THE GALERKIN METHOD SOLUTION OF THE CONJUGATE HEAT TRANSFER PROBLEMS FOR THE CROSS-FLOW CONDITIONS

2004 ◽  
Author(s):  
Andrej Horvat ◽  
Borut Mavko ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Galerkin Method ◽  
Conjugate Heat Transfer ◽  
Cross Flow ◽  
Flow Conditions ◽  
The Cross ◽  
The Galerkin Method ◽  
Transfer Problems

scholarly journals Conjugate Heat Transfer CFD Predictions of Impingement Jet Array Flat Wall Cooling Aerodynamics With Single Sided Flow Exit

2013 ◽  
Author(s):  
Abubakar M. El-Jummah ◽  
Gordon E. Andrews ◽  
John E. J. Staggs
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Conjugate Heat Transfer ◽  
Cross Flow ◽  
Diameter Ratio ◽  
Significant Feature ◽  
Axial Distance ◽  
Impingement Jet ◽  
The Cross

Conjugate heat transfer CFD studies were undertaken on impingement square jet arrays with self induced crossflow in the impingement gap with a single sided exit. The aim was to understand the aerodynamic interactions that result in the deterioration of heat transfer with axial distance, whereas the addition of duct flow heat transfer would be expected to lead to an increase in heat transfer with axial distance. A square array of impingement holes was investigated for a common geometry investigated experimentally, pitch to diameter ratio X/D of 5 and impingement gap to diameter ratio Z/D of 3.3 for 11 rows of holes in the crossflow direction. A metal duct wall was used as the impingement surface with an applied heat flux of 100kW/m2, which for a gas turbine combustor cooling application operating at steady state with a temperature difference of ∼450K corresponds to a convective heat transfer coefficient of ∼200 W/m2K. A key feature of the predicted aerodynamics was recirculation in the plane of the impingement jets normal to the cross-flow, which produced heating of the impingement jet wall. This reverse flow jet was deflected by the cross flow which had its peak velocity in the plane between the high velocity impingement jets. The cross-flow interaction with the impingement jets reduced the interaction between the jets on the surface, with lower surface turbulence as a result and this reduced the surface convective heat transfer. A significant feature of the predictions was the interaction of the cross-flow aerodynamics with the impingement jet wall and associated heat transfer to that wall. The results showed that the deterioration in heat transfer with axial distance was well predicted, together with predictions of the impingement wall surface temperature gradients.

Effects of alternating elliptical chamber on jet impingement heat transfer in vane leading edge under different cross-flow conditions

2021 ◽  
pp. 1-17
Author(s):  
K. Xiao ◽  
J. He ◽  
Z. Feng
Keyword(s):  
Heat Transfer ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Leading Edge ◽  
Longitudinal Vortices ◽  
Impingement Jet ◽  
Flow And Heat Transfer ◽  
Impingement Heat Transfer ◽  
Cross Flow Velocity ◽  
The Cross

ABSTRACT This paper proposes an alternating elliptical impingement chamber in the leading edge of a gas turbine to restrain the cross flow and enhance the heat transfer, and investigates the detailed flow and heat transfer characteristics. The chamber consists of straight sections and transition sections. Numerical simulations are performed by solving the three-dimensional (3D) steady Reynolds-Averaged Navier–Stokes (RANS) equations with the Shear Stress Transport (SST) k– $\omega$ turbulence model. The influences of alternating the cross section on the impingement flow and heat transfer of the chamber are studied by comparison with a smooth semi-elliptical impingement chamber at a cross-flow Velocity Ratio (VR) of 0.2 and Temperature Ratio (TR) of 1.00 in the primary study. Then, the effects of the cross-flow VR and TR are further investigated. The results reveal that, in the semi-elliptical impingement chamber, the impingement jet is deflected by the cross flow and the heat transfer performance is degraded. However, in the alternating elliptical chamber, the cross flow is transformed to a pair of longitudinal vortices, and the flow direction at the centre of the cross section is parallel to the impingement jet, thus improving the jet penetration ability and enhancing the impingement heat transfer. In addition, the heat transfer in the semi-elliptical chamber degrades rapidly away from the stagnation region, while the longitudinal vortices enhance the heat transfer further, making the heat transfer coefficient distribution more uniform. The Nusselt number decreases with increase of VR and TR for both the semi-elliptical chamber and the alternating elliptical chamber. The alternating elliptical chamber enhances the heat transfer and moves the stagnation point up for all VR and TR, and the heat transfer enhancement is more obvious at high cross-flow velocity ratio.

