Heat Flux Profiles Research Articles

Radiative Thermostat Driven by the Combined Dynamics of Electrons, Phonons, and Photons

Based on the metal-insulator transition of two phase-change materials (PCMs) with asymmetric thermal conductivities and emissivities sensitive to temperature, a radiative thermostat capable of maintaining a constant temperature without consuming energy is proposed. This is done by deriving explicit expressions for the heat flux and temperature profiles of the thermostat surrounded by these PCMs, and demonstrating that the thermostat can be maintained at a temperature nearly equal to the common transition temperature of both PCMs as the environmental temperature changes by more than 20 K. I show that the combined operation of two PCMs is much better than two non-PCMs to develop energy-free thermostats, especially those supporting poor thermal conduction or dominant heat radiation. The obtained results thus establish a fundamental theoretical method that exploits the nonlinear heat transport driven by electrons, phonons, and photons to maximize temperature preservation and thermal insulation.

Enhanced flow boiling heat transfer on chromium coated zircaloy-4 using cold spray technique for accident tolerant fuel (ATF) materials

Flow boiling heat transfer tests were conducted to evaluate the Critical Heat Flux (CHF) and Heat Transfer Coefficient (HTC) of conventional and accident tolerant fuel (ATF) cladding materials, i.e., bare Zircaloy-4 (Zr4), and Zircaloy-4 coated with Chromium using physical vapor deposition (PVD) (Zr4-Cr-PVD) and cold spray process (Zr4-Cr-CS), respectively. The tests were performed on a single heater rod with a uniform heat flux profile, at the atmospheric pressure, inlet temperature (24 °C) and mass flow rate (750 kg/m2s). HTC’s were increased by 5.2% and 3.3% on Zr4-Cr-CS compared to bare Zr4 and Zr4-Cr-PVD. Improved HTCwas attributed to the increased void fraction and high roughness (Ra = 532 nm) of the Zr4-Cr-CS. In detail, the micro-cavities, which act as bubble seeds, were entirely distributed on the Zr4-Cr-CS, and these micro-cavities generated smaller and faster bubbles, thus the void fraction increased by 10.9% compared to bare Zr4. HTC is improved by these smaller and faster bubbles which can remove heat from the heater rod surface more efficiently. To identify the exact location of CHF, the surface temperature profile was measured using advanced fiber-optic sensors which have high temporal/spatial resolution (distance between point to point: ~2.5 mm, frequency ~100 Hz). CHF occurred at 80–95% along the heated length and showed an 11.6% reduction on Zr4-Cr-CS compared to bare Zr4. We hypothesize the CHF reduction was caused by the lower wettability of the Zr4-Cr-CS which reduces the liquid supply to the surface, and vigorous bubble accumulation owing to high void fraction near the outlet, which results in early formation of the vapor film. During the post-CHF quenching phase, the rougher Zr4-Cr-CS showed larger cooling rates compared to the bare Zr4 and Zr4-Cr-PVD, preventing of oxidation by chromium layer. In conclusion, we demonstrate that the high roughness on the Zr4-Cr-CS increased the number of micro-cavities on the surface, resulting in 5.2% increase in HTC and improvement in the quenching heat transfer performance whereas CHF was 11.6% reduced compared to bare Zr4. Overall statistically there is little effect in the coating with regards to CHF and slight improvement in HTC.

Effects of variable heat flux at supercritical pressure in vertical pipe flow

It is a well-established fact that the heat transfer at supercritical pressure is complex and several numerical investigations have been conducted to address this issue. However, the focus of such studies remains uniform heat flux. Therefore, here we report the outcomes of direct numerical simulations performed with different profiles of non-uniform heat flux for supercritical carbon dioxide. Flow in a small pipe with a diameter of 2 mm is considered and vertical orientation with upward direction of fluid flow was chosen. The heat flux was varied in the axial and circumferential direction of the pipe. The circumferential heat flux induces the thermal stratification which resulted in a higher wall temperature at one side where heat flux was maximum. While axially varying wall heat flux results in the peak and valley in the wall temperature. The study also suggests that axially varying heat flux can be a possible strategy to control the heat transfer deterioration.

