Schmidt-Boelter Heat Flux Gage Sensitivity Coefficients in Radiative and Convective Environments

2011 ◽  
Author(s):  
James T. Nakos ◽  
Alexander L. Brown
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat ◽  
Radiative Heat ◽  
Sensitivity Coefficient ◽  
Calibration Standard ◽  
Convective Heat Flux ◽  
Sensitivity Coefficients ◽  
Theoretical Sensitivity ◽  
Flux Calibration

Commercial Schmidt-Boelter heat flux gages are always calibrated by using a radiative heat flux source where convection is minimized. This is because one can establish a reliable link to a National Institute of Standards and Technology (NIST) calibration standard. To the authors’ knowledge, no NIST traceable link exists for convective heat flux calibration. When heat flux gages are used in typical applications, convection is often not negligible. It has been common practice to assume that the sensitivity coefficient supplied by the manufacturer also applies for convective environments. This assumption is believed to be incorrect. If incorrect, this would result in uncertainties larger than typically reported (e.g., ±3%). This paper analyzes the heat transfer from an idealized Schmidt-Boelter heat flux gage. The analysis shows that the theoretical sensitivity coefficients in purely radiative and convective environments are not the same and, in fact, differ by the emissivity of the gage surface. The implication of this difference is that the accuracy specification supplied by the manufacturer (typically ± 3%) is not correct for measurement applications where convection is not negligible.

Unsteady Heat Transfer Around Low Aspect Ratio Cylinders in an Array

2016 ◽  
Author(s):  
Shawn Siroka ◽  
Melissa Shallcross ◽  
Stephen Lynch
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Convective Heat Flux ◽  
Pin Fin ◽  
Low Aspect Ratio ◽  
Minimum Heat

Cylindrical pins, often called pin fins, are used to create turbulence and promote convective heat transfer within many devices, ranging from computer heat sinks to the trailing edge of jet engine turbine blades. Previous experiments have measured the time-averaged heat transfer over a single pin as well as the flow fields around the pin. However, in this study, focus is placed on the instantaneous heat flux around the centerline of a low aspect-ratio pin within an array. Time-mean and unsteady convective heat flux are measured around the circumference of an isothermal heated test pin via a microsensor located at the surface. The pin is positioned at various locations within a staggered array in a large-scale wind tunnel. Reynolds numbers from 3,000 to 50,000, based on pin diameter and maximum velocity between pins, are tested with a streamwise spacing of 1.73 diameters between rows, a spanwise spacing of 2 diameters, and a pin height of 1 diameter. The time-averaged and standard deviation of convective heat flux around the pin is higher over most of the pin surface for pins in downstream row positions of an array relative to the first row pin, except in the wake which has similar levels for all rows. For a given pin position in the array, as the Reynolds number increases, the point of minimum heat transfer moves circumferentially upstream on the pin fin, corresponding to earlier transition of the pin boundary layer. Also, for a given Reynolds number, the minimum heat transfer point on the pin circumference moves upstream for pins further into the array, due to the high turbulence levels within the array which cause early transition. For a single pin row with no downstream pins, heat transfer fluctuations are very high on the backside of the pin due to the significant unsteadiness in the pin wake, but heat transfer fluctuations are suppressed for a pin with downstream rows due to the confining effects of the close spacing. The results from this study can be used to design pin-fin arrays that take advantage of unsteadiness and increase overall convective heat transfer for various industry components.

Engine-Scalable Rotor Casing Convective Heat Flux Evaluation Using Inverse Heat Transfer Methods

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
David Gonzalez Cuadrado ◽  
Francisco Lozano ◽  
Valeria Andreoli ◽  
Guillermo Paniagua
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Green’S Function ◽  
Convective Heat ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Filter Method ◽  
Convective Heat Flux ◽  
Inverse Heat Transfer

In this paper, we propose a two-step methodology to evaluate the convective heat flux along the rotor casing using an engine-scalable approach based on discrete Green's functions . The first step consists in the use of an inverse heat transfer technique to retrieve the heat flux distribution on the shroud inner wall by measuring the temperature of the outside wall; the second step is the calculation of the convective heat flux at engine conditions, using the experimental heat flux and the Green functions engine-scalable technique. Inverse methodologies allow the determination of boundary conditions; in this case, the inner casing surface heat flux, based on measurements from outside of the system, which prevents aerothermal distortion caused by routing the instrumentation into the test article. The heat flux, retrieved from the inverse heat transfer methodology, is related to the rotor tip gap. Therefore, for a given geometry and tip gap, the pressure and temperature can also be retrieved. In this work, the digital filter method is applied in order to take advantage of the response of the temperature to heat flux pulses. The discrete Green's function approach employs a matrix to relate an arbitrary temperature distribution to a series of pulses of heat flux. In this procedure, the terms of the Green's function matrix are evaluated with the output of the inverse heat transfer method. Given that key dimensionless numbers are conserved, the Green's functions matrix can be extrapolated to engine-like conditions. A validation of the methodology is performed by imposing different arbitrary heat flux distributions, to finally demonstrate the scalability of the Green's function method to engine conditions. A detailed uncertainty analysis of the two-step routine is included based on the value of the pulse of heat flux, the temperature measurement uncertainty, the thermal properties of the material, and the physical properties of the rotor casing.

