The terrestrial biosphere impacts considerably on the global carbon cycle. In particular, ecosystems contribute to set off anthropogenic induced fossil fuel emissions and hence decelerate the rise of the atmospheric CO₂ concentration. However, the future net sink strength of an ecosystem will heavily depend on the response of the individual processes to a changing climate. Understanding the makeup of these processes and their interaction with the environment is, therefore, of major importance to develop long-term climate mitigation strategies. Mathematical models are used to predict the fate of carbon in the soil-plant-atmosphere system under changing environmental conditions. However, the underlying processes giving rise to the net carbon balance of an ecosystem are complex and not entirely understood at the canopy level. Therefore, carbon exchange models are characterised by considerable uncertainty rendering the model-based prediction into the future prone to error. Observations of the carbon exchange at the canopy scale can help learning about the dominant processes and hence contribute to reduce the uncertainty associated with model-based predictions. For this reason, a global network of measurement sites has been established that provides long-term observations of the CO₂ exchange between a canopy and the atmosphere along with micrometeorological conditions. These time series, however, suffer from observation uncertainty that, if not characterised, limits their use in ecosystem studies. The general objective of this work is to develop a modelling methodology that synthesises physical process understanding with the information content in canopy scale data as an attempt to overcome the limitations in both carbon exchange models and observations. Similar hybrid modelling approaches have been successfully applied for signal extraction out of noisy time series in environmental engineering. Here, simple process descriptions are used to identify relationships between the carbon exchange and environmental drivers from noisy data. The functional form of these relationships are not prescribed a priori but rather determined directly from the data, ensuring the model complexity to be commensurate with the observations. Therefore, this data-led analysis results in the identification of the processes dominating carbon exchange at the ecosystem scale as reflected in the data. The description of these processes may then lead to robust carbon exchange models that contribute to a faithful prediction of the ecosystem carbon balance. This work presents a number of studies that make use of the developed data-led modelling approach for the analysis and interpretation of net canopy CO₂ flux observations. Given the limited knowledge about the underlying real system, the evaluation of the derived models with synthetic canopy exchange data is introduced as a standard procedure prior to any real data employment. The derived data-led models prove successful in several different applications. First, the data-based nature of the presented methods makes them particularly useful for replacing missing data in the observed time series. The resulting interpolated CO₂ flux observation series can then be analysed with dynamic modelling techniques, or integrated to coarser temporal resolution series for further use e.g., in model evaluation exercises. However, the noise component in these observations interferes with deterministic flux integration in particular when long time periods are considered. Therefore, a method to characterise the uncertainties in the flux observations that uses a semi-parametric stochastic model is introduced in a second study. As a result, an (uncertain) estimate of the annual net carbon exchange of the observed ecosystem can be inferred directly from a statistically consistent integration of the noisy data. For the forest measurement sites analysed, the relative uncertainty for the annual sum did not exceed 11 percent highlighting the value of the data. Based on the same models, a disaggregation of the net CO₂ flux into carbon assimilation and respiration is presented in a third study that allows for the estimation of annual ecosystem carbon uptake and release. These two components can then be further analysed for their separate response to environmental conditions. Finally, a fourth study demonstrates how the results from data-led analyses