Quasi Three-dimensional Model Research Articles

Numerical quasi-three dimensional modeling of stratified oil-water flow in horizontal circular pipe

The stratified oil-water two-phase flow is commonly encountered in offshore oil production systems, and is considered to be among the fundamental flow configuration in two-phase systems. A numerical quasi-three dimensional model for the calculations of the axial pressure gradient, interface height, water holdup, and the flow field in a fully developed oil-water two-phase stratified pipe flow has been developed. The oil-water curved interface configuration is predicted by using minimum energy model. The model solves the governing equations of the steady axial momentum and mass conservation equations together with a low Reynolds number k～ε model of turbulence for the eddy viscosity, performed in the bipolar coordinate system, for convenient describing the curved interface and mapping of the physical domain. The predicted dynamic parameters, such as interface height of close to the pipe wall and in the middle of the pipe cross-section, water holdup, pressure gradient and flow filed are compared with the experiments. At the same time, this model is utilized to study the variation of these dynamic parameters with increasing superficial oil and water velocities. In addition, the numerical model with concave oil-water interface gives more accurate results than a flat interface. It indicates that the interfacial configuration effects are significant.

Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams

A quasi-three dimensional model is proposed for the vibration analysis of functionally graded (FG) micro-beams with general boundary conditions based on the modified strain gradient theory. To consider the effects of transverse shear and normal deformations, a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness. The conventional beam theories including the classical beam theory, the first-order beam theory, and the higherorder beam theory are regarded as the special cases of this model. The material properties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme. The energy-based formulation is derived by a variational method integrated with the penalty function method, where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables. The formulation is validated by some comparative examples, and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.

Dynamic model of a micro-tubular solid oxide fuel cell stack including an integrated cooling system

Abstract A novel dynamic micro-tubular solid oxide fuel cell (MT-SOFC) and stack model including an integrated cooling system is developed using a quasi three-dimensional, spatially resolved, transient thermodynamic, physical and electrochemical model that accounts for the complex geometrical relations between the cells and cooling-tubes. The modeling approach includes a simplified tubular geometry and stack design including an integrated cooling structure, detailed pressure drop and gas property calculations, the electrical and physical constraints of the stack design that determine the current, as well as control strategies for the temperature. Moreover, an advanced heat transfer balance with detailed radiative heat transfer between the cells and the integrated cooling-tubes, convective heat transfer between the gas flows and the surrounding structures and conductive heat transfer between the solid structures inside of the stack, is included. The detailed model can be used as a design basis for the novel MT-SOFC stack assembly including an integrated cooling system, as well as for the development of a dynamic system control strategy. The evaluated best-case design achieves very high electrical efficiency between around 75 and 55% in the entire power density range between 50 and 550 mW / cm 2 due to the novel stack design comprising an integrated cooling structure.

Evaluation and optimization of a micro-tubular solid oxide fuel cell stack model including an integrated cooling system

A micro-tubular solid oxide fuel cell stack model including an integrated cooling system was developed using a quasi three-dimensional, spatially resolved, transient thermodynamic, physical and electrochemical model that accounts for the complex geometrical relations between the cells and cooling-tubes. For the purpose of model evaluation, reference operating, geometrical and material properties are determined. The reference stack design is composed of 3294 cells, with a diameter of 2 mm, and 61 cooling-tubes. The stack is operated at a power density of 300 mW/cm2 and air is used as the cooling fluid inside the integrated cooling system. Regarding the performance, the reference design achieves an electrical stack efficiency of around 57% and a power output of 1.1 kW. The maximum occurring temperature of the positive electrode electrolyte negative electrode (PEN)-structure is 1369 K. As a result of a design of experiments, parameters of a best-case design are determined. The best-case design achieves a comparable power output of 1.1 kW with an electrical efficiency of 63% and a maximum occurring temperature of the PEN-structure of 1268 K. Nevertheless, the best-case design has an increased volume based on the higher diameter of 3 mm and increased spacing between the cells.

