Large Prandtl Number Fluids Research Articles

Natural convection of large Prandtl number fluids: A controversy answered by a new thermal lattice Boltzmann model

The purpose of this work is to deepen our understanding of natural convection with large Prandtl number fluids and to resolve some controversies in the previous publications. To achieve this purpose, a new thermal multiple-relaxation-time lattice Boltzmann model is proposed. Natural convection in a square cavity, a benchmark test case, is investigated numerically using the new model. The Prandtl number is up to 100. For the first time, it is numerically observed that there are two critical Prandtl numbers in the natural convection, which will affect the correlation between the Nusselt number and Prandtl number critically. Three heat transfer characteristic ranges of natural convection are defined in this work, according to the two critical Prandtl numbers. In each range, the dominant heat transfer mechanism is different, which can solve a long-standing issue in the discipline of heat and mass transfer: completely opposing statements on the correlation between the Nusselt number and Prandtl number for natural convection, were published in the open literature. For the first time, this work reveals cause behind the controversial reports and provides the guidance for the future research.

Heat transfer of large Prandtl number fluids in porous media by a new lattice Boltzmann model

With the fast development of sustainable energy technologies and the extreme urgency to protect the living environment, it is crucial to deepen our understanding on the heat transfer characteristics of natural convection of large Prandtl number fluids in porous media. In this study a novel lattice Boltzmann approach is developed as a powerful numerical tool to close the knowledge gap on this important topic. With the aid of this new numerical tool, four new findings are reported and they show that the heat transfer characteristics and correlations of natural convection of large Prandtl number fluids in porous media are quite different from their small Prandtl number counterparts. Through the present analysis, it is found that such inconsistences result from that a transition from a convection-dominated heat transfer process to a conduction-dominated one will appear more easily for large Prandtl number fluids in porous media.

Flow structure and heat transfer of electro-thermo-convection in a dielectric liquid layer

Electrothermohydrodynamic flow of dielectric liquid in a square cavity driven by the simultaneous action of Coulomb and buoyancy forces is studied numerically. A high resolution upwind scheme is applied to study the flow bifurcations and heat transfer. We focus on the strong injection case with the nondimensional injection parameter C fixed at C = 10. Two Prandtl numbers Pr = 1 and Pr = 10, two Rayleigh numbers Ra = 105 and Ra = 106, as well as two mobility numbers M = 10 and M = 20 are considered to evaluate the dependence of flow structure and heat transfer on these parameters. Multistates are found to coexist in a wide range of parameter regimes. Various flow patterns such as one-cell, two-cell, four-cell, and multicell flow are observed. The electric field is found to enhance heat transfer more efficiently for large Prandtl number fluid at low mobility parameter and relatively low Rayleigh number.

Influence of Ambient Airflow on Free Surface Deformation and Flow Pattern Inside Liquid Bridge With Large Prandtl Number Fluid (Pr > 100) Under Gravity

The influence of airflow shear on the free surface deformation and the flow structure for large Prandtl number fluid (Pr = 111.67) has been analyzed numerically as the parallel airflow shear is induced into the surrounding of liquid bridge from the lower disk or the upper disk. Contrasted with former studies, an improved level set method is adopted to track any tiny deformation of free surface, where the area compensation is carried out to compensate the nonconservation of mass. Present results indicate that the airflow shear can excite flow cells in the isothermal liquid bridge. The airflow shear induced from the upper disk impulses the convex region of free interface as the airflow shear intensity is increased, which may exceed the breaking limit of liquid bridge. The free surface is transformed from the “S”-shape into the “M”-shape as the airflow shear is induced from the lower disk. For the nonisothermal liquid bridge, the flow cell is dominated by the thermocapillary convection at the hot corner if the airflow shear comes from the hot disk, and another reversed flow cell near the cold disk appears. While the shape of free surface depends on the competition between the thermocapillary force and the shear force when the airflow is induced from the cold disk.

