High Prandtl Number Research Articles

Simulation of solid-liquid phase change at pore scale using lattice Boltzmann method with central moments in thermal energy storage

The solid-liquid phase change process is of significant importance to the thermal energy storage and electronics cooling using phase change material. In this paper, the central moments multiple-relaxation time (CM-MRT) collision model has been introduced into the solid-liquid phase change lattice Boltzmann model, in order to solve the solid-liquid phase change problem in porous medium at pore scale. To evaluate the influences of different collision functions, the problems of one-region phase change and natural convection with phase change at pore scale have been investigated. The results have showed that the CM-MRT model possessed higher accuracy in revealing temperature and liquid fraction distribution. Compared with mesh system of 256 × 256, the CM-MRT model with 64 × 64 possess the minimum error, 0.014%. Besides, in the case of high Rayleigh number (5 × 107) and low Prandtl number (0.005), the CM-MRT model presented extraordinary stability and the clear phase interface when investigating the heat transfer of porous medium composite phase change materials at the pore scale.

Thermal flow analysis of self-driven temperature-sensitive magnetic fluid between partially heated parallel plates

To develop a heat transfer device based on a temperature-sensitive magnetic fluid (TSMF), it is necessary to investigate its flow and heat transfer characteristics. This study used the fractional step method to numerically investigate the flow and heat transfer characteristics of TSMF between parallel plates with small spacing when the solenoidal magnetic field is applied. Due to the influence of the magnetic field and temperature, the flow characteristics of the TSMF between the plates are significantly different from ordinary working fluids such as oil, and the fluid near the plate flows faster than the fluid near the center. We used numerical analysis to analyze the formation of this phenomenon and investigated the influence of dimensionless Prandtl number and magnetic effect parameter on this phenomenon. As the result, the heat transfer increased with the increase of the magnetic effect parameter which is affected by the magnetic field or the distance between the plates. The center between the two plates in the heating region formed a vortex under high Prandtl number conditions, and the generation of the vortex enhanced the heat transfer.

Coherent structures of m=1 by low-Stokes-number particles suspended in a half-zone liquid bridge of high aspect ratio: Microgravity and terrestrial experiments

Coherent strucutres of m = 1 are investigated via microgravity and terrestrial experiments in thermocapillary-driven convection in half-zone liquid bridge of high Prandtl number. Individual behaviors of low Stokes number particles are monitored in the laboratory frame and the rotating frame of reference to illustrate the correlation between the coherent structure and the thermal flow field induced by the hydrothermal wave instability.

Application of Arrhenius chemical process on unsteady mixed bio-convective flows of third-grade fluids having temperature-dependent in thermo-rheological properties

This article presents the unsteady mixed convective flow of third-grade fluid flow comprising nanoparticles and gyrotactic microorganisms past a stretching sheet. The fluid flow is assumed to be laminar and incompressible. The fluid flow is considered to be highly magnetized by applying a strong magnetic field. Newtonian viscous dissipation, chemical reactions, and Arrhenius activation energy are taken into consideration. The transformed system of equations is solved by HAM. Convergence analysis of the HAM is displayed with the help of figures. The relations of physical factors with fluid flow profiles are displayed with the help of figures and tables. It is reported that the greater material and mixed convection factors have escalated the fluid’s velocity. The higher Eckert number and thermal conductivity constant have augmented the thermal function, while the higher Prandtl number has reduced the temperature profile. The greater activation energy factor has augmented the concentration profile, while the augmenting chemical reaction and Schmidt number have reduced the concentration profile. In the streamlines of the steady and unsteady flows, there is also a significant difference in behavior.

A Comparative Study of 3d Cumulant and Central Moments Lattice Boltzmann Schemes with Interpolated Boundary Conditions for the Simulation of Thermal flows in High Prandtl Number Regime

