Sink Term Research Articles

Prediction of wind‐turbine fatigue loads in forest regions based on turbulent LES inflow fields

AbstractLarge‐eddy simulations (LES) were used to predict the neutral atmospheric boundary layer over a sparse and a dense forest, as well as over grass‐covered flat terrain. The forest is explicitly represented in the simulations through momentum sink terms. Turbulence data extracted from the LES served then as inflow turbulence for the simulation of the dynamic structural response of a generic wind turbine. In this way, the impact of forest density, wind speed and wind‐turbine hub height on the wind‐turbine fatigue loads was studied. Results show for example significantly increased equivalent fatigue loads above the two forests. Moreover, a comparison between LES turbulence and synthetically generated turbulence in terms of load predictions was made and revealed that synthetic turbulence was able to excite the same spectral peaks as LES turbulence but lead to consistently lower equivalent fatigue loads. Copyright © 2016 John Wiley & Sons, Ltd.

Improving the Altimeter-Derived Surface Currents Using High-Resolution Sea Surface Temperature Data: A Feasability Study Based on Model Outputs

AbstractAccurate knowledge of ocean surface currents at high spatial and temporal resolutions is crucial for a gamut of applications. The altimeter observing system, by providing repeated global measurements of the sea surface height, has been by far the most exploited system to estimate ocean surface currents over the past 20 years. However, it neither permits the observation of currents moving away from the geostrophic balance nor is it capable of resolving the shortest spatial and temporal scales of the currents. Therefore, to overcome these limitations, in this study the ways in which the high-spatial-resolution and high-temporal-resolution information from sea surface temperature (SST) images can improve the altimeter current estimates are investigated. The method involves inverting the SST evolution equation for the velocity by prescribing the source and sink terms and employing the altimeter currents as the large-scale background flow. The method feasibility is tested using modeled data from the Mercator Ocean system. This study shows that the methodology may improve the altimeter velocities at spatial scales not resolved by the altimeter system (i.e., below 150 km) but also at larger scales, where the geostrophic equilibrium might not be the unique or dominant process of the ocean circulation. In particular, the major improvements (more than 30% on the meridional component) are obtained in the equatorial band, where the geostrophic assumption is not valid. Finally, the main issues anticipated when this method is applied using real datasets are investigated and discussed.

Interfacial area transport due to shear collision of bubbly flow in small-diameter pipes

In view of the practical importance of the interfacial area transport equation in flow analysis based on the two-fluid model, especially for flow analysis in a reactor core which has a relatively small channel configuration, the dominant mechanism in the interfacial area transport in small diameter pipes was firstly identified by evaluating the experimental data obtained for pressurized bubbly flows under microgravity, where the source and sink terms of the interfacial area concentration due to bubble expansion and wake entrainment collision are negligible. The sink term of the interfacial area concentration of bubbly flow in small diameter pipe was modeled in terms of the shear collision mechanism. The one-dimensional interfacial area transport equation with the developed sink term was evaluated by using 74 datasets obtained for adiabatic gas-liquid bubbly flows, including upward flows and microgravity flows in pipes with inside diameters of 9.0, 5.0 and 3.0mm. A detailed discussion was provided on the interfacial area transport mechanism in small-diameter pipe. The overall standard deviation of the absolute error between predicted and measured interfacial area concentrations was 11.8%. The present model will reproduce the interfacial area transport of bubbly two-phase flows in small-diameter pipes with inside diameters of 3.0–9.0mm, at superficial liquid and gas velocities over the ranges 〈jf〉=0.073–0.949m/s, and 〈jg〉=0.00434–0.0500m/s, and also over a wide range of axial distances, z/D=5–188.

Prediction of interfacial area transport in a scaled 8×8 BWR rod bundle

In the two-fluid model, it is important to give an accurate prediction for the interfacial area concentration. In order to achieve this goal, the interfacial area transport equation has been developed. This study focuses on the benchmark of IATE performance in a rod bundle geometry. A set of interfacial area concentration source and sink term models are proposed for a rod bundle geometry based on the confined channel IATE model. This model was selected as a basis because of the relative similarity of the two geometries. Benchmarking of the new model with interfacial area concentration data in an 8×8 rod bundle test section which has been scaled from an actual BWR fuel bundle is performed. The model shows good agreement in bubbly and cap-bubbly flows, which are similar in many types of geometries, while it shows some discrepancy in churn-turbulent flow regime. This discrepancy may be due to the geometrical differences between the actual rod bundle test facility and the facility used to collect the data which benchmarked the original source and sink models.

Numerical Simulation of the Freeze-Thaw Behavior of Mortar Containing Deicing Salt Solution.

