scholarly journals Multi-Fidelity Surrogate Models for Predicting Averaged Heat Transfer Coefficients on Endwall of Turbine Blades

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 482
Author(s):  
Woosung Choi ◽  
Kanmaniraja Radhakrishnan ◽  
Nam-Ho Kim ◽  
Jun Su Park
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Computing Time ◽  
Turbine Blades ◽  
High Fidelity ◽  
Two Dimensional ◽  
Transfer Coefficients ◽  
One Dimensional ◽  
Wide Range ◽  
Input Variables

This paper proposes a multi-fidelity surrogate (MFS) model for predicting the heat transfer coefficient (HTC) on the turbine blades. First, the low-fidelity (LF) and high-fidelity (HF) surrogates were built using LF-data from numerical simulation and HF-data from an experiment. To evaluate the prediction by these two surrogates, the averaged HTC distribution on the endwall of the gas turbine blade predicted by these two surrogates was compared for input variables as Reynolds number (Re) and boundary layer (BL) thickness. This shows that the prediction by LF surrogate is saturated with an increase in Re, while has monotonic behavior with an increase in BL thickness, which is contrary in general. The prediction by HF surrogate is linear with Re and is increased with BL thickness up to 30 mm and then decreased after 30 mm. Following this, a one-dimensional projection of the two-dimensional HTC distribution was presented to show the prediction tendency of the surrogates by varying the Re and fixing the BL thickness, and vice versa. Second, the MFS was built by combining the LF and HF data. The HTC distribution by the MFS model for the same input variables was shown with the HF data points. It is observed that the prediction by MFS is agreed well with the high-fidelity data. The MFS’s one-dimensional projection of the two-dimensional HTC distribution was compared with the LF surrogate prediction by varying the Re and fixing the BL thickness, and vice versa. This shows that the MFS model has more variations due to the included LF data. It is worth to mention that the averaged HTC distribution with an increase in boundary layer thickness predicted by the MFS is agreed well with the LF and HF data in the available dataset and has a large confidence interval between 30 and 50 mm due to the unavailable data in the specified range. To check the MFS accuracy, the root-mean-square error (RMSE) and error rate were evaluated to compare with the experimental uncertainty for a wide range of high-fidelity data. The present study shows that MFS would be expected to be an effective model for saving computing time and experimental costs.

Heat and Mass Transfer in an Incompressible Turbulent Boundary Layer

1972 ◽  
Vol 94 (1) ◽  
pp. 23-28 ◽  
Author(s):  
E. Brundrett ◽  
W. B. Nicoll ◽  
A. B. Strong
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Porous Plate ◽  
Mixing Length ◽  
Two Dimensional ◽  
Transfer Data ◽  
Incompressible Turbulent Boundary Layer ◽  
Wide Range ◽  
Incompressible Boundary

The van Driest damped mixing length has been extended to account for the effects of mass transfer through a porous plate into a turbulent, two-dimensional incompressible boundary layer. The present mixing length is continuous from the wall through to the inner-law region of the flow, and although empirical, has been shown to predict wall shear stress and heat transfer data for a wide range of blowing rates.

Laminar and Transitional Boundary Layer Structures in Accelerating Flow With Heat Transfer

1986 ◽  
Vol 108 (1) ◽  
pp. 116-123 ◽  
Author(s):  
K. Rued ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Gas Turbine ◽  
Turbine Blades ◽  
Pressure Gradients ◽  
Transfer Coefficients ◽  
Gas Turbine Blades ◽  
Heat Transfer Coefficients ◽  
Layer Structures ◽  
Flow Heat

The accurate prediction of heat transfer coefficients on cooled gas turbine blades requires consideration of various influence parameters. The present study continues previous work with special efforts to determine the separate effects of each of several parameters important in turbine flow. Heat transfer and boundary layer measurements were performed along a cooled flat plate with various freestream turbulence levels (Tu = 1.6−11 percent), pressure gradients (k = 0−6 × 10−6), and cooling intensities (Tw/T∞ = 1.0−0.53). Whereas the majority of previously available results were obtained from adiabatic or only slightly heated surfaces, the present study is directed mainly toward application on highly cooled surfaces as found in gas turbine engines.

