High Prandtl Number Liquid Research Articles

Correlation of single-phase convective heat transfer on spray cooled plain surfaces with high Prandtl number liquids

Spray cooling with transmission oils is an innovative cooling concept for electrical machines, whereby the coolant wets the end windings directly. The thermal design process of such machines requires reliable correlations of the heat transfer coefficients obtainable. Thereby, the majority of the literature only focuses on low Prandtl number coolants at ideal nozzle distances. The transferability of the existing heat transfer models to highly viscous coolants above and below the optimal nozzle distance has yet to be investigated. Therefore, the heat transfer coefficients of spray cooling on plain surfaces with aqueous glycerol solutions (model fluid) and a transmission oil of type ATF VI was investigated. The model fluid serves the purpose of covering the entire range of material properties of commercial transmission oils with only one liquid. Prandtl numbers ranging from 80 to 340 were investigated. Various cases of spray coverage were researched by varying the nozzle distance (2mm−100mm), the spray angle (20∘−80∘) and the size of the spray cooled surface (6.35×6.35mm2;12.7×12.7mm2). Regarding the case of the optimal nozzle distance, where the spray impact area just inscribes the cooled surface, the experimental data was validated with models from the literature. Large deviations of up to 450% resulted at nozzle distances above and below the optimum. Therefore, a dimensionless correlation of the heat transfer coefficient is proposed which includes all cases of spray coverage investigated, exceeding the applicability range of the existing models. The model describes the experimental data with a mean absolute percentage error of 15%.

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

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.

On three-dimensional flow structures and oscillatory instability due to free surface heat loss in half-floating zones under microgravity

Present work describes a numerical investigation concerning the response of oscillatory thermo-capillary convection to free surface heat loss in a cylindrical half floating zone of high Prandtl number liquid (Pr=67) under microgravity conditions. Unsteady and three-dimensional computations have been carried out in the liquid domain using the finite volume method (FVM) to reveal the oscillatory thermo-fluid dynamic regimes at the onset of instability. The influence of different free surface heat loss conditions on the bifurcation from the basic steady axisymmetric state has been discussed in terms of critical azimuthal wavenumber, m. The dynamic evolution of the temperature disturbances at supercritical conditions are characterized by ‘pulsating’ and ‘rotating’ modes of spatio-temporal convection. The development of counter-propagating hydrothermal waves in azimuthal direction is found to be followed by an even mode of convection characterised by m = 2. The liquid bridge system exhibiting the well-known transition from periodic (m=2) to quasi-periodic behaviour (m=1) with an increase in Biot number, Bi has been analysed from both spatial and temporal points of view. The existence of both symmetric and asymmetric modes of the supercritical state for different Bi are presented. The dominant fluid dynamic information of 3D oscillatory state are extracted from a specific set of disturbance temperature data by employing a data-driven computational technique ‘dynamic mode decomposition’ (DMD). Various neutral, stable and unstable dynamic modes responsible for bifurcation to the 3D supercritical state are depicted with the help of DMD spectrum and the frequency spectrum.

Rayleigh-Bénard convection in a newtonian liquid bounded by rigid isothermal boundaries

A non-linear stability analysis of Rayleigh-Bénard convection is reported in the paper for the case of rigid isothermal boundaries. The Ginzburg-Landau equation with cubic non-linearity is obtained. Out of the three fixed points of the equation, one arises in the pre-onset regime and two during post-onset. The pre-onset one is unstable at post-onset times and hence we have a pitchfork bifurcation point. Comparing heat transports it is found that the Nusselt number of the rigid isothermal boundary condition is less than that of the free isothermal case. Prandtl number influence on the Nusselt number is negligible in very high Prandtl number liquids at all times and at long times this is true for all liquids. Using vital information from the procedure leading to the Ginzburg-Landau equation a minimal Fourier-Galerkin expansion is proposed to derive a generalized Lorenz model for rigid-isothermal boundaries. The Hopf bifurcation point signaling onset of chaos is obtained by transforming the Lorenz model of rigid isothermal boundaries to a standard form resembling the classical one. The possibility of regular, chaotic, periodic and mildly chaotic motions in the Lorenz system is shown through the plots of the maximum Lyapunov exponent and the bifurcation diagram.

