scholarly journals Existence and approximation for Navier–Stokes system with Tresca’s friction at the boundary and heat transfer governed by Cattaneo’s law

2017 ◽  
Vol 23 (3) ◽  
pp. 519-540
Author(s):  
Mahdi Boukrouche ◽  
Imane Boussetouan ◽  
Laetitia Paoli
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Stokes System ◽  
Transfer Problem ◽  
Propagation Speed ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Splitting Technique ◽  
Tresca’S Friction ◽  
Cattaneo’S Law

We consider an unsteady non-isothermal incompressible fluid flow. We model heat conduction with Cattaneo’s law instead of the commonly used Fourier’s law, in order to overcome the physical paradox of infinite propagation speed. We assume that the fluid viscosity depends on the temperature, while the thermal capacity depends on the velocity field. The problem is thus described by a Navier–Stokes system coupled with the hyperbolic heat equation. Furthermore, we consider non-standard boundary conditions with Tresca’s friction law on a part of the boundary. By using a time-splitting technique, we construct a sequence of decoupled approximate problems and we prove the convergence of the corresponding approximate solutions, leading to an existence theorem for the coupled fluid flow/heat transfer problem. Finally, we present some numerical results.

Steady and Unsteady Modeling for Heat Transfer Predictions of High Pressure Turbine Blade Internal Cooling

2012 ◽  
Author(s):  
Rémy Fransen ◽  
Nicolas Gourdain ◽  
Laurent Y. M. Gicquel
Keyword(s):  
Heat Transfer ◽  
Large Scale ◽  
Cooling System ◽  
Transfer Problem ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Wall Region ◽  
Internal Cooling ◽  
Computational Domain ◽  
Complex Flow

This work focuses on numerical simulations of flows in blade internal cooling system. Large Eddy Simulation (LES) and Reynolds-Averaged Navier Stokes (RANS) approaches are compared in a typical blade cooling related problem. The case is a straight rib-roughened channel with high blockage ratio, computed and compared for both a periodic and full spatial domains. The configuration was measured at the Von Karman Institute (VKI) using Particle Image Velocimetry (PIV) in near gas turbine operating conditions. Results show that RANS models used fail to predict the full evolution of the flow within the channels where massive separation and large scale unsteady features are evidenced. In contrast LES succeeds in reproducing these complex flow motions and both mean and fluctuating components are clearly improved in the channels and in the near wall region. Periodic computations are gauged against the spatial computational domain and results on the heat transfer problem are addressed.

Developing Fluid Flow and Heat Transfer in a Semi-Porous Square Channel

2003 ◽  
Author(s):  
Tien-Chien Jen ◽  
Tuan-Zhou Yan ◽  
S. H. Chan
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Porous Channel ◽  
Navier Stokes ◽  
Axial Position ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer

A three-dimensional computational model is developed to analyze fluid flow in a semi-porous channel. In order to understand the developing fluid flow and heat transfer process inside the semi-porous channels, the conventional Navier-Stokes equations for gas channel, and volume-averaged Navier-Stokes equations for porous media layer are adopted individually in this study. Conservation of mass, momentum and energy equations are solved numerically in a coupled gas and porous media domain in a channel using the vorticity-velocity method with power law scheme. Detailed development of axial velocity, secondary flow and temperature fields at various axial positions in the entrance region are presented. The friction factor and Nusselt number are presented as a function of axial position, and the effects of the size of porous media inside semi-porous channel are also analyzed in the present study.

scholarly journals Efficient Simulations of Large Scale Convective Heat Transfer Problems

2021 ◽  
Vol 22 (4) ◽  
Author(s):  
Damian Goik ◽  
Krzysztof Banaś ◽  
Jan Bielański ◽  
Kazimierz Chłoń
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Large Scale ◽  
Stokes Equations ◽  
Parallel Implementation ◽  
Navier Stokes ◽  
Flow Equations ◽  
Transfer Problems

