Turbulent Convection Research Articles

Topology optimization of heat sink in turbulent natural convection using k-ω turbulent model

The geometric structure of two-dimensional (2-D) heat sinks cooled by turbulent natural convection is optimized using a density-based topology optimization approach. The governing equations are the coupled equations of the k-ω turbulent equation, which is one type of the Reynolds-Averaged Navier-Stokes (RANS) equations, and the thermal convection-diffusion equation based on the Bousinessq approximation. In order to facilitate topology optimization, we make some modifications to the original governing equations to control the fluid/solid distribution by introducing a material density as the design variable. Specifically, several penalization terms are added to the original k-ω turbulent model for immersing the solid material, and the thermophysical properties are interpolated to obtain a generalized thermal equation suitable for both the fluid and solid materials. During the optimization process, the design variable is updated according to the gradient information obtained through adjoint-based sensitivity analysis. In numerical examples, the effects of the Grashof number and the solid thermal conductivity on optimal configurations are, respectively, investigated for two types of heat sinks. The numerical results indicate that the Grashof numbers and the solid thermal conductivity can significantly affect the optimal results; the flow channels will become narrower to accommodate the flow and heat transfer conditions with the increase of the Grashof number; and the design characteristics and heat transfer performance vary greatly for increasing the solid thermal conductivity when the conductivity is low, while at the case of high conductivity, this variation slows down obviously.

Using of large eddy simulation model for a spatially developing turbulent natural convection boundary layer in water along a side-heated vertical wall with high Rayleigh number ([formula omitted

To further understand the turbulent natural convection in the residual heat removal process of a nuclear reactor in accidental condition, a spatially developing natural convection boundary layer along a side-heated vertical plane in water is simulated with Large Eddy Simulation (LES) strategy. The maximum modified Rayleigh number (Ra*=Ra×Nu) reaches 8×1014 with the uniform heat flux input (≈10000W/m2). In particular, the buoyancy driven flow is simulated by an incompressible flow solver with Boussinesq approximation. The Wall Adaptive Local Eddy (WALE) model is selected as the sub-grid scale model for the LES simulation. After comparing with available measurements, it is found that reasonable agreement has been achieved in wall temperature distribution along the heated wall, heat transfer rate as well as mean temperature, mean velocity and turbulent statistics in the boundary layer. The detailed vortex structure and velocity spectra in the boundary layer corresponding to different regime are clearly demonstrated. It is shown that the transition process in the boundary layer can be accurately presented with the refined mesh (x+≈0.1) in the near wall region. To be more specific, the appeared ordered vortex street in the transition stage and the estimated critical Rayleigh number for turbulence inception correspond well to previous experimental observations. The significant effect of early transformation of two-dimensional (2D) linear Tollmien–Schlichting waves on the heat transfer is also proved. It is expected that current study can enhance the understanding of turbulent boundary layer at high heat flux and high Rayleigh number.

Numerical investigation of turbulent mixed convection flow and heat transfer characteristics of 2 × 2 subchannels with spacer grids

AbstractIn turbulent mixed convection conditions, flow and heat transfer can deteriorate under specific conditions, thus affecting the performance of the safety of the system, which could imperil the safety of the nuclear reactor. In this paper, by analyzing the velocity, temperature distributions, and other thermal‐hydraulic parameters, the steady‐state computational fluid dynamics approach with the SST k–ω turbulence model used in this study was verified. Then, flow and heat transfer characteristics in turbulent mixed convection inside 2 × 2 subchannels with and without spacer grids were investigated. The results showed that the velocity profiles were distorted and the heat transfer capacity was impaired due to the influence of buoyancy. The Nusselt number ratio (Nu/Nuf) between turbulent mixed convection and forced convection increased with the increase of Reynolds number (Re) until unity but decreased with the increases of Grashof number (Gr) and Buoyancy parameter (Bo*).