This paper presents a one-dimensional finite difference model that is developed to describe the freeze-thaw behavior of an air-entrained mortar containing deicing salt solution. A phenomenological model is used to predict the temperature and the heat flow for mortar specimens during cooling and heating. Phase transformations associated with the freezing/melting of water/ice or transition of the eutectic solution from liquid to solid are included in this phenomenological model. The lever rule is used to calculate the quantity of solution that undergoes the phase transformation, thereby simulating the energy released/absorbed during phase transformation. Undercooling and pore size effects are considered in the numerical model. To investigate the effect of pore size distribution, this distribution is considered using the Gibbs-Thomson equation in a saturated mortar specimen. For an air-entrained mortar, the impact of considering pore size (and curvature) on freezing was relatively insignificant; however the impact of pore size is much more significant during melting. The fluid inside pores smaller than 5 nm (i.e., gel pores) has a relatively small contribution in the macroscopic freeze-thaw behavior of mortar specimens within the temperature range used in this study (i.e., +24 °C to -35 °C), and can therefore be neglected for the macroscopic freeze-thaw simulations. A heat sink term is utilized to simulate the heat dissipation during phase transformations. Data from experiments performed using a low-temperature longitudinal guarded comparative calorimeter (LGCC) on mortar specimens fully saturated with various concentration NaCl solutions or partially saturated with water is compared to the numerical results and a promising agreement is generally obtained.

A model for mass diffusion in infarcted tissues by using LBM

In the present study, a new mathematical model for mass transfer in extra-vascular space is presented to indicate the effect of dead cells in infarcted tissues. This model is useful for predicting the results of experiments which are designed to distinguish normal from infarcted tissues and it can be used to approximate the percent of damaged cells in the infarcted tissue. The increase of permeability due to existence of dead cells caused by infarction is modeled as a sink term. The present model is validated for two different solutes by comparing their results with the existing experimental data. It is shown that the presented model is an appropriate model for simulating mass transfer in tissues. Furthermore, the sensitivity of the model to the effective diffusion coefficient, Schmidt number, porosity and Damkohler number is examined. The simulations show that permeability of dead cells significantly affects the volume of the contrast agent in the infarcted tissue. The results also indicate that the Schmidt number not only affects the mass diffusion through damaged tissues, but also influences the partition coefficient. The other parameters mentioned above have effects on the amount of mass diffusion into the infarcted tissue when the extent of damage in tissues is changed.

Locally conservative groundwater flow in the continuous Galerkin method using 3‐D prismatic patches

AbstractA new procedure has been developed to improve the velocity field computed by the continuous Galerkin finite element method (CG). It enables extending the postprocessing algorithm proposed by Cordes and Kinzelbach (1992) to three‐dimensional (3‐D) models by using prismatic patches for saturated groundwater flow. This approach leverages a dual mesh to preserve local mass conservation and provides interpolated velocities based on consistent fluxes. To develop this 3‐D approach, a triangular conservative patch is introduced by computing not only advection fluxes, but also vertical infiltrations, storage changes, and other sink or source terms. This triangular patch is then used to develop a prismatic patch, which consists of subprisms in two layers. By dividing a single two‐layer patch into two separate one‐layer patches, two dimensional (2‐D) algorithms can be applied to compute velocities. As a consequence, each subelement is able to preserve local mass conservation. A hypothetical 3‐D model is used to evaluate the precision of streamlines and flow rates generated by this approach and the FEFLOW simulation program.

A photochemical model of the dust‐loaded ionosphere of Mars

AbstractThe ionization of the lower Martian atmosphere and the presence of charged species are fundamental in the understanding of atmospheric electricity phenomena, such as electric discharges, large‐scale electric currents, and Schumann resonances. The present photochemical model of the lower ionosphere of Mars (0–70 km) is developed to compute the concentration of the most abundant charged species (cluster ions, electrons, and charged aerosols) and electric conductivity, at the landing site and epoch of the ExoMars 2016 mission. The main sources of ionization are galactic cosmic rays (during daytime as well as nighttime) and photoionization of aerosols due to solar UV radiation during daytime. Ion and electron attachment to aerosols is another major source of aerosol charging. The steady state concentration of charged species is computed by solving their respective balance equations (also known as continuity equations), which include the source and sink terms of their photochemical reactions. Since the amount of suspended dust can vary considerably and it has an important effect on atmospheric properties, several dust scenarios, in addition to the day‐night variations, are considered to characterize the variability of the concentration of charged species. It has been found that during daytime, aerosols tend to become positively charged due to electron photoemission and, during nighttime, tend to charge negatively due to electron attachment. The most dominant day‐night variability in ion and electron concentration occurs when the amount of suspended dust is the largest. The electric conductivity has been found to vary in the 10−13–10−7 S/m range, depending on the altitude, dust scenario, and local time.

