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A Hybrid Finite-Element/Finite-Difference Scheme for Solving the 3-D Energy Equation in Transient Nonisothermal Fluid Flow over a Staggered Tube Bank
Abstract
This article presents a hybrid finite-element/finite-difference approach. The approach solves the 3-D unsteady energy equation in nonisothermal fluid flow over a staggered tube bank with five tubes in the flow direction. The investigation used Reynolds numbers of 100 and 300, Prandtl number of 0.7, and pitch-to-diameter ratio of 1.5. An equilateral triangle (ET) tube pattern is considered for the staggered tube bank. The proposed hybrid method employs a 2-D Taylor-Galerkin finite-element method, and the energy equation perpendicular to the tube axis is discretized. On the other hand, the finite-difference technique discretizes the derivatives toward the tube axis. Weighting the 3-D, transient, convection-diffusion equation for a cube verifies the numerical results. The L2 norm of the error between numerical and exact solutions is also presented for three different hybrid meshes. A grid independence study for the energy equation preceded the final mesh. The outcome is found to be in acceptable concurrence with those from the previous studies. After the temperature field is attained, the local Nusselt number is computed for the tubes in the bundle at different times. The isotherms are also obtained at different times until a steady-state solution is reached. The numerical results converge to the exact results through refining the mesh. The implemented hybrid scheme requires less computation time compared with the conventional 3-D finite-element method, requiring less program coding.
... In a gesture to determine the distribution range of the heat dissipation structure, the internal temperature distribution of the CCAPT is investigated with the knowledge of heat transfer path. With the aim of decreasing the maximum temperature of shell, the effects of fin height h, fin pitch p and fin thickness t on the thermal performance are studied by the means of numerical simulation, considering that the finite volume method is a useful tool [30,31]. The flow field and temperature field on the outside of the fin structure are also obtained as a guidance for improving the heat dissipation effect. ...
... investigated with the knowledge of heat transfer path. With the aim of decreasing the maximum temperature of shell, the effects of fin height h, fin pitch p and fin thickness t on the thermal performance are studied by the means of numerical simulation, considering that the finite volume method is a useful tool [30,31]. The flow field and temperature field on the outside of the fin structure are also obtained as a guidance for improving the heat dissipation effect. ...
... The governing equations indicating continuity, momentum and energy conservation have been illustrated in published literature many times, which are not listed in the paper. Learn from Amiri et al. [30] and Alavi et al. [31], the heat transfer performance is investigated through the finite volume method on the basis of the Reynolds equation and the energy equation. Besides the Realizable κ-ε turbulence model, the SIMPLE algorithm is used for pressure-velocity coupling and the least square cell-based option for the spatial discretization of the gradient. ...
Realizing conversion between fluid power and mechanical energy, the closed circuit axial piston transmission (CCAPT) plays a vital and indispensable role in miscellaneous industries. The frictional loss and leakage loss inside the system give rise to the inevitable temperature rise. In order to prolong the life of the device, a cooling structure on the outside of the CCAPT is designed for promoting heat dissipation. Based on the relevant heat transfer law and the temperature distribution of internal machinery elements, a spiral fin structure is designed at the shell side. With the help of numerical simulation, the effects of fin height, fin pitch, and fin thickness on the thermal performance are studied. The flow field and temperature field on the outside of the fin structure are obtained as a guidance for enhancing heat dissipation effect. Results indicate that the area of rotating elements tend to accumulate heat, where more attention should be paid for a better cooling effect. In addition to this, a moderate increase of fin height, fin pitch and fin thickness has a positive effect on heat transfer enhancement. The peak value of Nusselt number is obtained with a fin height of 7.5 mm, which is about 2.09 times that of the condition without the fin structure. An increase in fin pitch improves both heat transfer performance and comprehensive performance at the same. When fin pitch is 30 mm, Nusselt numberincreases 104% over the original condition.
... Development of the hybrid systems in order to generate cold duty, heat duty, and power, simultaneously has been considered by energy researchers [1,2]. By increasing the energy demand, the development of the energy conversion systems to provide the sustainable energy is one of the main targets of scholars [3]. ...
... General equations of the dried biomass steam reforming process can be seen in Eqs. (1)(2)(3)(4) and reaction kinetics for each component k ai can be also written by Eq. 5 [40]. In the end, ash is removed from syngas in a cyclone, and outlet syngas at 827 °C enters two exchangers to produce air and steam at mentioned conditions for drying and gasification, respectively. ...
... Significant increase of convective HT coefficient without substantial loss of pressure becomes one of the considerable advantage causes for using nanoparticles. To reveal the thermos-physical characteristics of nanofluids, many authors have considered different channel geometries such as backward and forward-facing contracting channels (Alavi et al. 2015), rectangular channel in presence of ribs 8 (Sarlak et al. 2017, Toghraie et al. 2019. ...
In the last few years, the thermo-hydraulic simulation of nanofluid flow bifurcation phenomena has become of great interest to researchers and a useful tool in many engineering applications. FVM has been employed in this article to numerically explore the laminar water flow over a backward facing channel with or without carbon nanoparticles (CN). The problem formulated in this paper has been solved by considering the effects of nanoparticle weight percentages (%), such as 0.00, 0.12, and 0.25 for different Reynolds number (). Nusselt number distribution (()), coefficient of skin friction (), characteristics of pressure drop (∆), velocity contours, static temperature, pumping power () and thermal resistance factor () have been investigated to know the behavior of thermo-hydraulic flow bifurcation phenomena. The present study shows that the surface temperature and coefficient of heat transfer can be reduced due to the effect of or w%. For different w%, it has been found that in the rise in the values of causes the increase of vortex length and as a result velocity gradient and ∆ arises. Furthermore, it has also been studied that the enhancement of causes the increaseof and ∆ .
... Significant increase of convective HT coefficient without substantial loss of pressure becomes one of the considerable advantage causes for using nanoparticles. To reveal the thermos-physical characteristics of nanofluids, many authors have considered different channel geometries such as backward and forward-facing contracting channels (Alavi et al. 2015), rectangular channel in presence of ribs 8 (Sarlak et al. 2017, Toghraie et al. 2019. ...
In the last few years, the thermo-hydraulic simulation of nanofluid flow bifurcation phenomena has become of great interest to researchers and a useful tool in many engineering applications. FVM has been employed in this article to numerically explore the laminar water flow over a backward facing channel with or without carbon nanoparticles (CN). The problem formulated in this paper has been solved by considering the effects of nanoparticle weight percentages (ð‘¤%), such as 0.00, 0.12, and 0.25 for different Reynolds number (ð‘…ð‘’). Nusselt number distribution (ð‘ð‘¢(ð‘¥)), coefficient of skin friction (ð¶ð‘“), characteristics of pressure drop (Δð‘), velocity contours, static temperature, pumping power (ð‘ƒð‘) and thermal resistance factor (ð‘…) have been investigated to know the behavior of thermo-hydraulic flow bifurcation phenomena. The present study shows that the surface temperature and coefficient of heat transfer can be reduced due to the effect of ð‘…ð‘’ or w%. For different w%, it has been found that in the rise in the values of ð‘…ð‘’ causes the increase of vortex length and as a result velocity gradient and Δð‘ arises. Furthermore, it has also been studied that the enhancement of ð‘…ð‘’ causes the increaseof ð‘ƒð‘ and Δð‘.
