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A special issue of Energies (ISSN 1996-1073). This special issue belongs to the section "J1: Heat and Mass Transfer".

Deadline for manuscript submissions: closed (25 February 2022) | Viewed by 32247

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Prof. Dr. Artur Bartosik

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Department of Production Engineering, Faculty of Management and Computer Modelling, Kielce University of Technology, 25-314 Kielce, Poland
Interests: engineering; non-Newtonian flows; modeling of turbulence in slurry flows; technical sciences; heat transfer
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Dear Colleagues,

In the era of digital transformation, which includes converting any processes into a quantified format, suitable for future analysis, there is increasing demand on simulations and experiments on heat and fluid flow for a variety of single and multiphase flows, and boundary conditions. The importance of heat and fluid flow is still growing in all aspects of our lives, starting from nature and ending on industrial processes. Thanks to computational fluid dynamics and its commercial packages, we can design and perform optimization of various processes. The increasing ability and understanding of heat and mass transfer phenomena has contributed significantly to effectively managing a variety of processes.

This Special Issue on “Numerical Heat Transfer and Fluid Flow” in Energies is addressed to specialists from all over the world who deal with mathematical modeling and experiments on heat and fluid flow. We expect papers dealing with solutions of problems of scientific and industrial relevance in the broad fields of heat transfer and fluid transportation, including natural resources, biomedical, industrial processes, etc. Papers addressed to the Special Issue will not only solve specific engineering problems but will serve as a catalyst on future directions and priorities in numerical heat transfer and fluid flow.

Topics of interest for publication include but are not limited to the following:

Numerical simulations of mass and/or heat transfer;
Computational fluid dynamics;
Experiments and simulations of single or multiphase flows, including Newtonian and non-Newtonian fluids;
Modeling, optimization and control of heat transfer, fluid flow;
Mini and macro-flows;
Turbulence;
Modelling of turbulence;
Flowing phase interactions;
Energy saving processes, including heat transfer enhancement and decrease in frictional losses.

Prof. Dr. Artur Bartosik
Guest Editor

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Related Special Issue

Numerical Heat Transfer and Fluid Flow 2024 in Energies

Published Papers (14 papers)

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Editorial

Jump to: Research

8 pages, 223 KiB

Open AccessEditorial

Numerical Heat Transfer and Fluid Flow: A Review of Contributions to the Special Issue

by Artur S. Bartosik

Energies 2022, 15(8), 2922; https://doi.org/10.3390/en15082922 - 15 Apr 2022

Cited by 1 | Viewed by 1723

Abstract

The paper contains a summary of successful invited papers addressed to the Special Issue on ‘Numerical Heat Transfer and Fluid Flow’, which were published in 2021 in the scientific journal ‘Energies’ [...] Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

Research

Jump to: Editorial

17 pages, 2153 KiB

Open AccessArticle

A Case Study of Open- and Closed-Loop Control of Hydrostatic Transmission with Proportional Valve Start-Up Process

by Paweł Bury, Michał Stosiak, Kamil Urbanowicz, Apoloniusz Kodura, Michał Kubrak and Agnieszka Malesińska

Energies 2022, 15(5), 1860; https://doi.org/10.3390/en15051860 - 3 Mar 2022

Cited by 13 | Viewed by 2879

Abstract

This paper concerns the start-up process of a hydrostatic transmission with a fixed displacement pump, with particular emphasis on dynamic surplus pressure. A numerically controlled transmission using a proportional directional valve was analysed by simulation and experimental verification. The transmission is controlled by the throttle method, and the variable resistance is the throttling gap of the proportional spool valve. A mathematical description of the gear start-up process was obtained using a lumped-parameters model based on ordinary differential equations. The proportional spool valve was described using a modified model, which significantly improved the performance of the model in the closed-loop control process. After assuming the initial conditions and parameterization of the equation coefficients, a simulation of the transition start-up was performed in the MATLAB–Simulink environment. Simulations and experimental studies were carried out for control signals of various shapes and for various feedback from the hydraulic system. The pressure at the pump discharge port and the inlet port of the hydraulic motor, as well as the rotational speed of the hydraulic motor, were analysed in detail as functions of time. In the experimental verification, complete measuring lines for pressure, speed of the hydraulic motor, flow rate, and temperature of the working liquid were used. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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14 pages, 7153 KiB

