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Marko Draskic
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FluidsDraskic, M.Westerweel, J.Pecnik, R. display sharp, non-linear variations of thermodynamic properties when they are heated at a supercritical pressure. As such, near-pseudo-critical heat transfer is often characterized by large variations in density, leading to sharp near-wall accelerations or strong stratifications when buoyancy becomes dominant. We study the modulation of heat transfer and turbulence by non-negligible buoyancy in such property-variant flows, for the development of near-pseudo-critical heat exchangers for supercritical energy conversion systems. In particular, a liquid-like, horizontal base flow of carbon dioxide at 88.5 bar and 32.6 ∘C is considered, which is subjected to a vertical heat flux of up to 12.0 kW/m2 at Reynolds numbers of up to ReDh≤10.000. Here, optical- and surface temperature measurements are used concurrently to evaluate the flow. Integratced visualizations of the flow field show the onset of strong stratifications with limited heating rates in the near-pseudo-critical region. During unstable stratification, the channel flow is dominated by the upward motion of thermal plumes. When the stratification is stable, any vertical motion and turbulence present in an equivalent neutrally buoyant flow is suppressed. As a result, wall heat is removed more effectively in the unstably stratified configuration than in a forced convective flow, whereas the opposite is true for a stably stratified flow. The difference in the perceived heat transfer between the considered configurations increases as buoyancy becomes more dominant.
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FluidsDraskic, M.Westerweel, J.Pecnik, R. display sharp, non-linear variations of thermodynamic properties when they are heated at a supercritical pressure. As such, near-pseudo-critical heat transfer is often characterized by large variations in density, leading to sharp near-wall accelerations or strong stratifications when buoyancy becomes dominant. We study the modulation of heat transfer and turbulence by non-negligible buoyancy in such property-variant flows, for the development of near-pseudo-critical heat exchangers for supercritical energy conversion systems. In particular, a liquid-like, horizontal base flow of carbon dioxide at 88.5 bar and 32.6 ∘C is considered, which is subjected to a vertical heat flux of up to 12.0 kW/m2 at Reynolds numbers of up to ReDh≤10.000. Here, optical- and surface temperature measurements are used concurrently to evaluate the flow. Integratced visualizations of the flow field show the onset of strong stratifications with limited heating rates in the near-pseudo-critical region. During unstable stratification, the channel flow is dominated by the upward motion of thermal plumes. When the stratification is stable, any vertical motion and turbulence present in an equivalent neutrally buoyant flow is suppressed. As a result, wall heat is removed more effectively in the unstably stratified configuration than in a forced convective flow, whereas the opposite is true for a stably stratified flow. The difference in the perceived heat transfer between the considered configurations increases as buoyancy becomes more dominant.
Buoyancy-dominated flows of supercritical carbon dioxide
Mixed convection & natural circulation at supercritical pressures
A desire to transition away from fossil fuels to more sustainable alternatives has driven the development of energy conversion systems at pressures beyond the vapor-liquid critical point. Transcritical heat pumps, for instance, can decarbonize industrial processes that require heat beyond 100°C, such as drying processes in the food and chemical industry, when powered by renewable electricity. Additionally, supercritical power cycles enable the conversion of heat from previously unsuitable sustainable heat sources into electricity. Therewith, these power cycles can meet the rising demand for non-fossil power, partly driven by the electrification of heat.
However, these systems operate in a highly non-ideal thermodynamic region, where a fluid no longer undergoes a discrete phase transition from liquid to gas when it is heated. Instead, at supercritical pressures, fluids undergo a boiling-like process in which they remain in a continuous phase. During this pseudo-boiling process, fluids exhibit considerable non-linear variations of thermodynamic properties. These variations are most pronounced in the pseudo-critical region, where thermophysical gradients strongly influence flow behavior and heat transfer. The consequences of the variations are most pronounced in the heat exchangers of these energy conversion systems, which operate in the near-pseudo-critical region. In these heat exchangers, buoyancy effects are significantly more dominant than in similar heat exchangers operating with subcritical pressure fluids, leading to highly configuration-dependent heat transfer behavior. Currently, the understanding of these non-ideal effects remains limited, especially in an experimental context, hindering the design of efficient and safe equipment for supercritical energy conversion systems. To bridge this knowledge gap and support the successful implementation of supercritical pressure energy conversion systems, this dissertation investigates the influence of buoyancy on heat transfer in supercritical carbon dioxide (sCO2) flows, with a specific emphasis on thermal stratification in near-pseudo-critical heat exchangers.
