Transient Heat Flux Research Articles

Inverse approach for estimating boundary properties in a transient fin problem

A solution methodology is proposed for an inverse estimation of boundary conditions from the knowledge of transient temperature data. A forward model based on prevalent time-dependent heat conduction fin equation is solved using a fully implicit finite volume method. First, the inverse model is formulated and accomplished for time-invariant heat flux at the fin base, and later extended to transient heat flux, base temperature and average heat transfer coefficient. Secondly, the Nusselt number is then replaced with Rayleigh number in the forward model to realistically estimate the base temperature, which varies with respect to time, based on in-house transient fin heat transfer experiments. This scenario further corroborates the validation of the proposed inverse approach. The experimental set-up consists of a mild steel \(250 \times 150 \times 6\, \hbox {mm}^3\) fin mounted centrally on an aluminium base \(250 \times 150 \times 8\, \hbox {mm}^3\) plate. The base is attached to an electrical heater and insulated with glass-wool to prevent heat loss to surroundings. Five calibrated K-type thermocouples are used to measure temperature along the fin. The functional form of the unknown parameters is not known beforehand; sensitivity studies are performed to determine suitability of the estimation and location of sensors for the inverse approach. Conjugate gradient method with adjoint equation is chosen as the inverse technique and the study is performed as a numerical optimization; subsequently, the estimates show satisfactory results.

Transient heat transfer characterization of impinging hot / cold jets by analytical IHCP

Unknown transient surface temperature and heat flux distribution at the impingement side (front side) is estimated from known temperature distribution at non-impingement side (back side) using analytical solution to three dimensional inverse heat conduction problem (IHCP). Back side input temperature data are obtained by running forward code in Fluent. Hot as well as cold impinging jets are characterized with the help of this solution. Laminar and turbulent jets at nozzle to plate spacing (Z/d) equal to 4 are considered. Hot gas at temperature 500 K and 3000 K is impinged on a 1 mm flat plate which considered initially at temperature 300 K in case of heating application. Whereas in cooling application, flat plate is initially assumed at temperature 673 K and isothermal air jet at 293 K is impinged on it. The temperature and heat flux estimation data by present technique is in very good agreement with the simulation data.

Theoretical analysis on the damages for tungsten plasma facing surface under superposition of steady-state and transient heat loads

In ITER and future fusion devices, the plasma facing surfaces are expected to suffer from the superposition of steady-state and transient heat loads. The extreme high transient heat fluxes cause the deterioration of material surface that increases from roughing to cracking even melting. And, the high heat flux tests on pre-heated tungsten implied that the steady-state heat load induced initial surface base temperature would have great influence on the transient heat flux induced damages. The present efforts tried to explain the mechanism of this phenomenon in view of the thermal-mechanical analysis by means of finite element simulation.The surface temperature and stress-strain distribution and evolution of a cylindrical W/Cu block under superposition of the steady-state heat loads corresponding to base temperature (20–600 °C) and transient heat fluxes (5 ms, 0–900 MW m−2) were successfully simulated. The corresponding relations between stress-strain and temperature are compared with the yield strength-temperature relation to analyze the surface event evolution during the heating and cooling phases, which showed how the base temperature influenced the transient heat flux induced damages. The analysis results theoretically identified that the pre-heating by steady-state heat load indeed influenced the transient heat flux induced damages. Typically, no any crack would be generated even under extreme high transient heat fluxes close to the melting threshold if the base temperature exceeded the ductile to brittle transition temperature, and the surface also showed deterioration from roughing to cracking while then roughing with increasing of transient heat flux under a certain base temperature, which were in good agreement with the experiments results.

