Pulsed Heat Flux Research Articles

Analysis of dual-phase-lag heat conduction in cylindrical system with a hybrid method

The dual-phase-lag heat transfer model is applied to investigate the transient heat conduction in an infinitely long solid cylinder for an exponentially decaying pulse boundary heat flux and for a short-pulse boundary heat flux. A hybrid application of the Laplace transform method and the control volume scheme is used to obtain the numerical solutions. Comparison between the numerical results and the analytic solution for an exponentially decaying heat flux pulse evidences the accuracy of the present numerical results. Results further show that the present numerical scheme can overcome the mathematical difficulties to analyze such problems. Effects of the thermal lag ratio τ q / τ T , the shift time τ q – τ T , the function form of heating pulse, and geometry of medium on the behavior of heat transfer are investigated.

727 ウェーブレット変換を用いたパルス加熱赤外線サーモグラフィ欠陥評価法の開発(GS-3 欠陥評価,研究発表講演)

Pulse thermography has been developed by several researchers as one of effective quantitative thermographic NDT techniques. The interest of the researchers has been focused on how to process transient temperature data after pulse heating to conduct successful identification of defect parameters such as its depth, shape and size. In this paper, a new data processing technique based on the wavelet transform is proposed. When a pulse heat flux is applied to the surface of material containing a defect inside, characteristic temperature change is observed on the surface due to the heat insulation effect of the defect. Especially defect depth influences the time profile of the transient temperature change after pulse heating. In this study, numerical analyses are conducted to obtain a calibration relation between defect parameters and coefficients calculated from wavelet transform of the transient temperature change.

Nonlinear Heat Transport in Anisotropic Divertor Targets Irradiated by Laser Pulses

AbstractIn order to derive plasma energy outflux from thermographic measurements an inverse heat conduction problem must be solved. A solution method for the time‐dependent three‐dimensional heat conduction equation is presented which improves an analytical Green's function solution by a numerical iteration method to include nonlinear effects. The measured temperature excursion of a graphite surface irradiated by laser heat flux pulses can be well described by the model calculations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect upon the core plasma radiation due to high power laser injection onto C, W and Ta test-limiters in TEXTOR

To investigate the effect due to localized high heat flux pulses onto plasma facing components, light pulses from a ruby laser (15 J in maximum energy, 0.3 ms in duration) were injected onto test-limiter (C, W, and Ta) surfaces immersed in TEXTOR edge plasmas. When the laser pulses irradiated the C limiter surface, the CVI signal from the plasma core increased slightly. In laser injection onto high- Z limiters, the increment of the quasi-continuum around 5 nm of the Ta signal was larger than that of the W signal. With the laser focusing down to 2 mm in diameter, small high- Z particles were found to be ejected from the limiter surfaces which penetrated into the plasma beyond the LCFS. However, the plasma withstood the core cooling due to the radiation loss of high- Z impurity. The amounts of impurities in the core were also estimated by a laser blow-off experiment.

NON-FOURIER HEAT CONDUCTION PHENOMENA IN POROUS MATERIAL HEATED BY MICROSECOND LASER PULSE

Experiments on porous material heated by a microsecond laser pulse and the corresponding theoretical analysis are carried out. Some non-Fourier heat conduction phenomena are observed in the experimental sample. The experimental results indicate that only if the thermal disturbance is strong enough (i.e., the pulse duration is short enough and the pulse heat flux is great enough) is it possible to observe apparent non-Fourier heat conduction phenomenon in the sample, and evident non-Fourier heat conduction phenomenon can only exist in a very limited region around the thermal disturbance position. The hyperbolic heat conduction (HHC) equation and the dual-phase lag (DPL) model are employed, respectively, to describe the non-Fourier heat condution process happening in the experimental sample, and the finite-difference method (FDM) is used to solve them numerically. The numerical solutions show that both the HHC equation and the DPL model can predict the non-Fourier heat conduction phenomenon emerging in the experimental sample qualitatively. Moreover, if τq and τT are assumed to have suitable values, the theoretical result of the DPL model is more agreeable to the experimental result.