Retraction Note: Numerical assessment of the influence of helical baffle on the hydrothermal aspects of nanofluid turbulent forced convection inside a heat exchanger

Retraction Note: Numerical assessment of the influence of helical baffle on the hydrothermal aspects of nanofluid turbulent forced convection inside a heat exchanger

Effects of temperature gradient and beam path height from heat source on phase structure and mutual coherence functions of a light beam propagating through convective air turbulence

In this paper, we investigate the effects of different values of temperature gradient (TG) and the distance of a plane wave path from a flat heat source generating an anisotropic and non-Kolmogorov convective air turbulence medium on the phase structure function (PSF) and mutual coherence function (MCF) of the light beam propagating through the medium. The non-Kolmogorov and anisotropic convective air turbulence is created using an electrical heater with a surface size of 50 cm × 100 cm. The heater temperature is changeable from room temperature to 100 °C. The laser beam with a diameter of 20 cm passes through the turbulent medium at different distances from the heater surface. At the end of the path, the wavefront of the light beam is reconstructed using a two-channel moiré wavefront sensor. Then, the PSF and MCF are calculated, and the effects of different TGs and the different beam path heights from the heater are studied. Results show that with increasing the TG and decreasing the beam path distance from the heat source, the turbulence intensity and PSF increase, while the MCF decreases.

Large eddy simulations of the accumulation of buoyant material in oceanic wind-driven and convective turbulence

Buoyant material such as microplastics accumulate near the ocean surface in regions with convergent surface currents where they can be harmful to marine life. Here, we use large eddy simulations to investigate the transport and accumulation of buoyant material in a turbulent ocean mixed layer under combined wind and convection forcing. We model non-inertial buoyant particles with a combination of buoyant tracers and Lagrangian surface particles, which allows us to explore a wide range of particle buoyancies. Surface cooling drives convection, and under this regime persistent convective vortices form that trap buoyant particles, leading to large concentrations. Despite their small size, the convective vortices exhibit a bias towards cyclonic vorticity that has not been reported previously. Based on an analysis of Lagrangian trajectories, the average time that a particle spends inside a convective vortex is long enough for planetary vorticity to become important and further vortex stretching causes an exponential increase in vorticity. When wind forcing is included, there is a transition from convective cells to longitudinal wind rolls with three distinct flow patterns observed under weak, moderate and strong wind forcing. For sufficiently weak winds, convective vortices survive but are less effective at trapping buoyant material. Under strong wind forcing, convective vortices no longer exist, but some clustering occurs in regions of high speed associated with longitudinal wind rolls. We quantify the degree of clustering using the Gini coefficient and find that clustering is strongly influenced by the relative size of the friction and convective velocities and the particle buoyancy.

Turbulent forced convective flow in a conical diffuser: Hybrid and single nanofluids

Turbulent forced convective flow of hybrid and single nanofluids in a conical diffuser is investigated numerically. Simulations are conducted for various Reynolds (Re=10000-70000) and different concentrations (ϕ=0-1.5 vol%) at equal ratio of TiO2:SiO2. The impact of using theoretical and experimental correlations for dynamic viscosity and thermal conductivity on turbulent forced convection of TiO2 showed that the mean Nusselt (Nu) number is considerably reduced with the use of the experimental model. However, when the theoretical model is used, Nu varies insignificantly. Addition of TiO2 nanoparticles decreases the heat transfer inside the diffuser, whereas addition of TiO2–SiO2 nanoparticles either enhances or decreases the heat transfer rate. Compared to the pure fluid, hybrid nanofluids show a maximum enhancement of 5% and a maximum decrease of 9.7% at ϕ= 0.5 vol% and ϕ= 0.5 vol% at Re=10000, respectively. However, TiO2 nanofluids show a maximum decrease of 19% at ϕ=1.5 vol% and Re= 30000. As Re increases, the deviations between TiO2 and SiO2-TiO2 nanofluids diminish. Moreover, the Gene Expression Programming model can accurately evaluate Nu versus Re number and nanoparticle concentration.