... To simulate laminar forced convection of nanofluid over a flat plate, the coupled continuity, X and Y momentum and energy equations are solved. The corresponding governing equations are given as [13][14][15]: ...
... In recent years, significant research effort has been directed at improving thermal efficiency and energy utilization across all engineering operations including heat exchange equipment [1][2][3][4][5][6][7], direct contact membrane distillation method [8] as well as to enhance fundamental understanding of transport phenomena in model configurations such as in diverging pipe sections [9][10][11], zigzag profiled wavy channels [12,13], which, in turn, are used as a launching pad to undertake the modelling of complex realistic systems of pragmatic interest. With this backdrop, over the past 50 years or so, there has been a growing recognition of the fact that many complex (high molecular weight polymers, surfactant solutions, foams, emulsions, suspensions, food batters, etc.) materials encountered in a broad spectrum of industrial settings display a variety of non-Newtonian flow characteristics including shear-thinning, dilatant, yield stress, etc. ...
The Poiseuille flow of power-law fluids past a heated sphere in a tapered tube is studied over the following ranges: Blockage ratio, BR (0.1 to 0.5), Separation ratio, SR (0.1 to 0.7), taper angle, α (1o to 20o), Reynolds number, Re (1 to 100), Prandtl number, Pr (10 to 100), and the power law index, n (0.2 to 1). The hydrodynamic force exerted on the sphere is expressed using the total drag coefficient and its pressure component. Both exhibit the expected inverse dependence on Re while it bears a positive dependence on n, SR and BR. The normalized drag for a confined sphere also exhibits a complex functional relationship with each of these parameters. The normalized drag is significantly influenced by the taper angle. In general, SR, BR and α delay the boundary layer separation and hence, stabilize the flow. Similarly, the heat transfer characteristics are described in terms of isotherms, local and surface average Nusselt number. The Nusselt number shows a positive relationship both with SR and BR. The taper angle exerts only a weak effect on the Nusselt number. The heat transfer coefficient is augmented up to 59% in shear-thinning fluids above that in a Newtonian fluid.
... Mahmood et al. [20] presented a hybrid approach to solve the three-dimensional fluid flow over five staggered tubes in the direction of the flow. The values of Reynolds numbers chosen for the investigation was 100 and 300. ...
Flow over arrays of cylinders of different cross-sections has been an essential area of research interest for a long time. For the estimation of flow characteristics around arrays of cylinders, numerical simulation of the flow past four elliptic cylinders in a square arrangement for a range of spacing ratios is analysed in this paper. Three spacing ratios considered in the present study are 3.45, 4.14 and 5.17. The results from the numerical simulation are compared with the experimental findings obtained previously using square cylinder arrays. The fluid flow modelling is performed by applying three-dimensional LES (Large-eddy simulation) with commercial software ANSYS Fluent 19R1. The results from the simulation for elliptic cylinder arrays involve both quantitative and qualitative analyses in the form of various patterns of flow, drag and lift coefficients, St (Strouhal number) and PSD (Power Spectral Density) plots. The Strouhal number values found for cylinder 1 and cylinder 2 in case of elliptic cylinder arrays are 0.642 and 0.703. It is observed that the force coefficients encountered by the cylinders are moderately varying for different spacing ratios.
... And new sampling probes have been devised. Seyyed [13] et al. present a hybrid finite-element/finite-difference approach. The implemented hybrid scheme requires less computation time compared with the conventional 3-D finite-element method, requiring less program coding. ...
During the working period of decay heat removal system, the flow rate of liquid sodium in wire-wrapped fuel assembly is very low, generally Re < 1000 . In the present study, both experimental methods and numerical simulation methods are applied. First, water experiment of 37-pin wire-wrapped rod bundle was carried out. Then, the numerical simulation study was carried out, the experimental data and the numerical simulation results were compared and analyzed, and a suitable turbulence model was selected to simulate the liquid sodium medium. Finally, numerical simulations under different boundary conditions were performed. Results indicate that except for the low Reynolds number k - ε turbulence model, other turbulence models have little difference with the experimental results. The results of realizable k - ε turbulence model are the most close to the experimental results. Compared with the friction factor obtained by using water medium and liquid sodium medium, the calculation results of water medium and sodium medium under the same condition are basically consistent, with the deviation within 1%. The reason is that the velocity of water is higher than sodium medium at the same Reynolds number, and the transverse disturbance caused by helical wire is larger.
... There are few types of research about the effect of particle size and viscosity of GO nanofluids. [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] In this paper, GO synthesized via the MH method. After that, GO added to water, and nanofluid prepared at mass fractions 1.0 to 3.5 mg/ml. ...
Graphene oxide (GO) is a mixture of carbon, oxygen, and hydrogen. GO sheets used to make tough composite materials, thin films, and membranes. GO‐water nanofluid's rheological behavior was investigated in this research. Various mass fractions: 1.0, 1.5, 2.0, 2.5, and 3.5 mg/ml; different temperature ranges: 25°C, 30°C, 35°C, 40°C, 45°C, and 50°C; and several shear ranges: 12.23, 24.46, 36.69, 61.15, 73.38, and 122.3 s⁻¹ were studied. X‐ray diffraction analysis (XRD), energy dispersive X‐ray analysis (EDX), dynamic light scattering analysis (DLS), and Fourier‐transform infrared (FTIR) tests studied to analyze phase and structure. Field emission scanning electron microscope (FESEM) and transmission electron microscopy (TEM) tests studied for microstructural observation. The stability of nanofluid was checked by the zeta‐potential test. Non‐Newtonian behavior of nanofluid, similar to power‐law model (with power less than one), revealed by results. Also, results showed that viscosity increased by increment of mass fraction, and on the contrary, increment of temperature, caused a decrease in viscosity. Then, to calculate nanofluid's viscosity, a correlation presented 1.88% (for RPM = 10) and 0.56% (for RPM = 100) deviation. Finally, to predict nanofluid's viscosity in other mass fractions and temperatures, an artificial neural network has been modeled by R² = 0.99. It can be concluded that GO can be used in thermal systems as stable nanofluid with agreeable viscosity.
... Energy equation [30,31]: ...
To investigate the effect of operational parameter and transport phenomena on para-xylene production from toluene methylation with methanol, a fixed bed tubular reactor packed with Al-HMS-5 mesoporous catalyst was numerically studied. A mechanistic Longmuir–Hinshelwood-type kinetic study has been implemented on a proposed reaction network based on former experimental observation and theoretical background. Kinetic parameters and activation energy related to proposed reaction network for toluene methylation were evaluated using nonlinear regression and Arrhenius plot, respectively. In addition, heat transfer, fluid flow, and chemical reaction equations consisting of toluene methylation and xylene isomerization were solved using finite element method. In order to optimize toluene methylation process, reaction temperature and residence time were investigated. The results showed that uniform distribution of temperature exists at the reactor. There is only deviation from uniform temperature at the reactor entrance, but in other places, the temperature distribution is uniform. As a result, fluid temperature quickly becomes the same as the wall temperature, making the toluene methylation reaction highly efficient. Finally, the residence time of 60 s and wall temperature of 425 K were recommended as optimum working values.
