Design Charts for Transient Temperature and Thermal Stress Distributions in Thermally Thick Plates

1960 ◽  
Vol 11 (3) ◽  
pp. 269-284
Author(s):  
J. S. Przemieniecki
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Thermal Stress ◽  
Transfer Coefficient ◽  
Wall Temperature ◽  
Transient Temperature ◽  
Stress Distributions ◽  
Adiabatic Wall ◽  
Design Charts ◽  
The Heat Transfer Coefficient

SummaryA set of design charts is presented for the calculation of transient temperature and thermal stress distributions in thermally thick plates subjected to aerodynamic heating.The method is particularly useful for determining temperatures and thermal stresses in plates with an arbitrary variation of the heat transfer coefficient and the adiabatic wall temperature of the boundary layer. The present method is based on repetitive applications of the exact analytical solution to a unit triangular variation of the adiabatic wall temperature and a constant heat transfer coefficient. The actual variation of the adiabatic wall temperature is represented as a series of straight lines while the heat transfer coefficient is approximated by a step function. The temperature distribution through the plate is separated into linear and “self-equilibrating” temperature distributions to facilitate thermal stress calculations; these distributions can be obtained directly from the design charts presented in this paper.The general principle of this semi-numerical method is also applied to thermally thin plates subjected to arbitrary heating conditions.

High Resolution Heat Transfer Measurements on the Stator Endwall of an Axial Turbine

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Benoit Laveau ◽  
Reza S. Abhari ◽  
Michael E. Crawford ◽  
Ewald Lutum
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
High Resolution ◽  
Surface Temperature ◽  
Transfer Coefficient ◽  
Mass Flow ◽  
Wall Temperature ◽  
Adiabatic Wall ◽  
Axial Turbine ◽  
The Heat Transfer Coefficient

In order to continue increasing the efficiency of gas turbines, an important effort is made on the thermal management of the turbine stage. In particular, understanding and accurately estimating the thermal loads in a vane passage is of primary interest to engine designers looking to optimize the cooling requirements and ensure the integrity of the components. This paper focuses on the measurement of endwall heat transfer in a vane passage with a three-dimensional (3D) airfoil shape and cylindrical endwalls. It also presents a comparison with predictions performed using an in-house developed Reynolds-Averaged Navier–Stokes (RANS) solver featuring a specific treatment of the numerical smoothing using a flow adaptive scheme. The measurements have been performed in a steady state axial turbine facility on a novel platform developed for heat transfer measurements and integrated to the nozzle guide vane (NGV) row of the turbine. A quasi-isothermal boundary condition is used to obtain both the heat transfer coefficient and the adiabatic wall temperature within a single measurement day. The surface temperature is measured using infrared thermography through small view ports. The infrared camera is mounted on a robot arm with six degrees of freedom to provide high resolution surface temperature and a full coverage of the vane passage. The paper presents results from experiments with two different flow conditions obtained by varying the mass flow through the turbine: measurements at the design point (ReCax=7.2×105) and at a reduced mass flow rate (ReCax=5.2×105). The heat transfer quantities, namely the heat transfer coefficient and the adiabatic wall temperature, are derived from measurements at 14 different isothermal temperatures. The experimental data are supplemented with numerical predictions that are deduced from a set of adiabatic and diabatic simulations. In addition, the predicted flow field in the passage is used to highlight the link between the heat transfer patterns measured and the vortical structures present in the passage.

