Control Volume Finite Method Research Articles

Neural Koopman operator-assisted model predictive control of an Organic Rankine Cycle

This study deals with the Neural Koopman operator-assisted model predictive control of an Organic Rankine Cycle (ORC). The modeling of the evaporator and condenser is accomplished by utilizing the Finite Control Volume (FCV) method, and the modeling of the turbine and pump is fulfilled with pseudo-steady state equations. Afterward, the identification of the neural Koopman model is carried out with the input–output data obtained from the developed ORC model. The identification process resulted in 0.01121 and 0.01119 training and validation losses, respectively, which are sufficiently acceptable values. A linear MPC design is proposed to control the system in the Koopman-identified linear state space. Four different controllers are designed, each having different objectives, and their performances are compared with each other. The results reveal that the second law controller comes up with the most desirable exergy destruction rate of 2349 W, which is 1.44 % lower than the worst performer entropy generation controller. Moreover, the first and second law controllers result in the highest overall first and second law efficiencies, 0.14258 and 0.42945, respectively, through the simulation time. It is realized that the performance of the controllers is in line with their assigned objectives, and the proposed controller effectively regulates the system.

Comparative study on static and dynamic characteristics of pumping-out and pumping-in herringbone grooved journal bearings

The aim of this paper is to compare the static and dynamic performances of two types of herringbone grooved journal bearings (HGJBs), that is, pumping-out HGJB and pumping-in HGJB. Firstly, based on finite control volume method and the principle of flow balance, an equivalent Reynolds equation considering the turbulence effect is derived. Then, the journal motion considering angular displacement is analyzed with linear perturbation method. The equivalent Reynolds equation is linearized into static-form one and perturbed-form ones. These equations are solved by finite difference method and their solutions are integrated on the bearing surface to determinate the static characteristics and dynamic coefficients of HGJB. Additionally, the critical mass and critical whirl frequency are defined for evaluating the stability and rigidity of bearing by solving a motion equation with four degree of freedoms (DOFs). Finally, the static and dynamic characteristics of two types of HGJBS are analyzed and compared symmetrically in consideration of effects of eccentricity ratio, length to diameter ratio, groove angle, groove depth, the width of sealing damp, tilting degree of journal, and rotation speed. The results show that, within the interested range of investigated parameters, static performances of pumping-out HGJB are superior to that of pumping-in HGJB generally. Stability of pumping-in HGJB is better than pumping-out HGJB but bearing rigidity of pumping-in HGJB is inferior to pumping-out HGJB.

Natural convective nanofluid flow characteristics with Brownian motion effect in an annular space between confocal elliptic cylinders

The principal aim of this work is to study numerically the natural convection in an annular space between confocal elliptic cylinders. The Brownian motion was added based on the thermal conductivity model and the simulation was carried out using finite volume control method. Various nanofluids with different volume concentrations were undertaken ranging from 2% to 6% and various Rayleigh numbers were tested for different particles. The isotherms and stream function are presented and it was clearly seen that by increasing the Rayleigh number, the heat transfer rate increases on the domain. On the other hand it was noticed that the heat transfer enhancement is less sensitive to the nanoparticles when the Brownian motion was considered

Investigation of the impact of pipe geometric form on earth-to-air heat exchanger performance using Complex Finite Fourier Transform analysis. Part I: Operation in cooling mode

This paper deals with the impact of the geometric form of pipe section upon the performance of earth-to-air heat exchangers operating in cooling mode. For this purpose, three different configurations, namely circular, rectangular and elliptical were selected. Based on the heat balance analysis, a transient two-dimensional model was developed for the disturbed soil around the buried pipe. The discretization of the partial differential equation by applying the Finite Control-Volume Method yields a new generalized heat equation valid for all kinds of cylinders. Then, the resulting set of ordinary differential time-equations was linearized by using the technique of Complex Finite Fourier Transform. After successfully validating the model against available data in the literature, a thorough sensitivity analysis was carried out for assessing the impact of geometric and operating parameters including pipe length and cross-section and air speed. Further, the effect of pipe flatness relating to the rectangular and elliptical configurations was also considered through the geometric aspect ratio.The results show that the rectangular and elliptical buried pipes are more effective because they possess large exchange surfaces compared to the circular (conventional) one. For instance, at a pipe cross-section of 0.07 m2 and a geometric aspect of 9, the exchange surface between the flowing air and pipe wall in the rectangular and elliptical exchangers are larger of 88.3% and 93.6% than that of the conventional system, respectively. Moreover, at a geometric aspect of 4 and a pipe length of 60 m, the outlet temperatures supplied by the rectangular and elliptical systems are of 1.5 and 1.3 °C less than that obtained with the conventional one. Regarding the influence of pipe dimensions, it is shown that the effect of pipe length is dominant compared to that of pipe section and the performance of the system is proportional to the pipe length. Likewise, the EAHE performance increases with the increasing of the pipe geometric aspect, but a value of 4 is found to be a good compromise. Though, the performance of EAHE is found to drop dramatically at high speeds of air.

