Session J17: Free and Forced Convection

An experimental study on the onset of centrifugal effects in turbulent rotating thermal convection

Due to its relevance to the geo- and astrophysical flows, geostrophic turbulence, involving strong Coriolis effect and intensive turbulence, is of interests in the studies of turbulent rotating Rayleigh-Bénard convection (RRBC). However, the effect of the unavoidable centrifugal force on the geostrophic turbulence is often overlooked. Even the basic issue concerning when the centrifugal effect starts to manifest itself is still unresolved. In this talk we present an experimental study of the onset of centrifugal effect (characterized by the onset Froude number Fr_c) in RRBC. The onset Froude number Fr_c was first inferred from the increased bulk temperatures measured at cell center, which was found to scale with the Rayleigh number as Fr_c ~ Ra^0.55. This behavior can be understood qualitatively by a local force balance argument, which gives out Fr_c ~ l₀/H and thus predicts that l₀/H ~ Ra^0.55. Here, l₀ is the mean free distance of the columnar vortices in RRBC. However, the directly measured PIV results of l₀ does not support this 0.55 scaling. We thereby revised the local force balance argument by introducing a correction term, and the measured results agreed well with the revised argument. These results should be useful for future theoretical studies on the centrifugal effect in RRBC.

 

This work was supported by the National Natural Science Foundation of China (Grants No. 12072144 and 12232010).   

Rayleigh-Bénard thermal convection perturbed by a horizontal heat flux

Controlling Rayleigh-Bénard convection is important in many scientific and practical applications. In this talk, we present a simple means to control the vertical heat transfer in Rayleigh-Bénard convection by injecting heat through one lateral side of the fluid domain and extracting the same amount of heat from the opposite side. This horizontal heat flux regulates the large-scale circulation, and increases the heat transfer rate in the vertical direction. Our numerical and theoretical studies demonstrate how a classical Rayleigh-Bénard convection responds to such a perturbation, when the system is near or well above the onset of convection.   

Stability of convection with horizontal buoyancy gradients

Horizontal convection, in which variations in buoyancy exist on horizontal boundaries, are often contrasted to Rayleigh-Bénard convection as having no steady states. In fact there exist exact solutions to the equations of motion with constant horizontal buoyancy gradients and induced flows. The study of these flows goes back to Hart and Weber in the 1970s. We revisit this situation, with a focus on geophysically-relevant boundary conditions. Unlike the case of Rayleigh-Bénard and Orr-Sommerfeld stability, the marginal modes are no longer two-dimensional with zero frequency. We explore the stabilty boundary given by horizontal Rayleigh number in terms of vertical Rayleigh number. Fully three-dimensional modes are investigated. Finallly the energy stability problem is examined.   

Critical modes of convection induced by Joule heating in a liquid metal battery

Liquid metal batteries (LMB)  consists of three super-imposed liquids in  stable stratificationof density  where two liquid metals (electrodes) sandwich a molten salt that serves as an electrolyte [1]. An electric current of density J₀ is applied through the liquid system. As the electrical conductivity of the electrolyte is much lower than the electrical conductivities of liquid metals, the electric current induces an internal Joule heating with the density q  through the electrolyte. In conduction regime, the temperature profile is linear in both the liquid metals and it has a parabolic profile in the electrolyte. The upper part of the electrolyte and the upper electrode are thermally unstable while the lower part of the electrolyte and the lower electrode are thermally stable.

Many hydrodynamic phenomena can develop in the battery: natural convection, interfacial instabilities, electro-magneto-hydrodynamic instabilities [1]. In the present study, we have neglected the magnetic effects induced by the applied current or any external magnetic fields. We have formulated the natural convection model in LMB with the appropriate boundary conditions.  We have performed linear stability analysis and determined the critical parameters of natural convection in the battery for imposed temperatures of LMB boundaries. We found that,  above a critical value of the electric current J_0c, natural convection modes develop in the electrolyte and they invade the upper electrode while the lower electrode remains stable.  A parametric study of the critical modes is performed with respect to the relative size of the elecrodes with respect to the electrolyte.  The dependence of the critical value of Rayleigh number with the Marangoni number is analysed for three types of batteries [2, 3,4].