To explore these phenomena, a novel experimental facility was developed, featuring a naturally circulated flow loop operating at supercritical pressures. The four-meter-tall structure exploits the substantial density gradients of sCO2 to induce a buoyancy force over its vertical legs, driving the flow. By integrating buoyancy-driven natural circulation as the flow-driving mechanism, the facility eliminates the need for mechanical pumps and ensures stable flow conditions for controlled experimentation. The current Natural Circulation Loop (NCL) provides a steady and stable circulation across a broad range of operating conditions. In this work, a steady-state flow rate equation for the natural circulation of supercritical pressure fluids is proposed and validated against experimental data, demonstrating close agreement between predictions and measured flow rates.
Under specific conditions, when the system’s mass flow rate is sufficiently reduced at a constant heating rate, the natural circulation loop becomes unstable. This instability manifests as system-wide oscillations in temperature and pressure, posing a thermal fatigue risk for high-pressure loops. These oscillations are identified as dynamically induced, driven by traveling density waves resulting from periodic deterioration in heat transfer within the NCL heaters. However, these oscillations occur only under a narrow set of conditions and can be mitigated by diffusing the density waves through the system. When appropriate mitigation measures are implemented, natural circulation loops can provide a reliable and stable passive circulation mechanism, making them well-suited for critical applications such as nuclear reactor cooling or for sensitive applications such as the current heat transfer experiments.
A test section integrated within the circulation loop enables optical investigations of flow behavior in a horizontal plate heat exchanger channel, providing insight into buoyancy-induced thermal stratification. The test section employs optical techniques that visualize refractive index variations to capture CO2 flow motion. These optical methods, used alongside heat transfer measurements, reveal highly transient flow phenomena within the heat exchanger channel for the first time in experiment. Shadowgraphy, in particular, proves effective in visualizing fluid motion in turbulent supercritical CO2 flows with imhomogeneous temperatures.
In the test section, a hydrodynamically developed flow is examined, with heating applied either from the top or bottom to impose a one-sided density gradient in the CO2. The results reveal strong stratifications in both heating configurations, occurring much earlier than expected compared to subcritical fluids.
In the two heat transfer configurations, buoyancy effects act in opposite ways. When CO2 is heated from the bottom, creating an unstable stratification, the channel flow is characterized by secondary motion away from the heated wall. Here, buoyancy enhances heat transfer, enhancing the effect of an increasing specific heat near the wall. As buoyancy effects intensify at higher heating rates, heat transfer progressively improves. Conversely, under stable stratification, when CO2 is heated from the top downward, the imposed density gradient suppresses turbulence-induced vertical motion, hindering heat removal from the heated wall. As a result, buoyancy opposes the heat transfer enhancement by variable specific heat. As buoyancy effects become more significant, the heat transfer deteriorates beyond an optimum. The heat transfer rates between the two configurations differ by up to an order of magnitude in the current experiments.
The current findings confirm that supercritical CO2 flows are highly susceptible to buoyancy effects and demonstrate how buoyancy can significantly alter heat transfer relative to a neutrally buoyant setting, often overshadowing other property variation effects. As such, this research contributes to the validation of numerical models and the resolution of previously divergent experimental heat transfer results, thereby aiding in the development of improved predictive models and optimized heat exchanger designs. By enhancing the reliability of supercritical energy conversion system designs, this work supports the broader goal of defossilizing industrial heating and power generation.
...
