Range Of Flow Parameters Research Articles

Wall friction and effective viscosity of a homogeneous dispersed liquid–liquid flow in a horizontal pipe

AbstractHomogenous oil in water dispersion has been investigated in a horizontal pipe. The mean droplet size is 25 μm. Experiments were carried out in a 7.5‐m‐long transparent pipe of 50‐mm internal diameter. The wall friction has been measured and modeled for a wide range of flow parameters, mixture velocities ranging from 0.28 to 1.2 m/s, and dispersed phase volume fractions up to 0.6, including turbulent, intermediate, and laminar regimes. Flow regimes have been identified from velocity profiles measured by particle image velocimetry in a matched refractive index medium. It is shown that the concept of effective viscosity is relevant to scale the friction at the wall of the dispersed flow. Based on mixture properties, the friction factor follows the Hagen‐Poiseuille and the Blasius' law in laminar and turbulent regimes, respectively. Interestingly, the transition toward turbulence is delayed as the dispersed phase fraction is increased. © 2010 American Institute of Chemical Engineers AIChE J, 2011

Unsteady natural convection in a triangular enclosure under isothermal heating

The fluid flow and heat transfer inside a triangular enclosure due to instantaneous heating on the inclined walls are investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer under the inclined walls may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. A new triple-layer integral approach of scaling analysis has been considered to obtain major scaling relations of the velocity, thicknesses, Nusselt number and the flow development time of the natural convection boundary layer and verified by direct numerical simulations over a wide range of flow parameters.

Bridging the gap: A nested-pipe reactor for slow reactions in continuous flow chemical synthesis

A multi-purpose production facility for continuous flow operation of medium-fast to slow chemical reactions was realised. The reactor concept followed the typical three-stage sequence for numerous organic reactions: non-reactive mixing at low temperature, main conversion with selectivity control at medium temperature, and completion of the reaction at high temperature. For the first two stages, a static mixer for immediate mixing and a micro-structured heat exchanger for efficient heat transfer were utilised, respectively. A lack of equipment availability was experienced for the third stage, requiring reaction times in the hours range at well-defined flow conditions. In order to bridge this gap between (micro-)structured low-volume devices and traditional macro-scale equipment for long reaction times, a novel nested-pipe reactor design based on annular slit geometries was realised. These reactor modules provide reaction volumes between 0.25 and 8.0 L, depending on the width of the slit and the number of reactor modules connected in series. The entire unit was constructed as a compact, mobile, self-consistent device with a high degree of automation. As a representative process example, the solvent-free synthesis of the ionic liquid [EMIM]EtSO 4 from N-methylimidazole and diethylsulfate was selected, since this reaction is characterised by high initial rates of reaction and heat release, and requires long reaction times in order to achieve high conversion. A characterisation of the residence time behaviour of the annular slit reactors was performed by means of fibre optical mid-infrared spectroscopy. Tracer experiments in step-change mode showed a well predictable response behaviour with a pronounced laminar contribution in the studied flow parameter range.

Forced Flow of Vapor Condensing Over a Horizontal Plate (Problem of Cess and Koh): Steady and Unsteady Solutions of the Full 2D Problem