Open AccessArticle

Low-Cost Air-Cooling System Optimization on Battery Pack of Electric Vehicle

by Robby Dwianto Widyantara, Muhammad Adnan Naufal, Poetro Lebdo Sambegoro, Ignatius Pulung Nurprasetio, Farid Triawan, Djati Wibowo Djamari, Asep Bayu Dani Nandiyanto, Bentang Arief Budiman and Muhammad Aziz

Energies 2021, 14(23), 7954; https://doi.org/10.3390/en14237954 - 28 Nov 2021

Cited by 26 | Viewed by 5377

Abstract

Temperature management for battery packs installed in electric vehicles is crucial to ensure that the battery works properly. For lithium-ion battery cells, the optimal operating temperature is in the range of 25 to 40 °C with a maximum temperature difference among battery cells of 5 °C. This work aimed to optimize lithium-ion battery packing design for electric vehicles to meet the optimal operating temperature using an air-cooling system by modifying the number of cooling fans and the inlet air temperature. A numerical model of 74 V and 2.31 kWh battery packing was simulated using the lattice Boltzmann method. The results showed that the temperature difference between the battery cells decreased with the increasing number of cooling fans; likewise, the mean temperature inside the battery pack decreased with the decreasing inlet air temperature. The optimization showed that the configuration of three cooling fans with 25 °C inlet air temperature gave the best performance with low power required. Even though the maximum temperature difference was still 15 °C, the configuration kept all battery cells inside the optimum temperature range. This finding is helpful to develop a standardized battery packing module and for engineers in designing low-cost battery packing for electric vehicles. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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16 pages, 5937 KiB

Open AccessArticle

Novel Method of the Seal Aerodynamic Design to Reduce Leakage by Matching the Seal Geometry to Flow Conditions

by Damian Joachimiak

Energies 2021, 14(23), 7880; https://doi.org/10.3390/en14237880 - 24 Nov 2021

Cited by 3 | Viewed by 1652

Abstract

This paper presents a novel method of labyrinth seals design. This method is based on CFD calculations and consists in the analysis of the phenomenon of gas kinetic energy carry-over in the seal chambers between clearances. The design method is presented in two variants. The first variant is designed for seals for which it is impossible to change their external dimensions (length and height). The second variant enables designing the seal geometry without changing the seal length and with a slight change of the seal height. Apart from the optimal distribution of teeth, this variant provides for adjusting chambers geometry to flow conditions. As the result of using both variants such design of the seal geometry with respect to leakage is obtained which enables achieving kinetic energy dissipation as uniform as possible in each chamber of the seal. The method was developed based on numerical calculations and the analysis of the flow phenomena. Calculation examples included in this paper show that the obtained reduction of leakage for the first variant ranges from 3.4% to 15.5%, when compared with the initial geometry. The relation between the number of seal teeth and the leakage rate is also analyzed here. The second variant allows for reduction of leakage rate by 15.4%, when compared with the geometry with the same number of teeth. It is shown that the newly designed geometry reveals almost stable relative reduction of leakage rate irrespective of the pressure ratio upstream and downstream the seal. The efficiency of the used method is proved for various heights of the seal clearance. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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13 pages, 3058 KiB

