Richardson Number Ri Research Articles

A statistical study of convective and dynamic instabilities in the polar upper mesosphere above Tromsø

We have studied the convective (or static) and dynamic instabilities between 80 and 100 km above Tromsø (69.6° N, 19.2° E) using temperature and wind data of 6 min and 1 km resolutions primarily almost over a solar cycle obtained with the sodium lidar at Tromsø. First, we have calculated Brunt–Väisälä frequency (N) for 339 nights obtained from October 2010 to December 2019, and the Richardson number (Ri) for 210 nights obtained between October 2012 to December 2019. Second, using those values (N and Ri), we have calculated probabilities of the convective instability (N2 < 0) and the dynamic instability (0 ≤ Ri < 0.25) that can be used for proxies for evaluating the atmospheric stability. The probability of the convective instability varies from about 1% to 24% with a mean value of 9%, and that of the dynamic instability varies from 4 to 20% with a mean value of 10%. Third, we have compared these probabilities with the F10.7 index and local K-index. The probability of the convective instability shows a dependence (its correlation coefficient of 0.45) of the geomagnetic activity (local K-index) between 94 and 100 km, suggesting an auroral influence on the atmospheric stability. The probability of the dynamic instability shows a solar cycle dependence (its correlation coefficient being 0.54). The probability of the dynamic instability shows the dependence of the 12 h wave amplitude (meridional and zonal wind components) (C.C. = 0.52). The averaged potential energy of gravity waves shows decrease with height between 81 and 89 km, suggesting that dissipation of gravity waves plays an important role (at least partly) in causing the convective instability below 89 km. The probability of the convective instability at Tromsø appears to be higher than that at middle/low latitudes, while the probability of the dynamic instability is similar to that at middle/low latitudes.Graphical

Forced, natural and mixed convection of Non-Newtonian fluid flows in a square chamber with moving lid and discrete bottom heating

The aim of the present study is to examine the thermal performance of a power-law fluid for a discretely heated lid-driven enclosure. This numerical outcome can determine the ideal heat transfer medium for a given design, thus reducing unnecessary expenditures on experiments. The chamber's side walls move at a constant speed under constant ambient conditions. The finite element approach is used to solve governing Navier-Stokes and energy equations. A parametric investigation is carried out by varying the Richardson number (Ri) within the range of 2 × 10−3 ≤ Ri ≤ 105 at a fixed Reynolds or Grashof number in different cases and changing them simultaneously while keeping the Richardson number at unity. In all cases, the power-law index (n) is varied within 0.6 ≤ n ≤ 1.4. The results have been presented in terms of a quantitative evaluation of the average Nusselt number of the heated source, the average fluid temperature of the chamber, the maximum temperature of the heat source, and the normalized average Nusselt number. Furthermore, qualitative contour plots of stream function and temperature for different cases are presented. This research shows that the higher the power-law index, the greater the heat transfer for forced and pure mixed convection and that heat transfer performance differs with the increment/decrement of the Richardson number while keeping either Reynolds or Grashof number constant. Besides, the highest heat transfer performance is observed during the natural convection case of the pseudo-plastic fluid, and the lowest heat is transferred when the fluid is dilatant.

Enhancement of mixed convection in a lid driven enclosure based on magnetic field presence with nanofluid

Computational analysis is utilized to examine the effects of introducing nanoparticles to a square lid-driven cavity to enhance the hydro-magnet mixed convection. Constant temperatures are imposed along the square container’s vertical edges. Both the top and bottom surfaces are covered with insulation. The lid is thought to move in two ways: increasing or decreasing free convection. In addition, a horizontal magnetic field is applied uniformly. For various Hartmann numbers (Ha) (0:100), Richardson numbers (Ri) (0.001:10), and solid volume fractions (0:0.1), the results are reported. This research is based on a constant Grashof number (Gr) of 104. The effects of parameters, including the Richardson number, Hartmann number, solid volume percentage on the stream, isothermal lines, and local Nusselt numbers (Nu), were investigated numerically. In addition, given various parametric settings, the anticipated results for the average Nusselt (Nuavg) are shown and discussed. For all tested parameters, increasing the magnetic field makes the orientation of the lid more effective on heat and fluid movement. The magnetic field reduces heat and fluid flow. The heat transmission is aided by increasing the solid volume percentage. The effect of nanoparticles on flow and heat transmission is being studied. At Ri = 0.001, the effect of lid orientation is not significant. The highest reduction in heat transfer occurs when adding flow at Ri = 10, = 0, and Ha = 100.

