Sub-Grid Filtering Model for Multiphase Heat Transfer With Immersed Tubes

2014 ◽  
Author(s):  
William A. Lane ◽  
Emily M. Ryan ◽  
Avik Sarkar ◽  
Sankaran Sundaresan
Keyword(s):  
Heat Transfer ◽  
Solid Phase ◽  
Constitutive Relations ◽  
Conservation Equation ◽  
Coarse Grid ◽  
Computational Grids ◽  
Constitutive Function ◽  
Flow Simulations ◽  
Energy Conservation Equation ◽  
Functional Forms

Adequately resolving the hydrodynamics and heat transfer in gas-solid flow simulations typically requires computational grids on the order of 1–10 particle diameters. This requirement is not feasible for most full-scale applications. To overcome these impracticalities, we consider a sub-grid filtering approach where the microscopic heat transfer mechanisms are approximated through coarse grid simulations using constitutive relations. Using the open source CFD code Multiphase Flow with Interphase Exchanges (MFIX), we simulate a periodic unit cell domain with immersed horizontal heat transfer cylinders under varying solid-phase fractions and temperatures. The simulation results are averaged over the domain and are used to fit functional forms describing relations between the flow properties and input conditions. The result is a constitutive function that is added as a source term to the solid-phase energy conservation equation to approximate the effective heat transfer between the cylinders and flow with coarse grid simulations.

Heat Transfer Analysis of a Novel Pressurized Air Receiver for Concentrated Solar Power via Combined Cycles

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
I. Hischier ◽  
D. Hess ◽  
W. Lipiński ◽  
M. Modest ◽  
A. Steinfeld
Keyword(s):  
Heat Transfer ◽  
Thermal Efficiency ◽  
Porous Ceramic ◽  
Conservation Equation ◽  
Heat Transfer Analysis ◽  
Operational Parameters ◽  
Small Aperture ◽  
Solar Absorber ◽  
Energy Conservation Equation ◽  
Combined Cycles

A novel design of a high-temperature pressurized solar air receiver for power generation via combined Brayton–Rankine cycles is proposed. It consists of an annular reticulate porous ceramic (RPC) bounded by two concentric cylinders. The inner cylinder, which serves as the solar absorber, has a cavity-type configuration and a small aperture for the access of concentrated solar radiation. Absorbed heat is transferred by conduction, radiation, and convection to the pressurized air flowing across the RPC. A 2D steady-state energy conservation equation coupling the three modes of heat transfer is formulated and solved by the finite volume technique and by applying the Rosseland diffusion, P1, and Monte Carlo radiation methods. Key results include the temperature distribution and thermal efficiency as a function of the geometrical and operational parameters. For a solar concentration ratio of 3000 suns, the outlet air temperature reaches 1000°C at 10 bars, yielding a thermal efficiency of 78%.

Mathematical Modelling of Thermo-Hydro-Mechanical Behaviour for Concrete under Elevated Temperature

2014 ◽  
Vol 670-671 ◽  
pp. 355-364
Author(s):  
Shao Bo Zhang ◽  
Xiao Chun Wang ◽  
Xin Pu Shen
Keyword(s):  
Elevated Temperature ◽  
Stokes Equations ◽  
Constitutive Relations ◽  
Gaseous Mixture ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Energy Conservation Equation

A hydro-thermo-mechanical model was presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air, liquid water, and solid skeleton of concrete. Mass conservation equations, linear momentum conservation equation, and energy conservation equation were derived on the basis of the macroscopic Navier-Stokes equations for a general continuum, along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables were given with existing data from references. Specifications of the constitutive relations were made for the kinetic variables and their conjugate forces.

Chebyshev Collocation Spectral Method for Three-Dimensional Transient Coupled Radiative–Conductive Heat Transfer

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Ya-Song Sun ◽  
Jing Ma ◽  
Ben-Wen Li
Keyword(s):  
Heat Transfer ◽  
Spectral Method ◽  
Three Dimensional ◽  
Conservation Equation ◽  
Conductive Heat Transfer ◽  
Discrete Ordinates ◽  
Conductive Heat ◽  
Chebyshev Collocation ◽  
Energy Conservation Equation ◽  
Collocation Spectral Method

Abstract A Chebyshev collocation spectral method (CSM) is presented to solve transient coupled radiative and conductive heat transfer in three-dimensional absorbing, emitting, and scattering medium in Cartesian coordinates. The walls of the enclosures are considered to be opaque, diffuse, and gray and have specified temperature boundary conditions. The CSM is adopted to solve both the radiative transfer equation (RTE) and energy conservation equation in spatial domain, and the discrete ordinates method (DOM) is used for angular discretization of RTE. The exponential convergence characteristic of the CSM for transient coupled radiative and conductive heat transfer is studied. The results using the CSM show very satisfactory calculations comparing with available results in the literature. Based on this method, the effects of various parameters, such as the scattering albedo, the conduction–radiation parameter, the wall emissivity, and the optical thickness, are analyzed.

