User Defined Scalar Research Articles

Modeling of the technological process of convective drying of lumber

A calculation of the technological process of lumber drying in convection drying chamber of periodic action is presented. For this purpose, a three-dimensional geometric model of a drying chamber with a lumber pile is developed. A physico-mathematical model describing the processes of heat and mass transfer both in the drying agent and in the stack is presented. The three-dimensional geometry of the problem was taken into account by using the Ansys Fluent package. The process of mass transfer in wood was described on the basis of User-Defined Function and User-Defined Scalar. The result of calculation of a specific technological regime of drying of stack from pine sawn timber is given, which allowed finding detailed spatial distributions and temporary changes of the temperature and humidity fields for the drying agent and wood. On their basis, graphs of the time variation of the mean values are plotted. The nonlinearity and interrelationship of the processes of heat and mass transfer in a convective drying chamber leads to unsteadiness of the drying process. So, during the warm-up stage, it is not possible to avoid moisture removal from the lumber. At the drying stages, the unsteadiness leads to an oscillatory character of changes of the temperature, the mass fraction of vapour and the relative humidity of air in the gaps between the wood boards at the intensive heat input. Therefore, it is necessary to take additional procedures to keep the drying agent parameters constant at the drying stages. The obtained results can be used for the design of drying chambers and the development of drying regimes of lumber based on the mathematical modeling and computational experiment.

Mixing Efficiency Analysis on Droplet Formation Process in Microchannels by Numerical Methods

Liquid–liquid two-phase flow in microchannels has attracted much attention, due to the superiority of mass transfer enhancement. One of the biggest unresolved challenges is the low mixing efficiency at the microscale. Suitable mixing efficiency is important to promote the mass transfer of two-phase flow in microchannels. In this paper, the mixing efficiency in three junction configurations, including a cross-shaped junction, a cross-shaped T-junction, and a T-junction, is investigated by the volume of fluid (VOF) method coupled with user-defined scalar (UDS) model. All three junction configurations are designed with the same hydraulic diameter of 100 μm. Mixing components are distributed in the front and back parts of the droplet. The mixing efficiency in the droplet forming stage and the droplet moving stage are compared quantitatively. Results show that different junction configurations create very different mixing efficiencies, and the cross-shaped T-junction performs best, with relatively lower disperse phase fractions. However, with an increase of the disperse phase fraction, the cross-shaped junction is superior.

Coupling of CFD and population balance modelling for a continuously seeded helical tubular crystallizer

A comprehensive model coupling the computational fluid dynamics with the population balance equation (CFD−PBE) for a continuous seeded mixed suspension mixed product removal (MSMPR)-helical tubular (HT) crystallizer assembly has been developed. The model accurately depicts the fluid dynamics, mass transfer, heat transfer and crystal size distribution (CSD) in the MSMPR-HT crystallizer. The crystallization system considered was to produce metastable α-form of L-glutamic acid. The PBE was discretized using a high-resolution central scheme and solved simultaneously with CFD equations in COMSOL Multiphysics® utilizing user-defined scalars. A good agreement was observed between the model and experimental data for the metastable α-form crystals of L-glutamic acid with uniform particles and a mean crystal size of 160 µm. The continuous crystallization under different stirrer speeds, saturated solution flow rates, inlet saturated solution concentrations and temperature was investigated. It was found the higher stirrer speeds, saturated solution flow rate and temperature lead to uniform distribution with smaller crystal size. Moreover, the mean crystal size becomes larger and the CSD wider when the saturated solution concentration increase.

Effect of Mixing on the Particle Size Distribution of Paracetamol Continuous Cooling Crystallization Products Using a Computational Fluid Dynamics–Population Balance Equation Simulation

Continuous crystallization is a widely viewed topic as it has many advantages in industrial production. However, it is very resource intensive and time-consuming to determine operation conditions through trial and error. Computer simulation appears to an effective method in continuous crystallization design. The continuous cooling crystallization of paracetamol in a 5 L crystallizer was modeled to investigate the effect of mixing on the particle size distribution (PSD). A novel coupled computational fluid dynamics–population balance equation (CFD–PBE) simulation was developed in which the PBE was discretized using a high-resolution central scheme and solved simultaneously with CFD equations in ANSYS FLUENT 15.0 utilizing user-defined scalars. The influences of both internal grid and external (spatial) grid on the final PSD were studied, and an appropriate grid was chosen. The spatial distribution of velocity, temperature, slurry density, and nucleation rate were simulated. The continuous cooling crystallization under different stirrer speeds, bath temperatures, and residence times was investigated. It was found that (a) higher stirrer speeds lead to uniform distribution but smaller PSD, and (b) as the average temperature gets higher, or the residence time gets longer, the influence of mixing on final PSD gets smaller.