We describe an approach for efficient solution of large scale convective heat transfer problems, formulated as coupled unsteady heat conduction and incompressible fluid flow equations. The original problem is discretized in time using classical implicit methods, while stabilized finite elements are used for space discretization. The algorithm employed for the discretization of the fluid flow problem uses Picard's iterations to solve the arising nonlinear equations. Both problems, heat transfer and Navier-Stokes quations, give rise to large sparse systems of linear equations. The systems are solved using iterative GMRES solver with suitable preconditioning. For the incompressible flow equations we employ a special preconditioner based on algebraic multigrid (AMG) technique. The paper presents algorithmic and implementation details of the solution procedure, which is suitably tuned, especially for ill conditioned systems arising from discretizations of incompressible Navier-Stokes equations. We describe parallel implementation of the solver using MPI and elements of PETSC library. The scalability of the solver is favourably compared with other methods such as direct solvers and standard GMRES method with ILU preconditioning.  

Heat Transfer Mode and Effect of Fluid Flow on the Morphology of the Weld Pool

2021 ◽  
Vol 406 ◽  
pp. 66-77
Author(s):  
Abdel Halim Zitouni ◽  
Pierre Spiteri ◽  
Mouloud Aissani ◽  
Younes Benkheda
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Weld Pool ◽  
Stokes Equations ◽  
Solid Phase ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Transfer Mode ◽  
Thermal Fields ◽  
Welding Properties

In this work, the heat transfer by conduction and convection mode and effect of fluid flow on the morphology of the weld pool and the welding properties is investigated during Tungsten Inert Gas (TIG) process. In the first part, a computation code under Fortran was elaborated to solve the equations resulting from the finite difference discretization of the heat equation, taking into account the liquid-solid phase change with the associated boundary conditions. In order to calculate the velocity field during welding, the Navier-Stokes equations in the melt zone were simplified and solved considering their stream-vorticity formulation. A mathematical model was developed to study the effect of the melted liquid movement on the weld pool. The evolution of the fraction volume of the liquid and the thermal fields promoted the determination of the molten zone (MZ) and the Heat Affected Zone (HAT) dimensions, which seems to be in good agreement with literature.

scholarly journals Numerical investigation of fluid flow and heat transfer characteristics in sine, triangular, and arc-shaped channels

2007 ◽  
Vol 11 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Zakir Hossain ◽  
Sadrul Islam
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Critical Reynolds Number ◽  
Navier Stokes ◽  
Heat Transfer Characteristics ◽  
Single Wave ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Wavy Channels

Time dependent Navier-Stokes and energy equations have been solved to investigate the fluid flow and heat transfer characteristics in wavy channels. Three different types of two dimensional wavy geometries (e.g. sine-shaped, triangular, and arc-shaped) are considered. All of them are of single wave and have same geometric dimensions. Periodic boundary conditions are used to attain fully developed flow. The flow in the channels has been observed to be steady up to a critical Reynolds number, which depends on the geometric configuration. Beyond the critical Reynolds number a self-sustained oscillatory flow has been observed. As a result of this oscillation, there is increased mixing between core and the near-wall fluids, thereby increasing the heat transfer rate. For the same geometric dimensions, flow becomes unsteady at relatively lower Reynolds number in the arc-shaped channel. .

scholarly journals Topology Optimization of Time Dependent Viscous Incompressible Flows

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Maatoug Hassine
Keyword(s):  
Fluid Flow ◽  
Stokes System ◽  
Incompressible Flows ◽  
Navier Stokes ◽  
Dissipated Energy ◽  
Viscous Incompressible Flows ◽  
Topology And Shape Optimization ◽  
Design Function ◽  
Flow Domain ◽  
Small Obstacle

In this paper, we consider topology and shape optimization problem related to the nonstationary Navier-Stokes system. The minimization of dissipated energy in the fluid flow domain is discussed. The proposed approach is based on a sensitivity analysis of a design function with respect to the insertion of a small obstacle in the fluid flow domain. Some numerical results show the efficiency and accurate of the proposed approach.

