High Richardson Number Research Articles

Experimental study of liquid metal heat transfer in a vertical duct affected by coplanar magnetic field: Downward flow

Liquid metal flows under a high thermal load and strong magnetic field are of great interest in the context of the development of fusion reactor cooling systems. In this study, a downward flow of mercury in a heated duct, affected by a coplanar magnetic field (directed transverse to the main flow and along the long side of the duct), is studied experimentally for symmetrical (two-sided) and asymmetrical (one-sided) duct heating, showing different flow behaviors in the magnetic field. We show that in spite of the qualitatively different structure of the downward flow in the duct with different heating modes, the applied coplanar magnetic field provides a rather general reaction, which includes two scenarios determined by the Richardson number. At high Richardson numbers (Ri≳1), the Nusselt number tends toward the turbulent limit, as expected in the channel without a magnetic field, and at low Richardson numbers (Ri≲1), the Nusselt number tends to its laminar limit.

Mixed convection heat transfer and entropy generation of Cu-water nanofluid in wavy-wall lid-driven cavity in presence of inclined magnetic field

An investigation is performed into the effects of an inclined magnetic field on the mixed convection heat transfer characteristics and entropy generation in a nanofluid-filled lid-driven cavity with a wavy surface. The heat energy transport processes within the cavity are visualized by plotting the energy flux vectors. The simulations investigate the effects of the Hartmann number, Richardson number, volume fraction of nanoparticles, inclination angle of the applied magnetic field, wave amplitude of the wavy surface, Reynolds number, and irreversibility distribution ratio on the energy flux vectors, mean Nusselt number, total entropy generation, and Bejan number. The range of the studied parameters is as follows: Richardson number from 10 − 2 to 102, Reynolds number from 1 to 300, Hartmann number from 0 to 50, inclination angle of the applied magnetic field from 0° to 360°, nanoparticle volume fraction from 0% to 4%, wavy-surface amplitude from 0.0 to 0.7, irreversibility distribution ratio from 10 − 6 to 100. It is shown that the energy flux vectors form large closed circulations under higher Richardson numbers and Reynolds numbers. In other words, the mean Nusselt number and total entropy generation increase with an increasing Richardson number and Reynolds number. By contrast, the size of the circulation structures reduces with an increasing Hartmann number. Hence, a larger Hartmann number gives rise to a lower mean Nusselt number and total energy generation. The mean Nusselt number and total entropy generation increase with an increasing volume fraction of nanoparticles and a larger amplitude of the wavy surface. In addition, for a given Richardson number, the mean Nusselt number and total entropy generation can be enhanced by tuning the inclination angle of the magnetic field. Finally, the Bejan number reduces with an increasing Hartmann number, a larger irreversibility distribution ratio, and a lower Richardson number.

Mixed convection heat transfer in a differentially heated cavity with two rotating cylinders

Mixed convection heat transfer in a differentially heated cavity with two rotating cylinders was studied numerically for various pertinent parameters such as Richardson number, Reynolds number, non-dimensional rotation speed of the cylinder, and the location of the cylinders. The results from these simulations were validated using an open-source spectral element code, Nek5000. The results of this study were presented in terms of streamlines, isotherms, local and average Nusselt number, and temperature profiles. The results illustrated that the average Nusselt number depends strongly on the rotation speed of the cylinder, Reynolds number, and Richardson number. However, the average Nusselt number was found to be independent of the rotation speed at high Richardson number (Ri = 10). In addition, the direction of the rotation speed of the cylinders has a profound effect on the average Nusselt. The study illustrated that the magnitude and direction of the rotation speed of the cylinders have a significant effect on the flow pattern and isotherms.

