Investigation Into the Effect of Uncertainty in Thermal Properties on Turbomachinery Disc Heat Transfer Using Both a Monte Carlo Simulation Technique and a Taylor Series Uncertainty Propagation Method

2007 ◽  
Author(s):  
Adam Cooke ◽  
Peter Childs ◽  
Christopher Long
Keyword(s):  
Heat Transfer ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Thermal Properties ◽  
Boundary Conditions ◽  
Taylor Series ◽  
Uncertainty Propagation ◽  
Outer Radius ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients

The effect of uncertainties in the thermal properties of components and surrounding fluids is often ignored in the field of experimental turbomachinery heat transfer. The work reported here uses two different methods of uncertainty analysis to help quantify these effects: 1) a stochastic Monte Carlo simulation and 2) a Taylor series uncertainty propagation. These two methods were used on a steady state free disc test case having a turbulent flow regime. The disc modelled was made from IMI 318 titanium and had an inner and outer radius of 0.115 m and 0.22 m respectively, representative of engine and test rig geometry. The disc thickness was 0.016 m. Convective boundary conditions were derived from the relevant equation for local Nusselt number. The applied boundary conditions resulted in local heat transfer coefficients in the range of approximately 120 W/m2 K to 170 W/m2 K. Uncertainties for these heat transfer coefficients were a near identical match between the two different uncertainty methods and were found to be ± 0.66%. Calculated heat flux values fell within the range of approximately 1500 W/m2 and 5200 W/m2. The Monte Carlo uncertainty method returned uncertainty values varying from ± 1.17% to ± 0.47% from the inner and outer radii respectively. An extended Taylor series of uncertainty propagation returned uncertainties varying from ± 1.82% to ± 0.96%, from the inner and outer radius respectively and increased and decreased a number of times in between. These differences are due to assumptions and simplifications which need to be made when using the Taylor series method and shows that a Monte Carlo simulation analysis offers a better way of quantifying the uncertainties associated with disc to air heat transfer as it is more realistic. Studying the magnitudes of uncertainty allows the analyst to understand the impact that uncertainties in thermal properties can have on calculated values of disc to air heat fluxes and heat transfer coefficients.

Temperature Rise Times in Pneumatic Tires

1976 ◽  
Vol 4 (3) ◽  
pp. 181-189 ◽  
Author(s):  
S. K. Clark
Keyword(s):  
Heat Transfer ◽  
Thermal Properties ◽  
Temperature Rise ◽  
Thermal Equilibrium ◽  
Transfer Coefficients ◽  
Pneumatic Tire ◽  
Heat Transfer Coefficients ◽  
Idealized Model ◽  
Pneumatic Tires

Abstract An idealized model is proposed for heating of a pneumatic tire. A solution is obtained for the temperature rise of such a model. Using known thermal properties of rubber and known heat transfer coefficients, the time to reach thermal equilibrium is estimated.

scholarly journals Heat Transfer Boundary Conditions in the RELAP5-3D Code

2008 ◽  
Author(s):  
Richard A. Riemke ◽  
Cliff B. Davis ◽  
Richard R. Schultz
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Volume Fraction ◽  
Control Variable ◽  
Time Dependent ◽  
Fluid Temperature ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
General Table

The heat transfer boundary conditions used in the RELAP5-3D computer program have evolved over the years. Currently, RELAP5-3D has the following options for the heat transfer boundary conditions: (a) heat transfer correlation package option, (b) non-convective option (from radiation/conduction enclosure model or symmetry/insulated conditions), and (c) other options (setting the surface temperature to a volume fraction averaged fluid temperature of the boundary volume, obtaining the surface temperature from a control variable, obtaining the surface temperature from a time-dependent general table, obtaining the heat flux from a time-dependent general table, or obtaining heat transfer coefficients from either a time- or temperature-dependent general table). These options will be discussed, including the more recent ones.

Heat Transfer and Friction Studies in a Tilted and Rib-Roughened Trailing-Edge Cooling Cavity With and Without the Trailing-Edge Cooling Holes

2014 ◽  
Author(s):  
Mohammad Taslim ◽  
Joseph S. Halabi
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Flow Direction ◽  
Transfer Coefficients ◽  
Trailing Edge ◽  
Cross Sectional ◽  
Heat Transfer Coefficients ◽  
Cfd Models ◽  
Cooling Cavity ◽  
Rib Roughened

