Surface Heat Flux Measurements Research Articles

Measurement of divertor surface heat flux by infra-red thermographic inversion in ST40.

Diagnostic tools for understanding the edge plasma behavior in fusion devices are essential. The main focus of the present work is to present the infra-red (IR) diagnostics installed on Tokamak Energy's spherical tokamak (ST40) and the IR thermographic inversion tool, Functional Analysis of Heat Flux (FAHF). FAHF is designed for multi-2D thermographic inversions within the divertor tiles using the finite difference method and an explicit time stepping scheme. ST40's re-entrant endoscope allows the acquisition of IR data with the highest available effective spatial resolution. With these data, FAHF calculates the plasma perpendicular heat flux density on the divertor-a crucial quantity for edge plasma analysis. Although FAHF demonstrates significant sensitivity to user-selected settings, precise heat flux values are recoverable by ensuring a sufficiently high resolution. Implications for the optimal resolution of both the code and the IR diagnostic system are discussed. FAHF's simplifications are shown to give an error within 10% with respect to COMSOL Multiphysics® simulations. Finally, by means of comparison with Langmuir probe heat flux data, the accuracy of the FAHF heat fluxes is estimated to be satisfactory. As such, FAHF is proven to be a precise and accurate tool for IR thermographic inversions in ST40.

Investigation of Coaxial Surface Junction Thermocouples Under Different Materials on Thermal Measurement

Coaxial surface junction thermocouples (CSJTs) are commonly applied to transient thermal measurements. Based on the measurement principle of CSJT, one-dimensional analytical inversion is applied for obtaining surface heat fluxes. However, with the thermophysical properties difference between the wall material and CSJT, transverse thermal conduction occurs that leads to a measurement error of surface temperature by CSJT. Hence, conventional temperature data processing methods can lead to surface heat flux measurement error. Therefore, quantitative analysis of lateral structural heat transfer should be carried out in the junction region and the interface between the sensor and the wall. In this paper, the multidimensional transmission of heat between three types of CSJTs and wall material under transient and long duration was investigated by numerical simulations. And the derivation of the axisymmetric heat transfer government equation was obtained by the improved Crank–Nicolson discrete scheme. We found the best wall materials for thermal matching with E-, J-, and K-type CSJTs, respectively. And the stainless steel tube can maintain a stable heat flux curve within a certain period. The conclusions of this study offer practical guidance for the selection of wall material and design improvement of CSJTs.

Optimization of geometric configurations for enhanced thermal performance in microchannel finned plates

This study investigates the thermal performance of microchannel finned plates by comparing various geometric configurations and operating conditions. Twelve models (a to l) were evaluated by varying parameters such as fin height, fin spacing, and channel width, as well as operating factors like inlet velocity and heat flux. The results reveal that increasing the fin height and decreasing the fin spacing enhance heat transfer by expanding the surface area, though at the cost of increased pressure drops and higher pumping power requirements. Variations in channel width impact flow characteristics, with wider channels reducing temperature but potentially lowering convective efficiency. Higher inlet velocities improve convective cooling but increase pressure drops, while elevated heat fluxes lead to steeper temperature gradients. Model k was found to provide an optimal balance between heat transfer efficiency and pressure drop, while Model l’s novel fin geometry showed unique temperature distributions warranting further exploration. Temperature contours and volume renders demonstrated air temperature increases across the models, ranging from 4.78 K to 17.36 K, and surface heat flux measurements confirmed the significant influence of fin configuration on thermal performance. The findings offer valuable insights for optimizing the design of microchannel finned plates for enhanced heat transfer and effective thermal management in various applications.