Heat transfer and entropy generation of laminar mixed convection in an inclined lid driven enclosure with a circular porous cylinder

Convective heat transfer and entropy generation in an inclined lid driven square enclosure with a circular porous cylinder positioned at the center have been investigated numerically. The governing transport equations within the porous media are treated according to the volume-average theory while the transport phenomena in the rest of the enclosure are represented with Navier–Stokes equations. The bottom wall of the enclosure is assumed to have higher temperature than the top wall and the sidewalls are insulated. In addition, the top horizontal wall is moving in its own plane with a constant speed while all other walls remain stationary. Computations have been conducted over a wide range of pertinent parameters: Richardson number (Ri = 0.01, 1, 5 and 10), Darcy number (Da = 10−5, 10−4, 10−3 and 10−2), and inclination angle (α = 0, 30, 45, 75 and 90). Results revealed that the effects of Darcy number and inclination angle on heat transfer depends on the Richardson number. The effect of the inclination angle on the heat transfer and entropy generation inside the enclosure is more noticeable at high Richardson numbers. Second law analysis also indicated that the proportion of the irreversibilities due to the fluid friction and heat transfer varies as the scrutinized parameters change.

Investigation of thermo-fluid behavior of mixed convection heat transfer of different dimples-protrusions wall patterns to heat transfer enhancement

This study is a numerical investigation of the effect of improving heat transfer namely, modified rough (dimples and protrusions) surfaces on the mixed convective heat transfer of a turbulent flow in a horizontal tube. The effects of different dimples-protrusions arrangements on the improving the thermal performance of a rough tube are investigated at various Richardson numbers. Three dimensional governing equations are discretized by the finite-volume technique. Based on the obtained results the dimples-protrusions arrangements are modified to find a suitable configuration for which heat transfer coefficient and pressure drop to be balanced. Modified dimples-protrusions arrangements that shows higher performance is presented. Its average thermal performance 18% and 11% is higher than the other arrangements. In addition, the results show that roughening a smooth tube is more effective at the higher Richardson number.

Laminar mixed convection of power-law fluids in cylindrical enclosures with heated rotating top wall

Laminar mixed convection of inelastic non-Newtonian fluids obeying a power law model in a cylindrical enclosure with a heated rotating top cover has been investigated numerically in this study. The steady-state axisymmetric simulations have been carried out for a range of different nominal Reynolds, Prandtl, Richardson numbers (i.e. 500⩽Re⩽2000;10⩽Pr⩽500 and 0⩽Ri⩽1) and power-law index (i.e. 0.6⩽n⩽1.8) for an aspect ratio (height/radius) of unity (i.e. AR=1.0). It has been found that mean Nusselt number Nu‾ increases as Re and Pr increase, whereas Nu‾ decreases with increasing values of Ri for shear-thinning (i.e. n<1), Newtonian (i.e. n=1) and shear-thickening (i.e. n>1) fluids. It has also been observed that the variation of Nu‾ with n differs depending on the values of Re and Ri. For instance, for small values of Reynolds number, Nu‾ exhibits a non-monotonic trend (i.e. increases before reaching a maximum followed by a decreasing trend) with increasing n for small values of Richardson number, whereas Nu‾ monotonically increases with increasing values of n for high Richardson number cases. However, in the case of high Reynolds number, Nu‾ increases with n before reaching a maximum value which is followed by a decreasing trend for all values of Ri considered here. Detailed physical explanations are provided for the influences of Re, Pr, Ri, and n on Nu‾ based on an elaborate scaling analysis. Finally, the numerical findings have been used to propose a correlation for Nu‾ for the ranges of Re,Pr,Ri,n considered here.

Mixing of Stratified Miscible Liquids in an Unbaffled Tank with Application in High Concentration Protein Drug Product Manufacturing

During high-concentration protein drug product compounding, the property difference between the drug substance solution and the buffer excipient solution can potentially cause the formation of stratified layers, which may prohibit effective mixing. In this study, mixing of two stratified liquids in an unbaffled tank with an angle-mounted impeller was investigated using both experiments and computational fluid dynamics (CFD) simulations. The results revealed that the mixing time under the stratified conditions could be over an order of magnitude longer than that predicted by a commonly used blend time correlation. Further analysis showed that the observed long mixing time occurred when the buoyancy force due to density difference between the liquids was dominant over the impeller stir and was correlated with high Richardson number. The study also looked into the impact of factors such as liquid height and impeller size, and a new correlation was proposed based on the experimental data.

