Discrete Green’s Function Measurements in Internal Flows

2005 ◽  
Vol 127 (7) ◽  
pp. 692-698 ◽  
Author(s):  
Charles Booten ◽  
John K. Eaton
Keyword(s):  
Heat Transfer ◽  
Green’S Function ◽  
Green's Function ◽  
Thermal Response ◽  
Turbulent Pipe Flow ◽  
Transfer Coefficients ◽  
Flow Solver ◽  
Numerical Predictions ◽  
Discrete Green’S Function ◽  
Transfer Measurement

The discrete Green’s function (DGF) for convective heat transfer was measured in a fully developed, turbulent pipe flow to test a new technique for simple heat transfer measurement. The 10×10 inverse DGF, G−1, was measured with an element length of approximately one pipe diameter and Reynolds numbers from 30,000 to 100,000 and compared to numerical predictions using a parabolic flow solver called STANTUBE. The advantages of using the DGF method over traditional heat transfer coefficients in predicting the thermal response for flows with nonuniform thermal boundary conditions are also demonstrated.

scholarly journals Online Fatigue-Monitoring Models with Consideration of Temperature Dependent Properties and Varying Heat Transfer Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
HengLiang Zhang ◽  
Shi Liu ◽  
Danmei Xie ◽  
Yangheng Xiong ◽  
Yanzhi Yu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Thermal Stress ◽  
Transfer Coefficient ◽  
Green’S Function ◽  
Green's Function ◽  
Fluid Temperature ◽  
Transfer Coefficients ◽  
Temperature Dependent ◽  
Heat Transfer Coefficients

Thermal stress failure caused by alternating operational loads is the one of important damage mechanisms in the nuclear power plants. To evaluate the thermal stress responses, the Green’s function approach has been generally used. In this paper, a method to consider varying heat transfer coefficients when using the Green’s function method is proposed by using artificial parameter method and superposition principle. Time dependent heat transfer coefficient has been treated by using a modified fluid temperature and a constant heat transfer coefficient. Three-dimensional temperature and stress analyses reflecting entire geometry and heat transfer properties are required to obtain accurate results. An efficient and accurate method is confirmed by comparing its result with corresponding 3D finite element analysis results for a reactor pressure vessel (RPV). From the results, it is found that the temperature dependent material properties and varying heat transfer coefficients can significantly affect the peak stresses and the proposed method can reduce computational efforts with satisfactory accuracy.

The Discrete Green's Function for Convective Heat Transfer—Part 1: Definition and Physical Understanding

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
John K. Eaton
Keyword(s):  
Heat Transfer ◽  
Green’S Function ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Green's Function ◽  
Plate Boundary ◽  
Direct Calculation ◽  
Discrete Green’S Function ◽  
The Matrix ◽  
Flow Situation

Abstract The discrete Green's function (DGF) is a superposition-based descriptor of the relationship between the surface temperature and the convective heat transfer from a surface. The surface is discretized into a finite number of elements and the DGF matrix elements relate the heat transfer out of any element i to the temperature rise on every element j of the surface. For a given flow situation, the DGF is insensitive to the thermal boundary condition so it allows direct calculation of the heat transfer for any temperature distribution and noniterative solution of conjugate heat transfer problems. The diagonal elements of the matrix are determined solely by the local velocity field while the off-diagonals are determined by the spread of the thermal wake downstream of a heated element. An analytical DGF for the laminar flat-plate boundary layers is included as an example.