... Today, due to the high expanses of experimental platforms, the computational fluid dynamics (CFD) and numerical simulation have become the effective tools for predicting the results in the industrial and laboratory scales [56][57][58][59][60][61][62]. In this numerical analysis, the finite volume method has been used for solving the numerical domain [63][64][65]. ...
In recent years, the study of rheological behavior and heat transfer of nanofluids in the industrial equipment has become widespread among the researchers and their results have led to great advancements in this field. In present study, the laminar flow and heat transfer of water/functional multi-walled carbon nanotube nanofluid have been numerically investigated in weight percentages of 0.00, 0.12 and 0.25 and Reynolds numbers of 1–150 by using finite volume method (FVM). The analyzed geometry is a two-dimensional backward-facing contracting channel and the effects of various weight percentages and Reynolds numbers have been studied in the supposed geometry. The results have been interpreted as the figures of Nusselt number, friction coefficient, pressure drop, velocity contours and static temperature. The results of this research indicate that, the enhancement of Reynolds number or weight percentage of nanoparticles causes the reduction of surface temperature and the enhancement of heat transfer coefficient. By increasing Reynolds number, the axial velocity enhances, causing the enhancement of momentum. By increasing fluid momentum at the beginning of channel, especially in areas close to the upper wall, the axial velocity reduces and the possibility of vortex generation increases. The mentioned behavior causes a great enhancement in velocity gradients and pressure drop at the inlet of channel. Also, in these areas, Nusselt number and local friction coefficient figures have a relative decline, which is due to the sudden reduction of velocity. In general, by increasing the mass fraction of solid nanoparticles, the average Nusselt number increases and in Reynolds number of 150, the enhancement of pumping power and pressure drop does not cause any significant changes. This behavior is an important advantage of choosing nanofluid which causes the enhancement of thermal efficiency.
... Recently, the prediction of forced convective heat transfer through any geometric bed such as a circular tube conveying hot nanofluids is a fundamental issue in the heat transfer augmentation field. Almost all engineers and researchers have faced with such a problem in vast majority of industries such as heat exchangers, transportation, HVAC, etc.[1][2][3][4][5][6][7]. Those industries performance have been limited by heat transfer; therefore, they need the upgraded fluids to effectively and efficiently transfer the heat[8][9][10]. ...
Many claims of strange/unpredictable change of convective heat transfer in different flow regimes, especially laminar flow regime have been included in nanofluid literature. In this present work, convection of different nanofluids mostly including Al2O3, TiO2 and CuO in various base fluids such as water has been carried out experimentally. The influence of various parameters including volume concentration, Reynolds, Nusselt, Rayleigh and Peclet Numbers, thermophoresis, decreasing thickness of thermal boundary layer, nanoparticles thermal dispersion and nanoparticles migration on heat transfer rate or heat transfer coefficient are considered. Moreover, heat transfer experiments show the heat transfer coefficients of nanofluids are higher than the base fluid. There are some significant factors such as quantity of the aforementioned numbers and the geometries inclinations that have been explained in details in this study. Likewise, the results depict that rate of heat transfer or heat transfer coefficient is enhanced with augmentation of some parameters including volume concentration, Nusselt and Reynolds numbers. However, according to the results, the classical Shah model is failed to forecast the convective heat transfer behavior of nanofluids in laminar flow.
... To simulate laminar forced convection of nanofluid over a flat plate, the coupled continuity, X and Y momentum and energy equations are solved. The corresponding governing equations are given as [13][14][15]: ...
... To simulate laminar forced convection of nanofluid over a flat plate, the coupled continuity, X and Y momentum and energy equations are solved. The corresponding governing equations are given as [13][14][15]: ...
In the present study, the heat transfer and flow of water/FMWCNT (functionalized multi-walled carbon nanotube) nanofluids over a flat plate was investigated using a finite volume method. Simulations were performed for velocity ranging from 0.17 mm/s to 1.7 mm/s under laminar regime and nanotube concentrations up to 0.2%. The 2-D governing equations were solved using an in-house FORTRAN code. For a specific free stream velocity, the presented results showed that increasing the weight percentage of nanotubes increased the Nusselt number. However, an increase in the solid weight percentage had a negligible effect on the wall shear stress. The results also indicated that increasing the free stream velocity for all cases leads to thinner boundary layer thickness, while increasing the FMWCNT concentration causes an increase in the boundary layer thickness.
... A variety of heat exchangers has been widely employed in different engineering applications. Examples are double-pipe or plate heat exchangers used in power production and recovery, food processing, chemical industry, and mechanical appliances such as air conditions, refrigerators, and ventilators [1]. Recent efforts have tried to enhance heat transfer performance of heat exchangers. ...
Nitrogen-doped graphene (NDG) nanofluids are prepared using a two-step method in an aqueous solution of 0.025 wt.% Triton X-100 as a surfactant with various nanosheets at several concentrations (0.01, 0.02, 0.04, 0.06 wt.%). This paper reports results of experiments on thermal conductivity, specific heat capacity, and viscosity of the NDG nanofluids, as well as their convective heat transfer behavior flowing in a double-pipe heat exchanger. To assess the thermal properties, we used various water-based nanofluids as coolants to analyze the total heat transfer coefficient, convective heat transfer coefficient, the percentage of wall temperature reduction, pressure drop, and pumping power in a counter-flow double-pipe heat exchanger. A novel MATLAB code carried out the calculations for Reynolds numbers between 5000 and 15,000 (turbulent flow) and nanosheet weight percentages between 0.00% and 0.06%. An increase in Reynolds number or the percentage of nanomaterial could perhaps enhance the heat transfer of the working fluid. As an example, using 0.06 wt.% nanomaterial in the base fluid led to 15.86% enhancement of the convective heat transfer coefficient in comparison with water. Nonetheless, the penalty in terms of the rise in the pumping power was rather small. For a particular material, increasing Reynolds number or nanomaterial weight percentage would augment pumping power. Power consumption, heat removal, and heat transfer rate were greater for nanofluids than for water in all investigated cases, for a particular pumping power. The average increase in heat transfer coefficient was nearly 16.2%. As a result, choosing NDG/water as the working fluid can improve the performance of double-pipe heat exchangers.
... Recently, flow in small sizes has been widely considered and efforts have been made to make smaller and yet more efficient devices. One of the applications of microchannels is in the cooling of electronic chips, where heat transfer rate is of great importance [1][2][3]. Choi [4] was the first who gave the name of nanofluid to the suspension of nanoparticles in a host fluid and showed considerable increase in their heat transfer coefficient. In recent years, CNTs have attracted many attentions due to their significant mechanical, electrical, and thermal properties. ...
Membrane distillation technology, which combines the membrane process with evaporation, has many benefits, including operation at atmospheric pressure, simple configuration, usage of low-grade heat sources, etc. In the current work, a new type of curved spacers was invented for the direction contact membrane distillation. A three dimensional numerical method was established, which coupled the transmembrane mass transfer with fluid flow in the channel by adding user-defined functions. Different distances between the spacer and the top wall, defined as d, were studied. 4 straight spacers (Sd0, Sd1.5, Sd3,Sd4.5) and 4 curved spacer (Cd0, Cd1.5,Cd3,Cd4.5) were investigated in detail. The curved spacers performed better in mixing and enhancing permeate flux than the straight spacers. The averaged performance enhancement factor (αc) was introduced to evaluate the performance enhancement of the curved spacers compared to the straight spacers. When d was 1.5 mm, αc was 1.33, which was the maximal among the studied cases. The curved spacer performed better in terms of heat transfer, but at a considerable cost in terms of pressure drop. The comprehensive evaluation index (Pec) was proposed to evaluate the overall performance of heat transfer and pressure drop. Pec varied with Reynolds number (Re) and spacer configurations. When Re was in 200 - 550, the maximal value of Pec was achieved by Cd1.5 spacer. When Re was in 500 - 920, the maximal value of Pec was achieved by Cd3 spacer.