Thermal flows characterized by high Prandtl number are numerically challenging as the transfer of momentum and heat occurs at different time scales. To account for very low thermal conductivity and obey the Courant-Friedrichs-Lewy condition, the numerical diffusion of the scheme has to be reduced. As a consequence, the numerical artefacts are dominated by dispersion errors commonly known as wiggles. In this study, we explore possible remedies in the framework of the lattice Boltzmann method by applying novel collision kernels, lattices with a large number of discrete velocities, namely D3Q27, and second-order boundary conditions. For the first time, the cumulant-based collision operator is utilised to simulate both the hydrodynamic and the thermal field. Alternatively, the advected field is computed using the central moments' collision operator. Different relaxation strategies have been examined to account for additional degrees of freedom introduced by a higher-order lattice. To validate the proposed kernels for a pure advection-diffusion problem, the numerical simulations are compared against an analytical solution of a Gaussian hill. The structure of the numerical dispersion is shown by simulating advection and diffusion of a square indicator function. Finally, a study of steady forced heat convection from a confined cylinder is performed and compared against a FEM solution. It has been found, that the relaxation scheme of the advected field must be adjusted to profit from lattice with a larger number of discrete velocities. Obtained results show clearly that it is not sufficient to assume that only the first-order central moments/cumulants contribute to solving the macroscopic advection-diffusion equation. In the case of central moments, the beneficial effect of the two relaxation time approach is presented.

MHD mixed convection in a partitioned rectangular enclosure

A numerical study is carried out to explore the influence of external magnetic field on mixed convective heat transfer in a partitioned rectangular cavity with on side moving wall. The vertical walls are isothermally heated while the horizontal walls are thermally insulated. The left vertical wall is moving in + y direction and remaining walls are maintained no-slip condition. A magnetic field of uniform strength is imposed transverse to the temperature gradient. The governing equations are solved utilizing the finite element method for several physical parameters including Richardson number, Hartmann number and Prandtl number. The numerical results are presented graphically using streamlines, isotherms, local and average Nusselt numbers. It is observed that the flow filed is affected significantly for moving wall and the variation in Hartmann and Richardson numbers. The velocity field is found more effective in natural convection regime than forced convection. The results demonstrated that maximum amount of heat transfer is obtained in natural convection domination and higher values of Prandtl number. The enhancement of heat transfer rate is found 14.25% more at higher Prandtl number (Pr =2.56) than lower (Pr =0.71) and it reduction is found 3.03% more at Ha = 50 compared to Ha = 0.

Cfd Simulations to Characterize Near Wall Heat Transfer in High Prandtl Number Packed Bed Conditions

Cfd Simulations to Characterize Near Wall Heat Transfer in High Prandtl Number Packed Bed Conditions

油冷モータコイルエンドを模した角柱群における油流れ解析の基礎研究

An oil-cooling method is often used for electric vehicle motors, in which oil is directly sprayed onto motor coil ends. Computational fluid dynamics (CFD) is utilized in the research and development processes of the oil-cooling system, but the accuracy has not been quantitatively verified because of the high Prandtl number flow with the free surface of the oil. Another reason is that the coil end, in which copper wires are bundled, has some complicated structures and many narrow gaps, making it difficult to confirm and comprehend the oil flow quantitatively. In this study, acrylic rectangular columns with gaps imitating oil-cooling motor coil end were created, and visualization experiments of how dropped oil flows on the side of columns and through the gaps were conducted. The simulations using the particle-based and finite volume methods were performed and compared with the experiments. On the side of the columns, the particle-base method well reproduced oil flow, while there was no flow in the finite volume method. In the gaps, both CFD methods reproduced the same qualitative flow. In the gap of the upper column near the dropping point, the flow simulated by both CFD methods were faster than those in the experiment.

Conjugate Heat Transfer Simulations of High Prandtl Number Liquid Jets Impinging on a Flat Plate

Conjugate Heat Transfer Simulations of High Prandtl Number Liquid Jets Impinging on a Flat Plate

Boundary layers in turbulent vertical convection at high Prandtl number

Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers ${Pr}$ . This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $\mbox {{Ra}}$ and Prandtl number ${Pr}$ . For the considered parameter range $1\leq {Pr} \leq 100$ , $10^{6} \leq \mbox {{Ra}} \leq 10^{9}$ , we find the flow to be consistent with a ‘buoyancy-controlled’ regime where the heat flux is independent of the wall separation. For given ${Pr}$ , the heat flux is found to scale linearly with the friction velocity $V_\ast$ . Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice–ocean interfaces.

