A comparative study of the Mellor-Yamada and k-ε two-equation turbulence models in atmospheric application

The present study systematically compares the Mellor-Yamada (MY) model and the k−ε algebraic stress model in order to verify the possibility of using the k−ε algebraic stress model in atmospheric applications. The results of the parameterization process and atmospheric application of both models confirmed that the MY model neglected the pressure redistribution effect of buoyancy due to 〈u_iu_j〉 and 〈u_iθ〉 and that of shear due to 〈u_iθ〉. In addition, the MY model overestimated the turbulent energy dissipation. Based on the formulation of the k−ε algebraic stress model, we modified the constant value C_μ(=0.09) in the standard k−ε model to obtain the variables C_μM and C_μH to account for atmospheric stability. Finally, the results of the simulation obtained from the Wangara experiment verify the possibility of using the k−ε algebraic stress model in atmospheric application.     

A new method to calculate wind profile parameters of the wind tunnel boundary layer

This paper introduces a new method to process wind profile data of simulated atmospheric boundary layer flows in the wind tunnel so as to obtain the two important wind profile parameters—the surface roughness length z₀ and the friction velocity u_*. Instead of using the wind speed profile, the turbulent intensity profile of the turbulent surface layer, which is measured with a single probe hot-wire anemometer, is used to calculate the surface roughness length z₀. Then, the calculated surface roughness length z₀ is substituted into the mean wind speed profile of the constant flux layer to calculate friction velocity u_*. From our results this method is better than the simple regression method using the wind speed profile, which has been widely used.     

Thermal storage and nonlinear heat-transfer characteristics of PCM wallboard

For the materials with constant thermophysical properties, the thermal performance of wallboards (or floor, ceiling) can be described by decrement factor f and time lag φ. However, the phase change material (PCM) may charge large heat during the melting process and discharge large heat during the freezing process, which takes place at some certain temperature or a narrow temperature range. The behavior deviates a lot from the material with constant thermal physical properties. Therefore, it is not reasonable to analyze the thermal performance of PCM wallboard by using the decrement factor f and time lag φ. How to simply and effectively analyze the thermal performance of a PCM wallboard is an important problem. In order to analyze and evaluate the energy-efficient effects of the PCM wallboard and floor, two new parameters, i.e., modifying factor of the inner surface heat flux ‘α’ and ratio of the thermal storage ‘b’, are put forward. They can describe the thermal performance of PCM external and internal walls, respectively. The analysis and simulation methods are both applied to investigate the effects of different PCM thermophysical properties (heat of fusion H_m, melting temperature T_m and thermal conductivity k) on the thermal performance of PCM wallboard for the residential buildings. The results show that the PCM external wall can save more energy by increasing H_m, decreasing k and selecting proper T_m (α < 1); that the PCM internal wall can save more energy by increasing H_m and selecting appropriate T_m, k. The most energy-efficient approach of applying PCM in a solar house is to apply it in its internal wall.     

On the numerical study of contaminant particle concentration in indoor airflow

The application of three turbulence models—standard k–ε, re-normalization group (RNG) k–ε and RNG-based large eddy simulation (LES) model—to simulate indoor contaminant particle dispersion and concentration distribution in a model room has been investigated. The measured air phase velocity data obtained by Posner et al. [Energy and Buildings 2003;35:515–26], are used to validate the simulation results. All the three turbulence model predictions have shown to be in good agreement with the experimental data. The RNG-based LES model has shown to yield the best agreement. The flow of contaminant particles (with diameters of 1 and 10 μm) is simulated within the indoor airflow environment of the model room. Comparing the three turbulence models for particle flow predictions, the RNG-based LES model through better accommodating unsteady low-Reynolds-number (LRN) turbulent flow structure has shown to provide more realistic particle dispersion and concentration distribution than the other two conventional turbulence models. As the experimental approach to access indoor contaminant particle concentration can be rather expensive and unable to provide the required detailed information, the LES prediction can be effectively employed to validate the widely used k–ε models that are commonly applied in many building simulation investigations.     

