Scalable Heat Transfer Characterization on Film Cooled Geometries Based on Discrete Green’s Functions

2021 ◽  
Vol 143 (2) ◽  
Author(s):  
Jorge Saavedra ◽  
Venkat Athmanathan ◽  
Guillermo Paniagua ◽  
Terrence Meyer ◽  
Doug Straub ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Flat Plate ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Green's Functions ◽  
Green’S Functions ◽  
Numerical Procedure ◽  
Local Heat Transfer ◽  
Sensitivity Matrix

Abstract The aerothermal characterization of film-cooled geometries is traditionally performed at reduced temperature conditions, which then requires a debatable procedure to scale the convective heat transfer performance to engine conditions. This paper describes an alternative engine-scalable approach, based on Discrete Green’s Functions (DGF) to evaluate the convective heat flux along film-cooled geometries. The DGF method relies on the determination of a sensitivity matrix that accounts for the convective heat transfer propagation across the different elements in the domain. To characterize a given test article, the surface is discretized in multiple elements that are independently exposed to perturbations in heat flux to retrieve the sensitivity of adjacent elements, exploiting the linearized superposition. The local heat transfer augmentation on each segment of the domain is normalized by the exposed thermal conditions and the given heat input. The resulting DGF matrix becomes independent from the thermal boundary conditions, and the heat flux measurements can be scaled to any conditions given that Reynolds number, Mach number, and temperature ratios are maintained. The procedure is applied to two different geometries, a cantilever flat plate and a film-cooled flat plate with a 30 degree 0.125 in. cylindrical injection orifice with length-to-diameter ratio of 6. First, a numerical procedure is applied based on conjugate 3D unsteady Reynolds-averaged Navier–Stokes (URANS) simulations to assess the applicability and accuracy of this approach. Finally, experiments performed on a flat plate geometry are described to validate the method and its applicability. Wall-mounted thermocouples are used to monitor the surface temperature evolution, while a 10 kHz burst-mode laser is used to generate heat flux addition on each of the discretized elements of the DGF sensitivity matrix.

Scalable Heat Transfer Characterization on Film Cooled Geometries Based on Discrete Green’s Functions

2020 ◽  
Author(s):  
Jorge Saavedra ◽  
Venkat Athmanathan ◽  
Guillermo Paniagua ◽  
Terrence Meyer ◽  
Doug Straub ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Flat Plate ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Green's Functions ◽  
Green’S Functions ◽  
Numerical Procedure ◽  
Local Heat Transfer ◽  
Sensitivity Matrix

Abstract The aerothermal characterization of film cooled geometries is traditionally performed at reduced temperature conditions, which then requires a debatable procedure to scale the convective heat transfer performance to engine conditions. This paper describes an alternative engine-scalable approach, based on Discrete Green’s Functions (DGF) to evaluate the convective heat flux along film cooled geometries. The DGF method relies on the determination of a sensitivity matrix that accounts for the convective heat transfer propagation across the different elements in the domain. To characterize a given test article, the surface is discretized in multiple elements that are independently exposed to perturbations in heat flux to retrieve the sensitivity of adjacent elements, exploiting the linearized superposition. The local heat transfer augmentation on each segment of the domain is normalized by the exposed thermal conditions and the given heat input. The resulting DGF matrix becomes independent from the thermal boundary conditions, and the heat flux measurements can be scaled to any conditions given that Reynolds number, Mach number, and temperature ratios are maintained. The procedure is applied to two different geometries, a cantilever flat plate and a film cooled flat plate with a 30 degree 0.125” cylindrical injection orifice with length-to-diameter ratio of 6. First, a numerical procedure is applied based on conjugate 3D Unsteady Reynolds Averaged Navier Stokes simulations to assess the applicability and accuracy of this approach. Finally, experiments performed on a flat plate geometry are described to validate the method and its applicability. Wall-mounted thermocouples are used to monitor the surface temperature evolution, while a 10 kHz burst-mode laser is used to generate heat flux addition on each of the discretized elements of the DGF sensitivity matrix.