Turbulence Structure and Mixing in Strongly Stable Boundary-Layer Flows over Thermally Heterogeneous Surfaces

Direct numerical simulations (DNS) at bulk Reynolds number Re =10^4 and bulk Richardson number Ri =0.25 of plane Couette flow are performed with the results used to analyze the structure and mixing intensity in strongly stable boundary-layer flows. The Couette flow set-up is used as a proxy for a real-world stable boundary layer flow with surface thermal heterogeneity. Along the upper and lower walls, the temperature is either homogeneous or varies sinusoidally, but the horizontal-mean surface temperature is the same in all cases. Over homogeneous surfaces, the strong stratification always quenches turbulence resulting in linear velocity and temperature profiles. However, over a heterogeneous surface turbulence survives. Molecular diffusion and turbulence contribute to down-gradient momentum transfer. The total (diffusive plus turbulent) heat flux is directed downward, but its turbulent contribution is positive, i.e., up the mean temperature gradient. Analysis of covariances of velocity and temperature, their skewness, and the flow structure suggests that counter-gradient heat transport is due to quasi-organized cell-like vortical motions generated by surface thermal heterogeneity. These motions transfer heat upwards similar to their counterparts in highly convective boundary layers. Thus, the flow over heterogeneous surface features local convective instabilities and upward eddy heat transport, although the overall stratification remains stable with downward mean heat transfer. The DNS results are compared to the results from large-eddy simulations of weakly stable boundary layers (Mironov and Sullivan in J Atmos Sci 73:449–464, 2016). The DNS findings corroborate the key role of temperature variance in setting the structure and transport properties of stably stratified flow over heterogeneous surfaces, and the importance of third-order transport of the temperature variance.

Examine the lattice Boltzmann method for the mixed convection simulation of water/Al2O3 nanofluid in a 2D rectangular cavity under radiation with isothermal semicircular obstacles

The present study simulated the mixed convection (MCXN) of the water/Al2O3 nanofluid (NFs) in a two-dimensional rectangular cavity in the presence of radiation. The top and bottom walls were assumed to be cold and hot, respectively, with the lateral walls being insulated. A magnetic field (MGF) with a Hartmann number (Ha) of 0–40 was applied to the NFs within the cavity. The simulations were carried out at a Richardson number (Ri) of 1 and a Rayleigh number (Ra) of 105 for cavity heights of 0.5–2.0 to evaluate heat transfer (HTF) on the walls and analyze fluid rotation within the cavity. The lattice Boltzmann method (LBM) was used to perform the simulations. It was found that the incorporation of radiation into the system reversed the flow rotation in the cavity and increased the Nu. A rise in the radiation parameter from 0 to 0.2 led to a 2.8-fold larger Nu on the cold wall. A rise in the cavity height decreased the Nu, and a further increase in the height increased the Nu on the wall. An increased Ha had an insignificant effect on the Nu at small cavity heights but decreased the Nu on the wall at large cavity heights.

Fine Structure of Vertical Density Distribution in the Black Sea and Its Relationship with Vertical Turbulent Exchange

This paper is concerned with the analysis of the long-term regular time series of current velocity and conductivity, temperature, and depth (CTD) profiles, measured with the moored autonomous profiler Aqualog over the upper part of the continental slope at a fixed geographical location in the Northeastern Black Sea. This study focuses on the fine structure of the density profiles to show that the fine-structure Cox number (C) is a power function of the Richardson number (Ri). A similar inverse power relationship with the same exponent was found earlier for the coefficient of vertical turbulent mass exchange (Kρ) and Ri. Based on those results, the analysis indicated a statistically significant correlation between C and Kρ, which suggests that the estimations of Kρ could be conducted from the CTD data only.