Numerical investigation of the effect of road structures on ambient air quality—for their better design

Two-dimensional numerical simulation for investigating wind and concentration field around a double-decked road structure was performed using a standard k-ε turbulence model. The main objective of this paper is to study how road fences installed at a double-decked road affect ambient air quality, especially, pollutant concentration at some downstream locations. For model validation, calculated results were compared with available field experiment. Performance of the standard k-ε model was also compared with that of the renormalization group k-ε model for the double-decked road. Obtained results clarified how and how much pollutant concentration distribution is influenced by road structures with and without fences: the fences on the upper deck have generally positive effect on decreasing of air pollution near ground level while those on the ground always not. The computer code we used is CFX4.     

Simulation of mean flow and turbulence over a 2D building array using high-resolution CFD and a distributed drag force approach

A numerical simulation has been performed of the disturbed flow through and over a two-dimensional array of rectangular buildings immersed in a neutrally stratified deep rough-walled turbulent boundary-layer flow. The model used for the simulation was the steady-state Reynolds-averaged Navier-Stokes equations with linear and non-linear eddy viscosity formulations for the Reynolds stresses. The eddy viscosity was determined using a high-Reynolds number form of the k-ε turbulence-closure model with the boundary conditions at the wall obtained with a standard wall-function approach. The resulting system of partial differential equations was solved using the SIMPLE algorithm in conjunction with a non-orthogonal, colocated, cell-centered, finite volume procedure. The predictive capabilities of the high-resolution computational fluid dynamics (CFD) simulations of urban flow are validated against a very detailed and comprehensive wind tunnel data set. Vertical profiles of the mean streamwise velocity and the turbulence kinetic energy are presented and compared to those measured in the wind tunnel simulation.It is found that the performance of all the turbulence models investigated is generally good—most of the qualitative features in the disturbed turbulent flow field through and over the building array are correctly reproduced. The quantitative agreement is also fairly good (especially for the mean velocity field). Overall, the non-linear k-ε model gave the best performance among four different turbulence closure models examined. The turbulence energy levels within the street canyons and in the exit region downstream of the last building were underestimated by all four turbulence closure models. This appears to contradict the ‘stagnation point anomaly’ associated with the standard k-ε model which is a result of the excessive turbulence energy production due to normal straining. A possible explanation for this is the inability of the present models to account properly for the effects of secondary strains on the turbulence and/or for the effects of large-scale flapping of the strong shear layer at the canopy top.The results of the high-resolution CFD simulations have been used to diagnose values of the drag coefficient to be used in a distributed drag force representation of the obstacles in the array. Comparisons of the measured spatially-averaged time-mean mean velocity and turbulence kinetic energy in the array with predictions of the disturbed flow using the distributed drag force approach have been made.     

Effects of Horizontal and Vertical Seismic Loads on the Bearing Capacity of a Surface Footing Adjacent to a Slope

The correction factor (η_ie) for the ultimate bearing capacity of a footing placed adjacent to a slope, taking into account the combined effect of horizontal and vertical seismic loads, represented by horizontal and vertical seismic coefficients, k_h and k_v, respectively, was derived using a modified Janbu's slice method. The influence of slope angles ‘α’ on the values of ‘η_ie’ are studied here. It was found that the values of η_ie can be expressed as an exponential function of ‘k_h/(1-k_v)’ and ‘α’, with a measurable interdependency between ‘α’ and ‘η_ie’. The influence of ‘α’ on the value of ‘η_ie’ increases as the input value of ‘k_h/(1-k_v)’ increases. Equations derived based on the analytical results are proposed to account for this effect. Based on the analyses of 11 near-fault seismographers obtained in the 1999 Chi-Chi earthquake in Taiwan, a ratio between the vertical and the horizontal seismic coefficients, λ, of between ±0.25 is suggested for including the combined effect of vertical and horizontal seismic forces in evaluating the seismic bearing capacity of footings located in near-fault areas.     

