Calculation Of Heat Flux Research Articles

Measurement of local wall temperature and heat flux using the two-thermocouple method for a heat transfer tube

Abstract The two-thermocouple method was investigated experimentally to evaluate its accuracy for the measurement of local wall temperature and heat flux on a heat transfer tube with an electric heater rod installed in an annulus channel. This work revealed that a thermocouple flush-mounted in a surface groove serves as a good reference method for the accurate measurement of the wall temperature, whereas two thermocouples installed at different depths in the tube wall yield large bias errors in the calculation of local heat flux and wall temperature. These errors result from conductive and convective changes due to the fin effect of the thermocouple sheath. To eliminate the bias errors, we proposed a calibration method based on both the local heat flux and Reynolds number of the cooling water. The calibration method was validated with the measurement of local heat flux and wall temperature against experimental data obtained for single-phase convection and two-phase condensation flows inside the tube. In the manuscript, Section 1 introduces the importance of local heat flux and wall temperature measurement, Section 2 explains the experimental setup, and Section 3 provides the measured data, causes of measurement errors, and the developed calibration method.

Design and numerical simulation of a clamshell-shaped inlet cover for air-breathing hypersonic vehicles

An efficient clamshell-shaped inlet cover configuration based on a shockwave interference methodology is proposed, which has the advantage of an autonomous opening using the aerodynamic force and moment. A preliminary design method for the inlet cover is introduced and used to produce cover models of two different lengths, with contributions similar to those of cowlings, rocket fairings, shrouds, or false ogives. The clamshell-shaped inlet cover features a practical design with a wide range of applications, including utilization in air-breathing hypersonic vehicles under specific constraints. In this investigation, aerodynamic numerical simulations were conducted to evaluate the extent to which the objectives and design principles are achieved for two typical ballistic separation states. The results show that both configurations can prevent an excessive accumulation of shockwaves in the nose cone area. In addition, the inlet cover generates negative lift, which results in the generation of an opening moment. The calculated heat flux at the leading edge of the clamshell-shaped inlet cover is approximately 13 MW/m2, which is within the limit of the composite material but slightly higher than that of the stagnation point of the nose cone.

Calculation of Heat Fluxes Exiting a CANDU Calandria During In-Vessel Retention

Finite element analysis is used to study heat transfer from a corium pool at the bottom of the calandria to its surroundings during a severe accident in a CANDU 6 reactor. The shape of the corium crust around the pool and the steady-state heat fluxes exiting the calandria are calculated for representative accident conditions. The sensitivity of the results to several model parameters is examined. Calculated heat fluxes can be compared to measurements of the critical heat flux at different locations on the outside of the calandria in order to assess the possibility of in-vessel retention of the molten core.

Modeling of A Single Turn Pulsating Heat Pipe based on Flow Boiling and Condensation Phenomena

Demand for high-performance cooling systems is one of the most challenging and virtual issues in the industry and Pulsating heat pipes are effective solutions for this concern. In the present study, the best predictor correlations of flow boiling and condensation are taken into account to model a single turn pulsating heat pipe mathematically. These considerations, result in derivation of more accurate results. The nucleate boiling phenomenon has been considered as the dominant mechanism of the boiling process in the evaporator. However, due to the annular flow assumption, a thin film of liquid is considered in calculation of the mass transfer out of the vapor plugs. All the fundamental relations such as momentum, mass and energy equations are solved implicitly, except the energy equation of liquid slug. The liquid slug displacement results are compared with the previous studies and the comparison indicates increase in both the frequency and the amplitude of the slug displacement. Moreover, the calculated heat flux is verified with the empirical results. The comparison shows an acceptable agreement between the findings, which is better than previous modelings without boiling and condensation. Furthermore, the effect of pipe diameter on the flow and heat transfer mechanisms has been derived. According to the results, by increasing the pipe diameter, despite a frequency decrease, the oscillation amplitude of liquid slug and total heat flux transferred into the pulsating heat pipe increases. Sensible heat contribution in the heat trasnfer mechanism reduces by higher pipe diameter values.