Comparative analysis of eccentric evacuated tube solar collector with circular and rectangular absorber working with nanofluid

Abstract This paper reports the results of a comparative study on a low concentration eccentric evacuated tube solar collector with two different absorber tubes of circular and rectangular cross sections. The two arrangements are intended for flow through applications although the collector with rectangular section can be adapted for PV applications. The governing equations of the model are approximated by the finite volume control method (FVM) in association with the SIMPLE algorithm. A home-built numerical code is developed to simulate both a single tube and a collector arrangement of 18 tubes of circular and rectangular cross sections. The evacuated tubes are connected to operate in single flow-through arrangement. The working fluid is aluminium oxide/water nanofluid to enhance the heat absorbed by the collector. It is assumed that the sealed inner and outer parts of the glass cover are in adiabatic condition. The model and the simulation predictions are validated against available results showing good agreement. In the case of a single tube arrangement with water as the heat transfer fluid, it was found that the efficiency of the evacuated tube with circular absorber was 8% higher than that of the collector with rectangular absorber at the same conditions. The simulations for the collector arrangement were conducted for a nano Al2O3 volume fraction ( ϕ ) in the range 0.01 ≤ ϕ ≤ 0.1 and fluid velocities between 0.005 ≤ u ≤ 0.010 m/s. The results showed, for the case of nanofluid with velocities of 0.015 , 0.01 , 0.007 and 0.005 m / s , maximum efficiency enhancement of the collector with circular absorber of about 1.1%, 2.5%, 5.2% and 8.8%, respectively. For the rectangular absorber the enhancements were 0.5%, 1.14%, 2.41% and 4.79%, respectively.

The Effects of Hot Blocks Geometry and Particle Migration on Heat Transfer and Entropy Generation of a Novel I-Shaped Porous Enclosure

This paper studied the cooling performance of a hot electronic chip using nanofluids (NF) mixed convection, implementing Buongiorno’s model of the NF simulation. The NF were assumed water-Al2O3 nanoparticles (NP) in the range of 0 to 4% of volume concentration. Six different problems of the combinations of three internal hot blocks, including triangular, square, and circular geometries, and two porous media, including sand and compact metallic powder, were numerically solved. To discretize the governing equations, a finite control volume method was applied. As most of the proposed correlations for the thermophysical properties of the NF were inaccurate, especially for thermal conductivity, a new predictive correlation was proposed using the multi-variable regression method with acceptable accuracy. It was found that the cooling performance improved with any increase in the NP loading. A higher nanoparticle concentration yielded better cooling characteristics, which was 11.93% for 4% volume. The sand porous medium also yielded a much higher value of the normalized Nusselt number (Nu) compared to the other medium. The entropy generation (EG) enhancement was maximum for the triangular hot block in a sand porous cavity.

Numerical analysis of entropy generation in a square cavity filled with boron-water nanofluid

The entropy generation and natural convection in a square cavity filled with boron-water nanofluid is numerically investigated under the influence of different nanoparticle volume fractions and buoyancy forces when heated from left vertical wall and cooled from right vertical wall while horizontal walls are insulated. The results are compared with copper (Cu) and aluminum oxide (Al2O3) nanoparticles generally used in the applications. Differential equations are discretized over the SIMPLE algorithm and solved iteratively using the finite control volume method. Entropy generation contours due to heat transfer and fluid friction are presented. Local and average Bejan numbers are also investigated. The results of the study show that the entropy generation increases with the increase in Rayleigh number for all nanoparticles, and fluid friction irreversibility is more dominant in entropy generation with increasing Rayleigh number, and almost all entropy generation is caused by fluid friction in high Rayleigh numbers.