Understanding the Convection Heat-Transfer Mechanism in the Steam-Assisted-Gravity-Drainage Process

SPE Journal ◽  
2013 ◽  
Vol 18 (06) ◽  
pp. 1202-1216 ◽  
Author(s):  
Mazda Irani ◽  
Ian Gates
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat ◽  
Gravity Drainage ◽  
Heat Transfer Mechanism ◽  
Oil Sand ◽  
Convective Flux ◽  
Convective Heat Flux ◽  
Steam Chamber ◽  
Steam Assisted Gravity Drainage

Summary Steam-assisted gravity drainage (SAGD) is the preferred method to extract bitumen from Athabasca oil-sand reservoirs in western Canada. In SAGD, steam, injected outward from a horizontal injection well, loses its latent heat when it contacts the cold bitumen at the edge of a steam chamber. Consequently, the viscosity of the bitumen falls several orders of magnitude, enabling it to flow under gravity toward a horizontal production well directly below to the injection well. It is commonly believed that conduction is the dominant heat-transfer mechanism at the edge of the chamber. Heat transfer by convection is not considered in classic SAGD mathematical models such as the one derived by Butler. Researchers such as Butler and Stephens (1981), Reis (1992), Akin (2005), Liang (2005), Nukhaev et al. (2006), and Azad and Chalaturnyk (2010) considered the conduction from steam to cold reservoir to be the only heat-transfer component. Farouq-Ali (1997), Edmunds (1999a, b), Ito and Suzuki (1996, 1999), Ito et al. (1998), Sharma and Gates (2011), and Irani and Ghannadi (2013) questioned the assumption that thermal conduction dominates heat transfer at the edge of a SAGD chamber. Sharma and Gates (2011) and Irani and Ghannadi (2013) studied convective flux from condensate flow at the edge of an SAGD steam chamber. Irani and Ghannadi (2013) derived a new formulation that solves the energy balance and pressure-driven condensate flow normal to the steam-chamber interface into the cold bitumen reservoir and concluded that the assumption of conduction-dominated heat transfer is valid; however, all previous analyses do not include convective heat transfer arising from draining bitumen and condensate. Although a few researchers have studied convective flux from condensate flow at the edge of an SAGD steam chamber (e.g., Sharma and Gates 2011; Irani and Ghannadi 2013), there is a lack of understanding of bitumen and condensate drainage parallel to the edge of the chamber and of its effect on transverse heat transfer into the oil sand beyond the chamber. In this study, the relative roles of convective heat flux both parallel and normal to the edge of a steam chamber are examined. The results suggest that the convective heat flux associated with flow parallel to the chamber edge is minor compared with that normal to the edge.

Separation of Radiative and Convective Wall Heat Fluxes Using Thermal Infrared Measurements Applied to Flame Impingement

2015 ◽  
Author(s):  
David Gomez-Ramirez ◽  
Srinath V. Ekkad ◽  
Brian Y. Lattimer ◽  
Hee-Koo Moon ◽  
Yong Kim ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
High Temperature ◽  
Spatial Resolution ◽  
Convective Heat ◽  
Radiation Effects ◽  
Radiative Heat ◽  
Target Surface ◽  
Heat Fluxes ◽  
Small Contribution

Flame impingement is critical for the processing and energy industries. The high heat transfer rates obtained with impinging flames are relevant in metal flame cutting, welding, and brazing; in fire research to understand the effects of flames on the structures of buildings; and in the design of high temperature combustion systems. Most of the studies on flame impingement are limited to surfaces perpendicular to the flame, and measurements are often performed using heat flux sensors (such as Schmidt-Boelter heat flux transducers) at discrete locations along the target surface. The use of in-situ probes provides high accuracy but heavily limits the spatial resolution of the measurement. Moreover, flame radiation effects are often neglected, due to the small contribution in non-luminous flames, and the entire heat flux to the target is assumed to be due to convection. Depending on the character of the flame and the impingement surface, local radiative heat transfer can be significant, and the contribution of radiation effects has not been fully quantified. This study presents a novel non-intrusive method with high spatial resolution to simultaneously determine the convective and radiative heat fluxes at a wall interacting with a flame or other high temperature environment. Two initial proof of concept experiments were conducted to evaluate the viability of the technique: one consisting of a flame impinging normal to a target and another with a flame parallel to the target surface. Application of the methodology to the former case yielded a stagnation convective heat flux in the order of 106kWm−2 that decreased radially away from the stagnation point. The radiation field for the direct impingement case accounted on average for 4.4% of the overall mean heat flux. The latter experiment exemplified a case with low convective heat fluxes, which was correctly predicted by the measurement. The radiative heat fluxes were consistent between the parallel and perpendicular cases.