Ferrohydrodynamics Mixed Convection of a Ferrofluid in a Vertical Channel with Porous Blocks of Various Shapes

Numerical simulations of (water-Fe3O4) ferrohydrodynamics (FHD) mixed convection inside a vertical channel are performed. The magnetic field is produced by three sources positioned outside the channel’s right wall. The latter is provided with localized heat sources surmounted by variously shaped porous blocks: rectangular, trapezoidal, and triangular. The general model of Darcy-Brinkman-Forchheimer is employed to describe the fluid flow in the porous regions, and the resulting equations are numerically solved by the finite volume approach. The influence of significant parameters, including the magnetic number (Mn), the Richardson number (Ri), and the shape of blocks, is examined. The results essentially reveal that the enhanced heat transfer brought by the magnetic field and its intensity increase is suppressed by the augmentation of Ri until a critical value, rising with Mn, beyond which the global Nusselt number increases again. The mean friction coefficient increases with increased Mn and reduced Ri. Compared to the case with no magnetic field, the maximum enhancement in heat transfer rate is around 132% for the rectangular blocks, 146% for the trapezoidal blocks, and 160% for the triangular blocks, while the maximum increase in pressure drop is approximately 45% for all the shapes. The triangular shape seems the most efficient because it leads to high heat transfer rates and low mean friction coefficients; its performance factor is 2.32 for a dominant magnetic field and 2.62 for a dominant buoyancy force. The current research's conclusions will help optimize the operation of various thermal engineering systems, including electronic devices, where the improved heat removal rate will keep the electronic components at a safe operating temperature.

A three stages transition into chaos for mixed convection nanofluid inside a differentially-heated square ventilated cavity

In this paper, we present a numerical study of an unsteady Al2O3 water nanofluid mixed convection in a differentially-heated square ventilated cavity. The routes from steady state to chaotic mixed convection state have been also studied for a constant Reynolds Number (Re), Re = 50 and Richardson number (Ri) ranging from Ri = 40 to Ri = 150. The governing equations are solved using an implicit finite-volume scheme and TDMA algorithm. Results are presented through streamlines, isotherms, mean temperature, average Nusselt number, pressure drop, etc. It is observed that the average Nusselt number and the mean cavity temperature values are all the higher as the Ri number is great. The pressure drop slightly decreases as Ri number increases. The fully chaotic flow regime is reached after three stages. The first stage is similar to the Ruelle-Takens-Newhouse scenario. At the end of this stage, apparition of periodicity interrupted the development of a full chaos initiating the second stage of the route to chaos where another series of three supercritical Hopf type bifurcations and a period doubling bifurcation takes place. The third stage starts by the emergence of intermittencies which interrupts the apparition of a full chaotic flow. A complete chaos is achieved at the end of this third stage.

Turbulence in Particle-laden Midplane Layers of Planet-forming Disks

We examine the settled particle layers of planet-forming disks in which the streaming instability (SI) is thought to be either weak or inactive. A suite of low-to-moderate-resolution 3D simulations in a 0.2H-sized box, where H is the pressure scale height, are performed using PENCIL for two Stokes numbers, St = 0.04 and 0.2, at 1% disk metallicity. We find that a complex of Ekman-layer jet flows emerge subject to three co-acting linearly growing processes: (1) the Kelvin–Helmholtz instability (KHI), (2) the planet-forming disk analog of the baroclinic Symmetric Instability (SymI), and (3) a later-time weakly acting secondary transition process, possibly a manifestation of the SI, producing a radially propagating pattern state. For St = 0.2 KHI is dominant and manifests as off-midplane axisymmetric rolls, while for St = 0.04 the axisymmetric SymI mainly drives turbulence. SymI is analytically developed in a model disk flow, predicting that it becomes strongly active when the Richardson number (Ri) of the particle–gas midplane layer transitions below 1, exhibiting growth rates , where Ω is the local disk rotation rate. For fairly general situations absent external sources of turbulence it is conjectured that the SI, when and if initiated, emerges out of a turbulent state primarily driven and shaped by at least SymI and/or KHI. We also find that turbulence produced in 2563 resolution simulations are not statistically converged and that corresponding 5123 simulations may be converged for St = 0.2. Furthermore, we report that our numerical simulations significantly dissipate turbulent kinetic energy on scales less than six to eight grid points.