Open AccessArticle

Thermal Calculations of Four-Row Plate-Fin and Tube Heat Exchanger Taking into Account Different Air-Side Correlations on Individual Rows of Tubes for Low Reynold Numbers

by Mateusz Marcinkowski, Dawid Taler, Jan Taler and Katarzyna Węglarz

Energies 2021, 14(21), 6978; https://doi.org/10.3390/en14216978 - 25 Oct 2021

Cited by 7 | Viewed by 2068

Abstract

Currently, when designing plate-fin and tube heat exchangers, only the average value of the heat transfer coefficient (HTC) is considered. However, each row of the heat exchanger (HEX) has different hydraulic–thermal characteristics. When the air velocity upstream of the HEX is lower than approximately 3 m/s, the exchanged heat flow rates at the first rows of tubes are higher than the average value for the entire HEX. The heat flow rate transferred in the first rows of tubes can reach up to 65% of the heat output of the entire exchanger. This article presents the method of determination of the individual correlations for the air-side Nusselt numbers on each row of tubes for a four-row finned HEX with continuous flat fins and round tubes in a staggered tube layout. The method was built based on CFD modelling using the numerical model of the designed HEX. Mass average temperatures for each row were simulated for over a dozen different airflow velocities from 0.3 m/s to 2.5 m/s. The correlations for the air-side Nusselt number on individual rows of tubes were determined using the least-squares method with a 95% confidence interval. The obtained correlations for the air-side Nusselt number on individual rows of tubes will enable the selection of the optimum number of tube rows for a given heat output of the HEX. The investment costs of the HEX can be reduced by decreasing the tube row number. Moreover, the operating costs of the HEX can also be lowered, as the air pressure losses on the HEX will be lower, which in turn enables the reduction in the air fan power. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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17 pages, 8635 KiB

Open AccessArticle

Numerical Study on the Influence of Vortex Generator Arrangement on Heat Transfer Enhancement of Oil-Cooled Motor

by Junjie Zhao, Bin Zhang, Xiaoli Fu and Shenglin Yan

Energies 2021, 14(21), 6870; https://doi.org/10.3390/en14216870 - 20 Oct 2021

Cited by 4 | Viewed by 1703

Abstract

At present, vortex generators have been extensively used in radiators to improve the overall heat transfer performance. However, there is no research on the effect of vortex generators on the ends of motor coils. Meanwhile, the current research mainly concentrates on the attack angle, shape and size, and lacks a detailed study on the transverse and longitudinal distance and arrangement of vortex generators. In this paper, the improved dimensionless number R is used as the key index to evaluate the overall performance of enhanced heat transfer. Firstly, the influence of the attack angle on heat transfer enhancement is discussed through a single pair of rectangular vortex generators, and the results demonstrate that the vortex generator with a 45° attack angle is superior. On this basis, we compare the effects of different longitudinal distances (2 h, 4 h, and 6 h, h meaning the height of vortex generator) on enhanced heat transfer under four distribution modes: Flow-Up (FU), Flow-Down (FU), Flow-Up-Down (FUD), Flow-Down-UP (FDU). Thereafter, the performances of different transverse distances (0.25 h, 0.5 h, and 0.75 h) of the vortex generators are numerically simulated. When comparing the longitudinal distances, FD with a longitudinal distance of 4 h (FD-4 h) performs well when the Reynolds number is less than 4000, and FU with a longitudinal distance of 4 h (FU-4 h) performs better when the Reynolds number is greater than 4000. Similarly, in the comparison of transverse distances, FD-4 h still performs well when the Reynolds number is less than 4000, and FU with a longitudinal distance of 4 h and transverse distance of 0.5 h (FU-4 h–0.5 h) is more prominent when the Reynolds number is greater than 4000. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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22 pages, 1998 KiB

Open AccessArticle

Modeling Transient Pipe Flow in Plastic Pipes with Modified Discrete Bubble Cavitation Model

by Kamil Urbanowicz, Anton Bergant, Apoloniusz Kodura, Michał Kubrak, Agnieszka Malesińska, Paweł Bury and Michał Stosiak