References

[1] D. H. Kelley and T. Weier, Appl. Mech. Rev. 70 (2), 020801 (2018).

[2] Y. Shen and O.  Zikanov, Theor. Comput. Fluid Dyn. 30, 275-294 (2016).

[3] T. Köllner, T. Boeck and J. Schumacher, Phys. Rev. E 95, 053114 (2017).

[4] D. J. Bradwell, H. Kim, A. H. Sirk and D. R. Sadoway, J. Am. Chem. Soc. 134(4), 1895-1897 (2012).   

Melting dynamics of an ice surface in a turbulent shear flow

We study the dynamics and morphology of a solid as it melts in an idealized setup: we consider an initially flat solid surface between a heated and a cooled plate, with an imposed mean flow. By means of direct numerical simulations, and using the phase-field method, the equations of motion of the fluid phase are coupled with the heat equation within the solid, and a mean flow is sustained by imposing a fixed pressure gradient in the direction parallel to the plates, for Rayleigh numbers in the range 10ˆ5-10ˆ8 and friction Reynolds numbers in the range 10ˆ2-10ˆ3. We study the formation and evolution of patterns and surface roughness, the melt rate, and the heat exchange between the solid and liquid phases while systematically varying the intensity of the imposed mean flow.   

Melting of ice balls in homogeneous isotropic turbulence

We study the melting of thermalised large-scale ice balls in different turbulence intensities. For this a dodecahedral water tank of about 210 litres is fitted with twenty numerically-controlled electric motors mounted on the vertices, which agitate the water with impellers, reaching Reynolds numbers of 10⁶. Zero-mean velocity homogeneous isotropic turbulence (0MVHIT) is achieved in an approximately 20 cm diameter volume in the centre of the dodecahedron. A hole in the top part of the tank allows particles up to 15 cm diameter to be inserted in the tank. The silhouettes of the ice balls are captured with shadowgraphy. We studied the conductive heat transfer from the turbulent water to the ice ball. We found that the Nusselt number is constant throughout the melting process, and Nu and Re are related through a power-law. The ice balls melt isotropically, maintaining sphericity. To better describe the interaction between the turbulent flow and the (melting) ball we investigated the flow with both PIV and numerical simulations.   

Heat Transfer in the Wake of a Sectionally Heated Infinite Square Bluff Body

Bluff bodies are objects or structures with a non-streamlined shape that interact with some fluid flow and create complex flow patterns in their wake. Large bluff body structures with heating on multiple sides are common in human society. The heat transfer due to the wake of such structures directly affects the downstream environment and, as such, is of interest to researchers. Flow past bluff bodies and heated bluff bodies has been widely studied - This work expands on pervious research by numerically studying the heat transfer in the wake of a sectionally heated infinite square bluff body. The simulations are run at Reynolds number Re 750 and result in a wake that transitions to turbulent flow past the recirculation region. The bluff body is split into five sections in the spanwise axis and varying patterns of temperature differential is applied to the sections and their sides. The presentation will discuss the heat transfer characteristics, and heat dispersal patterns in the wake.   

Destruction of advective heat flux by toroidal flow in a non-rotating internally heated full sphere

We study thermal convection in a non-rotating internally heated full sphere at a Prandtl number of unity with fixed temperature boundary conditions using 3D Direct Numerical Simulations. The onset mode of this system is purely poloidal, steady-state and has spherical harmonic degree l=1 both for stress-free and no-slip boundary conditions. As the Rayleigh number is increased to slightly supercritical values, the poloidal flow intensifies, but no toroidal flow is produced. We analytically demonstrate the existence of a large class of poloidal modes whose non-linear interactions do not generate toroidal flow. The onset of toroidal flow occurs as a secondary instability at roughly 10Ra_c. In the case of stress-free boundary conditions, this leads to a decrease in the Nusselt number measuring the strength of advective heat flux. The resulting flow is still steady-state. As the Rayleigh number is increased further, there is a range of the Rayleigh number over which the share of kinetic energy of the toroidal flow continues to grow and the Nusselt number continues to decrease. We believe that this effect, which occurs only for stress-free boundary conditions, has not been demonstrated before in 3D simulations.