Preliminary mathematical and numerical transient models of convective heating and drying of a brick

The paper presents the initial approach to mathematical and numerical modelling and optimization of heat and mass transfer in elements of the masonry wall. The considered single moist brick is placed in the channel through which the dry air is flowing. Only one wall of the brick is in contact with the flowing air and through this boundary heat and moisture are exchanged. The non-equilibrium mathematical model is formulated for general case with three phases of moisture present in the porous building material, i.e., water vapour in the moist air filling the pores, liquid water (bound water) adsorbed at the surface of the solid component of the material and free liquid water either in a discontinuous form (funicular) or continuous one (pendular). However, at this stage of development of the numerical model the moisture in the form of motionless liquid water and water vapour which reside in the ceramic material are considered. Moreover, the moisture and heat diffusion in the porous hydroscopic material of the brick as well as moisture and heat convection in the flowing air are assumed. The numerical model is developed with the aid of the commercial software ANSYS Fluent and its advanced customisation functionalities like the User-Defined Function, User-Defined Scalar and User-Defined Memory. Subsequently, investigation of the influence of the mass transfer coefficient between the free liquid water and moist air in the porous building material are carried out.

Calculation of the Water Droplets Local Collection Efficiency on the Wind Turbines Blade

Wind turbines operating in cold climate are susceptible to icing events. In order to gain a better understanding of the blade icing, the water droplets local collection efficiency affected by different factors was investigated. First, the water droplets conservation equations which are based on the fluent user-defined scalar (UDS) were introduced. Second, the Eulerian method was validated. Two test cases indicate that the developed method is effective. Then, the local collection efficiency on the S809 airfoil was studied. Results show that as the angle of attack (AOA) increases, the water droplets impingement region moves toward the airfoil lower surface and the maximum local collection efficiency decreases. The local collection efficiency and the impingement region increase with the water droplets diameter and the air flow velocity but decrease with the airfoil chord length. Finally, the local collection efficiency affected by the three-dimensional (3D) effect was studied. Results show that the maximum local collection efficiency in the blade tip region decreases up to 96.29% due to the 3D effect.

Computational fluid dynamics (CFD) modeling of heat transfer in a polymeric membrane using finite volume method

The efficiency, robustness and reliability of recent numerical methods for finding solutions to flow problems have given rise to the implementation of computational fluid dynamics (CFD) as a broadly used analysis method for engineering problems like membrane separation system. The CFD modeling in this study observes steady and unsteady (transient) heat flux and temperature profiles in a polymeric (cellulose acetate) membrane. This study is novel due to the implementation of user defined scalar (UDS) diffusion equation by using user-defined functions (UDFs) infinite volume method (FVM). Some details of the FVM used by the solver are carefully discussed when implementing terms in the governing equation and boundary conditions (BC). The contours of temperature due to high-temperature gradient are reported for steady and unsteady problems.

Numerical study of turbulent porous media combustion coupled with thermoelectric generation in a recuperative reactor

This paper presents two-dimensional simulations of an adiabatic recuperative porous media burner in turbulent regime coupled with thermoelectric elements. Time and volume averaged transport equations and second order turbulence model were employed. FLUENT was used to simulate the reactor through its UDF (User Defined Functions) and UDS (User Defined Scalars) interfaces for extra terms involving turbulence and thermoelectric quantities. The study includes the production of thermal NOx modeled by the extended Zeldovich mechanism with postprocessing computation. Flow and electric field computations were obtained considering as variables gas inlet velocity and composition, porous media thermal conductivity and inner wall insulation material. Flammability limits for stable combustion were found alongside with the electric potential generated within the system. Higher values of electrical potential, thermoelectric efficiency and flame temperatures were reached when the gas mixture energy content and heat recovery capacity of the system were increased.