A modified phase change pseudopotential lattice Boltzmann model

Amongst all the multiphase models in the lattice Boltzmann (LB) community, the pseudopotential model has been the most popular approach due to its simplicity and high-efficiency. Recently a number of liquid-vapour phase change models were also proposed based on the pseudopotential LB model. Our study finds that most of the published pseudopotential phase change models rely on an entropy-based energy equation, while the entropy-based energy equation is derived with the equation of state of ideal gas. That means this entropy-based energy equation is not completely suitable for multiphase flow which applies non-ideal equation of state for the phase separation simulation. Therefore a new phase change LB model is proposed in this work, where an improved pseudopotential multiphase model [32] and a modified energy equation which is solved in the classical fourth-order Runge-Kutta scheme are coupled in a hybrid scheme. The results show that the numerical simulation can capture the basic liquid-vapour phase change features. The D2 law for droplet evaporation is validated and the square of diameter variation is in good agreement with experimental data. Moreover, the three boiling stages (nucleate boiling, transition boiling and film boiling) are accomplished using the modified model, and the corresponding transient heat fluxes are presented.

Insights into type‐I edge localized modes and edge localized mode control from JOREK non‐linear magneto‐hydrodynamic simulations

Edge localized modes (ELMs) are repetitive instabilities driven by the large pressure gradients and current densities in the edge of H‐mode plasmas. Type‐I ELMs lead to a fast collapse of the H‐mode pedestal within several hundred microseconds to a few milliseconds. Localized transient heat fluxes to divertor targets are expected to exceed tolerable limits for ITER, requiring advanced insights into ELM physics and applicable mitigation methods. This paper describes how non‐linear magneto‐hydrodynamic (MHD) simulations can contribute to this effort. The JOREK code is introduced, which allows the study of large‐scale plasma instabilities in tokamak X‐point plasmas covering the main plasma, the scrape‐off layer, and the divertor region with its finite element grid. We review key physics relevant for type‐I ELMs and show to what extent JOREK simulations agree with experiments and help reveal the underlying mechanisms. Simulations and experimental findings are compared in many respects for type‐I ELMs in ASDEX Upgrade. The role of plasma flows and non‐linear mode coupling for the spatial and temporal structure of ELMs is emphasized, and the loss mechanisms are discussed. An overview of recent ELM‐related research using JOREK is given, including ELM crashes, ELM‐free regimes, ELM pacing by pellets and magnetic kicks, and mitigation or suppression by resonant magnetic perturbation coils (RMPs). Simulations of ELMs and ELM control methods agree in many respects with experimental observations from various tokamak experiments. On this basis, predictive simulations become more and more feasible. A brief outlook is given, showing the main priorities for further research in the field of ELM physics and further developments necessary.

On-line estimation of the tool-chip interface temperature field during turning using a sequential inverse method

It is well known that the direct measurement of temperature distribution at the tool-chip interface in a machining process is difficult to accomplish. Thus, this paper provides an on-line inverse technique to estimate the temperature field at the tool-chip interface of a turning tool, using temperatures measured at some sensor-accessible locations. A sequential Tikhonov regularization method (STRM) is proposed to determine the transient heat flux imposed at the tool-chip interface, by solving an inverse heat conduction problem (IHCP). Then, the temperature field at the tool-chip interface is computed by solving the three-dimensional non-linear thermal model, with a method combining Duhamel’s superposition theorem with the finite element method. The procedure proposed shows a superiority in on-line applications due to its high computational efficiency and independence of future measurements. A comparison of the STRM with several other inverse methods in the literature was made through numerical tests. Experimental cutting tests on Ti-6Al-4V titanium alloy were done to validate the thermal model and method. Both numerical and experimental tests show that the proposed method can provide an efficient and easy-to-implement strategy for on-line temperature field monitoring of machine tools.

Development and Benchmarking of Mechanistic Channel Deformation Models in RELAP/SCDAPSIM/MOD3.6 for CANDU Severe Accident Analysis

