High Richardson Number Research Articles

On the role of buoyancy in determining the course of PWR boron dilution transients

A computational investigation is undertaken into the role of buoyancy in a PWR boron dilution transient initiated by a postulated Small Break Loss of Coolant Accident (SB-LOCA). The scenario envisages a flow of de-borated and relatively high temperature water entering the annular downcomer from a single cold leg; flow rates are typical of natural circulation conditions. The study focuses on the temporal and spatial development of boron concentration distributions in the downcomer. The physical framework consists of a 3D-unsteady formulation of the mean flow and standard high-Reynolds-number k-ε turbulence model equations. It is found that the Richardson number (Ri = Gr/Re2) is the most important group in relation to the parameterization of the course of a concentration transient, and at Ri values characterizing a ‘baseline’ scenario, the present results indicate that there is a stable, circumferentially-uniform, descent through the downcomer of a stratified region of low-borated fluid. The same qualitative behaviour is found at a higher Richardson number; however, when Ri is reduced to approximately one-fifth of the baseline level there is evidence of large-scale mixing and a consequent absence of concentration stratification.

Kuroshio‐induced wake in the lee of Green Island off Taiwan

AbstractThe wake of Green Island was investigated in the alongshore flowing Kuroshio east of Taiwan, where current speeds range from 1 to 1.5 ms–1. Vertical profiling with shipboard lowered acoustic Doppler current profiler and conductivity‐temperature‐depth profiler revealed sizable anomalies in flow and water characteristics in the lee of Green Island. Two different stages of wake evolution were observed from two shipboard surveys. In the first stage, a recirculation developed leeward of the island, followed by a wavy (wave‐like) tail that resembled a weak vortex street. In the second stage, a cold eddy probably originating from the leeward side of the island showed up 14 km downstream of the island. The wake water was colder, saltier, higher in chlorophyll‐a concentration, and produced isopycnal doming up to 60 m. In the recirculation area, the relative vorticity, either positive or negative, was 10 times of planetary vorticity, and the horizontal divergence or convergence was O (10–4 s–1) on average. Flow divergence and convergence in the wake were expected to form upwelling and downwelling zones, producing a vertical circulation that vertically displaces isotherms. High inverse Richardson number, produced by strong vertical shear of horizontal currents, was associated with intense overturning events in the wake. High vertical shear of horizontal currents drove the mixing. The dissipation rate of turbulent kinetic energy in the overturn regions is O (10–7–10–5) W Kg–1; the corresponding eddy diffusivity is O (10–3–10–1) m2 s–1. The wake water properties are vertically diffused via upwelling and turbulence and can be delivered downstream through eddy shedding or advection. The extent of downstream influence remains to be investigated.

A new observationally motivated Richardson number based mixing parametrization for oceanic mesoscale flow

AbstractOcean models require subgrid‐scale parametrizations of vertical mixing expressed in terms of a quantity that is easily diagnosable from model output, such as the Richardson number. To date parametrizing mixing for low (<1) Richardson number flows, such as the Equatorial Undercurrent, has received the most attention. Here a new Richardson number parametrization is proposed that provides estimates of vertical turbulent diffusivity in the high Richardson number stratified shear flow that is associated with mesoscale ocean features such as eddies and fronts. This parametrization is based on direct observations of vertical turbulent diffusivity from three separate ocean regions in the North Atlantic and Southern Ocean and is found to be robust for values of the Richardson number greater than 1 at depths below the ocean surface boundary layer. The new parametrization gives substantially improved agreement with the observed mixing in the presence of mesoscale ocean features compared to existing Richardson number parametrizations.

Heat transfer and fluid flow characteristics of laminar flow past an open cavity with heating from below

Laminar mixed convective flow over a three-dimensional open cavity with heating from below at constant temperature was numerically simulated using direct numerical simulation and the most hydrodynamic and thermal aspects of the flow are presented. The effects over the velocity and temperature distribution of the buoyancy forces acting perpendicular to the mainstream flow are studied for a range of Reynolds numbers between 100 and 1500, and Richardson numbers from 0.001 to 10 to obtain a phenomenological description of the convective air flowing through the channel and the cavity. At low Reynolds and Richardson numbers the flow becomes steady and the heat diffusion is predominant, whereas at high Richardson number the heat transfer by convection becomes important and the flow experiences unsteady behavior with a significant interaction between the external flow and the recirculating flow inside the cavity, and exhibits a three-dimensional nature.