A novel method for determining the three dimensional variation of non-linear thermal resistance at the mold-strand interface in billet continuous casting process

A three-dimensional numerical model has been developed to study the turbulent flow of the molten steel, heat transfer from the solidifying strand to the cooling water and the subsequent solidification within the mold of an industrial billet continuous casting process. Particular attention is paid to calculate the unknown non-linear thermal resistance at the mold-strand interface, based upon a physical formulation. The model results are validated with the data available in the literature, as well as from plant experimental data. Recirculation flows are observed near the mold walls, causing remelting of solidified shell. The results obtained from the simulations show that one of the major reasons for higher value of solidified shell thickness at the corner region than that at the off-corner region is the nature of recirculatory flows. The thermal resistance is found to vary along the casting direction as well as across the mold face. The plant data of solid shell thickness of the strand at mold exit shows that the current model involving physical formulation of thermal resistance at the mold-strand interface, provides a better estimation of the thermal behavior, compared to previous models involving empirical formulation for the thermal resistance or heat flux profiles at the interface.

Novel inverse heat transfer methodology for estimation of unknown interfacial heat flux of a continuous casting mould: A complete three-dimensional thermal analysis of an industrial slab mould

Accurate quantification of interfacial heat flux between the continuous casting mould and slab/billet is essential for the design and development of the products as well as operation and quality control of the casting process. Apart from empirical correlations, inverse heat transfer methods are typically employed to predict the heat flux variation by assuming a one-dimensional variation of heat flux along the casting direction. The assumption of one-dimensional heat flux often leads to significant error especially in determining the corner heat flux which affects the shrinkage behaviour and thereby, the quality of the products of casting. Previous studies have recognized this error and assumed this error of heat flux as a constant deviation to account for the longitudinal and transverse variation of heat flux. In this work, a novel methodology has been presented to predict the variable interfacial heat flux of a three-dimensional mould domain by estimating the parameters of a characteristic heat flux profile using an inverse heat transfer technique based on Salp Swarm Algorithm (SSA). This methodology uses limited experimental data or on-site plant recorded data. Representative cases of billet and slab moulds have been considered based on the available plant data. Results indicate that the mould corner heat flux is considerably different from that of the typically assumed value of 67% of the centre heat flux as reported in the literature with deviation reaching as high as 56% near the meniscus for a slab casting mould. The proposed methodology is simple to implement and is recommended for studies aimed towards realistic estimation of unknown boundary heat flux in a continuous casting process.

Investigation of CO recombination in the boundary layer of CH4/O2 rocket engines

In this work, the combustion and thermal recombination in the boundary layer of a single-element methane/oxygen rocket combustor is investigated using large-eddy simulations. The experimental configuration consists of a coaxial injector and an operating point with a nominal pressure of 20 bar and gaseous injection of both propellants are considered. A non-adiabatic flamelet model is utilized with the purpose of examining its capability to predict the wall heat transfer. Good agreement of the simulation results with measurements of heat flux and pressure profiles is obtained using the non-adiabatic model. By comparing results with a frozen flamelet model, the importance of the recombination reactions in the cold boundary layer is investigated. The species profiles of CO and CO2 are examined and the reaction pathways leading to the recombination reactions at the wall were analyzed. Results from this analysis show that the reaction of OH with CO forming CO2 is the main contributor to the additional heat release in the boundary layer.

Numerical simulations of the Rayleigh-Bénard-Marangoni convections in a thin metallic layer

Within the context of nuclear power safety, the In-Vessel Retention (IVR) strategy consists in sustaining the integrity of the reactor pressure vessel by External Reactor Vessel Cooling (ERVC). However, due to the ablation of the vessel wall and the thermochemical effects, a thin metallic layer may be formed on top of the corium pool and lead to the vessel failure. In this article, numerical simulations of the thermal–hydraulic behavior of the thin metallic layer are carried out to reduce the uncertainties in the heat flux evaluation. Specifically, the Rayleigh-Bénard and Bénard-Marangoni convections are considered in the heat transfer models of the metallic layer. The TrioCFD code is validated for the Bénard-Marangoni convection, then applied into the numerical simulations of the metallic layer with different top boundary conditions: pure radiative heat transfer, and radiative heat transfer plus positive or negative Marangoni effects. The temperature profile, mean temperature and focusing effect of the metallic layer are evaluated and compared for various cases. Results show that the Marangoni effects have to be considered for small metallic layer thicknesses. Furthermore, the layer can be divided into two regions, of which the heat flux correlations can be evaluated independently, giving a better estimation of the heat flux profile.