Global stability of buoyant jets and plumes

The linear global stability of laminar buoyant jets and plumes is investigated under the low-Mach-number approximation. For Richardson numbers in the range $10^{-4}\leqslant Ri\leqslant 10^{3}$ and density ratios $S=\unicode[STIX]{x1D70C}_{\infty }/\unicode[STIX]{x1D70C}_{jet}$ between 1.05 and 7, only axisymmetric perturbations are found to exhibit global instability, consistent with experimental observations in helium jets. By varying the Richardson number over seven decades, the effects of buoyancy on the base flow and on the instability dynamics are characterised, and distinct behaviour is observed in the low-$Ri$ (jet) and in the high-$Ri$ (plume) regimes. A sensitivity analysis indicates that different physical mechanisms are responsible for the global instability dynamics in both regimes. In buoyant jets at low Richardson number, the baroclinic torque enhances the basic shear instability, whereas buoyancy provides the dominant instability mechanism in plumes at high Richardson number. The onset of axisymmetric global instability in both regimes is consistent with the presence of absolute instability. While absolute instability also occurs for helical perturbations, it appears to be too weak or too localised to give rise to a global instability.

Interaction of vortex ring with a stratified finite thickness interface

This work experimentally investigates the dynamics of interaction between a propagating vortex ring and density stratified interface of finite thickness. The flow evolution has been quantified using a high speed shadowgraph technique and particle image velocimetry. The spatial and temporal behaviours of the vortex in the near and far field of the interface and the plume structure formed due to buoyancy are investigated systematically by varying the vortex strength (Reynolds number, Re) and the degree of stratification (Atwood number, At). Maximum penetration length (Lpmax) of the vortex ring through the interface is measured over a range of Reynolds (1350 ≤ Re ≤ 4600) and Richardson (0.1 ≤ Ri ≤ 4) numbers. It is found that for low Froude number values, the maximum penetration length varies linearly with the Froude number as in the study of Orlandi et al. [“Vortex rings descending in a stratified fluid,” Phys. Fluids 10, 2819–2827 (1998)]. However, for high Reynolds and Richardson numbers (Ri), anomalous behaviour in maximum penetration is observed. The Lpmax value is used to characterize the vortex-interface interactions into non-penetrative, partially-penetrative, and extensively penetrative regimes. Flow visualization revealed the occurrence of short-wavelength instability of a plume structure, particularly in a partially penetrative regime. Fluid motion exhibits chaotic behaviour in an extensively penetrative regime. Detailed analyses of plume structure propagation are performed by measuring the plume length and plume rise. Appropriate scaling for the plume length and plume rise is derived, which allows universal collapse of the data for different flow conditions. Some information concerning the instability of the plume structure and decay of the vortex ring is obtained using proper orthogonal decomposition.

Numerical Investigation on Flow and Mixed convective Heat Transfer of Non-Newtonian Impinging Slot Jets

Mixed convection heat transfer of non-Newtonian impinging slot jets was investigated numerically. The simulation was performed using a temperature dependent power-law viscosity model. The results showed that for high Richardson numbers, a recirculation zone is created in the vicinity of impingement wall which prevents the jet stream from penetration into near wall region and decreases the Nusselt number around the stagnation point. The effects of jet-to-plate spacing, inlet Peclet number and the jet inlet width on the flow structure and heat transfer characteristics of impinging jet were studied using the numerical results. By decreasing jet-to-plate spacing and jet inlet width and increasing inlet Peclet number, the flow reversal in the vicinity of heated wall was disappeared and the local Nusselt number increases as a result of deeper penetration of jet stream the near wall region. Furthermore, the results indicated that the maximum local and average Nusselt numbers belong to the shear-thinning jets with minimum inlet width and the minimum jet-to-plate spacing.

Conjugate-mixed convection heat transfer in a two-sided lid-driven cavity filled with nanofluid using Manninen's two phase model

