Non-isothermal Flow Research Articles

Simulation of Non-Isothermal Turbulent Flows Through Circular Rings of Steel

This article is intended to examine the fluid flow patterns and heat transfer in a rectangular channel embedded with three semi-circular cylinders comprised of steel at the boundaries. Such an organization is used to generate the heat exchangers with tube and shell because of the production of more turbulence due to zigzag path which is in favor of rapid heat transformation. Because of little maintenance, the heat exchanger of such type is extensively used. Here, we generate simulation of flow and heat transfer using non-isothermal flow interface in the Comsol multiphysics 5.4 which executes the Reynolds averaged Navier stokes equation (RANS) model of the turbulent flow together with heat equation. Simulation is tested with Prandtl number (Pr = 0.7) with inlet velocity magnitude in the range from 1 to 2 m/sec which generates the Reynolds number in the range of 2.2 × 105 to 4.4 × 105 with turbulence kinetic energy and the dissipation rate in ranges (3.75 × 10−3 to 1.5 × 10−2) and (3.73 × 10−3−3 × 10−2) respectively. Two correlations available in the literature are used in order to check validity. The results are displayed through streamlines, surface plots, contour plots, isothermal lines, and graphs. It is concluded that by retaining such an arrangement a quick distribution of the temperature over the domain can be seen and also the velocity magnitude is increasing from 333.15% to a maximum of 514%. The temperature at the middle shows the consistency in value but declines immediately at the end. This process becomes faster with the decrease in inlet velocity magnitude.

Численное исследование влияния неизотермичности на характеристики течения степенной жидкости в трубе с резким расширением

In this paper, a steady laminar non-isothermal flow of a power-law fluid in an axisymmetric sudden pipe expansion is numerically simulated. The rheological behavior of the fluid is described by the modified Ostwald-de Waele law; the apparent viscosity is an exponential function of temperature. The equations are written in terms of dimensionless stream function - vortex - temperature. No-slip conditions and zero temperature are used on the solid wall. At the inlet boundary, the velocity and temperature profiles correspond to a one-dimensional steady non-isothermal flow of the considered fluid. “Soft” boundary conditions are assigned at the outlet boundary. The formulated problem is solved using the finite-difference method. The structure of the flow through a sudden pipe expansion is shown to include one- and two-dimensional flow zones with a recirculation region occurring in the inner corner vicinity. The variation in the two-dimensional flow zone length is analyzed with respect to a power-law index and dimensionless criteria of the problem. Distributions of the velocity, temperature, and apparent viscosity are presented at various Peclet and Reynolds numbers for dilatant and pseudoplastic fluids.

Asymptotic Behavior of Weak Solutions of Nonisothermal Flow of Herschel–Bulkley Fluid to Free Boundary

In this manuscript, the behavior of a Herschel–Bulkley fluid has been discussed in a thin layer in ℝ3 associated with a nonlinear stationary, nonisothermal, and incompressible model. Furthermore, the limit problem has been considered, and the studied problem in Ωε is transformed into another problem defined in Ωε without the parameter Ωε (ε is the parameter representing the thickness of the layer tend to zero is studied). We also investigated the convergence of the unknowns which are the velocity, pressure, and the temperature of the fluid. In addition, we established the limit problem and the specific Reynolds equation.

Simulating the hydrocarbon waste pyrolysis in reactors of various designs

The study presents a simulation of pyrolysis reactors of various designs performed in the COMSOL Multiphysics software package. The non-isothermal flow (k–ε turbulent flow) module is used. The advantages this technique has over other commonly used ones are shown. The results indicate that under the same conditions, heating in sectional reactors is more intense. To achieve optimal results, the coolant flow rate in new reactors maybe by an order of magnitude less compared to the conventional design. The use of sectional reactors for multi-flow processing of hydrocarbon waste is advisable. Keywords: sectional reactor; pyrolysis; hydrocarbon waste; heat transfer; turbulent flow.