Accurate steady and unsteady numerical solutions of the full 2D governing equations—which model the forced film condensation flow of saturated vapor over a semi-infinite horizontal plate (the problem of Cess and Koh)—are obtained over a range of flow parameters. The results presented here are used to better understand the limitations of the well-known similarity solutions given by Koh. It is found that steady/quasisteady filmwise solution exists only if the inlet speed is above a certain threshold value. Above this threshold speed, steady/quasisteady film condensation solutions exist and their film thickness variations are approximately the same as the similarity solution given by Koh. However, these steady solutions differ from the Koh solution regarding pressure variations and associated effects in the leading part of the plate. Besides results based on the solutions of the full steady governing equations, this paper also presents unsteady solutions that characterize the steady solutions’ attainability, stability (response to initial disturbances), and their response to ever-present minuscule noise on the condensing-surface. For this shear-driven flow, the paper finds that if the uniform vapor speed is above a threshold value, an unsteady solution that begins with any reasonable initial-guess is attracted in time to a steady solution. This long time limiting solution is the same—within computational errors—as the solution of the steady problem. The reported unsteady solutions that yield the steady solution in the long time limit also yield “attraction rates” for nonlinear stability analysis of the steady solutions. The attraction rates are found to diminish gradually with increasing distance from the leading edge and with decreasing inlet vapor speed. These steady solutions are generally found to be stable to initial disturbances on the interface as well as in any flow variable in the interior of the flow domain. The results for low vapor speeds below the threshold value indicate that the unsteady solutions exhibit nonexistence of any steady limit of filmwise flow in the aft portion of the solution. Even when a steady solution exists, the flow attainability is also shown to be difficult (because of waviness and other sensitivities) at large downstream distances.

Viscous sheet retraction

We present the results of a combined theoretical and numerical investigation of the rim-driven retraction of flat fluid sheets in both planar and circular geometries. Particular attention is given to the influence of the fluid viscosity on the evolution of the sheet and its bounding rim. In both geometries, after a transient that depends on the sheet viscosity and geometry, the film edge eventually attains the Taylor–Culick speed predicted on the basis of inviscid theory. The emergence of this result in the viscous limit is rationalized by consideration of both momentum and energy arguments. We first consider the planar geometry considered by Brenner & Gueyffier (Phys. Fluids, vol. 11, 1999, p. 737) and deduce new analytical expressions for the speed of the film edge at the onset of rupture and the evolution of the maximum film thickness for viscous films. In order to consider the expansion of a circular hole, we develop an appropriate lubrication model that predicts the form of the early stage dynamics of film rupture. Simulations of a broad range of flow parameters confirm the importance of geometry on the dynamics, verifying the exponential hole growth reported in early experimental studies. We demonstrate the sensitivity of the initial retraction speed on the film profile, and so suggest that the anomalous rate of retraction reported in these experiments may be attributed in part to geometric details of the puncture process.

Formation of Bubbles and Droplets in Parallel, Coupled Flow‐Focusing Geometries

This paper describes the mechanism of formation of bubbles of nitrogen in water containing Tween 20 as a surfactant, and of droplets of water in hexadecane containing Span 80 as a surfactant. The study of these microfluidic systems compares two or four flow-focusing generators coupled through shared inlets, supplying the continuous phase, and through a common outlet channel. The processes that form bubbles in neighboring generators interact for a wide range of flow parameters; the formation of bubbles alternates in time and space, and the bubbles assemble into complex patterns in the outlet channel. The dynamics of formation of bubbles in these systems are stable for long time (at least 10 min). For a certain range of flow parameters, the coupled flow-focusing generators exhibit two stable modes of operation for a single set of flow parameters. The dynamics of formation of droplets of water in hexadecane by the coupled flow-focusing generators are simpler--the adjacent generators produce only monodisperse droplets over the entire range of flow parameters that are explored. These observations suggest that the mechanism of interaction between coupled flow-focusing generators relies on the compressibility of the dispersed phase (e.g., the gas or liquid), and on variations in pressure at the flow-focusing orifices induced by the breakup of bubbles or droplets.