Initial results from the hotspot detection scheme for protection of plasma facing components in Wendelstein 7-X

Abstract One of the main aims of Wendelstein 7-X (W7-X), an advanced stellarator, is to investigate the quasi-steady state operation of magnetic confinement devices for nuclear fusion, for which power exhaust is an important issue. A dominant fraction of the energy leaving from the confined plasma region will be removed by 10 so-called island divertor units, which are designed to sustain a maximum heat flux of up to 10 MW m − 2 . An essential prerequisite for the safe operation of a steady-state device is automatic detection of hot spots and other abnormal events. Simple temperature limits in infrared (IR) thermographic images will not be enough on their own, because of plasma-generated surface coatings and other effects summarized in the following. To protect divertor elements from overheating, and to monitor power deposition onto the divertor elements, near real-time hotspot detection algorithms for the analysis of carbon plasma facing components (PFCs) were implemented and tested in the GLADIS facility. One of the difficulties in hotspot detection in a carbon-based machine is the deposition of plasma impurities as layers with a reduced thermal connection to the underlying bulk material. We have developed and successfully tested a method to classify surface layers and benchmarked the performance of the method with the Tore Supra IR data operating with actively cooled carbon PFCs. The surface layers can be detected in a steady plasma discharge during the initial rise and decay in temperature when a strike line touches parts of the divertor or wall. It can also be detected by modulating electron cyclotron resonance heating (ECRH) input power. This feature allows detection of overheated areas while reducing false positives. For the recent operational campaign, inertially cooled test divertor units (TDU) were installed to prepare for steady-state operation with water-cooled divertor units. Automatic, near real-time detection of hot spots and identification of surface layers in the W7-X divertor are presented. Results are compared with a best fit estimate of the heat transmission coefficient α which is used to calculate heat flux onto the divertor in the presence of surface layers.

Development of an analytical model to predict the radiative heat flux to a vertical element due to a localised fire

This paper describes an analytical model developed for design purposes with the aim to assess the radiative heat flux to a vertical element subjected to a localised fire. It focuses on the calculation of the radiative heat flux, which represents the main source of heating of vertical members that are not engulfed into the fire. The model exploits the concept of virtual solid flame whose height and temperature are determined according to the correlations provided in Annex C of EN1991-1-2 and relies on an analytical formulation easy to implement in any spreadsheet. A major enhancement of the proposed model is the capability of providing a way to predict the heat flux on all faces of a vertical member. Moreover, it is deemed valid for any range of heat fluxes that can be expected in a localised fire and it is inherently conservative to be used for design calculations. The proposed model was validated against several experimental tests performed within the European LOCAFI project, as well as against tests found in the literature. Moreover, a parametric numerical analysis was carried out by means of Computational Fluid Dynamics (CFD) numerical simulations that were calibrated on the basis of the experimental outcomes. In this way, the validation of the analytical model was also performed numerically and useful information about the main parameters that significantly influenced the numerical simulation of localised fires fire was drawn. Conservative agreement in terms of heat flux predictions between the proposed model and experimental as well as numerical outcomes was found.

Investigation of thermal radiation of furnace gases generated from solid-fuel combustion in a steam boiler

The article presents a methodology of comprehensive study of thermal radiation emitted by furnace gases during solid fuel combustion. The characteristics of initial fuel and chemical composition of flyash are described. The absorption coefficients of the gaseous phase in relation to the wavelength, temperature, and concentration of the main gas components are measured. The gas composition was determined by calculation of the total combustion products, as well as experimentally (through a gas analyzer). The experimental results on the particle shapes and sizes, the distribution function of flyash particles, the fusibility of mineral part were used to calculate the radiation characteristics of the condensed phase. Calculations of emission characteristics of furnace gases (spectral and integral flux densities and emissivity factors) depending on the influence of each phase at different operating temperatures are presented. The method efficiency is estimated through comparing with calculated and experimental data on the emission characteristics for homogeneous and heterogeneous combustion products. Spectral ranges were chosen to determine the temperature for furnace gases, a plume, and the surface of flyash deposits on the furnace walls. Experimental dependences of the emissivity factors for flyash deposits on temperature are presented. The findings can be used to calculate heat fluxes, for the purposes of furnace gases pyrometry, and to determine the temperature level in the compilation of operational maps for the boiler.

Implicit heat flux correction-based immersed boundary-finite volume method for thermal flows with Neumann boundary conditions