Energies 2021, 14(20), 6756; https://doi.org/10.3390/en14206756 - 17 Oct 2021

Cited by 14 | Viewed by 1890

Abstract

Most of today’s water supply systems are based on plastic pipes. They are characterized by the retarded strain (RS) that takes place in the walls of these pipes. The occurrence of RS increases energy losses and leads to a different form of the basic equations describing the transient pipe flow. In this paper, the RS is calculated with the use of convolution integral of the local derivative of pressure and creep function that describes the viscoelastic behavior of the pipe-wall material. The main equations of a discrete bubble cavity model (DBCM) are based on a momentum equation of two-phase vaporous cavitating flow and continuity equations written initially separately for the gas and liquid phase. In transient flows, another important source of pressure damping is skin friction. Accordingly, the wall shear stress model also required necessary modifications. The final partial derivative set of equations was solved with the use of the method of characteristics (MOC), which transforms the original set of partial differential equations (PDE) into a set of ordinary differential equations (ODE). The developed numerical solutions along with the appropriate boundary conditions formed a basis to write a computer program that was used in comparison analysis. The comparisons between computed and measured results showed that the novel modified DBCM predicts pressure and velocity waveforms including cavitation and retarded strain effects with an acceptable accuracy. It was noticed that the influence of unsteady friction on damping of pressure waves was much smaller than the influence of retarded strain. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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18 pages, 4150 KiB

Open AccessArticle

Dependence of Conjugate Heat Transfer in Ribbed Channel on Thermal Conductivity of Channel Wall: An LES Study

by Joon Ahn, Jeong Chul Song and Joon Sik Lee

Energies 2021, 14(18), 5698; https://doi.org/10.3390/en14185698 - 10 Sep 2021

Cited by 5 | Viewed by 1963

Abstract

A series of large eddy simulations was conducted to analyze conjugate heat transfer characteristics in a ribbed channel. The cross section of the rib is square and the blockage ratio is 0.1. The pitch between the ribs is 10 times the rib height. The Reynolds number of the channel is 30,000. In the simulations, the effect of the thermal resistance of the solid wall of the channel on convective heat transfer was observed in the turbulent flow regime. The numerical method used was based on the immersed boundary method and the concept of effective conductivity is introduced. When the conductivity ratio between the solid wall and the fluid (K*) exceeded 100, the heat transfer characteristics resembled those for an isothermal wall, and the cold core fluid impinging and flow recirculation mainly influenced the convective heat transfer. For K* ≤ 10, the effect of the cold core fluid impinging became weak and the vortices at the rib corners strongly influenced the convective heat transfer; the heat transfer characteristics were therefore considerably different from those for an isothermal wall. At K* = 100, temperature fluctuations at the upstream edge of the rib reached 2%, and at K* = 1, temperature fluctuations in the solid region were similar to those in the fluid region. The rib promoted heat transfer up to K* = 100, but not for K* ≤ 10. The Biot number based on the channel wall thickness appears to adequately explain the variation of the heat transfer characteristics with K*. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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13 pages, 4008 KiB

Open AccessArticle

Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach

by Slawomir Blasiak

Energies 2021, 14(17), 5512; https://doi.org/10.3390/en14175512 - 3 Sep 2021

Cited by 5 | Viewed by 1342

Abstract

This article presents a variable-order derivative (VOD) time fractional model for describing heat transfer in the rotor or stator in non-contacting mechanical face seals. Most theoretical studies so far have been based on the classical equation of heat transfer. Recently, constant-order derivative (COD) time fractional models have also been used. The VOD time fractional model considered here is able to provide adequate information on the heat transfer phenomena occurring in non-contacting face seals, especially during the startup. The model was solved analytically, but the characteristic features of the model were determined through numerical simulations. The equation of heat transfer in this model was analyzed as a function of time. The phenomena observed in the seal include the conduction of heat from the fluid film in the gap to the rotor and the stator, followed by convection to the fluid surrounding them. In the calculations, it is assumed that the working medium is water. The major objective of the study was to compare the results of the classical equation of heat transfer with the results of the equations involving the use of the fractional-order derivative. The order of the derivative was assumed to be a function of time. The mathematical analysis based on the fractional differential equation is suitable to develop more detailed mathematical models describing physical phenomena. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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26 pages, 9398 KiB