In different stages of postulated severe accidents in CANDU reactors, the fuel channels may experience a series of thermomechanical deformations, some of which may have significant impacts on accident progression; however, they have not been mechanistically modeled by integrated severe accident codes such as MAAP-CANDU and SCDAP/RELAP5. This paper focuses on the development and benchmarking of mechanistic models for pressure tube (PT) ballooning and sagging phenomena during the fuel channel heatup phase as well as for the sagging of fuel channel assemblies during the core disassembly phase. These models, which are based on existing phenomena in literature, are coupled with RELAP5 and/or integrated into RELAP/SCDAPSIM/MOD3.6 as new SCDAP subroutines to provide more robust treatment of the deformation phases of severe accidents.The ballooning of a PT will lead to contact with its calandria tube (CT) and occurs during conditions where the coolant pressure is moderately high. At initial contact the high contact thermal conductance and the large temperature difference between the two tubes result in a large transient heat flux that challenges the channel integrity through potential film boiling on the outer calandria surface if moderator subcooling is low. A one-dimensional ballooning and contact model (BALLON) has been developed. BALLON calculates the ballooning-driven transverse strain of PT and CT and modifies the effective conductivity of the annulus before and after contact.Pressure tube sagging is the dominant deformation mechanism at low pressures and occurs at relatively high PT temperatures. A model based on simple beam theory (SAGPT) has been developed. SAGPT calculates the longitudinal strain and the deflection of PT, and it also determines PT-to-CT sagging contact. The sagging and disassembly of the entire fuel channel assembly occur when the fuel channels are uncovered and the moderator heat sink is lost; thus, the entire PT-CT assembly sags together, possibly contacting channels at lower elevations. A model named SAGCH is created to track fuel channel assembly sagging after moderator boil off and also determines the extent of channel-to-channel contact, channel disassembly, suspended debris bed characteristics, and eventual core collapse.This paper presents detailed descriptions of the models, the coupling schemes, and their benchmark against experiments, together with an extensive review of relevant studies in the literature.

Experimental investigation of two-dimensional wall thermal loads in the near-injector region of a film-cooled combustion chamber

Heat transfer management of the combustion chamber walls of rocket engines is key to predicting their life-cycle. This study used a test apparatus to measure heat transfer on the inner wall of a film-cooled combustion chamber. Experiments on a heat-sink GH2/GO2 combustion chamber with film cooling at the injector head were carried out to measure the distribution of wall heat flux and temperature under different chamber pressures and propellant mixture ratios. Averaged heat fluxes and transient values were obtained in the tests, which found a high correlation between transient heat flux and chamber pressure. A heat flux peak appeared in the near-injector region, and its distance from the injector head increased with chamber pressure. The thermal loads decreased obviously when the mixture ratio was increased from 5.0 to 7.0. The measurement data were used to interpolate two-dimensional contours of the wall’s thermal loads. The results will be useful for the thermal-structural analysis needed to provide detailed boundary conditions in the hot-gas-side walls of rocket combustion chambers.

Transient CHF enhancement in high pressure pool boiling on rough surface

Experimental investigation of transient pool boiling heat transfer (PBHT) to saturated water from thick, non-lumped 20 mm diameter copper sample is carried at 1 bar, 5 bar and 10 bar pressure. The time constant (γ) of exponential heat supply is varied from 1 to 6. The unidirectional scratches are made on the surface to obtain wide range of surface roughness varying from Ra = 0.106 μm to Ra = 4.03 μm. The effect of surface roughness, pressure and time constant on transient critical heat flux (CHF) is extensively studied. Transient CHF enhancement for Ra = 4.03 μm when γ = 1 is found to be 98.88%, 76.55% and 53.21% at pressures P = 1 bar, P = 5 bar and P = 10 bar, respectively, however it is found to be lower by 9.38%, 21.40% and 9.73%, compared to steady state CHF enhancement for Ra = 4.03 μm, at respective pressures. The Gorenflo correlation is modified by including the additional parameter γ and it predicts the present transient HTC values with mean absolute error (MAE) of 14.91%. The CHF model is developed by considering the effect of capillary wicking in the narrow unidirectional scratches and the bubble angle. This model predicts the present transient CHF values with MAE of 11.89%.