Aerodynamic forces and flow fields of a two-dimensional hovering wing

This paper reports the results of an experimental investigation on a two-dimensional (2-D) wing undergoing symmetric simple harmonic flapping motion. The purpose of this investigation is to study how flapping frequency (or Reynolds number) and angular amplitude affect aerodynamic force generation and the associated flow field during flapping for Reynolds number (Re) ranging from 663 to 2652, and angular amplitudes (αA) of 30°, 45° and 60°. Our results support the findings of earlier studies that fluid inertia and leading edge vortices play dominant roles in the generation of aerodynamic forces. More importantly, time-resolved force coefficients during flapping are found to be more sensitive to changes in αA than in Re. In fact, a subtle change in αA may lead to considerable changes in the lift and drag coefficients, and there appears to be an optimal mean lift coefficient \( \left( {\overline {C_{{\text{l}}} } } \right) \) around αA = 45°, at least for the range of flow parameters considered here. This optimal condition coincides with the development a reverse Karman Vortex street in the wake, which has a higher jet stream than a vortex dipole at αA = 30° and a neutral wake structure at αA = 60°. Although Re has less effect on temporal force coefficients and the associated wake structures, increasing Re tends to equalize mean lift coefficients (and also mean drag coefficients) during downstroke and upstroke, thus suggesting an increasing symmetry in the mean force generation between these strokes. Although the current study deals with a 2-D hovering motion only, the unique force characteristics observed here, particularly their strong dependence on αA, may also occur in a three-dimensional hovering motion, and flying insects may well have taken advantage of these characteristics to help them to stay aloft and maneuver.

Influence of hydrological regimes on the pre‐spawning entry of Atlantic salmon (Salmo salar L.) into an upland river

AbstractThe Girnock Burn is an Atlantic salmon (Salmo salar) spawning tributary of the river Dee, Aberdeenshire, Scotland. The dates, sexes and numbers of adult salmon entering the stream in the three months prior to spawning were determined between 1969 and 2005 using a permanent fish‐trap. During this time, the number of fish returning to spawn varied markedly. Here we analyze the whole of this unique long term data set in order to characterize and classify the hydrologic regimes of the pre‐spawning migration period and assess the extent to which these regimes help explain the timing and patterns of arrival of adult salmon into the stream. A range of flow parameters was calculated for the arrival period (September–November) for each of the 37 years. These parameters were used to ordinate and classify years according to their flow regimes. The analysis yielded six distinct groups or ‘flow regime types’ which separated principally in relation to flow magnitude and frequency parameters. The number of fish entering the burn on a given day was not significantly correlated to discharge on that day. However, patterns of arrival of fish differed markedly between years with different regime types, with the number of fish arriving on a given day related to patterns of discharge over the preceding part of the arrival period. Overall inter‐annual variability in entry corresponded to the defined regime types. In wetter years, fish entry to the stream usually starts relatively early and continues throughout the pre‐spawning period. In contrast, dry years may result in fish entry being delayed; this may result in lower numbers of spawning females entering the stream and sub‐optimal utilization of juvenile habitat in the following spring. Copyright © 2008 John Wiley & Sons, Ltd.

Calculation of the Time-Averaged Flow in Squirrel-Cage Blowers by Substituting Blades With Equivalent Forces

Radial fans of the squirrel-cage type are used in various industrial applications. The analysis of such fans via computational fluid mechanics can provide the overall fan performance coefficients, as well as give insights into the detailed flow field. However, a transient simulation of a 3D machine using a sliding grid for the rotating blades still requires prohibitively large computational resources, with CPU run times in the order of months. To avoid such long simulation times, a faster method is developed in this paper. Instead of solving the transient Navier–Stokes equations, they are first averaged over one impeller rotation, and then solved for the mean flow since only this flow is of practical interest. Due to the averaging process, the blades disappear as solid boundaries, but additional equation terms arise, which represent the blade forces on the fluid. An innovative closure model for these terms is developed by calculating forces in 2D blade rows with the same blade geometry as the 3D machine for a range of flow parameters. These forces are then applied in the 3D machine, and the resulting 3D time-averaged flow field and performance coefficients are calculated. The 3D flow field showed several characteristic features of squirrel-cage blowers, such as a cross-flow pattern through the fan at low flow coefficients, and a vortexlike flow pattern at the fan outlet. The 3D fan performance coefficients showed an excellent agreement with experimental data. Since the 3D simulation solves for the mean flow, it can be run as a steady-state problem with a comparatively coarse grid in the blade region, reducing CPU times by a factor of about 10 when compared to a transient simulation with a sliding grid. It is hoped that these savings in computational cost will encourage other researchers and industrial companies to adopt the new method presented here.