Open AccessArticle

Experimental and Numerical Study of Heat Pipe Heat Exchanger with Individually Finned Heat Pipes

by Grzegorz Górecki, Marcin Łęcki, Artur Norbert Gutkowski, Dariusz Andrzejewski, Bartosz Warwas, Michał Kowalczyk and Artur Romaniak

Energies 2021, 14(17), 5317; https://doi.org/10.3390/en14175317 - 27 Aug 2021

Cited by 6 | Viewed by 2588

Abstract

The present study is devoted to the modeling, design, and experimental study of a heat pipe heat exchanger utilized as a recuperator in small air conditioning systems (airflow ≈ 300–500 m³/h), comprised of individually finned heat pipes. A thermal heat pipe heat exchanger model was developed, based on available correlations. Based on the previous experimental works of authors, refrigerant R404A was recognized as the best working fluid with a 20% heat pipe filling ratio. An engineering analysis of parametric calculations performed with the aid of the computational model concluded 20 rows of finned heat pipes in the staggered arrangement as a guarantee of stable heat exchanger effectiveness ≈ 60%. The optimization of the overall cost function by the “brute-force” method has backed up the choice of the best heat exchanger parameters. The 0.05 m traversal (finned pipes in contact with each other) and 0.062 m longitudinal distance were optimized to maximize effectiveness (up to 66%) and minimize pressure drop (less than 150 Pa). The designed heat exchanger was constructed and tested on the experimental rig. The experimental data yielded a good level of agreement with the model—relative difference within 10%. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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21 pages, 8522 KiB

Open AccessArticle

Numerical Modelling of Heat Transfer in Fine Dispersive Slurry Flow

by Artur Bartosik

Energies 2021, 14(16), 4909; https://doi.org/10.3390/en14164909 - 11 Aug 2021

Cited by 1 | Viewed by 1662

Abstract

Slurry flows commonly appear in the transport of minerals from a mine to the processing site or from the deep ocean to the surface level. The process of heat transfer in solid–liquid flow is especially important for the long pipeline distance. The paper is focused on the numerical modelling and simulation of heat transfer in a fine dispersive slurry, which exhibits yield stress and damping of turbulence. The Bingham rheological model and the apparent viscosity concept were applied. The physical model was formulated and then the mathematical model, which constitutes conservative equations based on the time average approach for mass, momentum, and internal energy. The slurry flow in a pipeline is turbulent and fully developed hydrodynamically and thermally. The closure problem was solved by taking into account the Boussinesque hypothesis and a suitable turbulence model, which includes the influence of the yield shear stress on the wall damping function. The objective of the paper is to develop a new correlation of the Nusselt number for turbulent flow of fine dispersive slurry that exhibits yield stress and damping of turbulence. Simulations were performed for turbulent slurry flow, for solid volume concentrations 10%, 20%, 30%, and for water. The mathematical model for heat transfer of the carrier liquid flow has been validated. The study confirmed that the slurry velocity profiles are substantially different from those of the carrier liquid and have a significant effect on the heat transfer process. The highest rate of decrease in the Nusselt number is for low solid concentrations, while for C > 10% the decrease in the Nusselt number is gradual. A new correlation for the Nusselt number is proposed, which includes the Reynolds and Prandtl numbers, the dimensionless yield shear stress, and solid concentration. The new Nusselt number is in good agreement with the numerical predictions and the highest relative error was obtained for C = 10% and Nu = 44.3 and is equal to −12%. Results of the simulations are discussed. Conclusions and recommendations for further research are formulated. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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12 pages, 857 KiB