High Resolution Heat Transfer Measurements on the Stator Endwall of an Axial Turbine

2014 ◽  
Author(s):  
Benoit Laveau ◽  
Reza S. Abhari ◽  
Michael E. Crawford ◽  
Ewald Lutum
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
High Resolution ◽  
Surface Temperature ◽  
Transfer Coefficient ◽  
Mass Flow ◽  
Wall Temperature ◽  
Adiabatic Wall ◽  
Axial Turbine ◽  
The Heat Transfer Coefficient

In order to continue increasing the efficiency of gas turbines, an important effort is made on the thermal management of the turbine stage. In particular understanding and accurately estimating the thermal loads in a vane passage is of primary interest to engine designers looking to optimize the cooling requirements and ensure the integrity of the components. This paper focuses on the measurement of endwall heat transfer in a vane passage with a 3D airfoil shape and cylindrical endwalls. It also presents a comparison with predictions performed using an in-house developed RANS solver featuring a specific treatment of the numerical smoothing using a flow adaptive scheme. The measurements have been performed in a steady state axial turbine facility on a novel platform developed for heat transfer measurements and integrated to the nozzle guide vane row of the turbine. A quasi-isothermal boundary condition is used to obtain both the heat transfer coefficient and the adiabatic wall temperature within a single measurement day. The surface temperature is measured using infrared thermography through small view ports. The infrared camera is mounted on a robot-arm with six degrees of freedom to provide high resolution surface temperature and a full coverage of the vane passage. The paper presents results from experiments with two different flow conditions obtained by varying the mass flow through the turbine: measurements at the design point (ReCax = 7,2.105) and at a reduced mass flow rate (ReCax = 5,2.105). The heat transfer quantities, namely the heat transfer coefficient and the adiabatic wall temperature, are derived from measurements at 14 different isothermal temperatures. The experimental data are supplemented with numerical predictions that are deduced from a set of adiabatic and diabatic simulations. In addition, the predicted flow field in the passage is used to highlight the link between the heat transfer patterns measured and the vortical structures present in the passage.

A Novel Transient Liquid Crystal Technique to Determine Heat Transfer Coefficient Distributions and Adiabatic Wall Temperature in a Three-Temperature Problem

2003 ◽  
Vol 125 (3) ◽  
pp. 538-546 ◽  
Author(s):  
Andrew C. Chambers ◽  
David R. H. Gillespie ◽  
Peter T. Ireland ◽  
Geoffrey M. Dailey
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Liquid Crystal ◽  
Transfer Coefficient ◽  
Wall Temperature ◽  
Analytical Techniques ◽  
Single Test ◽  
Start Time ◽  
Adiabatic Wall ◽  
The Heat Transfer Coefficient

Transient liquid crystal techniques are widely used for experimental heat transfer measurements. In many instances it is necessary to model the heat transfer resulting from the temperature difference between a mixture of two gas streams and a solid surface. To nondimensionally characterize the heat transfer from scale models it is necessary to know both the heat transfer coefficient and adiabatic wall temperature of the model. Traditional techniques rely on deducing both parameters from a single test. This is a poorly conditioned problem. A novel strategy is proposed in which both parameters are deduced from a well-conditioned three-test strategy. The heat transfer coefficient is first calculated in a single test; the contribution from each driving gas stream is then deduced using additional tests. Analytical techniques are developed to deal with variations in the temperature profile and transient start time of each flow. The technique is applied to the analysis of the heat transfer within a low aspect ratio impingement channel with initial cross flow.

A Transient Infrared Thermography Method for Simultaneous Film Cooling Effectiveness and Heat Transfer Coefficient Measurements From a Single Test

2004 ◽  
Vol 126 (4) ◽  
pp. 597-603 ◽  
Author(s):  
Srinath V. Ekkad ◽  
Shichuan Ou ◽  
Richard B. Rivir
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Liquid Crystal ◽  
Transfer Coefficient ◽  
Infrared Thermography ◽  
Wall Temperature ◽  
Film Cooling ◽  
Initial Model ◽  
Adiabatic Wall ◽  
The Heat Transfer Coefficient