can be turned into a simple parametric model that is able to predict the carbon exchange of forest ecosystems. Given the global network of measurements available the derived model can now be tested for generality and transferability to other biomes. In summary, this work particularly highlights the potential of the presented data-led methodologies to identify and describe dominant carbon exchange processes at the canopy level contributing to a better understanding of ecosystem functioning. / Der Kohlenstoffhaushalt der Erde wird maßgeblich von der bewachsenen Landoberfläche beeinflusst. Insbesondere tragen terrestrische Ökosysteme dazu bei, den Anstieg der atmosphärischen Kohlenstoffdioxid- (CO₂-) Konzentration durch anthropogen verursachte Emissionen fossiler Brennstoffe zu verlangsamen. Die Intensität der Netto-CO₂-Aufnahme wird allerdings in einem sich verändernden Klima davon abhängen, wie einzelne Prozesse auf Änderungen der sie beeinflussenden Umweltfaktoren reagieren. Fundierte Kenntnisse dieser Prozesse und das Verständnis ihrer Wechselwirkungen mit der Umwelt sind daher für eine erfolgreiche Klimaschutzpolitik von besonderer Bedeutung. Mit Hilfe von mathematischen Modellen können Vorhersagen über den Verbleib des Kohlenstoffs im System Boden-Pflanze-Atmosphäre unter zukünftigen Umweltbedingungen getroffen werden. Die verantwortlichen Prozesse und ihre Wechselwirkungen mit der Umwelt sind jedoch kompliziert und bis heute auf der Ökosystemskala nicht vollkommen verstanden. Entwickelte Modelle und deren Vorhersagen sind deshalb derzeit mit erheblichen Unsicherheiten behaftet. Messungen von CO₂-Austauschflüssen zwischen einem Ökosystem und der Atmosphäre können dabei helfen, Vorgänge besser verstehen zu lernen und die Unsicherheiten in CO₂-Austausch-Modellen zu reduzieren. Allerdings sind auch diese Beobachtungen, wie alle Umweltmessungen, von Unsicherheiten durchsetzt. Ziel dieser Arbeit ist es Methoden zu entwickeln, die physikalisches Prozessverständnis mit dem dennoch großen Informationsgehalt dieser Daten vorteilhaft zu vereinigen. Dabei soll vereinfachtes Prozessverständnis dazu genutzt werden, Zusammenhänge zwischen dem CO₂-Austausch und den umgebenden Umweltbedingungen aus den Beobachtungen abzuleiten. Das Besondere hierbei ist, dass diese Zusammenhänge direkt aus den Daten geschätzt werden, ohne vorher Annahmen über ihre funktionale Form zu machen. Die Daten als Ausgangspunkt der Modellentwicklung zu wählen gewährleistet, dass die Komplexität der Modelle dem Informationsgehalt der Messungen entspricht. Auf diese Weise lassen sich diejenigen Prozesse identifizieren, welche für den CO₂-Austausch mit der Atmosphäre dominant sind. Die gewonnenen Erkenntnisse können dann in robuste CO₂-Austauschmodelle für Ökosysteme überführt werden und zur Vorhersage von Kohlenstoffbilanzen beitragen. In der vorliegenden Arbeit werden diese entwickelten, datenbasierten Methoden zur Analyse und Interpretation von Netto-CO₂-Flüssen eingesetzt. Die erste Studie führt ein datenbasiertes Modell ein, das unvermeidliche Lücken in Messzeitreihen zuverlässig interpoliert. Dies ermöglicht erweiterte Anwendungen der Daten. In einer nächsten Studie wird ein Verfahren vorgestellt, mit dem die Unsicherheiten in den Beobachtungen charakterisiert werden können. Dies ist nötig, um jährliche Kohlenstoffbilanzen von Ökosystemen unter Berücksichtigung der Messungenauigkeiten direkt aus den Daten herzuleiten. Dabei liegt die Unsicherheit in den betrachteten Waldstandorten bei maximal 11% des Jahreswertes. In einer weiteren Studie werden dieselben Modelle genutzt, um die Netto-CO₂-Flüsse in Einzelkomponenten der CO₂-Assimilation und -Abgabe zu bestimmen. Diese Komponenten sowie die Nettobilanz sind zusammen mit ihren Ungenauigkeiten für Vorhersagen über das Kohlenstoffsenkenpotential eines Ökosystems von besonderer Bedeutung und können Abschätzungen des globalen Kohlenstoffhaushaltes maßgeblich unterstützen. Abschließend zeigt die letzte Studie ein Beispiel für die datenbasierte Entwicklung eines Modells, das die dominanten Prozesse des Kohlenstoffaustausches in Waldökosystemen beschreibt und erfolgreich vorhersagen kann. Dies unterstreicht insbesondere das Potenzial des vorgestellten Modellierungsansatzes, vorherrschende Prozesse zu identifizieren, zu beschreiben und damit zum verbesserten Verständnis des CO₂-Austauschs zwischen Ökosystem und Atmosphäre beizutragen.

