Three-dimensional numerical experiments on thermal convection in a very viscous fluid: Implications for the dynamics of a thermal boundary layer at high Rayleigh number

2000 ◽  
Vol 12 (3) ◽  
pp. 609-617 ◽  
Author(s):  
E. M. Parmentier ◽  
C. Sotin
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Viscous Fluid ◽  
Thermal Convection ◽  
Numerical Experiments ◽  
Thermal Boundary Layer ◽  
Three Dimensional

Numerical simulations of turbulent thermal convection with a free-slip upper boundary

2019 ◽  
Vol 475 (2232) ◽  
pp. 20190601 ◽  
Author(s):  
W. A. Hay ◽  
M. V. Papalexandris
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Thermal Convection ◽  
Thermal Boundary Layer ◽  
Boussinesq Approximation ◽  
Density Fluctuations ◽  
Lower Wall ◽  
Mean Pressure ◽  
The Mean ◽  
Upper Boundary

In this paper, we report on direct numerical and large-eddy simulations of turbulent thermal convection without invoking the Oberbeck–Boussinesq approximation. The working medium is liquid water and we employ a free-slip upper boundary condition. This flow is a simplified model of thermal convection of water in a cavity heated from below with heat loss at its free surface. Analysis of the flow statistics suggests similarities in spatial structures to classical turbulent Rayleigh–Bénard convection but with turbulent fluctuations near the free-slip boundary. One important observation is the asymmetry in the thermal boundary layer heights at the lower and upper boundaries. Similarly, the budget of the turbulent kinetic energy shows different behaviour at the free-slip and at the lower wall. Interestingly, the work of the mean pressure is dominant due to the hydrostatic component of the mean-pressure gradient but also depends on the density fluctuations which are small but, critically, non-zero. As expected the boundary-layer heights decrease with the Rayleigh number, due to increased turbulence intensity. However, independent of the Rayleigh number, the height of the thermal boundary layer at the upper boundary is always smaller than that on the lower wall.

scholarly journals A Triggering Mechanism for Rapid Intensification of Tropical Cyclones

2015 ◽  
Vol 72 (7) ◽  
pp. 2666-2681 ◽  
Author(s):  
Yoshiaki Miyamoto ◽  
Tetsuya Takemi
Keyword(s):  
Boundary Layer ◽  
Numerical Experiments ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Convective Cell ◽  
Rapid Intensification ◽  
Rotating Fluid ◽  
Coriolis Parameter ◽  
Maximum Tangential Velocity

Triggering processes for the rapidly intensifying phase of a tropical cyclone (TC) were investigated on the basis of numerical experiments using a three-dimensional nonhydrostatic model. The results revealed that the rapid intensification of the simulated TC commenced following the formation of a circular cloud, which occurred about 12 h after the TC became essentially axisymmetric. The circular cloud (eyewall) evolved from a cloudy convective cell that was originally generated near the radius of maximum wind speed (RMW). The development of the convective cell in the eyewall was closely related to the radial location of the strong boundary layer convergence of axisymmetric flow. The radius of maximum convergence (RMC) was small relative to the RMW when the TC vortex was weak, which is consistent with the boundary layer theory for a rotating fluid system on a frictional surface. As the TC intensified, the RMC approached the RMW. An eyewall was very likely to form in the simulated TC when the RMC approached the RMW. Because the RMC is theoretically determined by a Rossby number defined by the maximum tangential velocity, RMW, and Coriolis parameter, a series of numerical experiments was conducted by changing the three parameters. The results were consistent with the hypothesis that intensification occurs earlier for larger Rossby numbers. This finding indicates that initial TC vortices with larger Rossby numbers are more likely to experience rapid intensification and, hence, to evolve into strong hurricanes.

scholarly journals Three-Dimensional Casson Nanofluid Thin Film Flow over an Inclined Rotating Disk with the Impact of Heat Generation/Consumption and Thermal Radiation

Coatings ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 248 ◽  
Author(s):  
Anwar Saeed ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Muhammad Jawad ◽  
Asad Ullah ◽  
...  
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Boundary Layer ◽  
Energy Transport ◽  
Film Flow ◽  
Three Dimensional ◽  
Concentration Profiles ◽  
Thin Film Flow ◽  
The Impact

In this research, the three-dimensional nanofluid thin-film flow of Casson fluid over an inclined steady rotating plane is examined. A thermal radiated nanofluid thin film flow is considered with suction/injection effects. With the help of similarity variables, the partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs). The obtained ODEs are solved by the homotopy analysis method (HAM) with the association of MATHEMATICA software. The boundary-layer over an inclined steady rotating plane is plotted and explored in detail for the velocity, temperature, and concentration profiles. Also, the surface rate of heat transfer and shear stress are described in detail. The impact of numerous embedded parameters, such as the Schmidt number, Brownian motion parameter, thermophoretic parameter, and Casson parameter (Sc, Nb, Nt, γ), etc., were examined on the velocity, temperature, and concentration profiles, respectively. The essential terms of the Nusselt number and Sherwood number were also examined numerically and physically for the temperature and concentration profiles. It was observed that the radiation source improves the energy transport to enhance the flow motion. The smaller values of the Prandtl number, Pr, augmented the thermal boundary-layer and decreased the flow field. The increasing values of the rotation parameter decreased the thermal boundary layer thickness. These outputs are examined physically and numerically and are also discussed.