Genetic Algorithm as the Solution of Non-Linear Inverse Heat Conduction Problems: A Novel Sequential Approach

Abstract Direct measurement of surface heat flux could be extremely challenging, if not impossible, in numerous applications. In such cases, the use of temperature measurement data from subsurface locations can facilitate the determination of surface heat flux and temperature through the solution of the inverse heat conduction problem (IHCP). Several different techniques have been developed over the years for solving IHCPs, with different levels of complexity and accuracy. The filter coefficient technique has proved to be a promising approach for solving IHCPs. Inspired by the filter coefficient approach, a novel method is presented in this paper for solving one-dimensional IHCPs in a domain with temperature-dependent material properties. A test case is developed in COMSOL Multiphysics where the front side of a slab is subject to known transient heat flux and the temperature distributions within the domain are calculated through numerical simulation. The IHCP solution in the form of filter coefficients is defined and a genetic algorithm (GA) is used for the calculation of filter matrix. The number of significant filter coefficients required to evaluate surface heat flux at each time-step is determined through trial and error and the optimal number is selected for evaluating the solution. The structure of the filter matrix is assessed and discussed. The resulting filter coefficients are then used to evaluate the surface heat flux for several different test cases and the performance of the proposed approach is assessed in detail. The results showed that the presented approach is robust and can result in finding optimal filter coefficients that can accurately estimate various types of surface heat flux profiles using temperature data from a limited number of time steps and in a near real-time fashion.

Spherical geometry convection in a fluid with an Arrhenius thermal viscosity dependence: The impact of core size and surface temperature on the scaling of stagnant-lid thickness and internal temperature

The rock and rock-ice mixtures of the core-enveloping spherical shells comprising terrestrial body interiors have thermally determined viscosities well described by an Arrhenius dependence. Accordingly, the implied viscosity contrasts determined from the activation energies (E) characterizing such bodies can reach values exceeding 1040, for a temperature range that spans the conditions found from the lower mantle to the surface. In this study, we first explore the impact of implementing a cut-off to limit viscosity magnitude in cold regions. Using a spherical annulus geometry, we investigate the influence of core radius, surface temperature, and convective vigour on stagnant lid formation resulting from the extreme thermally induced viscosity contrasts. We demonstrate that the cut-off viscosity must be increased with decreasing curvature factor, f (=rin/rout, where rin and rout are the inner and outer radii of the annulus, respectively), if the solutions are to be not only computationally manageable but physically valid. We find that for statistically-steady systems, the mean temperature decreases with core size, and that a viscosity contrast of at least 107 is required for stagnant lid formation as f decreases below 0.5. Inverting the results from over 80 calculations featuring stagnant lids (from a total of approximately 180 calculations), we apply an energy balance model for heat flow across the thermal boundary layers and find that the non-dimensionalized temperature in the Approximately Isothermal Layer (AIL) in the convecting region under a stagnant lid is well predicted by TAIL′=12−2Tout′+γ+γ2+4γ1+Tout′ where γ is a function of E and f, and Tout′ is the non-dimensionalized surface temperature. Moreover, the normalized (i.e., non-dimensional) thickness of the stagnant lid, L′, can be obtained from a measurement of the non-dimensional surface heat flux once TAIL′ is determined. Stagnant-lid thicknesses increase from 10 to 30% of the shell thickness as f is decreased, and thick lids can overlie vigorously convecting underlying layers in small core bodies, potentially delaying secular cooling and suggesting that small objects with small cores may have developed thick elastic outer shells early in the solar system's history while maintaining vigorously convecting interiors. However, we also find that for the small number of 3-D calculations that we examined, parametrizations based on 2-D calculations overestimate the temperature of the convecting layer and the thickness of the conductive lid when f is small (less than 0.4).

Numerical and experimental estimation of building wall heat flux in presence of moisture transfer

Insulating building envelope is an efficient way to increase building energy efficiency and minimize greenhouse gas emissions related to heating. After building refurbishment, on-site measurements are suitable for verifying the actual thermal transmission properties of plane building components. For instance, the standard ISO 9869-1 describes a HFM method based on the measurement of surface heat flux with heat flow sensor (HFS). This method has been extensively investigated in the literature and successfully applied on vapor tight building walls. Nevertheless, hygroscopic building insulation materials (like biobased materials) are increasingly used, and heat transfer are coupled to moisture transfer within the wall. In this case, the HFS acts as a vapor barrier: it modifies the local moisture transfer and the associated latent heat flux. In this view, this study aims to clarify what it is measured with HFS in presence of moisture transfer. The question is first treated by numerical simulation of heat and moisture transfer within hygroscopic building wall. Then, experiments are carried out on hygroscopic building insulation where the moisture effects are exaggerated.