Numerical solution of two-dimensional axisymmetric hyperbolic heat conduction

Hyperbolic heat conduction in two-dimensional axisymmetric coordinates is investigated numerically using a second order TVD scheme. Complex boundary conditions such as convection and radiation on the surfaces, are considered in the numerical modeling, and their effects on the thermal wave propagation are presented. Newton's iteration method is used to treat the nonlinear nature of radiation boundary. Numerical experiments include a continuous heat flux, a single pulsed heat flux, and a periodically pulsed heat flux at the left boundary. Numerical solution agrees well with the known analytical solution in cases where analytical solution is available.

Runaway current termination in JT-60U

Termination of the runaway electroncurrent generated during plasma disruptions is found in JT-60U duringsimulated vertical plasma displacement events where the safetyfactor at the plasma surface qs decreases. For all discharges withrunaway electron generation, the runaway current disappears for qs⩾2 withthe appearance of spikes in the magnetic fluctuations. The growth rate of thespikes in the magnetic fluctuations decreases by an order of magnitudeduring the termination of runaway current. Corresponding to the lossof runaway electrons by magnetic fluctuations, heat flux pulses aremeasured at the inner divertor plates, which indicates interaction of the wall with the runaway electrons. The halo current during runaway termination is small and increases after runawaytermination with a dominant toroidal mode of n = 1.

The Hydratherm Hybrid Drilling Systems For Cheaper Heavy Oil Recovery

Abstract Nearly 20 years of research and field testing has resulted in the development of Hydratherm ™'s hybrid drilling system, which uses ultra-high pressure (UHP) drilling fluid jets and/or a variable thermal spallation gas jet. The gas jet subjects the host rock to pulsed heat fluxes at temperatures ranging from 200 °CDATA[C to 1,100 °CDATA[C, producing thermal expansion and strength reduction of the rock-forming minerals. The UHP jets then quench, cut and erode the rock momentarily after heating. The combined mechanisms enable ultra-fast rock penetration (20 - 50 m/hr in hard rock) by means of spallation, erosion, fracturing, chipping and cutting. This technology should bring about exciting developments in heavy oil recovery, tar sand and oil shale exploitation, as well as having wider applications in mining, tunnelling and geothermal energy recovery ("HDR heat mining"). Introduction When polycrystalline rock is heated rapidly, the outer surface expands first and thin flakes or chips are shed due to tensional stress. These are known as spalls, and the process as spallation. The process has been adapted as a drilling technique, and spallation drilling systems have been in common use for over 50 years in mining and quarry work. All have used air or oxygen and fuel, with water being used for cooling purposes only. Spallation systems offer a number of advantages over rotary drilling systems, not the least of which is that penetration rates in "hard" rocks can be extremely rapid. Because the burner (drill) head does not actually contact the rock face, wear on the equipment is kept to a minimum. As the drill string does not rotate, there is no torsional stress, further reducing wear and also the tendency of holes to wander off course. Flame jet spallation burners have already been developed to the extent whereby one was used to make a 335 m (1,100 ft.) hole at Conway, New Hampshire, USA(1). However, these apparently ideal drilling systems do not work in all rock types, but only in those which are able to sustain a rapid build-up of heat without undergoing partial melting. In practical terms, this ends to be those rocks which have a high quartz content. Some rocks are almost unspallable. It is primarily this limitation which has meant that spallation systems have not been adapted for soft rock drilling work in sedimentary basins. There are also considerable practical difficulties to supplying fuel and oxygen to a burner head operating at depth. The search for a solution to these problems has resulted in the drilling systems described in this paper. It is known that low temperature spallation is more efficient than high temperature spallation in rocks with low brittle-to-ductile transformation temperatures (e.g., certain limestones)(2). Therefore, a means of controlling the thermal flux from the spallation head is essential if such rocks are to be cut. The chosen solution was to design a system that could supply water to the rock face whilst simultaneously delivering fuel and air to the burner head. This is done at ultra-high pressure so as to impose another destructive mechanism on the rock.

Pulsed interferometric calorimetry

The possibility of using semiconductor single crystals (Si, GaP, etc.) as calorimeters for pulsed heat flux measurements is discussed. The method of laser interferometric thermometry in the reflected light at a wavelength of 1.15 μm makes it possible to detect changes δθ≈2×10−5 K in the temperature of a 1-mm-thick Si single crystal. The sensitivity of a calorimeter with laser readout is sufficient for detection of the absorbed energy δE≈15 μJ/cm2 and is independent of the Si plate thickness. The method for selecting the working point in the resonance curve for achieving maximum sensitivity in detection of pulse fluxes is discussed.