Simulations of particle and heat fluxes in an ELMy H-mode discharge on EAST using BOUT++ code

In order to study the distribution and evolution of the transient particle and heat fluxes during edge-localized mode (ELM) bursts on the Experimental Advanced Superconducting Tokamak (EAST), the BOUT++ six-field two-fluid model is used to simulate the pedestal collapse. The profiles from the EAST H-mode discharge #56129 are used as the initial conditions. Linear analysis shows that the resistive ballooning mode and drift-Alfven wave are two dominant instabilities for the equilibrium, and play important roles in driving ELMs. The evolution of the density profile and the growing process of the heat flux at divertor targets during the burst of ELMs are reproduced. The time evolution of the poloidal structures of T e is well simulated, and the dominant mode in each stage of the ELM crash process is found. The studies show that during the nonlinear phase, the dominant mode is 5, and it changes to 0 when the nonlinear phase goes to saturation after the ELM crash. The time evolution of the radial electron heat flux, ion heat flux, and particle density flux at the outer midplane (OMP) are obtained, and the corresponding transport coefficients D r, χ ir, and χ er reach maximum around 0.3 ∼ 0.5 m2 s−1 at ΨN = 0.9. The heat fluxes at outer target plates are several times larger than that at inner target plates, which is consistent with the experimental observations. The simulated profiles of ion saturation current density (j s) at the lower outboard (LO) divertor target are compared to those of experiments by Langmuir probes. The profiles near the strike point are similar, and the peak values of j s from simulation are very close to the measurements.

Development of a novel transient calorimeter

Thermal protection has always been the key technology in hypersonic vehicles development. Accurate prediction of aerodynamic thermal environment is an important basis for thermal protection structure design and material selection. The existing transient heat flux sensors include thin film thermometer and coaxial thermocouple. Thin film gages are brittle in hot flow, which is its main disadvantage. Besides, large corrections are needed to account for the variation of substrate thermal properties with temperature. Hot flow will damage the coaxial thermocouple, hence re-machining is required between two shots. The polish process will affect the physical parameters of the junction, thus introducing measurement uncertainties. The accuracy and reliability of heat flux measurements are affected by the above uncertainties. In this paper, a novel transient calorimeter is proposed. The temperature on reverse side of the calorimeter is measured by a thin film thermometer. The principle of the calorimeter is analyzed by one-dimensional infinite heat conduction calculation. With the influences of the sensor base and heat dissipation on back substrate being taken into account, numerical calculations are carried out with 2D heat conduction model. Error factors are analyzed, and key parameters of the calorimeter are designed and optimized. Wind tunnel experiments with wedge model are carried out. Results verified its accuracy and reliability. This type of calorimeter has a strong anti-erosion ability and high signal sensitivity. In addition, the diamond sheet is a non-metallic material, which can prevent the gas charge from interfering measurements. Therefore, the novel transient calorimeter has a wide range of applications.

Wall protection strategies for DEMO plasma transients

The present DEMO breeding blanked design heat load capability is limited to ≈1 MW/m2 for steady state plasma loading, due to the specific requirements on high neutron irradiation capable materials, and high coolant temperature for efficient energy conversion. While this limit is achievable in nominal conditions in the present DEMO blanket concept designs, the greatest challenges arise from the occurrence of plasma transients. The results of simulations of a number of plasma transients are presented in this paper. 3D field-line tracing codes have been used to analyses the maximum heat flux and energy density for a specific first wall shape design, and optimize it. A scoping study has been performed with the thermal analysis code RACLETTE, using a broad range of transient input heat fluxes, on a series of high heat flux (HF) components concepts with tungsten armor, Eurofer steel or copper alloy as heat sink materials, and helium or water as coolant. The results permit the identification of the operational space of the peak HF density that can be tolerated by different plasma facing components, for the different transient models.

Stagnation point transient heat flux measurement analysis from coaxial thermocouples

