Control Volume Finite Difference Method Research Articles

Investigation on the thermal performance of different lightweight roofing structures and its effect on space cooling load

The lightweight aluminum standing seam roofing system (LASRS) has been widely used as a building element in the construction of either commercial or governmental buildings, and has been proven to be an economic roofing system. However, little research has been conducted into its thermal performance and the effect of the absorptivity (colour) of its external surface on space cooling load in the hot humid area. This paper aims to investigate the thermal performance of the LASRS. A dynamic model is introduced for analyzing the transient heat transfer through the roofs, which was solved by the control volume finite-difference method employing an explicit scheme and validated by measured data. The simulation results show that the heat flux through the roofing system with a polyurethane insulation layer is smaller than that through the lightweight roof with glasswool insulation R1. The space cooling load reduction ratio for light painted envelop could reach about 9.3% compared with black painted one. The cooling load reduction ratio ranges from 1.3% to 9.3% for the roof structure R1 with various surface colour. Therefore, the space cooling load for air conditioning of the building can be considerably reduced (up to 20%) by employing a lightweight roof using polyurethane insulation with white painted surface colour.

Three-Dimensional CFD Modeling for Optimization of Invert Trap Configuration to Be Used in Sewer Solids Management

Flow field prediction and optimization of invert trap configuration have been carried out by using three-dimensional computational fluid dynamics (CFD) modeling with the help of FLUENT software using renormalization group (RNG) k-ϵ along with the discrete phase model (DPM). A hexagonal/tetrahedral shape and map-type nonuniform grid were chosen to discretize the entire computational domain, and a control volume finite difference method was used to solve the governing equations. In the present study, five different invert trap configurations (rectangular with and without lid on both sides, trapezoidal, trapezoidal with rectangular base, and rectangular with trapezoidal base with lid on both sides) have been simulated for the flow of three different inert sediment types (sand, styrocell, and plastic beads) at six flow rates (0.35, 0.70, 1.05, 1.35, 4.55, and 9.95 Lps) for each trap. The discharges selected in the present study cover the entire range of discharge expected in channels during dry weather flow and monsoon. The simulation results are capable of showing particle trajectories and the effect of flow rate and trap geometry on the flow patterns developed within the trap. Based on 3-D CFD modeling and experimental measurements, it has been concluded that the invert trap having a rectangular shape with trapezoidal base with lids on both sides is the most efficient trap configuration with highest sediment retention ratio.

Comparison of two- and three-dimensional modeling of invert trap for sewer solid management

In the present study, five different invert trap configurations (rectangular with and without lids on both sides; trapezoidal, trapezoidal with rectangular base and rectangular with trapezoidal base with lids on both sides) were simulated for both two-dimensional (2D) and three-dimensional (3D) flow conditions for three sediment types (sand, styrocell and plastic beads) at six flow rates (0.35, 0.70, 1.05, 1.35, 4.55 and 9.95 L/s) for each trap. Computational fluid dynamics (CFD)-based modeling using FLUENT software with Renormalization Group (RNG) k– ɛ model along with discrete phase model (DPM) were used in the simulations. A hexagonal/tetrahedral and map-type non-uniform grid was chosen to discretize the entire computational domain and a control volume finite difference method was used to solve the governing equations. The flow rates selected in the present study cover the entire range of flow rate expected for dry weather and monsoon. The simulation is capable of differentiating between 2D and 3D modeling of particle trajectories, the effects of flow rate and trap geometry on flow patterns developed in the trap. The sediment retention ratio for 2D is higher than that for 3D modeling for all flow conditions, particle types and model geometry due to inclusion of lateral effects in 3D modeling. The invert trap having rectangular shape with trapezoidal base is found to be the most efficient configuration in both 2D and 3D modeling.

Numerical studies of a tube-in-tube helically coiled heat exchanger

In the present study a tube-in-tube helically coiled (TTHC) heat exchanger has been numerically modeled for fluid flow and heat transfer characteristics for different fluid flow rates in the inner as well as outer tube. The three-dimensional governing equations for mass, momentum and heat transfer have been solved using a control volume finite difference method (CVFDM). The renormalization group (RNG) k– ɛ model is used to model the turbulent flow and heat transfer in the TTHC heat exchanger. The fluid considered in the inner tube is compressed air at higher pressure and cooling water in the outer tube at ambient conditions. The inner tube pressure is varied from 10 to 30 bars. The Reynolds numbers for the inner tube ranged from 20,000 to 70,000. The mass flow rate in the outer tube is varied from 200 to 600 kg/h. The outer tube is fitted with semicircular plates to support the inner tube and also to provide high turbulence in the annulus region. The overall heat transfer coefficients are calculated for both parallel and counter flow configurations. The Nusselt number and friction factor values in the inner and outer tubes are compared with the experimental data reported in the literature. New empirical correlations are developed for hydrodynamic and heat-transfer predictions in the outer tube of the TTHC.

