scholarly journals Calibration of thermopile heat flux gauges using a physically-based equation

2021 ◽  
pp. 095765092098210
Author(s):  
Oliver J Pountney ◽  
Mario Patinios ◽  
Hui Tang ◽  
Dario Luberti ◽  
Carl M Sangan ◽  
...  
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Likelihood Estimation ◽  
Calibration Method ◽  
Heat Fluxes ◽  
Theoretical Relationship ◽  
Voltage Output ◽  
Physically Based ◽  
Experimental Rig ◽  
Good Agreement

A thermopile, in which a number of thermocouple junctions are arranged on either side of a thin layer of insulation, is commonly used to determine the heat flux for steady-state measurements. Gauges using this method are available commercially and a new, generic calibration method is described here. For this purpose, an equation based on physical properties has been derived to determine the theoretical relationship between the measured voltage output of the gauge and the heat flux through it. An experimental rig has been built and used to calibrate gauges under steady-state conditions for heat fluxes between 0.5 and 8 kW/m2. The gauge temperature was controlled between 30 and 110 °C, and voltage-flux correlation – based on the theoretical relationship – was determined using maximum likelihood estimation (MLE). For tests with constant gauge temperature, there was a linear relationship between the voltage and heat flux; owing to the temperature dependency of the Seebeck constants of the thermoelectric materials, the voltage increased with increasing gauge temperature. In all cases, there was very good agreement between the measured and correlated values, and the overall uncertainty of the correlation was estimated to be less than 5% of the measured heat flux.

Inverse Determination of Temperature-Dependent Thermal Conductivity Using Steady Surface Data on Arbitrary Objects

2000 ◽  
Vol 122 (3) ◽  
pp. 450-459 ◽  
Author(s):  
T. J. Martin ◽  
G. S. Dulikravich
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Steady State ◽  
Measurement Errors ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Computational Procedure ◽  
Heat Fluxes ◽  
Computational Method ◽  
Transfer Coefficients

An inverse computational method has been developed for the nonintrusive and nondestructive evaluation of the temperature-dependence of thermal conductivity. The methodology is based on an inverse computational procedure that can be used in conjunction with an experiment. Given steady-state heat flux measurements or convection heat transfer coefficients on the surface of the specimen, in addition to a finite number of steady-state surface temperature measurements, the algorithm can predict the variation of thermal conductivity over the entire range of measured temperatures. Thus, this method requires only one temperature probe and one heat flux probe. The thermal conductivity dependence on temperature (k-T curve) can be completely arbitrary, although a priori knowledge of the general form of the k-T curve substantially improves the accuracy of the algorithm. The influence of errors of measured surface temperatures and heat fluxes on the predicted thermal conductivity has been evaluated. It was found that measurement errors of temperature up to five percent standard deviation were not magnified by this inverse procedure, while the effect of errors in measured heat fluxes were even lower. The method is applicable to two-dimensional and three-dimensional solids of arbitrary shape and size. [S0022-1481(00)01703-5]

Experimental and numerical simulation studies on heat transfer to calorimeters engulfed in diesel pool fires

2017 ◽  
Vol 35 (2) ◽  
pp. 156-176 ◽  
Author(s):  
Sudheer Siddapureddy ◽  
SV Prabhu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Surface Temperature ◽  
Heat Fluxes ◽  
Numerical Code ◽  
Pool Fires ◽  
Steel Pipes ◽  
Adiabatic Surface ◽  
In Fire ◽  
Good Agreement

Characterization of heat transfer to calorimeters engulfed in pool fires is extremely important. To estimate the heat flux to the calorimeters, experiments are performed with horizontal stainless steel 304L pipes engulfed in diesel pool fires. The concept of adiabatic surface temperature is applied to predict the incident heat flux to horizontally oriented calorimeters engulfed in diesel pool fires. Plate thermometers are used to measure the adiabatic surface temperature for diesel pool fires. The estimated subsurface temperatures inside the steel pipes using the adiabatic surface temperature concept and the measured temperatures are in good agreement. Adiabatic surface temperature is also computed from fire simulations. The incident heat fluxes to the steel pipes engulfed in fire predicted from the simulations are found to be in good agreement with the experiments. The fire numerical code is validated against the 1 m pool fire experimental results of centerline temperature distribution and irradiances away from fire. A correlation is provided for the estimation of adiabatic surface temperature for large diesel pool fires. These results would provide an effective way for thermal test simulations.