Thermal-Boundary-Layer Response to Convected Far-Field Fluid Temperature Changes

Fluid flows of varying temperature occur in heat exchangers, nuclear reactors, nonsteady-flow devices, and combustion engines, among other applications with heat transfer processes that influence energy conversion efficiency. A general numerical method was developed with the capability to predict the transient laminar thermal-boundary-layer response for similar or nonsimilar flow and thermal behaviors. The method was tested for the step change in the far-field flow temperature of a two-dimensional semi-infinite flat plate with steady hydrodynamic boundary layer and constant wall temperature assumptions. Changes in the magnitude and sign of the fluid-wall temperature difference were considered, including flow with no initial temperature difference and built-up thermal boundary layer. The equations for momentum and energy were solved based on the Keller-box finite-difference method. The accuracy of the method was verified by comparing with related transient solutions, the steady-state solution, and by grid independence tests. The existence of a similarity solution is shown for a step change in the far-field temperature and is verified by the computed general solution. Transient heat transfer correlations are presented, which indicate that both magnitude and direction of heat transfer can be significantly different from predictions by quasisteady models commonly used. The deviation is greater and lasts longer for large Prandtl number fluids.

Effect of time-periodic boundary temperatures/body force on Rayleigh–Benard convection in a ferromagnetic fluid

We discuss the thermal instability in a layer of a ferromagnetic fluid when the boundaries of the layer are subjected to synchronous/asynchronous imposed time-periodic boundary temperatures (ITBT)/time–periodic body force (TBF). Only infinitesimal disturbances are considered. The Venezian approach is adopted in arriving at the critical Rayleigh and wave numbers for small amplitudes of ITBT. A perturbation solution in powers of the amplitude of the applied temperature field is obtained. When the ITBT at the two walls are synchronized then, for moderate frequency values, the role of magnetization in inducing sub-critical instabilities is delineated. A similar role is shown to be played by the Prandtl number. The magnetization parameters and Prandtl number have the opposite effect at large frequencies. The system is most stable when the ITBT is asynchronous. The effect of TBF on the onset of convection is found to be qualitatively similar to the effect of an asynchronous ITBT. Low Prandtl number fluids are shown to be more easily vulnerable to destabilization by TBF compared to very large Prandtl number fluids. The problem has relevance in many ferromagnetic fluid applications wherein regulation of thermal convection is called for.

Influence of Aspect Ratio on the Onset of ThermocapillaryOscillatory Convection in a Floating Half Zone of Large Prandtl NumberFluid

The onset of oscillatory thermocapillary convection in afloating half zone of 10 cst silicon oil (Prandtl number 105.6) isstudied by the three-dimensional and unsteady numerical simulation inmicrogravity environment (g = 10-4gearth). The results showthat the steady and axi-symmetric convection, for a fixed liquid bridgevolume ratio Vℓ/V0 = 1, transits directly to theoscillatory convection if geometrical aspect ratio A is largerthan the critical value Ac = 1.25, but transits to theoscillatory convection via the steady and non-axisymmetric flow ifA is smaller than the critical value Ac. The result means thatthere are two bifurcation transitions in a liquid bridge of the largePrandtl number fluid with a smaller aspect ratio A.

Two bifurcation transitions of the floating half zone convection in a fat liquid bridge of larger Pr

The transient process of the thermocapillary convection was obtained for the large Pr floating half zone by using the method of three-dimensional and unsteady numerical simulation. The convection transits directly from steady and axisymmetric state to oscillatory flow for slender liquid bridge, and transits first from steady and axisymmetric convection to the steady and non-axisymmetric convection, then, secondly to the oscillatory convection for the fatter liquid bridge. This result implies that the volume of liquid bridge is not only a sensitive critical parameter for the onset of oscillation, but also relates to the new mechanism for the onset of instability in the floating half zone convection even in case of large Prandtl number fluid.

A numerical and experimental investigation of stability of natural convective flows within a horizontal annulus