Effects of Microstructure on Three-Dimensional Double-Diffusive Natural Convection Flow of Micropolar Fluid

This work presents a three-dimensional numerical study on double-diffusive natural convection in a cubic cavity filled with a micropolar fluid. The flow is driven by buoyancy forces due to temperature and solutal gradients. Constant temperature and concentration are imposed along the two vertical sidewalls of the cubic enclosure, while the remaining walls are adiabatic and impermeable. The governing equations are expressed in the vorticity-stream function formulation and then solved numerically using the control volume finite method. Numerical results are compared with the case of a Newtonian fluid. The influences of the micro-constituents of the micropolar fluid are depicted. The results show different transitions of the structure of the main flow when varying the vortex viscosity parameter. It is also observed that both the heat and mass transfer rates and the three-dimensional character of the flow are reduced by increasing the vortex viscosity parameter.

Effects of surface topography on hydrodynamic performance of liquid film seals considering cavitation

PurposeThe purpose of this paper is to investigate the effects of surface topography, including surface roughness, circumferential waviness and radial taper, on hydrodynamic performance of liquid film seals considering cavitation.Design/methodology/approachA mathematical model of liquid film seals with surface topography was established based on the mass-conservative algorithm. Liquid film governing equation was discretized by the finite control volume method and solved by the Gauss–Seidel relaxation iterative algorithm, and the hydrodynamic performance parameters of liquid film seals were obtained considering surface roughness, circumferential waviness and radial taper separately.FindingsThe results indicate that the values of load-carrying capacity and frication torque are affected by the surface topography in varying degrees, but the effect is limited.Originality/valueThe results presented in the study are expected to aid in determining the optimum value of structural parameters for the optimum seal performance because of the realistic model which considers both surface topography and cavitation.

Three-dimensional computational fluid dynamics modeling of proton exchange membrane electrolyzer with new flow field pattern

The performance of a proton exchange membrane electrolyzer cell directly depends on the arrangement of flow field in bipolar plates (BPs). The design of flow field in BPs should be in a way that a uniform distribution of flow is achieved; in this regard, a three-dimensional model of a new flow field arrangement with a cross section of 64 cm2 is proposed and the distribution of current density, temperature, and pressure drop is investigated. A numerical model is carried out at the steady-state, single-phase, and non-isothermal condition based on finite volume control method. The continuity, momentum, species, energy and electric charge balance equations together with electrochemical kinetics relations in different regions of PEM electrolyzer are solved in a single-domain model. The results of numerical model are compared against experimental data, and an acceptable agreement is observed at low and medium currents densities. The results reveal that the spiral flow field yields a uniform distribution of produced hydrogen and current density. Moreover, the proposed flow field design leads to a uniform distribution of temperature through the channel path. The availability of water and current density at vertical paths of the flow field are higher.

Estimation of surface heat flux for ablation and charring of thermal protection material

Ablation of the thermal protection material of the reentry hypersonic flight vehicle is a complex physical and chemical process. To estimate the surface heat flux from internal temperature measurement is much more complex than the conventional inverse heat conduction problem case. In the paper, by utilizing a two-layer pyrogeneration-plane ablation model to model the ablation and charring of the material, modifying the finite control volume method to suit for the numerical simulation of the heat conduction equation with variable-geometry, the CGM along with the associated adjoint problem is developed to estimate the surface heat flux. This estimation method is verified with a numerical example at first, the results show that the estimation method is feasible and robust. The larger is the measurement noise, the greater is the deviation of the estimated result from the exact value, and the measurement noise of ablated surface position has a significant and more direct influence on the estimated result of surface heat flux. Furthermore, the estimation method is used to analyze the experimental data of ablation of blunt Carbon-phenolic material Narmco4028 in an arc-heater. It is shown that the estimated surface heat flux agrees with the heating power value of the arc-heater, and the estimation method is basically effective and potential to treat the engineering heat conduction problem with ablation.

Double-diffusive natural convective in a porous square enclosure filled with nanofluid

In this work, effects of double-diffusive natural convection of Al2O3–water nanofluid on flow field and heat transfer in a porous square cavity are investigated. Homogeneous and two-component non-homogeneous of Buongiorno's model that includes the effects of Brownian motion and thermophoresis are utilized, while the Darcy model is used for the porous medium. The governing equations are discretized using the finite difference and control volume method. Properties of nanofluid have been assumed functions of temperature and volume fraction of nanoparticles. Since constant Rayleigh number could not be used, simulations have been performed for various physical conditions such as temperature difference between the hot and cold walls from 1 to 20 °C, bulk volume fraction of nanoparticles from 0 to 0.04, and porosity between 0.1 and 0.5. Both models suggest that by increasing the bulk volume fraction of nanoparticles heat transfer is reduced, but non-homogeneous model predicts a greater reduction compared to the homogeneous model. Also non-homogeneous model predicts reduced heat transfer with increased porosity.

