Three-dimensional Energy Equations Research Articles

MATHEMATICAL MODEL FOR RISK ASSESSMENT OF THERMAL DAMAGE IN CASE OF FIRE AT THE FACILITIES OF THE FUEL AND ENERGY COMPLEX

Problem statement. The task of prediction for thermal air pollution and assessing the risk of thermal damage to people during a fire at an industrial site is considered. The task is to calculate 3D temperature fields during a fire and, based on this, to assess the risk of thermal damage to people. The purpose of the article. Development of a 3D numerical model for calculating thermal air pollution and assessing the risk of thermal damage to workers at an industrial site in the case of a fire. Methodology. A three-dimensional energy equation was used to model the process of thermal air pollution at an industrial site in the case of a fire. A three-dimensional equation for the velocity potential is used to calculate the air flow velocity field at the industrial site. For the numerical integration of the equation for the velocity potential, the splitting method is used. For the numerical integration of the three-dimensional energy equation, it is split at the differential level into two equations. The first equation describes the spread of temperature due to the movement of air masses. The second equation describes the temperature distribution due to thermal conductivity. For the numerical integration of the first equation, a variable-triangular difference splitting scheme is used. An explicit difference scheme is used for the numerical integration of the second equation. Scientific novelty. A 3D numerical model was created, which allows to quickly calculate the dynamics of the formation of thermal air pollution areas at the industrial site and, based on this information, to predict the risk of thermal damage to people in the work zones at the industrial site. The model is based on the numerical integration of the aerodynamic and heat transfer equations. The model allows to quickly calculate the dynamics of the thermal zones’ formation at the industrial site in the case of a fire. Practical value. The developed model makes it possible to predict the dynamics of changes in temperature fields in the air that occur during a fire at an industrial site. The numerical model can be used to determine zones of intense thermal pollution and assess the risk of thermal damage to workers. Conclusions. On the basis of the developed 3D numerical model, a code was created for conducting a computational experiment. The developed code allows to quickly calculate the dynamics of the formation of thermal air pollution areas at an industrial site during a fire. Based on the received information, the risk of thermal damage to workers is assessed. The results of the computational experiment are presented.

Computational model of nano-pharmacological particles for the clinical management of stenotic and aneurysmatic coronary artery in the human body

This work presents a three-dimensional computational study of nanoparticles (metallic and non-metallic) suspended in blood flowing through a diseased artery with both stenosis and aneurysm. From the perspective of pharmacodynamics and heat transfer, the influence of nanoparticles on hemodynamic indicators was investigated in a diseased artery. The blood was flowing fluid, steady-state, incompressible, homogeneous, and Newtonian, while the artery was a rigid wall. The three-dimensional continuity, Navier-Stokes, and energy equations were solved numerically by using a RAN-based standard k-ω model, which was performed on the ANSYS commercial software package. The influence of different selected nanoparticles (Al2O3, CuO, SiO2, and ZnO), nanoparticle concentration (1.0%-4.0%), and nanoparticle diameters (25 nm - 100 nm) on hemodynamic parameters such as velocity, temperature, turbulence intensity, more particularly skin friction coefficient and Nusselt number of the blood flow on the diseased artery, was also investigated. The streamlines, contours, and plots were adopted to better visualize the blood flow behavior in an artery with stenosis and aneurysm. The numerical results revealed that at a 4.0% nanoparticle concentration, CuO nanoparticles greatly reduced the blood velocity by 1.96% compared to other nanoparticles. About 0.66%-2.05% reduction in the blood velocity could be achieved by increasing the nanoparticle concentration from 1.0% to 4.0%. The SiO2 blood nanofluid showed the best result in augmentation of the Nusselt number by 53.0%. However, the nanoparticle diameter and concentration showed an insignificant effect on the skin friction factor.