ABSTRACTThe transient heat flux measurement at stagnation point is a significant solicitation at highly compressed flow field environment. In aerodynamics surface heating point of view, the estimation of stagnation heat fluxes at the tip of a blunt body is very imperative. When the blunt body is exposed to high-speed flow field environments, at the stagnation point heat transfer would be maximum. The coaxial surface junction thermocouples (CSJTs) are convenient for short duration time scale due to the fast response in the range of millisecond or less (̴0.1 ms). These robust CSJTs have the tractability of intensifying them directly on any type of surface and can be used for routine measurement in ground-based impulse amenities as a temperature measuring devices where rapid heat loads are anticipated. In this work, three different types of coaxial thermocouples K-type, E-type, and J-type have been designed and contrived. The microstructural analysis of measuring surface property has been carried out to see the surface morphology using field emission scanning electron microscopy (FESME) and chemical characterization of these CSJTs materials using energy dispersive X-ray analysis (EDXA) technique is used to verify qualitatively appraise the CSJTs materials composition. The thermal coefficient of resistance (TCR) and sensitivity (S) of each coaxial thermocouple have been determined by using oil-bath calibration technique with the linear variation of resistance corresponding to the variation of temperature and found that these coaxial thermocouples are highly sensitive and suitable for highly transient heat transfer measurements. For this purpose, these three types of CSJTs have been tested under highly compressed heated air 310 K temperature for 100 ms at pressure 6.1 bar with Mach number unity (M = 1) using compressor test rig. Numerical simulation has also been carried out with these three RTDs to satisfy the experimental parameters using Ansys Fluent 15.0 and typical transient temperature recorded. Surface heat fluxes recovered from experimental and numerical transient temperatures histories using semi-infinite heat conduction modeling having good agreement with accuracy ±3% or less. This study divulges the expertise of these handmade coaxial thermocouples for transient surface heat flux measurement for short durations at highly compressed air facilities.

Characterization of an electrothermal plasma source for fusion transient simulations

The realization of fusion energy requires materials that can withstand high heat and particle fluxes at the plasma material interface. In this work, an electrothermal (ET) plasma source has been designed as a transient heat flux source for a linear plasma material interaction device. An ET plasma source operates in the ablative arc regime driven by a DC capacitive discharge. The current channel width is defined by the 4 mm bore of a boron nitride liner. At large plasma currents, the arc impacts the liner wall, leading to high particle and heat fluxes to the liner material, which subsequently ablates and ionizes. This results in a high density plasma with a large unidirectional bulk flow out of the source exit. The pulse length for the ET source has been optimized using a pulse forming network to have durations of 1 and 2 ms. The peak currents and maximum source energies seen in this system are 1.9 kA and 1.2 kJ for the 2 ms pulse and 3.2 kA and 2.1 kJ for the 1 ms pulse, respectively. This work is a proof of the principal project to show that an ET source produces electron densities and heat fluxes comparable to those anticipated in transient events in large future magnetic confinement fusion devices. Heat flux, plasma temperature, and plasma density were determined for each shot using infrared imaging and optical spectroscopy techniques. This paper will discuss the assumptions, methods, and results of the experiments.

A New Transient High Heat Flux Convection Calibration Facility for Heat Transfer Gauges in High Enthalpy Flows

This paper presents a novel transient method for calibrating heat transfer gauges for convective wall heat flux measurements in high enthalpy flows. The new method relies on the transient heating of sensor substrates under rapid exposure to a hot flow in order to obtain the necessary reference heat flux. Compared to previous calibration facilities, the new facility is simple, inexpensive, easy to adapt for different flow configurations and sensor geometries, and quick to run across a wide range of conditions. In this paper, the design of the new calibration facility is described and the transient calibration method explained. The method is demonstrated by calibrating a Gardon gauge at convective heat transfer coefficients between 300 and 600 W/m2 K. Typical facility data and calibration results are presented in terms of voltage-heat flux sensitivity and calibration correction ratio. These results are shown to agree with theoretical estimates within the estimated calibration uncertainty.

Transient Critical Heat Flux in Vertical Small Tube

Transient Critical Heat Flux in Vertical Small Tube

Wall heat flux measurements in a GO<sub>2</sub>/GH<sub>2</sub> heat-sink combustion chamber