Near-Wall Determination of the Turbulent Prandtl Number Based on Experiments, Numerical Simulation and Analytical Models

The Reynolds-averaged computation of turbulent flow with heat transfer most commonly models the turbulent heat flux as directly related to the turbulent flux of momentum through the turbulent Prandtl number. Its significant deviation from a uniform bulk flow value for high molecular Prandtl numbers needs to be adequately described to predict accurately the heat transfer. The present study derives a model for the near-wall variation of this important parameter, used as input into an analytical solution of heated turbulent pipe flow. The basic functional form of the profile of the turbulent Prandtl number is determined from direct numerical simulations (DNS), and experimental data are used for model calibration. The analytically predicted Nusselt numbers agree very well with experimental measurements, proving the reliability of the proposed model for the turbulent Prandtl number also for Reynolds numbers well beyond the scope of DNS. The validation against experiments further highlights the significant effect of the temperature-dependent material properties of the considered high Prandtl number liquids. Numerical simulations often discard this aspect to reduce the computational effort. The present combination of DNS, analytical solution, and experiments appears as a convenient approach for modeling turbulent key quantities such as the turbulent Prandtl number, which is well applicable to other convective flow conditions and Prandtl number regimes, as well.

Effects of external environment on thermocapillary convection of high prandtl number fluid

Numerical simulations have been carried out to investigate the influence of external environment on thermocapillary convection in high Prandtl number ( Pr =68) liquid. The geometric model of physical problem is that the the liquid bridge surrounded by ambient air under zero or ground gravity. The interface velocity, temperature, heat flux and flow pattern in the liquid bridge are presented and discussed under different conditions by changing the external environment. The buoyancy convection produces a symmetrical vortex in the liquid bridge. The ambient air affects the distributions of the temperature velocity and heat flux on the interface by changing the thermocapillary convection.

Modeling of the experiments on the Marangoni convection in liquid bridges in weightlessness for a wide range of aspect ratios

Hydrodynamic stability of a two-dimensional steady thermocapillary flow under weightlessness in a high-Prandtl number liquid bridge is studied by means of three-dimensional numerical modeling for a wide range of aspect ratios. We suggest an explanation of the findings of a series of microgravity experiments on Marangoni convection in liquid bridges. Stability of the flow with heat transfer through the interface, modeled by the classical Fourier law, is compared with the stability of the same system under adiabatic conditions. Cooling the interface may significantly shift the threshold of hydrothermal instability as soon as the Biot number deviates from zero. It may also affect the structure of the basic Marangoni flow and the mode of the supercritical flow. We demonstrate that the heat loss has a destabilizing effect for the aspect ratios (ratio of radius to height) below 2.4 (with the exception of a region between 1.6 and 1.8), and for the longer liquid bridges the prevailing effect is stabilizing. The heat transfer coefficient as a function of the length of the liquid zone is theoretically calculated using a model of heat transport for laminar forced convection. Comparison of the results of the modeling with the experimental data shows that an incorrect assessment of the heat transfer may lead to wrong conclusions concerning both the critical parameters of the flow and its structure.

Instability and associated roll structure of Marangoni convection in high Prandtl number liquid bridge with large aspect ratio

This paper reports the experimental results on the instability and associated roll structures (RSs) of Marangoni convection in liquid bridges formed under the microgravity environment on the International Space Station. The geometry of interest is high aspect ratio (AR = height/diameter ≥ 1.0) liquid bridges of high Prandtl number fluids (Pr = 67 and 207) suspended between coaxial disks heated differentially. The unsteady flow field and associated RSs were revealed with the three-dimensional particle tracking velocimetry. It is found that the flow field after the onset of instability exhibits oscillations with azimuthal mode number m = 1 and associated RSs traveling in the axial direction. The RSs travel in the same direction as the surface flow (co-flow direction) for 1.00 ≤ AR ≤ 1.25 while they travel in the opposite direction (counter-flow direction) for AR ≥ 1.50, thus showing the change of traveling directions with AR. This traveling direction for AR ≥ 1.50 is reversed to the co-flow direction when the temperature difference between the disks is increased to the condition far beyond the critical one. This change of traveling directions is accompanied by the increase of the oscillation frequency. The characteristics of the RSs for AR ≥ 1.50, such as the azimuthal mode of oscillation, the dimensionless oscillation frequency, and the traveling direction, are in reasonable agreement with those of the previous sounding rocket experiment for AR = 2.50 and those of the linear stability analysis of an infinite liquid bridge.

Velocity field in a high prandtl number liquid bridge

A numerical model is developed to investigate the velocity fields of high prandtl number liquid bridge with surface deformation under microgravity. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid. In the numerical calculations, the free surface deformation and the effects of ambient air are considered. The surface deformation of liquid bridge is captured by using level set method of mass conservation. Results of lateral and axial velocities on different radius are given. The lateral and axial velocities near the free surface are larger than that near the center of liquid bridge. The lateral velocity and axial velocities on the interface tend to be uniform with the development of thermocapillary convection.