Heat Transfer Analysis of a Novel Pressurized Air Receiver for Concentrated Solar Power Via Combined Cycles

2009 ◽  
Author(s):  
Illias Hischier ◽  
Daniel Hess ◽  
Wojciech Lipin´ski ◽  
Michael Modest ◽  
Aldo Steinfeld
Keyword(s):  
Heat Transfer ◽  
Thermal Efficiency ◽  
Porous Ceramic ◽  
Conservation Equation ◽  
Heat Transfer Analysis ◽  
Operational Parameters ◽  
Small Aperture ◽  
Solar Absorber ◽  
Energy Conservation Equation ◽  
Combined Cycles

A novel design of a high-temperature pressurized solar air receiver for power generation via combined Brayton-Rankine cycles is proposed. It consists of an annular reticulate porous ceramic (RPC) bounded by two concentric cylinders. The inner cylinder, which serves as the solar absorber, has a cavity-type configuration and a small aperture for the access of concentrated solar radiation. Absorbed heat is transferred by conduction, radiation, and convection to the pressurized air flowing across the RPC. A 2D steady-state energy conservation equation coupling the three modes of heat transfer is formulated and solved by the finite volume technique and by applying the Rosseland diffusion, P1, and Monte Carlo radiation methods. Key results include the temperature distribution and the thermal efficiency as a function of the geometrical and operational parameters. For a solar concentration ratio of 3000 suns, the outlet air temperature reaches 1000°C at 10 bars, yielding a thermal efficiency of 78%.

Methods for Monitoring the Temperature of GIS Bus Conductor

2014 ◽  
Vol 687-691 ◽  
pp. 770-773
Author(s):  
Gang Wu ◽  
Long Teng Li ◽  
Yun Feng Peng ◽  
Cheng Wen Zhu ◽  
Yong Liang Zhang
Keyword(s):  
Heat Transfer ◽  
Partial Discharge ◽  
Radiation Heat Transfer ◽  
Conservation Equation ◽  
Heat Radiation ◽  
Radiation Heat ◽  
Energy Conservation Equation ◽  
Heat Transfer Theory ◽  
Calculation Results ◽  
Long Time

The performance of GIS bus is directly linked with its heat radiation and temperature rise, and its long-time overheating may cause partial discharge and bus burn-up, posing a threat to the reliability of power system. This paper, based on heat transfer theory and taking into account convection and radiation heat transfer, builds the energy conservation equation and iteratively calculates the temperatures of the bus conductor and shell. The comparison of the calculation results with experimental data has confirmed the correctness of the calculation.

Semi-empirical heat transfer correlations for turbulent tube flow of liquid metals

2018 ◽  
Vol 28 (1) ◽  
pp. 151-172
Author(s):  
Dawid Taler
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Conservation Equation ◽  
Turbulent Prandtl Number ◽  
Content Type ◽  
Nusselt Numbers ◽  
Energy Conservation Equation

Purpose The purpose of this paper is to develop new semi-empirical heat transfer correlations for turbulent flow of liquid metals in the tubes, and then to compare these correlations with the experimental data. The Prandtl and Reynolds numbers can vary in the ranges: 0.0001 ≤ Pr ≤ 0.1 and 3000 ≤ Re ≤ 106. Design/methodology/approach The energy conservation equation averaged by Reynolds was integrated using the universal velocity profile determined experimentally by Reichardt for the turbulent tube flow and four different models for the turbulent Prandtl number. Turbulent heat transfer in the circular tube was analyzed for a constant heat flux at the inner surface. Some constants in different models for the turbulent Prandtl number were adjusted to obtain good agreement between calculated and experimentally obtained Nusselt numbers. Subsequently, new correlations for the Nusselt number as a function of a Peclet number was proposed for different models of the turbulent Prandtl number. Findings The inclusion of turbulent Prandtl number greater than one and the experimentally determined velocity profile of the fluid in the tube while solving the energy conservation equation improved the compatibility of calculated Nusselt numbers, with Nusselt numbers determined experimentally. The correlations proposed in the paper have a sound theoretical basis and give Nusselt number values that are in good agreement with the experimental data. Research limitations/implications Heat transfer correlations proposed in this paper were derived assuming a constant heat flux at the inner surface of the tube. However, they can also be used for a constant wall temperature, as for the turbulent flow (Re > 3,000), the relative difference between the Nusselt number for uniform wall heat flux and uniform wall temperature is very low. Originality/value Unified, systematic approach to derive correlations for the Nusselt number for liquid metals was proposed in the paper. The Nusselt number was obtained from the solution of the energy conservation equation using the universal velocity profile and eddy diffusivity determined experimentally, and various models for the turbulent Prandtl number. Four different relationships for the Nusselt number proposed in the paper were compared with the experimental data.