A numerical and experimental study of buoyancy-driven flow in the annulus between two horizontal coaxial cylinders at Rayleigh numbers approaching and exceeding the critical values is presented. The stability of the flow is investigated using linear theory and the energy method. Theoretical predictions of the critical Rayleigh number for onset of secondary flows are obtained for a wide range of radius ratio R and are verified by comparison with results of previous experimental studies. A subcritical Rayleigh number which provides a necessary condition for global flow stability is also determined. The three-dimensional transient equations of fluid flow and heat transfer are solved to study the manifestation of instabilities within annuli having impermeable endwalls, which are encountered in various applications. For the first time, a thorough examination of the development of spiral vortex secondary flow within a moderate gap annulus and its interaction with the primary flow is performed for air. Simulations are conducted to investigate factors influencing the size and number of post-transitional vortex cells. The evolution of stable three-dimensional flow and temperature fields with increasing Rayleigh number in a large gap annulus is also studied. The distinct flow structures which coexist in the large gap annulus at high Rayleigh numbers preceding transition to oscillatory flow, including transverse vortices at the end walls which have not been previously identified, are established numerically and experimentally. The solutions for the large-gap annulus are compared to those for the moderate-gap case to clarify fundamental differences in behaviour. Heat transfer results in the form of local Nusselt number distributions are presented for both the moderate- and large-gap cases. Results from a series of experiments performed with air to obtain data for validation of the numerical scheme and further information on the flow stability are presented. Additionally, the change from a crescent-shaped flow pattern to a unicellular pattern with centre of rotation at the top of the annulus is investigated numerically and experimentally for a Prandtl number of 100. Excellent agreement between the numerical and experimental results is shown for both Prandtl numbers studied. The present work provides, for the first time, quantitative three-dimensional descriptions of spiral convection within a moderate-gap annulus containing air, flow structures preceding oscillation in a large-gap annulus for air, and unicellular flow development in a large-gap annulus for large Prandtl number fluids.

Experiments on the multi-roll-structure of thermocapillary flow in side-heated thin liquid layers

Abstract The multi-roll-structure (MRS) with convection rolls, all with the same sense of rotation and axes perpendicular to the applied temperature gradient appears in thin layers driven by thermocapillarity prior to time dependent states. Detailed experimental and numerical results are reported. The MRS in large Prandtl-number fluids is dominated by thermocapillarity and separates from the buoyancy driven bulk flow for deep layers. We prepare a microgravity experiment MAGIA to study thermocapillary flow structures without coupling to buoyancy in a 20.0 mm wide annular layer with free surface of variable depth heated by the outer wall and cooled at the inside.

Square cells in gravitational and capillary thermoconvection

The onset of square convective cells in fluid layers heated from below is investigated. Amplitude equations an deduced from the Boussinesq equations and a standard stability analysis is performed. Square cells are shown to be preferred when the instability is mainly capillarity driven. The influence of the Prandtl and Blot numbers are examined. At small Pr, the Plot number has not very much influence and squares are always observed for thin enough layers. in large Prandtl number fluids, Pi must be larger than the limiting value 0.28 for squares to be stable.

Effect of gravity modulation on natural convection in a vertical slot

Abstract The effect of a sinusoidal gravity modulation on natural convection of fluids with constant property, in vertical slots of aspect ratio of 20 and 15, is studied numerically by a finite difference method. The gravity modulation is characterized by the nondimensional amplitude Rg and nondimensional frequency ωf. We find a low frequency g-modulation has a strong effect on the fluid flow but little effect on the heat transfer rate. The flow of air usually enters a periodic state after two cycles of g-modulation, much faster than that of large Prandtl number fluids. The response is generally in the synchronous mode, except at ωf = 10 and Rg = 1 for air where it appears to be subharmonic. For a multicellular primary flow of air, g-modulation at ωf = 25 and Rg = 1 changes the multicellular primary flow to a unicellular one, demonstrating significant stabilizing effect. For high Prandtl number fluids, a flow pattern, consisting of horizontal secondary cells, preceded the onset of the commonly observed vertical secondary cells. At low modulation frequencies, stability of convection is enhanced as demonstrated by the increase in the critical Grashof number, by approximately 154% at Rg = 1.6 and ωf = 40. The temperature remains unchanged within the cycle of the modulation, totally different from the case of air, and gives a critical gradient approximately 0.56 at the center.

Formation of cells in natural convection in a vertical slot at large Prandtl number

This paper presents several features at supercritical conditions of natural convection of large Prandtl number fluids in a vertical slot. Both experimental and numerical results show that even at slightly supercritical conditions the multicellular flow is in an unsteady state which is attributed to the moving and merging of cells. The effect of variable viscosity on the unsteadiness is investigated numerically. Successive merging and appearance of cells is characteristic of this convection so that the number of secondary cells changes with time. The bifurcation phenomena characterized by several modes of unsteady cellular flow are examined.