A numerical study of developing slurry flow in the entrance region of a horizontal pipe

In this paper, a simplified 3-D algebraic slip mixture (ASM) model was introduced to obtain the numerical solution in sand–water slurry flow. In order for the study to obtain the precise numerical solution in fully developed turbulent flow, the RNG k– ε turbulent model was used with the algebraic slip mixture model. An unstructured (block-structured), non-uniform grid was chosen to discretize the entire computation domain, and a control volume finite difference method (CVFDM) was applied to solve the governing equations. The mean pressure gradients from the numerical solution in the fully developed turbulent flow were compared with the authors’ experimental data and that in the open literature to validate the simulation results. The solutions were found to be in good agreement with the experimental data. The numerical investigations have focused mainly on illustrating and comparing the developing processes of volume fraction and density distributions, mean velocity profiles, and mean skin friction coefficient distributions in the entrance region. It was found that the difference of friction factors between single- and double-species slurries increases along flow direction in most part of the entrance region.

Effect of radiative heat transfer on the three-dimensional Boyancy flow in cubic enclosure heated from the side

This article presents a numerical study of the effect of the radiative heat transfer on the three-dimensional convection in a cubic differentially heated cavity for different optical parameters of the medium, Pr = 13.6 and Ra = 10 5. The natural convection equations, using the Boussinesq approximation for the treatment of buoyancy term in the momentum equation, are expressed using the vorticity-stream function formulation. These equations and the radiative transfer equation are discretized, respectively, with the control volume finite difference method and the FTn finite volume method. The successive relaxation-iterating scheme is used to solve the resultant algebraic system equations. Results show that the structure of the main flow is considerably altered by of the conduction–radiation parameter. The inner spiraling flows are found very sensible in location and direction to the radiative heat transfer. However, the peripheral spiraling motion is qualitatively insensitive to these parameters. It is also found that radiation favorites the merging of the vortices near the front and back walls.

Slug flow in curved microreactors: Hydrodynamic study

The need for eco-friendly and energy saving processes which are substantially compact and give higher efficiency has led to the concept of process intensification (PI). Curved microchannel is such innovative device, which has potential for the intensification of processes currently carried out in conventional straight or T-type microchannels. Curved microchannels utilize the benefits of centrifugal force to its advantage. The present study deals with the numerical simulation of the Taylor flow in curved microchannels, particularly on gas and liquid slugs with varying curvature ratios (i.e., coil to tube diameter = 5 , 10, 20 and 30). The three-dimensional, unsteady slug flow development in the curved microchannel was carried out using control volume finite difference method (CVFDM). The gas and liquid slug lengths at various operating and fluid conditions were obtained. The slug flow development for different inlet conditions and geometries (premixed feed, T-type and Y-type inlets) was also studied in the curved microchannels. It was found that for low curvature ratio ( D / d = 3 ) , the phenomenon of flow reversal and slug freezing takes place due to centrifugal and buoyancy forces. For the similar process conditions, with an increase in curvature ratio to 5 and 10, the phenomenon of flow reversal and slug freezing observed was very minor. The non-uniformity in the slug formation was observed for low curvature ratio as compared to the higher curvature ratios. Further the influence of surface tension, viscosity and wall adhesion was studied on slug flow development in the curved microchannels. From the results it was observed that the surface tension, viscosity and wall adhesion have significant influence on slug flow development in curved microchannels.

Numerical study of slip flow heat transfer of non-Newtonian fluids in circular microchannels

In the present investigation, numerical simulations are performed to study flow and thermal fields of non-Newtonian fluids in circular microchannels. The flow is considered to be slip, axisymmetric, steady, incompressible, laminar, and power law model is used to characterize the behavior of the non-Newtonian fluid. The constant wall heat flux and constant wall temperature are employed as thermal boundary conditions. The set of governing dimensionless differential equations with appropriate boundary conditions are solved together using control volume finite difference method. Results indicate the increasing slip coefficient decreases the product of friction factor and Reynolds number and centerline velocity while results in increasing of local Nusselt numbers. Slip effect enhances with increasing power law index. Also slip effect in constant wall heat flux is more than that of constant wall temperature boundary conditions.

