Anwendung der geoelektrischen 3D-Tomographie für die Analyse thermisch induzierter Strömungen im Labor

Sowohl in der Natur als auch in der Industrie existieren thermisch induzierte Strömungen. Von Interesse für diese Forschungsarbeit sind dabei die Konvektionen im Erdmantel sowie in den Glasschmelzwannen. Der dort stattfindende Materialtransport resultiert aus Unterschieden in der Dichte, der Temperatur und der chemischen Konzentration innerhalb des konvektierenden Materials. Um das Verständnis für die ablaufenden Prozesse zu verbessern, werden von zahlreichen Forschergruppen numerische Modellierungen durchgeführt. Die Verifikation der dafür verwendeten Algorithmen erfolgt meist über die Analyse von Laborexperimenten. Im Vordergrund dieser Forschungsarbeit steht die Entwicklung einer Methode zur Bestimmung der dreidimensionalen Temperaturverteilung für die Untersuchung von thermisch induzierten Strömungen in einem Versuchsbecken. Eine direkte Temperaturmessung im Inneren des Versuchsmaterials bzw. der Glasschmelze beeinflusst allerdings das Strömungsverhalten. Deshalb wird die geodynamisch störungsfrei arbeitende Impedanztomographie verwendet. Die Grundlage dieser Methode bildet der erweiterte Arrhenius-Zusammenhang zwischen Temperatur und spezifischer elektrischer Leitfähigkeit. Während der Laborexperimente wird ein zähflüssiges Polyethylenglykol-Wasser-Gemisch in einem Becken von unten her erhitzt. Die auf diese Weise generierten Strömungen stellen unter Berücksichtigung der Skalierung ein Analogon sowohl zu dem Erdmantel als auch zu den Schmelzwannen dar. Über mehrere Elektroden, die an den Beckenwänden installiert sind, erfolgen die geoelektrischen Messungen. Nach der sich anschließenden dreidimensionalen Inversion der elektrischen Widerstände liegt das Modell mit der Verteilung der spezifischen elektrischen Leitfähigkeit im Inneren des Versuchsbeckens vor. Diese wird mittels der erweiterten Arrhenius-Formel in eine Temperaturverteilung umgerechnet. Zum Nachweis der Eignung dieser Methode für die nichtinvasive Bestimmung der dreidimensionalen Temperaturverteilung wurden mittels mehrerer Thermoelemente an den Beckenwänden zusätzlich direkte Temperaturmessungen durchgeführt und die Werte miteinander verglichen. Im Wesentlichen sind die Innentemperaturen gut rekonstruierbar, wobei die erreichte Messgenauigkeit von der räumlichen und zeitlichen Auflösung der Gleichstromgeoelektrik abhängt.

Many natural bodies such as the Earth’s mantle, as well as materials inside industrial installations like molten glass inside furnaces, exchange matter through convection resulting from differences in temperature, density and chemical concentration. In Earth Sciences the analysis of plumes and convection inside the Earth’s mantle is a classical area for numerical modelling. However, experimental methods in the laboratory help as analogue models to verify the validity of computer models. The inherent problem of such analogue experiments is the visualisation of the flows and the determination of the parameters of interest as for example temperature. In nature and in industrial installations it is difficult to measure the temperature inside the object of interest directly. Therefore, the goal of this research study was the development of a new method for temperature measurements that allows temperature data acquisition without influencing the flow pattern in the laboratory simulation of Earth’s convection. Contrary to the three-dimensional optical techniques used by some of the scientist, DC-geoelectrical 3-D tomography works without tracers inside fluids. This is the precondition for the determination of temperatures inside molten glass, that has to remain uncontaminated. The basis for the use of DC-geoelectrical 3-D tomography is the adjusted Arrhenius temperature dependence of the electrical conductivity. In order to verify the applicability of the method, thermally driven flows were generated in a viscous material. Therefor, dissolved polymer polyethylene glycol was heated in a tank with a base of 48 x 30 cm and a height of 30 cm. During each geoelectrical measurement, two electrodes supplied a current into the tank to generate an electrical field. The further 26 electrodes, placed on the sides of the tank, contemporaneously recorded the voltages between themselves and the reference electrode. Finally, the voltages were inverted using a 3-D inversion program. The model of the three-dimensional distribution of electrical conductivities obtained was converted into temperatures. In order to verify the validity of the method these temperatures were compared with the temperatures recorded by the 29 thermocouples on the sides of the tank. There were high positive correlations between the temperatures measured directly and the temperatures determined by geoelectrical 3-D tomography. This, as well as the low root mean square deviations normalised to the mean of the temperatures of the respective geoelectrical model demonstrates the success of the new method presented in this thesis. It should be noted that small-sized structures such as hot plumes with a diameter of 3 cm possess lower temperatures in the reconstructed models than in reality because of the relatively low spatial resolution. This means that geoelectrical 3-D tomography can be used for the measurement of the general distribution of temperature, but not for analysis of small structures. A goal for the glass industry is to control flows in furnaces, because the molten basic elements for glass production have to be ideally homogenised with low energy usage. For this purpose the determination of the three-dimensional distribution of temperature is a basic prerequisite. However, the high temperature of the glass itself makes it impractical to measure the properties of the flows in situ. Therefore, the glass industry is interested in this non-invasive method and first measurements were carried out in a smelting furnace. The glass temperatures determined by geoelectrical 3-D tomography strongly diverged from the temperatures of the thermocouples on the sides of the furnace. Although the removal of the highest proportion of the electrical disturbances improved the results of inversion, a substantial error still remained. Furthermore, the spatial resolution was relatively low. In order to increase the resolution more data and additional electrodes on the walls would be required, however the geoelectrical measurements would take significantly longer. In addition, there is a limit to the number of electrodes that can be installed. Due to the low spatial resolution and the remaining substantial errors, geoelectrical tomography is unsuitable for application at glass smelting furnaces with the present state of technology.