The thermal boundary condition to a fire exposed surface was quantified with a hybrid heat flux gage. Methods were developed to determine the net heat flux through the gage, incident heat flux, cold surface heat flux, convective heat transfer coefficient, adiabatic surface temperature, and the separated components of radiative and convective heat flux. Experiments were performed in a cone calorimeter with the hybrid gage flush mounted into UNIFRAX Duraboard LD ceramic board. The results were then compared to results obtained with a Schmidt-Boelter gage and a plate thermometer. The hybrid heat flux gage predicted a cold surface heat flux within 5% of cold surface heat fluxes measured with a Schmidt-Boelter gage. Adiabatic surface temperature measurements compared well with the plate thermometer measurements at steady state. Hybrid gage measurements were performed on flat plate samples of Aluminum 5083, Marinite P, and UNIFRAX Duraboard LD ceramic board. The gage and sample assemblies were exposed to mixed-mode heat transfer conditions in a cone calorimeter. Temperature measurements were performed at the top, center, bottom surfaces of the marinite and ceramic board samples. A single midpoint temperature was performed on the aluminum. Boundary condition details obtained with the hybrid gage were then input to the commercial finite element analysis package Abaqus. Abaqus was used to create the flat plate geometries of the sample and variable temperature dependent material properties were used for each material. Measured temperatures were then compared to the model predicted temperatures with good results. Hybrid gage measurements were verified using a new experimental apparatus. The apparatus consisted of an impinging jet assembly, a tungsten lamp, and a gage holster assembly. The impinging jet was used to expose the gage to isolated convection and the lamp was used to expose the gage to isolated radiation. The gage holster assembly was used to water cool the gage when desired. Measurements performed with the gage water cooled in isolated convection allowed for the convective heat transfer coefficient to be determined. Two methods were developed to determine the convective heat transfer coefficient in mixed-mode heat transfer conditions. These methods were then verified by comparison to the isolated heat transfer coefficient. Similarly, the incident radiation was isolated by water cooling the gage while only the lamp was on. The components of heat flux were then separated for mixed-mode comparisons and were verified against this isolated radiation. The hybrid gage predicted convective heat transfer coefficients within 10% of the isolated heat transfer coefficient and incident heat fluxes within 11% of the isolated radiation. / Master of Science

<p dir="ltr">Boiling processes have long had an important role in power generation and air conditioning applications. The efficient and reliable heat dissipation afforded through the phase change process in the boiling has led to their generation of a substantial body of work in this field over several decades. Despite decades of efforts, the heat transfer performance prediction in boiling has been highly empirical with models working only for a narrow range of surface/fluids or other operating conditions. The limitation in these models is a result of a lack of mechanistic understanding of the underlying heat and mass transfer process. Surface dryout or boiling crisis is a process wherein there is a spontaneous formation of vapor film on top of the surface causing a catastrophic increase in surface temperature. The heat flux at which this formation of vapor film occurs is called critical heat flux (CHF). The CHF demarcates the upper limit to the regime of stable nucleating bubbles called nucleate boiling. The mechanism causing dryout is under debate for over half a century and several conflicting theories that cause dryout have been suggested since the 1950s including hydrodynamic, irreversible dryspot expansion, macrolayer dryout/liftoff, critical bubble distributions, vapor-recoil based theories and more. The lack of consensus is due to limitation in the information collected on the dynamic multiscale and chaotic bubble interactions. Recent advances in high-fidelity spatiotemporal phase, temperature, and heat flux measurements now enable diagnostic tools that can be leveraged to understand the complex heat transfer processes emerging from bubble-surface interaction on the boiling surface. In this work, we develop such techniques to understand various transport mechanisms underlying boiling and its crisis.</p><p dir="ltr">In this work, an experimental technique for collecting synchronized through-substrate visual and infrared (IR) measurements of a boiling surface is developed. An IR and visually transparent sapphire substrate with an IR-opaque indium-tin-oxide (ITO) heater layer is used to measure the phase (liquid and vapor areas) and temperature of the ITO layer. The visual camera collects the light reflected off the substrate from a red LED and the images collected show a contrast between liquid and vapor areas that is used to generate binarized phase maps. The temperature from the IR camera is used as boundary condition to solve a conduction problem for heat fluxes going into the fluid. Four distinct heat flux signatures corresponding to liquid, contact line, vapor and rewetting regions are observed. A post-processing methodology utilizing synchronous phase measurements to identify and partition these regions is introduced. The high-fidelity phase measurements allow for detection of fine features that are not discernable using heat flux maps alone. Analysis of the heat flux and temperature maps of partitioned regions for HFE-7100 fluid on the ITO surface show qualitative agreement with the trends in mechanisms underlying those areas. The experiment and post-processing methodology introduced in this work is the first to provide partitioning of underlying heat transfer mechanisms for multi-bubbles throughout the entire range of the boiling curve during both steady and transient scenarios.