Heat Transfer Predictions Using Accommodation Coefficients for a Dense Gas in a Micro/Nano-Channel

2008 ◽  
Author(s):  
S. V. Nedea ◽  
A. J. Markvoort ◽  
P. Spijker ◽  
A. A. van Steenhoven
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Md Simulations ◽  
Heat Fluxes ◽  
Dense Gas ◽  
Nano Channel ◽  
Accommodation Coefficients ◽  
Gas Interactions ◽  
Wall Interactions ◽  
Good Agreement

The influence of gas-gas and gas-wall interactions on the heat flux predictions for a dense gas confined between two parallel walls of a micro/nano-channel is realized using combined Monte Carlo (MC) and Molecular Dynamics (MD) techniques. The accommodation coefficients are computed from explicit MD simulations. These MD coefficients are then used as effective accommodation coefficients in Maxwell-like boundary conditions in MC simulations. We find that heat flux predictions from MC based on these coefficients compare good with the results of explicit simulations except the case when there are hydrophobic gas-wall/gas-gas interactions. For this case an artificial wall was introduced in order to measure these MD accommodation coefficients at this artificial border. Good agreement is found then for both hydrophilic and hydrophobic gas-wall interactions and we show this by confronting the heat fluxes from explicit MD simulations with the the MC heat flux predictions for all the generic accommodation coefficients.

A Revised Methodology to Assess In-Vessel Retention Strategy for High-Power Reactors

2018 ◽  
Author(s):  
F. Fichot ◽  
L. Carénini ◽  
W. Villanueva ◽  
S. Bechta
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
High Power ◽  
Molten Pool ◽  
Metal Layer ◽  
Heat Fluxes ◽  
Standard Approach ◽  
Primary Circuit ◽  
Focusing Effect ◽  
Safety Margins

The In-Vessel Retention (IVR) strategy for Light Water Reactors (LWR) intends to stabilize and isolate corium and fission products in the reactor pressure vessel and in the primary circuit. This type of Severe Accident Management (SAM) strategy has already been incorporated in the design and SAM guidances (SAMGs) of several operating small and medium capacity LWRs (reactors below 500 MWe, e.g. VVER440) and is part of the SAMG strategies for some Gen III+ PWRs of higher power such as the AP1000 or the APR1400. However, the demonstration of IVR feasibility for high power reactors requires using less conservative models as the safety margins are reduced. In Europe, the IVMR project aims at providing new experimental data and a harmonized methodology for IVR. A synthesis of the methodology applied to demonstrate the efficiency of IVR strategy for VVER-440 in Europe (Finland, Slovakia, Hungary and Czech Republic) was made. It showed very consistent results, following quite comparable methodologies. The main weakness was identified in the evaluation of the heat flux that could be reached in transient situations, e.g. under the “3-layers” configuration, where the “focusing effect” may cause higher heat fluxes than in steady-state (due to transient “thin” metal layer on top). Analyses of various designs of reactors with a power between 900 and 1300 MWe were also made. Different models for the description of the molten pool were used: homogeneous, stratified with fixed configuration, stratified with evolving configuration. The last type of model provides the highest heat fluxes (above 3 W/m2) whereas the first type provides the lowest heat fluxes (around 500 kW/m2) but this model is not realistic due to the immiscibility of molten steel with oxide melt. Obviously, there is a need to reach a consensus about best estimate practices for IVR assessment to be used in the major codes used for safety analysis, such as ASTEC, MELCOR, SOCRAT, MAAP, ATHLET-CD, SCDAP/RELAP, etc. Despite the model discrepancies, and leaving aside the unrealistic case of homogeneous pool, the average calculated heat fluxes can reach, in many cases, values which are well above 1 MW/m2. This could reduce the residual thickness of the vessel considerably and threaten its strength and integrity. Therefore, it is clear that the safety demonstration of IVR in high power reactors requires a more careful evaluation of the situations which can lead to formation of either a very thin top metal layer provoking the focusing effect or significantly overheated metal, e.g. after oxide and metal layer inversion. Both situations are illustrated in this paper. The demonstration also requires an accurate thermo-mechanical analysis of the ablated vessel. The standard approach based on “yield stress” (plastic behaviour) is compared with more detailed calculations made on realistic profiles of ablated vessels. The validity of the standard approach is discussed. The current approach followed by many experts for IVR is a compromise between a deterministic analysis using the significant knowledge gained during the last two decades and a probabilistic analysis to take into account large uncertainties due to the lack of data for some physical phenomena, e.g. associated with molten pool transient behaviour, and due to excessive simplifications of models. A harmonization of the positions of safety authorities on the IVR strategy is necessary to allow decision making based on shared scientific knowledge. Some elements that might help to reach such harmonization are proposed in this paper, with a preliminary revision of the methodology that could be used to address the IVR issue. In the proposed revised methodology, the safety criterion is not based on a comparison of the heat flux and the Critical Heat Flux (CHF) profiles as in the current approaches but on the minimum vessel thickness reached after ablation and the maximum pressure load that is applied to the vessel during the transient. The main advantage of this revised criterion is in consideration of both steady-state and transient loads on the RPV. Another advantage is that this criterion is more straightforward to be used in a deterministic approach.

