# Experimentelle Erfassung und Charakterisierung der dreidimensionalen großskaligen Strömungsstrukturen und -temperaturen in Rayleigh-Bénard-Konvektion

Experimental Aquisition and Characterization of the Three-Dimensional Large-Scale Flow Structures and Temperatures in Rayleigh-Bénard Convection

by Daniel Schiepel

Date of Examination:2017-09-26

Date of issue:2017-10-26

Advisor:Prof. Dr. Dr. Andreas Dillmann

Referee:Prof. Dr. Dr. Andreas Dillmann

Referee:Prof. Dr. Andreas Tilgner

## Files in this item

Name:Thesis-Schiepel-Final-WebView.pdf

Size:26.0Mb

Format:PDF

## Abstract

### English

In this work the flow structures in Rayleigh-Benard-Convection (RBC) are experimentally studied. For this purpose, two cuboidal convection samples are designed and installed. Using water as working fluid, these two experiments cover a large Rayleigh number range of 1.0 * 10^6 < Ra < 5.0 * 10^10. The ``large'' convection experiment is cubic and has an edge length of 500 mm. The ``small'' sample has a length and height of 100 mm, while the depth is 25 mm. The samples consist of a cooled top and a heated ground plate of constant temperature. The side walls are made of flint glass to provide optical access to the interior of the experiments. Thus, it is possible to apply different optical measurement techniques for the acquisition of the three-dimensional flow structures. The first main result is achieved using three-dimensional Particle Tracking Velocimetry (3D-PTV) in the small sample filled with water at a Prandtl number of Pr = 6.9 . The developing flow structures are studied in dependence of the Rayleigh number. Starting in the laminar range, a stable large-scale circulation (LSC) is found, which - with increasing temperature difference - transforms into a turbulent state with dominant two-cell structure at Ra = 2.8 * 10^7. From Ra = 8.5 * 10^7, a state with a dominant four-cell structure is reported, which develops into a one-cell structure in the highly turbulent region from Ra = 2.8 * 10^8. The second main result is found in the large sample in the highly turbulent regime. Using Tomo-PIV, the time-dependent large-scale circulation in water at Ra =1.0 * 10^10 and Pr =6.9 is measured. For this purpose, instantaneous 3D-velocity fields are determined in the entire 125 l convection sample. By temporal averaging of 1000 images, i.e 1.5 turn-arounds of the LSC, a large-scale circulation is observed, mainly oriented along a diagonal of the sample and spanning the whole diagonal plane. The shape of the LSC as well as the Reynolds number of Re = 6275 based on the velocity magnitude are computed. Both agree well with extrapolated results from other studies in the literature for similar configurations. The viscous boundary layer thickness, delta_u, in the vicinity of the heating and cooling plate is measured. An average value of 5.2 mm is determined for both plates. Both results reaffirm the scaling laws from literature for Re(Ra) and delta_u(Ra). The third main result deals with the simultaneous non-invasive measurement of the three-dimensional temperature and velocity fields in turbulent RBC. This result is of great importance for the investigations of thermal convection since the fields are dynamically coupled. For this purpose, a new measurement technique ist developed based on the combination of Tomo-PIV and PIT. The application of this new technique to turbulent RBC in the large sample filled with a water-glycol mixture at Ra = 7.0 * 10 ^9 and Pr = 21 allows for the simultaneous measurement of the velocity and temperature fields in a 20 l subvolume of the experiment, while the velocity information is obtained for the entire 62.5 l sample volume. In this respect, thermochromic liquid crystal particles serve as seeding particles for the velocity measurement and at the same time as ``floating thermometers'' for the temperature measurement. The warm upstream of the fluid from the heating plate is resolved in accordance with the velocity fields. This can be seen in the instantaneous temperature and velocity fields, reflecting the dependence of increased temperature and upflow velocity, as well as in the time-averaged field. The indicated behavior is studied in more detail by determining the correlation of vertical fluid velocity on the temperature. There is a positive linear dependence of the two variables. This is physically consistent with the density differences resulting from temperature increases and, consequently, the buoyancy which drives the flow. The fourth main result addresses the quantitative description of the flow structures over a large Ra range by combining all measured flow fields. For this purpose, the method of 2D-mode decomposition is used. Thereby, the development of the global flow structures in the transition area from the stationary to the highly turbulent convection can be described. It is shown that the large-scale circulation in the X-Y plane, starting from the laminar region, is increasingly breaking up in the non-stationary region and reforms again in the turbulent regime. In this plane, the composition of four fundamentally different flow states is found. Furthermore, in the orthogonal Y-Z plane, accessible through volumetric measurements, only two characteristic flow states exist. Thus, the dynamics of the fluid flow in the two planes are not directly coupled.**Keywords:**Rayleigh-Benard-Convection; RBC; PTV; Tomo-PIV