Three-dimensional analysis of gas flow and heat transfer in a regenerator with alumina balls

A three-dimensional (3D) unsteady mathematical model for regenerator with alumina balls has been developed based on the assumption of porous media and solved by a commercial computational fluid dynamics (CFD) software, FLUENT. The standard k–ɛ turbulence model combined with standard wall functions is used for modeling gas flow. Momentum equation is revised to consider the impact of porous media on fluid flow. Radiation from combustion gas to the storage materials is considered in the model. User-defined functions (UDFs) program has been developed in C language and linked to FLUENT to define user-defined scalar (UDS) transport equation of energy conservation for solid phase, and to calculate interphase heat transfer as well as thermophysical properties of gas and solid phases, which are dependent on temperature. The calculated results were compared with test data, and the maximum relative error is 3.73%. Results of the model calculation showed that after 25 times of alternate changes in heating and cooling cycles, the heat absorption of regenerative balls is equal to heat released to air, implying the operation of regenerator reaches steady state. As the ball diameter decreases, the pressure gradients become steep and fluid velocity decreases. To reduce temperature difference in the horizontal plane, the geometry of the regenerator has been optimized by the model.

Simulation of coalescence, break-up and mass transfer in a gas–liquid stirred tank with CQMOM

In this work oxygen mass transfer in a turbulent air–water stirred tank is investigated. A multivariate population balance model is coupled with the Eulerian multi-fluid approach to describe the spatial and temporal evolution of the bubble size and composition distributions. For the numerical solution of the population balance model the conditional quadrature method of moments is employed and implemented through user-defined scalars and functions in the computational fluid dynamics code ANSYS/Fluent 12. The approach is validated by comparing model predictions with experiments (from the literature) conducted in an air–water stirred tank equipped with a Rushton turbine and a porous sparger. First predictions are compared with the experimentally measured mean Sauter diameter. The comparison highlights that the modeling approach is capable of predicting the main feature of the system. Then oxygen mass transfer is simulated and predictions for the oxygen accumulation in water are validated against experiments. Also for this comparison good agreement is found.

Modeling ozone penetration through the wall assembly using computational fluid dynamics

Outdoor pollutants, such as ozone, can penetrate into the indoor environment through the wall assemblies and influence the indoor air quality (IAQ). Ozone can also react with chemical compounds (i.e., d-limonene, α-pinene, β-pinene, styrene, etc.) within the wall assemblies to create secondary emissions causing IAQ concerns. This study developed a modeling framework for predicting ozone penetration through building envelope systems. The transport process of ozone through leakage paths was numerically simulated by two approaches: (1) a species transport model plus a chemical reaction model and (2) a user-defined scalar (UDS) transport model plus a user-defined deposition model. A simplified method to simulate ozone transport through fibrous media was also developed in a UDS model based on the analysis of two deposition mechanisms: (1) transport-limited deposition and (2) surface uptake of the fiber. The model was successfully applied to a typical residential wall assembly, assuming crack heights of 1 mm (0.04 in.) in the vertical direction and 3 mm (0.12 in.) in the horizontal direction and with fiberglass insulation width of 0.14 m (5.5 in.). Theoretical analysis showed that gas phase reaction between ozone and unsaturated volatile organic compounds emitted from wall materials in leakage paths and fiberglass insulation could be neglected compared with the surface reaction. The calculated penetration factors through leakage paths by the species transport model and UDS transport model were in good agreement. Fiberglass insulation media greatly reduced ozone penetration by more than 60% under almost all circumstances when reaction probability was larger than 10−8.

Three dimensional simulation of melt flow in Czochralski crystal growth with steady magnetic fields

Three-dimensional transient numerical simulations were carried out to investigate the melt convection and temperature fluctuations within an industrial Czochralski crucible. To study the magnetic damping effects on the growth process, a vertical magnetic field and a cusp magnetic field were considered. Due to our special interest in the melt convection, only local simulation was conducted. The melt flow was calculated by large-eddy simulation (LES) and the magnetic forces were implemented in the CFD code by solving a set of user-defined scalar (UDS) functions. In the absence of magnetic fields, the numerical results show that the buoyant plumes rise from the crucible to the free surface and the crystal–melt interface, which indicates that the heat and mass transfer phenomena in Si melt can be characterized by the turbulent flow patterns. In the presence of a vertical magnetic field, the temperature fluctuations in the melt are significantly damped, with the buoyant plumes forming regular cylindrical geometries. The cusp magnetic field could also markedly reduce the temperature fluctuations, but the buoyant plumes would break into smaller vortical structures, which gather around the crystal as well as in the center of the crucible bottom. With the present crucible configurations, it is found that the vertical magnetic field with an intensity of 128 mT can damp the temperature fluctuations more effectively than the 40 mT cusp magnetic field, especially in the region near the growing crystal.