Characterizing Northeast Africa Drought and Its Drivers

This study explores the drivers of drought over northeast (NE) Africa as represented by monthly ERA5 potential evaporation during 1970–2022. The comparisons with surface heat flux and A-pan measurements suggest that potential evaporation quantifies moisture deficits that lead to drought. A principal component (PC) analysis of potential evaporation has the following leading modes: PC-1 in the Nile Basin and PC-2 in the Rift Valley. Time scores were filtered and regressed onto fields of SST, netOLR, and 500 hPa zonal wind to find teleconnections, and drought composites were analyzed for anomalous structure. The results identify that cold-phase Indian Ocean Dipole (IOD) couples with the overlying zonal Walker circulation. Deep easterly winds subside at −0.1 m/s over the west Indian Ocean and NE Africa, causing desiccation that spreads westward from the Rift Valley via diurnal heat fluxes. Insights are gained on IOD modulation based on the Pacific ENSO, but long-range forecasts remain elusive.

Assessment of thermal environment and thermal comfort in a typical composite ice shell building

Composite ice shell buildings are a special type of architecture found in severe cold regions and have played an important role in ice and snow tourism in recent years owing to their ability to offer tourists a romantic and novel experience. We conducted a field study to examine the thermal environment of a typical composite ice shell building in Harbin, China. In the unheated hall and separate small room, the indoor air had an average temperature and relative humidity of −20.64 °C and 76.94%, and −17.71 °C and 79.57%, respectively. Surface heat flux measurement of the north-facing building envelope revealed that the thermal properties of composite and plain ice differed significantly, suggesting that composite ice may have a lower thermal conductivity. The natural ventilation rate of 48,041 m3/h corresponded to an air change rate of 6.86 h−1, making the thermal environment highly susceptible to outdoor meteorological conditions. In addition, we conducted a questionnaire survey to study the thermal sensation and thermal comfort of the tourists. The results showed that the mean thermal sensation for the foot and head were approximately “cold " and “slightly cool”, respectively. The overall and mean thermal sensation for the hand were both between “cool” and “cold”, and the mean thermal comfort was approximately “slightly uncomfortable”. An adaptive thermal sensation prediction model suitable for composite ice shell buildings was developed through the study. These findings can assist in the design and construction of thermal environments that are better suited for short-term stays and specialty tourism.

Surface heat transfer coefficients in building envelopes: Uncertainty levels in experimental methods

There are several research methods for the on-site assessment of U-values that aim to avoid the use of surface heat flux measurements and rely on tabulated or empirically developed correlations to define this parameter. This works performs a detailed process to estimate indoor surface heat transfer coefficients based on several experimental campaigns over building walls. Data is filtered out to remove periods with large temperature variations and/or unstable convective conditions due to HVAC. A statistical analysis is conducted, and the outcomes used to test the validity of U-value estimation approaches. The outcomes show that the actual surface heat transfer coefficients are in the range of reference works, but variations in the range of up to 2 W/m2 K are found. Uncertainty levels associated to the estimation of surface heat transfer coefficient are in the range 60% for instantaneous values while this is reduced down to 12%–20% for 8-h averages. Variations and uncertainty levels are higher for low temperature gradient situations, which are considered to be very likely for modern insulation levels. It is concluded that methods seeking to avoid the use of surface heat flux measurements need to develop much deeper knowledge in this field to gain accuracy and reliability.

Peak heat flux prediction of hypersonic flow over compression ramp under vibrationally excited free-stream condition

In hypersonic shock tunnel experiments, the high-temperature reservoir gas expands and accelerates so rapidly that there is not enough time for vibrational energy relaxation. As a result, thermal nonequilibrium gas flow is frequently encountered in the test section, and this significantly affects the measured heat flux. In this paper, hypersonic compression-ramp flows are studied numerically to investigate the effect of incomplete vibrational energy accommodation on the separation flow structure and peak heat flux in the reattachment region under low-to-medium Reynolds number and high Mach number conditions. Numerical results and theoretical analysis suggest that the vibrational energy accommodation has no noticeable impact on the length scale of the separation zone, but strongly influences the peak heat flux of the separated ramp flows. Decomposing the peak heat flux into translational–rotational energy and vibrational energy components, qtr and qv, respectively, we find that qv/qtr characterizes the nonequilibrium degree of the vibrational energy accommodation. A formula for predicting the peak heat flux is then proposed, taking the effect of incomplete vibrational energy accommodation into consideration. Finally, surface heat flux measurements in a hypersonic shock tunnel indicate that a deviation of up to 13% in total peak heat flux could arise if vibrational energy accommodation is not considered under the vibrationally excited free-stream condition.