</p><p dir="ltr">The technique developed is used to probe the mechanisms underlying the boiling crisis. Theories suggested in the literature for boiling crisis are carefully evaluated and evidence against hydrodynamic instability, macrolayer dryout, vapor recoil, irreversible expansion of dryspots, macrolayer liftoff model, and bifurcations from critical distributions is observed. The signature in the peak of the spatially averaged fluid heat flux is observed to precede any other signs of dryout. Beyond the peak heat flux an increase in superheat leads to reduced heat dissipated by boiling and further increases the temperature causing a thermal runaway in the substrate that eventually leads to dryout. Hence, the boiling crisis is found to be a consequence of a peak in the nucleate boiling curve. The cause for the peak in the boiling heat flux for the surface-fluid combination tested was due to degradation of heat transfer caused by the replacement of high-heat-transfer contact line region with lower-heat-transfer vapor covered regions, among the multiple competing mechanisms. Hence, we propose that mechanistically modeling the boiling crisis rests on prediction of the peak in the upper portion of the nucleate boiling curve by considering all underlying heat transfer mechanisms. A modeling framework based on heat flux partitioning, where the overall heat transferred during boiling is calculated as the sum of the heat transferred by individual mechanisms is demonstrated as potential pathway to predict the upper portion of the nucleate boiling curve and thereby critical heat flux. Based on the terms involved in summation for individual mechanisms, we propose that the boiling curve for any given surface be interpreted as a path on a multidimensional surface (boiling manifold). Estimation of such a boiling manifold allows for prediction of the boiling curve for any surface, given development of the relations between these parameters and surface-fluid properties, and can further be used to backtrack relevant thermophysical or nucleation properties for enhanced boiling performance.</p><p dir="ltr">Enhancement of pool boiling heat transfer performance using surface modifications is of major interest to applications and this work further delves into characterizing the boiling performance using traditional surface averaged measurements of microstructured surfaces using HFE-7100. We find that microlayer evaporation from the imbibed liquid layer underneath the growing vapor bubbles is the key mechanism of boiling heat transfer enhancement in microstructures. Further, this implies that characterization of microstructured surfaces for evaporative performance can serve as an important proxy to enable heat transfer coefficient enhancement prediction during pool boiling. Hence, we also developed an easily calculated Figure of Merit (FOM) that characterizes the efficacy of evaporation from microstructured surfaces.</p><p dir="ltr">To summarize, in this work we developed an experimental technique using synchronous through-substrate high-speed visual and IR imaging methods. New post-processing techniques for partitioning of different heat transfer mechanisms are proposed and used to analyze boiling on an ITO-coated sapphire substrate with HFE-7100 as the working fluid. We reveal thermal runaway in the substrate caused due to a negative-sloping boiling curve as the mechanism of dryout. Mechanistic modeling of the critical heat flux thus involves calculating the peak in the nucleate boiling curve. A framework to predict the nucleate boiling curve and subsequently critical heat flux is proposed based on the partitioning analysis. The experimental method developed lays the groundwork for measuring heat flux and superheats associated with various mechanisms, and hence, enables validation of future partitioning-based boiling heat transfer models that intrinsically enable prediction of the peak.</p>

<p>To improve the prediction of two-phase local structure and heat transfer in subcooled boiling flow, the wall nucleation phenomenon was studied to accurately model the wall source term in the interfacial area transport equation (IATE) for the use with the two-fluid model. The existing experimental datasets and modeling works of departure diameter, departure frequency and active nucleation site density were comprehensively reviewed. Since these parameters are coupled in the bubble ebullition cycles, simultaneous measurements of departure diameter, departure frequency and active nucleation site density were performed in a vertical annular test section. The ranges of the existing experimental database were extended to high pressure and high heat flux conditions. The stochastic characteristics of the departure diameter and departure frequency measured from a single nucleation site and over multiple nucleation sites were investigated. Significant variations between different nucleation sites were observed. A parametric study of departure diameter, departure frequency and nucleation site density were conducted at varying system pressure, heat flux, flow rate and subcooling conditions. The existing models of these parameters were evaluated with the experimental dataset of the existing and the present works. Significant discrepancies were observed between model predictions and experimental data, which indicates that the mechanism of nucleate boiling is not fully understood. The heat flux partitioning model was also evaluated. The results show that the heat flux at high pressure or low flow rate conditions was significantly underestimated. This may suggest that major heat transfer mechanisms are missing in the heat flux partitioning model.</p>