Dimensionless Flow Rate Research Articles

Levantamento das Curvas do Comportamento Hidráulico do Mecanismo de Transposição de Peixes da UHE de Igarapava

The design of fishway mechanisms in Brazil has basically followed the design requirements and characteristics commonly used in Europe and North America. The determination of the flow condi tions in the pool system is a fundamental step for successful fishway design. In order to provide information for the design of vertical slot fishways, this work deals with an exp erimental study on the flow conditions of the fishway mechanism installed in Igarapa- va Dam, located at the border between Minas Gerais and Sao Paulo. A scale model of this mechanism is specially devised to study its behavior. Moreover, this work presents an analysis about the applicability of the classical flow equations employed in the fi shway design. For convenience of construction, the dimensions of the tanks used in the prototype of the Igarapava Dam are different from those generally used in fishway design. Estimates computed for the dimensionless flow rates are compared with measure- ments performed on the prototyp e. The fitted curve for the hydraulic parameters of the Igarapava fishway is also pre- sented in this work

Thermal Transport Characteristics of Mixed Pressure and Electro-Osmotically Driven Flow in Micro- and Nanochannels With Joule Heating

This study investigates convective transport phenomena of combined electro-osmotic and pressure-driven flow in a microchannel subject to constant surface heat flux, with Joule heating effect taken into account. The governing system of equations includes the electric potential field, flow field, and energy equations. Analytical solutions are obtained for constant fluid properties, while numerical solutions are presented for variable fluid properties. For constant properties, the problem is found to be governed by three ratios: the length scale ratio (the ratio of Debye length to half channel height), the velocity scale ratio (the ratio of pressure-driven velocity to electro-osmotic velocity), and the ratio of Joule heating to surface heat flux. A small length scale ratio corresponds to a microchannel, while finite length scale ratio represents a nanochannel. For electro-osmotic flow only, the momentum transport is solely a function of the length scale ratio. For combined electro-osmotic and pressure-driven flow, the velocity profile and therefore the friction factor depend on both the length scale ratio and the velocity scale ratio. Assuming a thermally fully developed flow, analytical expressions for the normalized temperature profile and Nusselt number are developed. The representative results for the friction factor, normalized temperature profile, and Nusselt number are illustrated for some typical values of the three ratios. For purely electro-osmotic flow, it is found that the Nusselt number increases with decreasing ε, approaching the value for slug flow as the length scale ratio approaches zero. For mixed flow with a given length scale ratio, the results show that the Nusselt number decreases with the velocity scale ratio, approaching the classical Poiseuille flow as the velocity scale ratio approaches infinite. When the effects of variable fluid properties are included in the analysis, numerical solutions are generated to explore the influence of thermal conductivity and viscosity variations with local temperature on the hydrodynamic and thermal characteristics of the fluid. These temperature-dependent property variations would initially develop pressure-driven flow, and correspondingly the dimensionless velocity and volume flow rate increase to account for such variations. The friction factor reduces considerably with viscosity variation, while the Nusselt number increases gently. Although the influence of thermal conductivity variation on the hydrodynamic characteristics is not impressive, it has certain impact on the heat transfer results; more specifically, increasing the conductivity variation will produce a sensible increase in Nusselt number but a small decrease in the normalized temperature.

A coupled DEM/CFD analysis of the effect of air on powder flow during die filling

AbstractDie filling from a stationary shoe in a vacuum and in the presence of air was numerically analyzed using an Eulerian‐Lagrangian model, which employs a discrete element method (DEM) for the particles and computational fluid dynamics (CFD) for the air with a two‐way air‐particle interaction coupling term. Monodisperse and polydisperse powder systems have been simulated to explore the effect of the presence of air on the die filling process. For die filling with monodisperse powders, the influences of particle size and density on the flow behavior were explored. The numerical simulations revealed that the presence of air has a significant impact on the powder flow behavior, especially for systems with smaller and/or lighter particles. Flow has been characterized in terms of a dimensionless mass flow rate, and it has been shown that for die filling in a vacuum this is constant. The flow characteristics for die filling in air can be classified into two regimes. There is an air‐inert regime in which the particle size and density are sufficiently large that the effect of air flow becomes negligible, and the dimensionless mass flow rate is essentially identical to that obtained for die filling in a vacuum. There is also an air‐sensitive regime, for smaller particle sizes and lower particle densities, in which the dimensionless mass flow rate increases as the particle size and density increase. The effects of particle‐size distribution and adhesion on the flow behavior have also been investigated. It was found that, in a vacuum, the dimensionless mass flow rate for polydisperse systems is nearly identical to that for monodisperse systems. In the presence of air, a lower dimensionless mass flow rate is obtained for polydisperse systems compared to monodisperse systems, demonstrating that air effects become more significant. Furthermore, it has been shown that, as expected, the dimensionless mass flow rate decreases as the surface energy increases (i.e., for more cohesive powders). © 2008 American Institute of Chemical Engineers AIChE J, 2009