Fully developed anelastic convection with no-slip boundaries

Anelastic convection at high Rayleigh number in a plane parallel layer with no slip boundaries is considered. Energy and entropy balance equations are derived, and they are used to develop scaling laws for the heat transport and the Reynolds number. The appearance of an entropy structure consisting of a well-mixed uniform interior, bounded by thin layers with entropy jumps across them, makes it possible to derive explicit forms for these scaling laws. These are given in terms of the Rayleigh number, the Prandtl number and the bottom to top temperature ratio, which also measures how much the density varies across the layer. The top and bottom boundary layers are examined and they are found to be very different, unlike in the Boussinesq case. Elucidating the structure of these boundary layers plays a crucial part in determining the scaling laws. Physical arguments governing these boundary layers are presented, concentrating on the case in which the boundary layers are so thin that temperature and density vary little across them, even though there may be substantial temperature and density variations across the whole layer. Different scaling laws are found, depending on whether the viscous dissipation is primarily in the boundary layers or in the bulk. The cases of both high and low Prandtl number are considered. Numerical simulations of no-slip anelastic convection up to a Rayleigh number of $10^7$ have been performed and our theoretical predictions are compared with the numerical results.

Prandtl number dependence of stellar convection: Flow statistics and convective energy transport

Context. The ratio of kinematic viscosity to thermal diffusivity, the Prandtl number, is much smaller than unity in stellar convection zones. Aims. The main goal of this work is to study the statistics of convective flows and energy transport as functions of the Prandtl number. Methods. Three-dimensional numerical simulations of compressible non-rotating hydrodynamic convection in Cartesian geometry are used. The convection zone (CZ) is embedded between two stably stratified layers. The dominant contribution to the diffusion of entropy fluctuations comes in most cases from a subgrid-scale diffusivity whereas the mean radiative energy flux is mediated by a diffusive flux employing Kramers opacity law. Here, we study the statistics and transport properties of up- and downflows separately. Results. The volume-averaged rms velocity increases with decreasing Prandtl number. At the same time, the filling factor of downflows decreases and leads to, on average, stronger downflows at lower Prandtl numbers. This results in a strong dependence of convective overshooting on the Prandtl number. Velocity power spectra do not show marked changes as a function of Prandtl number except near the base of the convective layer where the dominance of vertical flows is more pronounced. At the highest Reynolds numbers, the velocity power spectra are more compatible with the Bolgiano-Obukhov k−11/5 than the Kolmogorov-Obukhov k−5/3 scaling. The horizontally averaged convected energy flux (F̅conv), which is the sum of the enthalpy (F̅enth) and kinetic energy fluxes (F̅kin), is independent of the Prandtl number within the CZ. However, the absolute values of F̅enth and F̅kin increase monotonically with decreasing Prandtl number. Furthermore, F̅enth and F̅kin have opposite signs for downflows and their sum F̅↓conv diminishes with Prandtl number. Thus, the upflows (downflows) are the dominant contribution to the convected flux at low (high) Prandtl numbers. These results are similar to those from Rayleigh-Benárd convection in the low Prandtl number regime where convection is vigorously turbulent but inefficient at transporting energy. Conclusions. The current results indicate a strong dependence of convective overshooting and energy flux on the Prandtl number. Numerical simulations of astrophysical convection often use a Prandtl number of unity because it is numerically convenient. The current results suggest that this can lead to misleading results and that the astrophysically relevant low Prandtl number regime is qualitatively different from the parameter regimes explored in typical contemporary simulations.

Dynamic mode decomposition of oscillatory thermo-capillary flow in curved liquid bridges of high Prandtl number liquids under microgravity

• Influence of free surface heat transfer on the onset of oscillatory instability. • Thermo-capillary flow in curved liquid bridges under microgravity conditions. • Critical value for the onset of oscillatory flow instability. • ‘Dynamic mode decomposition’ technique to reveal the inherent flow dynamics. • Quantification of each characteristic mode. Three-dimensional and oscillatory thermo-capillary flow in a liquid bridge of 5 cSt silicone oil ( Pr = 67) has been numerically investigated by performing dynamic mode decomposition (DMD) analysis applied to the time-resolved thermal data generated by the ‘method of snapshots’. For various heat transfer conditions defined on the free surface of the curved liquid bridge, a series of dynamic modes has been extracted to unfold the underlying physical mechanism that governs the considered dynamical system. Unstable and neutral modes primarily accountable for the transition to the supercritical state established in the liquid bridge have been identified by decomposing the acquired temperature disturbances into spatial and temporal coherent structures. Under microgravity conditions, unsteady and three-dimensional computations are carried out in a liquid bridge of different volume ratios ( VR = 0.9 and 1.1) using the finite volume method (FVM) to capture the dynamical evolution of temperature disturbances at the onset of oscillatory instability. The present numerical investigation is mainly aimed at providing broader insight into the complex fluid dynamic processes associated with the oscillatory thermal convection by determining the growth/decay rate and frequency of each characteristic mode with the help of DMD spectra. For each oscillation pattern, the dominant behavior of oscillatory thermo-capillary flow is revealed by its coherent structures. The characteristic modes having more energy content (dominant modes) are also analyzed by the norm of modes || ϕ || by demonstrating the frequency spectra of DMD analysis.