An Inverse Analysis to Estimate Relaxation Parameters and Thermal Diffusivity with a Universal Heat Conduction Equation 1

This paper presents an inverse analysis for simultaneous estimation of relaxation parameters and thermal diffusivity with a universal heat conduction model by using temperature responses measured at the surface of a finite medium subjected to pulse heat fluxes. In the direct analysis, the temperature responses in a finite medium subjected to a pulse heat flux are derived by solving the universal heat conduction equation. The inverse analysis is performed by a nonlinear least-squares method for determining the two relaxation parameters and thermal diffusivity. Here, the nonlinear system of algebraic equations resulting from the sensitivity matrix is solved by the Levenberg–Marquardt iterative algorithm. The inverse analysis is utilized to estimate the relaxation parameters and the thermal diffusivity from the simulated experimental non-Fourier temperature response obtained by direct calculation.

Experimental Investigation into Melt-Layer Erosion of Plasma Facing Materials

This paper describes melt-layer erosion experiments conducted at North Carolina State University. Metallic samples are exposed to a pulsed plasma heat flux produced by an electrothermal plasma gun. Results for aluminum (2042 Al), copper (OFHC Cu), and stainless steel (316 SS) samples are discussed. The electrothermal plasma gun operated at discharge energies between 0.07 and 8.62 kJ. The sample absorbed fluence ranged between 0.09 and 1.93 MJ/m2. The net erosion depth of aluminum approached 1 mm at high energies. Following exposure the samples are bisected to reveal the thickness of material resolidified to the surface. A thickness of resolidified material on an aluminum sample in excess of 50 μm is observed.

Interfacial Stress in a Carbon-to-Metal Bond Joint under Thermal Shock Loading

The duplex bond joint consisting of a metallic substrate armored with carbon-base materials is a promising candidate configuration for application to high heat flux operations. When a bond joint is subjected to thermal loadings, significant thermal stresses may develop due to mismatch of the thermal expansion coefficients. Stress intensification occurs near the free surface edge of the interface, sometimes showing singularity. The singular stress fields are critical for understanding the loading nature of the bond interface in a joint system. In this paper, thermal stresses in the bond interface of a carbon-to-molybdenum joint element were investigated. A high heat flux (HHF) pulse was assumed as the reference load history to simulate the thermal shock condition. The thermomechanical behavior was described quantitatively in terms of the stress intensity factor. The stress solutions of the singular field computed by the theoretical approach showed a good agreement with the numerical results of the finite element analysis. The stress intensity factor of the singular stress fields near the free surface edge of the interface showed a time variation similar to that of the bulk stress. The temperature gradient induced by the transient HHF load affected the overall interfacial stress only slightly.

Loading nature of the interfacial cracks in a joint component under fusion-relevant thermal loads

One of the standard design concepts for divertor components in a fusion reactor is the bonded joint structure. Understanding the loading nature of interfacial cracks are significant for the assessment of structural integrity of divertor joint components. In this paper, the thermomechanical loading nature of interfacial cracks is discussed. A bi-material joint element consisting of the CFC/TZM system is considered. A typical fusion operation condition is simulated assuming a pulsed high heat flux loading. Stress singularities near the interfacial crack tips are characterized quantitatively in terms of the fracture mechanical parameters. The evolution of the stress intensity factors and the energy release rate during the given transient thermal load are determined. The difference in loading characteristics between the edge crack and the center crack is discussed. High heat flux cycling tests are performed on brazed CFC/TZM divertor elements in an electron beam test facility. The microstructures of the damaged interface agree with the predicted fracture modes. The loading nature and possible failure mechanisms are discussed for a fusion-relevant thermal loading.

