Non-uniform Volumetric Heat Research Articles

Marangoni convection in a dielectric fluid layer with an AC electric field and nonuniform volumetric heat source due to incident radiation

AbstractThe role of a uniform AC electric field and a nonuniform volumetric heat source arising due to an external incident radiation on the onset of Marangoni convection in a horizontal layer of an incompressible dielectric fluid is investigated. The bottom rigid surface is fixed at a constant temperature while the top free surface at which the surface tension acts is considered to be nondeformable and a Robin boundary condition on the perturbation temperature is invoked. The nonuniform internal heating within the fluid layer alters the conduction temperature profile from linear to nonlinear in the vertical coordinate. The linear stability of the quiescent basic solution is studied with respect to normal mode disturbances. The resulting stability eigenvalue problem with variable coefficient is solved numerically using the Galerkin method. The impact of governing parameters on the instability of the system is discussed thoroughly. The forces causing instability reinforce together and are found to be tightly coupled. It is observed that the strength of nonuniform heat source and the electric Rayleigh number is to hasten, while an increase in the Biot number is to delay the onset of Marangoni electroconvection. Finally, the results obtained under the limiting cases are shown to be in good agreement with those published earlier.

A Modified Analytical Heat Source Model for Numerical Simulation of Temperature Field in Friction Stir Welding

In the conventional analytical model used for heat generation in friction stir welding (FSW), the heat generated at the pin/workpiece interface is assumed to distribute uniformly in the pin volume, and the heat flux is applied as volume heat. Besides, the tilt angle of the tool is assumed to be zero for simplicity. These assumptions bring about simulating deviation to some extent. To better understand the physical nature of heat generation, a modified analytical model, in which the nonuniform volumetric heat flux and the tilt angle of the tool were considered, was developed. Two analytical models are then implemented in the FEM software to analyze the temperature fields in the plunge and traverse stage during FSW of AA6005A‐T6 aluminum hollow extrusions. The temperature distributions including the maximum temperature and heating rate between the two models are different. The thermal cycles in different zones further revealed that the peak temperature and temperature gradient are very different in the high‐temperature region. Comparison shows that the modified analytical model is accurate enough for predicting the thermal cycles and peak temperatures, and the corresponding simulating precision is higher than that of the conventional analytical model.

Numerical research of magnetohydrodynamics buoyant flow in dual functional lead lithium fusion blanket

Blanket is key component of fusion reactor, which functions as tritium breeder, energy conversion component and radiation shield. Liquid metal fusion blanket is a promising candidate of future fusion power plants for its high temperature operating characteristics and efficient thermoelectric conversion. However, motion of liquid metal under fusion reactor high magnetic field (∼4 T) causes serious magnetohydrodynamics (MHD) effect, and extreme non-uniform volumetric heat deposited by fusion neutrons produces strong buoyancy effect. Both effects greatly change flow field and heat transfer characteristics of liquid metal blanket, which are key issues for thermal-hydraulic design of liquid metal blankets. In this paper, MHD buoyant flow of Dual Functional Lead Lithium blanket (DFLL) under typical fusion magnetic field and non-uniform volumetric nuclear heating were studied. Buoyancy force induced drastic natural convection in LL1 (the 1st Lead Lithium channel) channel of blanket and increased the heat leaked to Helium coolant and reduced the outlet temperature. FCI (flow channel insert) material with heat conductivity <1W/m K was required to achieve high outlet temperature (700 K). Reversed direction of original flow in DFLL blanket would smooth the flow and reduce heat leakage of PbLi, which formed the idea of improvement. At the extreme condition of duct with steel wall, Lorentz force completely suppressed buoyancy. According to the founding above, we analyzed the MHD buoyant flow in an upside-down DFLL blanket and temperature distribution and heat leakage were significantly improved. This finding would be valuable for liquid blanket thermal hydraulic design.