Effects of geometrical parameters on thermohydrodynamic performance of a bearing operating with nanoparticle additive oil

PurposeBearing performance characteristics, such as stiffness and load capacity, are related to the viscosity of the fluid circulating through the gap. Nanoparticle additives in lubricant are one way to enhance of the viscosity. This study aims to investigate the effect of nanoparticle additives on the thermohydrodynamic performance of journal bearing with different bearing parameters.Design/methodology/approachThe temperature distribution is modeled using a three-dimensional energy equation. The velocity components are calculated on the pressure distribution governed by Dowson’s equation. Moreover, the heat transfer between the journal and lubricant is modeled with Fourier heat conduction equation. On the other hand, the viscosity equation is derived for Al2O3 nanoparticles as a function of the volume ratio and the temperature. An algorithm based on the finite difference method is developed, and a serial simulation is performed for different parameters and different volume ratio of nanoparticle.FindingsWith the increase in the nanoparticle volume ratio, the maximum temperature decreases for the lower clearance values, but the addition of the nanoparticle influence on the maximum temperature reverses when the clearance grows up. The nanoparticle additives increase further the maximum temperature for higher values of L/D ratios. Moreover, the effects of the nanoparticle additives on the pressure are stronger at high eccentricity ratios for all bearing parameters.Originality/valueThis paper provides valuable design parameters for journal bearing with lubricant containing the nanoparticle additives.

Theoretical and Experimental Comparisons for Rotordynamic Coefficients of a Multiscratched Tilting Pad Journal Bearing

Abstract This paper presents a thermo-elasto-hydrodynamics model (TEHD) based on a mass conservative generalized Reynolds equation, coupled with three-dimensional (3D) energy equation for the oil film, and a full 3D thermo-mechanical model for the pads. The model uses a regularization technique to consider film thickness discontinuities created by scratches. The numerical results are compared to the experimental results obtained from a rocker-backed, five tilting pads journal bearing (TPJB) with single and multiple scratches. The numerical model achieved good agreement, especially with respect to pad temperatures and dynamic coefficients. Discrepancies were observed at low speed but only on the stiffness in the load direction. The numerical model shows a significant drop in the pressure field at the location of the scratches, and a significant pressure rise between two consecutive scratches accompanied by a decrease in film thickness.

Heat transfer enhancement of water-cooled triply periodic minimal surface heat exchangers

Whether triply periodic minimal surface (TPMS) heat exchangers are applicable to cooling or cold storage systems as a cooler for supercritical carbon dioxide (SCO2) is undocumented. Here the conjugated heat transfer of SCO2 in TPMS Schoen-G heat exchanger and printed circuit heat exchanger (PCHE) was predicted based on three-dimensional steady turbulent Reynolds-averaged Navier-Stokes equations, energy equation and shear stress transport model using computational fluid dynamics software ANSYS CFX when SCO2 inlet temperature and pressure vary in 65–30 ℃ and (8–9)MPa. SCO2 in two heat exchangers is cooled under counter-flow conditions by a stream of cold water with given inlet temperature and mass flow rate. It was shown that the mean heat transfer coefficient of SCO2 in TPMS Schoen-G heat exchanger is larger than PCHE. As the inlet pressure rises, the friction factor increases and Nusselt number decreases in the heat exchangers due to decreased Reynolds number and Prandtl number, respectively. The friction factor ratio, Nusselt number ratio and performance evaluation criterion vary in the range of 0.38–0.50, 1.07–1.49, and 1.45–2.04 with Reynolds number and inlet temperature when the PCHE serves as a reference heat exchanger. The streamlines in TPMS Schoen-G heat exchanger are quite smooth even though the areas with a higher velocity appear. The streamlines in PCHE exhibit a spiral flow pattern to result in extra hydraulic loss. The heat transfer enhancement of TPMS Schoen-G heat exchanger is much better TPMS Schwarz-D heat exchanger at a Reynolds number higher than 16,000. The enhancement is attributed to a larger heat transfer surface area and more topological tortuosity without flow separation than PCHE.

A forced convection of water aluminum oxide nanofluid flow and heat transfer study for a three dimensional annular with inner rotated cylinder