In the frameworks of immersed boundary method (IBM) and finite volume method (FVM), an implicit heat flux correction-based IB-FVM is proposed for thermal flows with Neumann boundary conditions. With the use of a fractional-step technique, the preconditioned Navier–Stokes (N–S) equations are solved by the FVM to obtain the intermediate solution in the prediction step and the heat flux is corrected by enforcing the Neumann condition in the correction step. Different from existing IBMs, the cell face centers are defined as the Eulerian points due to the heat flux computation at each face in the FVM. The Neumann condition is implemented in such a way that the interpolated temperature gradient is equal to the specified boundary value at the same point when the corrected gradient field is interpolated from the face centers to the Lagrangian points. To achieve an implicit algorithm, the temperature derivative corrections at the Lagrangian points are set as unknowns and a system of algebraic equations is established by constructing hybrid thin-plate splines (TPS) interpolation/delta function distribution. In the derivative interpolation process, the much more accurate TPS is introduced because the use of cosine delta function yields a less accurate solution. After the distribution process, the heat flux correction of a fluid cell is evaluated by using the solved temperature derivative corrections at the face centers, but that of a solid cell is calculated by using their additive inverses to supplement the same amount of heat flux into the solid domain as that flowing into the fluid domain across the boundary. Finally, the heat flux of a cell is corrected by adding the correction to the intermediate value and the corrected heat flux is utilized to solve the N–S equations in the prediction step. As compared with the available implicit IBMs for Neumann conditions, the present method avoids the introduction of auxiliary layers of Lagrangian points as well as the approximate conversion from the Neumann to Dirichlet condition and thus is suitable for an arbitrary geometry. The proposed method is verified by simulating several benchmark thermal flows with Neumann conditions, the natural convection in an annulus and the steady or unsteady forced convection over a stationary or oscillating cylinder. All the computed results agree well with the literature data.

Global meridional eddy heat transport inferred from Argo and altimetry observations

Proportion and pathways of the eddy-induced heat transport are critical in maintaining world’s ocean and climate states. However, an observation-based three-dimensional picture of how oceanic eddies contribute to the global heat transport is yet not quantitatively specified, particularly due to insufficiency of data. Here, using refined methods, we have achieved this goal by analyzing millions of high-quality Argo hydrographic profiles and high-resolution satellite altimetric data. We first presented the spatial differences of individual eddies by reconstructing 254 representative eddies all over the ocean, and then calculated heat fluxes associated with eddies in 5° × 5° boxes. It is revealed that all parameters of eddies vary significantly with both latitudes and longitudes, which is crucial in yielding spatially varying heat fluxes and transports. The eddies not only transport heat towards high latitudes (down-gradient), but also towards low latitudes (up-gradient), particularly at subsurface layers of mid-latitude northern Pacific Ocean and low-latitude Atlantic Ocean. The eddy heat transport is mainly confined in the upper 1000 m of the western part and mid-latitudes of the world’s ocean basins, coinciding with maximum meridional temperature gradients. It peaks at 0.8 PW and 0.3 PW (1 PW = 1015 W) at 45°S and 35°N, respectively, stronger than previous estimates based on model results, and accounts for about one half and one third of the estimated total oceanic heat transport at the same latitudes, respectively. In any location except for the areas associated with the Antarctic Circumpolar Current, the eddy stirring component is distinctly (1–10 times) larger than the eddy trapping component.

Characteristics of atmosphere - sea ice energy exchange in the Central Arctic

Analysis of an interaction between long-term ice cover and atmosphere in different regions of the Arctic Ocean is conducted. For comparison the energy exchange characteristics in the western and eastern periphery of the Beaufort Gyre, the central part of the Arctic Ocean and in the area to the north of the Kara and Barents seas have been analyzed. The results of calculations based on special observations at Russian drifting station “North Pole-4” and its interpretation using a simple thermodynamic model of sea ice were used. As modern in situ data, meteorological observations at drifting stations “North Pole-35” (2007-2008) and “North Pole-39” (2011-2012) were used. Calculations of turbulent heat fluxes in the region of the drift of the American station “SHEBA” were performed. A good agreement between the calculated fluxes based on the historical data and NP-39 data for the summer period is shown. Monthly mean values and standard deviations of meteorological parameters for winter period are presented on the basis of data from drifting stations “North Pole-35” – “North Pole-40” (2007-2013).

Experimental investigation on thermal contact resistance of alumina fibrous insulation material with Ti-6Al-4V alloy at high temperature and its effective thermal conductivity

Heat transfer through thermal insulation material is an important process in the design and performance evaluation of an insulation system, which is a key component of space vehicles. Accurate information on heat transfer analysis requires determination of thermal contact resistance (TCR) between the insulation material and the super-alloy plate. In this study, test equipment was designed to measure the TCR as well as the effective thermal conductivity of low thermal conductivity fibrous insulation material at high temperatures and in atmospheric pressure conditions. Two heat-flux meters were used to measure the heat flux from the bottom (high temperature) to the top (low temperature) of a fibrous sample in the test column. The two-thickness method was used to obtain the TCR and the effective thermal conductivity. An uncertainty analysis was also evaluated, which proved that the most important factor in the TCR measurement was the heat flux calculation. The result reveals that the TCR values become high at small contact pressures. The TCR decreased with an increase in the compressive load and significantly contributed to the total thermal resistance of the fibrous sample, approximately 42% and 35% when the average temperature of the sample was 190 °C and 290 °C, respectively. The effective thermal conductivity of the fibrous sample decreased slightly with an increase in the average temperature due to the presence of the carbonization of the binder resin. The numerical method validated the experimental results well. In addition, the micrograph images of the contact surface were investigated.