Local and average heat transfer coefficients and friction factors were measured in a test section simulating the trailing edge cooling cavity of a turbine airfoil. The test rig with a trapezoidal cross sectional area was rib-roughened on two opposite sides of the trapezoid (airfoil pressure and suction sides) with tapered ribs to conform to the cooling cavity shape and had a 22-degree tilt in the flow direction upstream of the ribs that affected the heat transfer coefficients on the two rib-roughened surfaces. The radial cooling flow traveled from the airfoil root to the tip while exiting through 22 cooling holes along the airfoil trailing edge. Two rib geometries, with and without the presence of the trailing-edge cooling holes, were examined. The numerical model contained the entire trailing-edge channel, ribs and trailing-edge cooling holes to simulate exactly the tested geometry. A pressure-correction based, multi-block, multi-grid, unstructured/adaptive commercial software was used in this investigation. Realizable k–ε turbulence model in conjunction with enhanced wall treatment approach for the near wall regions, was used for turbulence closure. The applied thermal boundary conditions to the CFD models matched the test boundary conditions. Comparisons are made between the experimental and numerical results.

Calculation of Disk Temperatures in Gas Turbine Rotor-Stator Cavities Using Conjugate Heat Transfer

2010 ◽  
Author(s):  
Aneesh Sridhar Vadvadgi ◽  
Savas Yavuzkurt
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Conjugate Heat Transfer ◽  
Computational Cost ◽  
Disk Surface ◽  
Turbine Rotor ◽  
Transfer Coefficients ◽  
Constant Wall Temperature ◽  
Heat Transfer Coefficients ◽  
Variable Surface

The present study deals with the numerical modeling of the turbulent flow in a rotor-stator cavity with or without imposed through flow with heat transfer. The commercial finite volume based solver, ANSYS/FLUENT is used to numerically simulate the problem. A conjugate heat transfer approach is used. The study specifically deals with the calculation of the heat transfer coefficients and the temperatures at the disk surfaces. Results are compared with data where available. Conventional approaches which use boundary conditions such as constant wall temperature or constant heat flux in order to calculate the heat transfer coefficients which later are used to calculate disk temperatures can introduce significant errors in the results. The conjugate heat transfer approach can resolve this to a good extent. It includes the effect of variable surface temperature on heat transfer coefficients. Further it is easier to specify more realistic boundary conditions in a conjugate approach since solid and the flow heat transfer problems are solved simultaneously. However this approach incurs a higher computational cost. In this study, the configuration chosen is a simple rotor and stator system with a stationary and heated stator and a rotor. The aspect ratio is kept small (around 0.1). The flow and heat transfer characteristics are obtained for a rotational Reynolds number of around 106. The simulation is performed using the Reynolds Stress Model (RSM). The computational model is first validated against experimental data available in the literature. Studies have been carried out to calculate the disk temperatures using conventional non-conjugate and full conjugate approaches. It has been found that the difference between the disk temperatures for conjugate and non-conjugate computations is 5 K for the low temperature and 30 K for the high temperature boundary conditions. These represent differences of 1% and 2% from the respective stator surface temperatures. Even at low temperatures, the Nusselt numbers at the disk surface show a difference of 5% between the conjugate and non-conjugate computations, and far higher at higher temperatures.

scholarly journals Heat Transfer and Friction Studies in a Tilted and Rib-Roughened Trailing-Edge Cooling Cavity with and without the Trailing-Edge Cooling Holes

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
M. E. Taslim ◽  
J. S. Halabi
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Flow Direction ◽  
Transfer Coefficients ◽  
Trailing Edge ◽  
Cross Sectional ◽  
Heat Transfer Coefficients ◽  
Cfd Models ◽  
Cooling Cavity ◽  
Rib Roughened

Local and average heat transfer coefficients and friction factors were measured in a test section simulating the trailing-edge cooling cavity of a turbine airfoil. The test rig with a trapezoidal cross-sectional area was rib-roughened on two opposite sides of the trapezoid (airfoil pressure and suction sides) with tapered ribs to conform to the cooling cavity shape and had a 22-degree tilt in the flow direction upstream of the ribs that affected the heat transfer coefficients on the two rib-roughened surfaces. The radial cooling flow traveled from the airfoil root to the tip while exiting through 22 cooling holes along the airfoil trailing-edge. Two rib geometries, with and without the presence of the trailing-edge cooling holes, were examined. The numerical model contained the entire trailing-edge channel, ribs, and trailing-edge cooling holes to simulate exactly the tested geometry. A pressure-correction based, multiblock, multigrid, unstructured/adaptive commercial software was used in this investigation. Realizablek-εturbulence model in conjunction with enhanced wall treatment approach for the near wall regions was used for turbulence closure. The applied thermal boundary conditions to the CFD models matched the test boundary conditions. Comparisons are made between the experimental and numerical results.

