measurements. Profiles of the mean velocity, turbulent intensities, Reynolds stress ratios, mixing length, eddy viscosity and the production terms were then obtained to document the effects of adverse pressure gradient (APG) on low Reynolds number rough-wall turbulent boundary layers. The results indicate that APG thickens the boundary layer and roughness sublayer. The APG and surface roughness also enhanced the production of turbulence as well as the turbulence level when compared with the smooth-wall data.     

Visualization of three-dimensional flow in a four-roll mill

Flow visualization has been used to study the motion of a Newtonian fluid in a four-roll mill. Observations of the effect of increasing Reynolds number on the evolution of steady three-dimensional flow between the rollers are reported. The flow visualization experiments have been conducted for two values of the aspect ratio (defined as the ratio of roller length to gap width between rollers). The rollers have been constrained to rotate in a manner which generates an approximately two-dimensional pure extensional flow near the center of the apparatus at low speeds. Steady, symmetrically positioned vortices grow near the top and bottom walls of the container as the Reynolds number is increased up to a critcal value. An increase in Reynolds number beyond this critical value results in a loss of symmetry in the flow pattern. The nature of this transition is strongly dependent upon the aspect ratio.     

Flow fields in a simulated axisymmetric terminal aneurysm with symmetric and asymmetric outflows

Laser-Doppler velocimetric measurements and flow visualization were performed in a glass axisymmetric aneurysm model with symmetric and asymmetric outflows through the branches. The bifurcation angle was fixed at 140°, and the Reynolds number based on the steady bulk average velocity and diameter of the affarent conduit was 500. The flow characteristics such as flow separation in the afferent conduit and flow activity inside the aneurysm for the symmetric and asymmetric outflow cases were compared in detail, and the case that is susceptible to thrombosis was identified. In addition, the onset of transition from laminar to turbulent flow inside the aneurysm was evidenced by the presence of vortex breakdown and the steep increase in the fluctuation level. Finally, the effect of pulsation on the flow pattern in the aneurysm was examined.