Scaling Effects of an Aerodynamic Plasma Actuator

We present experimental results to yield insight into the scalability and control effectiveness of single-dielectricbarrier-discharge plasma actuators for leading-edge separation control on airfoils. The parameters investigated are chord Reynolds number, Mach number, leading-edge radius, actuator amplitude, and unsteady frequency. This includes chord Reynolds numbers up to 1:0 � 106 and a maximum freestream speed of 60 m=s corresponding to a Mach number of 0.176. The main objective of this work is to examine the voltage requirements for the plasma actuators to reattach the flow at the leading edge of airfoils at poststall angles of attack for a range of flow parameters in order to establish scaling between laboratory and full-flight conditions. For the full range of conditions, an optimum unsteady actuator frequency f is found to minimize the actuator voltage needed to reattach the flow, such that F� � fLsep=U1 � 1. At the optimum frequencies, the minimum voltage required to reattach the flow is weakly dependent on chord Reynolds number and strongly dependent on the poststall angle of attack and leading-edge radius. The results indicate that the voltage required to reattach the flow scales as the square of the leading-edge radius.

Optical diagnostics of intermittent flows

The efficiency of combined use of different optical techniques for flow diagnostics is demonstrated with the practically important case of intense swirling flows. It is shown that, when applied separately, commonly used optical measuring techniques, such as laser Doppler anemometry and particle image velocimetry, frequently give erroneous results, especially for the transition flow and developed nonstationary flow. However, their combined use in diagnostics of unsteady (intermittent) flows significantly improves both the temporal and spatial resolution of measurements. Such a complex approach is for the first time applied for diagnostics of the flow pattern in a closed cylinder with a rotating end face with the aim of studying the changeover from the steady axisymmetric to unsteady asymmetric flow over a wide range of flow parameters. It is found that such a transition is notable for azimuthal disturbances with characteristic modes and frequencies.

Consideration for the tropopause’s displacements in the problem of flow over mountains

Within the framework of a two-dimensional, inviscid, stationary model, the problem of an unbounded (in height) two-layer quasi-static airflow over mesoscale mountains is considered. The airflow is characterized by a constant velocity and a discontinuity of temperature stratification at the inner interface (tropopause). The conjugation conditions for the flow fields at the boundary between the layers are formulated exactly, without the standard assumption of small perturbations. According to calculations, partial reflection of wave energy from the tropopause is substantially controlled by nonlinear effects associated with a finite height and shape of terrain. The tropopause’s displacement from the initial (equilibrium) level has a stabilizing effect on the flow, thus interfering with the development of anomalously strong disturbances. As a result, the flow field remains statically stable within a considerably wider range of flow parameters and for a larger mountain heights than predicted in the context of the conventional linear theory. The results obtained in this study are indicative of the importance of a correct consideration of the dynamic interaction between the troposphere and the overlying layers during both simulation of the process of flow and analysis of real atmospheric situations over mountains.

Eddy Influences on Hadley Circulations: Simulations with an Idealized GCM

An idealized GCM is used to investigate how the strength and meridional extent of the Hadley circulation depend on the planet radius, rotation rate, and thermal driving. Over wide parameter ranges, the strength and meridional extent of the Hadley circulation display clear scaling relations with regime transitions, which are not predicted by existing theories of axisymmetric Hadley circulations. For example, the scaling of the strength as a function of the radiative-equilibrium equator-to-pole temperature contrast exhibits a regime transition corresponding to a regime transition in scaling laws of baroclinic eddy fluxes. The scaling of the strength of the cross-equatorial Hadley cell as a function of the latitude of maximum radiative-equilibrium temperature exhibits a regime transition from a regime in which eddy momentum fluxes strongly influence the strength to a regime in which the influence of eddy momentum fluxes is weak. Over a wide range of flow parameters, albeit not always, the Hadley circulation strength is directly related to the eddy momentum flux divergence at the latitude of the streamfunction extremum. Simulations with hemispherically symmetric thermal driving span circulations with local Rossby numbers in the horizontal upper branch of the Hadley circulation between 0.1 and 0.8, indicating that neither nonlinear nearly inviscid theories, valid for Ro → 1, nor linear theories, valid for Ro → 0, of axisymmetric Hadley circulations can be expected to be generally adequate. Nonlinear theories of axisymmetric Hadley circulations may account for aspects of the circulation when the maximum radiative-equilibrium temperature is displaced sufficiently far away from the equator, which results in cross-equatorial Hadley cells with nearly angular momentum-conserving upper branches. The dependence of the Hadley circulation on eddy fluxes, which are themselves dependent on extratropical circulation characteristics such as meridional temperature gradients, suggests that tropical circulations depend on the extratropical climate.

