Steady-state Heat Flux Research Articles

The Likely Thickness of Europa’s Icy Shell

Abstract The icy outer shell of Jupiter's moon Europa is believed to be geologically active, and geological processes within the ice may be key to sustaining chemical disequilibria and potentially habitable environments within the icy shell and ocean. Currently, there are insufficient observational data to determine the thickness of the icy shell, obfuscating crucial aspects of interior processes. Although a range of icy shell thicknesses (∼10−1–102 km) have been proposed, not all are equally likely given the current knowledge of Europa. In this study, I construct a probability density distribution for Europa's present-day mean icy shell thickness using a heat flux balance, assuming a simple two-layered model consisting of a partially porous conductive upper layer, and a ductile interior layer that may be experiencing solid-state convection. Current best estimate (CBE) values and uncertainties for ∼20 key parameters are propagated through this steady-state heat flux balance to construct ∼107 independent simulations. Additionally, I estimate present-day values for the icy shell layer thicknesses, the rocky interior and icy heat fluxes, icy shell thermal properties, and convective ice viscosity. I predict Europa’s total icy thickness to be ∼23–47 km, with a CBE thickness of 24.3 − 1.5 + 22.8 km . This result is highly skewed; icy shells many tens of kilometers thick are much more probable than icy shells <10 km thick. The resulting distributions have key implications for future spaceborne, landed, and subsurface exploration of Europa, as well as studies of icy shell processes, thermal and mechanical state, and habitability across the icy ocean worlds.

Prospects for Disruption Handling in a Tokamak-Based Fusion Reactor

Disruptions present a great challenge to achieving an economically viable commercial tokamak fusion reactor. Disruption handling, including prevention, mitigation, and resilient design, must be incorporated into future reactor designs at the same priority as core performance and steady-state heat flux removal. Prevention requires avoiding unstable regimes; actively stabilizing instabilities if they do appear; or, if those steps should fail, terminating the plasma-controlled rampdown. Mitigation is a last resort that utilizes massive impurity injection to reduce a damaging concentration of thermal and mechanical loads. Extremely robust disruption prevention will be of paramount importance to ensure high duty factor and capital return on the reactor investment, but the reactor environment poses significant technical challenges exceeding those in ITER. The long-term mission of a commercial reactor motivates investment in passive resilient design to survive disruptions in the absence of active intervention.

Analysis of Shroud and Disk Heat Transfer in Aero-Engine Compressor Rotors

Abstract Heat transfer within the rotating compressor cavity of an aero-engine is predominantly governed by buoyancy, which can be characterized by the Grashof number. Unsteady and unstable buoyancy-induced flow structures influence the temperatures and stresses in the compressor rotors, and these affect the radial growth of the disks. In addition, the heat transfer from the disks and shroud increases the temperature of the throughflow of cooling air. This paper contains two connected parts. First, a heat transfer correlation for the shroud of a rotating cavity was determined from steady-state heat flux measurements collected in the bath compressor-cavity rig at engine-simulated conditions. The Nusselt numbers were based on the cavity air temperature adjacent to the shroud, which was predicted using the Owen–Tang buoyancy model. Heat transfer from the shroud was consistent with free convection from a horizontal plate in a gravitational field. Maximum likelihood estimation was used with a Rayleigh–Bénard equation to correlate the shroud Nusselt number with the local Grashof number. Second, an energy balance was used to calculate the enthalpy rise of the axial throughflow from the measured disk and shroud heat fluxes. Disk fluxes were derived from radial distributions of measured steady-state disk temperatures using a Bayesian model and the equations for a circular fin. The calculated throughflow temperature rise was consistent with direct thermocouple measurements. The complex, three-dimensional flow near the cavity entrance can result in enthalpy exchange penetrating upstream in the throughflow, and rotationally induced flow can create upstream axial flow in the outer part of the annulus.