Influence of Surface Heating Condition on Local Heat Transfer in Enclosed Corotating Disks With Axial Throughflow

1993 ◽  
Author(s):  
S. Y. Kim ◽  
J. C. Han ◽  
G. L. Morrison ◽  
E. Elovic
Keyword(s):  
Heat Transfer ◽  
Axial Flow ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Outer Radius ◽  
Surface Heating ◽  
Heating Condition ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Rotating Cavity

Local heat transfer in a rotating cavity with axial throughflow was experimentally investigated. The rotating cavity was bounded by two plane disks and a cylindrical rim (shroud). The ratio of the rim span to the disk outer radius was 0.4 and the ratio of the disk inner radius to outer radius was 0.25. This study investigated the effects of axial coolant flow rate, rotation speed, and disk surface heating condition on the local heat transfer coefficient distributions inside the cavity. Three cavity surface heating conditions were tested: case 1 - upstream and downstream disks with radially increasing temperature but colder than rim; case 2 - upstream and downstream disks at uniform temperature but colder than rim; and case 3 - upstream and downstream disks and rim at uniform temperature. Tests were systematically performed for the axial flow Reynolds numbers between 2500 and 25,000, the rotational Reynolds numbers between 0 and 5.11 × 105, and the rotational Grashof numbers between 5 × 106 and 1.3 × 1010, respectively. The results show that the local heat transfer coefficients for the non-rotating cavity increase with increasing axial flow Reynolds number. However, the local heat transfer coefficients initially decrease and then increase with increasing rotational Reynolds number. In general, the heat transfer coefficients on the rim for case 2 surface heating condition are higher than those for case 1 and case 3 whereas the heat transfer coefficients on the upstream and downstream disks for case 3 surface heating condition are higher than those for case 1 and case 2.

The Concept of Adiabatic Heat Transfer Coefficient and its Application to Turbomachinery

2013 ◽  
Author(s):  
Reinaldo A. Gomes ◽  
Reinhard Niehuis
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Constant Heat Flux ◽  
Transfer Coefficients ◽  
Constant Wall Temperature ◽  
Heat Transfer Coefficients ◽  
Thermal Boundary Conditions ◽  
Critical Components

Typical turbomachinery flows are too complex to be predicted by analytical solutions alone. Therefore numerous correlations and test data are used in conjunction with numerical tools in order to design thermally critical components. This approach can be problematic because these correlations and data are not fully independent of the boundary conditions applied. The heat transfer coefficients obtained are not only dependent on the aerodynamics of the flow but also on the thermal boundary layer created along the surface. The adiabatic heat transfer coefficient is the only one which is independent of the thermal boundary conditions, as long as the energy equation can be considered linear with respect to the temperature. However, a proper prediction of the surface temperature cannot be obtained with the adiabatic heat transfer coefficient alone. This paper first reviews the concept of adiabatic heat transfer coefficient and its application to turbomachinery flows. Later, a concept is introduced to allow interchanging between different definitions of heat transfer coefficient and boundary conditions, i.e. constant heat flux or constant wall temperature. Finally, a typical configuration for measuring the adiabatic heat transfer coefficient on a turbine blade and the conversion to other definitions of heat transfer coefficient is presented and evaluated. It is shown that with the technique presented here even small deficiencies of some experiments can be compensated for.

Inverse Determination of Steady Heat Convection Coefficient Distributions

1998 ◽  
Vol 120 (2) ◽  
pp. 328-334 ◽  
Author(s):  
T. J. Martin ◽  
G. S. Dulikravich
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Measurement Data ◽  
Cost Effective ◽  
Heat Fluxes ◽  
Transfer Coefficients ◽  
Simple Modification ◽  
Heat Transfer Coefficients ◽  
Thermal Boundary Conditions

An inverse Boundary Element Method (BEM) procedure has been used to determine unknown heat transfer coefficients on surfaces of arbitrarily shaped solids. The procedure is noniterative and cost effective, involving only a simple modification to any existing steady-state heat conduction BEM algorithm. Its main advantage is that this method does not require any knowledge of, or solution to, the fluid flow field. Thermal boundary conditions can be prescribed on only part of the boundary of the solid object, while the heat transfer coefficients on boundaries exposed to a moving fluid can be partially or entirely unknown. Over-specified boundary conditions or internal temperature measurements on other, more accessible boundaries are required in order to compensate for the unknown conditions. An ill-conditioned matrix results from the inverse BEM formulation, which must be properly inverted to obtain the solution to the ill-posed problem. Accuracy of numerical results has been demonstrated for several steady two-dimensional heat conduction problems including sensitivity of the algorithm to errors in the measurement data of surface temperatures and heat fluxes.

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