Prediction of the Turbine Tip Convective Heat Flux Using Discrete Green Functions

2017 ◽  
Author(s):  
Valeria Andreoli ◽  
David G. Cuadrado ◽  
Guillermo Paniagua
Keyword(s):  
Heat Flux ◽  
Green Function ◽  
Convective Heat ◽  
Wall Temperature ◽  
Transfer Problem ◽  
Bottom Wall ◽  
Random Pattern ◽  
Inlet Temperature ◽  
Green Functions ◽  
Backward Facing Step

The complex heat and mass transfer across the turbine tip gap requires a detailed analysis which cannot be expressed using the classical Newton heat convection approach. In this portion of the turbine, characterized by tight moving clearances, pressure gradients are counterbalanced by viscous effects. Hence, non-dimensional analysis, based on the boundary layer, is inadequate and therefore the use of an adiabatic wall temperature is questionable. In this paper, we propose an alternative approach to predict the convective heat transfer problem across the turbine rotor tip using Discrete Green Functions. The linearity of the energy equation can be applied with a superposition technique to measure the data extracted from flow simulations to determine the Green’s function distribution. The Discrete Green Function is a matrix of coefficients that relate the increment of temperature observed in a surface with the heat flux integrated on the same surface. These coefficients are independent on the inlet temperature of the flow and are associated to the geometry. The controlled surface is discretized into cells and each cell is associated to a vector of coefficients. The Discrete Green Function coefficients are calculated using the temperature response of the cell to a heat flux pulse imposed at different locations. The methodology was previously applied to a backward facing step to prove its validity. Several simulations were performed applying a representative pulse of heat flux in different locations in the bottom wall of the backward facing step. From these simulations, the increment of temperature in each node of the geometry was retrieved and the Discrete Green Function coefficients associated to the bottom wall were calculated. A numerical validation was performed imposing a random pattern of heat flux and predicting the increment of temperature on the bottom wall under different inlet flow conditions. The final aim of this paper is to demonstrate the method in the rotor turbine tip. A turbine stage at engine-like conditions was assessed using a CFD software. The heat flux pulses were applied at different locations in the rotor tip geometry, and the increment of temperature in this zone was evaluated for different clearances, with a consequent variation of the Discrete Green Function coefficients. A validation of the rotor tip heat flux was accomplished by imposing different heat flux distributions in the studied region. Ultimately, a detailed uncertainty analysis of the methodology was included based in the magnitude of the heat flux pulses used in the Discrete Green Function coefficients calculation and the uncertainty in the experimental measurements of the wall temperature.

Investigation of Convective Heat Transfer of Aqueous Nanofluids in Microchannels Integrated With Temperature Nanosensors

2011 ◽  
Author(s):  
Jiwon Yu ◽  
Seok-won Kang ◽  
Saeil Jeon ◽  
Debjyoti Banerjee
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Wall Temperature ◽  
Pure Water ◽  
Bulk Temperature ◽  
Inlet Temperature ◽  
Experimental Conditions ◽  
Forced Convective Heat Transfer

Forced convective heat transfer experiments were performed for internal flow of de-ionized water (DIW) and aqueous nanofluids (ANF) in microchannels that were integrated with a calorimeter apparatus and an array of temperature nanosensors. The heat flux and wall temperature distribution was measured for the different test fluids as a function of fluid inlet temperature, wall temperature, heat flux, nanoparticles concentration, nanoparticle materials (composition, nanoparticle size and shape) and flow rates. Anomalous behavior of the nanofluids in convective heat transfer was observed where the heat flux varied as a function of flow rate and bulk temperature. The heat exchanging surfaces were characterized using electron microscopy (SEM, TEM) to monitor the change in surface characteristics both before and after the experiments. Precipitation of nanoparticles on the walls of the microchannels can lead to the formation of “nano-fins” at low concentrations of the nanoparticles while more rampant precipitation at high concentration of the nanoparticles in the nanofluids can lead to scaling (fouling) of the microchannel surfaces leading to degradation of convective heat transfer — compared to that of pure water under the same experimental conditions. Also, competing effects resulting from the decrease in the specific heat capacity as well as anomalous enhancement in the thermal conductivity of aqueous nanofluids can lead to counter-intuitive behavior of these test liquids during forced convective heat transfer.

