scholarly journals Internal Heat Transfer Coefficient Determination in a Packed Bed From the Transient Response Due to Solid Phase Induction Heating

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
David Geb ◽  
Feng Zhou ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Internal Heat ◽  
Temperature Response ◽  
Packed Bed ◽  
Spherical Particles ◽  
Fluid Temperature ◽  
The Core ◽  
Internal Heat Transfer

Nonintrusive measurements of the internal heat transfer coefficient in the core of a randomly packed bed of uniform spherical particles are made. Under steady, fully-developed flow the spherical particles are subjected to a step-change in volumetric heat generation rate via induction heating. The fluid temperature response is measured. The internal heat transfer coefficient is determined by comparing the results of a numerical simulation based on volume averaging theory (VAT) with the experimental results. The only information needed is the basic material and geometric properties, the flow rate, and the fluid temperature response data. The computational procedure alleviates the need for solid and fluid phase temperature measurements within the porous medium. The internal heat transfer coefficient is determined in the core of a packed bed, and expressed in terms of the Nusselt number, over a Reynolds number range of 20 to 500. The Nusselt number and Reynolds number are based on the VAT scale hydraulic diameter, dh=4ɛ/S. The results compare favorably to those of other researchers and are seen to be independent of particle diameter. The success of this method, in determining the internal heat transfer coefficient in the core of a randomly packed bed of uniform spheres, suggests that it can be used to determine the internal heat transfer coefficient in other porous media.

The Measurement of Full-Surface Internal Heat Transfer Coefficients for Turbine Airfoils Using a Non-Destructive Thermal Inertia Technique

2002 ◽  
Author(s):  
Nirm V. Nirmalan ◽  
Ronald S. Bunker ◽  
Carl R. Hedlung
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
External Surface ◽  
Internal Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Turbine Airfoils ◽  
Non Destructive ◽  
Internal Heat Transfer

A new method has been developed and demonstrated for the non-destructive, quantitative assessment of internal heat transfer coefficient distributions of cooled metallic turbine airfoils. The technique employs the acquisition of full-surface external surface temperature data in response to a thermal transient induced by internal heating/cooling, in conjunction with knowledge of the part wall thickness and geometry, material properties, and internal fluid temperatures. An imaging Infrared camera system is used to record the complete time history of the external surface temperature response during a transient initiated by the introduction of a convecting fluid through the cooling circuit of the part. The transient data obtained is combined with the cooling fluid network model to provide the boundary conditions for a finite element model representing the complete part geometry. A simple 1D lumped thermal capacitance model for each local wall position is used to provide a first estimate of the internal surface heat transfer coefficient distribution. A 3D inverse transient conduction model of the part is then executed with updated internal heat transfer coefficients until convergence is reached with the experimentally measured external wall temperatures as a function of time. This new technique makes possible the accurate quantification of full-surface internal heat transfer coefficient distributions for prototype and production metallic airfoils in a totally non-destructive and non-intrusive manner. The technique is equally applicable to other material types and other cooled/heated components.

Non-Intrusive Heat Transfer Coefficient Determination in a Packed Bed of Spheres

2010 ◽  
Author(s):  
David J. Geb ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Generation ◽  
Packed Bed ◽  
Computational Procedure ◽  
Spherical Particles ◽  
Average Heat Transfer Coefficient ◽  
Heat Generation Rate ◽  
Average Heat

Non-intrusive measurements of the internal average heat transfer coefficient [1] in a randomly packed bed of spherical particles are made. It is desired to establish accurate results for this simple geometry so that the method used can then be extended to determine the heat transfer characteristics in any porous medium, such as a compact heat exchanger. Under steady, one-dimensional flow the spherical particles are subjected to a step change in volumetric heat generation rate via induction heating. The fluid temperature response is measured. The average heat transfer coefficient is determined by comparing the results of a numerical simulation based on volume averaging theory with the experimental results. More specifically, the average heat transfer coefficient is adjusted within the computational procedure until the predicted values of the fluid outlet temperature match the experimental values. The only information needed is the basic material properties, the flow rate, and the experimental data. The computational procedure alleviates the need for solid and fluid phase temperature measurements, which are difficult to make and can disturb the solid-fluid interaction. Moreover, a simple analysis allows us to proceed without knowledge of the heat generation rate, which is difficult to determine due to challenges associated with calibrating an inductively-coupled, sample specific, heat generation system. The average heat transfer coefficient was determined, and expressed in terms of the Nusselt number, over a Reynolds number range of 20–600. The results compared favorably to the work of Whitaker [2] and Kays and London [3]. The success of this method, in determining the average heat transfer coefficient in a randomly packed bed of spheres, suggests that it can be used to determine the average heat transfer coefficient in other porous media.