Fluid flow and heat transfer of water-based nanofluids over a stretching/shrinking permeable sheet with porous environment under velocity slip and temperature jump conditions is investigated. The flow phenomenon is instigated by a two-dimensional boundary layer flow. On exercising suitable similarity variables, the resulting physical system of nonlinear partial differential equations is transformed into a set of ordinary differential equations. The existence and nonexistence of multiple exact solutions in both the stretching and shrinking problems for various parameters domains is shown. The prominency of stretching or shrinking and velocity slip parameters in shaping the flow behavior and resulting in special exact solutions are reported under various parametric values. The shrinking surface flow exhibit different behavior than the stretching case problem and produces physically meaningful dual solutions. The solutions for the flow and temperature equations are obtained in the form of Kummers function, exponential integral and Eulers gamma function. Morover, results are shown for velocity and temperature profiles for inclusive graphical illustration that includes the influence of velocity slip parameter, temperature jump, permeability and Prandtl number. Moreover, the critical values and plotting curves for obtaining single or dual solution are successfully presented.
The main target of this work is to optimize a novel hybrid system which includes solid oxide fuel cell, gas turbine, and transcritical CO2 power cycle. The system is driven by the biomass gasification process and is supposed to supply thermal and electrical load of a residential subsector in Tehran (the capital of Iran). Furthermore, in order to maximize the waste heat utilization, a novel adaption of active thermal storage units and cooler of the transcritical cycle is proposed. The Aspen Plus V9 and Aspen HYSYS V9 software are utilized to simulate the proposed hybrid system. Also, the calculations of the loads are implemented by the TRNSYS software. In the final optimum model, about 10% of the total electrical load is generated by transcritical cycle and the rest of 90% is produced by SOFC/GT combination with the optimum ratio of power produced by fuel cell to gas turbine considered to be 50%. The results illustrated that by applying the transcritical CO2 cycle, the exergy and energy efficiency increase up to 4.7% and 1.3%, respectively. Also, the total cost reduces by 2.7%. Moreover, it was found that by using the 27.5% of anode and 50% of cathode of gas recirculation, the efficiency of fuel cell subunit is maximized. Finally, the optimum model is compared to the ones having the same configuration of fuel cell/gas turbine with different downstream models including the heat recovery steam generator unit and steam turbine (with and without transcritical cycle).
Purpose
The purpose of this paper is to improve the lattice Boltzmann method’s ability to simulate a microflow under constant heat flux.
Design/methodology/approach
Develop the thermal lattice Boltzmann method based on double population of hydrodynamic and thermal distribution functions.
Findings
The buoyancy forces, caused by gravity, can change the hydrodynamic properties of the flow. As a result, the gravity term was included in the Boltzmann equation as an external force, and the equations were rewritten under new conditions.
Originality/value
To the best of the authors’ knowledge, the current study is the first attempt to investigate mixed-convection heat transfer in an inclined microchannel in a slip flow regime.
A numerical simulation study was performed to examine the effect of nozzle geometry and divergent length on gas-particle flows in dual hose dry ice blasting. The simultaneous model of mass momentum and energy exchange between two phases was solved iteratively. The phases are solid dry ice particle and compressible air fluid as a working medium. The results were presented in the gas flow field along the nozzle centerline. The results showed that increasing divergent length decreases the gas-particle density along the centerline; and the density development along the nozzle centerline decreased along the length. Eddy viscosity of the nozzle cavity was steady for length of 0.25 m, but increased drastically for higher values. The substantial increase in eddy viscosity after that position is due to the mixing flow between dry ice pellet and compressed gas which is diverging out from the nozzle outlet area. Thus, the mixing flow experienced back pressure from the atmospheric pressure. The particle mass concentration decreased by increasing nozzle centerline coordinates. The pressure increased along the length; however, it dropped at the end due to the reverse pressure. The temperature increased steadily because of conversion of turbulence to internal thermal energy. The characteristics of gas-particle flow in the nozzle cavity provide better understanding of multiphase flow in turbine and jet engine flow analysis.
In this study, the numerical analysis of energy and exergy has been performed for a gas turbine cycle coupled with an ORC cycle. Validation of current analysis has been justified with a previous study. Optimization of the working pressure of ORC cycle has been investigated through both energy and exergy analysis with two purposes of finding the optimum working pressure and determining the optimum working fluid. Different constraints have been taken into account, and optimum criteria are discussed. Six different working fluids have been considered for analysis through which dimethyl carbonate and o-xylene showed the most and least desirable criteria in both energy and exergy analysis. Moreover, results indicate that the optimum working pressure is the maximum available pressure, defined in this paper. The optimum working fluid was found to be dimethyl carbonate throughout the analysis.
The parameters of foaming and nano-clay percentage on the density of polymer foam and cell size with the PVC field is studied. Cell size and density have a significant impact on the strength of foam and its insulation (including sounds and thermal insulation). By optimizing cell size and density, foam can be produced with the best mechanical properties. In foaming process of the nanocomposite samples by mass method, the design variables (input parameters) are foaming time and temperature and MMT content. The controlled elitist multi-objective GA is applied to minimize both the foam density and the cell size. To that end, the population size and the Pareto fraction are selected as 100 and 0.5, respectively. The noninferior solution obtained by the controlled elitist multi-objective GA is illustrated. When both the MMT and the temperature are high, the resulting foam does not have ideal characteristics.
The main purpose of this research is the numerical modeling of laminar mixed convection heat transfer inside an open square cavity with different heat transfer areas. In the considered geometry, cold fluid enters the cavity. At the middle of the cavity, there is a hot isothermal circular heat source. For increasing the heat transfer, solid silver nanoparticles with volume fractions (φ) of 0, 2 and 4% are added to water. Studied Re numbers are 10, 50, 120 and 200. The location of the hot zone changes the temperature distribution in the fluid layers. If the heat transfer area is located in an appropriate location, temperature distribution becomes more uniform. Increasing Re leads to smaller temperature gradients in regions near the hot surface and higher temperature at fluid layers close to the surface. By increasing fluid velocity, backflows do not improve heat transfer but it is able to change the heat transfer mechanism. By decreasing the fluid velocity, the effects of velocity gradients and extension of the velocity boundary layer increase and friction coefficient attains the maximum value.
Purpose
Although many studies have been conducted on the nanofluid flow in microtubes, this paper, for the first time, aims to investigate the effects of nanoparticle diameter and concentration on the velocity and temperature fields of turbulent non-Newtonian Carboxymethylcellulose (CMC)/copper oxide (CuO) nanofluid in a three-dimensional microtube. Modeling has been done using low- and high-Reynolds turbulent models. CMC/CuO was modeled using power law non-Newtonian model. The authors obtained interesting results, which can be helpful for engineers and researchers that work on cooling of electronic devices such as LED, VLSI circuits and MEMS, as well as similar devices.