The article examines a water alumina nanofluid and heat transfer through the three-dimensional annular. The annular is constructed by the two concentric cylinders in which the inner cylinder can rotate along the tangential direction at a constant speed. A slip boundary condition will be imposed to vanish the viscous effect in the vicinity of the outer cylinder wall. Moreover, the rotating cylinder is kept at a hot temperature, and the outer one is at a cold temperature. A three-dimensional incompressible Navier Stokes and energy equations were carried in cylindrical coordinates. The simulation was observed using the emerging computational tool of COMSOL Multiphysics 5.6, which implements Least Square Galerkin's scheme of finite element method. The parametric study will be done by altering the speed of rotation of the inner cylinder from 1 to 4, volume fraction from 0.001 to 0.9, and the aspect ratio from 0.4 to 0.6 for a fixed Reynolds number of 35,000. The results will be displayed with graphs and tables for average values of the Nusselt number, the percentage change in the temperature, and the skin friction at the middle plan. It was found that the average Nusselt number at the middle of the annular increases before the volume fraction of 0.2 and then decreases for all values of the volume fraction for a fixed rotation of the inner cylinder. The average percentage change relative to the inner cylinder's hot temperature decreases with the volume fraction increase for the fixed rotation. Also, it was found that the quantity of nanoparticles in the domain is improving the average skin friction in the middle of the channel, and it can be reduced by improving the rotation of the inner cylinder by about 10–23% strictly depending upon the aspect ratio for a particular case.

Transient-mixed lubrication model numerically for friction and wear of journal bearings under heavy load during start-up

Purpose Friction and wear are very important factors in predicting the performance of journal bearings, particularly under heavy load in start-up processes. However, there are few relevant studies on the numerical model. This study aims to establish a transient-mixed lubrication model to predict the performance of journal bearings, focusing on the friction and wear behavior under heavy load during start-up. Design/methodology/approach The average Reynold equation, three-dimensional energy equation, shear stress model for friction and Archard model for wear are coupled in the transient model by finite difference method. The linear wear simulation method is bought out to reduce the update times and the calculation time. Findings The different start-up accelerations and linear wear times set are compared and discussed, which indicates a reasonable start-up acceleration is necessary for journal bearings under heavy load during start-up, and setting linear wear times is an effective method to reduce the simulation time significantly. Furthermore, the wear profile in the start-up process spreads in both the clearance and circumferential directions, but mainly in the clearance direction, which increases the minimum film thickness and affects the friction performance. Originality/value This study is of great significance for the numerical prediction of the transient performance of journal bearings during start-up considering friction and wear.

Entropy generation and natural convection on a cubic cavity with a pair of heat source at different configurations

Entropy generation and natural convection in a discretely heated cubic air-filled cavity has been numerically investigated in this study. A pair of discrete heat sources located at the bottom wall is at first considered for three different configurations. Both side walls are fixed at ambient condition, while the remaining walls are kept insulated. The three-dimensional, time-dependent continuity, momentum and thermal energy equations are selected as the governing equations of the present analysis. Galerkin finite element method is employed to solve those equations in non-dimensional forms. Parametric investigation is carried out by varying Rayleigh number within the range of 103–106 at fixed Prandtl number of 0.71. Results are presented in terms of qualitative plots of 3D velocity and thermal fields, and the quantitative evaluation of average Nusselt number and total entropy generation. A functional dependence of Nusselt number on the Rayleigh number and the distance between the symmetrically positioned heaters has also been presented in terms of empirical correlation. This comparative study shows that the configuration of the heaters has a great impact on the thermal characteristics, and thus provides one the opportunity to obtain an optimum arrangement for the system.

Unsteady numerical investigation of nanofluid mixed convection within a cubic cavity with periodic motion of double oscillatory walls

PurposeThe purpose of this study is to investigate the impact of the oscillatory movement on heat transfer within a double periodic lid-driven cubic enclosure filled with copper-water nanofluid and to figure out how the oscillations impact the fluid flow and thermal behavior inside the enclosure. The authors asserted that this study will help to improve the heat transfer efficiency and the thermal performance of various technical engineering equipments.Design/methodology/approachThe cubic enclosure is heated differentially; the left side is cold, the right one is warm and the remaining walls are insulated. Based on the movement directions of the upper and bottom lids, two cases for lid-driven walls are examined (Case 1: same movement for both lids; Case 2: opposite movement for the lids). The finite volume approach was implemented to solve the time-dependent three-dimensional momentum and energy equations, adopting the power low as a scheme of resolution. The numerical study was carried out for a range of parameters: volume fraction (0 ≤ φ ≤ 0.06), Richardson number (0.1 ≤ Ri ≤ 10), non-dimensional lid frequency (2π/50 ≤ Ω ≤ 2π/10) and fixed Grashof number 105.FindingsThe numerical simulations were executed for two different cases of the direction of the motion of the oscillatory lids. Based on the findings obtained, decreasing the Richardson number with low lids frequency gives the best heat transfer enhancement for both cases. Furthermore, in the same conditions, swapping from Case 2 to Case 1 leads to enhancing the maximum average Nusselt number obtained by 29.74%. At a high Richardson number, using high lids frequency increases the heat transfer rate compared to using low lids frequency (an enhancement of 4.32% for Case 1 and 3.63% for Case 2). The best heat transfer rate was established for Case 1 when the lids move positively, transporting the cold flow to the hot side. In all cases, increasing the concentration of nanoparticles improves the heat transfer.Originality/valueThe current study gives an understanding of the problem of mixed convection in a cubic enclosure with oscillatory walls, which has received little attention. And also, there has been no study published on unsteady mixed convection within a double oscillatory lid-driven cavity.