Laminar convective heat transfer in chaotic configuration

The convective heat transfer in chaotic configuration of circular cross-section under laminar flow regime at different values of Dean number and Prandtl number is investigated numerically. The chaotic configuration is the combination of 90° bends and coils. The insertion of equidistant 90° bends between the two consecutive coil produces the phenomenon of flow inversion. The hydrodynamics and heat transfer under laminar flow conditions in the chaotic configuration with constant wall flux as a boundary condition is studied. The control-volume finite difference method with second-order accuracy is used. The chaotic configuration shows a 25–36% enhancement in the heat transfer due to chaotic mixing while relative pressure drop is 5–6%. The effect of Prandtl number on fully developed heat transfer coefficient is also reported. It is observed that heat transfer increases with increase in Prandtl number. The stretching and folding phenomenon in chaotic configuration is observed and discussed for heat transfer coefficient and pressure drop in the chaotic configuration. The cyclic oscillation behavior in the heat transfer coefficient with downstream distance in the chaotic configuration and coiled tube is also observed and discussed. It appeared that heat transfer is strongly influenced by flow inversion. The effect of boundary conditions on heat transfer performance in the chaotic configuration as well as in the coiled tube is also carried out. The study is further extended to predict hydrodynamics and heat transfer with temperature-dependent viscosity in the chaotic configuration. A comparative study for heat transfer and friction factor is also carried out for constant and temperature-dependent viscosity in coiled tube and chaotic configuration. It was observed that the heat transfer under heating condition with temperature-dependent viscosity is higher as compared to the constant viscosity result while friction factor shows the reverse phenomenon in the chaotic configuration.

Mathematical modeling and numerical simulation of a short term thermal energy storage system using phase change material for heating applications

The main objective of this paper is to analyze the heat and mass transfer in a ventilation duct filled with encapsulated paraffin wax RII-56. A mathematical model and its numerical solution are presented. A new approach for approximating the specific heat of the PCM as a function of its temperature is proposed for all range of operating conditions. The interpolating cubic spline function method is used for determining an effective specific heat in each time step of temperature calculations. Equations for three-dimensional transient thermal analysis with associated boundary and initial conditions are solved by the control volume finite difference method with the fully implicit scheme. Proper trends and a good agreement between the results of theoretical modeling and physical reality for the solidification/melting process are obtained. Finally, 24 h operation of the proposed short term latent heat storage system is analyzed and the influence of the PCM capsules geometry on the thermal performance of the tested storage module is shown.

Numerical simulation of steady flow fields in coiled flow inverter

Flatter velocity profiles and more uniform thermal environments are extremely desirous factors for improved performance in flow reactors and heat exchangers. One means of achieving it in laminar flow systems is to use mixers and flow inverters. In the present study a new device is introduced based on the flow inversion by changing the direction of centrifugal force in helically coiled tubes. The objective of the present study is to characterize flow development and temperature fields in the proposed device made up from the configurations of bent coils. The main mechanism generating the flow is the production of spatially chaotic path by changing the direction of flow using a 90° bend in helical coils (alternating Dean flow). If the direction of centrifugal force is rotated by any angle, the plane of vortex formation also rotates with the same angle. Thus in helical flow a 90° shift in the direction of centrifugal force cause a complete flow inversion. Complete flow fields and thermal fields in helical coil and bent coil configuration were studied using computational fluid dynamics software (FLUENT 6.0). The three-dimensional governing equations for momentum and energy under the laminar flow conditions were solved with a control-volume finite difference method (CVFDM) with second-order accuracy. The flow pattern obtained for the helical coil was in good agreement to those observed by the previous investigators [S.W. Jones, O.M. Thomas, H. Aref, Chaotic advection by laminar flow in twisted pipe. J. Fluid Mech. 209 (1989) 335–357; Ch. Duchene, H. Peerhossaini, P.J. Michard, On the velocity field and tracer patterns in a twisted duct flow. Phys. Fluids 7 (1995) 1307–1317]. The comparison of the flow fields and temperature fields in the helical tube and bent coil configuration are discussed. The bent coil configuration shows a 20–30% enhancement in the heat transfer due to chaotic mixing while relative pressure drop is 5–6%. The results of the present study can be used to model transport processes for developing flows in curved tubes such as chromatographic columns (less axial dispersion [A.K. Saxena, K.D.P. Nigam, Coiled configuration for flow inversion and its effect on residence time distribution. AIChE J. 30 (1984) 363–368]), Chemical reactors (narrower RTD), heat transfer devices, and some biomedical devices.