Numerical research on flow and thermal transport in cooling pool of electrical power station using three depth-averaged turbulence models

This paper describes a numerical simulation of thermal discharge in the cooling pool of an electrical power station, aiming to develop general-purpose computational programs for grid generation and flow/pollutant transport in the complex domains of natural and artificial waterways. Three depth-averaged two-equation closure turbulence models, {m1}, {m2}, and {m3}, were used to close the quasi three-dimensional hydrodynamic model. The {m3} model was recently established by the authors and is still in the testing process. The general-purpose computational programs and turbulence models will be involved in a software that is under development. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm and multi-grid iterative method are used to solve the hydrodynamic fundamental governing equations, which are discretized on non-orthogonal boundary-fitted grids with a variable collocated arrangement. The results calculated with the three turbulence models were compared with one another. In addition to the steady flow and thermal transport simulation, the unsteady process of waste heat inpouring and development in the cooling pool was also investigated.

A hydrodynamic model of nearshore waves and wave-induced currents

In This study develops a quasi-three dimensional numerical model of wave driven coastal currents with accounting the effects of the wave-current interaction and the surface rollers. In the wave model, the current effects on wave breaking and energy dissipation are taken into account as well as the wave diffraction effect. The surface roller associated with wave breaking was modeled based on a modification of the equations by Dally and Brown (1995) and Larson and Kraus (2002). Furthermore, the quasi-three dimensional model, which based on Navier-Stokes equations, was modified in association with the surface roller effect, and solved using frictional step method. The model was validated by data sets obtained during experiments on the Large Scale Sediment Transport Facility (LSTF) basin and the Hazaki Oceanographical Research Station (HORS). Then, a model test against detached breakwater was carried out to investigate the performance of the model around coastal structures. Finally, the model was applied to Akasaki port to verify the hydrodynamics around coastal structures. Good agreements between computations and measurements were obtained with regard to the cross-shore variation in waves and currents in nearshore and surf zone.

A hydrodynamic model of nearshore waves and wave-induced currents

In This study develops a quasi-three dimensional numerical model of wave driven coastal currents with accounting the effects of the wave-current interaction and the surface rollers. In the wave model, the current effects on wave breaking and energy dissipation are taken into account as well as the wave diffraction effect. The surface roller associated with wave breaking was modeled based on a modification of the equations by Dally and Brown (1995) and Larson and Kraus (2002). Furthermore, the quasi-three dimensional model, which based on Navier-Stokes equations, was modified in association with the surface roller effect, and solved using frictional step method. The model was validated by data sets obtained during experiments on the Large Scale Sediment Transport Facility (LSTF) basin and the Hazaki Oceanographical Research Station (HORS). Then, a model test against detached breakwater was carried out to investigate the performance of the model around coastal structures. Finally, the model was applied to Akasaki port to verify the hydrodynamics around coastal structures. Good agreements between computations and measurements were obtained with regard to the cross-shore variation in waves and currents in nearshore and surf zone.

A novel analytical analysis of PEM fuel cell

In this study, a quasi three-dimensional model was developed for a single proton exchange membrane (PEM) fuel cell. The model was used for a half-cell which includes the cathode gas channel, gas diffusion layer (GDL), cathode catalyst layer and membrane is modeled. This model includes mass transfer in the gas channel and GDL, electrochemistry reaction in cathode catalyst layer, and charge transfer in the membrane phase. These expressions were solved by analytical methods. An agglomerate approach was used to describe cathode catalyst layer. By using analytical solution, the expressions can predict the PEM fuel cell behavior in different conditions which is the advantage of this method.

Forecasting the oil temperatures along the proposed China–Russia Crude Oil Pipeline using quasi 3-D transient heat conduction model

