Effects Of Wall Boundary Conditions Research Articles

Validation and application of numerical modeling for in-vessel melt retention in corium pools

In a hypothetical severe accident scenario in light water reactors (LWR), after the loss of primary coolant, the melted core moves to the lower plenum of the reactor pressure vessel and accumulate there. The melted core cautiously releases the decay heat which forms a pool of melted core, called corium, and turbulent natural convection starts. The decay heat transferred by the corium to the vessel may result in vessel failure due to the focusing effect in the absence of an effective cooling system. A numerical analysis is carried out using STAR-CCM+ commercial software to investigate the ability of the existing turbulence models and Algebraic Heat Flux Model (AHFM) to simulate the natural convective heat transfer phenomena in the corium pools. Efforts have been made to predict the BALI experimental results which are designed to simulate the heat transfer in corium pools, in the framework of severe accident studies. For BALI experiments various test campaigns are run varying the internal Rayleigh number, the viscosity of the simulant fluid, and test facility height. Various such experimental cases are verified and compared with numerical simulations. Temperature profiles along a vertical line, surface heat flux along the curved surface, average Nusselt number on the top, and curved surfaces are estimated. The effect of wall boundary conditions on heat transfer is analyzed. The numerical analysis is extended to Pressurized Water Reactor (PWR) and Boiling Water Reactor (BWR) geometries. The CFD analysis predicts the stratified zone and upper mixing zone very well, and the temperature profiles and average heat transfer values are in agreement with the experiments.

Effect of Wall Boundary Conditions on a Wall-Modeled Large-Eddy Simulation in a Finite-Difference Framework

We studied the effect of wall boundary conditions on the statistics in a wall-modeled large-eddy simulation (WMLES) of turbulent channel flows. Three different forms of the boundary condition based on the mean stress-balance equations were used to supply the correct mean wall shear stress for a wide range of Reynolds numbers and grid resolutions applicable to WMLES. In addition to the widely used Neumann boundary condition at the wall, we considered a case with a no-slip condition at the wall in which the wall stress was imposed by adjusting the value of the eddy viscosity at the wall. The results showed that the type of boundary condition utilized had an impact on the statistics (e.g., mean velocity profile and turbulence intensities) in the vicinity of the wall, especially at the first off-wall grid point. Augmenting the eddy viscosity at the wall resulted in improved predictions of statistics in the near-wall region, which should allow the use of information from the first off-wall grid point for wall models without additional spatial or temporal filtering. This boundary condition is easy to implement and provides a simple solution to the well-known log-layer mismatch in WMLES.

Effect of wall boundary conditions on the nonlinear response of turbulent premixed flames

Fully compressible Large Eddy Simulations (LES) are performed to investigate the effect of wall boundary conditions on the nonlinear response of turbulent premixed flames. For the unforced flames, the flame length and flame angle from the present LES results in the isothermal case are in better agreement with experimental results than those in the adiabatic case. For the forced flames, both amplitudes and phases of nonlinear flame response at moderate frequency are well reproduced in the isothermal case. While in the adiabatic case, the amplitudes are well reproduced, the prediction of phases is slightly underestimated. At high frequency, LES results from the isothermal case provide reasonable agreement with the experimental results in general, while the adiabatic case gives unreasonable prediction of nonlinear flame response. Results show that wall boundary conditions affect the spatial distributions of heat release fluctuations by changing the temperature field, which is affected by the evolutions of the flame structure and flow field in the nonlinear oscillation cycle. At moderate frequency, heat release fluctuations in different parts of the combustor are in phase, and wall boundary conditions have limited influence on the global flame response, while at high frequency, wall boundary conditions have significant influence on the global flame response since the heat release fluctuations in different parts of combustor are out of phase. Accurate prediction of flame response at high frequency needs accurate calculation of the wall temperature.

Numerical study of premixed flame dynamics in a closed tube: Effect of wall boundary condition

Numerical simulations were conducted to study the dynamics of premixed flames propagating in a closed tube by solving the fully compressible reactive Navier–Stokes equations using a high-order numerical method on a dynamically adapting grid. A simplified chemical-diffusive model was used to describe the reactions and energy release in a stoichiometric hydrogen-air mixture. The influence of wall boundary condition on the flame dynamics was explored by considering three different types of condition on the walls: adiabatic no-slip, adiabatic free-slip, and isothermal. The calculations show that the wall boundary condition has a significant effect on the generation and amplification of pressure waves and consequently on the flame dynamics. In the early stages of flame propagation, the flame behaves in a similar manner for different boundary conditions, that is, the flame develops a tulip shape that further evolves into a distorted tulip flame (DTF) through Rayleigh-Taylor instability arising from acoustic-flame interaction. Significant differences, however, arise after DTF formation in the late stages, especially when the primary acoustic wave is amplified to form a shock wave in the adiabatic free-slip and isothermal cases. The shock-flame interactions facilitate the formation of a series of increasingly corrugated flames by triggering the Richtmyer–Meshkov instabilities. The way how the lateral flame fronts touch the tube sidewalls to generate the primary acoustics and the heat conduction through the tube sidewalls play an important role in the generation and amplification of the pressure waves.