NUMERICAL STUDY OF FREE CONVECTION Ag-WATER NANOFLUID FLOW IN A SQUARE ENCLOSURE WITH VISCOUS DISSIPATION AND HEAT GENERATION/ABSORPTION EFFECTS IN A POROUS MEDIUM WITH COMPLEX WALL CONDITIONS

Nanofluids hold great promise in improving transport processes in energy systems including hybrid fuel cells. In this present work, a mathematical model is developed for laminar free convection flow of Ag-water nano-additives in an enclosure in a porous medium with complex boundary conditions. Additionally, heat generation/absorption and viscous dissipation effects are included. Via appropriate scaling transformations, the conservation equations for mass, primary and secondary momentum, energy, and nanoiparticle vorticity with wall boundary conditions are rendered dimensionless. A finite-difference computational scheme known as the marker and cell (MAC) method, developed by Harlow and Welch, is occupied to solve the dimensionless, nonlinear coupled boundary value problem. A mesh independence study is included. The impact of parameters such as Eckert number (Ec), Darcy number (Da), Grashof number (Gr), Prandtl number (Pr), Reynolds number (Re), and Richardson number (Ri) are observed with physical framework. Graphical plots are presented for the impact of key control parameters on streamline contours, isotherm contours, and local Nusselt number. By heat sink (absorption), the Nusselt number is increased, whereas by heat generation it is reduced since there is a decrease in heat transferred to the boundary. The presence of viscous dissipation effects moves the streamlines toward the blue core and allows the temperature to increase in the neighborhood of the hot wall of the envelope. An increase in Richardson number induces a flip in vortex cell structures from an initially strong circulation cell on the left and weaker cell on the right, to the opposite distribution. Significant cooling is also induced in the core zone with an increasing Richardson number, and a decrease in vorticity is observed.

Study of heat transfer and the nanofluid flow inside a rectangular enclosure with five rectangular baffles in the middle affected by a magnetic field

This article simulates free and forced convection (FCN) in a two-dimensional rectangular enclosure. In the center of the cage are five rectangular heat sources with high temperatures. The two side walls are insulated, and the top (moving) and bottom walls are maintained at a low temperature. In the presence of a magnetic field (MFD) along the length of the enclosure, which is saturated with copper/water nanofluid, the enclosure is affected. The study examines the impact of the Richardson number (Ri) ranging from 0.1 to 100 and Hartmann number (Ha) changing from 0 to 40 on average Nusselt number (NUA). Lattice Boltzmann method (LBM) and FORTRAN software are employed for numerical simulations. The results of this study demonstrate that an increment in the Ha enhances the Nusselt number (Nu) at the Ri of 0.1. At other Ri, enhancing the Ha reduces the NUA. The maximum NUA is 6.89 for the Ha of 40 and the Ri of 0.1. The enhancement in the Ri and the reduction of FCN strength reduce the NUA. The horizontal enclosure has the maximum Nu, which is equal to 3.10, and the vertical enclosure has the minimum NUA.

Numerical investigation of the fluid retention in the tank with a horizontal negatively buoyant jet

The fluid retention in the volume control tank (VCT) will delay the boric concentration of the Reactor Coolant System (RCS) during the boration process in the nuclear power plant. In this work, we studied the fluid retention in the tank with a horizontal negatively buoyant jet employing an experimentally validated computational fluid dynamics (CFD) model. The effects of concentration difference, inlet volume flow rate, nozzle diameter, and Richardson number (Ri) on fluid retention are analyzed to provide insights into the design and operation of VCT and other similar industrial equipment. The results show that there are two typical mixing patterns in the tank, the stratified pattern and the unstratified pattern. A criterion is provided to distinguish the mixing pattern. Increasing the concentration difference/nozzle diameter and decreasing the inlet volume flow can suppress the mixing process inside the tank and consequently weaken fluid retention. The variation of the fluid retention with the Ri is divided into three regimes by two critical numbers. The fluid retention is almost insensitive to the Ri when the number is inferior to the first critical number or exceeds the second critical number. Otherwise, the rise of the Ri inhibits fluid retention. Hence, the Ri is recommended to be maintained above the second critical value to minimize fluid retention in practice.