Code Validation for Magnetohydrodynamic Buoyant Flow at High Hartmann Number

In liquid metal fusion blanket, the non-uniform volumetric heat deposited by the fusion neutrons leads to the non-uniform density distribution of liquid metal. With the force of gravity, buoyant flows would happen. In the fusion blanket where the magnetic field is up to 4T or even higher and the Hartmann number is ~104, these effects caused by the buoyancy will significantly influence the flow and heat transfer characteristics. In this paper, a module for magnetohydrodynamic (MHD) buoyant flow at high Hartmann number was added to the code MTC. A current density conservative scheme was used to ensure the conservation of current, and the Boussinesq model was used to simulate the buoyancy force. This code was validated by two benchmarks, and the results showed that it can give an accurate simulation for MHD buoyant flows. Main characteristics of buoyancy effects of MHD flows were investigated, and the suppression of buoyant convection by strong magnetic field was studied to understand how the direction of magnetic field and electric conductivity of wall affects the suppression.

Electrolyte film evaporation under the effect of externally applied electric field

The effect of an externally applied electric field and bulk ion-concentration on the evaporation rate of an electrolyte film in contact with a wall is studied numerically. A mathematical model for steady state condition is developed to couple momentum, energy, and mass conservation equations together with the Poisson–Boltzmann equation that describes charge distribution in the liquid film. The model also describes the interaction with humid air flowing above the electrolyte film. The results show a non-uniform volumetric heat generation due to Joule heating that induces a temperature variation along the film length and in the direction away from the wall.

Comparative thermal analysis of Nd- and Yb-doped YAG and KGdW laser crystals under diode- and flashlamp-pumping

Temperature distribution in the Nd- and Yb- doped YAG and KGdW laser crystals under flashlamp- and diode-pumping was characterized by means of finite element analysis. For KGdW, two laser crystal orientations were considered for light propagation along the Np and Ng optical indicatrix axes, taking into account the anisotropy of thermal conductivity coefficient. The influence of the cooling conditions, pump spot size and dopant concentration on the temperature distribution was analyzed. For flashlamp-pumping conditions, the applicability of the quasi-steady-state model is discussed. The main concerns in the thermal management of KGdW laser host is the relatively low thermal conductivity that results in poor cooling and significant absorption coefficients under diode pumping that result in highly non-uniform volumetric heat deposition. “Athermal” Ng-cut KGdW crystal was found to produce higher temperature gradients that the “standard” Np-cut one, that should results in higher internal stresses and higher probability of thermally-induced cracks.

NUMERICAL SIMULATIONS OF INVISCID AIRFLOWS IN RAMJET INLETS

The performances of three different ramjet inlets and an entire ramjet are numerically studied in this paper. The fluid is assumed to be inviscid. Inlet 1 is a SCRAMJET inlet and is chosen from the literature. Inlets 2 and 3 are instead designed based on the Oswatitsch principle. Inlets 2 and 3 produce a series of oblique shocks merging at the engine cowl lip followed by a terminating normal shock just downstream of the inlet throat. In ramjet, the combustion is modeled using a non-uniform volumetric heat source distributed in the combustor area. The position of the terminating normal shock in Inlets 2 and 3 is controlled via the inlet’s back pressure. Instead, in ramjet it is bounded by the amount of heat rate added in combustor and the exhaust nozzle throat area. For the numerical simulations, the Roe (1981) and MacCormack (1969) schemes are used. To prevent the spurious numerical oscillations in high resolution computations by Roe scheme the van Albada flux limiter (1982) is used, while in MacCormack scheme artificial viscosity terms are added to damp the oscillations. To double check the accuracy of the computations, the Fluent software package has also been used. Comparisons show very good agreement.