Engine-Scalable Rotor Casing Convective Heat Flux Evaluation Using Inverse Heat Transfer Methods

2018 ◽  
Author(s):  
David G. Cuadrado ◽  
Francisco Lozano ◽  
Valeria Andreoli ◽  
Guillermo Paniagua
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Green’S Function ◽  
Convective Heat ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Filter Method ◽  
Convective Heat Flux ◽  
Inverse Heat Transfer

In this paper, we propose a two-step methodology to evaluate the convective heat flux along the rotor casing using an engine-scalable approach based on Discrete Green’s Functions. The first step consists in the use of an inverse heat transfer technique to retrieve the heat flux distribution on the shroud inner wall by measuring the temperature of the outside wall; the second step is the calculation of the convective heat flux at engine conditions, using the experimental heat flux and the Green Functions engine-scalable technique. Inverse methodologies allow the determination of boundary conditions, in this case the inner casing surface heat flux, based on measurements from outside of the system, which prevents aerothermal distortion caused by routing the instrumentation into the test article. The heat flux, retrieved from the inverse heat transfer methodology, is related to the rotor tip gap. Therefore, for a given geometry and tip gap, the pressure and temperature can also be retrieved. In this work, the Digital Filter Method is applied in order to take advantage of the response of the temperature to heat flux pulses. The Discrete Green’s Function approach employs a matrix to relate an arbitrary temperature distribution to a series of pulses of heat flux. In the present procedure, the terms of the Green’s Function matrix are evaluated with the output of the inverse heat transfer method. Given that key dimensionless numbers are conserved, the Green’s Functions matrix can be extrapolated to engine-like conditions. A validation of the methodology is performed by imposing different arbitrary heat flux distributions, to finally demonstrate the scalability of the Green’s Function Method to engine conditions. A detailed uncertainty analysis of the two-step routine is included based on the value of the pulse of heat flux, the temperature measurement uncertainty, the thermal properties of the material and the physical properties of the rotor casing.

Effect of Variable Properties and Radiation on Convective Heat Transfer Measurements at Engine Conditions

2014 ◽  
Author(s):  
Nathan J. Greiner ◽  
Marc D. Polanka ◽  
James L. Rutledge ◽  
Andrew T. Shewhart
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Flat Plate ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Variable Properties ◽  
Radiative Component

Experiments measuring film cooling performance are often performed near room temperature over small ranges of driving temperature. For such experiments, fluid properties are nearly constant within the boundary layer and radiative heat transfer is negligible. Consequently, the heat flux to the wall is a linear function of driving temperature. Therefore, the convective heat transfer coefficient and adiabatic wall temperature can be extracted from heat flux measurements at two or more driving temperatures. For large driving temperatures, like those seen in gas turbine engines, significant property variations exist within the boundary layer. In addition, radiative heat transfer becomes sufficiently large such that it can no longer be neglected. As a result, heat flux becomes a non-linear function of driving temperature. Thus, for these high temperature cases, ambient temperature methods utilizing a linear heat flux assumption cannot be employed to characterize the convective heat transfer. The present study experimentally examines the non-linearity of heat flux for large driving temperatures flowing over a flat plate. The results are first used to validate the temperature ratio method presented in a previous study to account for variable properties within a boundary layer. This validation highlighted the need to account for the radiative component of the overall heat transfer. A method is subsequently proposed to account for the effects of both variable properties and radiation simultaneously. Finally, the method is validated with the experimental data. While this methodology was developed in a flat plate rig, it is applicable to any relevant configuration in a hot environment. The method is general and independent of the overall radiative component magnitude and direction. Overall, the technique provides a means of quantifying the impact of both variable properties and the radiative flux on the conductive heat transfer to or from a surface in a single experiment.

Design and Uncertainty Analysis of a Second-Generation Convective Heat Flux Calibration Facility

1999 ◽  
Author(s):  
David G. Holmberg ◽  
Carole A. Womeldorf ◽  
William L. Grosshandler
Keyword(s):  
Heat Flux ◽  
Convective Heat ◽  
Second Generation ◽  
Reference Value ◽  
Copper Plate ◽  
Heat Flux Sensor ◽  
Heated Plate ◽  
Convective Heat Flux ◽  
Flux Calibration ◽  
Flux Sensor

Abstract The National Institute of Standards and Technology has developed a convective heat flux facility to allow calibration of heat flux sensors. The facility consists of a small wind tunnel that produces a two-dimensional laminar boundary layer across a heated isothermal copper plate. Sensors are mounted flush in the copper plate alongside a reference to measure the heat leaving the plate. Convective calibrations up to 5 kW/m2 are possible. Sensor output is compared with the reference value, and contrasted with a standard radiation calibration. Recognizing that many sensors are used in mixed radiation and convection environments, this facility provides a unique opportunity to assess a sensor’s convective response. This report describes a second-generation heated plate and provides an analysis of the system uncertainty. Redundant references, improved sensor heating and mounting, improved reference isolation, and a minimized radiation component has reduced the combined relative expanded uncertainty of the reference to ±2.5 %. The benefits of an embedded temperature sensor in the heat flux sensor are described. The facility is available for comparative calibrations and for heat transfer studies by individual researchers.

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