Climatology of Clear‐Air Turbulence in Upper Troposphere and Lower Stratosphere in the Northern Hemisphere Using ERA5 Reanalysis Data

AbstractSpatial and temporal distributions of Clear‐Air Turbulence (CAT) in the Northern Hemisphere were investigated using 41 years (1979–2019) of the European Centre for Medium‐range Weather Forecast Reanalysis version 5 (ERA5) data. We used two groups of CAT diagnostics to determine occurrence frequencies: (a) commonly used empirical turbulence indices (TI1, TI2, and TI3) and their components [vertical wind shear (VWS), deformation, ‐divergence, and divergence tendency], and (b) theoretical instability indicators [Richardson number (Ri), potential vorticity (PV), and Brunt‐Vӓisӓlӓ frequency]. The empirical indices showed high frequencies of moderate‐or‐greater (MOG)‐level CAT potential over the East Asian, Eastern Pacific, and Northwestern Atlantic regions in winter. Over East Asia, the entrance region of strong upper‐level jets showed the highest frequencies in TI1, TI2, and TI3 due mainly to strong VWS. The Eastern Pacific and Northwestern Atlantic areas near the exit region of jets had relatively high frequencies of these indices and also Ri. PV frequency was high on the southern side of jet primarily due to negative relative vorticity. Long‐term increasing trends of MOG‐level CAT potential also appeared in those three regions mainly due to warming in lower latitudes. The most significant increasing trend was found over East Asia, due to the strengthening of the East Asian jet and increased VWS due to the strong meridional temperature gradients in the mid‐troposphere induced by warming in the tropics and cooling in eastern Eurasia. These trends over East Asia, if continued, are expected to be of importance to efficient aviation operations across the northwestern Pacific Ocean.

Numerical study on plume bifurcation in longitudinally ventilated tunnel fires

The buoyant plume theory is one of the essential fundamental theories of tunnel fire dynamics. In this work, a special phenomenon, “plume bifurcation,” was studied numerically. The multi-dimensional characteristics of the buoyant plume under different ventilation conditions and aspect ratios are analyzed. The plume bifurcation is formed by the density-gradient counter-rotating vortex (CVP). Results show that the plume bifurcation only occurs when the longitudinal ventilation velocity reaches a certain value. The bifurcation angle increases rapidly at first and decreases slowly as the ventilation velocity increases. Meanwhile, the bifurcation angle increases with tunnel width when the tunnel aspect ratio is small; and is insensitive to the tunnel width under a large tunnel aspect ratio. A modified Richardson number Ri’ is proposed to determine the plume morphology. When Ri’ > 3.8, the plume is dominated by buoyancy and keeps single; when Ri’ < 2.7, the entrainment intensity is large enough to tear the plume into two sub-streams and results in plume bifurcation; and when 2.7 ≤ Ri’ ≤ 3.8, there is a transition region, where the plume has the trend to extend along the transverse direction, but no obvious bifurcation can be found. Finally, the relationship between the “plume bifurcation” and “smoke layer bifurcation” is analyzed and discussed. This research reveals the multi-dimensional plume characteristics and improves the classical plume theory under tunnel fire scenarios.

Numerical Study of Jet Impingement on Heated Sink Covered by a Porous Layer

This numerical study aims to enhance the heat transfer efficiency by dissipating the heat Emitted from electronic processors. A jet impingement technique is utilized with porous layer covering a metal fin as a heat sink. Forced convection and normal convection (due to the buoyancy effect) are taken into consideration. The two equations model (Local Thermal Non-Equilibrium LTNE) employed to describe the energy equations of the two phases of the porous surface. Finite Element Method (FEM) used to discretize these equations to obtain the numerical solution. To make this study closest to the reality, constant heat flux boundary condition is applied underneath the metallic heat sink. The geometry comprises of three domains: Free flow channel, Porous layer and Metal fined heat sink. In order to simulate the heat transfer, isotherms; streamlines and Nusselt number have been considered. Investigation has been done by inspecting the effects of the pertinent non-dimensional parameters such as: Reynolds number (Re = 100-900), Darcy number (Da = 10-1-10-6), Richardson number (Ri = 0.1-100) and Porosity (ε = 0.85-0.95). The results show that increasing Re and decreasing ε lead to enhance Nusselt number. Richardson number below 100 has no significant effects on Nu. At Re above 400, Nusselt number proportional with Darcy number. The enhancement of Nusselt number is found to be 250 % by increasing Re from 100 to 900, 290 % by decreasing ε from 0.95 to 0.85 and about 13 % by increasing Darcy number from 10-6 to 10-1.