Mixed Convection Heat Transfer for Nanofluids in a Lid-Driven Shallow Rectangular Cavity Uniformly Heated and Cooled from the Vertical Sides: The Opposing Case

An investigation on flow and heat transfer due to mixed convection, in a lid-driven rectangular cavity filled with Cu- water nanofluids and submitted to uniform heat flux along with its vertical short sides, has been conducted numerically by solving the full governing equations with the finite volume method and the SIMPLER algorithm. In the case of a slender enclosure, these equations are considerably reduced by using the parallel flow concept. Solutions, for the flow and temperature fields, and the heat transfer rate, have been obtained depending on the governing parameters, which are the Reynolds, the Richardson numbers and the solid volume fraction of nanoparticles. A perfect agreement has been found between the results of the two approaches for a wide range of the abovementioned parameters. It has been shown that at low and high Richardson numbers, the convection is ensured by lid and buoyancy-driven effects, respectively, whereas between these extremes, both mechanisms compete. Moreover, the addition of Cu-nanoparticles, into the pure water, has been seen enhancing and degrading heat transfer by lid and buoyancy-driven effects, respectively.

Lattice Boltzmann simulation of mixed convection heat transfer in a corrugated wall cavity utilizing water‐based nanofluids

AbstractIn the present study, the effects of Cu and CuO nanoparticles' presence on mixed convection heat transfer in a lid‐driven cavity with a corrugated wall are investigated using the lattice Boltzmann method. The boundary fitting method with second‐order accuracy at both velocity and temperature fields is used to simulate the curved boundaries in the LBM. The problem is investigated for different Richardson numbers (0.1–10), volume fractions of nanoparticles (0–0.05), curve amplitudes (0.05–0.25), and phase shifts of corrugated wall (0–270) when the Reynolds number is equal to 25. The volume fraction of added nanoparticles to the water‐based fluid is less than 0.05 to make dilute suspensions. Results show that adding nanoparticles enhances the rate of heat transfer. It is found that nanoparticles have significant effects on both fluid flow and heat transfer of the mixed convection, especially for low Richardson numbers. A comparison between Cu and CuO nanoparticles shows the Cu nanoparticles have a better effect on heat transfer enhancement for all tested conditions. The results also represent the effective role of a corrugated wall on the rate of nanofluid heat transfer. It is observed that increasing the wavy wall's amplitude leads to a decrease of the average Nusselt numberfor a high Richardson number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21024

Mixed convection in an inclined channel with heated porous blocks

PurposeThe purpose of this paper is to study numerically the fluid flow and heat transfer in an inclined channel provided with heated porous blocks on its lower plate.Design/methodology/approachThe Brinkman‐Forchheimer extended Darcy model with the Boussinesq approximation is adopted for the flow in the porous regions. The governing equations with the appropriate boundary conditions are solved by the control volume method. The effect of some pertinent parameters such as the buoyancy force intensity, the porous blocks shape and height, the porous medium permeability and the Reynolds number are analyzed for various inclination angles ranging from −90° to +90°.FindingsThe results reveal, essentially, that the inclination angle of the channel can alter substantially the fluid flow and heat transfer mechanisms, especially at high Richardson and Darcy numbers. In this case, the maximum and minimum global Nusselt numbers are reached for α=+90° and α=−90°, respectively.Research limitations/implicationsThe results obtained in this work are valid for an inclined channel with porous blocks attached on the heated parts of the lower plate, whereas the upper wall is thermally insulated.Practical implicationsThe results obtained in this worky can be used in the thermal control of electronic components. The use of porous blocks mounted on the heat sources will increase the rate of heat removal in order to maintain the electronic components at an acceptable operating temperature.Originality/valueThe paper provides an interesting method to improve the cooling of electronic devices by use of a porous medium.