Numerical investigation of aspect ratio influences on Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli

Purpose This paper aims to conduct numerical simulations to investigate steady-state laminar Rayleigh–Bénard convection of yield stress fluids obeying Bingham model in rectangular cross-sectional cylindrical annular enclosures. In this investigation, axisymmetric simulations have been carried out for nominal Rayleigh number range Ra = 103 to 105, aspect ratio range AR = 0.25 to 4 (i.e. AR = H/L where H is the enclosure height and L is the difference between outer and inner radii) and normalised inner radius range ri/L = 0 to 16 (where ri is internal cylinder radius) for a nominal representative Prandtl number Pr = 500. Both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions have been considered for differentially heated horizontal walls to analyse the effects of wall boundary condition. Design/methodology/approach The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity. Findings It is found that the convective transport strengthens (weakens) with an increase in Ra (AR) for both Newtonian (i.e. Bn = 0) and Bingham fluids, regardless of the boundary conditions. Moreover, the strength of convection is stronger in the CWT configuration than that is for CWHF boundary condition due to higher temperature difference between horizontal walls for both Newtonian (i.e. Bn = 0) and Bingham fluids. The mean Nusselt number Nūcy does not show a monotonic increase with increasing Ra for AR = 1 and ri/L = 4 because of the change in flow pattern (i.e. number of convection rolls/cells) in the CWT boundary condition, whereas a monotonic increase of Nūcy with increasing Ra is obtained for the CWHF configuration. In addition, Nūcy increases with increasing ri/L and asymptotically approaches the corresponding value obtained for rectangular enclosures (ri/L → ∞) for both CWT and CWHF boundary conditions for large values of ri/L. It is also found that both the flow pattern and the mean Nusselt number Nūcy are dependent on the initial conditions for Bingham fluid cases, as hysteresis is evident for AR = 1 for both CWT and CWHF boundary conditions. Originality value Finally, the numerical findings have been used to propose a correlation for Nūcy in the range of 0.25 ≤ ri/L ≤ 16, 0.25 ≤ AR ≤ 2 and 5 × 104 ≤ Ra ≤ 105 for the CWHF configuration.

Totally videoscopic retroperitoneal necrosectomy in severe necrotizing pancreatitis

A computational fluid dynamics study of three-phase counter-current fluidization occurring in a turbulent contact absorber was performed. A two-dimensional, transient Eulerian multi-fluid model was used, in which the dispersed solid phase was modeled employing a kinetic theory of granular flow. The grid independence of the model, the effect of wall boundary conditions, the choice of granular temperature model, the effects of order of discretization scheme and drag models were studied for a base case setting. The results of simulations were validated against experimental results obtained from the literature. Once the model settings were finalized, simulations were performed for different gas and liquid velocities to predict the hydrodynamics of the absorber. Computed bed expansion and pressure drop were compared with experimental data. Good agreement between the two was found for low velocities of gas and liquid.

Start-up flow of a yield-stress fluid in a vertical pipe

We have investigated the start-up flow and yielding of a simple yield-stress fluid (Carbopol 940) in a vertical pipe. The Carbopol was displaced from below by a Newtonian liquid (Fluorinert FC-40) injected at the bottom of the pipe. Rough and smooth-walled pipes were used to study the effects of wall boundary conditions. The shear stress at the wall was known from the pressure in the Carbopol measured by a pressure gauge fixed on the pipe wall. The shear rate was known from measurements of velocity profile in the Carbopol made using particle-image velocimetry. In the rough-walled pipe, the yielding involved a long transit with several steps: elastic deformation, the onset of wall slip, yielding at the wall, and finally a steady-state plug flow that is well-described by the predictions of the Herschel–Bulkley model. In contrast, in the smooth-walled pipe, the wall shear stress never exceeded the yield stress. Our results demonstrate the importance of elasticity during the yielding process, particularly for faster displacements.