Temperature and flow fields in a high prandtl number liquid bridge under microgravity

The temperature and flow fields of high prandtl number liquid bridge with surface deformation have been investigated under microgravity by a developed numerical model, and numerical simulations have been carried out based on the Navier-Stokes equations coupled with the energy conservation equation on a staggered grid. In numerical calculations, the free surface deformation and the effects of ambient air are considered. The surface deformation of liquid bridge is monitored by level set method of mass conservation to capture two phase interfaces. Simultaneously, results of temperature and flow fields in liquid bridge are given.

A numerical simulation on high prandtl number liquid bridge

The free surface characteristics of high prandtl number liquid bridge with dynamic deformation have been investigated under microgravity based on the Navier-Stokes equations coupled with the energy conservation equation on a staggered grid. The free surface deformation and the effects of ambient air were considered by using level set method of mass conservation to capture two phase interfaces in numerical calculations. The variation of surface velocity is presented and discussed.

Hydrodynamic and thermal interactions of a cluster of solid particles in a pool of liquid of different Prandtl numbers using two-fluid model

The knowledge of thermal interaction between hot particles and liquid is essential for many engineering applications. The main focus of the present study is to understand the underlying phenomena of transient interaction between the hot particles and the liquid of varying Prandtl number under different parametric conditions. Analysis is carried out numerically using in-house multiphase code based on Eulerian two-fluid laminar model. The code is validated against existing results. The dispersion and penetration characteristics of the particles are observed to be a strong function of Prandtl number as well as volume fraction and particle diameter, with a stronger mushrooming observed for lower particle size or high Prandtl number liquid. The thermal interaction is observed to be between the particles and the narrow thermal envelope surrounding the particles. The particles cooling rate are observed to be several orders faster in a liquid with lower Prandtl number.

Temperature Distribution of High Prandtl Number Liquid Bridge under Zero Gravity

A numerical model has been developed to investigate temperature field of high prandtl number liquid bridge under zero-gravity condition, and numerical simulations have been carried out. The Navier-Stokes equations coupled with the energy conservation equation on a staggered grid. In numerical calculations, we considered not only the free surface deformation but also the effects of ambient air. Overall numerical analysis of liquid bridge was carried out by level set method of mass conservation to capture two phase interfaces. Simultaneously, results of temperature field in liquid bridge and ambient gas-phase were given.

Impact of conditions at start-up on thermovibrational convective flow

The development of thermovibrational convection in a cubic cell filled with high Prandtl number liquid (isopropanol) is studied. Direct nonlinear simulations are performed by solving three-dimensional Navier-Stokes equations in the Boussinesq approximation. The cell is subjected to high frequency periodic oscillations perpendicular to the applied temperature gradient under zero gravity. Two types of vibrations are imposed: either as a sine or cosine function of time. It is shown that the initial vibrational phase plays a significant role in the transient behavior of thermovibrational convective flow. Such knowledge is important to interpret correctly short-duration experimental results performed in microgravity, among which the most accessible are drop towers ( approximately 5s) and parabolic flights ( approximately 20s) . It is obtained that under sine vibrations, the flow reaches steady state within less than one thermal time. Under cosine acceleration, this time is 2 times longer. For cosine excitations, the Nusselt number is approximately 10 times smaller in comparison with the sine case. Besides, in the case of cosine, the Nusselt number oscillates with double frequency. However, at the steady state, time-averaged and oscillatory characteristics of the flow are independent of the vibrational start-up. The only feature that always differs the two cases is the phase difference between the velocity, temperature, and accelerations. We have found that due to nonlinear response of the system to the imposed vibrations, the phase shift between velocity and temperature is never equal exactly to pi2 , at least in weightlessness. Thus, heat transport always exists from the beginning of vibrations, although it might be weak.

Direct numerical simulation of transitions towards structural vacillation in an air-filled, rotating, baroclinic annulus

The route to chaos of baroclinic waves in a rotating, stratified fluid subjected to lateral heating can occur via several possible routes, involving either low-dimensional, quasiperiodic states or via a series of secondary small-scale instabilities. In a recent paper, we have discussed direct numerical simulations (DNS) of the low-dimensional route to chaos in a baroclinic annulus filled with air as the working fluid and compared results to those obtained in the laboratory for high Prandtl number liquids. In the present paper, we consider further DNS in the air-filled annulus at higher rotation rates. A transition in the flow structure is observed, where the centrifugal acceleration exceeds gravity and the dominant physical process changes from baroclinic instability to convection due to radial buoyancy. The transition of this convection to chaotic behavior is fundamentally different from that observed in the transition to the chaotic flow observed at lower rotation rates. Rather than via a sequence of low-dimensional, quasiperiodic states, the large-scale convection developed small-scale instabilities, which has been previously suggested as the origin of structural vacillation on the transition to geostrophic turbulence.