In order to understand heat transfer mechanisms in the combustion chamber with multi-elements injector and provide benchmark data of wall heat fluxes for the CFD code validation, experiments were carried out in a GH2/GO2 heat-sink combustion chamber. To obtain the transient heat flux in the experiments, the Levenberg-Marquardt method was modified and applied to the rocket combustion chamber based on the temperature measured by single coaxial thermocouple (Named “single-point method”). The comparison between the single-point method and the two-point method with temperatures measured in two points shows that the single-point method could be used as heat flux measurements of the heat-sink combustion chamber in engineering. Heat flux distribution was obtained in experimental conditions of different work time and chamber pressure by the modified method, feasibly and efficiently. For the transient variations of the heat flux, an inverse variation trend of heat flux to time in the cylindrical segment and the nozzle segment was observed. A typical variation of the averaged heat flux was obtained under the conditions with different chamber pressure and work time. The results of wall heat flux scaled with pressure to the power 0.8 can be uniformized for all pressure levels. The heat fluxes obtained in the cylindrical chamber and nozzle section may be applied for the life cycle prediction of rocket engines.

Surface Characterization of Cashmere Fabrics Using Optical and Transient Thermal Properties

Fine hairs on a cashmere fabric (i.e., its hairiness) generate its softness, warmth, and unique luster. To make cashmere more popular, we require value-adding elements and quality specification to develop new clothing products. In this study, a surface characterization method was examined to specify the effect of hairs on the softness, luster, and warmth of cashmere fabrics. The luster was measured using a goniospectrophotometer as the fabric was rotated. A high CIELAB L* was found for rotation angles θω around 90°, corresponding to an aligned fiber surface, but not for random fiber assemblies. The shape of the plot of L* versus θω was affected by the degree of hairiness and its direction. By measuring the surface roughness (SMD) with a surface tester, a difference in light reflection between the warp and weft directions of the fabric was observed according to the hairiness direction. Fabric surfaces with smaller values of SMD showed larger values of L*. These surface hairs and hairiness were also observed clearly as differences in the surface friction. For the transient heat flux (qmax) related to the warmth perception, hairier samples showed lower values than did less hairy samples.

Fire behaviors of flame-retardant cables part I: Decomposition, swelling and spontaneous ignition

Electrical cable is a potential ignition source and fire hazard in residential houses, nuclear power plants, aircraft, and spacecraft. In this work, a bench-scale flame-retardant cable, consisted of the outer PVC sheath, middle XLPE insulation, and inner copper core, was heated uniformly inside a novel cylindrical heating chamber. The applied heat flux was transient, which increased with time close to a parabolic function. Once heated, the outer PVC sheath swelled and shrank under multiple stages. Before ignition, the swelling behavior was found to follow the same trend as the mass-loss rate. Analysis showed that the observed spontaneous ignition was likely a result of pyrolysis gas from inner XLPE insulation piloted by the smoldering hot spot (600~700 °C) on the outer charring PVC sheath. For the first time, the spontaneous ignition time was found to linearly increase with the integral heat flux, and it was different from other ignition experiments under the transient heat flux in the literature. Moreover, the measured critical mass flux of ignition increased with the heating power, and the critical surface temperature of PVC was above 500 °C. The results of this work provide important information about the swelling and ignition behaviors of the flame-retardant cable under a real fire, and may guide the design of future fire-safety cable.

Parametric analyses of DEMO Divertor using two dimensional transient thermal hydraulic modelling

Among the options considered for cooling of the Plasma facing components of the DEMO reactor, water cooling is a conservative option because of its high heat removal capability. In this work a two-dimensional transient thermal hydraulic code is developed to support the design of the divertor for the projected DEMO reactor with water as a coolant. The mathematical model accounts for transient 2D heat conduction in the divertor section. Temperature-dependent properties are used for more accurate analysis. Correlations for single phase flow forced convection, partially developed subcooled nucleate boiling, fully developed subcooled nucleate boiling and film boiling are used to calculate the heat transfer coefficients on the channel side considering the swirl flow, wherein different correlations found in the literature are compared against each other. Correlation for the Critical Heat Flux is used to estimate its limit for a given flow conditions. This paper then investigates the results of the parametric analysis performed, whereby flow velocity, diameter of the coolant channel, thickness of the coolant pipe, thickness of the armor material, inlet temperature and operating pressure affect the behavior of the divertor under steady or transient heat fluxes. This code will help in understanding the basic parameters´ effect on the behavior of the divertor, to achieve a better design from a thermal hydraulic point of view.