A numerical study is carried out concerning conjugate mixed convection heat transfer of various type of the nanofluid in a two-dimensional square enclosure using Manninen's model (Two phase mixture model). In the both cases of internal/external heating and cooling, hot and cold surfaces are kept at different constant temperatures while other walls of the enclosure are thermally insulated. Two-dimensional Navier–Stokes, energy and volume fraction equation are solved using the finite volume method and SIMPLE algorithm. This study has been conducted to investigate the effects of the certain pertinent parameters such as: Richardson number (10 − 2 ≤ Ri ≤ 102), thermal conductivity ratio (0.1 ≤ Kr ≤ 10), presence of the conductive obstacles, number of the hot obstacles, volume fraction (0 ≤ ϕ ≤ 0.05), size (25 nm ≤ dp ≤ 145 nm) and type (Cu, Al2O3 and TiO2) of the nanoparticles on the fluid flow and heat transfer characteristics. The simulation results indicate that depending on the boundary conditions of the problem, there is an optimal volume fraction of the solid particles at which the maximum heat transfer rate can be obtained within the enclosure. It is also observed that at high Richardson numbers, the particle distribution is fairly non-uniform while by decreasing the Richardson number and nanoparticles diameter, distribution of solid particles becomes uniform. Moreover, it is found that at low values of Richardson numbers, type of the nanoparticles has nominal effect on heat transfer rate while at high Ri by increasing the thermal conductivity of the solid particles, the total Nusselt number and optimal particle loading increase. Finally, the results demonstrate that, adding a vertical conductive wall into the enclosure leads to a significant reduction of the heat transfer rate at all values of Richardson numbers.

Numerical simulation of double-diffusive mixed convection in an enclosure filled with nanofluid using Bejan’s heatlines and masslines

In this study, double-diffusive mixed convection of temperature-dependent alumina-water nanofluid in a lid-driven square enclosure is numerically investigated. The governing equations are discretized using finite volume method and solved by SIMPLER algorithm. The temperature and concentration of the left wall are higher than those of the right wall, while the two other walls are adiabatic and impermeable. The simulations are conducted for Richardson numbers of 0.01≤Ri≤100, buoyancy ratios of −5≤Br≤5, and nanoparticle volume fractions of 0≤ϕ≤4%. The results show that at high Richardson numbers, increasing the nanoparticle volume fraction results in a decrease in the average Nusselt number, while at low Richardson numbers this leads to an increase in the average Nusselt number. Additionally, by comparing the Nusselt or Sherwood numbers for positive and negative values of a same buoyancy ratio, the positive values always lead to higher average Nusselt or Sherwood number. Moreover, the heatlines are more compressed for nanofluid than pure fluid, which demonstrates better convective heat transfer by nanofluid than pure fluid. Masslines are always similar to streamlines due to domination of mass transfer on fluid flow at high Lewis numbers.

Characteristics of ripple structures revealed in OH airglow images

AbstractSmall‐scale ripple structures observed in OH airglow images are most likely induced by either dynamic instability due to large wind shear or convective instability due to superadiabatic lapse rate. Using the data set taken in the mesopause region with an OH all‐sky imager at Yucca Ridge Field Station, Colorado (40.7°N, 104.9°W), from September 2003 to December 2005, we study the characteristics and seasonal variations of ripple structures. By analyzing the simultaneous background wind and temperature observed by the nearby sodium temperature/wind lidar at Fort Collins, Colorado (40.6°N, 105°W), and a nearby medium‐frequency radar at Platteville, Colorado (40.2°N, 105.8°W), we are able to statistically study the possible relation between ripples and the background atmosphere conditions. Characteristics and seasonal variations of ripples are presented in detail in this study. The occurrence frequency of ripples exhibits clear seasonal variability, with peak in autumn. The occurrence of ripples shows a local time dependence, which is most likely associated with the solar tides. The lifetime and spatial scale of these ripples are typically 5–20 min and 5–10 km, respectively, and most of the ripples move preferentially either southward or northward. However, more than half of the observed ripples do not advect with background flow; they have higher Richardson numbers than those ripples that advect with background flow. It is possible that they are not instability features but wave structures that are hard to be distinguished from the real instability features.