A comprehensive assessment of different wall boundary conditions on the simulation of bubbling fluidized beds

There are different particle-wall boundary conditions available in the literature to account for the particle slip velocity and the granular energy flux at the wall. However, it is not yet clear how these different wall boundary conditions affect the simulated flow behavior, nor is it clear which are the most realistic. To this end, three different particle-wall boundary conditions are examined to assess their ability to predict the dynamics of a dense gas-particle flow inside a three-dimensional bubbling bed, using the two-fluid model. To understand how the wall models affect structural features of the flow, a quantitative analysis is performed on some important aspects of the mechanics of bubbling beds that have received relatively little attention in the literature. Accordingly, the effect of each wall model on the velocity field, three-dimensional bubble statistics, gas-pressure fluctuations, and particle resolved-scale Reynolds stress are investigated. Also, the predicted dominant mixing regions inside the bed are identified and visualized in order to quantitatively describe the bed performance. It is found that the more energetic bubbles result in a lower level of granular temperature, a less-expanded bed, and more extensive mixing regions inside the bed. It is also observed that, in the case of bubbling beds, the mixing caused by the Reynolds normal stress is much stronger than that caused by the Reynolds shear stress. Overall, the flows predicted by the three wall models are structurally similar. However, some specific features can differ in a systematic way that can be tracked to the effect of wall boundary condition on the bubble behavior. The numerical results are validated against published experimental data and demonstrate the significant role of the particle-wall boundary condition.

Simulating the impacts of internals on gas–liquid hydrodynamics of bubble column

Impacts of vertical internals on gas–liquid hydrodynamic of bubble columns were simulated using an Eulerian two fluid model coupled with a population balance method (TFM-PBM). The interfacial drag force, the shear induced lift force, and the radial wall lubrication force exerted on bubbles were included in the model. The effects of wall boundary conditions were investigated numerically. The numerical results showed the radial wall lubrication force greatly impacts the radial distribution of time-averaged gas holdup, especially in the internals affecting region. When the internals were present, the turbulent dissipation rates increased significantly in the gaps between the internal walls, and more bubbles with smaller bubble size were predicted in the bubble column. Meanwhile, the gas holdup increased with dense internals insertion, especially in r/R equal to 0.6–0.9 region. The internals and the configurations influence the overall liquid circulation. When 31 thin internals are inserted in column at a low superficial gas velocity, large scale liquid circulations are replaced by small local vortex. However, the variations of liquid circulations are different at a high superficial gas velocity, when the large scale liquid circulations are always present in the column regardless of inserting 31 thin internals or 8 thick internals.

Counter-current three-phase fluidization in a turbulent contact absorber: A CFD simulation

A computational fluid dynamics study of three-phase counter-current fluidization occurring in a turbulent contact absorber was performed. A two-dimensional, transient Eulerian multi-fluid model was used, in which the dispersed solid phase was modeled employing a kinetic theory of granular flow. The grid independence of the model, the effect of wall boundary conditions, the choice of granular temperature model, the effects of order of discretization scheme and drag models were studied for a base case setting. The results of simulations were validated against experimental results obtained from the literature. Once the model settings were finalized, simulations were performed for different gas and liquid velocities to predict the hydrodynamics of the absorber. Computed bed expansion and pressure drop were compared with experimental data. Good agreement between the two was found for low velocities of gas and liquid.

Influence of Specularity Coefficient on the Hydrodynamics and Bubble Statistics of an Annular Fluidized Bed Reactor

Abstract This paper presents the results of a computational investigation on the effects of wall boundary conditions on the hydrodynamics of an annular fluidized bed (AFB). The objective is to develop better understanding of the hydrodynamics of an AFB, which are very complex as there are two wall surfaces with which the particles interact and fall along. The wall boundary conditions are investigated by varying the values of specularity coefficient. Simulations are performed using an open source code MFiX by employing the two-fluid model which considers solid and gas as the interpenetrating continua where the solid viscous stress tensor is calculated using the kinetic theory of granular flow. Geldart-B particles with a diameter of 530 μm and air as a fluidizing agent are used. A circumferential core-annulus structure is observed in the reactor. The hydrodynamics of AFB is very sensitive to the specularity coefficient. Low values of specularity coefficient produce high particle velocities in the bed as there is less loss of tangential momentum to the walls. However, the bed height predicted by all the values is found to be similar. Concerning the bubble statistics, it was found that low specularity coefficient values produce large bubbles usually in the form of slugs whereas as the specularity coefficient value is increased, small bubbles begin to form.