Investigation of novel turbulator with and without twisted configuration under turbulent forced convection of a CuO/water nanofluid flow inside a parabolic trough solar collector

<abstract> <p>In this study, we numerically investigated the hydrothermal performance of a parabolic trough solar collector system in which nanofluids are used to transfer thermal energy. The single-phase model has been used to evaluate the respective influences of the spherical shape of nanoparticles with a volume fraction of (φ = 3%), Reynolds number varying between 50,000 ≤ Re ≤ 250,000 and the insertion of a turbulator with and without a twisted configuration on the hydrothermal characteristics created by the turbulent forced convection of a CuO/water nanofluid. The shaped turbulator (+) inserted in the absorber tube had a length turb_L = 2.4 m, a height turb_H = 40 mm and a width turb_t = 2 mm. In the second configuration, the considered turbulator was twisted (N_twist = 5, 10 and 15 twists). The turbulator was positioned at 0.6 m from the inlet of the tube and 1 m from the outlet of the collector. The studied performances included the heat transfer characteristics, pressure drop, friction factor, thermal efficiency, temperature and velocity distribution of the outlet field. The most significant contribution of this study is the proposal of the best parameters to increase the thermal and hydraulic efficiency of parabolic troughs by adding a new turbulator with the considered twists.</p> </abstract>

Scaling transition of thermal dissipation in turbulent convection

Direct numerical simulation (DNS) of non-slip two dimensional (2D) Rayleigh–Benard convection (RBC) is conducted for a wide range of Rayleigh number (Ra up to 1013) at Prandtl number Pr = 0.7 and aspect ratio Γ = 1. The thermal dissipation rate is shown to display an evident scaling transition through the compensated plot, i.e., ⟨εθ⟩∝Raγ with γ≈−0.17 for 106≤Ra≤109, while γ≈−0.19 for Ra=109≤Ra≤1013. To track the transition, separate contributions from the thermal boundary layer (BL) and the bulk flow region are examined, incorporated also with the mean and fluctuation decomposition. It turns out that the mean temperature gradient in the BL is the dominant contribution, and together with other parts (i.e., fluctuations in the BL and bulk, and the mean gradient in the bulk), they all exhibit an obvious transition at Ra≈109. We have further checked the Nusselt number (Nu), which also shows the transition at Ra≈109. Interestingly, Nu∝Ra0.33 is observed for small Ra, while Nu∝Ra2/7 is absent in 2D RBC cases. To understand the physical origin of transition, spatial distributions and probability density functions of thermal dissipation rate are finally discussed, with notable statistical features changed at Ra≈109.

Vortex structure and small scale characteristics in turbulent Rayleigh–Bénard convection with mixed isothermal–adiabatic bottom boundary

Turbulent Rayleigh–Bénard convection with a mixed isothermal–adiabatic bottom boundary is simulated to investigate the effect of a nonideal thermal boundary on vortex structure and small-scale characteristics in turbulent convection. Simulations of convection with element aspect ratios of the mixed isothermal–adiabatic boundary cell ranging from 116 to 14 are performed at fixed Rayleigh and Prandtl numbers. Within the parameters adopted in this paper, the large-scale circulation under the mixed boundary condition is found to be consistent with that under the classical isothermal condition. However, the shape characteristics and distribution of plumes are strongly affected by the presence of a mixed isothermal–adiabatic boundary. Compared with the isothermal system, the mixed boundary breaks up the corner vortex structures and reduces the vortex intensity at the corners. Some complex vortex structures, such as a horseshoe vortex, appear in the case of a mixed isothermal–adiabatic thermal boundary. The vortices in side and face regions are governed by an enhancement rule that is related to the ratio of the element width to the typical plume size. The structure functions of scales above the element scale are greatly affected by the presence of a mixed boundary. The temperature structure function exhibits discrete characteristics, especially in the near-bottom region. However, the velocity structure function of the velocity retains continuous characteristics in all regions. The small-scale characteristics observed here help provide better understanding of the effect of a discrete boundary on buoyancy-driven turbulent convection.

Turbulence-induced vibrations prediction through use of an anisotropic pressure fluctuation model

In nuclear fuel rod bundles, turbulence-induced pressure fluctuations caused by an axial flow can create small but significant vibrations in the fuel rods, which in turn can cause structural effects such as material fatigue and fretting wear. Fluid-structure interaction simulations can be used to model these vibrations, but for affordable simulations based on the URANS approach, a model for the pressure fluctuations must be utilised. Driven by the goal to improve the current state-of-the-art pressure fluctuation model, AniPFM (Anisotropic Pressure Fluctuation Model) was developed. AniPFM can model velocity fluctuations based on anisotropic Reynolds stress tensors, with temporal correlation through the convection and decorrelation of turbulence. From these velocity fluctuations and the mean flow properties, the pressure fluctuations are calculated. The model was applied to several test cases and shows promising results in terms of reproducing qualitatively similar flow structures, as well as predicting the root-mean-squared pressure fluctuations. While further validation is being performed, the AniPFM has already demonstrated its potential for affordable simulations of turbulence-induced vibrations in industrial nuclear applications.