Investigations on the Heat Transfer and Flow Characteristics in a Trapezoid Duct for Turbine Blade Leading Edge

2018 ◽  
Author(s):  
Hai-yong Liu ◽  
Cun-liang Liu ◽  
Lin Ye
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Cross Flow ◽  
Side Wall ◽  
Swirl Flow ◽  
Transfer Enhancement ◽  
Impingement Cooling ◽  
Exit Side ◽  
Target Wall ◽  
The Cross

To evaluate the application of the impingement cooling in a trapezoidal duct, particularly the influence on internal cooling of the cross flow and swirl flow. Experimental and numerical studies have been performed. The experiment focuses on the heat transfer characteristics in the duct, when the numerical simulation focuses on the flow characteristics. Four Reynolds numbers (10000, 20000, 30000 and 40000), six cross flow mass flow ratios (0, 0.1, 0.2, 0.3, 0.4 and 0.5) and two impingement angle (35° and 45°) are considered in both the experiment and the numerical simulation. The temperature on the target wall and the exit side wall is measured by the thermocouples, when the realizable k-ε turbulence model and enhanced wall treatment are performed using a commercial code Fluent. The results show that only part of the jets contribute in the heat transfer enhancement on the target wall, the other jets improve a large anticlockwise vortex occupied the upper part of the duct and drive strong swirl flow. The heat transfer on the exit side wall is enhanced by the swirl flow. The cross flow is induced in the duct by the outflow of the end exit hole. It deflects the jets and abates the impingement cooling on the target wall in the downstream region but has no evidently effect on the heat transfer on the exit side wall. Higher impingement angle helps to augment the impingement cooling on the target wall and improves the resistance ability of the jets against the effect of the cross flow. The heat transfer enhancement ability on the target wall and exit side wall in the present duct is compared to that of a smooth duct. The Nusselt number of the former is about 3 times higher than that of the latter. It indicates that the impingement and swirl play equally important roles in the heat transfer enhancement in the present duct. Empirical dimensionless correlations based on the present experiment data are presented in the paper.

scholarly journals Construction of a parallel computational algorithm based on the Galerkin discontinuous method for solving convective heat transfer problems on unstructured staggered grids

2018 ◽  
Vol 20 (4) ◽  
pp. 448-459
Author(s):  
R. V. Zhalnin ◽  
V. F. Masyagin ◽  
E. E. Peskova
Keyword(s):  
Heat Transfer ◽  
Galerkin Method ◽  
Convective Heat Transfer ◽  
Parallel Algorithm ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Convective Heat ◽  
Computational Algorithm ◽  
Staggered Grids ◽  
Transfer Problems

The present paper is devoted to the construction of a parallel computational algorithm for solving convective heat transfer problems using the discontinuous Galerkin method on unstructured staggered grids. The computational algorithm is implemented on the basis of MPI parallel computing technology. A special feature of the algorithm is that auxiliary variables that occur when the diffusion terms are approximated by the discontinuous Galerkin method are not involved in interprocessor exchange. The developed parallel algorithm is applied to modelling of temperature dynamics in formation with a vertical injection well and hydraulic fracturing. The paper presents the results of a computational experiment and estimates the effectiveness of a parallel algorithm.

A Meshless Finite Difference Method for Conjugate Heat Conduction Problems

2009 ◽  
Author(s):  
Chandrashekhar Varanasi ◽  
Jayathi Y. Murthy ◽  
Sanjay Mathur
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Conjugate Heat Transfer ◽  
Sparse Matrix ◽  
Complex Geometries ◽  
Meshless Finite Difference Method ◽  
Transfer Problems

In recent years, there has been a great deal of interest in developing meshless methods for computational fluid dynamics (CFD) applications. In this paper, a meshless finite difference method is developed for solving conjugate heat transfer problems in complex geometries. Traditional finite difference methods (FDMs) have been restricted to an orthogonal or a body-fitted distribution of points. However, the Taylor series upon which the FDM is based is valid at any location in the neighborhood of the point about which the expansion is carried out. Exploiting this fact, and starting with an unstructured distribution of mesh points, derivatives are evaluated using a weighted least squares procedure. The system of equations that results from this discretization can be represented by a sparse matrix. This system is solved with an algebraic multigrid (AMG) solver. The implementation of Neumann, Dirichlet and mixed boundary conditions within this framework is described, as well as the handling of conjugate heat transfer. The method is verified through application to classical heat conduction problems with known analytical solutions. It is then applied to the solution of conjugate heat transfer problems in complex geometries, and the solutions so obtained are compared with more conventional unstructured finite volume methods. Metrics for accuracy are provided and future extensions are discussed.

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