Numerical study of natural and mixed convection in a square cavity filled by a Cu–water nanofluid with circular heating and cooling cylinders

The present study investigates the role of natural and mixed convection heat transfer of a Cu–water nanofluid in a square cavity with inside circular heating and cooling bodies. The finite volume discretization method with the Semi-Implicit Method for Pressure Linked Equations algorithm is employed for solving the two-dimensional Navier–Stokes and energy equations. The effects of various design parameters on the heat transfer rate are investigated. Design parameters used in this numerical simulation are the position and size of circular bodies. A wide range of parameters such as the Rayleigh number (103 ≤ Ra ≤ 106 ), volume fraction (0 ≤ ϕ ≤ 0.05), Richardson number (0.01 ≤ Ri ≤ 1000), and the Grashof number (102 ≤ Gr ≤ 104 ) has been used. The numerical analysis is carried out for the circular body’s positions on the vertical centerline of the cavity. The circular body’s positions on the vertical left-line of the cavity are also presented and discussed for comparison purposes. The results show that the optimal heat transfer is obtained when placing the circular body near the bottom wall. Furthermore, the effects of pair of circular bodies on the heat transfer rate are investigated. The simulations show that the heat transfer rate increases with changing the orientation of the pair of circular bodies from the horizontal to the vertical directions. For the case of the mixed convection process, it is found that at high Richardson numbers, the effect of moving walls decreases and the heat transfer rate changes significantly.

Study of convection heat transfer enhancement inside lid driven cavity utilizing fins and nanofluid

In the present study, the effect of suspension of nanoparticle on mixed convection flow is investigated numerically in lid driven cavity with fins on its hot surface. Study is carried out for Richardson numbers ranging from 0.1 to 10, fin(s) height ratio change from 0.05 to 0.15 and volume fraction of nanoparticles from 0 to 0.03, respectively. The thermal conductivity ratio (kfin/kf) is equal to 330 and Grashof number is assumed to be constant (104) so that the Richardson numbers changes with Reynolds number. Results show that the heat transfer enhances by using nanofluid for all studied Richardson numbers. Adding fins on hot wall has different effects on heat transfer depend to Richardson number and height of fins. Use of low height fin in flow with high Richardson number enhances the heat transfer rate while by increasing the height of fin the heat transfer reduces even lower than it for pure fluid. The overall enhancement in Nusselt number by adding 3% nanoparticles and 3 fins is 54% at Ri=10. They cause reduction of Nusselt Number by 25% at Ri=0.1. Higher fins decrease the heat transfer due to blocking fluid at corners of fins.

Numerical analysis of mixed convection characteristics inside a ventilated cavity including the effects of nanoparticle suspensions

A numerical study of mixed convection flow and heat transfer inside a square cavity with inlet and outlet ports is performed. The position of the inlet port is fixed but the location of the outlet port is varied along the four walls of the cavity to investigate the best position corresponding to maximum heat transfer rate and minimum pressure drop in the cavity. It is seen that the overall Nusselt number and pressure drop coefficient vary drastically depending on the Reynolds and Richardson numbers and the position of the outlet port. As the Richardson number increases, the overall Nusselt number generally rises for all cases investigated. It is deduced that placing the outlet port on the right side of the top wall is the best position that leads to the greatest overall Nusselt number and lower pressure drop coefficient. Finally, the effects of nanoparticles on heat transfer are investigated for the best position of the outlet port. It is found that an enhancement of heat transfer and pressure drop is seen in the presence of nanoparticles and augments with solid volume fraction of the nanofluid. It is also observed that the effects of nanoparticles on heat transfer at low Richardson numbers is more than that of high Richardson numbers. &lt;br&gt;&lt;br&gt;&lt;font color="red"&gt;&lt;b&gt; This article has been retracted. Link to the retraction &lt;u&gt;&lt;a href="http://dx.doi.org/10.2298/TSCI190625278E"&gt;10.2298/TSCI190625278E&lt;/a&gt;&lt;u&gt;&lt;/b&gt;&lt;/font&gt;

Rayleigh-Bénard Convection in Shear Enclosure: The Role of Thermal Instabilities

DNS has been carried out for Rayleigh-Bénard convection for two-dimensional flow in a shear enclosure at fixed Reynolds number of 10,000 and Richardson numbers 0, 25, 50, 75, 87.5, while Prandtl number was fixed as 7.0. The key effect observed was that (apart from the basic vortical flow in an enclosure due to the shearing effects) there was simultaneous induction of buoyancy driven flow in an enclosure due to the convection of heat in the flow. For the cases with low and moderate Richardson number the resulting flow was found to be unperturbed, steady and laminar with an original vortical flow unaltered while for cases with high Richardson numbers the resulting flow was found to be unstable and chaotic in nature that attains a quasi-steady state after a certain period of time with strong bifurcations.