Energy and exergy analysis of conjugate 3D unsteady heat conduction with solidification of water by turbulent buoyancy-driven freezing of solid food in air

In this work, the influence of the position of salmon in a cooling cavity on heat transfer, freezing rate and local exergy destruction was investigated using mathematical modeling and numerical simulation. The predicted temperature evolution in the food during freezing by turbulent heat convection in air inside a cooling chamber was validated with experimental results. The conjugate turbulent model in three dimensions included the natural heat convection and the unsteady heat diffusion with the phase change of water to ice in the food meat. Three positions of the block of salmon in the freezer were studied: bottom-left, bottom-center, and center of the freezer. The local exergy destruction was calculated to quantify the contribution of viscous dissipation and heat transfer during the salmon freezing process. The unsteady description of air velocity, temperature, and freezing rate were analyzed. The highest cooling rate calculated was for the food at the bottom left, and the lowest when located at the center of the cooling cavity. The exergy destruction analysis determined the useful energy lost during the freezing process.

CORRELATIONS OF INTERFACIAL HEAT TRANSFER COEFFICIENT AND THERMAL DISPERSION FOR TURBULENT CONVECTIVE FLOW IN POROUS MEDIUM

Effective properties like interfacial heat transfer coefficient and longitudinal and transverse thermal dispersion play an important role in the up-scaled mathematical models of porous medium. However, most of the existing correlations are obtained by assuming that fluid flow in porous medium is laminar. Therefore, numerical simulations were conducted in the study to investigate interfacial heat transfer coefficient and longitudinal thermal dispersion for turbulent convective flow in porous medium. For the sake of simplification, a two-dimensional (2D) periodic array of square rods was chosen as physical geometry. Moreover, a low-Re turbulence model suitable for backward-facing step geometry was applied to better capture the turbulent characteristic in porous medium. By the exhausted numerical results, an interfacial heat transfer coefficient correlation was obtained. Furthermore, due to the inverse relationship between interfacial heat transfer coefficient and longitudinal thermal dispersion, the expression of longitudinal thermal dispersion was derived. By comparing with existing experimental data and correlations in the literature, the correlations of interfacial heat transfer coefficient and longitudinal and transverse thermal dispersion were validated. In light of the proposed correlations, it is feasible to establish a more reliable macroscopic mathematical model of porous medium.

Transition from anti-solar to solar-like differential rotation: Dependence on Prandtl number

Context. Late-type stars such as the Sun rotate differentially due to the interaction of turbulent convection and rotation. Aims. The aim of the study is to investigate the effects of the effective thermal Prandtl number, which is the ratio of kinematic viscosity to thermal diffusivity, on the transition from anti-solar (slow equator, fast poles) to solar-like (fast equator, slow poles) differential rotation. Methods. Three-dimensional hydrodynamic and magnetohydrodynamic simulations in semi-global spherical wedge geometry were used to model the convection zones of solar-like stars. Results. The overall convective velocity amplitude increases as the Prandtl number decreases, in accordance with earlier studies. The transition from anti-solar to solar-like differential rotation is insensitive to the Prandtl number for Prandtl numbers below unity, but for Prandtl numbers greater than unity, solar-like differential rotation becomes significantly harder to excite. Magnetic fields and more turbulent regimes with higher fluid and magnetic Reynolds numbers help to achieve solar-like differential rotation in near-transition cases where anti-solar rotation is found in more laminar simulations. Solar-like differential rotation occurs only in cases with radially outward turbulent angular momentum transport due to the Reynolds stress at the equator. The dominant contribution to this outward transport near the equator is due to prograde propagating thermal Rossby waves. Conclusions. The differential rotation is sensitive to the Prandtl number only for large Prandtl numbers in the parameter regime explored in this study. Magnetic fields have a greater effect on the differential rotation, although the inferred presence of a small-scale dynamo did not lead to drastically different results. The dominance of the thermal Rossby waves in the simulations is puzzling because they are not detected in the Sun. The current simulations are shown to be incompatible with the currently prevailing mean-field theory of differential rotation.