Two-Phase Microscopic Heat Transfer Model for Three-Dimensional Stagnation Boundary-Layer Flow in a Porous Medium

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shashi Prabha Gogate S.
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Thermal Boundary Layer ◽  
Solid Phase ◽  
Boundary Layer Equation ◽  
Three Dimensional ◽  
Fluid Phase ◽  
Transfer Model ◽  
Layer Flow

Abstract This work examines the steady three-dimensional forced convective thermal boundary-layer flow of laminar and incompressible fluid in a porous medium. In this analysis, it is assumed that the solid phase and the fluid phase, which is immersed in a porous medium are subjected to local thermal nonequilibrium (LTNE) conditions, which essentially leads to one thermal boundary-layer equation for each phase. Suitable similarity transformations are introduced to reduce the boundary-layer equations into system of nonlinear ordinary differential equations, which are analyzed numerically using an implicit finite difference-based Keller-box method. The numerical results are further confirmed by the asymptotic solution of the same system for large three-dimensionality parameter, and the corresponding results agree well. Our results show that the thickness of boundary layer is always thinner for all permeability parameters tested when compared to the nonporous case. Also, it is noticed that the temperature of solid phase is found to be higher than the corresponding fluid phase for any set of parameters. There is a visible temperature difference in the two phases when the microscopic interphase rate is quite large. The physical hydrodynamics to these parameters is studied in some detail.

Thermal Convection in Porous Media at High Rayleigh Numbers

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Daniel J. Keene ◽  
R. J. Goldstein
Keyword(s):  
Boundary Layer ◽  
Porous Media ◽  
Thermal Convection ◽  
Thermal Boundary Layer ◽  
Packed Bed ◽  
Horizontal Layer ◽  
Homogeneous Fluid ◽  
Fluid Systems ◽  
Dimensionless Groups ◽  
Rayleigh Numbers

An experimental study of thermal convection in a porous medium investigates the heat transfer across a horizontal layer heated from below at high Rayleigh number. Using a packed bed of polypropylene spheres in a cubic enclosure saturated with compressed argon, the pressure was varied between 5.6 bar and 77 bar to obtain fluid Rayleigh numbers between 1.68 × 109 and 3.86 × 1011, corresponding to Rayleigh–Darcy numbers between 7.47 × 103 and 2.03 × 106. From the present and earlier studies of Rayleigh–Benard convection in both porous media and homogeneous fluid systems, the existence and importance of a thin thermal boundary layer are clearly demonstrated. In addition to identifying the governing role of the thermal boundary layer at high Rayleigh numbers, the successful correlation of data using homogeneous fluid dimensionless groups when the thermal boundary layer thickness becomes smaller than the length scale associated with the pore features is shown.

Experimental studies of the viscous boundary layer properties in turbulent Rayleigh–Bénard convection

2008 ◽  
Vol 605 ◽  
pp. 79-113 ◽  
Author(s):  
CHAO SUN ◽  
YIN-HAR CHEUNG ◽  
KE-QING XIA
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Rayleigh Number ◽  
Power Law ◽  
Thermal Boundary Layer ◽  
Viscous Sublayer ◽  
Viscous Boundary Layer ◽  
Velocity Boundary Layer ◽  
Viscous Boundary