In film cooling situations, there is a need to determine both local adiabatic wall temperature and heat transfer coefficient to fully assess the local heat flux into the surface. Typical film cooling situations are termed three temperature problems where the complex interaction between the jets and mainstream dictates the surface temperature. The coolant temperature is much cooler than the mainstream resulting in a mixed temperature in the film region downstream of injection. An infrared thermography technique using a transient surface temperature acquisition is described which determines both the heat transfer coefficient and film effectiveness (nondimensional adiabatic wall temperature) from a single test. Hot mainstream and cooler air injected through discrete holes are imposed suddenly on an ambient temperature surface and the wall temperature response is captured using infrared thermography. The wall temperature and the known mainstream and coolant temperatures are used to determine the two unknowns (the heat transfer coefficient and film effectiveness) at every point on the test surface. The advantage of this technique over existing techniques is the ability to obtain the information using a single transient test. Transient liquid crystal techniques have been one of the standard techniques for determining h and η for turbine film cooling for several years. Liquid crystal techniques do not account for nonuniform initial model temperatures while the transient IR technique measures the entire initial model distribution. The transient liquid crystal technique is very sensitive to the angle of illumination and view while the IR technique is not. The IR technique is more robust in being able to take measurements over a wider temperature range which improves the accuracy of h and η. The IR requires less intensive calibration than liquid crystal techniques. Results are presented for film cooling downstream of a single hole on a turbine blade leading edge model.

A Novel Transient Liquid Crystal Technique to Determine Heat Transfer Coefficient Distributions and Adiabatic Wall Temperature in a Three Temperature Problem

2002 ◽  
Author(s):  
Andrew C. Chambers ◽  
David R. H. Gillespie ◽  
Peter T. Ireland ◽  
Geoffrey M. Dailey
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Liquid Crystal ◽  
Transfer Coefficient ◽  
Wall Temperature ◽  
Analytical Techniques ◽  
Single Test ◽  
Start Time ◽  
Adiabatic Wall ◽  
The Heat Transfer Coefficient

Transient liquid crystal techniques are widely used for experimental heat transfer measurements. In many instances it is necessary to model the heat transfer resulting from the temperature difference between a mixture of two gas streams and a solid surface. To non-dimensionally characterise the heat transfer from scale models it is necessary to know both the heat transfer coefficient and adiabatic wall temperature of the model. Traditional techniques rely on deducing both parameters from a single test. This is a poorly conditioned problem. A novel strategy is proposed in which both parameters are deduced from a well conditioned three test strategy. The heat transfer coefficient is first calculated in a single test; the contribution from each driving gas stream is then deduced using additional tests. Analytical techniques are developed to deal with variations in the temperature profile and transient start time of each flow. The technique is applied to the analysis of the heat transfer within a low aspect ratio impingement channel with initial cross flow.

Identification of three-dimensional transient temperature fields in thick-walled elements using the inverse method

2018 ◽  
Vol 28 (1) ◽  
pp. 138-150 ◽  
Author(s):  
Magdalena Jaremkiewicz
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Inverse Method ◽  
Thermal Stresses ◽  
Computing Time ◽  
Transient Temperature ◽  
Content Type ◽  
Inner Surface ◽  
The Heat Transfer Coefficient

Purpose The purpose of this paper is to propose a method of determining the transient temperature of the inner surface of thick-walled elements. The method can be used to determine thermal stresses in pressure elements. Design/methodology/approach An inverse marching method is proposed to determine the transient temperature of the thick-walled element inner surface with high accuracy. Findings Initially, the inverse method was validated computationally. The comparison between the temperatures obtained from the solution for the direct heat conduction problem and the results obtained by means of the proposed inverse method is very satisfactory. Subsequently, the presented method was validated using experimental data. The results obtained from the inverse calculations also gave good results. Originality/value The advantage of the method is the possibility of determining the heat transfer coefficient at a point on the exposed surface based on the local temperature distribution measured on the insulated outer surface. The heat transfer coefficient determined experimentally can be used to calculate thermal stresses in elements with a complex shape. The proposed method can be used in online computer systems to monitor temperature and thermal stresses in thick-walled pressure components because the computing time is very short.