Design/methodology/approach
Present numerical simulation was performed with finite volume method. For obtaining higher accuracy in the numerical solving procedure, second-order upwind discretization and SIMPLEC algorithm were used. For all Reynolds numbers and volume fractions, a maximum residual of 10⁻⁶ is considered for saving computer memory usage and the time for the numerical solving procedure.
Findings
In constant Reynolds number and by decreasing the diameter of nanoparticles, the convection heat transfer coefficient increases. In Reynolds numbers of 2,500, 4,500 and 6,000, using nanoparticles with the diameter of 25 nm compared with 50 nm causes 0.34 per cent enhancement of convection heat transfer coefficient and Nusselt number. Also, in Reynolds number of 2,500, by increasing the concentration of nanoparticles with the diameter of 25 nm from 0.5 to 1 per cent, the average Nusselt number increases by almost 0.1 per cent. Similarly, In Reynolds numbers of 4,500 and 6,000, the average Nusselt number increases by 1.8 per cent.
Research limitations/implications
The numerical simulation was carried out for three nanoparticle diameters of 25, 50 and 100 nm with three Reynolds numbers of 2,500, 4,500 and 6,000. Constant heat flux is on the channel, and the inlet fluid becomes heated and exists from it.
Practical implications
The authors obtained interesting results, which can be helpful for engineers and researchers that work on cooling of electronic devices such as LED, VLSI circuits and MEMS, as well as similar devices.
Originality/value
This manuscript is an original work, has not been published and is not under consideration for publication elsewhere. About the competing interests, the authors declare that they have no competing interests.
In this study, we numerically investigated the forced heat-transfer and laminar flow in a two-dimensional microchannel whose lower half was filled with a porous medium. The nanoparticles used were Fe3O4 and a water-based fluid. The nanoparticles were considered in the form of a completely stable suspension in a water-based fluid. The nanofluid flow in this microchannel was modeled employing the Darcy–Forchheimer equation. We also hypothesized that there was a thermal equilibrium between the solid phase and nanofluid for energy transfer. And the walls of the microchannels were assumed at a constant temperature higher than the inlet fluid temperature. Also, the slip boundary condition was assumed along the walls. The effects of Darcy number, porosity and slip coefficients, and Reynolds number on the velocity and temperature profiles, and local Nusselt number were studied in both porous and non-porous regions in this research. In this study, the Darcy number was assumed to be Da = 0.1 and 0.01, Reynolds number Re = 25, 50, and 100, slip coefficient B = 0.1, 0.01, and 0.001, the porosity of the porous medium ε = 0.5 and 0.9, and the volume percentage of the nanoparticles φ = 0%, 2%, and 4%. With the Darcy number decreasing, the local Nusselt number increased in the non-porous region, and decreased in the porous region. And this phenomenon was observed for the first time. The increase in the Reynolds number increased the heat transfer in both regions. For instance, the local Nusselt number increased 4 times with the Reynolds number changing from 25 to 100 under the same conditions. The decreased Darcy number in the porous medium increased the amount of slip velocity near the walls in the non-porous region, and on the other hand, the decreased Darcy number in the porous medium reduced the slip velocity in the porous region. Also, the jump observed in the slip velocity, was due to the presence of the fluid velocity in the microchannel width.
Mixed convection heat transfer of water–alumina nanofluid in a square chamber with a rotating blade in its center is studied numerically. The governing equations are discretized by using a finite-difference method and solved simultaneously using the SIMPLE algorithm. The blade thickness is assumed to be negligible, the vertical walls of the chamber are at constant temperature of \(T_{\text{c}}\) and \(T_{\text{h}}\), and the horizontal walls are insulated. The effects of Rayleigh number (\(10^{3} \le Ra \le 10^{6}\)) and Richardson (\(0.1 \le Ri \le 100\)) number, the dimensionless length of the blade (\(0.6 \le a \le 0.8\)) and the volumetric percentage of nanoparticles (\(0 \le \varphi \le 0.03\)) on flow and thermal fields are investigated. The results show that an increase in Rayleigh number, volumetric percentage of nanofluid and blade length leads to heat transfer increasing in most cases, but an increase in Richardson number results in a reduction in heat transfer. It is revealed that the maximum blade rotation occurs at small Richardson numbers.
The dry cooling towers (HELLER) are one of the most current cooling towers used in steam power plants. These cooling towers are mostly used in dry areas. The environmental effects are one of the important problems on the performance of these kinds of cooling towers and the most challenging problem is the velocity of wind blow inside and around the cooling tower. In present research, finite volume method and k-ε model have been used for 3-D modeling. In this study, the dual and quadruple external breakers next to the cooling tower in different wind blow velocities have been examined. By using wind breakers, the heat loss retrieves. However, this enhancement is more for quadruple wind breaker, compared to the dual wind breaker. Condenser vacuum has a direct relation with the outlet water temperature of cooling tower. By using wind breakers, outlet water temperature increment of cooling tower reduces.
The thermal and hydraulic performance of plain and oval tubes closed wet cooling tower (CWCT) are investigated numerically. Computational fluid dynamics (CFD), ANSYS Fluent 12.1, is implemented for the numerical solution. Species transport without reactions is adopted to simulate the mass transfer from the air-deluge water interface to the air. Different turbulence models and near-wall treatments are used to assess which model fits the data better. The mass transfer Colburn factor j m , and friction factor f are presented and compared with experimental data. The proposed CFD model is also applied to predict the mass transfer coefficient of another CWCT and compares well with the experimental data.
Different numerical methods have been implemented to simulate internal natural convection heat transfer and also to identify the most accurate and efficient one. A laterally heated square enclosure, filled with air, was studied. A FORTRAN code based on the lattice Boltzmann method (LBM) was developed for this purpose. The finite difference method was applied to discretize the LBM equations. Furthermore, for comparison purpose, the commercially available CFD package FLUENT, which uses finite volume Method (FVM), was also used to simulate the same problem. Different discretization schemes, being the first order upwind, second order upwind, power law, and QUICK, were used with the finite volume solver where the SIMPLE and SIMPLEC algorithms linked the velocity-pressure terms. The results were also compared with existing experimental and numerical data. It was observed that the finite volume method requires less CPU usage time and yields more accurate results compared to the LBM. It has been noted that the 1st order upwind/SIMPLEC combination converges comparatively quickly with a very high accuracy especially at the boundaries. Interestingly, all variants of FVM discretization/pressure-velocity linking methods lead to almost the same number of iterations to converge but higher-order schemes ask for longer iterations.
In this paper, the lattice Boltzmann method (LBM) is applied to solve the energy equation of a transient conduction–radiation heat transfer problem in a two-dimensional cylindrical enclosure filled with an emitting, absorbing and scattering media. The control volume finite element method (CVFEM) is used to obtain the radiative information. To demonstrate the workability of the LBM in conjunction with the CVFEM to conduction–radiation problems in cylindrical media, the energy equation of the same problem is also solved using the finite difference method (FDM). The effects of different parameters, such as the grid size, the scattering albedo, the extinction coefficient and the conduction–radiation parameter on temperature distribution within the medium are studied. Results of the present work are compared with those available in the literature. LBM-CVFEM results are also compared with those given by the FDM-CVFEM. In all cases, good agreement has been obtained.