Engine-Scalable Rotor Casing Convective Heat Flux Evaluation Using Inverse Heat Transfer Methods

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
David Gonzalez Cuadrado ◽  
Francisco Lozano ◽  
Valeria Andreoli ◽  
Guillermo Paniagua
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Green’S Function ◽  
Convective Heat ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Filter Method ◽  
Convective Heat Flux ◽  
Inverse Heat Transfer

In this paper, we propose a two-step methodology to evaluate the convective heat flux along the rotor casing using an engine-scalable approach based on discrete Green's functions . The first step consists in the use of an inverse heat transfer technique to retrieve the heat flux distribution on the shroud inner wall by measuring the temperature of the outside wall; the second step is the calculation of the convective heat flux at engine conditions, using the experimental heat flux and the Green functions engine-scalable technique. Inverse methodologies allow the determination of boundary conditions; in this case, the inner casing surface heat flux, based on measurements from outside of the system, which prevents aerothermal distortion caused by routing the instrumentation into the test article. The heat flux, retrieved from the inverse heat transfer methodology, is related to the rotor tip gap. Therefore, for a given geometry and tip gap, the pressure and temperature can also be retrieved. In this work, the digital filter method is applied in order to take advantage of the response of the temperature to heat flux pulses. The discrete Green's function approach employs a matrix to relate an arbitrary temperature distribution to a series of pulses of heat flux. In this procedure, the terms of the Green's function matrix are evaluated with the output of the inverse heat transfer method. Given that key dimensionless numbers are conserved, the Green's functions matrix can be extrapolated to engine-like conditions. A validation of the methodology is performed by imposing different arbitrary heat flux distributions, to finally demonstrate the scalability of the Green's function method to engine conditions. A detailed uncertainty analysis of the two-step routine is included based on the value of the pulse of heat flux, the temperature measurement uncertainty, the thermal properties of the material, and the physical properties of the rotor casing.

Engine-Scalable Rotor Casing Convective Heat Flux Evaluation Using Inverse Heat Transfer Methods

2018 ◽  
Author(s):  
David G. Cuadrado ◽  
Francisco Lozano ◽  
Valeria Andreoli ◽  
Guillermo Paniagua
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Green’S Function ◽  
Convective Heat ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Filter Method ◽  
Convective Heat Flux ◽  
Inverse Heat Transfer

In this paper, we propose a two-step methodology to evaluate the convective heat flux along the rotor casing using an engine-scalable approach based on Discrete Green’s Functions. The first step consists in the use of an inverse heat transfer technique to retrieve the heat flux distribution on the shroud inner wall by measuring the temperature of the outside wall; the second step is the calculation of the convective heat flux at engine conditions, using the experimental heat flux and the Green Functions engine-scalable technique. Inverse methodologies allow the determination of boundary conditions, in this case the inner casing surface heat flux, based on measurements from outside of the system, which prevents aerothermal distortion caused by routing the instrumentation into the test article. The heat flux, retrieved from the inverse heat transfer methodology, is related to the rotor tip gap. Therefore, for a given geometry and tip gap, the pressure and temperature can also be retrieved. In this work, the Digital Filter Method is applied in order to take advantage of the response of the temperature to heat flux pulses. The Discrete Green’s Function approach employs a matrix to relate an arbitrary temperature distribution to a series of pulses of heat flux. In the present procedure, the terms of the Green’s Function matrix are evaluated with the output of the inverse heat transfer method. Given that key dimensionless numbers are conserved, the Green’s Functions matrix can be extrapolated to engine-like conditions. A validation of the methodology is performed by imposing different arbitrary heat flux distributions, to finally demonstrate the scalability of the Green’s Function Method to engine conditions. A detailed uncertainty analysis of the two-step routine is included based on the value of the pulse of heat flux, the temperature measurement uncertainty, the thermal properties of the material and the physical properties of the rotor casing.