Prediction of the Turbine Tip Convective Heat Flux Using Discrete Green's Functions

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Valeria Andreoli ◽  
David G. Cuadrado ◽  
Guillermo Paniagua
Keyword(s):  
Heat Flux ◽  
Convective Heat ◽  
Wall Temperature ◽  
Green's Functions ◽  
Green’S Functions ◽  
Transfer Problem ◽  
Turbine Rotor ◽  
Heat Fluxes ◽  
Viscous Effects ◽  
Adiabatic Wall

The heat fluxes across the turbine tip gap are characterized by large unsteady pressure gradients and shear from the viscous effects. The classical Newton heat convection equation, based on the turbine inlet total temperature, is inadequate. Previous research from our team relied on the use of the adiabatic wall temperature. In this paper, we propose an alternative approach to predict the convective heat transfer problem across the turbine rotor tip using discrete Green's functions (DGF). The linearity of the energy equation in the solid domain with constant thermal properties can be applied with a superposition technique to measure the data extracted from flow simulations to determine the Green's function distribution. The DGF is a matrix of coefficients that relate the temperature spatial (GF) distribution with the heat flux. This methodology is first applied to a backward facing step, validated using experimental data. The final aim of this paper is to demonstrate the method in the rotor turbine tip. A turbine stage at engine-like conditions was assessed using cfd software. The heat flux pulses were applied at different locations in the rotor tip geometry, and the increment of temperature in this zone was evaluated for different clearances, with a consequent variation of the DGF coefficients. Ultimately, a detailed uncertainty analysis of the methodology was included based on the magnitude of the heat flux pulses used in the DGF coefficients calculation and the uncertainty in the experimental measurements of the wall temperature.

Investigation on Convective Heat Transfer over a Rotating Disk with Bottom Wall Subjected to Uniform Heat Flux

2012 ◽  
Vol 249-250 ◽  
pp. 443-451
Author(s):  
Jing Zhou Zhang ◽  
Xiao Ming Tan ◽  
Xing Dan Zhu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Study ◽  
Rotating Disk ◽  
Outer Radius ◽  
Bottom Wall ◽  
Uniform Heat Flux ◽  
Uniform Heat

A three-dimensional numerical study on the flow and heat transfer characteristics over a rotating disk with bottom wall subjected to uniform heat flux was conducted with the use of RNG k- turbulent model. And some experiments were also made for validation. The effects of rotating angular speed and pin configuration on the temperature maps and convective heat transfer characte-ristics on rotating surface are analyzed. As the increase of rotating velocity, the impingement of pumping jet on the centre of rotating disk became stronger and the transition from laminar to turbu-lent occurred at the outer radius of rotating disk, which resulted in heat transfer enhancement. The pins on the disk made the pumping action of a rotating disk weaker. Simultaneously, they also acted as disturbing elements to the cyclone flow near the rotating disk surface, which made the overall heat transfer to be enhanced. Under the same extend areas of different pins, needle pin has higher convective heat transfer capacity than the discrete ring pin.

Analysis of the Heat Transfer Driving Parameters in Tight Rotor Blade Tip Clearances

2014 ◽  
Author(s):  
S. Lavagnoli ◽  
C. De Maesschalck ◽  
G. Paniagua
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Wall Temperature ◽  
Convective Heat Transfer Coefficient ◽  
Tip Clearance ◽  
Adiabatic Wall ◽  
Engine Operation ◽  
Flow Parameters

Turbine rotor tips and casings are vulnerable to mechanical failures due to the extreme thermal loads they undergo during engine operation. In addition to the heat flux variations during the transient phase, high-frequency unsteadiness occurs at every rotor passage, with amplitude dependent on the tip gap. The development of appropriate predictive tools and cooling schemes requires the precise understanding of the heat transfer mechanisms. The present paper analyzes the nature of the overtip flow in transonic turbine rotors running at tight clearances, and explores a methodology to determine the relevant flow parameters that model the heat transfer. Steady-state three-dimensional Reynolds-Averaged Navier-Stokes calculations were performed to simulate engine-like conditions considering two rotor tip gaps, 0.1% and 1% of the blade span. At tight tip clearance, the adiabatic wall temperature is not anymore independent of the solid thermal boundary conditions. The adiabatic wall temperature predicted with the linear Newton’s cooling law was observed to rise to non-physical levels in certain regions within the rotor tip gap, resulting in unreliable convective heat transfer coefficients. This paper investigates different approaches to estimate the relevant flow parameters that drive the heat transfer. The present study allows experimentalists to retrieve information on the gap flow temperature and convective heat transfer coefficient based on the use of wall heat flux measurements. Such approach is required to improve the accuracy in the evaluation of the heat transfer data while enhancing the understanding of tight-clearance overtip flows.