Cooling Optimization Theory—Part II: Optimum Internal Heat Transfer Coefficient Distribution

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Benjamin Kirollos ◽  
Thomas Povey
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Flow Rate ◽  
Wall Temperature ◽  
Internal Heat ◽  
Cooling Systems ◽  
Uniform Wall Temperature ◽  
Uniform Wall ◽  
Internal Heat Transfer

Gas turbine cooling system design is constrained by a maximum allowable wall temperature (dictated by the material, the life requirements of the component, and a given stress distribution), the desire to minimize coolant mass flow rate (requirement to minimize cycle-efficiency cost), and the requirement to achieve as close to uniform wall temperature as possible (to reduce thermal gradients, and stress). These three design requirements form the basis of an iterative design process. The relationship between the requirements has received little discussion in the literature, despite being of interest from both a theoretical and a practical viewpoint. In Part I, we show analytically that the coolant mass flow rate is minimized when the wall temperature is uniform and equal to the maximum allowable wall temperature. In this paper, we show that designs optimized for uniform wall temperature have a corresponding optimum internal heat transfer coefficient (HTC) distribution. In this paper, analytical expressions for the optimum internal HTC distribution are derived for a number of cooling systems, with and without thermal barrier coating (TBC). Most cooling systems can be modeled as a combination of these representative systems. The optimum internal HTC distribution is evaluated for a number of engine-realistic systems: long plate systems (e.g., combustors, afterburners), the suction-side (SS) of a high pressure nozzle guide vane (HPNGV), and a radial serpentine cooling passage. For some systems, a uniform wall temperature is unachievable; the coolant penalty associated with this temperature nonuniformity is estimated. A framework for predicting the optimum internal HTC for systems with any distribution of external HTC, wall properties, and film effectiveness is outlined.

Heat Transfer Coefficient for a Packed Bed of Shredded Materials

2003 ◽  
Author(s):  
Mohammad S. Saidi ◽  
Firooz Rasouli ◽  
Mohammad R. Hajaligol
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Flow Distribution ◽  
Packed Bed ◽  
Spherical Particles ◽  
Channeling Effect ◽  
Nusselt Number Correlation ◽  
Good Agreement

Heat transfer coefficient of packed beds of shredded materials such as biomass fuels at low Peclet numbers is of interest. Due to the dependence of flow distribution on particle shape, the application of the Nusselt number correlation of packed bed of spherical particles overestimates the rate of heat transfer. This discrepancy is even more pronounced due to channeling effect at low Peclet numbers. Here, based on applying a pore submodel and combining the numerical simulation and experimental results of a cylindrical packed bed, a new correlation is derived for apparent Nusselt number of the packed bed of shredded materials. The correlation is approximated by a power law formulation for Pecelt < 25. The Nusselt number calculated from this correlation is in a good agreement with other experimental data.

Cooling Optimisation Theory: Part 2 — Optimum Internal Heat Transfer Coefficient Distribution

2015 ◽  
Author(s):  
Benjamin Kirollos ◽  
Thomas Povey
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Flow Rate ◽  
Wall Temperature ◽  
Internal Heat ◽  
Cooling Systems ◽  
Uniform Wall Temperature ◽  
Uniform Wall ◽  
Internal Heat Transfer

Gas turbine cooling system design is constrained by a maximum allowable wall temperature (dictated by the material, the life requirements of the component and a given stress distribution), the desire to minimise coolant mass flow rate (requirement to minimise cycle-efficiency cost) and the requirement to achieve as close to uniform wall temperature as possible (to reduce thermal gradients, and stress). These three design requirements form the basis of an iterative design process. The relationship between the requirements has received little discussion in the literature, despite being of interest from both a theoretical and a practical viewpoint. In the companion paper, we show analytically that the coolant mass flow rate is minimised when the wall temperature is uniform and equal to the maximum allowable wall temperature. In this paper, we show that designs optimised for uniform wall temperature have a corresponding optimum internal heat transfer coefficient (HTC) distribution. In this paper, analytical expressions for the optimum internal HTC distribution are derived for a number of cooling systems, with and without thermal barrier coating. Most cooling systems can be modelled as a combination of these representative systems. The optimum internal HTC distribution is evaluated for a number of engine-realistic systems: long plate systems (e.g., combustors, afterburners), the suction-side of a high pressure nozzle guide vane, and a radial serpentine cooling passage. For some systems, a uniform wall temperature is unachievable; the coolant penalty associated with this temperature non-uniformity is estimated. A framework for predicting the optimum internal HTC for systems with any distribution of external HTC, wall properties and film effectiveness is outlined.