Thermo-mechanical analysis of a FGM plate subjected to thermal shock – A new numerical approach considering real time temperature dependent material properties

2021 ◽  
Vol 63 (4) ◽  
pp. 341-349
Author(s):  
Mete Onur Kaman ◽  
Nevin Celik ◽  
Resul Das
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Thermal Shock ◽  
Temperature Variation ◽  
Material Properties ◽  
Ambient Air ◽  
Transient Temperature ◽  
Heated Plate ◽  
The Heat Transfer Coefficient

Abstract In present the study, sudden cooling, in other words thermal shock, is applied to a plate that is originally a functionally graded material (FGM). The flat plate is assumed to have an edge crack on it. Hence a numerical couple-field analysis is performed on the plate. The FGM is a combination of Ni and Al2O3. The thermal and mechanical properties of the FGM are assumed to depend on temperature variation. The mixing percentages of the Ni and Al2O3 throughout the plate are considered to vary (i) linearly, (ii) quadratically and (iii) in half-order. In order to solve the problem, a new subroutine depending on temperature is written using APDL (ANSYS Parametric Design Language) codes. Three values of the heat transfer coefficient are applied to the initially heated plate. As a result, the transient temperature variation and stress intensity factor are presented to show the thermo-mechanical relation of the plate. The material properties changing with temperature results in more reliable temperature values. Increasing the heat transfer coefficient results in better cooling and in a lesser amount of time to reach ambient air temperature.

scholarly journals Local Heat Transfer Coefficient and Adiabatic Wall Temperature Measurement Beneath Arrays of Staggered and Inline Impinging Jets

1994 ◽  
Author(s):  
Kenneth W. Van Treuren ◽  
Zuolan Wang ◽  
Peter T. Ireland ◽  
Terry V. Jones ◽  
S. T. Kohler
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Wall Temperature ◽  
Impinging Jets ◽  
Hole Diameter ◽  
Channel Height ◽  
Published Data ◽  
Target Plate ◽  
Adiabatic Wall

Recent work, Van Treuren et al. (1993), has shown the transient method of measuring heat transfer under an array of impinging jets allows the determination of local values of adiabatic wall temperature and heat transfer coefficient over the complete surface of the target plate. Using this technique, an inline array of impinging jets has been tested over a range of average jet Reynolds numbers (10,000–40,000) and for three channel height to jet hole diameter ratios (1, 2, and 4). The array is confined on three sides and spent flow is allowed to exit in one direction. Local values are averaged and compared with previously published data in related geometries. The current data for a staggered array is compared to those from an inline array with the same hole diameter and pitch for an average jet Reynolds number of 10,000 and channel height to diameter ratio of one. A comparison is made between intensity and hue techniques for measuring stagnation point and local distributions of heat transfer. The influence of the temperature of the impingement plate through which the coolant gas flows on the target plate heat transfer has been quantified.

scholarly journals Online Determining Heat Transfer Coefficient for Monitoring Transient Thermal Stresses

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 704
Author(s):  
Magdalena Jaremkiewicz ◽  
Jan Taler
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Thermal Stresses ◽  
Thermal Power ◽  
Computer Calculation ◽  
Transient Temperature ◽  
Unsteady Temperature ◽  
The Heat Transfer Coefficient

This paper proposes an effective method for determining thermal stresses in structural elements with a three-dimensional transient temperature field. This is the situation in the case of pressure elements of complex shapes. When the thermal stresses are determined by the finite element method (FEM), the temperature of the fluid and the heat transfer coefficient on the internal surface must be known. Both values are very difficult to determine under industrial conditions. In this paper, an inverse space marching method was proposed for the determination of the heat transfer coefficient on the active surface of the thick-walled plate. The temperature and heat flux on the exposed surface were obtained by measuring the unsteady temperature in a small region on the insulated external surface of a pressure component that is easily accessible. Three different procedures for the determination of the heat transfer coefficient on the water-spray surface were presented, with the division of the plate into three or four finite volumes in the normal direction to the plate surface. Calculation and experimental tests were carried out in order to validate the method. The results of the measurements and calculations agreed very well. The computer calculation time is short, so the technique can be used for online stress determination. The proposed method can be applied to monitor thermal stresses in the components of the power unit in thermal power plants, both conventional and nuclear.

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