The influence of the location of the downstream boundary on unsteady incompressible flow solutions is investigated in a series of numerical experiments performed for flow past a circular cylinder at Reynolds number 100. The governing equations are the velocity-pressure formulation of the Navier-Stokes equations, and at the downstream boundary the traction-free condition is imposed. Temporally periodic flow fields obtained by using computational domains with various lengths are compared. It is observed that as far as the near-field solution, the Strouhal number, and the lift and drag coefficients are concerned, the downstream boundary can be placed as close as 14.5 diameters from the center of the cylinder with virtually no difference in the solution. Furthermore, only third-digit variations in the Strouhal number and the lift and drag coefficients and very minor changes in the near-field solution are observed when the downstream boundary is brought as close as 6.5 diameters from the center of the cylinder. Bringing the downstream boundary closer than this seems to result in more significant changes in the solution. In particular, if the distance is 2.6 diameters or closer, the solution becomes symmetric and steady.
In the present study, a code based on the nonorthogonal curvilinear coordinates is developed with a collocated grid system generated by the two-boundary method. After validation of the code, it is used to compare simulated results for a fin-and-tube surface with coupled and decoupled solution methods. The results of the coupled method are more agreeable with the test data. Simulation for dimpled and reference plain plate fin-and-tube surfaces are then conducted by the coupled method within a range of inlet velocity from 1.0 m/s to 5 m/s. Results show that at identical pumping power the dimpled fin can enhance heat transfer by 13.8–30.3%. The results show that relative to the reference plain plate fin-and-tube surface, heat transfer rates and pressure drops of the dimpled fin increase by 13.8%–30.3% and 31.6%–56.5% for identical flow rate constraint. For identical pumping power constraint and identical pressure drop constraint, the heat transfer rates increase by 11.0%–25.3% and 9.2%–22.0%, respectively. By analyzing the predicted flow and temperature fields it is found that the dimples in the fin surface can improve the synergy between velocity and fluid temperature gradient.
A scheme for handling the numerical analysis of viscous flow and heat transfer in tube banks is presented. It involves the use of a cylindrical network of nodes in the vicinity of the tubes with a Cartesian mesh covering the remainder of the flow domain. The approach has been incorporated into the numerical solving algorithm for the Navier Stokes equations of Gosman, et al. A number of demonstration calculations is presented including a numerical simulation of the staggered square bank for which Bergelin and co-workers have reported experimental results for pressure drop and heat transfer rate.
This paper represents the results of an experimental study on the flow structure around a single sphere and three spheres in an equilateral-triangular arrangement. Flow field measurements were performed using a Particle Image Velocimetry (PIV) technique and dye visualization in an open water channel for a Reynolds number of Re = 5 × 103 based on the sphere diameter. The distributions and flow features at the critical locations of the contours of the velocity fluctuations, the patterns of sectional streamlines, the vorticity contours, the turbulent kinetic energy, the Reynolds stress correlations and shedding frequency are discussed. The gap ratios (G/D) of the three spheres were varied in the range of 1.0 ⩽ G/D ⩽ 2.5 where G was the distance between the sphere centers, and D was the sphere diameter which was taken as 30 mm. Due to the interference of the shedding shear layers and the wakes, more complex features of the flow patterns can be found in the wake region of the two downstream spheres behind the leading sphere. For G/D = 1.25, a jet-like flow around the leading sphere through the gap between the two downstream spheres occurred, which significantly enhanced the wake region. It was observed that a continuous flow development involving shearing phenomena and the interactions of shedding vortices caused a high rate of fluctuations over the whole flow field although most of the time-averaged flow patterns were almost symmetric about the two downstream spheres.
In this paper the two-dimensional, non-isothermal fluid flow past an in-line tube
bank has been numerically analyzed by the finite element method. The flow is
assumed to be incompressible, laminar and unsteady. To stabilize the discretized
equations of the continuity and momentum, the streamline-upwind/Petrov-
Galerkin scheme is employed and also the energy equation is solved using the
Taylor-Galerkin method. Reynolds number of 100, Prandtl number of 0.7, and
pitch-to diameter ratios (PDRs) of 1.5 and 2.0 are chosen for this investigation.
Having obtained the flow and the temperature fields, the local skin friction
coefficient and the local Nusselt number are calculated for the tubes in the
bundle at different times. A comparison of the present study results with the
results of experiments of other investigators, showed good overall agreement
between them.
Keywords: finite-element, tube bank, in-line, skin friction, Nusselt number.
In this paper the two-dimensional, non-isothermal fluid flow past a staggered tube bank is analyzed numerically by the finite element method. The flow is assumed to be incompressible, laminar and unsteady. To stabilize the discretized equations of the continuity and momentum, the streamline upwind/Petrov-Galerkin scheme is employed and the energy equation is solved using the Taylor-Galerkin method too. The computational domain for ten tubes in the direction of flow is meshed by using the four noded-quadrilateral elements. Equilateral-triangle (ET) tube pattern is considered for staggered tube bank. Reynolds numbers of 100, 200 and 300, Prandtl number of 0.71, and pitch-to-diameter ratios (PDR) of 1.25, 1.5 and 2.0 are chosen for the investigation. Having obtained the flow and the temperature fields, the local skin friction coefficient and the local Nusselt number are calculated for the tubes in the bundle at different times. A comparison of the results of the present study with the results of experiments of other investigators, for the steady-state case, shows good agreement between them.
In the present study, an attempt has been made to summarize and analyze the results of an examination of the air-side performance of spiral (or helical) fin-and-tube heat exchangers. Currently, the spiral fin-and-tube heat exchanger is a favored type of heat exchanger for the waste heat recovery unit (WHRU), a kind of economizer system. The present paper is broadly divided into an experimental section and numerical and simulation sections. A significant fraction of the papers herein reviewed pertains to the effect of fin configurations, tube arrangements, operating conditions, and other factors on the air-side performance of the spiral fin-and-tube heat exchangers. Approximately 40 published articles related to spiral fin-and-tube heat exchangers are briefly described. Moreover, the air-side performance correlations of spiral fin and circular fin-and-tube heat exchangers are compiled into this work for practical industrial applications.
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3D computational analysis was performed to investigate heat transfer and pressure drop characteristics of flow in SWFET (Smooth Wavy Fin-and-Elliptical Tube) heat exchanger with four new VGs (vortex generators), RTW (rectangular trapezoidal winglet), ARW (angle rectangular winglet), CARW (curved angle rectangular winglet) and WW (Wheeler wishbone). The numerical model was well validated with the available experimental results. Numerical results illustrate that vortex generators can bring about further heat transfer enhancement through careful adjustment of the position with respect to the elliptical tube, type and attack angle of vortex generators. The influences of the geometrical factors including attack angles of the winglets (αVG = 15∘,30∘,45∘,60∘ and 75°) and width/length aspect ratio (w/l = 0.5,1.0) of the Wheeler wishbones on enhancing the heat transfer performance of a smooth wavy fin heat exchanger with a three-row staggered elliptical tube bundle are investigated. A parametric study on the winglet vortex generators indicated that for the small attack angle, CARW vortex generators gives better thermohydraulic performance under the present conditions. The best thermal performance with winglet VGs in larger attack angle, was obtained at RTW VGs arrangement. For the SWFET heat exchangers, the WW VGs with w/l = 0.5 provide the best heat transfer performance.