Numerical Modeling of the Conjugate Heat Transfer Problem for Annular Laminar Film Condensation in Microchannels

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Stefano Nebuloni ◽  
John R. Thome
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Wall Temperature ◽  
Conjugate Heat Transfer ◽  
Channel Wall ◽  
Transfer Problem ◽  
Film Condensation ◽  
Laminar Film Condensation

This paper presents numerical simulations of annular laminar film condensation heat transfer in microchannels of different internal shapes. The model, which is based on a finite volume formulation of the Navier–Stokes and energy equations for the liquid phase only, importantly accounts for the effects of axial and peripheral wall conduction and nonuniform heat flux not included in other models so far in the literature. The contributions of the surface tension, axial shear stresses, and gravitational forces are included. This model has so far been validated versus various benchmark cases and versus experimental data available in literature, predicting microchannel heat transfer data with an average error of 20% or better. It is well known that the thinning of the condensate film induced by surface tension due to gravity forces and shape of the surface, also known as the “Gregorig” effect, has a strong consequence on the local heat transfer coefficient in condensation. Thus, the present model accounts for these effects on the heat transfer and pressure drop for a wide variety of geometrical shapes, sizes, wall materials, and working fluid properties. In this paper, the conjugate heat transfer problem arising from the coupling between the thin film fluid dynamics, the heat transfer in the condensing fluid, and the heat conduction in the channel wall has been studied. In particular, the work has focused on three external channel wall boundary conditions: a uniform wall temperature, a nonuniform wall heat flux, and single-phase convective cooling are presented. As the scale of the problem is reduced, i.e., when moving from mini- to microchannels, the results show that the axial conduction effects can become very important in the prediction of the wall temperature profile and the magnitude of the heat transfer coefficient and its distribution along the channel.

Analysis of the Heat Transfer Driving Parameters in Tight Rotor Blade Tip Clearances

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sergio Lavagnoli ◽  
Cis De Maesschalck ◽  
Guillermo Paniagua
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Wall Temperature ◽  
Turbine Rotor ◽  
Tip Clearance ◽  
Transfer Coefficients ◽  
Adiabatic Wall ◽  
Flow Parameters

Turbine rotor tips and casings are vulnerable to mechanical failures due to the extreme thermal loads they undergo during engine service. In addition to the heat flux variations during the engine transient operation, periodic unsteadiness occurs at every rotor passage, with amplitude dependent on the tip gap. The development of appropriate predictive tools and cooling schemes requires the precise understanding of the heat transfer mechanisms. The present paper analyses the nature of the overtip flow in transonic turbine rotors running at tight clearances and explores a methodology to determine the relevant flow parameters that model the heat transfer. Steady-state three-dimensional Reynolds-averaged Navier–Stokes (RANS) calculations were performed to simulate engine-like conditions considering two rotor tip gaps, 0.1% and 1%, of the blade span. At tight tip clearance, the adiabatic wall temperature is no longer independent of the solid thermal boundary conditions. The adiabatic wall temperature predicted with the linear Newton's cooling law was observed to rise to unphysical levels in certain regions within the rotor tip gap, resulting in unreliable convective heat transfer coefficients (HTCs). This paper investigates different approaches to estimate the relevant flow parameters that drive the heat transfer. A novel four-coefficient nonlinear cooling law is proposed to model the effects of temperature-dependent gas properties and of the heat transfer history. The four-parameter correlation provided reliable estimates of the convective heat transfer descriptors for the 1% tip clearance case, but failed to model the tip heat transfer of the 0.1% tip gap rotor. The present study allows experimentalists to retrieve information on the gap flow temperature and convective HTC based on the use of wall heat flux measurements. The use of nonlinear cooling laws is sought to improve the evaluation of the rotor heat transfer data while enhancing the understanding of tight-clearance overtip flows.

Experimental and Numerical Investigation of Convection Heat Transfer of CO2 at Super-Critical Pressures in a Vertical Mini Tube

2006 ◽  
Author(s):  
Peixue Jiang ◽  
Yu Zhang ◽  
Runfu Shi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Wall Temperature ◽  
Flow Direction ◽  
Convection Heat Transfer ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Heat Fluxes ◽  
Inlet Temperature ◽  
Convection Heat

Convection heat transfer of CO2 at supercritical pressures in a 0.27mm diameter vertical mini tube was investigated experimentally and numerically. The tests investigated the effects of inlet temperature, pressure, mass flow rate, heat flux, buoyancy and flow direction on the convection heat transfer. The experimental results indicate that for inlet Reynolds numbers exceeding 4000, the flow direction and buoyancy force have little influence on the local wall temperature, with no deterioration of the convection heat transfer observed in either flow direction. The convection heat transfer coefficient initially increases with increasing heat flux and then decreases with further increases in the heat flux for both upward and downward flows. These effects are due to the variation of the thermophysical properties, especially cp. For inlet Reynolds numbers less than 2900, the local wall temperature varies nonlinearly for both flow directions. The numerical results correspond well with the experimental data for inlet Reynolds numbers exceeding 4000 using several turbulence models, especially the Realizable k-ε turbulence model. However, for inlet Reynolds numbers less than 2900, none of the turbulence models could properly simulate the convection heat transfer at super-critical pressures with high heat fluxes.

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