A desire to transition away from fossil fuels to more sustainable alternatives has driven the development of energy conversion systems at pressures beyond the vapor-liquid critical point. Transcritical heat pumps, for instance, can decarbonize industrial processes that require heat beyond 100°C, such as drying processes in the food and chemical industry, when powered by renewable electricity. Additionally, supercritical power cycles enable the conversion of heat from previously unsuitable sustainable heat sources into electricity. Therewith, these power cycles can meet the rising demand for non-fossil power, partly driven by the electrification of heat.
However, these systems operate in a highly non-ideal thermodynamic region, where a fluid no longer undergoes a discrete phase transition from liquid to gas when it is heated. Instead, at supercritical pressures, fluids undergo a boiling-like process in which they remain in a continuous phase. During this pseudo-boiling process, fluids exhibit considerable non-linear variations of thermodynamic properties. These variations are most pronounced in the pseudo-critical region, where thermophysical gradients strongly influence flow behavior and heat transfer. The consequences of the variations are most pronounced in the heat exchangers of these energy conversion systems, which operate in the near-pseudo-critical region. In these heat exchangers, buoyancy effects are significantly more dominant than in similar heat exchangers operating with subcritical pressure fluids, leading to highly configuration-dependent heat transfer behavior. Currently, the understanding of these non-ideal effects remains limited, especially in an experimental context, hindering the design of efficient and safe equipment for supercritical energy conversion systems. To bridge this knowledge gap and support the successful implementation of supercritical pressure energy conversion systems, this dissertation investigates the influence of buoyancy on heat transfer in supercritical carbon dioxide (sCO2) flows, with a specific emphasis on thermal stratification in near-pseudo-critical heat exchangers.
To explore these phenomena, a novel experimental facility was developed, featuring a naturally circulated flow loop operating at supercritical pressures. The four-meter-tall structure exploits the substantial density gradients of sCO2 to induce a buoyancy force over its vertical legs, driving the flow. By integrating buoyancy-driven natural circulation as the flow-driving mechanism, the facility eliminates the need for mechanical pumps and ensures stable flow conditions for controlled experimentation. The current Natural Circulation Loop (NCL) provides a steady and stable circulation across a broad range of operating conditions. In this work, a steady-state flow rate equation for the natural circulation of supercritical pressure fluids is proposed and validated against experimental data, demonstrating close agreement between predictions and measured flow rates.
Under specific conditions, when the system’s mass flow rate is sufficiently reduced at a constant heating rate, the natural circulation loop becomes unstable. This instability manifests as system-wide oscillations in temperature and pressure, posing a thermal fatigue risk for high-pressure loops. These oscillations are identified as dynamically induced, driven by traveling density waves resulting from periodic deterioration in heat transfer within the NCL heaters. However, these oscillations occur only under a narrow set of conditions and can be mitigated by diffusing the density waves through the system. When appropriate mitigation measures are implemented, natural circulation loops can provide a reliable and stable passive circulation mechanism, making them well-suited for critical applications such as nuclear reactor cooling or for sensitive applications such as the current heat transfer experiments.
A test section integrated within the circulation loop enables optical investigations of flow behavior in a horizontal plate heat exchanger channel, providing insight into buoyancy-induced thermal stratification. The test section employs optical techniques that visualize refractive index variations to capture CO2 flow motion. These optical methods, used alongside heat transfer measurements, reveal highly transient flow phenomena within the heat exchanger channel for the first time in experiment. Shadowgraphy, in particular, proves effective in visualizing fluid motion in turbulent supercritical CO2 flows with imhomogeneous temperatures.
In the test section, a hydrodynamically developed flow is examined, with heating applied either from the top or bottom to impose a one-sided density gradient in the CO2. The results reveal strong stratifications in both heating configurations, occurring much earlier than expected compared to subcritical fluids.