Laminar forced convection in a helicoidal pipe with finite pitch

This paper presents a numerical investigation of fully developed laminar convective heat transfer in a helicoidal pipe with a finite pitch coiled pipe. Three major parameters are identified to affect laminar convective heat transfer in a helicoidal pipe: the Dean number, torsion and the Prandtl number. The results indicate that torsion will increase the temperature gradient on one side of the pipe wall and decrease the temperature gradient on the other side. In the case of a small Prandtl number fluid, the Nusselt number declines slightly as torsion increases. However, in the case of a large Prandtl number fluid, the Nusselt number is significantly reduced as torsion increases. The predicted results for the limiting cases are also compared with other numerical and experimental results.

Experiments on Convective Instability of Large Prandtl Number Fluids in a Vertical Slot

The stability of thermal convection of large Prandtl number fluids in a vertical slot (aspect ratio = 10, 15, or 20) was studied experimentally. Secondary cells began to appear from the center of the slot and then prevailed. The critical Rayleigh number showed an increasing trend as the aspect ratio was increased, and became higher than that obtained from a linear stability analysis owing to a possible traveling wave mode of instability. As the Rayleigh number was increased, either the onset of the tertiary cells or the traveling waves occurred depending on the Prandtl number. In the transition process from laminar to turbulent flow, the secondary cells around the end regions split into smaller cells and an unsteady flow structure appeared with an original secondary cell in the center region and some smaller cells along the sidewalls.

Forced-Convection Cooling of a Linear Array of Blocks in Open and Porous Matrix Channels

Abstract Steady laminar forced-convection cooling of discrete heated blocks in open and porous matrix channels has been analyzed for different types of coolants, porous material porosities, and mass flow rates. As expected, the low-porosity porous material-filled channel configuration with large Prandtl number fluids flowing at high Reynolds numbers yields the best results in terms of net heat removal. However, the pressure drop for porous material-filled channel flow is measurably higher than that for open-channel flow. As a compromise, using a high porous matrix (say, n = 0.3), the efficiency of the new configuration is 46% higher using water and 58% higher for air when compared with the traditional open-channel cooling system.

Onset of periodic convection in a vertical slot

New observations of the convective states in a vertical slot in the neighborhood of the transition to multicellular motion are reported. Experiments in large Prandtl number fluids reveal that the departure from unicellular flow develops gradually in the central region of the slot with an initial closure of the distorted primary flow. Subsequently, as the Rayleigh number increases, a multiplicity of transverse stationary eddies occur in the same vicinity within the primary flow. Similar observations in an air-filled slot display a different response. In this case the initial perturbation of the base flow, resulting in closure of the unicellular motion takes place near the end walls. These and other observations illustrate that differences arise because of the Prandtl number. Measurements of the thermal stratification in the core of the oil-filled cavity are in good agreement with recent numerical solutions, based on the boundary layer approximation. The results are also found to be in reasonable accord with the neutral curve predicted from a linear stability analysis.

Laminar mixed convection in the entrance region of shrouded arrays of heated rectangular blocks

AbstractLaminar mixed convection in the entrance region of shrouded arrays of heated rectangular blocks is approximated numerically for large Prandtl number fluids. The problem considered is related to the convective cooling of electronic components mounted on horizontal circuit boards. Two heating conditions are investigated; in case 1, the uniformly heated components are facing upwards and, in case 2, the heated components are facing downwards. Typical fluid streamlines and isotherms, block wall temperature distributions and local Nusselt numbers are presented. It is found that the secondary flow leads to a significant enhancement in heat transfer for cases where the block faces upwards rather than downwards.

Geometrical effect on laminar mixed convection in the entrance region of shrouded arrays of heated rectangular blocks

Abstract The effect of geometric parameter on laminar mixed convection in the entrance region of shrouded arrays of heated rectangular blocks is approached numerically for large Prandtl number fluid. The problem considered is related to convective cooling of electronic components mounted on horizontal circuit boards. Typical development of streamline and isotherm, block wall temperature distribution, and local Nusselt number are presented. It is found that the secondary flow leads to a significant enhancement in heat transfer. The multiple eddies above the block, induced by the combined geometric and buoyancy effect, lead to a more uniform block wall temperature distribution and then reduce the magnitude of the highest wall temperature.

On the viscous dissipation in the boundary layer of a high Prandtl number fluid in laminar flow over a flat plate

An asymptotic expansion for large Prandtl number fluids has been obtained for the recovery factor in a laminar flow over flat plate. The expression underestimates the recovery factor by no more than 1% as long as the Prandtl number is greater than seven.