Effect of Variable Properties and Radiation on Convective Heat Transfer Measurements at Engine Conditions

2014 ◽  
Author(s):  
Nathan J. Greiner ◽  
Marc D. Polanka ◽  
James L. Rutledge ◽  
Andrew T. Shewhart
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Flat Plate ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Variable Properties ◽  
Radiative Component

Experiments measuring film cooling performance are often performed near room temperature over small ranges of driving temperature. For such experiments, fluid properties are nearly constant within the boundary layer and radiative heat transfer is negligible. Consequently, the heat flux to the wall is a linear function of driving temperature. Therefore, the convective heat transfer coefficient and adiabatic wall temperature can be extracted from heat flux measurements at two or more driving temperatures. For large driving temperatures, like those seen in gas turbine engines, significant property variations exist within the boundary layer. In addition, radiative heat transfer becomes sufficiently large such that it can no longer be neglected. As a result, heat flux becomes a non-linear function of driving temperature. Thus, for these high temperature cases, ambient temperature methods utilizing a linear heat flux assumption cannot be employed to characterize the convective heat transfer. The present study experimentally examines the non-linearity of heat flux for large driving temperatures flowing over a flat plate. The results are first used to validate the temperature ratio method presented in a previous study to account for variable properties within a boundary layer. This validation highlighted the need to account for the radiative component of the overall heat transfer. A method is subsequently proposed to account for the effects of both variable properties and radiation simultaneously. Finally, the method is validated with the experimental data. While this methodology was developed in a flat plate rig, it is applicable to any relevant configuration in a hot environment. The method is general and independent of the overall radiative component magnitude and direction. Overall, the technique provides a means of quantifying the impact of both variable properties and the radiative flux on the conductive heat transfer to or from a surface in a single experiment.

Analysis of flow and heat transfer over stretching/shrinking and porous surfaces

2021 ◽  
pp. 875608792110258
Author(s):  
Azhar Ali ◽  
Dil Nawaz Khan Marwat ◽  
Aamir Ali
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Current Model ◽  
Uniform Heat Flux ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Special Cases ◽  
Porous Surfaces

Flows and heat transfer over stretching/shrinking and porous surfaces are studied in this paper. Unusual and generalized similarity transformations are used for simplifying governing equations. Current model includes all previous cases of stretched/shrunk flows with thermal effects discussed so far. Moreover, we present three different cases of thermal behavior (i) prescribed surface temperature (ii) Variable/uniform convective heat transfer at plat surface and (iii) prescribed variable/uniform heat flux. Stretching/shrinking velocity Uw(x), porosity [Formula: see text], heat transfer [Formula: see text], heat flux [Formula: see text] and convective heat transfer at surface are axial coordinate dependent. Boundary layer equations and boundary conditions are transformed into nonlinear ODEs by introducing unusual and generalized similarity transformations for the variables. These simplified equations are solved numerically. Final ODEs represent suction/injection, stretching/shrinking, temperature, heat flux, convection effects and specific heat. This current problem encompasses all previous models as special cases which come under the scope of above statement (title). The results of classical models are scoped out as a special case by assigning proper values to the parameters. Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter. A stability analysis is accomplished and apprehended in order to establish a criterion for determining linearly stable and physically compatible solutions. The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable (uniform) thickness with variable (uniform) stretching/shrinking and injection/suction velocities.

Convective Heat Transfer Performance of FC-72 in a Pin-Finned Channel

2008 ◽  
Author(s):  
Liang-Han Chien ◽  
S.-Y. Pei ◽  
T.-Y. Wu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Flow Rate ◽  
Smooth Surface ◽  
Heat Transfer Performance ◽  
Fluid Temperature ◽  
Transfer Performance ◽  
Finned Surface

This study investigates the influence of the heat flux and mass velocity on convective heat transfer performance of FC-72 in a rectangular channel of 20mm in width and 2 mm in height. The heated side has either a smooth surface or a pin-finned surface. The inlet fluid temperature is maintained at 30°C. The total length of the test channel is 113 mm, with a heated length of 25mm. The flow rate varies between 80 and 960 ml/min, and the heat flux sets between 18 and 50 W/cm2. The experimental results show that the controlling variable is heat flux instead of flow rate because of the boiling activities in FC-72. At a fixed flow rate, the pin-finned surface yields up to 20% higher heat transfer coefficient and greater critical heat flux than those of a smooth surface.

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