Critical properties and stability of stationary solutions in multitransonic pseudo-Schwarzschild accretion

For inviscid, rotational accretion flows, both isothermal and polytropic, a simple dynamical system analysis of the critical points has given a very accurate mathematical scheme to understand the nature of these points, for any pseudo-potential by which the flow may be driven on to a Schwarzschild black hole. This allows us for a complete classification of the critical points for a wide range of flow parameters, and shows that the only possible critical points for this kind of flow are saddle points and centre-type points. A restrictive upper bound on the angular momentum of critical solutions has been established. A time-dependent perturbative study reveals that the form of the perturbation equation, for both isothermal and polytropic flows, is invariant under the choice of any particular pseudo-potential. Under generically true outer boundary conditions, the inviscid flow has been shown to be stable under an adiabatic and radially propagating perturbation. The perturbation equation has also served the dual purpose of enabling and understanding the acoustic geometry for inviscid and rotational flows.

Bubbly flow through fixed beds: Microscale experiments in the dilute regime and modeling

AbstractIn order to predict the pressure drop and the mean void fraction for bubbly flows in packed beds, a new one‐dimensional (1‐D) model is proposed. The balance equations for both phases are derived from local Eulerian two‐fluid equations which are spatially averaged at a mesoscale, that is, at a length‐scale large compared with the microscale that characterizes the fixed bed. This model, that differs from previous mechanistic models, has been supplemented by closure laws for the liquid‐solid and the gas‐liquid interactions, those structures account for the flow dynamics at the pore scale. It is first experimentally demonstrated that, in dilute conditions, the bubble‐size distribution only depends on the pore size, when the later is smaller than the capillary length scale. It is also shown that the mean‐bubble dynamics is similar to that of a slug, with a relative velocity at mesoscale linearly increasing with the liquid superficial velocity. Besides, that relative velocity monotonically increases with the gas flow rate ratio, a behavior that can be attributed to the formation of preferential paths for the gas phase. Concerning the liquid‐solid interactions, the two‐phase flow pressure drop scaled by its single‐phase flow counterpart at the same superficial liquid velocity is predicted to linearly increase with the void fraction, with a prefactor evolving with the Capillary number. These closures prove consistent with available experiments, both in upward and in downward situations. Although these proposals deserve to be further tested over an extended range of flow parameters, this model paves the way to reasonably accurate predictions of bubbly flows in packed beds able to account for refined parameters related with the flow dynamics. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Soaring interfaces, vortices and vortex systems inside the internal waves wake past the horizontally moving cylinder in a continuously stratified fluid

The flow pattern around a horizontal cylinder towed at constant velocity along isopycnic plane in a continuously stratified liquid is visualized by conventional techniques of "Vertical slit-Foucault's knife", "Maksoutov's slit-thread" and "horizontal slit-regular grating". Using sensitive high-resolution methods allows detail studying such component of stratified flow structures as soaring interfaces, singular soaring vortices and vortex systems, which arise directly inside the internal waves field past the cylinder. These flow elements having high level of vorticity are separated from the downstream wake by a strip of fluid without any small-scale inhomogeneities. Formation of singular vortex dipoles on leading edges of soaring interfaces is investigated in details in a wide range of flow parameters.