Abstract The China–Russia Crude Oil Pipeline (CRCOP) faces significant challenges due to differential frost heaving and thaw settlement resulting from significant variations of oil temperatures along the pipeline. Oil temperature distribution along the pipeline during the long-term operation period is a very important factor in pipeline foundation design under future climate warming and various frozen soil conditions. It is important for the assessment and prediction of differential frost heave and thaw settlement of the pipeline foundations soils, forecasting the development of the seasonal and inter-annual frozen and thawed cylinders around the operating pipeline, stress–strain analysis of the pipeline, and mitigation of subsequent frost hazards. A quasi three-dimensional computational model was developed to predict the oil temperature along the pipeline. It was verified by analytic solutions of the minimum oil temperatures along the route provided by the Daqing Oilfield Engineering (DOE) Co. The oil temperatures were predicted and analyzed for two proposed annual oil flow rates of 15 million tons (0.3 mbpd) and 30 million tons (0.6 mbpd) with and without mitigative measures (only pipe insulation was considered here) during the operation period. Also, the inter-annual variations of oil temperature at key typical locations were investigated to understand the impact of climate warming. The results indicated that the maximum oil temperature cools southwards, but the minimum oil temperature warms southwards (with the inlet oil temperatures from − 6 to +10 °C). However, the average annual oil temperature decreases southwards in the northern part of the pipeline, then it starts to slowly increase. The amplitudes of oil temperature change will decrease southwards. Oil temperatures will slightly increase with elapsing time due to the imposed boundary conditions of climate warming. The oil temperatures with a lower flow rate vary more significantly than that with a higher flow rate because the oil temperature with a low flow rate is more affected by the thermal regime of the surrounding soils and the external environments. Insulation around the pipeline tends to reduce the oil temperature variations along the pipeline during pipeline operation period. Therefore, pipe insulation can effectively reduce the development of frozen and thawed cylinders in the permafrost zone. The phase change of water in soils around the pipeline has a distinct influence on the oil temperature during the freeze–thaw transition periods. The oil temperature tends to be equal to the ambient ground temperature around the pipeline with southward distance and with elapsing operation time. The pipeline oil temperature is controlled by the incoming oil temperature and the surrounding ground temperature before the equalization. It would be mainly controlled by the ground temperature around the pipeline afterwards.

Effect of molecular weight and density of ambient gas on shock wave in laser-induced surface nanostructuring

This paper presents the results of molecular dynamics studies about the shock wave during laser-induced surface nanostructuring. A quasi-three dimensional model is constructed to study systems consisting of over 2 million atoms. Detailed studies are carried out about the shock wave front and Mach number, evolution of plume and ambient gas interaction zone, and energy exchange between the ambient gas and plume. Under an ambience of lower pressure or lighter molecular mass, the plume affects a larger area while the strength of the shock wave front is weaker. With the same ambient pressure, the ablated material features the same kinetic energy at the late stage regardless of the molecular weight of the ambient gas. The same conclusion holds for the energy increase of the ambient gas as well. When the ambient pressure is reduced, more kinetic energy is carried out by the ablated material while less energy is transferred to the ambient gas. It is observed that heavier ambient gas could bounce back the ablated material to the target surface.

Operating temperature margin and heat load in PF superconducting coils of KSTAR

The code SAITOKPF has been developed for the design and analysis of the poloidal field (PF) coil system of KSTAR (Korean Superconducting Tokamak Advanced Research) device. The plasma operation is studied by consideration of flux conservation. An equivalent circuit model is used to simulate the magnetic coupling among the plasma current, superconducting coils, the tokamak supporting structure and the cryostat. Due to the high changing rates in the operating currents of the PF coils, the magnetic coupling can generate high AC losses including the hysteresis loss, the eddy current loss, and the coupling loss. The helium is forced-flowed through the cable in conduit conductor (CICC) to remove the losses and to keep the temperature rise in the superconducting cable lower than its current sharing temperature. The thermal coupling between pancakes, layers, and cooling channels in PF coils is simulated by a quasithree-dimensional thermo-hydraulic model. In this paper, the physical model, the numerical method and the structure of the simulation code are introduced. A nominal operating scenario of the KSTAR device is used to simulate these phenomena.

Experimental validation of a quasi three-dimensional conjugate heat transfer model for the metering section of a single-screw plasticating extruder

This paper presents a quasi three-dimensional computer model and its validation with experimental results of the thermal transport processes in the metering section of a single-screw plasticating extruder. A finite volume based approach (SIMPLEC) has been used to obtain flow, thermal and pressure fields of a power-law fluid in the screw channel. The accuracy of the present model has been confirmed by the satisfactory tally of the numerical results with the experimental data for the extruder with fully open exit valve, and also by the excellent matching of the dimensionless exit pressure gradient with the experimental data.