An investigation into the sheltering performance of porous windbreaks under various wind directions

This study performs a series of simulations utilizing the Navier–Stokes equations and the RNG k–ε turbulence model to investigate the efficacy of porous windbreaks in preventing the wind erosion of stockpiles in an open storage yard. The simulations focus specifically on the effects of the fence porosity, the geometric configuration of the wind fence, and the direction of the incident wind. The basic validity of the simulation model is confirmed by performing scale-model wind-tunnel experiments. In general, the results show that the dust control efficiency of the windbreak is fundamentally dependent on the direction of the incident wind. It addition, it is shown that a rectangular wind fence provides a poor sheltering effect for wind incident with an angle of 45°, but is relatively more effective for winds incident in a normal direction. By contrast, an octagonal wind fence yields higher dust control efficiency for oblique incident angles, but is less effective for normally incident winds. Finally, it is shown that the shelter effect can be improved, via the deployment of additional wind fences within the storage yard or at either end of the yard.     

A computational model to calculate the flow-induced pressure fluctuations on buildings

A computational model to predict the flow-induced pressure fluctuation on bluff bodies is presented. Unlike direct and large-eddy simulation, the present model employs a stochastic model to generate plausible velocity fluctuations (synthetic turbulence) that satisfy the mean turbulent quantities such as turbulent kinetic energy (k) and dissipation energy rate (ε). This model has three main components: (1) prediction of mean flow quantities by solving the 3D Navier-Stokes equations using the standard k-ε model with Kato and Launder modifications; (2) generating a synthetic turbulent velocity field using a stochastic model and finally (3) solving the Poisson equation that governs the pressure fluctuations field. Flow around the low-rise building at Texas Tech was analyzed using the developed model. Two different wind angles of attack are considered for the analysis. Results obtained using the developed model are compared with wind tunnel and field measurements. The computed rms values for pressure fluctuations show good agreement with the experimental results.     

Numerical investigation of unsteady airflow in subway influenced by piston effect based on dynamic mesh

The piston effect has a significant influence on unsteady airflows in subway stations and tunnels. This study uses in situ experimental data and a computational fluid dynamics (CFD) method to analyze the three-dimensional unsteady air flow in a subway station and tunnel. An experimental analysis of train-induced unsteady flow was measured in an actual station with platform bailout doors (PBD), and air velocity variations were recorded at regular time intervals. The unsteady numerical analysis uses a dynamic mesh method for the full-scale model. The results indicate that Standard k–ε and RNG k–ε equations are both appropriate for simulating the high Reynolds numbers in tunnel and station airflow because these equations coincide with the experimental data. Specific diversion and suction ratios exist in each channel of the airflow for piston wind. The proportions between bypass ducts and platforms are stable no matter in open or close systems. And the draught relief shaft located before station plays more important role for piston wind than the one located after the station.     

Numerical prediction of gas concentrations and fluctuations above a triangular hill within a turbulent boundary layer

The objective of the present work is to propose a numerical and statistical approach, using computational fluid dynamics, for the study of the atmospheric pollutant dispersion. Modifications in the standard k-ε turbulence model and additional equations for the calculation of the variance of concentration are introduced to enhance the prediction of the flow field and scalar quantities. The flow field, the mean concentration and the variance of a flow over a two-dimensional triangular hill, with a finite-size point pollutant source, are calculated by a finite volume code and compared with published experimental results. A modified low Reynolds k-ε turbulence model was employed in this work, using the constant of the k-ε model C_μ=0.03 to take into account the inactive atmospheric turbulence. The numerical results for the velocity profiles and the position of the reattachment point are in good agreement with the experimental results. The results for the mean and the variance of the concentration are also in good agreement with experimental results from the literature.     

Sensitivity and importance measures in structural reliability

In multivariate reliability problems, which depend on one or more parameters τ, a sensitivity factor α_E[τ] is defined as the derivative of the equivalent reliability index β_E(τ)=?φ^?1[P _f (τ)] with P _f (τ) the failure probability. α_E[τ] expresses the change of α_E(τ) due to small variations of τ. Since the numerical evaluation of α_E[τ] is usually impractical, an approximation α_E[τ]≈α[τ] is derived, which is asymptotically exact for extreme reliability levels. Simple formulae for α[τ] are given. The approximation α_E[τ]:a[τ] also provides the basis for a better understanding of the commonly used alpha values α_i=?1/βu i? as importance measures for stochastic variables.     