A comparative study of turbulence models performance for separating flow in a planar asymmetric diffuser

This paper presents a computational study of the separated flow in a planar asymmetric diffuser. The steady RANS equations for turbulent incompressible fluid flow and six turbulence closures are used in the present study. The commercial software code, FLUENT 6.3.26, was used for solving the set of governing equations using various turbulence models. Five of the used turbulence models are available directly in the code while the v 2– f turbulence model was implemented via user defined scalars (UDS) and user defined functions (UDF). A series of computational analysis is performed to assess the performance of turbulence models at different grid density. The results show that the standard k– ω, SST k– ω and v 2– f models clearly performed better than other models when an adverse pressure gradient was present. The RSM model shows an acceptable agreement with the velocity and turbulent kinetic energy profiles but it failed to predict the location of separation and attachment points. The standard k– ε and the low-Re k– ε delivered very poor results.

CFD Method To Couple Three-Dimensional Transport and Reaction inside Catalyst Particles to the Fixed Bed Flow Field

A new method is presented to couple the fluid flow in a fixed bed to the transport and reaction inside a catalyst particle, using computational fluid dynamics (CFD). The particle is modeled as solid, allowing no-slip surface flow boundary conditions to be used. Species transport inside the particle is represented by user-defined scalars, and the catalytic reactions are represented by user-defined functions. The new method is validated using standard cases for which exact results are known. Previous work has used a porous representation of the catalyst particle, which results in inaccurate temperature and species profiles due to an artifact of convective flux across the particle−fluid interface. This also gives incorrect values of the particle-to-fluid heat transfer coefficient, compared to standard correlations. Simulation results are presented for methane steam reforming using spherical particles in a wall segment, under tube inlet and midtube conditions, to illustrate the solid particle method.

Research on flow loss of inlet duct of marine waterjets

In the process of performance prediction of waterjet system, the flow loss of inlet duct is usually reckoned by the rule of thumb. But its value is often overestimated to some extent, resulting in error of prediction accuracy. This paper introduces a new method to determine the flow loss by means of computational fluid dynamic (CFD). Firstly, the fluid field around waterjet system is simulated by solving the Reynolds Averaged Navier-Stokes (RANS) equations using commercial CFD code Fluent. Then an additional User-Defined Scalar (UDS) equation is embedded into Fluent to get the virtual dividing surface between the internal flow ingested into the inlet duct and the external flow beneath the hull, which is named as streamtube. By virtual of the streamtube the flow loss can be calculated according to the difference of total pressure between the duct outlet and the capture area ahead of the intake. The results from CFD calculation show that the flow loss coefficient of a typical flush-type inlet duct is varying from 0.05 to 0.12 at different operation conditions, being obviously less than the value of 0.2–0.3 from empirical rules. With the results of this paper the prediction accuracy on propulsive performance of the waterjet system can be improved further.

Three-dimensional modelling of industrial flashing flows

This paper summarises the development and validation of a three-dimensional numerical flashing flow model for use in industrial applications. The flashing flow process was modelled using the commercial CFD code FLUENT, with a User-Defined Scalar (UDS) transport equation used for bubble nucleation and transport. Predicted mass flow rates, vapour fractions and pressures were compared with values observed experimentally. The CFD model was also used to simulate a piping system connecting two industrial flash tanks at Rusal Aughinish in which flashing occurs owing to reduction in pressure. The calculated mass flows are within 5% of the estimated plant flows.

Investigation of batch fluidized‐bed drying by mathematical modeling, CFD simulation and ECT measurement

AbstractMathematical modeling, computational fluid dynamics (CFD) analysis and electrical capacitance tomography (ECT) is used to develop an understanding of batch fluidized‐bed drying, which is a complex air‐solids, multiphase process. The mathematical model is based on a three‐phase theory that describes the mass‐and heat‐transfer between the air and solids phases. The CFD model is based on a two‐fluid model (TFM) approach, in which both phases are considered to be continuous and fully interpenetrating. The hydrodynamic parameters used to model the heat‐and mass‐transfer between the two phases are determined by a correlation approach, and the estimated parameters are incorporated into a user defined function (UDF) in FLUENT. The moisture diffusion in the air and solids phases is simulated using the user defined scalar (UDS) transport equation in the software package. ECT is used for the online solids concentration and moisture measurement, based on dynamic calibration. Comprehensive comparisons between results from mathematical modeling, CFD simulation and ECT measurement are presented, and are validated using experiment results. Online measurement of moisture content is compared with a static calibration. The mathematical model, CFD and ECT presented are being integrated into an online process control system for a batch fluidized‐bed drying application in the pharmaceutical industry. © 2007 American Institute of Chemical Engineers AIChE J, 2008