Numerical investigation of laminar Rayleigh-Bénard convection of Bingham fluids in square cross-sectioned cylindrical enclosures

Numerical simulations have been conducted under the assumption of axisymmetry to analyse steady-state laminar natural convection of yield stress fluids obeying Bingham model in square cross-sectioned cylindrical annular enclosures heated from below (i.e. Rayleigh-Bénard configuration). The simulations have been carried out for a representative value of nominal Prandtl number (i.e. Pr = 500) for different internal cylinder radius (0≤ri/L≤16 where ri and L are the inner radius and the cylinder height respectively) for a nominal Rayleigh number range 103≤Ra≤105. Both constant wall temperature and constant wall heat flux boundary conditions have been imposed for differentially heated horizontal walls to analyse the effects of wall boundary condition. Although the buoyancy-driven transport strengthens with increasing Ra, the mean Nusselt number Nu¯cy does not show a monotonic increase with increasing Ra for small values of ri/L because of the change in flow pattern (i.e. number of convection rolls/cells). By contrast, Nu¯cy monotonically increases with increasing Ra, and only one cell flow pattern is obtained for large values of ri/L. Furthermore, Nu¯cy has been found to increase with increasing ri/L but asymptotically approaches the corresponding value obtained for square enclosures (ri→∞) for both CWT and CWHF boundary conditions for large values of ri/L. It has also been found that both the flow pattern and the mean Nusselt number Nu¯cy are dependent on the initial conditions for Bingham fluid cases since hysteresis is evident for small values of ri/L for both CWT and CWHF boundary conditions. It has been found that convection could be sustained up to a higher value of Bingham number due to stronger convection arising from higher temperature difference between horizontal walls in the case of CWT boundary condition than in the corresponding CWHF configuration. Finally, the numerical findings have been used to propose a correlation for Nu¯cy in the range of 2≤ri/L≤16 (0.25≤ri/L≤16) and 103≤Ra≤105 for the CWT (CWHF) boundary condition.

A multi-zone building energy simulation of a data center model with hot and cold aisles

Abstract In this paper, a building energy simulation code, EnergyPlus, was used to study the effects of wall boundary conditions, climatic locations, supply air temperatures, and volumetric flow rates, on the energy consumption and thermal performance of a popular data center model. The data center model having 1120 servers distributed in four rows of rack was investigated under two major climatic conditions–hot and humid (Miami, FL), and cool and humid (Chicago, IL). A multi-zone modeling approach was proposed to resolve the hot and cold aisles in the data center, and was compared to existing well-mixed single-zone model. Using the multi-zone approach that is believed more reasonable, both monthly and annual overall energy consumptions as well as cooling load were analyzed under various boundary conditions. In addition, monthly thermal behavior in the zones for hot and cold aisles within the data center was analyzed. The simulation results show that thermal performance of the data center is significantly affected by locations or climatic conditions. The effects of location and wall boundary conditions are particularly appreciable during the summer and winter seasons. An optimal supply temperature of 11.8 °C, and air flow rate of 2.5 m 3 /s were found to be most preferred selections for the data center model.

Evaluation of the effect of wall boundary conditions on numerical simulations of circulating fluidized beds

A computational fluid dynamics (CFD) modeling of the gas–solids two-phase flow in a circulating fluidized bed (CFB) riser is carried out. The Eularian–Eularian method with the kinetic theory of granular flow is used to solve the gas–solids two-phase flow in the CFB riser. The wall boundary condition of the riser is defined based on the Johnson and Jackson wall boundary theory (Johnson & Jackson, 1987) with specularity coefficient and particle–wall restitution coefficient. The numerical results show that these two coefficients in the wall boundary condition play a major role in the predicted solids lateral velocity, which affects the solid particle distribution in the CFB riser. And the effect of each of the two coefficients on the solids distribution also depends on the other one. The generality of the CFD model is further validated under different operating conditions of the CFB riser.

Effect of wall boundary condition on CFD simulation of CFB risers

The effect of solid-phase wall boundary condition on the numerical simulation of gas–solid flow in CFB risers containing FCC particles was investigated using the two-fluid model incorporating the kinetic theory of granular flow. Both the Gidaspow drag model and the EMMS-based drag model were used. The Johnson and Jackson (1987) wall boundary condition was applied to describe the interaction between particles and wall. Based on the experimental system of Li and Kwauk (1994), parametric studies of specularity coefficient (φ=1.0, 0.6, 0.0005, 0.00005, 0) and particle–wall restitution coefficient (ew=0.6, 0.9, 0.95, 0.99, 0.999) were performed to evaluate their effects on axial voidage profile, solids flux, meso-scale and heterogeneous structures. Simulation results showed that solid-phase wall boundary condition had little effect on axial voidage profile when the Gidaspow drag model was used. However, the specularity coefficient φ had a pronounced influence on flow behavior when the EMMS-based drag model was used, and a small specularity coefficient (φ=0.00005, 0) could result in better agreement with experimental data. The particle–wall restitution coefficient ew plays but a minor role in the holistic flow characteristics.