Evaluation of hydro-mechano-chemical behaviour of bentonite-sand mixtures

Bentonite-sand mixtures are widely used in engineering barrier of deep geological disposal of high-level radioactive nuclear waste and anti-seepage barrier of civil geotechnical engineering. Under the action of groundwater solution infiltration and external stress, the hydro-mechanical (HM) behaviour of bentonite-sand mixtures, i.e. the swelling characteristics and permeability, will change. Once the anti-seepage and filtration effect is weakened or lost, the pollutants will spread to the biosphere. Therefore, it is necessary to study the swelling characteristics and permeability of bentonite-sand mixtures under coupled mechano-chemical (MC) effect and to establish corresponding prediction model. For this reason, swelling tests under salt solution with different concentrations are conducted on pure bentonite and its mixtures with 30%, 70% and 90% sand contents, the compression tests are carried out on saturated samples, and the saturated permeability coefficient k of the sample under each load is calculated by Terzaghi's one-dimensional consolidation theory. The concepts of true effective stress p_e, montmorillonite void ratio e_m and critical sand content α_s are introduced to determine the e_m-p_e relationship and finally the k-e_m relationship of bentonite-sand mixtures. It is found that when the sand content α ≤ α_s, the e_m-p_e relationship of the mixture is linear and independent of the salt solution concentration, and when α > α_s, the e_m-p_e relationship of bentonite-sand mixture is bi-linear with the true effective deviatoric stress p_esα as the intersection. In addition, the e_m-k relationship also shows the linear trend when α ≤ α_s, and the slope of the line increases with the increase of the salt solution concentration. When α > α_s, the k-e_m relationship will deviate from the linear relationship. Moreover, the larger the sand content is, the farther the deviation is. On the basis of summing the regularity, a model for predicting the HM behaviour of bentonite-sand mixture under the coupled MC effect is proposed. By comparing the swelling and permeability test results with model prediction results of different types of bentonite and its sand mixtures, the predictive model is verified. The study on the HM behaviour of bentonite-sand mixtures under salt solution infiltration and the model establishment can provide experimental and theoretical basis for the design and construction of anti-seepage engineering by bentonite-sand mixtures.     

Numerical model of the three-dimensional isothermal flow patterns and mass fluxes in a pitched-roof greenhouse

The three-dimensional isothermal flow patterns and mass fluxes in a full-scale, pitched-roof, single-span greenhouse were numerically resolved, and data from tests on a full scale were used to validate the code, the inlet boundary conditions and the greenhouse design grid method. For numerical solution of turbulent flow, a high-Reynolds-number k-ε model is suitable. Computational domain sizes were selected so as to fulfil the requirements of free-stream conditions whilst ensuring that grid geometrical characteristics satisfy the physical limitations of the standard k-ε model. A special feature of a case of a wind blowing parallel to a ridge (0°) is that the flow in the leeward half of the greenhouse comprises two vortexes with opposite senses of rotation, which bring in air mass through the vents and deliver it to the windward half. A spiral type of flow was found for winds blowing at 15-75° to the ridge direction: part of the air enters via the windward wall vent near the leeward gable-wall and emerges through the leeward roof vent near the windward gable-wall.Mass fluxes and flow patterns on wind direction, and on the opening angles of the windward and leeward vents. Thus, the ventilation rate induced by a wind directed perpendicularly to the greenhouse ridge is 4-4.9 times as great as that induced by a wind parallel to the ridge. A ventilation rate of a simulated greenhouse type was found to be significantly less responsive to a change in wind direction from 45° to 90° than to one from 0° to 45°. Present numerical results are in good agreement with those of other experiments and observations.     