The physical aspects of gas dynamic and thermal physics processes mathematical modelling of descent spacecraft’s

The article discusses the physical aspects and assumptions in the formulation of the gas dynamics and thermal physics models in conditions of ?Luna - Resource? spacecraft landing on the Moon surface. It was proposed to divide the problem into two stages: calculation of the gas phase and determination of trajectories and heating of particles of lunar dust. The use of the continuum equations and not taking into account the reverse effect of particles on gas was substantiated. The calculation results of parameters impingement exhaust jet of spacecraft propulsion system with Moon surface are given. It was obtained that a reverse external force is added to the streamlined surfaces equal to 196 N, the gas temperature at the bottom of the cargo compartment reaches 2000 K, and the calculated heat flux was 400 kW. The trajectories of the particles of lunar dust was determined and it was found that with a size of 1 ?m the distance of their flight range was 3.5 km.

Software Sensors for Biomass Concentration Estimation in Filamentous Microorganism Cultivation Process

In this study, the potential of two software sensors for on-line estimation of biomass concentration during cultivation of filamentous microorganisms is examined. The first sensor is based on common bioreactor off-gas analyses, and uses the assumption of the biomass concentration linear dependence on the square root of cumulative O2 consumption. Parameters of the semi-empirical data-driven software sensor based on off-gas analysis were calculated from experimental cultivation data using linear regression. The second sensor is based on biocalorimetry, i.e., the on-line calculation of metabolic heat flux from general enthalpy balance of the bioreactor. The software sensor based on biocalorimetry thus essentially represents a model-driven approach, making use of a fundamental process model based on the enthalpy balance around the bioreactor. This approach has been combined with the experimental identification of the specific biomass heat production, which represents the main process-specific parameter of the software sensor based on biocalorimetry. For this sensor, the accuracy requirements on the process variable on-line measurements were also analysed. The experimental data from the pilot-scale antibiotics Nystatin production by a bacterium Streptomyces noursei were used to calculate the specific bioprocess heat production value using linear regression. The achieved results enabled us to propose a new on-line indicator calculated as the ratio of the outputs of both sensors, which can serve as a timely warning of the risk of undesired nutritional conditions of a culture characterized as underfeeding.

地球静止轨道变姿态空间相机的外热流计算

地球静止轨道变姿态空间相机的外热流计算

Analysis of the ideal gas flow over body of basic geometrical shape

An approximate mathematical model of the heat transfer processes in the laminar and turbulent boundary layers, which occur near the surface of an aircraft moving at the hypersonic speed in the Earth’s atmosphere, is derived. This mathematical model makes it possible to calculate the convective heat transfer on the surface of typical structural elements of modern perspective aircrafts. 2D versions of the calculations of convective heat fluxes for bodies of simple geometric shapes are performed.

Application of a variance reduction technique to Surface-to-Surface Monte Carlo radiation exchange calculations

An easy-to-implement variance reduction technique based on the control variate method is proposed and demonstrated for Monte Carlo (MC) calculations of surface-to-surface (S-to-S) radiation exchange. The method is general, and is applicable to any S-to-S radiation exchange problem—gray or non-gray. The control function used in the proposed method is the Planck function evaluated at the minimum temperature of the domain. The Radiative Transfer Equation (RTE) and its boundary conditions are recast into a deviational form, and it is shown that only two minor changes are necessary within the standard S-to-S MC algorithm to implement the proposed variance reduction technique. No computational overheads are incurred is using the proposed technique. Three test cases are considered, and exact (deterministic) solutions are used to assess the accuracy of the MC results. It is found that in all cases, the statistical error in the computed heat flux, as measured by the variance, is reduced. The variance reduction can be substantial (almost an order of magnitude) if the problem at hand is dominated by temperatures sufficiently close to the control temperature. In the third test case, radiation is also iteratively coupled to convection, and it is shown that the variance reduced MC solutions for steady state temperatures are far more accurate than those produced by the standard MC method for the same number of rays.