A Method to Identify the Heat Flux From Photons and Neutrals at the Divertor Target

The surface eroding thermocouple (SETC) is a diagnostic designed for fast surface heat flux measurement and has been successfully applied in DIII-D tokamak to investigate divertor detachment. A novel method has been developed of using a combination of surface-facing and recessed SETCs to distinguish between the heat flux from charged particles, and that from neutrals and radiative heating. This technique suggests that at least 20% of the total incident heat flux is attributable to the latter sources not trapped in the magnetic field in a fully detached open divertor condition. It not only indicates the noncharged particle heating significantly contributes to the total surface heat flux in detached divertor conditions but also demonstrates the feasibility of using two operational modes of SETCs to distinguish between the two surface heating mechanisms.

The impacts of wildfires on ozone production and boundary layer dynamics in California's Central Valley

Abstract. We investigate the role of wildfire smoke on ozone photochemical production (P(O3)) and atmospheric boundary layer (ABL) dynamics in California's Central Valley during June–September from 2016 to 2020. Wildfire events are identified by the Hazard Mapping System (HMS) and the Hybrid Single Particle Lagrangian Integrated Trajectory Model (HYSPLIT). Air quality and meteorological data are analyzed from 10 monitoring sites operated by the California Air Resources Board (CARB) across the Central Valley. On average, wildfires were found to influence air quality in the Central Valley on about 20 % of the total summer days of the study. During wildfire-influenced periods, maximum daily 8 h averaged (MDA8) O3 was enhanced by about 5.5 ppb or 10 % of the median MDA8 (once corrected for the slightly warmer temperatures) over the entire valley. Overall, nearly half of the total exceedances of the National Ambient Air Quality Standards (NAAQS) where MDA8 O3 > 70 ppb occur under the influence of wildfires, and approximately 10 % of those were in exceedance by 5 ppb or less indicating circumstances that would have been in compliance with the NAAQS were it not for wildfire emissions. The photochemical ozone production rate calculated from the modified Leighton relationship was also found to be higher by 50 % on average compared with non-fire periods despite the average diminution of j(NO2) by ∼ 7 % due to the shading effect of the wildfire smoke plumes. Surface heat flux measurements from two AmeriFlux sites in the northern San Joaquin Valley show midday surface buoyancy fluxes decrease by 30 % on average when influenced by wildfire smoke. Similarly, afternoon peak ABL heights measured from a radio acoustic sounding system (RASS) located in Visalia in the southern San Joaquin Valley were found to decrease on average by 80 m (∼ 15 %) with a concomitant reduction of downwelling shortwave radiation of 54 Wm−2, consistent with past observations of the dependence of boundary layer heights on insolation.

About the 3D simulation of the boiling of liquid films and spray droplets during their contact with hot substrates

Boiling of liquids upon impact of the spray on heated surfaces is common in many practical applications. However, a comprehensive modelling approach for these phenomena is still not available in commercial software, despite decades of experimental, theoretical, and numerical research efforts. The motivation of this paper is to clarify the state of the art on the three-dimensional (3D) simulation of the boiling of liquid films and spray droplets during their contact with hot substrates. Based on recent experimental and theoretical research, this paper proposes a set of heat transfer models for 3D simulation of spray cooling considering conjugate heat transfer (CHT). These updated models and correlations were implemented in a computational fluid dynamics (CFD) solver, which already included a classical two-phase Lagrangian–Eulerian approach and CHT modelling functionality. A detailed validation of the improved modelling proposals is performed using a unique and novel database including wall surface temperature and heat flux measurements for different flow rates and spray impact velocities. Excellent agreement with experiments was obtained for all boiling regimes using a Leidenfrost-like temperature to manage the prompt heat flux change between the film boiling regime and the transition boiling regime. Most notable are the great results produced by the recent film boiling model summarized in this article.Graphical Abstract

