Matthias Kaczorowski

Analysis of the large-scale circulation and the boundary layers in turbulent Rayleigh-Bénard convection

Rayleigh-Benard convection (RBC) is a phenomenon occurring in fluids heated and cooled by a wall from below and above, respectively. The vertical heat transfer through the fluid is primarily defined by the Rayleigh number Open image in new window , the Prandtl number Open image in new window and the aspect ratio Γ=W/H of the convection cell, where the fluid is characterized through the thermal expansion coefficient α, the kinematic viscosity ν and the thermal diffusivity κ. The geometry is characterized by the height H and the width W of the cell and the temperature difference between the horizontal plates is ΔT.

Study on the Resolution Requirements for DNS in Turbulent Rayleigh-Bénard Convection

In fundamentel research the geometrically simple Rayleigh-Benard experiment is often chosen to investigate the turbulent heat exchange between a thermally driven fluid and a hot bottom and a cold top wall, respectively.

Influence of the Lateral Walls on the Thermal Plumes in Turbulent Rayleigh–Bénard Convection in Rectangular Containers

Turbulent Rayleigh–Benard (RB) convection is one of the classical problems in fluid mechanics, where fluid with a Prandtl number Pr = ν/k is exposed to a vertical temperature gradient between a hot lower and a cold upper surface. The Rayleigh number Ra = αgH 3 ΔT/(νk) is a non-dimensional parameter to specify the ratio between the buoyancy and viscous forces, where α, ν and k denote the thermal expansion coefficient, kinematic viscosity and thermal diffusivity, respectively. ΔT is the vertical temperature gradient between the two bounding surfaces, H the height of the fluid layer and g the gravitational acceleration. For high enough Ra the thermal plumes that are rising and falling from the respective hot and cold surfaces become increasingly irregular.

Direct Numerical Simulations of Turbulent Mixed Convection in Enclosures with Heated Obstacles

To simulate turbulent forced and mixed convection flows in complicated three-dimensional domains, a fast finite-volume high-order method based on the Chorin ansatz is developed. The Poisson solver, which is applied to compute the pressure, uses the separation of variables together with capacitance matrix technique as suggested in [Shishkina, Shishkin & Wagner, J. Comput. & Appl. Maths 2009 226, 336–344]. The developed numerical method generally allows to use hexahedral computational meshes, which are non-equidistant in all three directions and non-regular in any two directions. By means of Direct Numerical Simulations (DNS) we investigate instantaneous and statistical characteristics of turbulent forced and mixed convection flows which develop in parallelepiped convective cells with heated parallelepiped obstacles inside. Cold fluid comes into the cell through thin slits close to the top. The outlet slits are located close to the bottom. The working fluid is air with Prandtl number ℘r=0.714. The considered Grashof number \(\mathcal{G}r=4.22\times10^{8}\) and Reynolds number based on the velocity of the inlet flow ℛe=2.37×104 and 1.18×104. It is shown that in the cases of forced and mixed convection principally different large-scale circulations of air are developed inside the domain, although the same geometry and the same Reynolds numbers are considered. In particular, for ℛe=2.37×104 a downward flow is developed in the case of forced convection, while mixed convection leads to an upward flow in the central part of the domain. Distribution of the mean heat fluxes at the surfaces of the obstacles is shown to be very irregular and strongly dependent on the positions of the surfaces (vertical or horizontal) as well as on their locations inside the domain.

Wall Effects in Turbulent Rayleigh-Bénard Convection in a Long Rectangular Cell

Direct numerical simulations of turbulent Rayleigh-B´enard convection have been carried out in a rectangular geometry with two different configurations employing either solid walls or periodic boundaries in longitudinal direction. The results show that the infinitely long rectangular cell delays the onset of convection, and hence the transition to a three-dimensional flow field. The analysis of energy spectra at various wall distances indicates that thermal energy held by small scale fluctuation in the vicinity of the wall is transferred into the large scales of the velocity field as wall distance increases.