Hyperbolic heat conduction effects caused by temporally modulated laser pulses

In non-destructive testing (NDT), the intensity of laser pulses may be temporally modulated to improve the signal-to-noise ratio of ultrasonic signals. The purpose of this work is to determine the time scale on which hyperbolic heat conduction effects are significant in ultrasonic displacements and stresses for temporally modulated laser pulses, under the assumption that the heat wave speed equals the longitudinal wave speed. A one-dimensional model with a finite train of heat flux pulses is investigated. Using the Green and Lindsay model, it is found that the critical modulation frequency in steel, above which hyperbolic heat conduction effects will become signficant, is 2.26 GHz. A dimensionless factor is given to calculate critical modulation frequencies in other isotropic materials. The signal enhancement potential of temporal intensity modulation is apparent in the numerical results.

Finite-difference approximation of the adiabatic cross-section technique in a numerical analysis of the single-side heating process of a cooled pipe with the twisted tapeinside by an external heat flux pulse

Abstract The correct finite-difference diagram for the numerical study of the dynamics of single side heating of the pipe, with the twisted tape inside it, cooled with a forced coolant flow by an external heat flux pulse is proposed as a development of the adiabatic cross-section techniaue, the principal statements of which are given in1,4. This technique is illustrated by the results of numerical calculations for thermophysical and strength parameters of a full-scale pipe, as a heat absorbing element in the collector of deviated ions which is included into the injection system of T-15 tokamak under heating by an ion beam pulse, 1.5 sec. long, as well as by that, 0.5 sec. long, with successive cooling for one second. The results of comparison between the calculations, according to the analytical model proposed in4, and those by the finite-difference diagram under single side heating of a pipe by an external heat flux pulse, 1.5 sec. long are given.

Analytical model for estimating thermophysical and strength parameters of the cooled pipe with the twisted tape under asymmetric heating by a pulse of external heat flux

Abstract The main statements of the model are formulated from the statement of a general problem on determination of a temperature field in the material of a finite length-pipe, single-side heated by an external quasi-stationary heat flux with the high power density, qm ≈10 MW/m2, and with the heat removal by a coolant from the parts of wetted pipe cross-section perimeter in the surface boiling regime, as well as under forced turbulent heat removal without phase transitions in the coolant. The obtained relationships are illustrated with the corresponding calculation for a cooper pipe, within a collector, with inserted twisted tape-heated by a pulse of critical heat flux from the directed ion beam, characteristic for the prescribed mode of operation under plasma heating by injection in T-15 tokamak.

Measurement of dynamic heat fluxes by gauges with sensitive elements on their surfaces

A new algorithm is proposed for processing the results of direct measurements, which allows one to change the requirements to the gauge construction. An automated system has been developed for the measurement of pulsed heat fluxes in the ignition and combustion of condensed substances.

Asymptotic solution of heat-conduction problems for shells of variable thickness

The temperature field in thin cylindrical shells of variable thickness on heating by a plane-parallel pulsed heat flux in the presence of convective heat transfer with the surrounding medium are approximately determined. By introducting well-founded practical constraints on the thermophysical parameters, the nonlinear problem is reduced to linear form.

Calculation of ignition parameters and the transition to combustion in a heterogeneous system

A model for ignition of a heterogeneous condensed system by a pulsed heat flux is studied. Pyrolysis of condensed components and ignition of the pyrolysis products in the gaseous phase are assumed. The dependences of various ignition characteristics on the external parameters are studied. The conditions for stable ignition of a heterogeneous system are investigated. The region of stable transition to self-sustained combustion after removal of the external heat flux is calculated.

Initiation of Melting and Evaporating of Materials under Plasma Disruption.

Abstract In a tokamak reactor, a pulsed high heat flux, whose heat flux should result in up to 2x105MW/m2, would be injected to the plasma facing components (PFCs) due to a plasma disruption. By this heat load the PFCs are melted, evaporated and cracked. In this study melting and evaporation behavior was investigated through performing the experiment with use of an electron beam to simulate heat loads due to plasma disruptions and the numerical and approximate analyses. Experimental and analytical results show that the evaporated mass increases abruptly at a curtain heat flux and time, and that the thickness of melting layer has the maximum at a curtain heat flux. From dimensionless expressions of such results the simple dimensionless correlations between the relevant values were obtained to estimate the significant characteristics such as evaporation thresholds and maximum melting layer thickness. Applying them to evaluation of the thermal resistance of materials against various heat loads due to a plasm...