Open AccessArticle

An Integral Method for Natural Convection of Van Der Waals Gases over a Vertical Plate

by A. A. Avramenko, I. V. Shevchuk, Yu. Yu. Kovetskaya and N. P. Dmitrenko

Energies 2021, 14(15), 4537; https://doi.org/10.3390/en14154537 - 27 Jul 2021

Cited by 6 | Viewed by 1566

Abstract

This paper focuses on a study of natural convection in a van der Waals gas over a vertical heated plate. In this paper, for the first time, an approximate analytical solution of the problem was obtained using an integral method for momentum and energy equations. A novel simplified form of the van der Waals equation for real gases enabled estimating the effects of the dimensionless van der Waals parameters on the normalized heat transfer coefficients and Nusselt numbers in an analytical form. Trends in the variation of the Nusselt number depending on the nature of the interaction between gas molecules and the wall were analyzed. The results of computations for a van der Waals gas were compared with the results for an ideal gas. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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17 pages, 8731 KiB

Open AccessArticle

Effects of Bent Outlet on Characteristics of a Fluidic Oscillator with and without External Flow

by Nam-Hun Kim and Kwang-Yong Kim

Energies 2021, 14(14), 4342; https://doi.org/10.3390/en14144342 - 19 Jul 2021

Cited by 6 | Viewed by 1492

Abstract

A fluidic oscillator with a bent outlet nozzle was investigated to find the effects of the bending angle on the characteristics of the oscillator with and without external flow. Unsteady aerodynamic analyses were performed on the internal flow of the oscillator with two feedback channels and the interaction between oscillator jets and external flow on a NACA0015 airfoil. The analyses were performed using three-dimensional unsteady Reynolds-averaged Navier-Stokes equations with a shear stress transport turbulence model. The bending angle was tested in a range of 0–40°. The results suggest that the jet frequency increases with the bending angle for high mass flow rates, but at a bending angle of 40°, the oscillation of the jet disappears. The pressure drop through the oscillator increases with the bending angle for positive bending angles. The external flow generally suppresses the jet oscillation, and the effect of external flow on the frequency increases as the bending angle increases. The effect of external flow on the peak velocity ratio at the exit is dominant in the cases where the jet oscillation disappears. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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12 pages, 4618 KiB

Open AccessArticle

Hydraulic Transients in Viscoelastic Pipeline System with Sudden Cross-Section Changes

by Michał Kubrak, Agnieszka Malesińska, Apoloniusz Kodura, Kamil Urbanowicz and Michał Stosiak

Energies 2021, 14(14), 4071; https://doi.org/10.3390/en14144071 - 6 Jul 2021

Cited by 7 | Viewed by 1886

Abstract

It is well known that the water hammer phenomenon can lead to pipeline system failures. For this reason, there is an increased need for simulation of hydraulic transients. High-density polyethylene (HDPE) pipes are commonly used in various pressurised pipeline systems. Most studies have only focused on water hammer events in a single pipe. However, typical fluid distribution networks are composed of serially connected pipes with various inner diameters. The present paper aims to investigate the influence of sudden cross-section changes in an HDPE pipeline system on pressure oscillations during the water hammer phenomenon. Numerical and experimental studies have been conducted. In order to include the viscoelastic behaviour of the HDPE pipe wall, the generalised Kelvin–Voigt model was introduced into the continuity equation. Transient equations were numerically solved using the explicit MacCormack method. A numerical model that involves assigning two values of flow velocity to the connection node was used. The aim of the conducted experiments was to record pressure changes downstream of the pipeline system during valve-induced water hammer. In order to validate the numerical model, the simulation results were compared with experimental data. A satisfactory compliance between the results of the numerical calculations and laboratory data was obtained. Full article

(This article belongs to the Special Issue Numerical Heat Transfer and Fluid Flow 2021)

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