In the two heat transfer configurations, buoyancy effects act in opposite ways. When CO2 is heated from the bottom, creating an unstable stratification, the channel flow is characterized by secondary motion away from the heated wall. Here, buoyancy enhances heat transfer, enhancing the effect of an increasing specific heat near the wall. As buoyancy effects intensify at higher heating rates, heat transfer progressively improves. Conversely, under stable stratification, when CO2 is heated from the top downward, the imposed density gradient suppresses turbulence-induced vertical motion, hindering heat removal from the heated wall. As a result, buoyancy opposes the heat transfer enhancement by variable specific heat. As buoyancy effects become more significant, the heat transfer deteriorates beyond an optimum. The heat transfer rates between the two configurations differ by up to an order of magnitude in the current experiments.
The current findings confirm that supercritical CO2 flows are highly susceptible to buoyancy effects and demonstrate how buoyancy can significantly alter heat transfer relative to a neutrally buoyant setting, often overshadowing other property variation effects. As such, this research contributes to the validation of numerical models and the resolution of previously divergent experimental heat transfer results, thereby aiding in the development of improved predictive models and optimized heat exchanger designs. By enhancing the reliability of supercritical energy conversion system designs, this work supports the broader goal of defossilizing industrial heating and power generation.
Fluids at supercritical pressures exhibit large variations in density near the pseudo-critical line, such that buoyancy plays a crucial role in their fluid dynamics. Here, we experimentally investigate heat transfer and turbulence in horizontal hydrodynamically developed channel flows of carbon dioxide at 88.5 bar and 32.6∘C, heated at either the top or bottom surface to induce a strong vertical density gradient. In order to visualise the flow and evaluate its heat transfer, shadowgraphy is used concurrently with surface temperature measurements. With moderate heating, the flow is found to strongly stratify for both heating configurations, with bulk Richardson numbers Ri reaching up to 100. When the carbon dioxide is heated from the bottom upwards, the resulting unstably stratified flow is found to be dominated by the increasingly prevalent secondary motion of thermal plumes, enhancing vertical mixing and progressively improving heat transfer compared with a neutrally buoyant setting. Conversely, stable stratification, induced by heating from the top, suppresses the vertical motion, leading to deteriorated heat transfer that becomes invariant to the Reynolds number. The optical results provide novel insights into the complex dynamics of the directionally dependent heat transfer in the near-pseudo-critical region. These insights contribute to the reliable design of heat exchangers with highly property-variant fluids, which are critical for the decarbonisation of power and industrial heat. However, the results also highlight the need for further progress in the development of experimental techniques to generate reliable reference data for a broader range of non-ideal supercritical conditions.
...
Fluids at supercritical pressures exhibit large variations in density near the pseudo-critical line, such that buoyancy plays a crucial role in their fluid dynamics. Here, we experimentally investigate heat transfer and turbulence in horizontal hydrodynamically developed channel flows of carbon dioxide at 88.5 bar and 32.6∘C, heated at either the top or bottom surface to induce a strong vertical density gradient. In order to visualise the flow and evaluate its heat transfer, shadowgraphy is used concurrently with surface temperature measurements. With moderate heating, the flow is found to strongly stratify for both heating configurations, with bulk Richardson numbers Ri reaching up to 100. When the carbon dioxide is heated from the bottom upwards, the resulting unstably stratified flow is found to be dominated by the increasingly prevalent secondary motion of thermal plumes, enhancing vertical mixing and progressively improving heat transfer compared with a neutrally buoyant setting. Conversely, stable stratification, induced by heating from the top, suppresses the vertical motion, leading to deteriorated heat transfer that becomes invariant to the Reynolds number. The optical results provide novel insights into the complex dynamics of the directionally dependent heat transfer in the near-pseudo-critical region. These insights contribute to the reliable design of heat exchangers with highly property-variant fluids, which are critical for the decarbonisation of power and industrial heat. However, the results also highlight the need for further progress in the development of experimental techniques to generate reliable reference data for a broader range of non-ideal supercritical conditions.