Entropy generation analysis of fully developed turbulent convection in a twisted elliptical duct with constant heat flux

Entropy generation analysis of fully developed turbulent convection in a twisted elliptical duct with constant heat flux

Entropy generation analysis of fully developed turbulent convection in a twisted elliptical duct with constant heat flux

In this study, the entropy generation and exergy efficiency of turbulent flow through a twisted elliptical tube were investigated. The effects of the fluid properties, the aspect ratio (1.05-10.00) and the twist pitch ratio (4-200) were considered. The results indicated that the total dimensionless entropy generation increased whereas the exergy efficiency decreased as the twist pitch ratio increased. Moreover, the total dimensionless entropy generation decreased, whereas the exergy efficiency increased with an increase in the aspect ratio. The minimum total dimensionless entropy generation of 0.01 is obtained with an aspect ratio of 10.00 and a twist pitch ratio of 16.36.

Wall-bounded thermal turbulent convection driven by heat-releasing point particles

In this work we investigate the thermal convection driven by heat-releasing point particles. Three-dimensional direct numerical simulations are conducted for$1\times 10^7\le {\textit {Ra}} \le 1\times 10^{10}$and$0.01\le {\textit {St}} \le 10$, where the Rayleigh number${\textit {Ra}}$and Stokes number${\textit {St}}$measure the strengths of the heat releasing rate and the Stokes drag, respectively. A regime at intermediate Stokes numbers is identified with most particles accumulating into the top boundary layer region, while for other cases particles are constantly advected over the entire domain. For the latter state, the flow motions are stronger at the upper part of the domain. The thicknesses of both momentum and thermal boundary layers at the top plate follow the same scaling law with${\textit {Ra}}$and show minor dependences on${\textit {St}}$. The volume-averaged temperature and convective flux exhibit non-monotonic variations as${\textit {St}}$increases and reach their minimums at intermediate${\textit {St}}$. The fraction coefficient of heat flux, i.e. the ratio between the heat flux through the bottom plate and the total flux through both plates, shares the similar dependence on${\textit {St}}$as the convective flux. The relation between these scaling laws can be explained by using the global balance between the dissipation and convective flux. The scaling laws for the transition between different flow regimes are also proposed and agree with the numerical results. The preferential concentration of particles is observed for all cases and is strongest at intermediate Stokes numbers, for which multiscale clustering emerges with small clusters forming larger ones.

Layer formation in a stably stratified fluid cooled from above: Towards an analog for Jupiter and other gas giants

Composition gradients in the interior of Jupiter can affect and even suppress convective motions. In some situations, a composition gradient can trigger the formation of multiple convective layers separated by sharp diffusive interfaces, preventing further mixing. This fluid state, called layered convection, has been proposed to occur in giant planets. However, it is not guaranteed that secondary convective layers can form and survive underneath a turbulent convection zone. Our simulations find that below an evolving convection zone, layer formation is difficult and the fluid always fully mixes. This may have bearing on the survival of composition gradients in Jupiter's interior.

Statistics of temperature and velocity fluctuations in supergravitational convective turbulence

Statistics of temperature and velocity fluctuations in supergravitational convective turbulence

Numerical Study of Turbulent Mixed Convection in a Square Lid Driven Cavity with an Inside Hot Bloc

In this study, we are interested in the two-dimensional numerical simulation of the turbulent mixed convection in the case of a square with two side lid-driven cavity containing a hot obstacle. The transfer equations coupled with those of the K - ε closure model and the boundary conditions were presented and discretized using the finite volume method. The coupling between the velocity and pressure fields is achieved by the SIMPLE algorithm. The technique of line-by-line scanning with the Thomas algorithm (TDMA) is used for the iterative resolution of discretized equations. The control parameters of the present study are the temperature gradient between the hot walls and the cold walls, and the speed imposed on the mobile walls. Streamlines generally show flow characterized by the presence of two counter-rotating cells. The areas adjacent to the isothermal walls and to the moving walls are the site of the development of thermal and dynamic boundary layers, where significant temperature and velocity gradients have been observed, subsequently influencing the profiles of turbulent quantities such as turbulent viscosity, the production and dissipation of turbulent kinetic energy and the intensity of turbulence.