Two-Phase Flow Control of Electronics Cooling With Pseudo-CPUs in Parallel Flow Circuits: Dynamic Modeling and Experimental Evaluation

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Nicolas Lamaison ◽  
Jackson Braz Marcinichen ◽  
John Richard Thome
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Flow Control ◽  
Parallel Flow ◽  
Heat Fluxes ◽  
Vapor Quality ◽  
Two Phase ◽  
Cooling Cycle ◽  
Chip Temperature ◽  
Test Loop

On-chip two-phase cooling of parallel pseudo-CPUs integrated into a liquid pumped cooling cycle is modeled and experimentally verified versus a prototype test loop. The system's dynamic operation is studied since the heat dissipated by microprocessors is continuously changing during their operation and critical heat flux (CHF) conditions in the microevaporator must be avoided by flow control of the pump speed during heat load disturbances. The purpose here is to cool down multiple microprocessors in parallel and their auxiliary electronics (memories, dc/dc converters, etc.) to emulate datacenter servers with multiple CPUs. The dynamic simulation code was benchmarked using the test results obtained in an experimental facility consisting of a liquid pumped cooling cycle assembled in a test loop with two parallel microevaporators, which were evaluated under steady-state and transient conditions of balanced and unbalanced heat fluxes on the two pseudochips. The errors in the model's predictions of mean chip temperature and mixed exit vapor quality at steady state remained within ±10%. Transient comparisons showed that the trends and the time constants were satisfactorily respected. A case study considering four microprocessors cooled in parallel flow was then simulated for different levels of heat flux in the microprocessors (40, 30, 20, and 10 W cm−2), which showed the robustness of the predictive-corrective solver used. For a desired mixed vapor exit quality of 30%, at an inlet pressure and subcooling of 1600 kPa and 3 K, the resulting distribution of mass flow rate in the microevaporators was, respectively, 2.6, 2.9, 4.2, and 6.4 kg h−1 (mass fluxes of 47, 53, 76 and 116 kg m−2 s−1) and yielded approximately uniform chip temperatures (maximum variation of 2.6, 2, 1.7, and 0.7 K). The vapor quality and maximum chip temperature remained below the critical limits during both transient and steady-state regimes.

Dryout Heat Flux During Penetration of Water Into Solidifying Rock

2006 ◽  
Vol 128 (8) ◽  
pp. 847-850 ◽  
Author(s):  
Michael Epstein
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Steady State ◽  
Nuclear Reactor ◽  
Change Theory ◽  
Reactor Core ◽  
Core Material ◽  
One Dimensional ◽  
Nuclear Reactor Core ◽  
Good Agreement

A model for the dryout heat flux during penetration of water into solidifying rock is developed by combining steady-state one-dimensional phase change theory with available semiempirical equations for (i) the dryout heat flux in a porous medium and (ii) the permeability of hot rock cooled by water. The model is in good agreement with measurements made during the pouring of water onto molten magma. The implication of the model with respect to stabilizing molten-nuclear-reactor-core material by flooding from above is discussed.