Conjugate Heat Transfer Analysis Using the Discrete Green's Function

2020 ◽  
Author(s):  
Davis Hoffman ◽  
John Eaton
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Green’S Function ◽  
Green's Function ◽  
Conjugate Heat Transfer ◽  
Temperature Fields ◽  
Heat Transfer Analysis ◽  
Transient Heating ◽  
Discrete Green’S Function ◽  
Linear Algebraic Equations

Abstract Conjugate heat transfer problems generally require a coupled solution of the temperature fields in the fluid and solid domains. Implementing the boundary condition at the surface of the solid using a discrete Green's function (DGF) decouples the solutions. A DGF is determined first considering only the fluid domain with prescribed thermal boundary conditions, then the temperature distribution in the solid is calculated using standard numerical methods. The only compatibility requirement is that the DGF must be specified with the same discretization as the surface of the solid. The method is demonstrated for both steady-state and transient heating of a thin plate with laminar boundary layers flowing over both sides. The resulting set of linear algebraic equations for the steady-state problem or linear ordinary differential equations for the transient problem are easily solved using conventional scientific programming packages. The method converges with nearly second-order accuracy as the discretization resolution is increased.

Discrete Green’s Function Measurements in a Single Passage Turbine Model

2005 ◽  
Vol 127 (4) ◽  
pp. 366-377 ◽  
Author(s):  
Debjit Mukerji ◽  
John K. Eaton
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Green’S Function ◽  
Green's Function ◽  
Uniform Heat Flux ◽  
Specific Flow ◽  
Full Field ◽  
Single Passage ◽  
Discrete Green’S Function ◽  
Uniform Heat

The superposition-based Discrete Green’s Function (DGF) technique provides a general representation of convective heat transfer that can capture the numerous flow and thermal complexities of the gas turbine environment and provide benchmark data for the validation of computational codes. The main advantages of the DGF technique are that the measurement apparatus is easier to fabricate than a uniform heat flux or uniform temperature surface, and that the results are applicable to any choice of discretized thermal boundary condition. Once determined for a specific flow condition, the DGF results can be used, for example, with measured surface temperature data to estimate the surface heat flux. In this study, the experimental DGF approach was extended to the suction side blade surface of a single passage model of a turbine cascade. Full-field thermal data were acquired using a steady state, liquid crystal-based imaging technique. The objective was to compute a 10×10 one-dimensional DGF matrix in a realistic turbomachinery geometry. The inverse 1-D DGF matrix, G−1, was calculated and its uncertainties estimated. The DGF-based predictions for the temperature rise and Stanton number distributions on a uniform heat flux surface were found to be in good agreement with experimental data. The G matrix obtained by a direct inversion of G−1 provided reasonable heat transfer predictions for standard thermal boundary conditions.

Discrete Green’s Function Measurements in a Serpentine Cooling Passage

2007 ◽  
Vol 129 (12) ◽  
pp. 1686-1696 ◽  
Author(s):  
Charles W. Booten ◽  
John K. Eaton
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Green’S Function ◽  
Green's Function ◽  
Turbine Blade Cooling ◽  
Discrete Green’S Function ◽  
Rib Turbulators ◽  
Four Square ◽  
Cooling Passage

The inverse discrete Green’s function (IDGF) is a heat transfer coefficient that is valid for arbitrarily complex thermal boundary conditions. It was measured using a rapid experimentation technique in a generic serpentine turbine-blade cooling passage with rib turbulators for Reynolds numbers from 15,000 to 55,000. The model was designed to adhere closely to industry design practice. There were four square cross-section passages with ribs on two opposing walls at 45deg to the main flow. The rib pitch-to-height ratio was 8.5:1 and the blockage ratio was 0.1. The IDGF was measured with an element length of one rib pitch and was used to determine Nusselt numbers that were then compared to the literature. An increase in Nusselt number over thermally fully developed pipe flow of 2.5–3.0 is common in the literature and was consistent with the results in this work. The results showed that the heat transfer coefficient in such complex passages is weakly affected by the thermal boundary condition, which simplifies measurement of this quantity.