Evaluation of the Radiative Heat Flux in Absorbing, Emitting and Linear-Anisotropically Scattering Cylindrical Media

1981 ◽  
Vol 103 (2) ◽  
pp. 350-356 ◽  
Author(s):  
F. H. Azad ◽  
M. F. Modest
Keyword(s):  
Heat Transfer ◽  
Anisotropic Scattering ◽  
Conservation Equation ◽  
Substantial Improvement ◽  
Radial Coordinate ◽  
Differential Approximation ◽  
Approximate Methods ◽  
Radial Temperature ◽  
Conservation Of Energy ◽  
Energy Conservation Equation

The contribution of thermal radiation to heat transfer in an emitting, absorbing and linear-anisotropically scattering medium of one-dimensional cylindrical geometry is investigated. It is assumed that the radial temperature distribution in the medium is known or is found in conjunction with overall conservation of energy. The exact solution results in a first-order integral equation in the radial coordinate which is a substantial improvement over previous formulations developed for nonscattering media. Also, two approximate methods are established and tested for their accuracy. The first method is the differential approximation modified to accommodate linear-anisotropic scattering. The second method consists of an exponential kernel approximation in which the geometric integrand functions are replaced by simple exponential functions. The results presented indicate that in engineering applications either approximate method may be used to accurately model the radiative contribution to overall heat transfer rates, reducing the nonlinear integrodifferential energy conservation equation to a nonlinear differential equation.

A Numerical Study of Decoupled Bubble Dynamics in Nucleate Boiling

2009 ◽  
Vol 283-286 ◽  
pp. 329-334
Author(s):  
Muhammad Sajid ◽  
Rachid Bennacer
Keyword(s):  
Heat Transfer ◽  
Level Set ◽  
Bubble Dynamics ◽  
Stokes Equations ◽  
Numerical Study ◽  
Nucleate Boiling ◽  
Conservation Equation ◽  
Interface Motion ◽  
Energy Conservation Equation ◽  
Rate Of Evaporation

Nucleate boiling is an efficient mechanism of heat transfer. The rate of bubble growth and the subsequent bubble motion has a tremendous influence on heat transfer. The study of bubble dynamics is a coupled problem. The rate of evaporation controls the interface speed. One approach to study bubble dynamics is to decouple the problem from energy conservation equation and use an input value of rate of evaporation. The objective is to observe how irregular evaporation rate controls bubble dynamics and the shape of bubble and to study the local over-pressure. The level set method is used to track the liquid-vapor interface. The model consists of the Navier-Stokes equations which govern the momentum and mass balances and the level set equation which governs the interface motion due to phase change. The dynamics of a single bubble under different rates of evaporation and varying levels of gravity have been studied. The results of the numerical simulation show that this model adequately describes bubble dynamics in nucleate boiling, including conditions of microgravity.

Measurement of Mass Flow Rate by Employing Thermometry

2005 ◽  
Author(s):  
Jean F. B. Machado ◽  
Cezar O. R. Negra˜o ◽  
Silvio L. M. Junqueira ◽  
Ricardo A. Mazza ◽  
Rigoberto E. M. Morales
Keyword(s):  
Heat Transfer ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Tube Wall ◽  
Industrial Applications ◽  
Flow Speed ◽  
Conservation Equation ◽  
Energy Conservation Equation ◽  
Heat Transfer Phenomenon

Sudden changes of flow temperature along a tube are common in industrial applications. One may suggest those changes can be related to the flow rate. The current work presents a feasibility analysis to evaluate the mass flow rate by measuring changes of temperature at two positions along a tube wall separated by a known distance. The ratio of the distance and the time to change the temperature at the two points may be related to the average flow speed. This is a convection-conduction heat transfer phenomenon at the flow and tube wall. This conjugated heat transfer is modeled by the energy conservation equation that is solved numerically. The study identifies the ranges of parameters, such as, Reynolds and Biot numbers, wall thickness, etc., on which the technique can be applied. The model results are compared to an analytical solution and preliminary experimental results.

scholarly journals Prediction of 3-dimensional heat treatment model during the friction stir spot welding of AA 6061

2021 ◽  
Author(s):  
Ritesh Jaiswal ◽  
◽  
Rajnish Singh ◽  
Dr. Saadat Ali Rizvi ◽  
◽  
...  
Keyword(s):  
Heat Transfer ◽  
Spot Welding ◽  
Solid Phase ◽  
Research Work ◽  
Conservation Equation ◽  
Friction Stir Spot Welding ◽  
Transfer Model ◽  
Die Steel ◽  
Friction Stir ◽  
Steel Tool

In this research work, a die steel tool was used to join the two aluminium sheets together on a radial drill machine. For this, a cylindrical-shaped tool was fabricated. This tool is then clamped into the drill machine tool post. This rotating tool is then inserted/indented into the workpiece thus generating heat due to friction. The of the deformation of aluminium starts near the vicinity of the die steel tool impression. The tool transferred the soft material from the tip to the plunger. The plunger is in contact with the Aluminum sheet. Soften material is forged on the sheet with the help of a plunger and thus creating a solid phase joint between the Aluminum sheets. Three-dimensional numerical modelings were performed on Ansys software. A 3-D heat transfer model was used to solve the problem of friction stir spot welding (FSSW). This model was solved by applying the energy conservation equation. This model involves the heat generated at the boundary of the workpiece (AA) and the rotating tool and for study, the problem, steady-state heat transfer equation was used. The numerically computed and the measured values are compared to validate the results.

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