Jonathan W. Woolley

Thermocouple Data in the Inverse Heat Conduction Problem

The presence of thermocouples inside a heat-conducting body will distort the temperature field in the body and may lead to significant bias in the temperature measurement. If temperature histories obtained from thermocouples are used in the inverse heat conduction problem (IHCP), errors are propagated into the IHCP results. The bias in the thermocouple measurements can be removed through use of appropriate detailed thermocouple models to account for the dynamics of the sensor measurement. The results of these models can be used to generate correction kernels to eliminate bias in the thermocouple reading, or can be applied as sensitivity coefficients in the IHCP directly. Three-dimensional and axisymmetric models are compared and contrasted and a simple sensitivity study is conducted to evaluate the significance of thermal property selection on the temperature correction and subsequent heat flux estimation. In this paper, a high-fidelity thermocouple model is used to account for thermocouple bias in an experiment to measure heat fluxes from solidifying aluminum to a sand mold. Correction kernels are obtained that are used to demonstrate the magnitude of the temperature measurement bias created by the thermocouples. The corrected temperatures are used in the IHCP to compute the surface heat flux. A comparison to IHCP results using uncorrected temperatures shows the impact of the bias correction on the computed heat fluxes.

Internal Flow of Rarefied Air and Heat Transfer in a Near Space Payload

In order to realize the full potential of unmanned vehicle technology in near space, a full understanding of the heat transfer phenomena in the rarefied environment of near space is necessary. In the current work, a two-dimensional model is employed with a commercial computational fluid dynamics (CFD) software package to investigate the heat transfer phenomena within a near space payload. Convection and radiation heat transfer within a square cavity are evaluated for various boundary conditions including velocity slip and temperature jump conditions.

From Experimentation to Analysis: Considerations for Determination of the Metal/Mold Interfacial Heat Transfer Coefficient via Solution of the Inverse Heat Conduction Problem

Casting solidification simulation has been established as an effective tool used to improve the efficiency of the casting design process. Knowledge of the interfacial heat transfer coefficient at the metal/mold interface of metal castings is crucial to the simulation of casting solidification. The characterization of the heat transfer from metal to mold has been the focus of many researchers. The solution of the inverse method has been used to determine the interfacial heat flux and/or the interfacial heat transfer coefficient (IHTC) and has been applied to a variety of casting techniques and geometries. While the inverse method is a legitimate technique to determine the metal/mold interfacial heat transfer coefficient, there are a number of important issues to consider before applying the method to actual castings. The present work is a discussion of practical and important issues related to various common casting techniques that must be considered when collecting temperature measurements to be used in an inverse calculation and when developing a heat transfer model of the system.Copyright

Obtaining Temperature-Dependent Thermal Properties of Investment Casting Mold

An experiment is conducted to determine the temperature dependent thermal properties (k, ρcp ) of a fused silica shell commonly used as a mold material for investment castings. The mold is constructed by building up alternating layers of binder and silica. Different binder and silica are used for the inner layer, resulting in a thin region with different thermal properties than the rest of the shell. A search algorithm based on the simplex method is used to determine the thermal properties of both kinds of layers by finding the minimum of the error between measured and computed temperatures. Two approaches are used to find the thermal conductivity: steady state and dynamic.Copyright

Temperature and heat flux errors in thin film thermometry

Thin platinum resistance thermometers (herein called thin film sensors) are often used in applications where rapid measurements of surface temperature are required. These gauges are typically vapour-deposited onto a non-conducting substrate surface and electrically connected with small wires through access holes to the surface. The time response of the gauge is measured in milliseconds and surface temperature data obtained with this gauge are often combined with a pseudo-inverse heat conduction algorithm to provide information about the surface heat flux. However, the thermal mass of the connecting wires, though small in absolute terms, is large compared to that of the thin film, and the capacitive effect of this mass gives rise to distortions in the temperature field in the area of the gauge, resulting in a small error in the sensed temperature. This temperature error, when used in the inversion for heat flux, also results in an error. In this article, a detailed model of a particular thin film gauge is used to compute the response of the sensor to supposed heating conditions. The response of the sensor and the undisturbed surface temperature are compared to estimate the temperature error. The effect of thermal contact resistance in the model is investigated. Finally, the error in the computed heat flux is determined. A simple technique based on superposition is applied to reduce the error in the estimated heat flux.