Development of the algorithm for calculating the optimal molding modes of the BeO slurry using various rheological models

This paper presents the results of calculating a mathematical model of the flow and heat transfer of thermoplastic beryllium oxide in a round channel of a molding installation. An algorithm for calculating the system of equations based on the Herschel-Bulkley rheological model has been developed. The finite-difference analogue of the equations system of motion, continuity, and energy is solved numerically using the CrankNicholson difference scheme. The three-parameter equation is used to test the consistency of experimental, data, and how adequately the physical features of the non-isothermal flow of the slurry convey comparing to the Shvedov-Bingham model. The calculation results illustrate that the proposed model reflects the most important features of the thixotropic flow character of the slurry and is in better agreement with the experimental data of viscoplastic fluids. It provides the calculations of speed of viscous-plastic flow of the slurry based on Shvedov-Bingham and Herschel Bulkley’s two rheological models considering the peculiarities of coagulation structure formation and flow mechanism with boundary conditions. As a result of calculations, the fields of velocity, temperature, and density were obtained, which describe the regularities of the flow and heat transfer of a thermoplastic slurry. The change in the Nusselt criterion along the length of the shaping cavity is shown, which coincides with the analytical solution of Nusselt under first kind boundary conditions. The optimal conditions for the process of ceramics molding by hot casting method have been found, allowing to obtain a hardened product with a homogeneous structure of beryllium ceramics at the outlet.

Вычислительная схема для расчета температурного поля при решении задач нефтедобычи

The paper presents an approach to coupled modeling of hydrodynamic and thermal processes occurring in the oil reservoir during field development using thermal methods of enhanced oil recovery. To simulate the processes of non-isothermal multiphase flow, an approach based on implicit calculation of pressure using the finite element method and an explicit calculation of phase saturations is used. A computational scheme for calculating the temperature field is considered. This scheme makes it possible to take into account both heat transfer between phases and heat transfer of a fluid mixture and matrix-rock. In order to take into account the effect of thermal conductivity, a coefficient characterizing the rate of heat transfer between the fluid mixture and the rock is used. The proposed scheme also takes into account the effect of the temperature field on the phases flow in the field reservoir and provides for the possibility of heat sources and sinks occured due to chemical reactions or thermodynamic processes in gaseous phases. Numerical experiments were carried out on a model of a real oil field obtained as a result of history matching of well data. The model contains a large number of wells and is characterized by a high heterogeneity of the porous medium. The applicability of the considered computational scheme is demonstrated on the example of modeling hot water injection into wells crossing a formation with super-viscous oil. The efficiency of thermal methods for the development of super-viscous oil fields is shown. When hot water was injected into the reservoir, the increase in oil production was about 25 % due to a significant decrease in oil viscosity. The time spent for calculating the temperature field while simulating a multiphase flow did not exceed 6 % of the total computational time.

Two Wire Sensor for Measuring the Velocity of Non-Isothermal Flows.

Changes in the temperature of the medium significantly affect the static characteristics of hot-wire anemometry measuring wires, which causes errors in the results of flow velocity measurements. High temperatures of the medium make it necessary to additionally heat the sensor to even higher temperatures, which may lead to its damage due to wire burnout. The article proposes a solution to the problem of measuring the flow velocity in conditions of non-stationary temperatures with the use of the method of cross-correlation of signals from two-wire resistance thermometers. The main assumptions of the method and its experimental verification were presented.

Study on the leakage of plunger pair under static condition in high-pressure common rail injector considering deformation effect

Plunger pair is the key component of high pressure common rail injector and its sealing performance is very important. Therefore, it is of great significance to study the leakage mechanism of plunger pair. Under static condition, the high-pressure fuel flow in the gap of the plunger pair caused the deformation of the plunger pair structure and the temperature rise of fuel. For a more comprehensive and accurate study, the effect of deformation, including elastic deformation and thermal expansion, the physical properties of fuel, including density, viscosity and specific heat capacity, as well as the influence of plunger posture in the plunger sleeve, including concentric, eccentric, and inclination condition, are considered in this paper. Firstly, the mathematical models including Reynolds equation, film thickness equation, non-isothermal flow equation, parametric equation of fuel physical property, and section velocity equation are established. The numerical analysis based on finite difference method for the solution of these models is given, which can simultaneously solve for the fuel film pressure distribution, temperature distribution, thickness distribution, distribution of fuel physical properties, and leakage rate. The models are validated by comparing the calculated leakage rates with the measurements. The effects under different posture of plunger are discussed too. Some of the conclusions provided good guidance for the design of high-pressure common rail injector.