A quasi three dimensional model of water flow in the subsurface of Milano (Italy): the stationary flow

Abstract. A quasi three-dimensional model is developed to simulate the behaviour of the aquifer system which is the resource of drinkable water for the town of Milano (Italy). Non continuous semipermeable layers locally separate permeable levels in a multilayered system, consisting of a phreatic and three confined aquifers. The numerical model is a conservative finite difference scheme based on the discretisation of the water balance equation for stationary flow. The grid spacing is 500 m and has been chosen, taking into account the distribution of the data in an area of about 400 km2. The model has been calibrated with a "trial and error" procedure, by comparison of the results of the model with the observations for three years (1950, 1974 and 1982) which correspond to different flow situations. Once calibrated, the model has been used as a predictive tool, to forecast the behaviour of the aquifer system for other years of the 20th century; the comparison between the model forecasts and observations is good. The model is capable of describing both the strong drawdown of the water table in the 1970s, when the water demand for domestic and industrial needs was very high, and the rise of the water table in the 1990s, when water extraction decreased. The results of the model confirm that the phreatic level is controlled largely by the local extraction of water; moreover, the aquifer system reacts to an increasing water demand with a small increase of the inflow and with a strong decrease of the outflow from its boundaries.

柔軟性界面相を有する一方向繊維強化複合材料の数値モデル化手法

The interphase has an important role, that is, conducts the stress transmission between fiber and resin. Authors introduced the concept of flexible interphase and established the fabrication method of prepregs. In this study, a new numerical model considering the fiber/resin interphase was proposed, in order to design the flexible interphase. For the mechanical behaviors of composite structures were predicted by the finite element method, the consideration of the heterogeneity is an important key. Authors have established a numerical modeling method, namely, a quasi-threedimensional model which can consider the heterogeneity. Based on the quasi-three-dimensional modeling concept, a new numerical model which can independently consider the fiber/matrix interphase was proposed. The mechanical behaviors of unidirectional CFRP laminates with various flexural interphase thickness under the three-point bending load were simulated. By comparing the prediction with experimental results, the validity of the proposed model was examined. It was concluded that the model was effective for the fiber/resin interphase designing in the CFRP composite structures.

Modified Quasi-three-dimensional 4-pointBending Simulation Method For CFRPCylindrical Tube

The damage propagation of a CFRP cylindrical tube subjected to 4-point bending load was investigated. A numerical simulation using a quasi-threedimensional model is attempted. The quasi-three-dimensional model is constructed of both shell elements and beam elements which represent fiber and matrix, respectively. The damage propagation analyses of three types have been performed. As a result, it is confirmed that the numerical simulation using the quasi-three-dimensional model is effective for predicting the damage propagation behaviours.

A quasi three-dimensional model for flow and transport in unsaturated and saturated zones: 1. Implementation of the quasi two-dimensional case

A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes.

Micro/macro modeling of CVD synthesis

We propose a CVD reaction scheme in which a source material undergoes a gas-phase reaction to produce an intermediate, and then the intermediate diffuses to the solid surface and changes into a solid film through a surface reaction. A series of simple Monte Carlo (SMC) codes has been developed to simulate the observed film shape on micro-trenches and holes. By using these codes, surface reaction rate constants were determined so as to reproduce the experimentally observed film shape. By means of a macro-scale reactive transport analysis of a hot wall tubular reactor, gas-phase reaction rate constants for single component systems were determined to simulate the experimental growth rate distributions. The composition and growth rate of Yttria stabilized Zirconia (YSZ) film, a solid solution of Yttria and Zirconia, were qualitatively explained by a sum of single component's growth rates. As an application of these reaction models, we simulated a rotating-disk CVD reactor under low pressure. The simulations based on a quasi three-dimensional model revealed that the susceptor rotation suppresses the buoyancy convection and forms steeper gradients in temperature and concentration near the susceptor uniformly over wide area. At higher temperatures, the growth rate increased with rotation speed, but at lower temperatures the growth rate decreased with increasing rotation speed because the reduced retention time in the high-temperature region suppressed the gas-phase reaction.