CFD modelling of BaSO4 precipitation inside microemulsion droplets in a semi-batch reactor

Nanoparticle production using microemulsion droplets has become a very interesting technique in the recent years. It allows a controlled adjustment of the particle size, which is an essential task due to the highly size-dependent properties of nanoparticles. For numerical investigations of this configuration a population balance model (PBM) framework based on discrete coordinates has been derived. An appropriate reduction concept is applied to obtain an efficient numerical solution. Although the resulting zero-dimensional (spatially homogeneous) calculations show a qualitatively good agreement with the experimental data for stoichiometric conditions, larger deviations have been observed for cases with a high concentration excess of one reactant inside the microemulsion droplets. Such deviations might result from the fact that the precipitation rate strongly depends on the local supersaturation. High concentration differences, especially near the feed lead to large local variations of the supersaturation profile. Thus, computational fluid dynamics (CFD) simulations have been performed for a refined analysis. This has been managed by implementing the reduced PBM model in the commercial CFD code FLUENT® 6.2 via user-defined scalars and functions. By this way, it becomes possible to investigate the reaction process for various three-dimensional inhomogeneous hydrodynamic conditions with acceptable computational times. The obtained results are finally compared with the homogeneous calculation results and with the experiments. Moreover, local variations within the reactor are also examined.

Comparison of electrostatic fine powder coating and coarse powder coating by numerical simulations

Powder coating has several key advantages over liquid coating, and fine powder coating makes the surface finish quality comparable with liquid coating. This work reports on the numerical simulation of a fine powder-coating process in comparison with coarse powder coating, using a commercial computational fluid dynamic code, Fluent v6.1. The purpose of the study is to understand the gas and particle flow fields inside the coating booth for various operating conditions and the effect of reducing particle size on the coating process. The air and powder particle flows in a coating booth were modeled as a three-dimensional turbulent continuous gas flow with solid particles as a discrete phase. The continuous gas flow was calculated by solving the Navier–Stokes equations, including the standard k–ε turbulence model with non-equilibrium wall function. The discrete phase was modeled based on the Lagrangian approach. In addition to drag force and gravity, the electrostatic force including the effect of space charge due to free ions was considered in the equation of motion and implemented using user-defined scalars and user-defined functions. The governing equations were solved using a second-order upwind scheme. This study demonstrates that the use of finer particles of size 15 μm or lower can give a very smooth and uniform surface finish, which may serve the requirement of automotive top-clear coating. This also provides useful information about optimum operating conditions such as the airflow rate, the applied external voltage and the powder-spray rate. The numerical model can also be used to optimize the gun-booth design for a better coating efficiency.

Comparison of different techniques for the FLUENT $^{\copyright}$ -based treatment of the electromagnetic field in inductively coupled plasma torches

A new technique for using the CFD commercial code FLUENT\(^{\copyright}\) to simulate inductively coupled plasma torches by means of two-dimensional axisymmetric models is presented. The method is based on an external user-defined function (UDF) which fully solves the electromagnetic field equations, letting the FLUENT\(^{\copyright}\) built-in module calculate only the plasma temperature and velocity fields inside the torch region. In this framework, computations have been carried out for LTE, optica lly thin argon plasmas at atmospheric pressure, using extended grid models with either magnetic dipole or vanishing vector potential boundary conditions for the electromagnetic field. It is shown that our newly developed technique is up to 60% faster on each iteration than that using user-defined scalars (UDS) previously proposed in the literature, as the need of solving flow field equations also outside the plasma zone is eliminated. Calculations are also performed using exact integral boundary conditions for the vector potential, as given by the standard electromagnetic field approach, taking into account the effects of both exciting and induced currents. The corresponding results are compared with the approximate ones obtained by employing extended grid models, showing that for small radial dimensions of the electromagnetic field domain, the magnetic dipole boundary conditions give more realistic solutions than those assuming a vanish ing vector potential.