We report high-resolution measurements of the properties of the velocity boundary layer in turbulent thermal convection using the particle image velocimetry (PIV) technique and measurements of the temperature profiles and the thermal boundary layer. Both velocity and temperature measurements were made near the lower conducting plate of a rectangular convection cell using water as the convecting fluid, with the Rayleigh number Ra varying from 109 to 1010 and the Prandtl number Pr fixed at 4.3. From the measured profiles of the horizontal velocity we obtain the viscous boundary layer thickness δυ. It is found that δυ follows the classical Blasius-like laminar boundary layer in the present range of Ra, and it scales with the Reynolds number Re as δυ/H = 0.64Re−0.50±0.03 (where H is the cell height). While the measured viscous shear stress and Reynolds shear stress show that the boundary layer is laminar for Ra < 2.0 × 1010, two independent extrapolations, one based on velocity measurements and the other on velocity and temperature measurements, both indicate that the boundary layer will become turbulent at Ra ~ 1013. Just above the thermal boundary layer but within the mixing zone, the measured temperature r.m.s. profiles σT(z) are found to follow either a power law or a logarithmic behaviour. The power-law fitting may be slightly favoured and its exponent is found to depend on Ra and varies from −0.6 to −0.77, which is much larger than the classical value of −1/3. In the same region, the measured profiles of the r.m.s. vertical velocity σw(z) exhibit a much smaller scaling range and are also consistent with either a power-law or a logarithmic behaviour. The Reynolds number dependence of several wall quantities is also measured directly. These are the wall shear stress τw ~ Re1.55, the viscous sublayer δw ~ Re−0.91, the friction velocity uτ ~ Re0.80, and the skin-friction coefficient cf ~ Re−0.34. All of these scaling properties are very close to those predicted for a classical Blasius-type laminar boundary layer, except that of cf. Similar to classical shear flows, a viscous sublayer is also found to exist in the present system despite the presence of a nested thermal boundary layer. However, velocity profiles normalized by wall units exhibit no obvious logarithmic region, which is likely to be a result of the very limited distance between the edge of the viscous sublayer and the position of the maximum velocity. Compared to traditional shear flows, the peak position of the wall-unit-normalized r.m.s. profiles is found to be closer to the plate (at z+ = z/δw ≃ 5). Our overall conclusion is that a Blasius-type laminar boundary condition is a good approximation for the velocity boundary layer in turbulent thermal convection for the present range of Rayleigh number and Prandtl number.

Thermal Boundary Layer in Turbulent Thermal Convection

1993 ◽  
Vol 23 (5) ◽  
pp. 379-379
Author(s):  
F Chillá ◽  
S Ciliberto ◽  
C Innocenti
Keyword(s):  
Boundary Layer ◽  
Thermal Convection ◽  
Thermal Boundary Layer

The thermal signature of a vortex pair impacting a free surface

2001 ◽  
Vol 444 ◽  
pp. 49-78 ◽  
Author(s):  
GEOFFREY B. SMITH ◽  
R. J. VOLINO ◽  
R. A. HANDLER ◽  
R. I. LEIGHTON
Keyword(s):  
Boundary Layer ◽  
Temperature Field ◽  
Surface Temperature ◽  
Numerical Experiments ◽  
Thermal Boundary Layer ◽  
Vortex Pair ◽  
Water Interface ◽  
Physical Experiments ◽  
Air Water Interface ◽  
Surface Temperature Field

The action of a rising vortex pair on the thermal boundary layer at an air–water interface is studied both experimentally and numerically. The objective is to relate variations in the surface temperature field to the hydrodynamics of the vortex pair below. The existence of a thermal boundary layer on the water side of an air–water interface is well known; it is this boundary layer which is disrupted by the action of the vortex system. Experimentally, the vortices were generated via the motion of a pair of submerged flaps. The flow was quantified through simultaneous measurement of both the subsurface velocity field, via digital particle image velocimetry (DPIV), and the surface temperature field, via an infrared (IR) sensitive imager. The results of the physical experiments show a clearly defined disruption of the ambient thermal boundary layer which is well correlated with the vorticity field below. Numerical experiments were carried out in a parameter space similar to that of the physical experiments. Included in the numerical experiments was a simple surfactant model which enabled the exploration of the complex role surface elasticity played in the vortex–free surface interaction. The results of this combined experimental and numerical investigation suggest that surface straining rate is an important parameter in correlating the subsurface flow with the surface temperature field. A model based on surface straining rate is presented to explain the interaction.

scholarly journals The global characteristics of the three-dimensional thermal convection inside a spherical shell

1997 ◽  
Vol 4 (1) ◽  
pp. 19-27 ◽  
Author(s):  
J. Arkani-Hamed
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Spherical Shell ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Horizontal Layer ◽  
Boundary Layer Theory ◽  
Physical Parameters ◽  
Rayleigh Numbers

Abstract. The Rayleigh number-Nusselt number, and the Rayleigh number-thermal boundary layer thickness relationships are determined for the three-dimensional convection in a spherical shell of constant physical parameters. Several models are considered with Rayleigh numbers ranging from 1.1 x 102 to 2.1 x 105 times the critical Rayleigh number. At lower Rayleigh numbers the Nusselt number of the three-dimensional convection is greater than that predicted from the boundary layer theory of a horizontal layer but agrees well with the results of an axisymmetric convection in a spherical shell. At high Rayleigh numbers of about 105 times the critical value, which are the characteristics of the mantle convection in terrestrial planets, the Nusselt number of the three-dimensional convection is in good agreement with that of the boundary layer theory. At even higher Rayleigh numbers, the Nusselt number of the three-dimensional convection becomes less than those obtained from the boundary layer theory. The thicknesses of the thermal boundary layers of the spherical shell are not identical, unlike those of the horizontal layer. The inner thermal boundary is thinner than the outer one, by about 30- 40%. Also, the temperature drop across the inner boundary layer is greater than that across the outer boundary layer.

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