Explicit Approximate Analytical Solution of the Horizontal Diffusion Equation

The solution of unsaturated flow is a never-ending quest for many scientists. Many methods exist with their corresponding advantages and disadvantages, such as semianalytic methods, finite difference and finite element methods, finite control volume method, and flux concentration method. This article produces an improved approximate analytical solution for nonlinear diffusion, in terms of the Boltzmann similarity variable, that has the advantages of being explicit, accurate, and relatively simple to evaluate. It is assumed that the diffusivity can be described with an exponential function, the profiles of soil water content are of finite extent, the concentration at the boundaries is constant, and the reduced flux of Philip (1973) is of the form of Vauclin and Haverkamp (1985). The proposed explicit approximate analytical solution has the Boltzmann transformation as the dependent variable and the soil water moisture as the independent variable. The solution is presented in normalized form as a function of normalized diffusivity and normalized soil moisture. It is tested with 12 soils and shows an excellent agreement with Philip’s method.

Prediction of Asphalt Pavement Temperature Profile with Finite Control Volume Method

The accurate prediction of the pavement temperature profile and history is critical for the calculation of the viscoelastic response of asphalt concrete pavements under traffic and thermal loadings. An accurate prediction is also essential in the estimation of the asphalt binder oxi-dative aging. A sound alternative approach is proposed to predict the pavement temperature profile with the finite control volume method in a fully implicit scheme. The model for the finite control volume method provides a fundamental and clear understanding of the heat energy balance, including the incoming and outgoing thermal energies, in addition to the dissipated heat in the system. Also, the variability in the materials’ thermal properties in a multilayered pavement structure can be remedied by assigning appropriate thermal properties to each control volume or cell. The fully implicit scheme improved the time efficiency of the calculation significantly. Moreover, enhancements were made by defining the accurate heat balance equations for the pavement surface and the bottom boundary conditions. With reliable meteorological data, solar radiation, and monthly variable pavement surface radiation properties, accurate prediction of the pavement temperature profile was made possible as validated by comparison with field measurements. Consequently, Windows-compatible software has been developed on the basis of the proposed model, which is capable of effectively predicting the pavement temperature profile and history.

Numerical study on thermo-hydraulic performance of an offset-bubble primary surface channels

In this paper, the thermo-hydraulic performance of an offset-bubble primary surface channel is presented. The idea of the present design comes from the cross corrugated (CC) primary surface channel and offset-strip plate-fin channel, which imports the transverse disturbance of plate-fin channel into the primary surface channel. The analysis is accomplished by the finite control volume method and the low Reynolds k–w turbulent model is used. Under the similar geometrical parameters, the comprehensive performance of the offset-bubble primary surface channel is the best, whose averaged area goodness factor is enhanced by 41% and 71% compared to the CC3.1-60 (pitch-over-height ratio of 3.1 and inclined angle of 60°) and offset-strip plate-fin channels. The comprehensive performance of the offset-bubble primary surface channel with the baseline dimension is superior to the CC4-45 (pitch-over-height ratio of 4 and inclined angle of 45°) and CC3.1-60 primary surface channels. The geometrical parameter studies indicate that variation of the comprehensive performance is very small when the wave length is greater than 18 mm and the effect of wave height is very small.

The Numerical Simulation of the Shell Side Flow and Heat Transfer for 600MW Steam Turbine Condenser

Detailed prediction of steam flow field and heat transfer process is significant for the condensers. The flow and heat transfer performance of the condenser of 600MW power unit is numerical simulated. A model of porous media with distributed resistance and mass sink is used to simulate the function of the tube bundle. The equations including the continuous, momentum and air concentration are numerically solved using the finite control-volume integration method and SIMPLE algorithm. The distribution of steam velocity, pressure, heat transfer coefficient and air concentration are obtained and analyzed. On the basis of results, the condenser is evaluated.