Thermal Characteristics Study of the Bump Foil Thrust Gas Bearing

In this paper, a thermo-hydrodynamic model of the bump foil thrust gas bearing is developed, which solves the coupled gas film three-dimensional energy equation, non-isothermal Reynolds equation, and the foil deformation equation. The effects of bearing speed, thrust load, and external cooling gas on the bearing temperature field are calculated and analyzed. The test rig of foil thrust gas bearing was built to measure the bearing temperature under different working conditions. Both simulation and experiment results show that there exist temperature gradients on the top foil both in the circumferential and radial directions. The simulation results also shows that the top foil side of the gas film has the highest temperature value in the entire lubrication field, and the position of highest temperature moves radially inward on the thrust plate side as the rotor speed increases. The gas film temperature increases with the increasing rotor speed and bearing static load, and rotor speed has greater effects on the temperature variation. Cooling air flow passing through the bump foil is also considered in the simulations, and the cooling efficiency decreases as the mass of gas flow increases.

Run-Up Simulation of a Semi-Floating Ring Supported Turbocharger Rotor Considering Thrust Bearing and Mass-Conserving Cavitation

The vibration behaviour of turbocharger rotors is influenced by the acting loads as well as by the type and arrangement of the hydrodynamic bearings and their operating condition. Due to the highly non-linear bearing behaviour, lubricant film-induced excitations can occur, which lead to sub-synchronous rotor vibrations. A significant impact on the oscillation behaviour is attributed to the pressure distribution in the hydrodynamic bearings, which is influenced by the thermo-hydrodynamic conditions and the occurrence of outgassing processes. This contribution investigates the vibration behaviour of a floating ring supported turbocharger rotor. For detailed modelling of the bearings, the Reynolds equation with mass-conserving cavitation, the three-dimensional energy equation and the heat conduction equation are solved. To examine the impact of outgassing processes and thrust bearing on the occurrence of sub-synchronous rotor vibrations separately, a variation of the bearing model is made. This includes run-up simulations considering or neglecting thrust bearings and two-phase flow in the lubrication gap. It is shown that, for a reliable prediction of sub-synchronous vibrations, both the modelling of outgassing processes in hydrodynamic bearings and the consideration of thrust bearing are necessary.

Superconducting lines cable inputs. Thermal processes modelling

The article considers the thermal state in the basic elements of a cryogenic energy transfer line with high-temperature superconductors. The temperature fields distribution in the heat-stressed elements of the cryogenic energy transmission line with high-temperature superconductors depends on the methods of supplying the cryogenic coolant to cable cryostats and current leads. A large contribution to the total heat flux, especially in cable power lines of short length, falls at the current leads. Computations of complex real current lead structures consist in the joint solution of the hydrodynamics and heat transfer equations for the flux, and the energy equation for the wall. The article considers a three-dimensional non-stationary motion of weakly compressible media (gas and liquid) with a free surface in a semi-closed volume at Mach numbers up to 0.3. The mathematical model is based on the Navier-Stokes equations and total enthalpy. These equations are being solved in conjunction with the equation of state for gas or liquid, the equations for the low Reynolds k-ε turbulence model, and the three-dimensional energy equation for the wall. Recently, Flow Vision application package, or specially designed software are being used for complex three-dimensional thermal calculations.