Analysis of Flow Structures and Global Parameters across a Heated Square Cylinder in Forced and Mixed Convection

In the present study, numerical simulations are performed to identify the role of Reynolds number (Re), Richardson number (Ri) and free-stream orientations (α) on flow structures, aerodynamic parameters and heat transfer characteristics for the conditions (20 ≤ Re ≤ 120, 0° ≤ α ≤ 90° and 0 ≤ Ri ≤ 1.6). Prandtl number (Pr) and cylinder orientation (ϕ) are kept fixed at 0.71 and 0°. The Oberbeck–Boussinesq approximation is used to account for buoyancy effects. The governing equations of continuity, momentum and energy are discretized on a colocated body-fitted grid by employing a finite difference method. A viscous implicit pressure correction scheme is employed to advance the discrete solution in time. Contour maps of mean/steady drag coefficient and Nusselt number on (α-Ri) plane are plotted for 20 ≤ Re ≤ 120. From these contour maps, it is possible to identify the ranges of parameters (α, Ri) that can yield a relatively high mean/steady heat transfer rate accompanied by relatively low values of mean/steady drag coefficient. For [70° ≤ α ≤ 90°, 0 ≤ Ri ≤ 1.6], such a scenario is possible for any Re ∈ [20, 120]. The Strouhal number is observed to be maximum for Re = 120 at α = 45° and Ri = 1.2. Mean or steady coefficient of lift for any free-stream orientation (α ≠ 0°) is found to be highest at Re = 20 and Ri = 1.6. Sensitivity of (CD)Ri = 0.0 to α is observed to be minimum for Re = 20 and maximum for Re = 120. Sensitivity of the ratio CD(Ri,α)/CD(0,α) to Re is observed to be lower for unsteady flows than for steady flows, and it decreases with an increase in Re at a fixed value of Ri. Mean Nusselt number (Nu) in the forced flow regime increases significantly with an increase in Re at a fixed α. The Nusselt number is observed to be more sensitive to Ri for steady flows than for unsteady flows. The percentage increase in the ratio Nu(Ri,α)/Nu(0,α) for the entire range of Re is found to be 14.07%, 14.13%, 11.74% and 10.62% at α = 30°, 45°, 60° and 90°. At a fixed Ri, the Nusselt number ratio is found to decrease with an increase in Re for the entire range of α except for α = 90°. It is observed that the rate of heat transfer from the faces of the cylinder increases with an increase in Re for the entire ranges of α and Ri.

Mixed convection in an open T-shaped cavity utilizing the effect of different inflow conditions with Al2O3-water nanofluid flow

Mixed convection in an open cavity has been growing into one of the most attractive topics of investigation for years, owing to its importance in many engineering applications. In this study, the effect of different inflow conditions on mixed convective flow inside an open cavity of T shape is investigated thoroughly to find the optimum condition for efficient heat transfer. Three different inlet conditions (uniform, Poiseuille, and Couette) have been considered, and a comparative study has been conducted to assess their performance of mixed convection heat transfer enhancement. Moreover, the presence of water-Al2O3 nanofluid over conventional fluid (water) to improve thermal performance is examined by varying solid volume fractions from 0 to 0.04. The Galerkin Weighted Residual based finite element analysis is used to resolve the current problem. Numerical solutions are obtained by varying Grashof number (Gr) from 0.1 to 104 and Reynolds number (Re) from 0 to 1000. Pure mixed convective heat transfer is also emphasized by keeping Richardson number (Ri) at unity while varying Gr and Re simultaneously. A profound effect for the uniform inflow condition has been observed on the rate of heat transfer inside the cavity with the variation of Gr and Re. In addition, the nanofluid increases the heat transfer performance, particularly at higher values of Grashof number (Gr > 103) at Ri = 1.

Effects of Radiant Floor Heating Integrated with Natural Ventilation on Flow and Dispersion in a Newly Decorated Residence.