Experimental/Numerical Analysis of Chaotic Advection in a Three-dimensional Cavity Flow

Abstract Advection of material volumes in a three-dimensional cavity flow is analyzed by using an experimental setup and a collection of computational tools. The experimental setup for the lid-driven cavity flow makes it possible to study the advection of drops for a wide range of flow parameters. The location of unmixed regions for a specific mixing protocol is predicted by means of the mapping method, which are then used to determine the initial location of the dyed drops in the experiments. Finally, an adaptive front tracking method is used to computationally follow the drops during flow in a precise way. In most cases, a qualitative comparison between the experiments and the simulations is found. In addition, the mapping method proves to be well suited to quickly predict unmixed regions in mixers.

One-Dimensional Drift-Flux Model at Reduced Gravity Conditions

The drift-flux model is of practical importance for two-phase flow analyses at reduced gravity conditions. In view of this, the drift-flux model, which takes the gravity effect into account, is studied in detail. The constitutive equation of the distribution parameter for bubbly flow, which takes the gravity effect into account, has been proposed, and the constitutive equations for slug, churn, and annular flows, which can be applicable to reduced gravity conditions, are recommended based on existing experimental and analytical studies. The previously derived constitutive equations of the drift velocity in various two-phase flow regimes, which takes the frictional pressure loss into account, are adopted in this study. A comparison of the model with various experimental data over various flow regimes and a wide range of flow parameters taken at microgravity conditions shows a satisfactory agreement. The drift-flux model has been applied to reduced gravity conditions such as 1.62 and 3.71 m/s 2 , which correspond to the lunar and Martian surface gravities, respectively, and the effect of the gravity on the void fraction in two-phase flow systems has been discussed.

On the role of the stratosphere in the process of overflow of mesoscale mountains

Abstract. A 2-D, two- and three-layer stratified airflow over a mountain of arbitrary shape is considered on the assumptions that upstream wind velocity and static stability within each layer are constant (Long's model). The stratosphere is simulated by an infinitely deep upper layer with enhanced static stability. The analytical solution for the stream function, as well as first (linear) and second order approximations to the wave drag, are obtained in hydrostatic limit N1L/U0→∞, where N1 is the Brunt-Väsälä frequency in the troposphere, L is a characteristic length of the obstacle, and U0 is upstream velocity. The results of numerical computations show the principal role of long waves in the process of interaction between the model layers for a typical mesoscale mountains for which the hydrostatic approximation proves valid in a wide range of flow parameters, in accordance with the earlier conclusions of Klemp and Lilly (1975). Partial reflection of wave energy from the tropopause produces strong influence on the value of wave drag for typical middle and upper tropospheric lapse rates, leading to a quasi-periodic dependance of wave drag on a reduced frequency ( is tropopause height) in the troposphere. The flow seems to be statically unstable for k≥2 for sufficiently large obstacles (whose height exceeds 1 km). In this case, vast regions of rotor motions and strong turbulence are predicted from model calculations in the middle troposphere and the lower stratosphere. The model calculations also point to a testify for possible important role of nonlinear effects associated with finite height of the mountain on the conditions of wave drag amplification in the process of overflow of real mountains.

Turbulent boundary layer over a flat plate with uniform wall suction

A complete theory of turbulent boundary layer flow over a flat plate with uniform wall suction is proposed. The theory relies on an asymptotic analysis of the Reynolds equations and dimensional considerations and does not involve any special closure hypotheses. Characteristics of the turbulent boundary layer with suction are calculated for the entire range of flow parameters by using the known characteristics of a reference flow (turbulent boundary layer over an impermeable flat plate). The velocity and shear stress profiles, the distribution of skin friction along the plate, and integral flow characteristics are obtained by using only the known velocity profile in the reference flow. The normal Reynolds stresses are calculated by using analogous characteristics of the reference flow. Results are presented in terms of scaling variables.