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In this paper the influence of an impressed Coriolis force field on the configuration of a turbulent Rayleigh-Bénard convection problem is investigated in an experimental and numerical study. The main purpose of both studies lie on the analysis of a possible stabilising effect of a Coriolis acceleration on the turbulent unsteady structures inside the fluid. The relative Coriolis acceleration which is caused in the atmosphere by the earth rotation is realised in the experimental study by a uniform-rotational movement of the setup in a large-scale centrifuge under hyper-gravity. The same conditions as in the atmosphere in the beginning of a twister or hurricane should be realised in the experiment. The investigated Rayleigh numbers lie between 2.33 × 106 ≤ Ra ≤ 4.32 × 107.

A Rayleigh-Bénard (RB) convection or Rayleigh-Bénard (RB) problem describes thermally driven flow against gravity between two horizontal, heated walls. The fluid is accelerated by local density differences and a resulting pressure gradient. Directly at the heated walls the temperature distribution is determinate by increasing temperature gradients, while convective mass exchange is dominant in the center region. Turbulent shear layers parallel to the direction of gravity develop between the walls. The first studies of a RB problem between horizontal, heated walls were performed by the French physicist Henri Claude Bénard and the English physicist Lord Rayleigh [

Maystrenko et al. [

The experimental RB cell consists of a rectangular, air-filled container with horizontal, heated walls. The container is heated isothermally from below and cooled from above with a constant temperature difference between both walls DT = T_{hot} – T_{cold}. The container has a length (L) of 0.58 m, a height (H) of 0.2 m and a depth (D) of 0.58 m. The sidewalls consist of polymethyl methacrylate (PMMA) and have all a thickness of 0.01 m. Despite an insulating effect of the PMMA side walls, a possible heat loss through the side walls has to be considered. An almost atmospheric pressure condition is generated inside the cell. An overview of the centrifuge system (left picture) and a photograph (right picture) of the experiment installed in the centrifuge is presented in

The blue coloured parts in _{IF} = T_{cold} = 293.15 K. The container can be characterised by the parameters of the Rayleigh number Ra, the Prandtl number Pr, the Nusselt number Nu and its aspect ratios

where _{res} = 1.4 g acting on the fluid. Thus, different Rayleigh numbers are realised in both modes. In case of the non-rotation mode and DT = 3 K a Rayleigh-number of Ra = 2.33 × 10^{6} is realised, for ^{6} is realised, for DT = 60 K it lies at Ra = 4.32 × 10^{7}. _{1} = 3.724 m, L_{2} = 4.72 m, L_{3} = 0.361 m, L_{4} = 1.411 m, L_{5} = 0.4 m, L_{6} = 5.1030 m, height H = 2.75 m, deflection angle α = 46.167˚ and two sensors S_{1}, S_{2}. The centrifuge system rotates with 13.704 revolutions per minute (rpm). The experimental setup has a total weight of 107.5 kg. It is helpful to divide the complete setup in two different systems. The system of the RB cell, marked by

In the 3-dimensional numerical simulation presented, the computational geometry of the container is analogously chosen to the experimental cell and displayed schematically in ^{5} Pa.

The simulation assumes a non-Boussinesq fluid. Temperature dependent fluid properties are calculated by the Sutherland model [

To record the flow profile in the experiment, the flow is visualised by tracer particles of magnesium carbonate (MgCO_{3}). Only visualised data is estimated at this point from the experiment. A camera, which is fixed in front of the container at point K (see

An overview of the estimated flow region in the experimental cell as well as a sketch of the camera installation are illustrated in

where μ is the dynamic viscosity of air, r the radius of the spherical particle and u its approaching velocity. The highest realisable temperature difference between the heated walls is DT = 60 K the lowest one is

with a supposed mean approaching velocity

Hence, the used tracer particles shall have at most a radius of

where St is the stokes number and H the height of the setup. The sketches in

If a particle is moving parallel to the rotation axis of the centrifuge, no effect of an acting Coriolis force can be seen. In all other cases a Coriolis acceleration affects the flow movement inside the cell. The left sketch in ^{6}, the PIV method detected more particles in the same estimated region than in case of the other results. Thus, one obtains a more “compact” velocity field. Note that it was not possible to obtain quantitative measured data from the experimental setup in this study. Only visualised data could be obtained. Measured values of fluid properties inside the container may be a possible step in future works. The red coloured arrows are added additionally in ^{6} than for Ra = 4.32 × 10^{7}. Small spatial scales of flow structures as well as visible vortex structures appear in case of Ra = 3.29 × 10^{6}. For Ra = 4.32 × 10^{7} these turbulent structures become larger and seem to be more regular.

In the study of King et al. in [^{2/7}. In the rotation mode, the experimental and numerical data lie beneath the given correlation law for smaller Rayleigh numbers, but converge with increasing Rayleigh numbers to the given Nu-Ra correlation law.

In this study, the LES performed uses a compressible coupled model. The analysed fluid is air and the Prandtl number lies at

In the study of [_{res} (see

of velocity structures show a wave-like character. In comparison to a non-rotating RB cell (left picture in

An experimental and a numerical study were performed for a turbulent RB convection in an air-filled enclosed container where the horizontal walls were heated isothermally, but with a constant temperature difference. The setup was accelerated in a large-scale centrifuge to investigate a possible influence of a Coriolis force on the development of turbulent structures inside the fluid. Compared to a non-rotating RB cell, which shows typically large-scale convection cells, the velocity structures in the rotation mode seemed to be smaller, mixed and more irregular. Furthermore, the development of turbulent structures rose. However, the structures became larger and seemed to be more regular with increasing Rayleigh numbers. Higher Nusselt number values could not be observed in the rotation mode compared to the non-rotation mode. Thus, comparing the rotating RB cell directly to the non-rotating cell, a stabilising effect of the Coriolis force could not be observed in both studies.

This study was funded by the Zentrale Forschungsförderung of the University Bremen.

Roman Symbols

a_{c}: Coriolis acceleration vector [m/s^{2}]

a,_{ZF}: Centrifugal acceleration vector in point A [m/s^{2}]

a,_{ ZP}: Centripetal acceleration vector in point A [m/s^{2}]

g: Gravitational acceleration vector [m/s^{2}]

u: Approaching velocity of a tracer particle [m/s]

m: Mass [kg]

x, y, z: Cartesian coordinates with respect to system S_{I}

x', y', z': Cartesian coordinates with respect to system S'_{R}

D: Depth of the RB cell [m]

F_{w}: Flow resistance [N]

H: Height of the RB cell setup [m]

L: Length of the RB cell [m]

L_{1},...L_{6}: Lengths in the centrifuge system [m]

S_{I}: Inertial system

S'_{R}: Relative to S_{I} rotating system

S_{1}, S_{2}: Sensors in the centrifuge system

T: Temperature [K]

T_{mean}: Mean temperature between heated walls [K]

r: Radius of a tracer particle [m]

V: Volume of a fluid particle [m^{3}]

Greek Symbols

α: Angle [°]

β: Thermal expansions coefficient [1/K]

μ: Dynamic viscosity [kg/ms]

ν: Kinematic viscosity [m^{2}/s]

κ: Thermal diffusivity coefficient [m^{2}/s]

ρ: Density [kg/m^{3}]

ω: Angular velocity vector [rad/s]

ΔT: Temperature difference between heated walls [K]

Dimensionless numbers

Nu: Nusselt number

Ra: Rayleigh number

Pr: Prandtl number

Γ: Aspect ratio

St: Stokes number