Confirmation of Gambill-Greene Straight-Flow Burnout Heat Flux Equation at Higher Flow Velocity

1964 ◽  
Vol 86 (2) ◽  
pp. 297-298 ◽  
Author(s):  
J. Mayersak ◽  
S. D. Raezer ◽  
E. A. Bunt
Keyword(s):  
Heat Flux ◽  
Ohmic Heating ◽  
Steel Tube ◽  
Heat Fluxes ◽  
Stainless Steel Tube ◽  
Plasma Arc ◽  
Linear Flow ◽  
Copper Electrodes ◽  
Straight Flow ◽  
Good Agreement

A test of the validity in a higher flow range of the Gunther equation (as modified by Gambill and Greene) for predicting burnout heat flux in linear flow was required during the development of copper electrodes for plasma arc heaters. An experiment employing ohmic heating of a stainless steel tube yielded a burnout value in good agreement with that predicted in the range of heat fluxes close to the maximum previously recorded.

Heat Transfer Evaluation on Curved Boundaries in Thermal Lattice Boltzmann Equation Method

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Like Li ◽  
Renwei Mei ◽  
James F. Klausner
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Steady State ◽  
Surface Area ◽  
Transient Heat Conduction ◽  
Heat Fluxes ◽  
Effective Surface ◽  
Curved Boundaries ◽  
Evaluation Scheme ◽  
Thermal Lattice Boltzmann

An efficient and accurate approach for heat transfer evaluation on curved boundaries is proposed in the thermal lattice Boltzmann equation (TLBE) method. The boundary heat fluxes in the discrete velocity directions of the TLBE model are obtained using the given thermal boundary condition and the temperature distribution functions at the lattice nodes close to the boundary. Integration of the discrete boundary heat fluxes with effective surface areas gives the heat flow rate across the boundary. For lattice models with square or cubic structures and uniform lattice spacing the effective surface area is constant for each discrete heat flux, thus the heat flux integration becomes a summation of all the discrete heat fluxes with constant effective surface area. The proposed heat transfer evaluation scheme does not require a determination of the normal heat flux component or a surface area approximation on the boundary; thus, it is very efficient in curved-boundary simulations. Several numerical tests are conducted to validate the applicability and accuracy of the proposed heat transfer evaluation scheme, including: (i) two-dimensional (2D) steady-state thermal flow in a channel, (ii) one-dimensional (1D) transient heat conduction in an inclined semi-infinite solid, (iii) 2D transient heat conduction inside a circle, (iv) three-dimensional (3D) steady-state thermal flow in a circular pipe, and (v) 2D steady-state natural convection in a square enclosure with a circular cylinder at the center. Comparison between numerical results and analytical solutions in tests (i)–(iv) shows that the heat transfer is second-order accurate for straight boundaries perpendicular to one of the discrete lattice velocity vectors, and first-order accurate for curved boundaries due to the irregularly distributed lattice fractions intersected by the curved boundary. For test (v), the computed surface-averaged Nusselt numbers agree well with published results.

Effect of Insertion of a Heat Flux Gage Into a High Temperature Cylindrical Blackbody Cavity on the Gage

2007 ◽  
Author(s):  
Amanie N. Abdelmessih ◽  
Thomas J. Horn
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Electrical Current ◽  
High Heat ◽  
Heat Fluxes ◽  
High Heat Flux ◽  
Calibration System ◽  
Turbine Engine ◽  
State Models ◽  
Transient Models

Detailed transient thermal models have been developed to simulate a heat flux gage calibration process capable of generating high heat flux levels. These heat flux levels are of interest to the reciprocating and gas turbine engine industries as well as the aerospace industry. The transient models are based on existing, experimentally validated steady state models of a cylindrical blackbody calibration system. The steady state models were modified to include insertion of a heat flux gage into the hot zone of the calibration system, time-varying electrical current that passes through the resistance heated blackbody, and the resulting heating of the heat flux gage. Heat fluxes computed using detailed transient models were compared to experimental measurements. The calculated and measured transient heat fluxes agreed to within 2 percent, indicating that the models had captured the physical phenomena in the transient calibration. The predicted and measured transient heat fluxes were also compared for two different blackbody configurations. The effect of convection on the blackbody extension was evaluated and found to be a minor factor.

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