Predicted Heat Flux Performance of Actively Cooled Tungsten-Armored Graphitic Foam Monoblocks

Tungsten (W)–armored graphitic foam monoblocks were developed for applications requiring high-Z plasma-facing material in long-pulse fusion experiments and ultimately deuterium-tritium fusion reactors. The monoblocks are an integrated material system combining the advantages of a chemical vapor deposited (CVD) W coating with a high-conductivity graphitic foam. The W is a high-melting-point, high-Z material with low tritium retention. The graphitic foam coupled to a swirl tube serves as a high-thermal-conductivity heat sink that cannot melt, although it can sublime at much higher temperatures than copper melts. Together, they comprise a robust plasma-facing component (PFC) weighing roughly 5% of an all-W component or 17% of a traditional W-coated copper heat sink. A single-channel mock-up consisting of four graphitic foam monoblocks equipped with a water-cooled swirl tube was fabricated for eventual testing in the 60-kW, EB-60, rastered electron beam at the Applied Research Laboratory of The Pennsylvania State University. Two monoblocks have a thin 50-μm-thick coating of pure W chemically vapor deposited over NbC and pure Nb interlayers. Two others have a 2-mm-thick pure W coating CVD on graphitic monoblocks using the same interlayers. The mock-up will be cooled with available 10 m/s, 0.7 MPa water with a 22°C inlet temperature and subjected to varying uniform heat loads up to 20 MW/m2. It is equipped with type-K thermocouples at various depths, and calibrated infrared thermography and spot pyrometry will be used to characterize the heated surface. Real-time water calorimetry will be used to ascertain the absorbed steady-state power and infer the heat flux during testing. Since testing cannot be done under prototypic divertor flow conditions, it is necessary to predict the thermal response of this novel PFC system and investigate the power sharing between radiation and convection at divertor heat flux levels and its inherent ability to avoid critical heat flux. Results are reported for predictions obtained from computational fluid dynamics models up to 30 MW/m2 of steady-state uniform heat flux. Leading-edge heat loads of 30 MW/m2 on a 2-mm-wide side strip were also investigated to ascertain if coating delamination is likely.

Rapid Steady-State Hypersonic Aerothermodynamic Loads Prediction Using Reduced Fidelity Models

Balancing accurate and efficient estimation of aerothermodynamic loads is a significant challenge for multidisciplinary modeling and analysis of high-speed vehicles. This study focuses on this issue by studying the impact of analytical and data-driven model reductions over a broad operational space. Reduced models are compared with Reynolds-averaged Navier–Stokes predictions for steady-state aerodynamic pressure and heat flux on the surface of a complete hypersonic vehicle geometry over a broad operational space. Both accuracy and computational requirements are considered so as to provide guidance on tradeoffs when carrying out multidisciplinary simulation of high-speed vehicles.

Near-Field Radiant Heat Flux from Open-Air Gasoline and Diesel Pool Fires: Modified Point Source and Discretized Solid Flame Models

This paper proposes novel modifications to existing solid flame and point source models to better predict the spatial contour of near-field, steady-state radiant heat flux from large circular pool fires (with diameters ranging from 1 m to 20 m) with gasoline and diesel fuel. The proposed models account for partial smoke obscuration of the flames, and the emissive power of the visible flame layer is calculated via a radiative fraction of the fire’s heat release rate as a function of the pool size. The modified discretized solid flame model uses a cylinder + cone shape combination whose surfaces are discretized to enable a flexible summation of total radiative energy emission. The modified point source model places its radiating point at the mid-height of the visible flame layer to capture the location of maximum radiation intensity. Predictions from both proposed models are benchmarked against available data from pool fire experiments, calibrated against computational fluid dynamic simulations, and compared with existing analytical solutions for a range of pool fire diameters at varying standoffs and gauge heights. The results demonstrate that the proposed models can effectively predict the spatial contour and peak value of radiant heat flux on nearby targets (i.e., at distances less than 2.5 times the pool diameter) with low computational effort.