The paper reports experiences from applying alternative strategies for modelling turbulent flow and local heat-transfer coefficients around in-line tube banks. The motivation is the simulation of conditions in the closely packed cross-flow heat exchangers used in advanced gas-cooled nuclear reactors (AGRs). The main objective is the flow simulation in large-scale tube banks with confining walls. The suitability and accuracy of wall-resolved large-eddy simulation (LES) and Unsteady Reynolds-Averaged Navier–Stokes (URANS) approaches are examined for generic, square, in-line tube banks, where experimental data are limited but available. Within the latter approach, both eddy-viscosity and Reynolds-stress-transport models have been tested. The assumption of flow periodicity in all three directions is investigated by varying the domain size. It is found that the path taken by the fluid through the tube-bank configuration differs according to the treatment of turbulence and whether the flow is treated as two- or three-dimensional. Finally, the important effect of confining walls has been examined by making direct comparison with the experiments of the complete test rig of Aiba et al. (1982).
We propose and develop a variational formulation dedicated to the simulation of parallel convective heat exchangers that handles possibly complex input/output conditions as well as connection between pipes. It is based on a spectral method that allows to re-cast three-dimensional heat exchangers into a two-dimensional eigenvalue problem, named the generalized Graetz problem. Our formulation handles either convective, adiabatic, or prescribed temperature at the entrance or at the exit of the exchanger. This formulation is robust to mode truncation, offering a huge reduction in computational cost, and providing insights into the most contributing structure to exchanges and transfer. Several examples of heat exchangers are analyzed, their numerical convergence is tested and the numerical efficiency of the approach is illustrated in the case of Poiseuille flow in tubes.
In this article, a two-dimensional incompressible flow of high moisture flue gas in tube banks has been numerically simulated. The flue gas released both sensible and latent heat, and was treated as a combined heat and mass transfer problem. The finite-volume method was used to solve the Navier-Stokes equations, energy conservation equation, and species conservation equation. A simplified model was adopted and modified to account for the condensation phenomena in the flue gas. The influences of number of tube rows, gas velocity, vapor concentration, wall temperature, and tube diameter on heat and mass transfer characteristics were studied. The results analyses were presented by various criterions.
Numerical analysis is made of forced-convection heat transfer in laminar, two-dimensional, steady crossflow in banks of plain tubes in staggered arrangements. A finite-volume method with a nonorthogonal, boundary-fitted grid and co-located variable storage is used to solve the Navier-Stokes equations and energy conservation equation for a tube bundle with 10 longitudinal rows, including inlet and outlet sections. Local and overall heat transfer and fluid flow results are presented at nominal pitch-to-diameter ratios of 1.25, 1.5, and 2.0 for equilateral triangle and rotated square tube arrangements with Reynolds numbers of 100 and 300 and a Prandtl number of 0.71. Sensitivity of the local Nusselt number and friction coefficient distributions to the computational grid distribution is noted. A comparison of the present study results with well-established experiments and empirical correlations showed good overall agreement.
W e develop a finite element–finite difference method for solving three-dimensional heat transport equations in a double-layered thin film with microscale thickness. The implicit scheme is solved by using a preconditioned Richardson iteration, so that only two block tridiagonal linear systems with unknowns at the interface are solved for each iteration. W e then apply a parallel Gaussian elimination procedure to solve these two block tridiagonal linear systems and develop a domain decomposition algorithm for thermal analysis of the double-layered thin film. Numerical results for thermal analysis of a gold layer on a chromium padding layer are obtained.
The present study investigated the effect of perforated circular finned-tube (PCFT) on the convective heat transfer performance of circular finned-tube heat exchangers. The air-side convective heat transfer coefficients increased by 3.55% and 3.31% for 2-hole and 4-hole PCFT cases, respectively. The increase in the convective heat transfer coefficient was related to the reduction of the recirculation region by introducing the perforations at the flow-separation locations on the finned tube. The pressure drop across the finned-tube bundles increased by 0.68% and 2.08% for the 2-hole PCFT and 4-hole PCFT cases, respectively. The greater pressure drop in the case of the 4-hole PCFT might be due to excessive flow disturbances produced by multiple perforations. The fin factor defined as the ratio of the % increase of the convective heat transfer coefficient and that of the pressure drop was 5.19 for the 2-hole PCFT case, whereas that was 1.59 for the 4-hole PCFT case.
The present study establishes an embedding finite element method appropriate for solving primitive variable forms of the Navier–Stokes equations and energy equation in a complex physical domain. The stationary solid obstacle in the flow domain is embedded in a non-uniform Cartesian grid and the governing equations are calculated through a finite element formulation. A compact interpolating scheme near the immersed boundaries is used to ensure the accuracy of the solution in the cut cells. We have developed a numerical algorithm based on the operator splitting technique, balance tensor diffusivity (BTD), Runge–Kutta time-stepping method, and a bi-conjugate gradient iterative solver. Three numerical examples are chosen to test the accuracy and flexibility of the proposed scheme. Simulation of flow past a stationary circular cylinder is conducted to validate the accuracy of the present method for solving heat transfer problems. Flow over circular cylinders in a tandem arrangement and a staggered tube bank with convective heat transfer is computed to demonstrate the model’s ability to handle complex geometries.
This article is concerned with duct flows in which the fluid encounters a patterned array of structures along its path of flow. A heat-exchanger tube bank is an example of a patterned array of structures, whose deployment repeats periodically in the flow direction. There are three issues to be highlighted here. The first relates to the model used in standard commercial software that deals with periodic structures. That model envisions the periodic structure to be a porous medium. This approach is also used in the analysis of heat-exchanger performance.The second issue concerns the nature of the flow that follows the breakdown of the friction-dominated laminar regime. The third focus is the identification of the location of the maximum velocity within the periodic structure. It was found that the porous-medium model is a viable approach, thereby adding support to current heat and fluid-flow models of heat exchangers. The nature of the flow following the breakdown of the friction-dominated laminar regime is shown to be a continuation of laminar flow, but with important contributions of momentum transfer. This finding definitively excludes the hypothesis that the onset of turbulence occurs immediately following the breakdown of laminar flow. The location of the maximum velocity was shown not to correspond to the location of the minimum free-flow area.
In fire-tube boilers, the flue gas passes inside boiler tubes, and heat is transferred to water on the shell side. A dynamic model has been developed for the analysis of boiler performance, and Matlab has been applied for integrating it. The mathematical model developed is based on the first principles of mass, energy and momentum conservations. In the model, the two parts of the boiler (fire/gas and water/steam sides), the economizer, the superheater and the heat recovery are considered. The model developed can capture the dynamics of the boiler level and boiler pressure with confidence, and it is adequate to approach the boiler performance and, hence, to design and test a control strategy for such boilers. Furthermore, it gives insight of dynamics performance not only during nominal operating conditions, or transient behavior when a parameter is changed, but also for the start-up. The model proposed can be easily implemented and thus, it is useful to assist plant engineers and even for training future operators. A case study of an 800 HP fire-tube boiler burning fuel-oil has been simulated to test the boiler performance by varying operating conditions using a pulse and a step change in fuel and steam flow-rate as well as simulating a start-up form the beginning up to achieve the steady state. The results match qualitatively well when compared to results from the literature.