Development of SPH for simulation of non-isothermal viscoelastic free surface flows with application to injection molding

In the present work, we focus on developing the smoothed particle hydrodynamics (SPH) method for simulation of non-isothermal viscoelastic free surface flows with application to the injection molding process. Specifically, the viscoelastic fluid is governed by the eXtended Pom-Pom (XPP) constitutive equation. The temperature-dependent viscosity and relaxation time are modeled using the Arrhenius relation. The governing equations are discretized by an improved SPH scheme, as presented by Xu and Yu, Appl. Math. Model. 73 (2019) pp. 715–731. We first verify the validity of the SPH method by solving the isothermal/non-isothermal Poiseuille flow of an XPP fluid and comparing the SPH solutions with the analytical solutions or finite volume method solutions. Then, we extend the method to 2D non-isothermal viscoelastic injection molding process of a C-shaped cavity. Some relevant physical information such as temperature, pressure, velocity, flow-induced stresses during the molding process are displayed. The convergence of the method is examined with several different particle sizes. The effects of the Péclet number, Reynolds number, Weissenberg number, viscous ratio, and XPP parameters, on the evolutions of the temperature and flow-induced stresses are analyzed in details. Results for 3D non-isothermal viscoelastic injection molding process of a door handle are lastly presented.

Near-wake flow and thermal characteristics of three side-by-side circular cylinders for large temperature differences using large-eddy simulation

The trailing edge of a gas turbine blade contains rows of short circular cylinders which extract the heat from blade, with the help of the coolant. Large temperature differences exist between the incoming coolant and the blade, and its effect on the flow and thermal characteristics need to be understood. To this end, in the present work, non-isothermal flow over three side-by-side circular cylinders is investigated for a Reynolds number of 3900 using large-eddy simulation (LES). The numerical solver used is validated for isothermal flow using reference experimental data. Large temperature differences, ranging from 25∘C to 300∘C, between the incoming flow and the surface of the cylinders are considered and their effect on the flow and thermal characteristics in the near wake region of cylinders are analyzed. The cylinder-surface and wake characteristics are analyzed using instantaneous and mean quantities. The surface characteristics of the cylinders are studied using Nusselt number, wall shear stress, and lift and drag coefficients. The wake characteristics are studied using Reynolds stresses, turbulent heat flux, and turbulence anisotropy invariant maps. Phase-averaging is used to analyze the unsteady flow and topology of the wake. It is observed that, compared to the middle cylinder the production of turbulence and diffusion of heat is higher behind the two outer cylinders, and their location remains stationed independent of the time. Convection and diffusion of heat takes place along the free shear layer of the wake of the middle cylinder. The vortex shedding behind the cylinders are noted to have multiple frequencies. Further, the vortices shed by the outer cylinders contain more energy and at higher-frequencies when compared to those shed by the middle cylinder.

Magnetic-field- and thermal-radiation-induced entropy generation in a multiphase nonisothermal plane Poiseuille flow.