Calculation of Heat Transfer to Convection-Cooled Gas Turbine Blades

1985 ◽  
Vol 107 (3) ◽  
pp. 620-627 ◽  
Author(s):  
W. Rodi ◽  
G. Scheuerer
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Gas Turbine ◽  
Turbine Blades ◽  
Complex Nature ◽  
Surface Boundary ◽  
Transfer Coefficients ◽  
Free Stream Turbulence ◽  
Gas Turbine Blades ◽  
Heat Transfer Coefficients

A mathematical model is presented for calculating the external heat transfer coefficients around gas turbine blades. The model is based on a finite-difference procedure for solving the boundary-layer equations which describe the flow and temperature field around the blades. The effects of turbulence are simulated by a low-Reynolds number version of the k-ε turbulence model. This allows calculation of laminar and transitional zones and also the onset of transition. Applications of the calculation method are presented to turbine-blade situations which have recently been investigated experimentally. Predicted and measured heat transfer coefficients are compared and good agreement with the data is observed. This is true especially for the pressure-surface boundary layer which is of a rather complex nature because it remains in a transitional state over the full blade length. The influence of various flow phenomena like laminar-turbulent transition and of the boundary conditions (pressure gradient, free-stream turbulence) on the predicted heat transfer rates is discussed.

Convective Heat Transfer Near One-Dimensional and Two-Dimensional Wall Temperature Steps

2004 ◽  
Vol 126 (2) ◽  
pp. 202-210 ◽  
Author(s):  
Debjit Mukerji ◽  
John K. Eaton ◽  
Robert J. Moffat
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Wall Temperature ◽  
Two Dimensional ◽  
Temperature Step ◽  
Transfer Data ◽  
One Dimensional ◽  
The One

Steady-state experiments with one-dimensional and two-dimensional calorimeters were used to study the convective heat transfer near sharp steps in wall temperature in a turbulent boundary layer. Data acquired under low and high freestream turbulence conditions indicated that spanwise turbulent diffusion is not a significant heat transport mechanism for a two-dimensional temperature step. The one-dimensional calorimeter heat transfer data were predicted within ±5 percent using the STAN7 boundary layer code for situations with an abrupt wall temperature step. The conventional correlation with an unheated starting length correction, in contrast, greatly under-predicts the heat transfer for the same experimental cases. A new correlation was developed that is in good agreement with near and far-field semi-analytical solutions and predicts the calorimeter heat transfer data to within ±2 percent for temperature step boundary condition cases.

Two-Dimensional Study of Heat Transfer and Fluid Flow in a Natural Convection Loop

1982 ◽  
Vol 104 (3) ◽  
pp. 508-514 ◽  
Author(s):  
A. Mertol ◽  
R. Greif ◽  
Y. Zvirin
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Natural Convection ◽  
A Priori ◽  
Two Dimensional ◽  
Transfer Coefficients ◽  
One Dimensional ◽  
Heat Transfer Coefficients ◽  
First Time ◽  
Good Agreement

A study has been made of the heat transfer and fluid flow in a natural convection loop. Previous studies of these systems have utilized a one-dimensional approach which requires a priori specifications of the friction and the heat-transfer coefficients. The present work carries out a two-dimensional analysis for the first time. The results yield the friction and the heat-transfer coefficients and give their variation along the loop with the Graetz number as a parameter. Comparison is also made with experimental data for the heat flux and good agreement is obtained.

Heat-Transfer Measurements in an Inexpensive Supersonic Wind Tunnel: 1—Apparatus and Results for a Laminar Boundary Layer Based on a Simple One-Dimensional Flow Model

1955 ◽  
Vol 22 (3) ◽  
pp. 289-296
Author(s):  
Joseph Kaye ◽  
J. H. Keenan ◽  
G. A. Brown ◽  
R. H. Shoulberg
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Boundary Layer ◽  
Flow Model ◽  
Transfer Coefficients ◽  
Supersonic Wind Tunnel ◽  
One Dimensional ◽  
Heat Transfer Coefficients ◽  
Dimensional Flow

Abstract Reliable experimental data, obtained at relatively low cost, are presented in the form of heat-transfer coefficients for air moving at supersonic speeds in a round tube. These data are analyzed, interpreted, and compared with available data in the literature. The experimental local heat-transfer coefficients are for laminar, transitional, and turbulent boundary layers. The data for a laminar boundary layer, comprising 17 runs, are discussed here for Mach numbers at tube inlet of 2.8 and 3.0. The range of values of diameter Reynolds number covered is from 20,000 to 100,000 for these laminar-flow tests, while the length Reynolds number extends to about 4,000,000. The computed quantities are obtained on the basis of a simple one-dimensional flow model, but a companion paper will analyze the same data in greater detail on the basis of a two-dimensional flow model.