Experimental Analysis of Limited Distance Effects on Self Induced Blow Off and Heat Transfer in Upward Flame Spread Over Thin Fabric Fuels

Most previous work concentrated on the one-sided upward flame spread under limited conditions. However, few investigations have studied the effects of limited distance between wall and fuel surface on two-sided upward flame spreading. In this paper, a series of upward flame spread experiments were conducted using 0.65 mm thick, 130 cm tall and 4.0 cm wide flax fabric sheets with various limited distance of 1.0 cm–3.5 cm. The flame shape, flame length, flame standoff distance, pyrolysis spread rate and surface temperature were measured and analyzed. An unexpected but interesting behavior of one-sided flame blow off was observed in upward flame spread. When limited distance is no more than 1.5 cm, the one-sided flame blow off behavior occurs on unlimited side, whereas this behavior occurs on limited side for 2.0 cm–3.5 cm limited distance. This result could be qualitatively explained by Damkohler number Da, which could be characterized by two parameters of induced flow velocity and heat flux received by virgin surface. Moreover, the maximum flame length, steady flame length, maximum spread rate and steady spread rate first increase and then decrease as the limited distance. This non-monotonicity trend is determined by heat flux profiles in the preheating zone, which is due to the combined limited distance effects of restricting oxygen supply, chimney effect and wall radiation. The surface temperature profile ahead of pyrolysis front is used to qualitatively describe the heat flux received by virgin surface. The results in this paper are essential for better understanding of self induced flame blow off mechanism and upward flame spread under limited distance conditions.

3D modeling and simulation of thermal effects during profile grinding

A new heat transfer model for profile grinding was developed to analyze distortions caused by residual tensile stresses in linear guide rails. The simulative analysis of the thermal effects caused by a non-uniform heat source on the surface using the finite element method depends on an accurate representation of the locally variable contact area. The complexity of the V-groove profile disqualifies a 2-dimensional simulation approches so far used in the literature. This paper focuses on the redefinition of these mathematical relationships of the process parameters and the resulting heat flux. The heat flux model is adapted to the geometry of the workpiece depending on the grinding parameters and approximating the V-groove of a linear guide rail. This 3-dimensional modeling allows a better understanding of the thermo-metallurgical effects that occur during the grinding process. Furthermore, the calculation of the internal stresses induced into the workpiece material through the grinding process is possible. The simulation model results in a generally valid model for the analysis of distortions. In order to confirm the validity of the new heat flux profile, a comparison of the different finite element simulation results was made and experiments under wet grinding conditions were conducted. The results show that the newly developed grinding process model allows a more accurate prediction of workpiece distortion caused by grinding forces and temperatures. This research also offers a new approach to a method based on a 2-dimensional implementation developed in the literature for predicting the distortions of linear guide rails and a derivation of possible simulation-based compensation strategies.

Analysis of the simulation of the PALM model for the Convective Boundary Layer in the Amazon (GOAMAZON 2014/5)

The present work had the objective to evaluate the development of the convective boundary layer in the Amazon region simulated by a high resolution Large Eddy Simulation model (named PALM model), for days representative for rainy and dry seasons. The study used data from the GOAmazon Project 2014/2015 (Green Ocean Amazon). Using data from radiosondes and Ceilometer as truth values, they were compared with the simulations performed through the PALM model. The results showed that, in general, the convective boundary layer cycle for the Amazon region was well represented by PALM model. It´s outputs has showed an overestimation of ≈ 35 m in a rainy day and an underestimation of ≈ 20 m in a dry day, both in development phase of the convective layer at late morning. It was also observed that the latent heat flux profile was higher than the sensible heat in the atmosphere, because it is a region with a lot of humidity, with the boundary layer responding rapidly to the maximum surface forcing.

Calculation of radiative heat flux on irregular boundaries in participating media* *Project supported by the Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology, the Anhui Provincial Natural Science Foundation, China (Grant No. 2008085ME151), and the National Natural Science Foundation of China (Grant Nos. 51976057 and 51827808).

Radiative heat flux at wall boundaries is important for its thermal design. Numerical methods based on structured grids are becoming trendy due to their simplicity and efficiency. Existing radiative transfer equation solvers produce oscillating radiative heat flux at the irregular boundary if they are based on structured grids. Reverse Monte Carlo method and analytical discrete ordinates method are adopted to calculate the radiative heat flux at complex boundaries. The results show that the reverse Monte Carlo method can generate a smooth radiative heat flux profile and it is smoother with larger energy bundles. The results from the analytical discrete ordinates method show that the fluctuations are due to the ray effect. For the total or the mean radiative heat flux, the results from the analytical discrete ordinates method are very close to those from the reverse Monte Carlo method.