Thermal Analysis of Satellite Libertad 2: a Guide to CubeSat Temperature Prediction

We present a model for predicting the temperature of three-unit CubeSat on a low Earth orbit, which supposes a single temperature common to all satellite components. Our exposition includes a detailed, to a large extent analytical, computation of the external heat fluxes for a particular orbit and spacecraft assumptions based on the features foreseen for satellite Libertad 2 under development at Universidad Sergio Arboleda. Moreover, supported by specialized thermal analysis software, we compute the heat fluxes and their associated temperature for all possible orbital orientations, and combine these results with a description of the satellite orbital plane rotation (nodal regression) and the solar motion on the ecliptic, to determine the minima and maxima of the orbital temperature oscillation for a mission lifetime of a year. We find that, for feasible model parameters, the temperature extremes are mostly within the operating temperature range of the most sensitive satellite component, 0 °C ≤ T ≤ 60 °C, suggesting mission viability. Finally, we discuss possible model improvements which would allow testing of satellite design upgrades. In this regard, it is worth noting that the calculation of the external heat fluxes here described can be carried over, almost unchanged, to a more accurate model describing heat transfer between satellite parts with different temperatures.

An interaction integral method for calculating heat flux intensity factor with the XFEM

The JT integral is defined to extract the heat flux intensity factor (HFIF), which is used to describe the singularity of heat flux near the tip of a crack, and the path-independence of the JT integral is theoretically proven. Based on the JT integral, the relationship between the HFIF and an interaction integral is established through introducing auxiliary field function. The extended finite element method (XFEM), which enriches the standard finite element approximation by additional functions, is utilized to solve the temperature field of a cracked structure under specified thermal boundary condition. Numerical examples of cracked plates respectively with an edge crack and a center crack are used to verify the presented method, and the method is also used to investigate the HFIF near the tip of an inclined crack and the interaction effect of two cracks on the HFIF. The presented method provides a foundation for the investigation into the crack propagation behavior of a structure under thermo-mechanical loading.

The Role of WISHE in Secondary Eyewall Formation

Abstract Numerical simulations are conducted to examine the role of the wind-induced surface heat exchange (WISHE) mechanism in secondary eyewall formation (SEF). The control experiment exhibits a coherent secondary eyewall structure as quantified by various parameters (e.g., the azimuthal-mean tangential wind and vertical velocity). Prior to SEF, an area characterized by increasing diabatic heating, enhanced inertial stability, and increasing supergradient winds at the top of the boundary layer is observed outside the eyewall. While these characteristics offer the possibility of both balanced and unbalanced dynamical pathways to SEF, the focus of this study is to evaluate the impact of WISHE. To examine the sensitivity of SEF to WISHE, the surface wind used for the calculation of surface heat fluxes is capped at several designated values and at different radial intervals. When the heat fluxes are moderately suppressed around and outside the SEF region observed in the control experiment, sensitivity experiments show that the formation of the outer eyewall is delayed, and the intensity of both eyewalls is weaker. When the heat fluxes are strongly suppressed in the same region, SEF does not occur. In contrast, suppressing the surface heat fluxes in the storm’s inner-core region has limited effect on the evolution of the outer eyewall. This study provides important physical insight into SEF, indicating that WISHE plays a crucial role in SEF and tropical cyclone evolution.

Evaluation of wall heat flux calculation methods for CFD simulations of an internal combustion engine under both motored and HCCI operation

In the present work, a study of different numerical heat transfer models is presented used for Homogeneous Charge Compression Ignition (HCCI) internal combustion engine simulations. Since the heat loss through the walls of an engine is an important parameter during engine optimization, as it influences power, efficiency and emissions, accurate modeling techniques need to be available. In this work, the predictive capability of different Computational Fluid Dynamics (CFD) models has been assessed, by using data obtained from experiments on a Cooperative Fuel Research (CFR) engine, a simple single cylinder pancake engine, which has been probed with local heat flux sensors into the combustion chamber walls. The open-source software OpenFOAM® was used to perform simulations of this engine, under both motored and HCCI operation, with a specific focus on the performance of different heat flux models. Due to the simple engine geometry, more numerically demanding heat flux modeling methods could be used, maintaining an acceptable computation time. This allowed a full comparison between the equilibrium wall models as in standard use, an improved empirical heat flux correlation and a numerically intensive low Reynolds formulation. The numerical results considering all aspects of the heat flux - both its progress in time as well as quantitative aspects such as the peak heat flux or the total heat loss - have then been compared to an extensive experimental database. This allowed a full analysis of the performance of the different methods. It was found that the low Reynolds formulation described the physical behavior near the wall the best, while predicting acceptable results concerning the heat flux through the engine walls. The best heat flux prediction was however obtained with an improved empirical model, which additionally has a much shorter computation time. This is crucial when moving on to heat flux simulations of more complex production-type engines. Lastly, the equilibrium models were never capable of accurately predicting the wall heat flux.