The effect of radiative heat transfer on the entropy generation in a two-phase nonisothermal fluid flow between two infinite horizontal parallel plates under the influence of a constant pressure gradient and transverse noninvasive magnetic field have been explored. Both fluids are considered to be viscous, incompressible, immiscible, Newtonian, and electrically conducting. The governing equations in Cartesian coordinates are solved analytically with appropriate boundary conditions to obtain the velocity and temperature profile inside the channel. Application of a transverse magnetic field is found to reduce the throughput and the temperature distribution of the fluids in a pressure-driven flow. The temperature and fluid flow inside the channel can also be noninvasively altered by tuning the magnetic field intensity, temperature difference between the channel walls and the fluids, and several intrinsic fluid properties. The entropy generation due to the heat transfer, magnetic field, and fluid flow irreversibilities can be controlled by altering the Hartmann number, radiation parameter, Brinkmann number, filling ratio, and ratios of fluid viscosities and thermal and electrical conductivities. The surfaces of the channel wall are found to act as a strong source of entropy generation and heat transfer irreversibility. The rate of heat transfer at the channel walls can also be tweaked by the magnetic field intensity, temperature differences, and fluid properties. The proposed strategies in the present study can be of significance in the design and development of next-generation microscale reactors, micro-heat exchangers, and energy-harvesting devices.

The influence of temperature dependent fluid properties on topology optimization of conjugate heat transfer

This paper investigates the influence of temperature dependent (TD) fluid properties on the topology optimization of conjugate heat transfer. The density-based method is used to study the topology optimization problem, in which the Brinkman penalty model and heat transfer equation are solved for fluid analysis and heat transfer analysis respectively. The optimization objective is to minimize the root mean square (RMS) of the temperature and the fluid flow dissipated power. During optimizing process, functions of material TD properties are introduced to demonstrate the coupling between fluid flow and heat transfer caused by non-isothermal flow. Comparative numerical experiments with TD fluid properties and temperature independent (TI) fluid properties are performed. Through numerical examples and experimental verification, it is shown that TD fluid properties will cause different topology optimization result and affect the heat dissipation capacity, in which the influence cannot be neglected in topology optimization studies.

Onset about non-isothermal flow of Williamson liquid over exponential surface by computing numerical simulation in perspective of Cattaneo Christov heat flux theory

In view of increaing significance of non-isothermal flow of non-Newtonian fluids over exponential surfaces in numerous industrial and technological procedures such as film condensation, extrusion of plastic sheets, crystal growth, cooling process of metallic sheets, design of chemical processing equipment and various heat exchangers, and glass and polymer industries current disquisition is addressed. For comprehensive examination Williamson model expressing the attributes of shear thickening and thinning liquids is taken under consideration. The physical aspects of magnetic field applied in transverse direction to flow is also accounted. Heat transfer aspects are incorporated and analyzed by employing Cattaneo-Christov heat flux model. Mathematical formulation of problem is conceded in the form of PDE’s by implementing boudary layer approach and later on converted into ODE’s with the assistance of transformation procedure. The resulting equations are solved numerically using shooting and Runge–Kutta methods. Impact of involved parameters on flow distributions is displayed through graphs. From the analysis it is inferred that Cattaneo Christov heat flux law exhibits hyperbolic equation which follows the causality principle and make the problem more compatible to real world applications. It is also deduced that magnetic field suppresses the velocity field and associated boundary layer region. Decrease in temperature profile and heat transfer coefficient is found against inciting magnitude of thermal relaxation parameter. Substantial decrease in velocity is found against increasing magnitude of Williamson fluid parameter and magnetic field parameter whereas skin friction coefficient increments. Confirmation about present findings is executed by making comparison with existing literature.

An Interpolated Bounce Back Thermable Method for Simulating Solid Particles Dynamics in a Viscous Medium

In this paper we discuss the mathematical and computer modeling of non-isothermal two-phase flows with suspended particles. Natural convection between an outer cubical cavity and an inner hot sphere is investigated. To simulate heat fluxes loaded with particles, a thermal model of the lattice Boltzmann equation in combination with the interpolated bounce back method (TLBM-IBB) has been developed. In TLBM-IBB, IBB is used to process liquid-solid interfaces, and TLBM is used to simulate the heat flow of a fluid. The momentum exchange method is used to calculate the hydrodynamic force on the particle surface. Simulation performed for a range of Rayleigh numbers . The accuracy and efficiency of the existing method is demonstrated by the example of solving the test problem of natural convection around a stationary particle and three-dimensional compressible natural convection in a square cavity filled with air, which has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The results obtained are in good agreement with the experimental and numerical results of other authors.