Impact of plasma-wall interaction and exhaust on the EU-DEMO design

Abstract In the present work, the role of plasma facing components protection in driving the EU-DEMO design will be reviewed, focusing on steady-state and, especially, on transients. This work encompasses both the first wall (FW) as well as the divertor. In fact, while the ITER divertor heat removal technology has been adopted, the ITER FW concept has been shown in the past years to be inadequate for EU-DEMO. This is due to the higher foreseen irradiation damage level, which requires structural materials (like Eurofer) able to withstand more than 5 dpa of neutron damage. This solution, however, limits the tolerable steady-state heat flux to ~1 MW/m2, i.e. a factor 3–4 below the ITER specifications. For this reason, poloidally and toroidally discontinuous protection limiters are implemented in EU-DEMO. Their role consists in reducing the heat load on the FW due to charged particles, during steady state and, more importantly, during planned and off-normal plasma transients. Concerning the divertor configuration, EU-DEMO currently assumes an ITER-like, lower single null (LSN) divertor, with seeded impurities for the dissipation of the power. However, this concept has been shown by numerous simulations in the past years to be marginal during steady-state (where a detached divertor is necessary to maintain the heat flux below the technological limit and to avoid excessive erosion) and unable to withstand some relevant transients, such as large ELMs and accidental loss of detachment. Various concepts, deviating from the ITER design, are currently under investigation to mitigate such risks, for example in-vessel coils for strike point sweeping in case of reattachment, as well as alternative divertor configurations. Finally, a broader discussion on the impact of divertor protection on the overall machine design is presented.

Non-Fourier heat transport across 1D nano film between thermal reservoirs with different boundary resistances

We describe the nonlocal heat transport across a thin film in contact with two thermal baths using discrete variable model. The effective thermal conductivities , the boundary temperature jumps, the steady-state heat flux, and the internal temperature gradient are calculated analytically as functions of the film size and the boundary resistances. As the system size decreases, all the parameters demonstrate the transition from diffusive (Fourier) heat conduction when the scattering occurs mainly inside the film to ballistic transport when scattering occurs at the boundaries, while inside the film there is no scattering and the temperature profile is flat. We show that when the boundary resistance increases, the temperature profile inside the film also tends to be flat, but in this case the scattering, though small, occurs inside the film. The predicted effective thermal conductivity is consistent with classical continuous theories and available experimental data. • We consider heat transport across 1D nano film. • Discrete variable model has been used. • Effective thermal conductivity is size and resistance dependent. • Transition to ballistic regime is described.

Minimizing the Effects of On-Chip Hotspots Using Multi-Objective Optimization of Flow Distribution in Water-Cooled Parallel Microchannel Heatsinks

Abstract The industry shift to multicore microprocessor architecture will likely cause higher temperature nonuniformity on chip surfaces, exacerbating the problem of chip reliability and lifespan. While advanced cooling technologies like two phase embedded cooling exist, the technological risks of such solutions make conventional cooling technologies more desirable. One such solution is remote cooling with heatsinks with sequential conduction resistance from chip to module. The objective of this work is to numerically demonstrate a novel concept to remotely cool chips with hotspots and maximize chip temperature uniformity using an optimized flow distribution under constrained geometric parameters for the heatsink. The optimally distributed flow conditions presented here are intended to maximize the heat transfer from a nonuniform chip power map by actively directing flow to a hotspot region. The hotspot-targeted parallel microchannel liquid cooling design is evaluated against a baseline uniform flow conventional liquid cooling design for the industry pressure drop limit of approximately 20 kPa. For an average steady-state heat flux of 145 W/cm2 on core areas (hotspots) and 18 W/cm2 on the remaining chip area (background), the chip temperature uniformity is improved by 10%. Moreover, the heatsink design has improved chip temperature uniformity without a need for any additional system level complexity, which also reduces reliability risks.

Numerical analysis of fatigue behaviors for tungsten armor of ITER divertor

Abstract Thermal responses and fatigue behaviors of the tungsten armor of monoblock divertor under steady-state and transient high heat flux (HHF) loads as well as the coupling of the two were simulated and analyzed by the finite element method. It was found that, under the action of thermal cycle loads, the earliest fatigue failure area of tungsten armor is on the surface, and with the increasing of HHF load, the damage area of the armor extends also, while the transient load only causes damage on surface of the armor. The fatigue lifetime of tungsten armor decreases rapidly with the increase of load, whether under steady-state load or transient load. Different transient load under the same steady-state load is researched. When two loads are coupled, the fatigue life is shorter as the load value is high, while the fatigue lifetime is basically unchanged when the transient load is the same under different steady-state loads, that is to say, the steady-state load has little influence on the results, and the transient load during ELMs is the leading factor for the fatigue lifetime.