Prediction of Heat Transfer Characteristics for Discrete Hole Film Cooling for Turbine Blade Applications

1990 ◽  
Vol 112 (3) ◽  
pp. 504-511 ◽  
Author(s):  
D. K. Tafti ◽  
S. Yavuzkurt
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Film Cooling ◽  
Three Dimensional ◽  
Hole Injection ◽  
Two Dimensional ◽  
Transfer Coefficients ◽  
Film Cooling Effectiveness ◽  
Injection Process ◽  
Prediction Scheme

A two-dimensional injection model is used with a two-dimensional low Reynolds number k-ε model boundary layer code. The three-dimensional effects of the discrete hole injection process are introduced in the two-dimensional prediction scheme through an “entrainment fraction” (Υ). An established correlation between Υ and the injection parameters obtained in a previous paper is used to predict the film cooling effectiveness (η) and heat transfer coefficients for multirow injection, injection into a laminar boundary layer, and finally injection on convex curved surfaces. Predictions of η are in good agreement with experimental data for most of the cases tested. Predictions of Stanton numbers defined by St(0) and St(l) are good for low injection ratios (M) but as M increases the values are underpredicted. In spite of some shortcomings, in the authors’ opinion the present two-dimensional prediction scheme is one of the most comprehensive developed so far. It is seen that the entrainment fraction Υ is quite universal in its application to two-dimensional predictions of the discrete hole film cooling process.

scholarly journals Effects of Leading-Edge Roughness on Fluid Flow and Heat Transfer in the Transitional Boundary Layer Over a Flat Plate

1994 ◽  
Author(s):  
Mark Pinson ◽  
Ting Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Stream ◽  
Turbine Blades ◽  
Leading Edge ◽  
Transition Process ◽  
Stanton Number ◽  
Edge Roughness ◽  
Wide Range ◽  
Edge Conditions

An experimental study was undertaken to gain insight into the physical mechanisms that affect the laminar-turbulent transition process downstream of the leading-edge roughness condition. Three sizes of sandpaper strips were chosen to simulate the randomly distributed roughness located near the leading edge of a turbine blade, and three sizes of cylinders were chosen to simulate the relatively isolated peak nature of the roughness structure. The roughness Reynolds numbers tested covered a wide range, from 2 to 2840. The roughness sizes were selected based on the measured roughness characteristics of used gas turbine blades. The results indicated that at low free-stream velocities (5 m/s), the maximum roughness height was the primary contributor to deviations from the undisturbed case. At higher free-stream velocities (5–7 m/s), three of the rough leading-edge conditions exhibited a dual-slope region between the laminar and turbulent Stanton number versus Reynolds number correlations. Analysis of the boundary layer indicated that the first segment of the dual-slope was laminar, but the wall heat transfer significantly deviates from the laminar correlation. The second segment was transitional. The dual-slope behavior and the waviness of the Stanton number distribution at higher free-stream velocities observed downstream of the rough leading-edge conditions are believed to have been caused by nonlinear amplification introduced by the finite disturbances at the leading edge.

A note on expansions for the two-dimensional, compressible, laminar boundary layer equations near a point of zero skin friction

1983 ◽  
Vol 94 (1-2) ◽  
pp. 93-96 ◽  
Author(s):  
G. Wilks
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Two Dimensional ◽  
Transfer Coefficients ◽  
Boundary Layer Equations ◽  
Heat Transfer Coefficients

SynopsisThe first non-arbitrary coefficient, α12, of the Buckmaster expansions is evaluated in the context of the extended Goldstein-Stewartson theory. Leading terms of the next order contributions to the skin friction and heat transfer coefficients are also obtained.

scholarly journals Heat Transfer to Turbine Blades, With Special Reference to the Effects of Mainstream Turbulence

1979 ◽  
Author(s):  
A. Brown ◽  
B. W. Martin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbine Blades ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Layer Behavior

The mainly empirical criteria used to predict boundary-layer behavior under the combined influence of velocity gradient factor and significant mainstream turbulence are reviewed and assessed by application to recently published blade heat-transfer measurements. Indications are that under the conditions experienced in gas turbine engines, the scale and frequency of mainstream turbulence may be as important as its intensity in determining local heat transfer coefficients round the blades.

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