The fate of particles in a volumetrically heated convective fluid at high Prandtl number

The dynamics of suspensions plays a crucial role in the evolution of geophysical systems such as lava lakes, magma chambers and magma oceans. During their cooling and solidification, these magmatic bodies involve convective viscous fluids and dispersed solid crystals that can form either a cumulate or a floating lid by sedimentation. We study such systems based on internal heating convection experiments in high Prandtl fluids bearing plastic beads. We aim to determine the conditions required to produce a floating lid or a sedimented deposit. We show that, although the sign of particles buoyancy is the key parameter, it is not sufficient to predict the particles fate. To complement the model we introduce the Shields formalism and couple it with scaling laws describing convection. We propose a generalized Shields number that enables a self-consistent description of the fate of particles in the system, especially the possibility to segregate from the convective bulk. We provide a quantification of the partition of the mass of particles in the different potential reservoirs (bulk suspension, floating lid, settled cumulate) through reconciling the suspension stability framework with the Shields formalism. We illustrate the geophysical implications of the model by revisiting the problem of the stability of flotation crusts on solidifying rocky bodies.

Non-Boussinesq convection at low Prandtl numbers relevant to the Sun

The figures on the left show the effect of the Prandtl number (Pr) of the Rayleigh-B\'enard problem with Boussinesq conditions, for the same Grashof number of ${10}^{9}$. Top: Pr = 12.73; bottom, Pr = ${10}^{\ensuremath{-}4}$. The plot on the right shows that low molecular Pr yields an inversely varying turbulent Prandtl number; that is, the flow behaves effectively as a high Prandtl number fluid. The data are for non-Boussinesq conditions. The qualitative effect is the same for the Boussinesq case as well, but the dependence has a weaker power law exponent of about $\ensuremath{-}1/3$.

Hall and ion‐slip effects on MHD natural convective flow past an unbounded vertical porous channel with thermodiffusion

AbstractThe consequences of Soret in addition to Dufour of natural convection heat and mass transfer for the unsteady three‐dimensional boundary layer flow through a perpendicular condition of the existence of viscous dissipation, invariable suction, Hall as well as ion slip consequences into relation. The prevailing partial differential equation is dissolved digitally utilizing the implicit Crank–Nicolson finite difference method. The velocity, temperature, as well as concentration dispensations, is addressed computationally and demonstrated by the graphs. Numerical values of the Nusselt number, skin friction as well as Sherwoods numbers nearby the plate are discussed for a choice of values of substantial parameters and are displayed in a tabular manner. It is noticed that the temperature of the fluid diminishes with higher Prandtl numbers. The resulting velocity diminishes with the growing Hartmann number. Rotation, Soret, and Dufour parameters strengthen the velocity and momentum boundary layer thickness. The velocity intensifies through growing Hall and ion‐slip parameters and the revoke trend is acquired with enhancement in suction parameter.

Stagnation point flow of Jeffrey nanofluid with activation energy and convective heat and mass conditions

This research reports stagnation flow of Jeffrey nanofluid toward a permeable stretching cylinder. Brownian motion, thermophoresis, thermal radiation and viscous dissipation are explored. Convective heat-mass conditions are implemented. Moreover, activation energy is taken into account. Transformations (variables) are utilized in order to convert PDEs (Partial DIfferential Equations). (continuity, momentum, energy and concentration equation) into ODEs (Ordinary Differential Equations). Resulting systems are solved by the optimal homotopy analysis method. Behaviors of involved flow, heat and mass transport parameters for velocity, concentration and temperature are examined. Surface friction and Sherwood number and Nusselt numbers are also examined. Velocity of the fluid can be minimized by higher estimations of parameter due to ratio of relaxation and retardation time, suction and injection parameters. Decay in fluid temperature is observed for higher Prandtl number and Deborah number for relaxation time parameter. Skin friction coefficient is controlled via higher values of parameter due to ratio of relaxation and retardation time. Intensification in heat transfer rate (Nusselt number) is seen via higher values of parameter due to ratio of relaxation and retardation time, radiation parameter, Prandtl number and Deborah number for relaxation time and curvature parameter.