Supercritical natural circulation loops (NCLs) promise passive cooling for critical systems like nuclear reactors and solar collectors, eliminating the need for mechanical pumps. However, instabilities similar to those seen in two-phase systems can emerge in supercritical NCLs, leading to undesirable oscillatory behaviour, marked by system-wide fluctuations in density, temperature, pressure, and flow rate. This study investigates the stability of NCLs at supercritical pressures (73.7≤p≤110.0bar) using CO2 in an experimental setup with vertical cooling and vertically adjustable heaters to control convective flow rates and to oppose flow reversal. Oscillations were found to originate in the heater of the NCL, and demonstrated a high sensitivity to the thermodynamic state and proximity to the pseudo-critical line of the system. Increased mass flow rates and added resistance upstream of the heater suppressed the oscillations, while increased pressures and reduced heating rates dampened them. A static model which takes into account the non-ideality of the heat exchangers is introduced to assess the presence of multiple steady states. The system is concluded to be statically stable, and the oscillations are considered to be dynamically induced. In particular, the modulation of the NCL velocity by the traversal of the current oscillations in density is assumed to periodically re-incite non-ideality in the heater. These findings intend to refine our understanding of the stability boundaries in NCLs, to ensure a safer operation of prospective passive cooling and circulation systems employing fluids at supercritical pressure.
...
Supercritical natural circulation loops (NCLs) promise passive cooling for critical systems like nuclear reactors and solar collectors, eliminating the need for mechanical pumps. However, instabilities similar to those seen in two-phase systems can emerge in supercritical NCLs, leading to undesirable oscillatory behaviour, marked by system-wide fluctuations in density, temperature, pressure, and flow rate. This study investigates the stability of NCLs at supercritical pressures (73.7≤p≤110.0bar) using CO2 in an experimental setup with vertical cooling and vertically adjustable heaters to control convective flow rates and to oppose flow reversal. Oscillations were found to originate in the heater of the NCL, and demonstrated a high sensitivity to the thermodynamic state and proximity to the pseudo-critical line of the system. Increased mass flow rates and added resistance upstream of the heater suppressed the oscillations, while increased pressures and reduced heating rates dampened them. A static model which takes into account the non-ideality of the heat exchangers is introduced to assess the presence of multiple steady states. The system is concluded to be statically stable, and the oscillations are considered to be dynamically induced. In particular, the modulation of the NCL velocity by the traversal of the current oscillations in density is assumed to periodically re-incite non-ideality in the heater. These findings intend to refine our understanding of the stability boundaries in NCLs, to ensure a safer operation of prospective passive cooling and circulation systems employing fluids at supercritical pressure.
The steady state behavior of thermodynamically supercritical natural circulation loops (NCLs) is investigated in this work. Experimental steady state results with supercritical carbon dioxide are presented for reduced pressures in the range of 1.1-1.5, and temperatures in the range of 20-65 ◦C. Distinct thermodynamic states are reached by traversing a set of isochors. A generalized equation for the prediction of the steady state is presented, and its performance is assessed using empirical data. Changes of mass flow rate as a result of changes of thermodynamic state, heating- and driving height are shown to be accurately captured by the proposed predictive equation. However, the enhanced viscous losses in the instrumentation of the loop and in the proximity of heat transfer equipment are shown to significantly limit the steady state flow rate. Subsequently, the findings are put forward in aid of the development of safe, novel supercritical natural circulation facilities.
...
The steady state behavior of thermodynamically supercritical natural circulation loops (NCLs) is investigated in this work. Experimental steady state results with supercritical carbon dioxide are presented for reduced pressures in the range of 1.1-1.5, and temperatures in the range of 20-65 ◦C. Distinct thermodynamic states are reached by traversing a set of isochors. A generalized equation for the prediction of the steady state is presented, and its performance is assessed using empirical data. Changes of mass flow rate as a result of changes of thermodynamic state, heating- and driving height are shown to be accurately captured by the proposed predictive equation. However, the enhanced viscous losses in the instrumentation of the loop and in the proximity of heat transfer equipment are shown to significantly limit the steady state flow rate. Subsequently, the findings are put forward in aid of the development of safe, novel supercritical natural circulation facilities.