To date, few studies have been conducted on the characteristics of flow and dispersion caused by indoor radiant floor heating integrated with natural ventilation. In this study, we employed reduced-scale numerical models validated by wind-tunnel experiments to investigate the influence of radiant floor heating integrated with natural ventilation on airflow, heat transfer, and pollutant dispersion within an isolated building. The Richardson number (Ri) was specified to characterize the interaction between the inflow inertia force and the buoyancy force caused by radiant floor heating. Several Ri cases from 0 to 26.65, coupled with cross- or single-sided ventilation, were considered. Model validation showed that the numerical model coupled with the RNG k-ε model was able to better predict the indoor buoyant flow and pollutant dispersion. The results showed that the similarity criterion of Ri equality should be first satisfied in order to study indoor mixed convection using the reduced-scale model, followed by Re-independence. For cross-ventilation, when Ri < 5.31, the incoming flow inertia force mainly dominates the indoor flow structure so that the ACH, indoor temperature, and pollutant distributions remain almost constant. When Ri > 5.31, the thermal buoyancy force becomes increasingly important, causing significant changes in indoor flow structures. However, for single-sided ventilation, when Ri > 5.31 and continues to increase, the buoyancy force mainly dominates the indoor flow structure, causing a significant increase in ACH, thus reducing the indoor average temperature and pollutant accumulation.

Mesoscopic simulation of MHD mixed convection of non-newtonian ferrofluids with a non-uniformly heated plate in an enclosure

Mixed convective study has been popular in recent years because of its large applications, including the cooling of electronic devices, furnaces, lubrication technologies, high-performance building insulation, multi-shield structures used in nuclear reactors, food processing, glass manufacturing, solar power collectors, drying technologies, chemical processing equipment, and others involve mixed convection in a lid-driven cavity flow problems. Graphics process unit (GPU) based multiple-relaxation-time(MRT) lattice Boltzmann method (LBM) has been employed for investigating the numerical simulation of magnetohydrodynamic(MHD) mixed convection with a non-uniformly heated plate at the mid of an enclosure. The physical model consists of a two-dimensional square enclosure with the top wall moving at a constant speed. Thermally adiabatic conditions are imposed on the top and bottom walls, while the two vertical walls are cold. In the center of the enclosure, a plate has been placed that is non-uniformly heated. A magnetic field is applied with different angles of inclination. Numerical simulations were performed for various influential parameters such as Richardson number (Ri), Hartmann number (Ha), power-law index (n), ferroparticles volume fraction (ϕ), magnetic field angle (γ) to study the flow phenomena in terms of the velocity and temperature distributions as well as streamlines and isotherms, respectively. The present study also investigates entropy generation due to the convective heat transfer flow for industrial purposes. The results reveal that as the Richardson number rises, the average Nusselt number rises, and as the Hartmann number rises, the average Nusselt number reduces. Furthermore, it is found that the average Nusselt number is inversely proportional to the power-law index. Total entropy generation increases with the increase of the power-law index and Richardson number. Entropy due to fluid friction, heat transfer, and total entropy shows a maximum at γ = 90°. Previously, MHD natural convection of the ferrofluid has been studied in a square cavity with a non-uniformly heated plate for the Newtonian fluid using the finite volume method. The aim of the present investigation is to study the MHD mixed convection with non-Newtonian ferrofluid using the GPU-based lattice Boltzmann method, which provides quicker and more robust results.

Thermal fluid–structural interaction of three cylinders undergoing flow-induced vibration with cross thermal buoyancy

The effect of cross thermal buoyancy on the characteristic of flow-induced vibration and mixed convection of three circular cylinders is numerically studied. Two-dimensional simulations were conducted for a Reynolds number (Re) of 100 and five Richardson numbers (Ri) of 0–1.00. The range of the reduced velocity is 3 ≤ U* ≤ 15. Three circular cylinders C1, C2, and C3 are arranged in an equilateral triangle with C1 in upstream. The results show that the maximum amplitude of the C1 increases by up to 21% with considering cross thermal buoyancy in comparison to the case of Ri = 0. The galloping-like response is observed on the C1 at Ri = 1.00. The lift coefficient of three circular cylinders increases with the increase in Ri at U* ≥ 6. When U* exceeds a critical value, the vibrations of the C2 and C3 are in-phase, and the “2S” pattern is observed in the near-wake of three circular cylinders. The near-wake becomes wider, and the vortex shedding frequency increases at U* = 6 and Ri = 0.25 and 0.50. The higher the reduced velocity, the more significant is the effect of cross thermal buoyancy in enhancing heat transfer. The maximum space time-averaged Nusselt number increases by 10.42% in comparison to the case of fixed cylinders.