Heat transfer through fibrous assemblies incorporating reflective interlayers

Fibrous insulation has many applications including functional protective clothing, sleeping bags, buildings and construction, and aircrafts, particularly under extreme climatic conditions. It has been realized that reflective interlayers can be incorporated into the fibrous materials to block radiative heat transfer. However, since reflective interlayers generally have greater thermal conductivity than the bulk fibrous materials, the optimization of the construction of the fibrous insulation is important in maximizing the overall thermal insulation. In order to analyze this complex optimization problem, a two-flux radiative heat transfer model was built for the heat transfer through fibrous assemblies incorporating reflective interlayers. By using finite control volume method, the solution was obtained. After validation it was applied to predict the optimum constructional parameters of such an assembly for maximizing thermal insulation. It was found that (1) although extinction coefficient of Al-coated interlayer fibers decrease unidirectionally as the fiber diameter increases, the total heat flux first decreases and then increases with minimum heat flux at the fiber diameter of about 2μm; Consequently, the thermal resistance reaches a maximum value when the fiber diameter d is about 2μm; (2) the optimum construction is determined by the balance of the weakening of conductive thermal resistance and enhancement of the radiative thermal resistance as a result of incorporating thin reflective interlayers. For relatively thick reflective interlayer, the assembly with lower interlayer fiber volume fraction has a higher thermal resistance. On the other hand, for very thin reflective interlayers, relatively high fiber volume fraction is beneficial to the overall thermal insulation.

Modeling of oxygen reduction mechanism for 3PB and 2PB pathways at solid oxide fuel cell cathode from multi-step charge transfer

Oxygen reduction at the mixed ionic and electronic conductive (MIEC) SOFC cathodes occur along a surface pathway with oxygen transport through a triple-phase boundary (3PB), and/or a bulk pathway via bulk cathode and electrolyte/cathode interface (2PB). The identification of the rate-limiting steps (RLSs) for each path and understand on their interactions are important to the SOFC cathode kinetics. In this research a modified one-dimensional continuum model is developed to analyze the oxygen reduction on LSM-type MIEC cathode by incorporating multi-step charge-transfer into the bi-pathway kinetics. Finite control-volume method is used to simulate the pathway kinetic competition, and a parametric study is performed with different equilibrium concentrations of surface oxygen ion ( C O − , eq ) and bulk oxygen vacancy ( C V,MIEC,eq). The I– V profiles show kinetic transition from 3PB-control to 2PB-control at overpotentials from −0.2 V to −0.4 V, and the active reaction zone in concentration profiles expands from 3PB/2PB interfaces by 2–4 μm. The exchange and local 3PB currents recognized from simulation indicate limit of surface oxygen diffusion as the mechanistic process for pathway transition. The results are compared to the reported experimental findings to examine the model's assumption of oxygen reduction scenario, and its potential implication on SOFC cathode performance improvement.

One-Dimensional Model of Heat and Mass Transports and Pressure Built Up in Unsaturated Porous Materials Subjected to Microwave Energy

In this article, the heat and mass transfer and pressure buildup in unsaturated porous media under microwave energy is theoretically investigated. The unsaturated porous media is composed of glass beads, water, and air. The microwave power generation is computed based on Lambert's law. The finite control volume (FCV) method is used to predict the heat and multiphase flow and pressure buildup in unsaturated porous media under various conditions. Most importantly, this work focuses on the influence of frequency, particle size, and electric field intensity to predict heat and mass transfer and pressure built up in porous media due to microwave energy. The results show that variations of frequency, particle size, and electric field intensity play an important role on overall drying kinetics. Furthermore, the findings of this research will serve as a fundamental tool for applications involving in the microwave drying process of porous media.

Numerical Study of Conjugated Heat Transfer in a Thick Walled Tube Subjected to a Nanofluid

In this paper, a numerical analysis is carried out to study the performance of conjugated convection−conduction heat transfer in a fin and thick-walled U-shaped tube heat exchanger subjected to a nanofluid. This geometry is mainly adopted for the aim of heating the chamber of Oghab Afshan bus (SCANIA). The problem is considered as two-dimensional, whereas the fins are treated as a one-dimensional conduction problem because of small thickness. So, the governing equations are derived based on the conceptual model in the Cartesian and polar coordinate systems for direct and bent paths, respectively. Then the governing equations have been approximated by means of a fully implicit finite volume control method (FVM). The effect of some geometrical variables and also the effect of applying various nanoparticles (a suspension of TiO3, Al2O3, and Cu nanoparticles in water) on the heat transfer and flow characteristic have been investigated. The results indicate that the lowest and greatest values of the Nusselt number are obtained for TiO3-water and Cu-water nanofluids, respectively.