Full 3D Conjugate Heat Transfer Simulation and Heat Transfer Coefficient Prediction for the Effusion-Cooled Wall of a Gas Turbine Combustor

2008 ◽  
Author(s):  
Andreas Jeromin ◽  
Christian Eichler ◽  
Berthold Noll ◽  
Manfred Aigner
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Gas Turbine ◽  
Conjugate Heat Transfer ◽  
Solid Wall ◽  
Heat Fluxes ◽  
Computational Domain ◽  
Transfer Coefficients ◽  
Wall Functions ◽  
Numerical Predictions

Numerical predictions of conjugate heat transfer on an effusion cooled flat plate were performed and compared to detailed experimental data. The commercial package CFX® is used as flow solver. The effusion holes in the referenced experiment had an inclination angle of 17 degrees and were distributed in a staggered array of 7 rows. The geometry and boundary conditions in the experiments were derived from modern gas turbine combustors. The computational domain contains a plenum chamber for coolant supply, a solid wall and the main flow duct. Conjugate heat transfer conditions are applied in order to couple the heat fluxes between the fluid region and the solid wall. The fluid domain contains 2.4 million nodes, the solid domain 300,000 nodes. Turbulence modeling is provided by the SST turbulence model which allows the resolution of the laminar sublayer without wall functions. The numerical predictions of velocity and temperature distributions at certain locations show significant differences to the experimental data in velocity and temperature profiles. It is assumed that this behavior is due to inappropriate modeling of turbulence especially in the effusion hole. Nonetheless, the numerically predicted heat transfer coefficients are in good agreement with the experimental data at low blowing ratios.

Analytical Prediction of Heat Transfer in Tape Generated Swirl Flow

2017 ◽  
Author(s):  
R. J. Yadav ◽  
Sandeep Kore ◽  
V. N. Riabhole
Keyword(s):  
Heat Transfer ◽  
Circular Tube ◽  
Swirl Flow ◽  
Twisted Tape ◽  
Analytical Prediction ◽  
Transfer Coefficients ◽  
Numerical Predictions ◽  
Twisted Tapes ◽  
Wide Range ◽  
Prandtl Numbers

Heat transfer and pressure drop characteristics in a circular tube with twisted tapes have been investigated experimentally and numerically using different working fluids by many researchers for wide range of Reynolds number. The swirl was generated by tape inserts of various twist ratios. The various twist ratios are considered Many researchers formed generalized correlations to predict friction factors and convective heat transfer coefficients with twisted tapes in a tube for a wide range of Reynolds numbers and Prandtl numbers. Satisfactory agreement was obtained between the present correlations and the data of others validate the proposed correlations. The experimental or numerical predictions were compared with earlier correlations revealing good agreement between them. From the literature review it is observed that most studies are mainly focused on the heat transfer enhancement using twisted tape by experimental or numerical solution. An investigation with analytical approach is rarely reported. Therefore, the main aim of the present work is to form a correlation from theoretical approach for Nusselt number for circular tube with twisted tape. Application of dimensional analysis to heat transfer in tape generated swirl flow is carried out.

Toward the Detailed Simulation of the Heat Transfer Processes in Unsaturated Porous Media

2009 ◽  
Author(s):  
F. A. Jafar ◽  
G. R. Thorpe ◽  
O¨. F. Turan
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Unsaturated Porous Media ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Transfer Processes ◽  
Numerical Predictions ◽  
Three Phase ◽  
Detailed Simulation ◽  
Horizontal Cylinders

Trickle bed chemical reactors and equipment used to cool horticultural produce usually involve three phase porous media. The fluid dynamics and heat transfer processes that occur in such equipment are generally quantified by means of empirical relationships between dimensionless groups. The research reported in this paper is motivated by the possibility of using detailed numerical simulations of the phenomena that occur in beds of irrigated porous media to obviate the need for empirical correlations. Numerical predictions are obtained using a CFD code (FLUENT) for 2-D configurations of three cylinders. Local and mean heat transfer coefficients around these non-contacting horizontal cylinders are calculated numerically. The present results compare well with those available in the literature. The numerical results provide an insight into the cooling mechanisms within beds of unsaturated porous media.

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