Overview of power exhaust experiments in the COMPASS divertor with liquid metals

Abstract Power handling experiments with a special liquid metal divertor module based on the capillary porous system technology were performed in the tokamak COMPASS. The performance of two metals (Li and LiSn alloy) were tested for the first time in a divertor under ELMy H-mode conditions. No damage of the capillary mesh and a good exhaust capability were observed for both metals in two separate experiments with up to 12 MW/m2 of deposited perpendicular, inter-ELM steady-state heat flux and with ELMs of relative energy ~3% and a local peak energy fluence at the module ~15 kJ.m−2. No droplets were directly ejected from the mesh top surface and for the LiSn experiment, no contamination of the core and SOL plasmas by Sn was observed. The elemental depth profile analysis of 14 stainless-steel samples located around the vacuum vessel for each experiment provides information about the migration of evaporated/redeposited liquid elements.

Active Radiative Liquid Lithium Divertor for Handling Transient High Heat Flux Events

The extreme heat flux anticipated in fusion reactor divertor plasma facing components (PFCs) is perhaps the most challenging technology issue for fusion energy development. Most divertor PFCs are designed based on the maximum steady-state operational limits. Application of lithium (Li) in NSTX resulted in improved H-mode confinement, H-mode power threshold reduction, and reduction in the divertor peak heat flux while maintaining essentially Li-free core plasma operation even during H-modes. These promising Li results in NSTX and related modeling calculations motivated the passive and active radiative liquid lithium divertor concepts (RLLD and ARLLD) (Ono et al. in Nucl Fusion 53:113030, 2013; Fusion Eng Des 89:2838, 2014). This radiative process has the desired effect of spreading the localized divertor heat load to the rest of the divertor chamber wall surfaces, facilitating divertor heat removal with relatively small amount of lithium ~ few moles/s to handle the expected steady-state high divertor heat load. However, in addition to the high steady-state heat flux, the fusion reactor divertor PFCs could also experience significant transient heat flux such as ELMs and/or other magnetic reconnection events which can deposit large transient heat flux onto the divertor PFCs. If unprotected, it could damage the divertor PFC surfaces which could lead to a highly undesirable unplanned shutdown for PFC repair and/or replacement. In this paper, we explore feasibility of LLD and ARLLD concepts in handling such transient heat flux to protect the divertor PFCs from the extreme transient heat flux while maintaining the normal plasma operations. We also suggest a possible implementation technique using inductive pellet injector for the reactor PFC protection from transient heat flux which can be tested on NSTX-U.

Phonon heat transport in cavity-mediated optomechanical nanoresonators

The understanding of heat transport in nonequilibrium thermodynamics is an important research frontier, which is crucial for implementing novel thermodynamic devices, such as heat engines and refrigerators. The convection, conduction, and radiation are the well-known basic ways to transfer thermal energy. Here, we demonstrate a different mechanism of phonon heat transport between two spatially separated nanomechanical resonators coupled by the cavity-enhanced long-range interactions. The single trajectory for thermalization and non-equilibrium dynamics is monitored in real-time. In the strong coupling regime, the instant heat flux spontaneously oscillates back and forth in the nonequilibrium steady states. The universal bound on the precision of nonequilibrium steady-state heat flux, i.e. the thermodynamic uncertainty relation, is verified in such a temperature gradient driven far-off equilibrium system. Our results give more insight into the heat transfer with nanomechanical oscillators, and provide a playground for testing fundamental theories in non-equilibrium thermodynamics.