Baroclinic waves in an air-filled thermally driven rotating annulus

In this study an experimental investigation of baroclinic waves in air in a differentially heated rotating annulus is presented. Air has a Prandtl number of 0.707, which falls within a previously unexplored region of parameter space for baroclinic instability. The flow regimes encountered include steady waves, periodic amplitude vacillations, modulated amplitude vacillations, and either monochromatic or mixed wave number weak waves, the latter being characterized by having amplitudes less than 5% of the applied temperature contrast. The distribution of these flow regimes in parameter space are presented in a regime diagram. It was found that the progression of transitions between different regimes is, as predicted by recent numerical modeling results, in the opposite sense to that usually found in experiments with high Prandtl number liquids. No hysteresis in the flow type, with respect to variations in the rotation rate, was found in this investigation.

Thermocapillary convection in a liquid bridge subjected to interfacial cooling

Influence of heat loss through interface on a supercritical three-dimensional thermoconvective flow in a long liquid bridge is numerically investigated under terrestrial conditions. A flow in a high Prandtl number liquid surrounded by an ambient gas of constant temperature is simulated for the large aspect ratio, Γ=1.8. It is shown that the heat loss plays a significant role in the flow dynamics. It modifies both the flow and the liquid temperature field. Moreover, for the relatively large aspect ratio and a high Prandtl number liquid the heat loss from interface leads to destabilization of the flow.

Onset of temporal aperiodicity in high Prandtl number liquid bridge under terrestrial conditions

The paper presents a three-dimensional numerical study of the bifurcations and onset of chaotic regime for the thermoconvective oscillatory flow in cylindrical liquid bridge. Three-dimensional Navier–Stokes equations in Boussinesq approximation are solved numerically by finite volume method. Silicone oil 1cSt, with rather large Prandtl number, Pr=18.8, is chosen as test liquid. The simulations are done at normal gravity conditions and unit aspect ratio. The dependence of viscosity of the fluid upon temperature allows us to be close to the real phenomenon. Both spatial and temporal changes occurring in the system are analyzed. The results are compared to the experimental data. A following sequence of well-defined dynamic regimes was detected when temperature difference between the supporting disks is increasing: steady, periodic, quasiperiodic, periodic, and chaotic. The observed succession of bifurcations on the way to chaos is similar to the one coming from experiments. Except for these dynamic bifurcations the system exhibits numerous transitions in spatial organization of the flow. Two-dimensional steady-state flow undergoes standing wave (SW) with azimuthal wave number m=1 as a result of supercritical Hopf bifurcation. Moving above the critical point the following succession of flow states has been numerically found: SW(m=1)→TW (m=1)→SW(m=1+2)→TW(m=1+2). The transition to chaos occurs while the flow pattern represents a traveling wave (TW) with a mixed mode m=1+2, while the m=2 is dominant. Particular attention is paid to the analysis of special properties of the flow: entropy, net azimuthal flow, frequency skips, splitting of maxima, and related phenomena.

Residual-g and g-jitter effects on the measurement of thermophysical properties in microgravity

For the evaluation of the thermo-fluid-dynamic disturbances induced by residual-g and g-jitter on the International Space Station (ISS) a numerical study is carried out for two classes of experiments that exhibit a large sensitivity to accelerations and that would benefit from conditions as close as possible to the purely diffusive fields: 1) measurement of the thermal conductivity in high Prandtl number liquids; 2) measurement of the thermodiffusion coefficient in binary mixtures. Numerical simulations are performed to compare the results of the direct integration of the full Navier-Stokes equations (that compute the instantaneous time-dependent flow) with the solutions of the equations for the time-averaged quantities (thermovibrational theory). The results show that, for the microgravity environment of the ISS, the two formulations give almost the same results. Simulations at different orientations of the residual-g and g-jitter show that, orienting the residual-g parallel to the density gradient, reduces the convective disturbances and can also help mitigating the disturbances induced by the g-jitter. Microgravity experiments will be performed during the UF#3 flight of the ISS (2003) to assess the relative importance of residual-g and g-jitter and the advantages of orienting the density gradient along the residual-g (i.e. in a stabilizing mode), to minimize the acceleration disturbances during sensitive experiments for the measurement of thermophysical properties.