Burial and Heat Flux Modelling along a Southern Vøring Basin Transect: Implications for the Petroleum Systems and Thermal Regimes in the Deep Mid-Norwegian Sea

A key aspect on the evolution of rifted terranes and the prospectivity of the overlying sedimentary basins is heat. Temperature determines the deformation regime of crustal and mantle rocks and, thus, the style of rifting and geometry of rift basins. The generation of hydrocarbons from organic-rich rocks and reservoir conditions depend primarily on temperature. In this study, we model the thermal–burial history of the southern Vøring Basin (Mid-Norway Margin) along a regional transect (2-D), integrating basin- and lithospheric-scale processes. A model that accounts for the main extensional pulses that shaped the Mid-Norway Margin is in good general agreement with the present–past geothermal gradients inferred from borehole temperature and maturity data and the surface heat flux measurements in the proximal and intermediate margin. This supports a near steady-state, post-rift margin setting, following the break-up in the early Eocene. Significant discrepancies are, however, observed in the distal margin, where the borehole temperatures suggest (much) higher thermal gradients than model predicted and implied by the average surface heat flux. We speculate that the higher thermal gradients may result from deep-seated (mantle dynamics) thermal anomalies and/or recurrent hydrothermalism during periods of greater tectonic stress (regional compression and glacial loading rebound) and test the implications for the maturity of the Vøring Basin. The modelling results show, for example, that, depending on the thermal model assumptions, the depth and age of the optimal mid-Late Cretaceous source-rock horizons may vary by more than 2 km and 10 Ma, respectively.

Gas-Surface Energy Exchange Characterization Around a Cone in the Free-Piston-Driven Shock Tunnel

This work describes numerical and experimental research in the Indian Hypersonic Shock Tunnel 3 on a blunt cone model and related computation of the facility parameters: nozzle reservoir conditions, nozzle transit time, and freestream conditions. Specialized codes accounting for real gas effects and nonequilibrium are used to obtain facility parameters. Starting at freestream conditions, a physicochemical model is developed in Fluent to simulate the dissociating environment within the shock layer over the model, assuming thermodynamic equilibrium. The model is validated, then invoked with a surface reaction of exothermic chromium oxidation, to study model erosion and gas-surface energy exchange. A mathematical analysis is performed to estimate surface oxidation rate, heat release, and its effect on shock layer temperature and aerodynamic heating. Both the quantities show considerable increase. Experimental measurement of surface heat flux and temperature using thin film gauges and two-color ratio pyrometry, respectively, also show an increase. The Fluent model with an iterative technique is used to show that the actual temperature at stagnation point is about 90 K higher than its counterpart based on line-of-sight averaged measurements. Finally, analytical calculations are performed to obtain the reaction rate parameter as a measure of the degree of dissociation in the shock layer.

Thermal properties of U-Mo alloys irradiated under high fission power density

A variety of physical and thermal property measurements made on irradiated U-Mo alloy monolithic fuel samples with a Zr diffusion barrier and clad in Al alloy 6061 are reported. These properties form the basis for additional investigations in thermal behavior of U-Mo fuel under high performance research reactor irradiation conditions. Measurements were performed on samples harvested from fuel plates irradiated under high fission power density and surface heat flux and complement previous measurements on samples subjected to moderate fission power density and surface heat flux. Sample measurements reported in this work represented fission density ranging from 2.42 – 4.81 × 1027 fissions•m−3 (20.8 – 36.5 235U depletion) and average plate surface temperatures from 355 – 414 K. Specific heat capacity of irradiated monolithic U-Mo increases with increasing temperature and fission density, but carries large uncertainties associated with thickness measurements used to determine the mass fraction of the layer constituents for extraction of the U-Mo specific heat capacity, specifically the very thin and nonuniform Zr diffusion barrier. Density of irradiated monolithic U-Mo decreases with increasing fission density resulting from fission gas swelling and porosity formation. Thermal diffusivity of irradiated monolithic U-Mo increased with increasing temperature and decreased with increasing fission density. Thermal conductivity of irradiated monolithic U-Mo increased with increasing temperature, and in general, appeared to decrease and become less sensitive to temperature with increasing fission density. Thermal conductivity measurements compared to a semi-empirical model agreed within ±30%. It is suspected that the main driver in deviation between model calculations and measurements is the fission gas swelling determination, which does not account for fission power density or irradiation temperature.