Three-dimensional thermal calculations of the radiation chamber of a cylindrical heating tube furnace

The paper briefly describes the method of thermal calculations of radiation chambers of tube furnaces on the basis of modelling interconnected processes taking place in the furnace by three-dimensional differential energy equations, the transfer of momentum components, mass concentrations of methane and air, continuity, a two-parameter model of turbulence and the equation of energy transfer by radiation. A software package using this method is applied to carry out numerical analysis of the spatial temperature distribution, the averaged values of velocities of the combustion products turbulent flow in the combustion chamber of a cylindrical heating tube furnace of the oil-processing industry. A furnace diagram with diffusion burners on the radiation chamber floor and differential equations describing physical processes taking place in the furnace are given. Methods for solution of the initial equations are described. The obtained distributions of the surface densities of heat fluxes to the coils along the chamber perimeter at different heights of the furnace are demonstrated. Graphs of the temperature change of the combustion products and the tubular reactor walls for different values of the angular coordinate are given.

Evolution of Designs for Constructal Cooling of a Square Plate Using Water, Ionic Liquid, and Nano-Enhanced Ionic Liquids

Abstract In this paper, we investigate the design-evolution of an embedded pipe based on the constructal theory to obtain the best design that cools a square plate subjected to a constant heat flux boundary condition. The water, ionic liquids (ILs), and nano-enhanced ionic liquids (NEILs, i.e., [C4mim][NTf2] + Al2O3 and [C4mpyrr][NTf2] + Al2O3) have been used as the coolants. Several designs (Case 1 to Case 11) have been tested to quantify the non-dimensional temperature of the heated substrate by implementing the finite volume method of ansys fluent. The three-dimensional continuity, momentum, and energy equations have been solved iteratively in the fluid region by incorporating SIMPLE algorithm with appropriate boundary conditions; while the conduction equation is solved in the solid region. Among all the considered designs, it has been found that Case 3 provides a better cooling effect for the heated substrate. For all of the considered configurations/designs, it is also found that the non-dimensional temperature decreases with the length of the morphing pipe. NEILs exhibit a better cooling effect of the substrate when compared with the ILs and water. The present numerical methodology is also validated with the previous literature.

Hybrid lattice Boltzmann––Finite difference formulation for combined heat transfer problems by 3D natural convection and surface thermal radiation

In this study, a hybrid model for 3D natural convection combined with surface thermal radiation in a closed differentially heated cube was developed. Within this model, numerical procedure for fluid flow was considered in terms of the lattice Boltzmann method under Bhatnagar-Gross-Krook approximation with D3Q19 scheme. On the other hand, unsteady three-dimensional energy equation was solved by means of the finite difference technique. Developed hybrid approach was validated against experimental and up to date numerical data. Mathematical modelling was conducted for two-dimensional and three-dimensional problem formulations under variation of Rayleigh number, conduction-radiation number and surface emissivity. It was found that discrepancy between 2D and 3D results was increased with an enhancement in the radiation heat transfer rate. Computational performance of hybrid lattice Boltzmann method was several times higher than conventional CFD approach.

Numerical Investigation of Forced Convection Heat Transfer from Longitudinal Perforated Fins in a Horizontal Rectangular Channel

The present paper reports a numerical study to investigate the heat transfer enhancement over horizontal channel with longitudinal rectangular fin arrays by laminar forced convection heat transfer. Fins are perforated with two types of holes, square and circular with different diameters. Three-dimensional steady-state continuity, momentum and energy equations along with the Boussinesq approximation were solved by finite volume method with commercial available software ANSYS FLUENT 15.1. The bottom finned wall of the channel was supplied with constant heat flux, while the other sides are insulated. Data used in performance analysis were obtained numerically for fin arrays of material aluminum, by varying geometry, diameter and number of perforation (12, 16 and 20) mm, (10-22) respectively. In addition at different channel inclinations ( 150?> , 1590?> and 15 180?> ), as well as by varying Reynolds number from 1800 to 2300, at modified Grashof number Gr * 5 15?108> . The results show that the Reynolds number and size perforation have a larger impact on average heat transfer coefficients for the both type of Perforations. Also the channel inclination increases the removal heat from the channel. Keywords: Force convection, heat transfer, perforated fin arrays, square holes, notch fins, ordination angle. DOI : 10.7176/JNSR/9-16-05 Publication date : August 31 st 2019