An ITER Challenge Absolute Surface Temperature Measurements of Low and Varying Emissivity Tungsten Plasma-Facing Components

One of the challenges that International Thermonuclear Experimental Reactor (ITER) will face during plasma operation is to determine the absolute divertor surface temperature of the actively water-cooled (70 °C, 3 MPa) tungsten plasma-facing units (PFUs) to ensure their integrity. The expected steady-state heat flux up to 10 MW/m2 is close to the operational limit and so one of the goals of the thermographic system is to make reliable measurements (wavelength band: 3.5– $4.5~\mu \text{m}$ ) with relatively low error bars to avoid tungsten melting and material damages. The tungsten emissivity is low and dependent on wavelength, temperature, and surface state (roughness, cracks, oxidation, and erosion/deposition processes) which can evolve during the time along with plasma operation. An error on the absolute emissivity can lead to large absolute temperature errors, and consequently to either a reduction of the operational window to fulfill safety limits, or an increased risk regarding the integrity of the components. For the past years, a number of emissivity measurements have been performed with ITER-like PFU mock-ups made of different grades of tungsten, with different techniques, from different material makers, and from different manufacturers. The overall emissivity discrepancy is large, indicating that tungsten emissivity is a major issue for temperature measurement and wall protection. The accuracy of the temperature measurement is investigated for both monocolor and bicolor IR thermography techniques. We present laboratory tests performed with an IR camera equipped with a rotating filter wheel for bicolor temperature measurement. It shows that the bicolor technique can reach high precision $\Delta \text {T}/\text {T} at high temperature assuming the emissivity ratio is constant regarding the two selected wavelengths.

Experimental study of detachment density threshold in L-mode plasmas on EAST

One of the critical challenges for long pulse operation of ITER and future fusion reactors is the excessively high heat and particle fluxes on the divertor targets. The divertor detachment offers an effective way for the control of steady state heat flux and erosion at the divertor target. Dedicated experiments have been systematically performed for both H-mode and L-mode plasmas on EAST with ITER-like W divertor in the last two years to further advance detachment physics understanding. The detachment is identified by the rollover of divertor peak particle flux near the strike point during the density ramping up, which correlates with the reduction of electron temperature down to 5 eV, the increase of Dδ/Dα ratio and radiated power. It has been demonstrated that the more closed divertor has a lower density threshold at the onset of detachment on EAST. Furthermore, the detachment density threshold will be reduced when the strike point moves towards the divertor corner. The onset of detachment exhibits a strong asymmetry between inner and outer targets, with the inner target accessing detachment at lower density due to the lower electron temperature, as expected. The effects of the heating power and plasma current on the detachment onset were also investigated. The experimental results show that the density at detachment onset is lower in L-mode relative to H-mode, and increases with the heating power. The detachment density threshold normalized to the Greenwald density limit is lower at a high plasma current.

Scaling of L-mode heat flux for ITER and COMPASS-U divertors, based on five tokamaks

This contribution aims to improve existing scalings of the L-mode power decay length , especially for plasma configurations with strike points at the ITER-relevant location—closed vertical divertor targets. We propose 13 new scalings based on data from the tokamaks JET, EAST, MAST, Alcator C-mod and COMPASS, and validate them against the output of the 2D turbulence code HESEL. The analysis covers 500 divertor heat flux profiles (obtained by probes or IR cameras), measured in L-mode discharges with varying 12 global plasma parameters (all well predictable). We find that the two previously published scalings (Eich 2013 J. Nucl. Mat. 438 S72) and (Scarabosio 2013 J. Nucl. Mat. 438 S426), which were based on outer target data from AUG and JET, describe the JET, C-mod and COMPASS profiles well. This holds not only at the outer horizontal and vertical targets, but surprisingly also at the inner vertical targets. In contrast, EAST, HESEL and especially MAST data are poorly described by these two scalings. We therefore derive 13 new scalings, which account for 85–92 % of the measured variability across all five tokamaks. Although each of the scalings is based on a different parameter combination, their predictions for the ITER and COMPASS-Upgrade tokamaks are very similar. Just before the L-H transition in the ITER baseline scenario, the presented scalings predict values mm. For the COMPASS-Upgrade tokamak, all the scalings predict mm with a single exception of the scaling based on the stored plasma energy which predicts only 1.2 mm for both tokamaks. We encourage the reader to use as many of these scalings as possible, depending on available data. In attached plasma and using significant assumptions, our results imply steady-state surface-perpendicular heat flux around 10 MW/m2 for ITER, and 20 MW/m2 for COMPASS-Upgrade.