Анализ теплообмена и трения в смесях инертных газов для замкнутых газотурбинных установок

The types of heat exchange surfaces used in closed gas turbines for space applications and their conversion version (ground application) as autonomous long-resource power plants of low power (less than 10 kW) are considered. The data of the works currently known in Russia and abroad on the developed turbulent flow in the tube when using gas mixtures with abnormally low Prandtl numbers (0.2) have been analyzed. Recommendations on the application of the analytical relations of Kays, Petukhov and Popov for the calculation of the Nusselt number in pipes are given. The influence of non-isothermal flow and initial pipe section on friction as well as the working body Prandtl number on heat exchange and friction for highly compact plate and fin heat exchange surfaces with staggered arrangement of ribs are analyzed. It is revealed that the relations obtained for the air model are inapplicable for working bodies with Prandtl numbers different from the air Prandtl number. The necessity of further experimental and analytical investigations of heat exchange and friction in tubes under transient flow regime and in highly compact finned surfaces with staggered ribs is confirmed

Retrieving Equivalent Shear Viscosity for Molten Polymers from 3-D Nonisothermal Capillary Flow Simulation.

For highly viscous polymer melts, considerable fluid temperature rises produced by viscous heating can be a disturbing factor in viscosity measurements. By scrutinizing the experimental and simulated capillary pressure losses for polymeric liquids, we demonstrate the importance of applying a viscous heating correction to the shear viscosity, so as to correct for large errors introduced by the undesirable temperature rises. Specifically, on the basis of a theoretical derivation and 3-D nonisothermal flow simulation, an approach is developed for retrieving the equivalent shear viscosity in capillary rheometry, and we show that the shear viscosity can be evaluated by using the average fluid temperature at the wall, instead of the bulk temperature, as previously assumed. With the help of a viscous Cross model in analyzing the shear-dominated capillary flow, it is possible to extract the viscous heating contribution to capillary pressure loss, and the general validity of the methodology is assessed using the experiments on a series of thermoplastic melts, including polymers of amorphous, crystalline, and filler-reinforced types. The predictions of the viscous model based on the equivalent viscosity are found to be in good to excellent agreement with experimental pressure drops. For all the materials studied, a near material-independent scaling relation between the dimensionless temperature rise (Θ) and the Nahme number (Na) is found, Θ ~ Na0.72, from which the fluid temperature rise due to viscous heating as well as the resultant viscosity change can be predicted.

Two-fluid modeling of heat transfer in flows of dense suspensions

We develop a two-fluid model (TFM) for heat transfer in dense non-Brownian suspensions. Specifically, we propose closure relations for the inter-phase heat transfer coefficient and the thermal diffusivity of the particle phase based on calibration against experimental data. The model is then employed to simulate non-isothermal flow in an annular Couette cell. We find that, when the shear rate is controlled by the rotation of the inner cylinder, both the shear and thermal gradients are responsible for particle migration. Within the TFM framework, we identify the origin and functional form of a “thermo-rheological” migration force that rationalizes our observations. Furthermore, we apply our model to flow in eccentric Couette cells. Our simulations reveal that the system’s heat transfer coefficient is affected by both the classic shear-induced migration of particles and the newly identified thermo-rheological migration effect.