Application of the mass balance equation in the estimation of beryllium and radium concentrations in the lower atmosphere

In this work the mass balance equation for estimation of changes in beryllium and radium concentrations was applied. The value of the coefficient of self-clearing of atmosphere, k₁, for beryllium and radium in the rainy and non-rainy period was calculated. In the industrial areas the values for beryllium and radium were very similar. In rainy days the value k₁ is 1.18h^?1. In the non-rainy period the self-clearing coefficient increases with wind speed. The change of k₁ together with the distance of emission source was also stated.The values of pollution background of beryllium and radium based on Reynolds model were also calculated.     

Applicability of linear type revised k-ε models to flow over topographic features

Accurate prediction of the wind energy distribution over terrains is essential for the appropriate selection of a suitable site for a wind power plant. This paper presents two-dimensional numerical simulations of flow over three common types of topographic features, i.e., a hill and two types of slopes (up-slope and down-slope). In a previous investigation by the present authors [Lun, Y.F., Mochida, A., Murakami, S., Yoshino, H., Shirasawa, T., 2003. Numerical simulation of flow over topographic features by revised k-ε models. J. Wind Eng. Ind. Aerodyn. 91(1-2), 231-245], the revised k-ε model proposed by P.A. Durbin [1996. Technical note: on the k-ε stagnation point anomaly. Int. J. Heat Fluid Flow 17, 89-90] was applied to flow prediction over a hill. Although, this model works well for flow around bluff bodies, a limitation was revealed in the area downstream of the hill. In this study, two new revised k-ε models proposed by Y. Nagano, H. Hattori and T. Irikado [2001. Prediction of flow over a complex terrain using turbulence model. In: Proceedings of the TED-Conference’01, JSME, in Japanese] and by Y. Nagano and H. Hattori [2003. A new low-Reynolds-number turbulence model with hybrid time-scales of mean flow and turbulence for complex wall flows. In: Proceedings of the Fourth International Symposium on Turbulence, Heat and Mass Transfer, Antalya, Turkey, October 12-17, 2003], i.e., the Ω and S-Ω models, were employed. These models are based on a mixed-time-scale concept. Their performance in predicting flow over various topographic features, namely a hill, up-slope and down-slope, was investigated. The problem of the Durbin model was corrected by the Ω model. However, a drawback of the Ω model was found in the upstream region. A new model, the S-Ω model, was introduced and was found to correct this problem. The S-Ω model showed best agreement with experiments for the hill case and the slope cases.     

Verification of a CFD model for indoor airflow and heat transfer

The SST k–ω based model is applied to calculate air-flow velocities and temperatures in a model office room. Calculations are compared with experiments and with the results of the standard k–ε, the RNG k–ε model and the laminar model. It is concluded that (a) all the three tested turbulent models predict satisfactorily the main qualitative features of the flow and the layered type of temperature fields and (b) computations with the SST k–ω based model show the best agreement with measurements. The use of this model is proposed combined with a suitable grid.     

Near-field pollutant dispersion in the built environment by CFD and wind tunnel simulations

Buildings are always found to be in the vicinity of other buildings, especially in urban areas. This causes effluents released from stacks located on one of the buildings to re-enter the same or an adjacent building, generating potential health problems to the occupants of the building. Earlier, Computational Fluid Dynamics (CFD) has been used in simulating pollutant transport for isolated buildings, with only few studies examining the effects of adjacent buildings. In this paper three cases that include an isolated low-rise building (source), a taller building placed upwind of the source and a case with taller buildings placed upwind and downwind of the source were considered. CFD simulations using the Realizable k-ε model for different turbulent Schmidt numbers (Sc_t) and wind tunnel experiments were performed for these cases. ASHRAE, 2007 was also used to assess plume dispersion for the isolated building. It was found that a strong dependence of Sc_t on CFD simulations of pollutant transport exists for the isolated building configuration. However, variations of Sc_t have less impact on assessing pollutant dispersion in the presence of adjacent buildings. The ASHRAE, 2007 model predicted very low dilutions for the isolated building, making it necessary to re-visit its formulations.