The Measurement of Full-Surface Internal Heat Transfer Coefficients for Turbine Airfoils Using a Nondestructive Thermal Inertia Technique

2003 ◽  
Vol 125 (1) ◽  
pp. 83-89 ◽  
Author(s):  
Nirm V. Nirmalan ◽  
Ronald S. Bunker ◽  
Carl R. Hedlund
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Surface Temperature ◽  
Transfer Coefficient ◽  
External Surface ◽  
Internal Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Turbine Airfoils ◽  
Internal Heat Transfer

A new method has been developed and demonstrated for the non-destructive, quantitative assessment of internal heat transfer coefficient distributions of cooled metallic turbine airfoils. The technique employs the acquisition of full-surface external surface temperature data in response to a thermal transient induced by internal heating/cooling, in conjunction with knowledge of the part wall thickness and geometry, material properties, and internal fluid temperatures. An imaging Infrared camera system is used to record the complete time history of the external surface temperature response during a transient initiated by the introduction of a convecting fluid through the cooling circuit of the part. The transient data obtained is combined with the cooling fluid network model to provide the boundary conditions for a finite element model representing the complete part geometry. A simple 1-D lumped thermal capacitance model for each local wall position is used to provide a first estimate of the internal surface heat transfer coefficient distribution. A 3-D inverse transient conduction model of the part is then executed with updated internal heat transfer coefficients until convergence is reached with the experimentally measured external wall temperatures as a function of time. This new technique makes possible the accurate quantification of full-surface internal heat transfer coefficient distributions for prototype and production metallic airfoils in a totally nondestructive and non-intrusive manner. The technique is equally applicable to other material types and other cooled/heated components.

Measuring Transport Coefficients in Heterogeneous and Hierarchical Heat Transfer Devices

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
David Geb ◽  
Michael Ge ◽  
Jonathan Chu ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Friction Factor ◽  
Transport Coefficients ◽  
Cross Flow ◽  
Internal Heat ◽  
Heat Sinks ◽  
Design Data ◽  
Internal Heat Transfer

Experimental determination of transport coefficients, in particular internal heat transfer coefficients, in heterogeneous and hierarchical heat transfer devices such as compact heat exchangers and high surface density heat sinks has posed a persistent challenge for designers. This study presents a unique treatment of the experimental determination of such design data. A new combined experimental and computational method for determining the internal heat transfer coefficient within a heterogeneous and hierarchical heat transfer medium is explored and results are obtained for the case of cross flow of air over staggered cylinders to provide validation of the method. Along with appropriate pressure drop measurements, these measurements allow for thermal-fluid modeling of a heat exchanger by closing the volume averaging theory (VAT)-based equations governing transport phenomena in porous media, which have been rigorously derived from the lower-scale Navier–Stokes and thermal energy equations. To experimentally obtain the internal heat transfer coefficient the solid phase is subjected to a step change in heat generation rate via induction heating, while the fluid flows through under steady flow conditions. The transient fluid phase temperature response is measured. The heat transfer coefficient is then determined by comparing the results of a numerical simulation based on the VAT model with the experimental results. The friction factor is determined through pressure drop measurements, as is usually done. With the lower-scale heat transfer coefficient and friction factor measured, the VAT-based equations governing the transport phenomena in the heat transfer device are closed and readily solved. Several configurations of staggered cylinders in cross flow were selected for this study. Results for the heat transfer coefficient and friction factor are compared to widely accepted correlations and agreement is observed, lending validation to this experimental method and analysis procedure. It is expected that a more convenient and accurate tool for experimental closure of the VAT-based equations modeling transport in heterogeneous and hierarchical media, which comes down to measuring the transport coefficients, will allow for easier modeling and subsequent optimization of high performance compact heat exchangers and heat sinks for which design data does not already exist.

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