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.

scholarly journals Numerical Simulation of Secondary Flow in Gas Turbine Disc Cavities, Including Conjugate Heat Transfer

1996 ◽  
Author(s):  
Y.-H. Ho ◽  
M. M. Athavale ◽  
J. M. Forry ◽  
R. C. Hendricks ◽  
B. M. Steinetz
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Conjugate Heat Transfer ◽  
Gas Flow ◽  
Numerical Study ◽  
Labyrinth Seal ◽  
Temperature Fields ◽  
Heat Transfer Analysis ◽  
Flow Rates ◽  
Turbine Disc

A numerical study of the flow and heat transfer in secondary flow elements of the entire inner portion of the turbine section of the Allison T-56/501D engine is presented. The flow simulation included the interstage cavities, rim seals and associated main path flows, while the energy equation also included the solid parts of the turbine disc, rotor supports, and stator supports. Solutions of the energy equations in these problems usually face the difficulty in specifications of wall thermal boundary conditions. By solving the entire turbine section this difficulty is thus removed, and realistic thermal conditions are realized on all internal walls. The simulation was performed using SCISEAL, an advanced 2D/3D CFD code for predictions of fluid flows and forces in turbomachinery seals and secondary flow elements. The mass flow rates and gas temperatures at various seal locations were compared with the design data from Allison. Computed gas flow rates and temperatures in the rim and labyrinth seal show a fair 10 good comparison with the design calculations. The conjugate heat transfer analysis indicates temperature gradients in the stationary intercavity walls, as well as the rotating turbine discs. The thermal strains in the stationary wall may lead to altered interstage labyrinth seal clearances and affect the disc cavity flows. The temperature, fields in the turbine discs also may lead to distortions that can alter the rim seal clearances. Such details of the flow and temperature fields are important in designs of the turbine sections to account for possible thermal distortions and their effects on the performance. The simulation shows that the present day CFD codes can provide the means to understand the complex flow field and thereby aid the design process.

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.

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.

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.

scholarly journals Fully Coupled Large Eddy Simulation of Conjugate Heat Transfer in a Ribbed Channel with a 0.1 Blockage Ratio

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2096
Author(s):  
Joon Ahn ◽  
Jeong Chul Song ◽  
Joon Sik Lee
Keyword(s):  
Heat Transfer ◽  
Gas Turbine ◽  
Conjugate Heat Transfer ◽  
Heat Transfer Analysis ◽  
Scale Model ◽  
Computational Domain ◽  
Blockage Ratio ◽  
Ribbed Channel ◽  
Large Eddy ◽  
Cooling Passage

Large eddy simulations are performed to analyze the conjugate heat transfer of turbulent flow in a ribbed channel with a heat-conducting solid wall. An immersed boundary method (IBM) is used to determine the effect of heat transfer in the solid region on that in the fluid region in a unitary computational domain. To satisfy the continuity of the heat flux at the solid–fluid interface, effective conductivity is introduced. By applying the IBM, it is possible to fully couple the convection on the fluid side and the conduction inside the solid and use a dynamic subgrid scale model in a Cartesian grid. The blockage ratio (e/H) is set at 0.1, which is typical for gas turbine blades. Through conjugate heat transfer analysis, it is confirmed that the heat transfer peak in front of the rib occurs because of the impinging of the reattached flow and not the influence of the thermal boundary condition. When the rib turbulator acts as a fin, its efficiency and effectiveness are predicted to be 98.9% and 8.32, respectively. When considering conjugate heat transfer, the total heat transfer rate is reduced by 3% compared with that of the isothermal wall. The typical Biot number at the internal cooling passage of a gas turbine is <0.1, and the use of the rib height as the characteristic length better represents the heat transfer of the rib.

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