Computational thermo-fluid exploratory design analysis for complex ITER first wall/shield components

Engineers in the ITER US Party Team used several computational fluid dynamics codes to evaluate design concepts for the ITER first wall panels and the neutron shield modules. The CFdesign code enabled them to perform design studies of modules 7 and 13 very efficiently. CFdesign provides a direct interface to the CAD program, CATIA v5. The geometry input and meshing are greatly simplified. CFdesign is a finite element code, rather than a finite volume code. Flow experiments and finite volume calculations from SC-Tetra, Fluent and CFD2000 verified the CFdesign results. Several new enhancements allow CFdesign to export temperatures, pressures and convective heat transfer coefficients to other finite element models for further analysis. For example, these loads and boundary conditions directly feed into codes such as ABAQUS to perform stress analysis. In this article, we review the use of 2- and 4-mm flow driver gaps in the shield modules and the use of 1-mm gaps along the tee-vane in the front water header to obtain a good flow distribution in both the first wall and shield modules for 7 and 13. Plasma heat flux as well as neutron heating derived from MCNP calculations is included in the first wall and shield module analyses. We reveal the non-uniformity of the convective heat transfer coefficient inside complex 3D geometries exposed to a one-sided heat flux and non-uniform volumetric heating. Most models consisted of 3–4 million tetrahedron elements. We obtained temperature and velocity distributions, as well as pressure drop information, for models of nearly exact geometry compared to the CATIA fabrication models. We also describe the coupling to thermal stress analysis in ABAQUS. The results presented provide confidence that the preliminary design of these plasma facing components will meet ITER requirements.

Free-convective heat transfer in fluids with non-uniform volumetric heat generation

The characteristics of natural convection of a heat-generating fluid with non-uniform distribution of volumetric heat release have been studied theoretically. The analysis was based on analytical estimates method and numerical simulation. It has been found that under particular conditions the details of volumetric heat release distribution over horizontal cross-sections of the liquid pool do not affect the convectional heat transfer characteristics. The vertical distribution of the horizontal cross-sectional mean value of volumetric heat generation completely determines the distribution of temperature in the bulk as well as the heat flux to the cooled boundary.

Onset of natural convection in a rotating fluid layer with non-uniform volumetric heat sources

A study of the thermal instability in an initially quiescent liquid, placed between two horizontal plates, irradiated by a volumetric heat source, and subject to rotation about the vertical axis is carried out. The eigenvalue problem is solved using Chebyshev pseudospectral methods employing the basis recombination technique for higher order problems. The effect of the orientation of the heat source, as well as boundary conditions on the onset of natural convection is studied for different rotation rates. Rotation is seen to unconditionally increase the stationary stability in all cases. Our results indicate a linear relationship between critical Rayleigh number and Taylor number at moderate values of Taylor number, and also show that convection in rotating fluid layer is more sensitive to the exact nature of the heat source distribution in case of stable and quasi stable temperature profiles.

Formulation and testing of the FT n finite volume method for radiation in 3-D complex inhomogeneous participating media

In the present study, an original three-dimensional formulation of the FT n finite volume method based on the bounded high-resolution CLAM schema and using the blocked-off-region technique has been developed. Firstly, this model is applied for 3D inhomogeneous L-shaped absorbing/emitting and isotropically scattering media. Both isothermal medium and medium with internal uniform and non-uniform volumetric heat generation are considered. Secondly, the present FT n FVM results for 3D combustion chamber with five baffles are illustrated and discussed. All tests bring to the fore the advantages, in 3D problems, of the FT n FVM comparatively with the standard FVM especially for inhomogeneous media with discontinuous volumetric heat sources. However these benefits still quantitative and no qualitative discrepancy between the FT n FVM and the popular FVM results are registered.

Laminar mixed convection in power law fluids in continuous flow electrophoresis systems

Laminar mixed convection in a power law fluid flowing between vertical parallel plates is considered. Heat is generated in the fluid by a non-uniform volumetric heat source and the plates are assumed to be adiabatic. The boundary-layer equations are solved using a finite-difference numerical technique. A knowledge of the resulting flow field is of interest in the study of continuous flow electrophoresis systems. Results are presented which show that flow redevelopments due to buoyancy effects occur as well as mixing due to a non-uniform velocity profile. It is shown that the use of pseudoplastic non-Newtonian fluids and the proper geometry and flow rates, can effectively prevent flow redevelopments and velocity profile dispersion under conditions for which they would otherwise occur.