Shear-driven flushing of dense fluid from a canyon

The mechanics of shear-driven flushing of a dense fluid from a canyon is considered through a series of laboratory experiments. Experiments are presented for a range of canyon aspect ratios and flow Richardson numbers. The dynamics of the mixing is discussed qualitatively and four separate flow regimes are identified. The flow regime observed is shown to be dependent on both the canyon aspect ratio and the flow Richardson number. For taller, narrower canyons and higher Richardson numbers a two-layer stratification is observed throughout the flushing process. For wider canyons and intermediate Richardson numbers the canyon remains stably stratified but no distinct layers are observed. For low Richardson numbers and wide canyons, the canyon is relatively well mixed during the whole flushing process. A regime diagram showing the flow observed in Richardson number–aspect ratio space is presented.

Flushing a finite volume of dense fluid from a square street canyon by a turbulent overflow

Experimental results are presented for the shear-driven flushing of a dense fluid from a square street canyon. The flow is both qualitatively and quantitatively influenced by the density of the fluid in the canyon, which is parameterized in terms of the flow Richardson number. A total of 26 experiments were conducted for Richardson numbers ranging from 0.08 to 4.5. For low Richardson numbers the canyon remains well mixed during the flushing process and the density difference decays exponentially (as observed in previous studies flushing a neutrally buoyant tracer). As the Richardson number increases the canyon becomes more stably stratified and the decay rate reduces. For very high Richardson numbers, a two-layer stratification is observed. Over time, for the two-layer case, the lower dense layer gets thinner, indicating that dense fluid is being skimmed from the top of the layer, and less dense, indicating that ambient fluid is being mixed down into the dense layer. Previous studies only observed flushing by skimming. The layer buoyancy decreases linearly over time until the shear layer reaches the bottom of the canyon at which point the rate of layer buoyancy reduction dramatically increases. Results also indicate that the density interface is thinner than the shear layer that is driving the mixing, and that the difference in thicknesses increases with an increasing Richardson number. This result is consistent with previous studies of mixing in stratified shear flows. The initial exponential decay rate was calculated for each experiment and is given by k=1/(18+84Ri)1.21. Following the initial period of exponential decay, the decay rate increases as the stratification weakens.

Lattice Boltzmann simulation of mixed convection in an inclined cavity with a wavy wall

AbstractIn the present study, the effect of inclination on mixed convection heat transfer and fluid flow in a lid‐driven cavity with a wavy wall is investigated using the lattice Boltzmann method. The double‐population approach with second‐order accuracy at velocity and temperature fields is used to simulate the curved boundary in the lattice Boltzmann method. The problem is investigated for different Richardson numbers (0.1 ≤Ri≤ 10), curve amplitudes (0.05 ≤A≤ 0.25), and inclination angles (0 ≤ θ ≤ 180) when the Reynolds number is equal to 100. Results show that the inclination phenomenon has important effects on both flow and temperature fields at high Richardson numbers. It is also found that the inclination loses its role on mixed convection heat transfer from the wavy wall by the increase of the curve amplitude of the wavy wall for all Richardson numbers. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21005

EFFECT OF WAVY WALL ON CONVECTION HEAT TRANSFER OF WATER-AL2O3 NANOFLUID IN A LID-DRIVEN CAVITY USING LATTICE BOLTZMANN METHOD

Abstract In the present study, the effects of wavy wall’s properties on mixed convection heat transfer of Water-Al2O3 Nanofluid in a lid-driven cavity are investigated using the Lattice Boltzmann Method. The Boundary Fitting Method with second order accuracy at both velocity and temperature fields is used to simulate the curved boundaries in the LBM. The problem is investigated for different Richardson numbers (0.1-10), volume fractions of nanoparticles (0-0.05), curve amplitudes (0.05-0.25) and phase shifts of corrugated wall (0-270) when the Reynolds number is equal to 25. The results represent the effective role of corrugated wavy wall on rate of nanofluid heat transfer. It is observed that increasing of the wavy wall’s amplitude leads to a decrease of the average Nusselt number in high Richardson number. It is found that the increasing the volume fraction of nanoparticles enhances the rate of heat transfer. Results also show that adding nanoparticles to the base fluid has significant effects on both fluid flow and temperature field of the mixed convection, especially for low Richardson number.