CFD modeling the hydrodynamics of binary particle mixtures in bubbling fluidized beds: Effect of wall boundary condition

The hydrodynamics of binary particle mixtures differing in size and density in low gas velocity bubbling fluidized beds were simulated by a multi-fluid Eulerian model incorporating the kinetic theory of granular flow. Parametric studies of the particle–wall restitution coefficient and specularity coefficient were performed to investigate the influence of wall boundary condition on the predicted segregation and mixing behavior in terms of jetsam concentration and velocity distribution. The predicted axial and radial concentration distributions were compared with available experimental data. The results demonstrate that the particle–wall restitution coefficient only plays a minor role in predicting the segregation and mixing of binary particle mixtures in bubbling fluidized beds. For the segregation process, the predicted segregation is significantly affected by the specularity coefficient. No segregation can be predicted for small specularity coefficients, while for the mixing process, the predicted jetsam concentration distributions are almost unaffected by the specularity coefficient, although the jetsam velocity distributions are significantly influenced. The predicted segregation behavior of binary particle mixtures is significantly affected by the specularity coefficient. No segregation can be predicted for small specularity coefficients. ► We used multi-fluid model to simulate segregation and mixing of binary mixtures. ► We investigated the effect of wall boundary condition on hydrodynamics. ► Particle–wall restitution coefficient plays a minor role. ► Specularity coefficient affects segregation behavior and unaffects mixing behavior. ► Small specularity coefficient cannot predict segregation behavior.

난류 파이프 유동 내 물질전달에서의 경계조건 영향

Direct Numerical Simulation(DNS) of turbulent mass transfer in fully developed turbulent pipe flow has been performed to study the effect of wall boundary conditions on the concentration fields at

Multidimensional Unstructured-Grid Liquid Rocket-Engine Nozzle Performance and Heat Transfer Analysis

The objective of this study is to conduct a unified computational analysis for computing design parameters such as axial thrust, convective and radiative wall heat fluxes for regeneratively cooled liquid rocket engine nozzles, so as to develop a computational strategy for computing those parameters through parametric investigations. The computational methodology is based on a multidimensional, finite-volume, turbulent, chemically reacting, radiating, unstructured-grid, and pressure-based formulation, with grid refinement capabilities. Systematic parametric studies on effects of wall boundary conditions, combustion chemistry, radiation coupling, computational cell shape, and grid refinement were performed and assessed. Under the computational framework of this study, it is found that the computed axial thrust performance, flow features, and wall heat fluxes compared well with those of available data and calculations, using a strategy of structured-grid dominated mesh, finite-rate chemistry, and cooled wall boundary condition.

A semi-implicit method for the analysis of two-dimensional fluid flow with moving free surfaces

Flow with moving free surfaces is analyzed with an the Eulerian coordinate system. This study proposes a semi-implicit filling algorithm using VOF in which the PLIC (Piecewise Linear Interface Calculation)-type interface reconstruction method and the donor-acceptor-type front advancing scheme are adopted. Also, a new scheme using extrapolation of the stream function is proposed to find the velocity of the node that newly enters the computational domain. The effect of wall boundary conditions on the flow field and temperature field is examined by numerically solving a two-dimensional casting process.

Effect of wall boundary condition on scalar transfer in a fully developed turbulent flume

We performed direct numerical simulation of fully developed turbulent velocity and temperature fields in a flume, for Reynolds number, based on the wall shear velocity and the height of the flume, Re=171 and Prandtl numbers Pr=1.0 and Pr=5.4. To elucidate exactly the role of the wall boundary condition for passive scalar, the system considered was the flow at constant properties of the fluid. Two types of thermal wall boundary conditions (BCs) for the dimensionless temperature equation were studied: isothermal wall boundary condition—H1, and isoflux wall boundary condition—H2. The profile of the mean temperature was not affected by the type of BC. However, the type of BC has a profound effect on the statistics of the temperature fluctuations in the near-wall region y+<10. Comparison of near-wall statistics of temperature fluctuations shows that at Pr=1 the buffer part of the turbulent boundary layer significantly influences the scalar transfer in the conductive sublayer, whereas at Pr=5.4 the near-wall temperature field may be associated with predominant motion in the viscous sublayer.