An entrainment model for lazy turbulent plumes

An entrainment model for lazy turbulent plumes is proposed, the resulting solutions of the plume conservation equations are developed and the implications for plume behaviour are considered and compared with the available experimental data. Indeed, the applicability of the classic solutions of the conservation equations subject to source conditions that produce lazy plumes, i.e. those with suitably high source Richardson number, contains an essential weakness: the underlying assumption of a constant entrainment coefficient. While entrainment models prescribing the dependence of the entrainment coefficient on the local Richardson number have been proposed for forced plumes, corresponding formulations for lazy plumes have not until now been considered. In the context of saline plumes, the model is applied directly. For hot gaseous plumes, we use a modified definition of buoyancy flux to recover a constant buoyancy flux in a non-stratified environment, despite the specific heat varying with the temperature. After a brief review of existing forced-plume formulations of entrainment, a power-law variation is adopted for the lazy plume. The plume equations are solved for the parameter $0\leqslant \unicode[STIX]{x1D714}&lt;1$, where $\unicode[STIX]{x1D714}$ denotes the exponent of the power law. The cases of pure plumes and lazy plumes are then analysed in more detail; to the best of our knowledge this represents the first modelling of variable entrainment for lazy plumes. Specifically, it is shown that classic plume theory is recovered for $\unicode[STIX]{x1D714}=0$, while for $\unicode[STIX]{x1D714}=1/5$ the plume equations may be solved using usual functions (notably polynomials) only. The results of the models for these cases are very similar, which advocates the idea of selecting systematically $\unicode[STIX]{x1D714}=1/5$, instead of $\unicode[STIX]{x1D714}=0$, for cases where the effect of variation of entrainment is weak, since the new model leads to simple calculations. In the case of very lazy plumes, it is shown that, provided that a relevant value of $\unicode[STIX]{x1D714}$ is chosen, the new model reproduces the available experimental results well.

Numerical simulation of mixed convection heat transfer of nanofluid in a double lid-driven cavity using lattice Boltzmann method

In this study, mixed convection heat transfer of water-Cu nanofluid in a double lid-driven cavity has been analyzed by lattice Boltzmann method. The double lid-driven are insulated and the side walls have sinusoidal temperature distribution. Simulations have been carried out at constant Grashof number 100, the Richardson numbers of 0.01, 0.1,1,10 and 100, temperature phase deviation of 0, π/4, π/2, 3π/4 and π, the solid volume fraction from zero to 0.06 and the Prandtl number of 6.57. The thermal modeling of passive scalar is applied and two separate distribution functions for the flow and temperature fields are considered. In order to calculate the thermal conductivity coefficient of nanofluid, constant and variable properties models are used. The results showed that in high Richardson numbers, the effect of the thermal phase deviation changes on the flow pattern is evident and in low Richardson numbers, the phase deviation changes do not affect the flow pattern. In all thermal phase deviations by reducing the Richardson number, the Nusselt number increases and thus the heat transfer increases. Also the average Nusselt number obtained for the constant properties model is higher compared with that of variable properties model.

Two phase mixture model of nano-enhanced mixed convection heat transfer in finned enclosure

This study presents the effect of nanofluid on mixed convection heat transfer inside a lid driven cavity by 2D and 3D numerical simulations. The 3D simulation is performed to examine the accuracy of 2D simulation for mixed convection. Two phase mixture model has been used for simulating the nanofluid. The effect of Brownian motion is considered in determining the effective thermal conductivity of nanofluid. The Richardson number changes from 0.1 to 10. In addition, thin fins have been mounted on hot wall to augment the heat transfer. Results indicate that there is a secondary flow at moderate and high Richardson numbers that 2D simulation cannot predict it. Also, results indicate that 2D simulation overestimated the enhancement of heat transfer at high concentration of nanofluid. Simulation depicts that heat transfer increases by adding low concentration of nano-particles and it decreases with higher concentrations. Adding fins on hot surface increases the heat transfer only at high Richardson number. Fins cannot enhance convective heat transfer at low and moderate Richardson numbers due to a blockage of flow at corners of the fins.