Inverse Heat Conduction Errors From Temperature Bias in Thin Film Sensors: Effect of Contact Resistance

Thin platinum resistance thermometers (herein called thin film sensors) are often used in applications where rapid measurements of surface temperature are required. These gages are typically vapor deposited onto a non-conducting substrate surface and electrically connected with small wires through access holes to the surface. The time response of the gage is measured in milliseconds and surface temperature data obtained with this gage is often combined with a pseudo-inverse heat conduction algorithm to provide information about the surface heat flux. However, the thermal mass of the connecting wires, though small in absolute terms, is large compared to that of the thin film, and the capacitive effect of this mass gives rise to distortions in the temperature field in the area of the gage, resulting in a small error in the sensed temperature. This temperature error, when used in the inversion for heat flux, also results in an error. In this report, a detailed model of a particular thin film gage is used to compute the response of the sensor to supposed heating conditions. The effect of contact resistance between the parent material and the lead wire connections is investigated. The response of the sensor, with and without the contact resistance, and the undisturbed surface temperature are compared to estimate the temperature error. Finally, the error in the computed heat flux is determined. A simple approximate technique based on superposition is applied to account for the sensor dynamics and correct the error in the estimated heat flux.Copyright

Obtaining the Sensed Temperatures From a Detailed Model of a Welded Thermocouple

When imbedded in dissimilar materials subject to large temperature gradients, thermocouples are known to yield erroneous (bias) temperature measurements. It has been established that the bias error may be accounted for with an appropriate computational model and the measured temperatures may be corrected with an appropriate kernel function. In this work, a thermocouple with a welded bead is considered. Early two-dimensional models considered the thermocouple to be a single wire with effective thermal properties. The model in the current investigation is three-dimensional and represents the sensor as two wires, each with unique thermal properties. The welded bead is represented as a separate entity with properties distinct from those of the wires. The problem of determining what location in the three-dimensional model corresponds to the measured temperature is considered. Earlier models have considered the sensed temperature to be the temperature at the tip of the two-dimensional thermocouple or, in three-dimensional models, the temperature at the center of the volume of the welded bead. In the current work, a theory is set forth for identifying the location at which the temperature is sensed by a thermocouple. This theory is in line with traditional thermoelectric theory and is supported with experimental evaluation with thermal imaging as well as examination of thermocouples by scanning electron microscopy and energy dispersive X-ray analysis. The significance of accurate modeling of the sensed temperatures is demonstrated with a numerical experiment.Copyright

Aluminum Sand Casting Interfacial Heat Flux Estimation Based on Corrected Temperature Measurements

The estimation of the heat flux at the interface between a solidifying metal casting and mold is a frequently investigated topic. Accurate knowledge of the interfacial heat transfer can be used in solidification simulation to reduce the time and cost of the casting design process. A common and well-established approach to estimating the interfacial heat flux is the solution of the inverse heat conduction problem. Temperature measurements from thermocouples imbedded in the sand mold are used as inputs to the inverse solver. It is well-documented that imbedded thermocouples which are subjected to high temperature gradients will yield biased temperature measurements. By accounting for the sensor dynamics with an appropriate model, the measured temperatures can be corrected to mitigate the effect of the bias error in the estimation of the heat flux. In a previous work, experimentally measured temperatures were obtained from aluminum sand castings and the interfacial heat transfer was evaluated. In other works, the temperature measurement error was demonstrated and the kernel method for correcting measured temperatures was demonstrated with a numerical experiment. In this paper, the simulation of the response of a thermocouple with a three-dimensional computational model is used with the kernel method to correct the experimentally measured temperatures. The previous interfacial heat flux estimates are updated by solving the inverse heat conduction problem with the corrected temperatures as the inputs.Copyright