A diffusion model for the development of a boundary layer in lakes

The development of a boundary layer characterised by very low gradients in temperature and salinity near the bottom boundary of a lake does not necessarily imply an increase in diapycnal mixing within the boundary layer. The results of a quasi three-dimensional diffusion model for a basin with sloping boundaries demonstrate that in lakes a boundary layer also develops when the diapycnal diffusivity is chosen to be constant.In the model mixing is assumed to be anisotropic and is described as an isopycnal and diapycnal turbulent diffusion process. Advective transport is not considered. Therefore, the model is restricted to the description of the purely diffusive response of a lake. It should be regarded as a contribution to the discussion of boundary mixing and not as a complete mixing model for a specific lake. The isopycnal and diapycnal turbulent diffusion coefficients are presumed to be constant in space and time. The direction of isopycnal and diapycnal density flux changes with time since mixing of the density distribution influences the orientations of the isopycnals. This interaction between mixing process and density distribution is accounted for by the model.According to the model the density distribution, and therefore the development of a boundary layer, only depends on diapycnal mixing while the distribution of a passive tracer depends on both, isopycnal and diapycnal mixing. The application of the model to the subalpine Lake Alpnach demonstrates that a simple diffusion model is sufficient to predict the development of a boundary layer. Considering that the model does not include advective processes and that diffusivities have been assumed to be constant in space and time, the structure of the boundary layer predicted agrees surprisingly well with experimental data.

Three-dimensional temperature control of palladium-nickel thermoseeds: A computer aided and experimental evaluation

The capability of self-regulating thermoseeds to compensate for nonuniform cooling along their longitudinal axis has been investigated in this study. For this purpose a quasi three-dimensional computer model has been developed. Calculations of the temperature profile in tissue with nonuniform heat loss demonstrated a clear improvement in the longitudinal temperature control of PdNi seeds compared to constant power seeds. Further, two strategies for improved control of nonuniform cooling along the longitudinal axis of ferromagnetic seeds have been investigated: (1) application of a ‘normal’ undivided seed; and (2) division of a long seed in smaller segments of which each segment is able to respond more directly to local variations in the temperature distribution. Calculations with the quasi three-dimensional model showed that the loose segments do respond more directly to their close proximity. However, the equilibrium temperature of a segment in an area with high local blood flow will be relatively low due the limited heat production of PdNi thermoseeds. In the undivided seeds the high thermal conductivity of PdNi causes some levelling of the longitudinal temperature gradient in the seed. In addition, calorimetric experiments have shown that the heat production of a segmented seed is less effective because of a demagnetizing field. Also, the absence of PdNi between the segments reduces the heat production of the seed.

A diffusion model for the development of a boundary layer in lakes

The development of a boundary layer characterised by very low gradients in temperature and salinity near the bottom boundary of a lake does not necessarily imply an increase in diapycnal mixing within the boundary layer. The results of a quasi three-dimensional diffusion model for a basin with sloping boundaries demonstrate that in lakes a boundary layer also develops when the diapycnal diffusivity is chosen to be constant. In the model mixing is assumed to be anisotropic and is described as an isopycnal and diapycnal turbulent diffusion process. Advective transport is not considered. Therefore, the model is restricted to the description of the purely diffusive response of a lake. It should be regarded as a contribution to the discussion of boundary mixing and not as a complete mixing model for a specific lake. The isopycnal and diapycnal turbulent diffusion coefficients are presumed to be constant in space and time. The direction of isopycnal and diapycnal density flux changes with time since mixing of the density distribution influences the orientations of the isopycnals. This interaction between mixing process and density distribution is accounted for by the model. According to the model the density distribution, and therefore the development of a boundary layer, only depends on diapycnal mixing while the distribution of a passive tracer depends on both, isopycnal and diapycnal mixing. The application of the model to the subalpine Lake Alpnach demonstrates that a simple diffusion model is sufficient to predict the development of a boundary layer. Considering that the model does not include advective processes and that diffusivities have been assumed to be constant in space and time, the structure of the boundary layer predicted agrees surprisingly well with experimental data.