A new solver for incompressible non-isothermal flows in natural and mixed convection over unstructured grids

In the present paper we propose a new numerical methodology for the solution of 2D non-isothermal incompressible flows for natural and mixed convection in irregular geometries. The governing equations are the Incompressible Navier-Stokes equations and the energy conservation equation. Fluid velocity and temperature are coupled in the buoyancy term of the momentum equations according to the Oberbeck-Boussinesq approximation. The governing equations are discretized over unstructured triangular meshes satisfying the Delaunay property. Thanks to the Oberbeck-Boussinesq hypothesis, the flow and energy problems are solved in an uncoupled way, and two fractional time step procedures are sequentially applied to solve each problem. The prediction steps of both procedures are solved applying a Marching in Space and Time (MAST) numerical Eulerian scheme, which explicitly handles the non-linear terms in the momentum equations of the fluid problem, and allows numerical stability for Courant numbers greater than one. An analytical solution is applied for the prediction thermal problem. The correction steps of the two fractional time step procedures involve the solution of large linear systems, whose matrices are sparse and symmetric and have the “M” property if the mesh satisfies the Delaunay condition. This allows a well performing condition number. The matrix coefficients are constant in time, so that they are calculated and factorized only once, before the simulations loop starts, saving a lot of computational time. We present four numerical applications. For the first test, an analytical solution is available, and this makes it possible to analyze the spatial convergence order of the numerical solver. In the other applications, we investigate the capability of the proposed algorithm to handle irregular geometries, and we compare the computed results with experimental data and the outputs of literature models. A study of the required computational costs is also presented.

Finite Element Analysis of Air Flow and Temperature Distribution on Surface of a Circular Obstacle with Resistance and Orientation of Screen

Nonisothermal flow through the rectangular channel on a circular surface under the influence of a screen embedded at the middle of a channel at angles θ is considered. Simulations are carried out via COMSOL Multiphysics 5.4 which implements the finite element method with an emerging technique of the least square procedure of Galerkin’s method. Air as working fluid depends upon the Reynolds number with initial temperature allowed to enter from the inlet of the channel. The nonisothermal flow has been checked with the help of parameters such as Reynolds number, angle of the screen, and variations in resistance coefficient. The consequence and the pattern of the velocity field, pressure, temperature, heat transfer coefficient, and local Nusselt number are described on the front surface of the circular obstacle. The rise in the temperature and the flow rate on the surface of the obstacle has been determined against increasing Reynolds number. Results show that the velocity magnitudes are decreasing down the surface and the pressure is increasing down the surface of the obstacle. The pressure on the surface of the circular obstacle was found to be the function of the y-axis and does not show any impact due to the change of the resistance coefficient. Also, it was indicated that the temperature on the front circular surface does not depend upon the orientation of the screen and resistance factor. The heat transfer coefficient is decreasing which indicates that the conduction process is dominating over the convection process.

Long-term Thermo-hydraulic Response of the Shallow Subsurface soil in the Vicinity of a Buried Horizontal Heat Source

Heat and mass transfer in the shallow subsurface and in the vicinity of buried heat sources has been often studied based on rather simplifying assumptions, such as the Equilibrium Phase Change (EPC), disregarding film flow, and adsorptive soil-water characteristics. In this study, a fully coupled non-isothermal multiphase flow model is developed that utilizes the Non-equilibrium Phase Change (NEPC) approach. First, the performance of the EPC and NEPC approaches is assessed and validated against the in-field experimental data. The second and main objective of this study is to analyze the thermo-hydraulic response of granular soil close to a buried horizontal heat source (e.g., electrical cables) for one year under real meteorological conditions. Numerical results indicate that the NEPC model has higher robustness in predicting the volumetric water content in the soil close to the soil-atmospheric boundary. However, NEPC and EPC approaches estimate the same temperature variations in the soil. In the case of precipitation (e.g., rainfall), the NEPC model predicts higher degrees of saturation in deeper soil in which the infiltrated water reaches 150 cm below the surface, while, in the EPC model, the infiltrated water barely reaches the 100 cm depth. The increase in moisture content close to the heat source facilitates the heat transfer in the medium and thus results in a 40% to 50% reduction in soil temperature close to the heat source. An accurate prediction of the soil moisture content in the medium is needed to evaluate the performance and thermal capacity of buried electrical cables. Furthermore, the heating/cooling cycles contribute to gradually drying the soil in the vicinity of the heater until the hydraulically equilibrated condition is attained.