Numerical simulation of single-phase heat transfer and nucleate boiling of liquid sodium in narrow annulus channel similar to that of SFR fuel subchannel

The sodium cooled fast reactor (SFR) is a Generation IV nuclear reactor that uses fast neutrons for fission and liquid sodium as the coolant for fission heat removal. Compared to conventional fluids, such as water, liquid sodium shows superior performance in heat transfer because of its high thermal conductivity and low Prandtl number. Understanding of single-phase and two-phase heat transfer characteristics of liquid sodium is essential for the analysis of the normal operation and certain postulated accidental events of SFR. This study is intended towards the development of computational fluid dynamics (CFD) based multiphase models for the safety analysis of SFR using the finite volume method. The numerical simulations of single-phase and two-phase heat transfer processes have been performed for the basic two-dimensional domain that has resemblance with the flow subchannel of SFR fuel subassembly. This study deals with heat transfer considerations under low Peclet number at high temperature, and its boiling inception and further to the nucleate boiling regime in a narrow vertical annulus channel. The Realizable k-ε model with Kays correlation for the turbulent Prandtl number better predicts the single-phase heat transfer characteristics under low Peclet number. A correlation for Nusselt number is fitted from the numerical results for low Peclet number flow conditions in an annulus channel. The flow boiling inception and nucleate boiling are numerically predicted by the Eulerian-Eulerian multiphase model with non-equilibrium wall-boiling for wall heat flux partitioning. The turbulence is modeled using Realizable k-ε model with standard wall function. Under the flow and heat flux values considered the near steady-state boiling conditions are predicted without much pulsating behavior as observed in the reference experiments and during this, the two-phase flow pattern varied from inception to the nucleate boiling regime. The mechanistic model based heat transfer coefficient is evaluated in the boiling zone from the flux partitioning components and compared with the available empirical correlations.

A new lattice Boltzmann method for melting processes of high Prandtl number phase change materials

The lattice Boltzmann method has shown its advantages to model melting processes in thermal energy storage systems. However, the organic phase change materials which are popularly used in modern thermal energy storage systems and featured by a large Prandtl number, have raised a big challenge for the simulation by the lattice Boltzmann method, as a large Prandtl number will cause a large discrepancy between the relaxation times for flow and temperature fields in the lattice Boltzmann method. And such discrepancy will cause serious numerical instability. In this work, a new lattice Boltzmann model is proposed to address this challenge. Three benchmark test cases are adopted to validate the capability of the present lattice Boltzmann model for simulating melting processes of organic phase change materials with large Prandtl numbers (Pr up to 56.2). The present numerical results are in good agreement with the existing data obtained numerically and experimentally. Compared with the available lattice Boltzmann approaches, the present model can capture the melting interface accurately with much less grid density.

Flow and heat transfer analysis of lead–bismuth eutectic flowing in a tube under rolling conditions

The investigation of flow and heat transfer of lead–bismuth eutectic (LBE) under rolling conditions is vital to the application of LBE cooled reactor in offshore engineering. In this paper, mature numerical method for modelling low Prandtl number liquid metal is used for LBE flow in a vertical tube under rolling conditions. Reynolds stress turbulent model is chosen to consider the complex secondary flow caused by additional force. It is found that the transverse additional force is the main reason accounting for the enhancement of heat transfer and secondary flow. The transient maximum heat transfer ability can be enlarged by 18% under condition of rolling angle of 30° and period of 8 s. And 10 times transverse additional force caused by rolling angle of 30° and period of 8 s is enough to change the flow resistance characteristic of LBE. Comparisons with water coolant indicate that the intensity of radial secondary flow play an important role in determining the heat transfer characteristic of fluid under rolling conditions. The high density and low Prandtl number also make the features of LBE under rolling conditions different from those of water. The empirical correlations used in system code now could not predict the flow and heat transfer of LBE under rolling conditions. Special attention should be paid to safety design criteria of the off-shore LBE cooled reactor. This paper may contribute to the thermal–hydraulic design of off-shore liquid metal cooled reactors.