Numerical modeling of turbulence mixed convection heat transfer in air filled enclosures by finite volume method

In the present study, first the turbulent natural convection and then laminar mixed convection of air flow was solved in a room and the calculated outcomes are compared with results of other scientists and after showing validation of calculations, aforementioned flow is solved as a turbulent mixed convection flow, using the valid turbulence models Standard k−e, RNG k−e and RSM. To solve governing differential equations for this flow, finite volume method was used. This method is a specific case of residual weighting method. The results show that at high Richardson Numbers, the flow is rather stationary at the center of the enclosure. Moreover, it is distinguished that when Richardson Number increases the maximum of local Nusselt decreases. Therefore, it can be said that less number of Richardson Number, more rate of heat transfer.

Color schlieren deflectometry study of jet mixing: effect of buoyancy and perforation

Mixing of jets is crucial for optimal performance of many industrial applications and there is a need to optimize both nozzle geometry and flow conditions. The present study reports the influence of buoyancy and perforation on mixing between a jet and its environment. Optical techniques are ideal for the study of jet mixing due to their non-intrusive and inertia free properties. The present study gives an account of mixing between helium jet and the ambient fluid using a combination of color schlieren deflectometry and radial tomographic mathematics. Four different perforation sizes have been used and the experiments are performed for Reynolds numbers 21–676 and Richardson numbers 3.27–0.0015. Color schlieren images show distinct influence of perforation and flow conditions (Richardson number). Oxygen concentration and jet width quantify effectiveness of jet mixing. Buoyancy plays an important role in mixing at high Richardson number. Perforation improves jet mixing i.e. there is about 120% increase in jet width and the size of perforation plays an important role.

Second law analysis in a three dimensional lid-driven cavity

Three dimensional analyses of laminar mixed convection and entropy generation in a cubic lid-driven cavity have been performed numerically. Left side of cavity moves in + y (Case I) or −y (Case II) direction. The cavity is heated from left side and cooled from right while other surfaces are adiabatic. Richardson number is the main parameter which changes from 0.01 to 100. Prandtl number is fixed at Pr = 0.71. Results are presented by isotherms, local and mean Nusselt number, entropy generation due to heat transfer and fluid friction, velocity vectors and Bejan number. Total entropy generation contours are also presented. It is found that direction of lid is an effective parameter on both entropy generation and heat and fluid flow for low values of Richardson number but it becomes insignificant at high Richardson number.

Numerical study of mixed convection in an inclined two sided lid driven cavity filled with nanofluid using two-phase mixture model

Mixed convection of a nanofluid consisting of water and SiO2 in an inclined enclosure cavity has been studied numerically. The left and right walls are maintained at different constant temperatures while upper and bottom insulated walls are moving lids. Two-phase mixture model has been used to investigate the thermal behaviors of the nanofluid for various inclination angles of enclosure ranging from θ = − 60° to θ = 60°, volume fraction from 0% to 8 %, Richardson numbers varying from 0.01 to 100 and constant Grashof number 10 4. The governing equations are solved numerically using the finite-volume approach. Results are presented in the form of streamlines, isotherms, distribution of nanoparticles and average Nusselt number. In addition, effects of solid volume fraction of nanofluids on the hydrodynamic and thermal characteristics have been investigated. The results reveal that addition of nanoparticles enhances heat transfer in the cavity remarkably and causes significant changes in the flow pattern. Besides, effect of inclination angle is more pronounced at higher Richardson numbers.