Heat transfer by convection, conduction and radiation in solar chimney systems for ventilation of dwellings

Numerical study by conjugate heat transfer is carried out of solar chimney systems for heating and ventilation of dwellings. Conservation equations are solved by finite difference-control volume numerical method. The governing parameters were: the Rayleigh numbers from 5 × 10 8 to 10 11, the Prandtl number, Pr = 0.7, constant for air, the chimney aspect ratio, A = H/L from 6 to 15, the air channel width l′/ L = 0.2 to 0.5, the air entrance port size, h/L = 0.167–0.667, the wall thickness l/ L = 0.25–0.4, the conductivity ratio k r from 5 to 50 and the surface emissivity, ε from 0 to 1. The Nusselt number, the dimensionless volume flow rate V ˙ and radiation heat flux ratio q r/ q tot are calculated as a function of the governing parameters, and streamlines and isotherms are produced. The results show that the surface radiation modifies the flow and temperature fields, affects the Nusselt number and the volume flow rate, both in a positive way, and improves the ventilation performance of the chimneys.

Mass and energy-capital conservation equations to study price evolution of non-renewable energy resources, Part III – Energy supply curve

The price evolution of non-renewable resources versus the consumption rate is investigated with the aim of constructing the energy supply curve. The case studied is without accumulation nor depletion of the resources and the mass and energy-capital conservation equations are solved under the condition of the same mass flow rate of extraction and sale. The energy supply curve of extracted resource is dependent on the newly defined parameter, RINE, Rate of Interest of Non-extracted resources on the Extraction rate. The energy supply curve of sold resource is dependent on the newly defined parameter, RISE, Rate of Interest of Sold resources on the Extraction rate, in case the rate of interest of non-extracted resources, r N , is nil. In general, the energy supply curve of sold resource is dependent also on two dimensionless parameters, Dimensionless Critical Initial Price of Sold resources , i.e. DCIPS, and Dimensionless Critical Initial Price Extreme of Sold resources, i.e. DCIPES. The energy supply curve of sold resources is investigated under different relations between three parameters, i.e. extraction rate and interest rates of non-extracted and extracted/sold resources. New trends are observed in the economic market of non-renewable energy resources. The energy supply curve of the difference between sold and extracted resource is also obtained and is dependent on two dimensionless parameters, Critical Initial Price Difference , i.e. CIPD, and Critical Extreme of the Initial Price Difference, i.e. CEIPD. Finally, the predictions obtained with the present approach are compared to the real evolution of the world price of oil and the European price of gas versus the world consumption during the last three decades, i.e. from 1980 until 2005 for oil and from 1984 until 2005 for gas, taking into account inflation, discount and prime rates of the economic market. The agreement is acceptable but, more important, the trend is correctly predicted. The price difference between sold and extracted resources is also investigated versus the dimensionless mass flow rate of extraction. The evolution is dependent on four parameters: RINE, RISE, DCIPS, and DCIPES.

Numerical prediction of natural convection in vented cavities using restricted domain approach

The present study reports the numerical simulation of natural convection heat transfer from an open square cavity with two side vents provided symmetrically on the side walls. The top wall which is maintained at a constant temperature ( T w), is the heat source for the cavity and the side walls are adiabatic. A restricted domain approach that predicts the regions of inflow, outflow and velocity distributions is employed. The applicability of two types of pressure boundary conditions at entry and exit regions are studied and compared. Non-linear coupled partial differential equations governing natural convection are solved on a structured non-uniform staggered grid using a second-order accurate upwind least square scheme for discretising the convection terms, central difference scheme for diffusion terms and SIMPLER algorithm for pressure–velocity decoupling. An in-house code is developed and is validated with the results of three classical natural convection problems. Simulations have been carried out for a wide range of thermal parameter, Rayleigh numbers (10 4 ⩽ Ra ⩽ 10 8), orientation of the cavity about horizontal (0 ⩽ δ ⩽ 180) and geometrical parameter, vent ratio ( 0.05 ⩽ D L ⩽ 0.25 ) . The numerical simulation predicts the dimensionless mass flow rate through the cavity and variation of local Nusselt number over the hot wall. A correlation for average Nusselt number is developed in terms of Rayleigh number and angle of tilt of the cavity for D L ⩾ 0.1 .