Enhanced heat transfer due to curvature-induced lateral vortices in laminar flows in sinusoidal corrugated-plate channels

Laminar periodically developed forced convection in sinusoidal corrugated-plate channels with uniform wall temperature, and single-phase constant property flows is considered. Numerical solutions are obtained using the control-volume finite-difference method for a wide range of channel corrugation aspect ratios (0⩽ γ⩽1), and flow rates (10⩽ Re⩽1000) of viscous liquids ( Pr=5, 35, and 150). The flow field is found to be strongly influenced by γ and Re, and it displays two distinct regimes: a low Re or γ undisturbed laminar-flow regime, and a high Re or γ swirl-flow regime. In the no-swirl regime, the flow behavior is very similar to that in fully developed straight-duct flows with no cross-stream disturbance. In the swirl regime, flow separation and reattachment in the corrugation troughs generates transverse vortex cells that grow spatially with Re and γ, and the transition to this regime also depends on Re and γ. The mixing produced by these self-sustained transverse vortices is found to significantly enhance the heat transfer, depending upon γ, Re, and Pr, with a relatively small friction factor penalty. The consequent exchanger compactness and heat transfer enhancement effectiveness ( j/ f) is up to 5.5 times that for parallel-plate channels.

Analysis of thermal and water management with temperature-dependent diffusion effects in membrane of proton exchange membrane fuel cells

In the present work, the detailed thermal and water management in the membrane of proton exchange membrane fuel cells (PEMFC) is investigated numerically. The coupling effects of mass diffusion and temperature gradient on the water distribution in the membrane are taken into account with consideration of the temperature-dependent diffusivity. Thermal and water transport equations with various boundary conditions are solved by the control volume finite difference method. Predictions show that under the conditions of fixed water concentration at the cathode side, the effect of cathode temperature, Tc, on the water concentration is significant. Increases in Tc may lead to an increase in membrane dehydration. At the water-flux condition on the cathode side, the influence of the operating temperature on the water distribution in the membrane shows a similar trend. The effects of the anode temperature, Ta, on the water management in the membrane are also examined. It is found that Ta has considerable impact on the water content in the membrane. In addition, high current density may cause non-uniformity of the temperature distribution in the membrane.

Numerical investigations of liquid–solid slurry flows in a fully developed turbulent flow region

In this paper, a simplified 3D algebraic slip mixture (ASM) model is introduced to obtain the numerical solution in sand–water slurry flow. In order for the study to obtain the precise numerical solution in fully developed turbulent flow, the RNG K– ε turbulent model was used with the ASM model. An unstructured (block-structured) non-uniform grid was chosen to discretize the entire computational domain, and a control volume finite difference method was used to solve the governing equations. The mean pressure gradients from the numerical solutions were compared with the authors’ experimental data and that in the open literature. The solutions were found to be in good agreement when the slurry mean velocity is higher than the corresponding critical deposition velocity. Moreover, the numerical investigations have displayed some important slurry flow characteristics, such as volume fraction distributions, slurry density, slip velocity magnitude, slurry mean velocity distributions, and slurry mean skin friction coefficient distributions in a fully developed section, that have never been displayed in the experiments.

Implementation of a Flux-Continuous Finite-Difference Method for Stratigraphic, Hexahedron Grids

Summary In this paper we present a 3D flux-continuous finite-difference formulation designed for flow simulation of models with nonorthogonal hexahedron grids with general tensor permeability. Our development follows that of Aavatsmark et al.,1 but we do not operate in transformed space. The new 27-point discretization formula has been implemented in a finite-difference reservoir simulator. This stencil has many desirable properties, including collapsing into a consistent form in two dimensions. We demonstrate that there are many practical situations in which neglecting the influence of nonorthogonality and general tensors results in firstorder errors in flow predictions. A rigorous implementation for this 27-point difference operator as a control-volume finite-difference method determines the upwinding of convection terms associated with multiphase computations. Results and issues associated with implementation of this operator in a conventional finite-difference reservoir simulator are discussed. As an alternative to directly solving the linear matrix associated with the 27-point stencil of the flux-continuous operator, we examine iterative methods that split the matrix into a 7-point stencil part and a remainder. The 7-point stencil part is solved by a direct or iterative method, with the remainder part updated from the previous timestep or iteration. This split operator may permit retention of the linear solver for the standard 7-point formulation while retaining nonorthogonal grid and tensor information.