Blending of miscible liquids with different densities starting from a stratified state

Homogenization of initially segregated and stably stratified systems consisting of two miscible liquids with different density and the same kinematic viscosity in an agitated tank was studied computationally. Reynolds numbers were in the range of 3000–12,000 so that it was possible to solve the flow equations without explicitly modeling turbulence. The Richardson number that characterizes buoyancy was varied between 0 and 1. The stratification clearly lengthens the homogenization process. Two flow regimes could be identified. At low Richardson numbers large, three-dimensional flow structures dominate mixing, as is the case in non-buoyant systems. At high Richardson numbers the interface between the two liquids largely stays intact. It rises due to turbulent erosion, gradually drawing down and mixing up the lighter liquid.

Optimal excitation of two dimensional Holmboe instabilities

Highly stratified shear layers are rendered unstable even at high stratifications by Holmboe instabilities when the density stratification is concentrated in a small region of the shear layer. These instabilities may cause mixing in highly stratified environments. However, these instabilities occur in limited bands in the parameter space. We perform Generalized Stability analysis of the two dimensional perturbation dynamics of an inviscid Boussinesq stratified shear layer and show that Holmboe instabilities at high Richardson numbers can be excited by their adjoints at amplitudes that are orders of magnitude larger than by introducing initially the unstable mode itself. We also determine the optimal growth that is obtained for parameters for which there is no instability. We find that there is potential for large transient growth regardless of whether the background flow is exponentially stable or not and that the characteristic structure of the Holmboe instability asymptotically emerges as a persistent quasi-mode for parameter values for which the flow is stable.

Effect of water-based Al 2O 3 nanofluids on heat transfer and pressure drop in periodic mixed convection inside a square ventilated cavity

A numerical study of unsteady mixed convection flows through an alumina-water nanofluid in a square cavity with inlet and outlet ports due to incoming flow oscillation is performed. It is found that an oscillating velocity at the inlet port cased to creating a periodic variation in the fluid flow and temperature field in the cavity after a certain time duration. The influence of the nanoparticle on the flow and temperature fields has been plotted and discussed. The effect of the oscillation frequency is concealed in a dimensionless number which is the Strouhal number. It is observed that the heat transfer is enhanced for all the Strouhal and Richardson numbers investigated by adding the nanoparticle to the base fluid. It is also found that the performance of the nanoparticle on the enhancement of the heat transfer at higher Richardson numbers is less than that of lower Richardson numbers.

Turbulence in the Stable Boundary Layer at Higher Richardson Numbers

We present some algebraic and numerical simulations of the stable boundary layer. We also discuss the problem of the existence of a critical Richardson number (Ri), beyond which the turbulence is suppressed. We compare the results of a second-order algebraic model with those of a third-order numerical model and, to this purpose, numerical simulations of a wind-tunnel flow, which is characterized by various Richardson numbers, were performed. As far as the second-order model is concerned, solutions, for the Richardson number greater than any critical value, can be obtained by modifying the time scales of the second-order equation pressure correlation terms in order to account for a buoyancy damping factor. We show that using a third-order model allows the same results (no critical Richardson number) to be obtained without modifications to the time scales. It is suggested that the non-locality, accounted for by the third-order moments, could allow the turbulence to persist also for Ri > 1.

Numerical study of the fin effect on mixed convection heat transfer in a lid-driven cavity

In this study, the mixed convective heat transfer in a lid-driven cavity was investigated numerically. The finite volume discritization method was used to solve the momentum and energy equations by using the classic Boussinesq incompressible approximation. The cavity vertical walls are insulated whereas the bottom (hot wall) and top (cold wall) surface are maintained at a uniform temperature and fins are located on bottom wall. The effect of fin numbers over the flow field and heat transfer was investigated at various Richardson numbers. Study was carried out for Richardson numbers ranging from 0.01 to 10, fin numbers between 1 and 7, fin height ratio change from 0.05 to 0.3, and thermal conductivity ratio (fin to fluid) from 10 to 104, respectively. The results are presented in the form of streamlines, temperature contours, and Nusselt number distributions. The results show that the Nusselt number increases when the number of fin and fin height decrease. In addition, in all cases an increasing Richardson number caused increasing the relative Nusselt number ( Nu / Nu0). The heat transfer enhancement was observed at low fin numbers (1 and 3) and high Richardson number in comparison with the cavity without fins.