Effect of Wall Temperature Profile Inputs on Thermal Hydraulic Characteristics in Long Vertical Steam Generator Tube

Flow boiling phenomenon in long vertical tubes at high pressure is of great importance in nuclear and thermal power plants. These tubes are associated with several complexities such as flow instabilities, flow-induced vibrations, pressure drop, dry out etc. which may lead to tube fatigue/damage (responsible for severe plant accident and safety issues). Therefore, precise modeling of complete flow boiling phenomenon (single phase liquid to single phase vapor including two-phase flow boiling region) is necessary to design boiler tube and to avoid complexities. Most of the work carried out in literature mostly deals with modeling of particular heat transfer region of the tube. The present work, effect of wall temperature profile inputs on the thermal hydraulic characteristics and pressure drop in 23 m long steam generator (SG) tube at 172 bar pressure has been studied. Wall temperature profile (TP) is given as input by two different ways. The TP-1 is obtained from DESOPT one-dimensional computer code. Linearly increasing TP-2 is given based on shell side bulk fluid temperatures. In our recent article, a new methodology for modeling of complete flow boiling of long vertical tube has been developed, the vertical tube is divided into four sections based on flow patterns (which are decided in terms of vapor fraction value) to model the complete flow boiling process. Simulations were carried out at 20 % and 60 % designed heat duties. The heat transfer coefficient and vapor fraction results with TP-1 shows shift in the peak in positive direction as that of TP-2. Also, TP-2 shows extra small peak in axial heat flux and heat transfer coefficient distribution profile. The magnitude of predicted pressure drop for both the temperature profiles is comparable. Overall, axial distribution profiles of thermal hydraulics parameters such as vapor fraction, heat transfer coefficient etc. showed almost same trend for both the temperature profile inputs.

Role of electric currents for the SOL and divertor target heat fluxes in ASDEX Upgrade

In divertor tokamaks electric currents flowing in the Scrape-Off Layer (SOL) are a frequently observed and well known feature. However, the convective heat flux carried by these currents is often assumed to be small compared to the total parallel heat flux. In this paper it is shown that in ASDEX Upgrade the electric current, which was measured by Langmuir probes at the outer target, can be several times larger than the ion saturation current in low density L- and H-mode discharges. Therefore they have to be taken into account when calculating the target heat flux from the Langmuir probe data. Moreover, a detailed analysis reveals that for low density L- and H-mode discharges the heat flux profile is mainly determined by the current profile. By applying a 1D heat flux transport model it is demonstrated that the electric current can carry a large fraction (> 50 %) of the electron heat flux along the SOL convectively. Thus a Spitzer-Härm approach, where it is assumed that heat is transported only conductively, might not be valid in the investigated regime.

Convective heat transfer of molten salt-based nanofluid in a receiver tube with non-uniform heat flux

To tackle thermal challenges of solar receiver tubes due to the non-uniform radiation heat flux, the heat transfer performance of molten salt-based nanofluid was numerically investigated. Parameters influenced on the thermal performance of the receiver tube and molten salt with or without Al2O3 nanoparticles were investigated, including particle concentrations, inlet velocities, and heat flux profiles. The simulation results showed that all nanofluid performed better heat transfer performance than pure molten salt under both cosine and Gaussian-cosine heat flux boundaries. The 0.063% nanofluid maximally enhanced the heat transfer coefficient by 7.29% and Nusselt number by 6.90% under cosine heat flux boundary, and 7.25% and 6.85% under Gaussian-cosine heat flux boundary. The temperature distributions of the tube wall surfaces and the heat transfer fluid were highly non-uniform and related to heat flux boundaries. The maximum temperature of the outer and inner surfaces could be reduced by nanofluid and the highest drop was achieved by the 0.063% nanofluid, which will protect the solar receiver and prohibit the decomposition of molten salt. According to the analysis of parameters, the specific heat capacity contributed to most of the change in heat transfer performance when the mass fraction of nanoparticles was smaller than 0.125%, while the thermal conductivity became an influencing factor as the mass fraction grew. The Gnielinski correlation was found to guide for designing molten salt-based nanofluid solar receivers exposed to non-uniform radiation heat flux, after comparing with simulation results. This work could be useful as a reference to the application of molten salt-based nanofluid in the absorber tube.

Effect of Al<sub>2</sub>O<sub>3</sub> Nanoparticles and Cylindrical Pins on Natural Convection Heat Transfer in a C-Shaped Enclosure

A numerical study has been conducted to investigate the transport mechanism of natural convection in a C-shaped enclosure filled with water-Al2O3 nanofluid for various pertinent parameters. The effects of the volume fraction of the Al2O3 nanoparticles, Rayleigh number, and radius of inserted cylindrical pins on the temperature, velocity, heat flux profiles and average Nusselt number have been investigated. General correlations for the effective thermal conductivity and viscosity of nanofluids are used for this analysis. The governing mass, momentum and energy equations are solved numerically with the finite volume method using the SIMPLER algorithm. The results show that addition of nanoparticle improves the heat transfer performance. Insertion of cylindrical pins of lower radius increases the average Nusselt number irrespective of Rayleigh number. But anomaly has been observed while pins of higher radius are inserted due to enormous disturbance in the fluid.