Simplified graphical correlation for determining flow rate in tight gas wells in the Sulige gas field

The Sulige tight gas reservoir is characterized by low-pressure, low-permeability and low-abundance. During production, gas flow rate and reservoir pressure decrease sharply; and in the shut-in period, reservoir pressure builds up slowly. Many conventional methods, such as the indicative curve method, systematic analysis method and numerical simulation, are not applicable to determining an appropriate gas flow rate. Static data and dynamic performance show permeability capacity, kh is the most sensitive factor influencing well productivity, so criteria based on kh were proposed to classify vertical wells. All gas wells were classified into 4 groups. A multi-objective fuzzy optimization method, in which dimensionless gas flow rate, period of stable production, and recovery at the end of the stable production period were selected as optimizing objectives, was established to determine the reasonable range of gas flow rate. In this method, membership functions of above-mentioned optimizing factors and their weights were given. Moreover, to simplify calculation and facilitate field use, a simplified graphical illustration (or correlation) was given for the four classes of wells. Case study illustrates the applicability of the proposed method and graphical correlation, and an increase in cumulative gas production up to 37% is achieved and the well can produce at a constant flow rate for a long time.

Thermal management of a symmetrically heated channel–chimney system

A parametric analysis of natural convection in air, in a channel–chimney system, symmetrically heated at uniform heat flux, obtained by means of a numerical simulation, is carried out. The analyzed regime is two-dimensional, laminar and steady-state. Results are presented in terms of wall temperature profiles in order to show the more thermally convenient configurations which correspond to the channel–chimney system with the lowest maximum wall temperature. For the considered Rayleigh number, the difference between the highest and the lowest maximum wall temperatures increases with increasing the channel aspect ratio. The optimal expansion ratio values depend strongly on the Rayleigh number and extension ratio values and slightly on the channel aspect ratio. Correlations for dimensionless mass flow rate, maximum wall temperature and average Nusselt number, in terms of Rayleigh number and dimensionless geometric parameters are presented in the ranges: 5 ⩽ Ra ∗ ⩽ 2.0 × 10 4 , 1.5 ⩽ L / L h ⩽ 4.0 and 1.0 ⩽ B / b ⩽ 4.0 .

Rarefied gas flow through short tubes into vacuum

A rarefied gas flow into vacuum through a tube of finite length is investigated over the whole range of gas rarefaction by the direct simulation Monte Carlo method. The nonequilibrium effects at the inlet and outlet of the tube have been considered by including in the computational domain large volumes of the upstream and downstream reservoirs. Results for the dimensionless flow rate and for the flow field are presented for a wide range of the gas rarefaction and for various values of the length to radius ratio in the range from 0 to 10. The influence of the gas-surface interaction model, as well as the effect of the intermolecular potential model on the gas flow, is examined. A good agreement has been obtained between the present numerical results and the corresponding experimental ones available in the literature.

Laser Doppler Anemometer Measurements of the Flow in the Impeller Blade Channels of a Centrifugal Blood Pump

Hemodynamics in the rotary blood pumps is of great importance for it is highly related to the blood hemolysis and thrombus generation in the blood pumps. In the present study, the flow in the impeller passages of Kyoto-NTN centrifugal blood pump with 16 forward-bending blades was measured using Laser Doppler Anemometer (LDA) on a 1:1 size pump model. The measurement results were compared with those of the numerical simulation study and the measurement results on a 5:1 enlarged pump model. The comparison indicated a reasonable agreement between the results of the present measurement and the numerical simulation. The comparison between the measurement results on the 1:1 and 5:1 enlarged pump models revealed, however, significant differences in the flow patterns. The main cause of the differences between the 1:1 and 5:1 pump model should be due to the incomplete similarity of the later, which has produced 31% higher dimensionless flow rate than the prototype. Therefore, it is important to require more elabor...