Numerical Investigation of Heat Transfer and Flow Field in Domestic Refrigerators

2013 ◽  
Author(s):  
Chaolei Zhang ◽  
Yongsheng Lian
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Stokes Equations ◽  
Transfer Problem ◽  
Radiation Heat Transfer ◽  
Circulation Pattern ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Air Circulation ◽  
The Impact

Air circulation and temperature distribution inside a domestic refrigerator chamber are two important factors in refrigerator design. They are critical for food quality control and energy saving and are affected by natural/forced convection, radiation and layout of the stored food. Knowledge about the actual air flow and temperature distributions inside a refrigerator is required to improve temperature homogeneity and reduce energy consumption. In present work we numerically study the air circulation and the heat transfer phenomena in a domestic frost-free refrigerator. The inner compartment, the evaporator and the outside thermal insulation foam are considered. The conjugate heat transfer problem is studied by solving the unsteady laminar Navier-Stokes equations using a finite volume method. The Boussinesq approximation is used to model the natural convection. The discrete ordinate method is adopted to take into account the radiation heat transfer between the cold back evaporator and warm surfaces to further understand the impact of radiation. The accuracy of the numerical methods is verified through grid sensitivity analysis and comparison with available numerical and experimental data. Comparisons are made with and without radiation. Our simulations show that radiation significantly changes the temperature distribution and air circulation pattern. The effects of shelf and food stored on the temperature distribution and air circulation are also studied by comparing three configurations: empty refrigerator, empty refrigerator with shelves and loaded refrigerator with food.

Optimization of Cost Subject to Uncertainty Constraints in Experimental Fluid Flow and Heat Transfer

1991 ◽  
Vol 113 (2) ◽  
pp. 314-320 ◽  
Author(s):  
J. Peterson ◽  
Y. Bayazitoglu
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Uncertainty Analysis ◽  
Numerical Solution ◽  
Transfer Problem ◽  
Quality Data ◽  
Experimental Equipment ◽  
Planning Stage ◽  
Flow And Heat Transfer ◽  
Experimental Fluid

Uncertainty analysis in the initial stages of any experimental work is essential in obtaining high-quality data. It insures that the proposed experiment has been thoroughly planned, and that the quantities to be calculated from the experimental measurements will be known with reasonable accuracy and precision. While an uncertainty analysis helps insure reliable results, there is another equally significant aspect in the experimental planning stage: minimization of experimental equipment expenses. A method is presented here in which these two essential experimental elements are combined and viewed as an optimization problem for systematic examination. The analysis allows a systematic search for the least expensive combination of experimental equipment that will give the desired accuracy of results. For the numerical solution the Sequential Gradient Restoration Algorithm (SGRA) is selected. A typical experimental fluid flow and heat transfer problem is given, demonstrating the analysis and numerical solution.

scholarly journals ON THE SENSITIVITY OF THE NONLINEAR TERM IN THE OUTFLOW BOUNDARY CONDITION

2021 ◽  
Vol 61 (SI) ◽  
pp. 117-121
Author(s):  
Tomáš Neustupa ◽  
Ondřej Winter
Keyword(s):  
Boundary Condition ◽  
Fluid Flow ◽  
Kinetic Energy ◽  
Stokes System ◽  
Nonlinear Term ◽  
Navier Stokes ◽  
Outflow Boundary Condition ◽  
Flow Through ◽  
Outflow Boundary

This paper studies the artificial outflow boundary condition for the Navier-Stokes system. This type of condition is widely used and it is therefore very important to study its influence on a numerical solution of the corresponding boundary-value problem. We particularly focus on the role of the coefficient in front of the nonlinear term in the boundary condition on the outflow. The influence of this term is examined numerically, comparing the obtained results in a close neighbourhood of the outflow. The numerical experiment is carried out for a fluid flow through the channel with so called sudden extension. Presented numerical results are obtained by means of the OpenFOAM toolbox. They confirm that the kinetic energy of the flow in the channel can be controlled by means of the proposed boundary condition.

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