This paper develops a finite element code based on the hyperbolic heat conduction equation including the non-Fourier effect in heat conduction. The finite element space discretization is used to obtain a system of differential equations for time. The time-related responses are obtained by solving the system of differential equations via finite difference technique. A relationship for the time step length and the element size was obtained to ensure that numerical oscillation in temperature be suppressed. Temperature-dependent material properties are taken into account in the proposed analysis model. In addition to the temperature field, the thermal stresses are also obtained from the developed method. The thermal stresses associated with the non-classical heat conduction are found to be considerably difference from those associated with classical heat conduction.
In this article incompressible viscous flow in a helical annulus is studied numerically. A second order finite difference method based on the projection algorithm is used to solve the governing equations written in the helical coordinate system. Considering the hydrodynamically fully developed flow, the effects of different physical parameters such as aspect ratio, torsion, curvature and Reynolds number on the flow field are investigated in detail. The numerical results obtained indicate that a decrease in the aspect ratio and torsion number leads to the increase of the friction factor at a given Dean number.
Purpose
– This paper aims to develop a hybrid finite difference‐finite element method and apply it to solve the three‐dimensional energy equation in non‐isothermal fluid flow past over a tube.
Design/methodology/approach
– To implement the hybrid scheme, the tube length is partitioned into uniform segments by choosing grid points along its length, and a plane perpendicular to the tube axis is drawn at each of the points. Subsequently, the Taylor‐Galerkin finite element technique is employed to discretize the energy equation in the planes; while the derivatives along the tube are discretized using the finite difference method.
Findings
– To demonstrate the validity of the proposed numerical scheme, three‐dimensional test cases have been solved using the method. The variation of L²‐norm of the error with mesh refinement shows that the numerical solution converges to the exact solution with mesh refinement. Moreover, comparison of the computational time duration shows that the proposed method is approximately three times faster than the 3D finite element method. In the non‐isothermal fluid flow around a tube for Re=250 and Pr=0.7, the results show that the Nusselt number decreases with the increase in the tube length and, for the tube length greater than six times the tube diameter, the average Nusselt number converges to the value for the two‐dimensional case.
Originality/value
– A hybrid finite difference‐finite element method has been developed and applied to solve the 3D transient energy equation for different test cases. The proposed method is faster, and computationally more efficient, compared with the 3D finite element method.
A two dimensional Eulerian–Eulerian simulation of tube-to-bed heat transfer is carried out for a cold gas fluidized bed with immersed horizontal tubes. The horizontal tubes are modelled as obstacles with square cross section in the numerical model. Simulations are performed for two gas velocities exceeding the minimum fluidisation velocity by 0.2 and 0.6 m/s and two operating pressures of 0.1 and 1.6 MPa. Local instantaneous and time averaged heat transfer coefficients are monitored at four different positions around the tube and compared against experimental data reported in literature. The effect of constitutive equations for the solid phase thermal conductivity on heat transfer is investigated and a fundamental approach to modelling the solid phase thermal conductivity is implemented in the present work. Significant improvements in the agreement between the predicted and measured local instantaneous heat transfer coefficients are observed in the present study as compared to the previous works in which the local instantaneous heat transfer coefficients were overpredicted. The local time averaged heat transfer coefficients are within 20% of the measured values at the atmospheric pressure. In contrast, underprediction of the time averaged heat transfer coefficient is observed at the higher pressure.
The present paper is concerned with the dynamic analysis of a tube bundle with fluid–structure interaction (FSI) modelling. Modelling of FSI is performed with a homogenisation approach which is compared with the classical coupled approach; this latter is based on a direct finite element discretisation of the coupled problem with all tubes modelling, while the former lies on a description of the fluid–tubes system through an equivalent continuous medium, characterised by a set of dynamic equations which describe the behaviour of the tubes and the fluid from a global point of view. Theoretical background of the method is recalled, numerical implementation in a finite element code is exposed and comparison of the “homogenisation” and “coupled” method is proposed in the case of a 10 × 10 tube bundle, in 2D and 3D configurations. Calculation of eigenmode shapes, frequencies and effective masses with the two methods is performed, as well as the dynamic response of the coupled system subjected to seismic loading. It is concluded that: (i) the computational time are significantly lowered when using the homogenisation method instead of the coupled method, since the problem size is reduced by 90%; (ii) the tube bundle dynamic is described in a space-averaged manner, which is sufficient to account for the main inertial coupling effects: no significant discrepancies are reported in the modal and dynamic analysis, when performed with the homogenisation and the coupled approaches, which makes the proposed method of practical interest for future engineering applications.
In this paper, two versions of a second-order characteristic-based split scheme are developed in the framework of incremental projection method for the solution of incompressible flow problem. After the demonstration of the good accuracy and effectiveness of the developed schemes, a flow over three equal circular cylinders arranged in equilateral-triangle arrangement is numerically investigated on unstructured mesh systems. The examined Reynolds number is 100 and the flow is supposed to be laminar. Computations by the developed algorithm are then performed for six gap spacings, s, ranging from 0.5 to 4.0, and for three incidence angles, α = 0°, 30° and 60°. Numerical results show that, at sufficiently small and large s, the range of which is different for different α, the flow interference is dominated by proximity and wake effect, respectively. And in the intermediate range of the spacing, the flow pattern is influenced by both of them. The mean force results are compared with the existing experimental measurements and that shows a similar trend in the variation of mean force with the spacing for different Reynolds number. It is also observed that the interference effect transitions plays an important role in the variation of the fluctuating forces and Strouhal number.
This article considers a stabilized finite element approximation for the branch of nonsingular solutions of the stationary Navier–Stokes equations based on local polynomial pressure projection by using the lowest equal-order elements. The proposed stabilized method has a number of attractive computational properties. Firstly, it is free from stabilization parameters. Secondly, it only requires the simple and efficient calculation of Gauss integral residual terms. Thirdly, it can be implemented at the element level. The optimal error estimate is obtained by the standard finite element technique. Finally, comparison with other methods, through a series of numerical experiments, shows that this method has better stability and accuracy.
Thesis (Ph. D.)--University of London, 1973.
Large Eddy Simulation of Flow over Cylindrical Bodies Using Unstructured Finite Volume Methods
- I Afgan
I. Afgan, Large Eddy Simulation of Flow over Cylindrical Bodies Using Unstructured
Finite Volume Methods, Ph.D. thesis, The University of Manchester, Manchester, UK,
2007.
Modelling Turbulent Flow within Nuclear Heat Exchangers
- H Iacovides
- B Launder
- A West
H. Iacovides, B. Launder, and A. West, Modelling Turbulent Flow within Nuclear Heat
Exchangers, in E. Oñate J. Oliver, and A. Huerta, (eds.), 11th. World Congress on Computational Mechanics (WCCM XI), 5th. European Conference on Computational
Mechanics (ECCM V) and 6th. European Conference on Computational Fluid Dynamics
(ECFD VI) pp. 1-12, International Association for Computational Mechanics (IACM)
and the European Community on Computational Methods in Applied Sciences
(ECCOMAS), Barcelona, Spain, 2014.