Response of yttria dispersion strengthened tungsten simultaneously exposed to steady-state and transient hydrogen plasma

W–Y2O3 alloy with low DBTT (ductile-brittle transition temperature) and high RCT (recrystallization temperature), processed by high energy rate forging (HERF) was exposed to ITER-like steady-state and transient hydrogen plasma in the linear plasma generator Magnum-PSI. The steady-state heat fluxes were in the range of 8.35–16.32 MW·m−2, resulting in surface base temperatures of the samples in the range of 1271 °C to 1982 °C. The applied transient peak heat flux with a frequency of 5 Hz (a total of 1000 pulses) was about 0.50 GW·m−2. The exposure time was ~220 s. No obvious morphological change of the exposed sample with a base temperature of 1271 °C was observed, except the preferential erosion of the W/Y2O3 interface. However, cracks along grain boundaries were formed on the surface of the exposed samples with base temperatures above 1389 °C. Pronounced recrystallization and grain growth also occurred for the samples with base temperatures of 1666 °C and 1982 °C. It is desirable to find that no wide and deep crack with preferential propagation direction with regard to the sample dimension was observed, even extensive recrystallization and cracking along grain boundaries occurred. This indicates that decreasing DBTT and increasing RCT simultaneously is desirable to broaden the safe operational temperature window of W as plasma-facing material, and therefore to increase the power handling capability of the plasma-facing units of a tungsten-based divertor in future fusion reactors. However, the formation of W/Y2O3 composite, melting and depletion of the Y2O3 particles gradually occurred with increasing the surface temperatures. It implies that the doping of Y2O3 particles complicates the plasma-material interaction, compared to the pure W case. For example, it raises concerns about the formation of complex dust which will potentially be a significant issue for the safe operation of future fusion reactors (e.g. core plasma contamination and fuel recycling).

Thermal characterization of materials used in rural housing constructions in Ayacucho, Peru

The thermal conductivity of construction materials used in rural areas of Ayacucho has been measured. For this purpose, a thermal conductivity meter for material sample plates of a size of 12 cm x 12 cm has been designed and built, based on “ASTM C177 - Standard Test Method for Steady-State Heat Flux”. The effect of the thickness of the samples and of the heating power of the central plate on the measurement results was evaluated, resulting that best results were obtained with samples less than 2 cm thick and heating powers of less than 3 W. The thermal conductivities obtained vary between 0.148± 0.005 W.m-1.K-1 for “tornillo” wood, and 0.663 ± 0.010 W.m-1.K-1 for red clay from Quinua.

Thermal Performance Prediction for Air Flow in a Wavy Corrugated Duct at Steady-State Constant Heat Flux Mode and Early Stages of Turbulent Flow Conditions

Thermal Performance Prediction for Air Flow in a Wavy Corrugated Duct at Steady-State Constant Heat Flux Mode and Early Stages of Turbulent Flow Conditions

Steady-state and time-dependent heat fluxes through building envelope walls: A quantitative analysis to determine their relative significance all year round

The selection of the best type of building envelope wall for a given location and the calculation of the heat flux exchanged with the exterior environment are key issues in avoiding undesirable heat losses and gains, thus contributing to energy saving. The total heat flux transmitted by conduction through opaque envelopes, driven by daily and seasonal variations in the outdoor air temperature and solar irradiance, can be regarded as the sum of steady-state and time-dependent contributions. This paper presents a novel analytical method to calculate and compare both heat fluxes for a full year and the most significant south and north wall orientations, considering the materials used and the location of the construction. The purpose is to provide builders with objective information to optimise the choice of the building envelope materials during the design stage, taking advantage of both steady-state and dynamic features of the walls. The quantitative analysis is applied to three types of envelope walls of buildings located at an intermediate latitude in the southern hemisphere and low altitude above sea level, but it can be extended to any other type of building envelope and geographical site. The effects of solar irradiance on heat conduction are considered using the equivalent sol-air temperature. The results show how the relative significance of each heat flux depends on the type and orientation of the wall and, consequently, the early comparison between the steady-state and dynamic heat approximations ensures the most suitable building envelope for the specific construction purposes.