Turbulent natural convection flow in a vertical channel with anti-symmetric heating

This paper presents the fluid flow characteristics of natural convection flow in an anti-symmetrically heated parallel-plate vertical channel using the Particle Image Velocimetry (PIV) system. The channel walls were subjected to uniform temperature conditions, with one wall heated above ambient and the opposing wall maintained below ambient temperature. Velocity measurements were conducted at three different sections on the horizontal plane to validate two-dimensionality of the flow and at three different heights in the vertical plane to establish vertical mean velocity profiles. The results indicate that the flow recirculation in the channel exhibits a similar character to that of a closed cavity and the induced flow rate is much lower than the one for a channel with both walls heated. A correlation for the dimensionless flow rate is developed.

Mixing in a vibrated granular bed: Diffusive and convective effects

In this study, Discrete Elementary Method (DEM) is employed to simulate the motion and mixing behavior of granular materials in a three-dimensional vibrated bed, which is energized by vertical sinusoidal oscillations under different vibrating conditions. With frictional sidewalls, the convection flow is a very important phenomenon in the vibrated granular bed. The influence of vibrating conditions, including vibration acceleration and frequency, on the formation of symmetric convection flow is investigated in this study. In order to characterize the convective flow and the diffusive motion of granular materials, the dimensionless convection flow rate, J conv, and the vertical self-diffusion coefficient, D yy , are defined, respectively. Péclet number, Pe, is employed to characterize the ratio of the convective flow to the diffusive motion in vertical direction. The role of Pe in the formation of symmetric convection flow is discussed in detail. Moreover, the top-bottom initial loading pattern of two groups of glass beads with different colors is employed to investigate mixing behavior of granular materials. The well-known Lacey index is employed as the mixing degree, M, to quantify the mixing quality. The mixing rate is calculated from a least-square fit using the time evolution of M. The simulation results demonstrate that the mixing rates increase with increasing J conv and D yy in exponential relations.

Numerical Investigation of Transient Natural Convection in Air in a Convergent Vertical Channel Symmetrically Heated at Uniform Heat Flux

A numerical investigation of natural convection in a convergent vertical channel is accomplished in order to study the thermal and fluid dynamics behavior of the transient regime in this configuration. The convergent channel has the two principal flat plates at uniform heat flux and the numerical analysis is carried out in a two-dimensional laminar regime. Results in terms of wall temperature profile, as a function of the time for inclination angle, between 0° and 10°, aspect ratios in the range of 10 to 58, and channel Rayleigh numbers from 5.0 to 3.8 × 103, are presented. Dimensionless wall temperature sensitivity to the convergence variation is almost 0° for larger angle values. Maximum wall dimensionless temperature, for all convergence angles considered, changes in a very small range at small values of dimensionless time. Overshoots and undershoots in maximum and average dimensionless wall temperature profiles, as well as for dimensionless mass flow rate, are detected. The Nusselt number decreases remarkably between the initial time and 0.2. According to previous results, for steady-state investigations, a channel with a convergence angle equal to 2° is the best configuration in terms of maximum wall temperature and heat transfer coefficient. Stream function and dimensionless air temperature fields allow analysis of fluid dynamics and thermal behavior for different times.

Numerical study of solar-wind tower systems for ventilation of dwellings

Numerical study is carried out of a simplified system of solar-wind tower for ventilation of dwellings. The conservation equations for mass, momentum and energy for mixed convection in two-dimensional coordinates are solved by the control volume method and Simpler algorithm. The governing parameters of the problem are Rayleigh number Ra, Reynolds number, Re (or Richardson number, Ri), the dimensionless conductivity of the solid medium, k r and the geometrical parameters. Nusselt number Nu and dimensionless volume flow rate V ˙ are calculated as a function of the governing parameters, and streamlines and isotherms are produced. The results show that the important parameters affecting the ventilation performance are Ra, Re (or Ri), and the geometrical parameters, the aspect ratio A, the exit port size h 1/ L and to a lesser degree, the wall thickness ℓ 1/ L.

Dynamics of liquid rope coiling

We present a combined experimental and numerical investigation of the coiling of a liquid "rope" falling on a solid surface, focusing on three little-explored aspects of the phenomenon: The time dependence of "inertio-gravitational" coiling, the systematic dependence of the radii of the coil and the rope on the experimental parameters, and the "secondary buckling" of the columnar structure generated by high-frequency coiling. Inertio-gravitational coiling is characterized by oscillations between states with different frequencies, and we present experimental observations of four distinct branches of such states in the frequency-fall height space. The transitions between coexisting states have no characteristic period, may take place with or without a change in the sense of rotation, and usually (but not always) occur via an intermediate "figure of eight" state. We present extensive laboratory measurements of the radii of the coil and of the rope within it, and show that they agree well with the predictions of a "slender-rope" numerical model. Finally, we use dimensional analysis to reveal a systematic variation of the critical column height for secondary buckling as a function of (dimensionless) flow rate and surface tension parameters.