Development of a Vertically Configured MEMS Heat Flux Sensor

Heat flux sensors (HFSs) have potential in enabling applications that require direct and instantaneous tracking of thermal energy transfer. To facilitate the widespread use of the sensors, the sensors have to be robust and feasible to implement, while maintaining high sensitivity, fast response time, and low thermal obtrusiveness. However, most of the currently available HFSs are either challenging to manufacture or ill-suited for surface heat flux measurement because of their mechanical or thermal characteristics. In this article, the design of a novel microelectromechanical systems (MEMS) HFS structure intended for surface heat flux measurements is presented. A prototype batch is manufactured and the electrical performance of the prototype sensors is compared with commercially available HFSs. Results show that sensors with similar sensitivity as commercial sensors can be made by using MEMS methods.

Skin friction estimation on a surface under shock-boundary layer interaction

This article presents correlations for indirect measurement of skin friction inside a laminar separation bubble induced by hypersonic shock-boundary layer interaction (SBLI) on a flat plate. The correlations, based on parameters that are known to influence the SBLI region, were developed using exhaustive numerical and analytical studies. Experiments were conducted in a hypersonic shock tunnel at Mach 8.6 (±0.22) to measure surface heat-flux and pressure in the zone of SBLI on a flat plate, which were then used to supplement and validate the correlations. The data predicted by the correlations agreed reasonably well with that of exact solutions. The case studies contained non-reacting air, behaving as a perfect gas on a flat surface.

Performance analysis of coaxial thermocouples for heat flux measurement of an aerodynamic model on shock tube facility

The K, E and J-types of coaxial thermo-sensors have been used to measure surface heat flux at the nose, spatial position-1 and spatial position-2 over an aerodynamic model subjected to a homemade shock tube flow facility. The high pressure shock has been applied to the aerodynamic model for 60 ms subsequently their variation in transient temperatures have been recorded for four experimental shots. The surface heat flux has been predicted from the transient temperatures by using one-dimensional heat transfer theory in a semi-infinite solid body. The average errors have been found between four experiments for transient temperature and surface heat flux are less than ±0.2% and ±4% respectively. A two-dimensional numerical model has been developed by using commercial software Ansys to solve the high enthalpy flow facility as exists in shock tube arrangement to validate the experimental results. The accuracy found in transient temperatures and surface heat fluxes are ±0.51% and ±0.633%. These coaxial thermo-sensors will help the design and development of aerodynamic vehicles in terms of measurement of heating rate on different inclined surfaces, missile nose, hypersonic aircraft technology, gun barrel test, advanced production technology, engine measurements etc.

Determining maize water stress through a remote sensing-based surface energy balance approach

Determining water stress levels of vegetated surfaces is crucial for irrigation scheduling. This paper aims to evaluate a new method for obtaining crop water stress index (CWSI) based on the estimation of sensible heat flux using an aerodynamic temperature gradient approach. Data were collected on a deficit irrigated maize field at a research farm located in Greeley, Colorado, USA, in 2017 and 2018. The irrigation treatment used subsurface drip. Weather data were measured on-site at 3.3 m above ground level. RED and NIR surface reflectance data were obtained on-site through multispectral radiometer measurements. Nadir surface temperature data were measured using infra-red thermometers at 1 m above canopy. CWSI estimated values were used to assess daily soil water stress index (SWSI), calculated from measurements of volumetric soil water content (VWC) and management allowed depletion (MAD) of 40%. Results show that SWSI is best represented through a non-linear rational CWSI function. Modeled CWSI estimates were compared to measured surface heat fluxes, resulting in a mean bias error of − 0.02 and a root mean square error of 0.09, while errors were 0.02 and 0.06 when compared with observed CWSI based on canopy transpiration measured with plant sap flow devices. Results seem to validate the proposed sensible heat flux-based CWSI model. The CWSI approach presented could be used to manage irrigation and conserve water resources for maize in semi-arid regions.