Convective instabilities induced in a critical fluid

We study temperature propagations and convective instabilities induced in critical fluids experimentally, theoretically and numerically. The analytical system is as follows: A critical fluid, the temperature of which is slightly higher than the critical temperature, is confined between two horizontal plates. The temperature of the bottom plate is raised at time zero and the temperature of the top plate is kept at the initial temperature of the fluid. An experimental system for the visualisation of convection induced in critical CO 2 is developed. In the theoretical analysis, we derive the thermofluiddynamics equations of critical fluids, in which the compressibility of the fluids and the pressure dependence of the entropy are taken into account. We solve the governing equations by the control volume finite difference method, in which the MacCormack scheme is employed for the time derivative, and investigate the temperature propagation modes on short, intermediate and long time scales. Through the analysis, the following results have been obtained; (1) On short time scales: Temperature propagates very quickly as acoustic waves because of the high compressibility of the critical fluids. (2) On intermediate time scales: The system temperature rises quickly and becomes constant in the central part of the fluid because of the quick temperature wave propagations. Thin thermal boundary layers are established near the bottom and top walls through the top wall is not cooled. (3) Long time scales: Thermal plumes are induced upwards from the bottom thermal boundary layer. Plumes are also initiated downwards from the top thermal boundary layer although the top wall temperature is not cooled. The convective mode of the thermal plumes driven in the critical fluids are different from that of Rayleigh-Bénard convection. Finally, we explain and discuss future problems related to transport phenomena in critical fluids.

Modelling of an aerodynamic technique of forming web structures in textile industries: I. Turbulent air flow past filters

In this study we develop a fundamental understanding of the dynamics of an aerodynamic method of forming fibrous web structures from short fibres. Computational fluid dynamics (CFD) is employed to model the web forming process which consists of fibre transportation through a turbulent air flow between two filters: a perforated screen of low resistance, which the fibres penetrate, and a belt of large resistance, onto which the fibres are deposited. In this first paper the fluid dynamics inside the machine used to form the web is analysed using a mathematical model which consists of a combination of the k-e turbulence model and the Darcy law on the two filters. Numerical results using a control volume finite-difference method are obtained for various machine geometries, filter resistances and inlet boundary conditions, in order to identify the important flow parameters. The fibre dynamics through the turbulent air flows presented here will be investigated in a subsequent paper.

A Numerical Investigation for the Heat and Mass Transfer Between Parallel Flow of Air and Desiccant Falling Film In a Fin-Tube Arrangement

A numerical investigation was conducted to study the heat and mass transfer between a falling film of calcium chloride desiccant solution and a parallel flow of air in a rectangular fin-tube arrangement. A control volume finite difference method was used to solve the governing equations for the air and the liquid desiccant solution subjected to the appropriate boundary conditions. A model was used to predict temperature distribution on the fin surface. In this model, two approaches were employed to determine the temperature distribution of the fin surface. The first approach utilized the analytical expression for the temperature distribution of a circular fin having the same area as the rectangular fin. The second approach used a finite difference algorithm to directly predict the temperature distribution of the rectangular fin surface. Both approaches were used to study the performance of the fin-tube arrangement for dehumidification of air at various operating conditions. The effects on the air dehumidification process, due to changing the inlet conditions of air and desiccant film; their mass flow rates; and the fin height were predicted. The results were used to developed correlations to predict the heat and mass transfer coeffiecients (on the airside) between the air and the liquid desiccant. These correlations can accurately be used to predict the outlet air and liquid desiccant conditions from the fin-tube arrangement. Correlations were developed to predict the rate of heat and mass transfer between the air and the desiccant film. Several numerical experiments showed agreement with the available data in literature.

Volumetric heat transfer coefficients in solid–fluid porous media: closure problem, thermal analysis and model improvement with fluid flow

This paper presents a detailed investigation on the volumetric transfer coefficient (VHTC) model in solid–fluid porous media based on the volume averaging method (VAM). The VHTC is obtained by solving the closure problem with the control-volume finite difference method. A thermal analysis is conducted to illustrate the thermal nature of the VHTC, based on which, an improved VHTC model has been proposed by taking into account the effects of the thermal entrance and the non-uniformity of the velocity field. With this model, the applicability of the VAM has been extended to large Peclet number laminar regime for convection heat transfer in porous media characterized by straight ducts.

Combined laminar forced convection and thermal radiation in a helical pipe

The interaction phenomena between laminar forced convection and thermal radiation in a participating medium inside a helical pipe were studied numerically. The P-1 radiation model was applied to the combined convection–radiation simulations. The three-dimensional governing equations for laminar flow and heat transfer were solved with a control-volume finite difference method (CVFDM) with second-order accuracy, and the O-type structure grid was adopted in this study. The effects of thermal radiation on the convective flow and heat transfer were measured by comparing the numerical results with and without thermal radiation. The comparison showed that under the conditions examined in this paper, although the thermal radiation had no significant influence for flow and temperature fields, especially in a fully developed region, it substantially enhanced the total heat transfer in the helical pipe.