Gas displacement of viscoplastic liquids in capillary tubes

The displacement of viscoplastic liquids in capillary tubes by gas injection is examined. The viscoplasticity alters the flow kinematics and changes dramatically the amount of mass left attached at the tube wall as compared to the Newtonian case, studied experimentally by G.I. Taylor in 1961 [G.I. Taylor, Deposition of a viscous fluid on the wall of a tube, J. Fluid Mech. 10 (1961) 161–165]. Experiments with Carbopol aqueous solutions were performed for different flow rates. A recently proposed viscosity function for viscoplastic liquids was fitted to the rheological data of the Carbopol solutions. A new dimensionless rheological property – the jump number – arises in the dimensionless version of this viscosity function. The results show the effect of the viscoplastic character of the liquid on the free surface shape and on the thickness of the film of liquid left attached to the wall. This thickness decreases with the jump number and increases with the flow rate. It is also observed that there is a critical dimensionless flow rate below which the displacement is apparently perfect, i.e. there is no observable liquid left attached to the wall. This behavior is shown to be directly related to the fully developed flow far ahead the air–liquid interface.

06/02337 Modeling of solar passive techniques for roof cooling in arid regions: Jain, D. et al. Building and Environment, 2006, 41, (3), 277–287.

A generalized correlation has been proposed to estimate the steady-state flow in two-phase natural circulation loops. The steady-state governing equations for homogeneous equilibrium model, viz. continuity, momentum and energy equations have been solved to obtain the dimensionless flow rate as a function of a modified Grashof number and a geometric number. To establish the validity of this correlation, two-phase natural circulation flow rate data from five different loops have been tested with the proposed correlation and found to be in good agreement.

Design of Simulated Moving Bed Separations: Generalized Langmuir Isotherm

In this paper, exact criteria for the complete separation of binary mixtures in simulated moving bed (SMB) units are developed. They apply to systems subject to the generalized Langmuir isotherm, whose definition yields four different types of isotherms corresponding to different combinations of Langmuir and anti-Langmuir behavior of the components to be separated. These criteria are derived in a similar way in the different cases using the equilibrium theory of chromatography applied to the equivalent true moving bed (TMB) unit. Separation performance is controlled by the dimensionless flow rate ratios. The complete separation region in the operating parameters space has boundaries that are constituted of straight lines and curves, defined through simple and easy-to-use equations. These in turn depend on the adsorption isotherm parameters and on the composition of the feed mixture. The analogies and differences observed among the four isotherms in terms of complete separation region are analyzed and discussed.

A generalized flow correlation for two-phase natural circulation loops

A generalized correlation has been proposed to estimate the steady-state flow in two-phase natural circulation loops. The steady-state governing equations for homogeneous equilibrium model, viz. continuity, momentum and energy equations have been solved to obtain the dimensionless flow rate as a function of a modified Grashof number and a geometric number. To establish the validity of this correlation, two-phase natural circulation flow rate data from five different loops have been tested with the proposed correlation and found to be in good agreement.

The drag-out problem in film coating

The classical coating flow problem of determining the asymptotic film thickness (and hence the load) on a flat plate being withdrawn vertically from an infinitely deep bath is examined via a numerical solution of the steady-state Navier-Stokes equations. Under creeping flow conditions, the dimensionless load q is computed as a function of the capillary number Ca and, for Ca<0.4, is found to agree with Wilson’s extension [J. Eng. Math. 16, 209 (1982)] of Levich’s well-known expression. On the other hand, for Ca→∞, q asymptotes to 0.582, well below the value of 2∕3 postulated by Deryagin and Levi [Film Coating Theory (Focal, London, 1964)]. For finite Reynolds numbers Re≡mCa3∕2, where m is a dimensionless number involving only the gravitational acceleration g and the properties of the fluid, q is found to remain essentially independent of m at a given Ca, but only up to a critical capillary number Ca*, dependent on m, beyond which our numerical scheme failed. Analogous results, but only for creeping flows, are presented for the case where the plate is inclined at an angle α from the vertical. Here, the corresponding dimensionless flow rate qα≡q(cosα)1∕2 depends on both Ca and α, and its maximum is found to increase monotonically with α and to become equal to 2∕3 when α exceeds a critical angle αc(∼π∕4), where the plate is inclined midway to the horizontal with its coating surface on the topside.