Thermal-mechanical coupling analysis of functionally graded cylindrical shells

Functionally graded materials is a new material for thermal protection in the aerospace field. It is extremely important to study the temperature and stress changes in the thermal environment to ensure the normal operation of the spacecraft and the safety of crews. In this paper, ABAQUS is used to perform sequential thermal coupling and full thermal coupling analysis. The temperature variation and mechanical properties of functionally graded cylindrical shells in thermal environment under temperature and force field and temperature field interacts with force field are studied. Based on the first law of thermoelasticity and thermodynamics, the three-dimensional stress and energy equations of functionally graded cylindrical shells in thermal environment are derived. The example shows that the temperature variation law and mechanical characteristics of the two types of thermo-mechanical coupling analysis are almost the same. The temperature value results of the sequential thermal-mechanical coupling analysis are the same as the results of the full thermal coupling, but the stress value results are lower than the results of the full thermal coupling.

A comparison of mixed convective heat transfer performance of nanofluids cooled heat sink with circular perforated pin fin

This paper presents a numerical study on the mixed convection of nanofluids in heat sinks with perforated circular fins. Four different types of nanofluids are used as cooling fluids, which are TiO2, Al2O3 and Cu dispersed in pure water as the base fluid. The selected volumetric concentration of nanofluids was chosen in the range (2–10)%. The Reynolds number has changed in the range of 100–400 to ensure that flow remains in the laminar regime and to have the Richardson number 1 ≤ Ri ≤ 22. To study the cooling performance of the heat sink, three-dimensional steady Navier Stokes and energy equations were discretized by the finite volume method using the power-law scheme and have been solved iteratively, using the SIMPLE algorithm. The results show that a significant improvement in heat transfer in the heat sink due to the suspension of nanoparticles in the base fluid compared to pure water, the improvement in heat transfer is intensified with increased Reynolds number and decrease in the volume fraction of nanoparticles. We also found that the low values of the average Nusselt number are obtained for the nanofluid TiO2, the average values for Al2O3 and the highest values for Cu. It is important to note that a slight increase in friction factor and pumping power has been reported when nanofluid is used in the system.

Hotspot management using a hybrid heat sink with stepped pin-fins

A hybrid heat sink design with microchannels and stepped pin-fins is introduced for the hotspot-targeted thermal management of microprocessors. The thermal and hydraulic performance were assessed numerically and compared to that of a hybrid heat sink with uniform pin-fins. Both hybrid heat sinks were designed to have two zones using rectangular microchannels above the processor’s background area and an array of pin-fins (stepped and uniform pin-fins) over the hotspot area. Conjugate heat transfer analysis was performed with the entire heat sink as the computational domain by solving the three-dimensional Navier-Stokes and energy equations. The hybrid heat sink with stepped pin-fins exhibited remarkable improvement in the temperature uniformity at the hotspot as compared to the one with uniform pin-fins, along with ample improvements in the thermal resistance, maximum temperature rise at the hotspot, and pumping power. A parametric investigation was also performed for the hybrid heat sink with uniform pin-fins to find an optimum geometry based on two geometric parameters: the ratio of the diameter of the pin-fins to their pitch and the total number of pin-fins in the array. The results revealed improvements in the thermal performance, but the pumping power was increased.

Numerical analysis of flow and conjugate heat transfer for supercritical CO2 and liquid sodium in square microchannels

A numerical analysis of the developing laminar flow and conjugate heat transfer in a rectangular micro-channel was performed for supercritical CO2 and liquid sodium as working fluids for better understanding of the flow and heat transfer mechanisms. Three-dimensional Navier-Stokes, energy, and Laplace equations describing simultaneously developing flow and conjugate heat transfer in multiple micro-channels were solved numerically using Fluent code for the parallel- and counter-flow arrangements. The physical and transport properties of CO2 at supercritical conditions and their influence on fluid flow and heat transfer are presented and discussed. Liquid sodium and supercritical CO2 (sCO2) were used as the heat transfer and hot and cold working fluids, respectively. The values of friction coefficient and Nusselt number predicted by the numerical analysis were compared to the analytical solutions from the literature. Numerical results show that large variations in sCO2 properties in the critical and pseudo-critical regions affect the flow and heat transfer. This effect diminishes for operating conditions (pressure and temperature) further away from the Critical Point. Also, in the fully-developed region the local values of wall shear stress and heat transfer coefficient are not constant, but are strong functions of the local heat flux at the solid-fluid interface which varies due to large variation in sCO2 properties.