Heat Flux Analysis From IR Imaging on Proto-MPEX

The Prototype Material Plasma Exposure eXperiment (Proto-MPEX) is a linear device used to develop the source and heating concept for MPEX, an experiment to study plasma-material interactions for future fusion reactors. This article will highlight recent analysis and results on Proto-MPEX using an infrared (IR) camera, a key tool for imaging heat fluxes measured at the material target. The target heat fluxes are crucial to understanding the source and heating concepts. The recent analysis includes the application of homography and 3-D finite-element methods to provide between-shot measurements of the 2-D target heat flux profile. The IR camera inferred heat flux is shown to correlate with Langmuir probe inferred heat fluxes for a range of parameters in helicon only and helicon + electron cyclotron heated discharges. Results show both desirable central and undesirable edge heat flux for helicon source and electron heating on the target. These heat flux measurements are shown to be important for better understanding of the source and heating physics.

Preliminary results from HEDGEHOG REXUS project – A sounding rocket experiment on accelerations, vibrations and heat flow

During flight, a sounding rocket is subject to a unique environment - severe vibrations and substantial heat flux. In order to design payloads, precise measurement of these conditions is required. This paper presents preliminary results from HEDGEHOG REXUS Project, whose scientific goal was to characterise the thermal and dynamic environment of REXUS sounding rockets. For this purpose, two new sensors have been designed - mechanical acceleration amplifier/filter and heat flux measuring device. Both provided interesting data - vibration and heat flux profiles allowed identification of key flight phases and quantitative description of certain phenomena during flight was performed. The experiment validated the sensors and provided heating and vibration profiles. Applicability of results and conclusions for future REXUS launches is discussed in the following paper.

Aiming clusters of heliostats over solar receivers for distributing heat flux using one variable per group

Abstract The performance of solar central receivers is inherently linked to the aiming distribution/cluster of heliostats over the surface of solar receivers. A reliable methodology is necessary to maintain the lifespan of these costly devices. This research presents a method for manipulating the heliostats’ aiming within a solar field by using a group behavior that relies on a single manipulated variable. This methodology addresses the problem by accounting for the heliostat position over the field, and a reduced number of the required groups. The work relies on the adaptation of an ordinary differential equation, commonly used to model conventional control valves, to establish the mean movement of the heliostats’ aiming within the group. Afterward, these values are coupled to predefined paths that set the direction of motion for each point. It is shown that the proposed approach can promote changes in the heat flux profiles on the receiver, thereby allowing for the reduction of the peak heat fluxes about 30% of the initial value, while maintaining spillage below 15% for a spread aiming point distribution.

In-Situ Determination of Buildings’ Thermo- Physical Characteristics: Method Development, Experimentation, and Computation

In-Situ Determination of Buildings’ Thermo- Physical Characteristics: Method Development, Experimentation, and Computation

Observation of sensible and latent heat flux profiles with lidar

Abstract. We present the first measurement of the sensible heat flux (H) profile in the convective boundary layer (CBL) derived from the covariance of collocated vertical-pointing temperature rotational Raman lidar and Doppler wind lidar measurements. The uncertainties of the H measurements due to instrumental noise and limited sampling are also derived and discussed. Simultaneous measurements of the latent heat flux profile (L) and other turbulent variables were obtained with the combination of water-vapor differential absorption lidar (WVDIAL) and Doppler lidar. The case study uses a measurement example from the HOPE (HD(CP)2 Observational Prototype Experiment) campaign, which took place in western Germany in 2013 and presents a cloud-free well-developed quasi-stationary CBL. The mean boundary layer height zi was at 1230 m above ground level. The results show – as expected – positive values of H in the middle of the CBL. A maximum of (182±32) W m−2, with the second number for the noise uncertainty, is found at 0.5 zi. At about 0.7 zi, H changes sign to negative values above. The entrainment flux was (-62±27) W m−2. The mean sensible heat flux divergence in the observed part of the CBL above 0.3 zi was −0.28 W m−3, which corresponds to a warming of 0.83 K h−1. The L profile shows a slight positive mean flux divergence of 0.12 W m−3 and an entrainment flux of (214±36) W m−2. The combination of H and L profiles in combination with variance and other turbulent parameters is very valuable for the evaluation of large-eddy simulation (LES) results and the further improvement and validation of turbulence parameterization schemes.