Understanding nitrogen and carbon biogeotransformations and transport dynamics in saturated soil columns

Nitrogen, originating from fertilizers, wastewater irrigation, livestock, septic tank leakages and other waste disposal sites, poses a major threat to surface and groundwater resources. Both hydrological and biogeochemical processes should be considered for accurate prediction of transport and transformations of nitrogen compounds. In this study, an attempt was made for better prediction of the existing advection-dispersion-reactive transport model by a coupled sorption-biodegradation sink term including advanced biokinetics and inhibition effect for nitrogen movement in saturated soil. The model addresses all the major biogeochemical transformations occurring in the soil similar to the flooded soil environment. The proposed numerical model was validated using a laboratory scale cylindrical soil column with immobile mixed bacteria operated under saturated conditions. Soil column experiments were performed to understand the dispersion, sorption, leaching and biodegradation of nitrogen (100mg/L of NH4+, NO3−) and carbon (3000mg/L of acetate) compounds during wastewater infiltration. It was observed that the model simulations matched closely in the case of sorption experiments for NH4+, NO3− and acetate with average model efficiency (E) of 0.986. In the case of sorption with leaching experiments, the model prediction was average for both NH4+ and NO3− at both low and high flow rates. The model predictability was improved by introducing a calibrated parameter λ which accounted for microbial activity in continuous column experiments when compared to the values obtained from the batch system, which was calculated by back fitting. As a result, the numerical model simulated the breakthrough profiles of NH4+ (E=0.812), NO3− (E=0.701) and acetate (E=0.611) well. Further, this study implies that relatively shallow aquifers with sandy soil are vulnerable to NO3− contamination at around 10days if continuous wastewater irrigation is practiced. Hence, long-term studies under field conditions under different irrigation scenarios in addition to simulation modeling must be carried out to generalize flow and nitrogen compound transport under various soil types.

Unsaturated flow behavior in double-scale porous reinforcement for liquid composite molding processes

We investigate the unsaturated resin flow behavior in a dual scale porosity preform by observing the pressure distribution and the void content. The experimental data show that the pressure profile in the unsaturated flow is nonlinear with positive curvature whereas that in the saturated flow is linear as expected from the classical Darcy’s law. To address this issue, the governing equation for mass conservation is modified by introducing a mass sink term. Eventually, it has been found that the discrepancy between the unsaturated and saturated permeability values comes from a misinterpretation of the pressure gradient at the flow front in the unsaturated permeability measurement method and the permeability for a given preform is a unique value regardless of measurement method or flow condition. Based on this investigation, the ratio of unsaturated permeability to saturated permeability is represented as a dimensionless number in terms of void content.

Modelling the effect of large arrays of tidal turbines with depth-averaged Actuator Disks

The Actuator Disk concept is suitable to simulate the flow interactions between tidal turbines. As the computational expense of AD simulations is too large for applications at regional scale, the “bed friction” method is generally preferred. It consists in applying an enhanced drag over the tidal farm area. The main drawback is that the flow around each turbine is not resolved and that the flow interactions between the turbines’ wakes are neglected. The extent to which this simplification affects the accuracy of the large scale flow is not well understood. Here, we propose a methodology for representing large arrays of tidal turbines in Shallow Water Equations solvers. It consists in representing individual turbines as small areas where a sink momentum term is applied. The sink term is calculated from the vertical integration of the force exerted on an AD. After validating the model, we apply the methodology to simulate the effect of 45 turbines placed in the Alderney Race. The results are compared to the results obtained with the “bed friction” method. The two approaches give similar results because the hydrodynamics conditions of the Alderney Race favor the mixing of the wakes which prevents the flow interactions between the turbines.

A numerical model for water and heat transport in freezing soils with nonequilibrium ice‐water interfaces

AbstractA one‐dimensional numerical model of heat and water transport in freezing soils is developed by assuming that ice‐water interfaces are not necessarily in equilibrium. The Clapeyron equation, which is derived from a static ice‐water interface using the thermal equilibrium theory, cannot be readily applied to a dynamic system, such as freezing soils. Therefore, we handled the redistribution of liquid water with the Richard's equation. In this application, the sink term is replaced by the freezing rate of pore water, which is proportional to the extent of supercooling and available water content for freezing by a coefficient, β. Three short‐term laboratory column simulations show reasonable agreement with observations, with standard error of simulation on water content ranging between 0.007 and 0.011 cm3 cm−3, showing improved accuracy over other models that assume equilibrium ice‐water interfaces. Simulation results suggest that when the freezing front is fixed at a specific depth, deviation of the ice‐water interface from equilibrium, at this location, will increase with time. However, this deviation tends to weaken when the freezing front slowly penetrates to a greater depth, accompanied with thinner soils of significant deviation. The coefficient, β, plays an important role in the simulation of heat and water transport. A smaller β results in a larger deviation in the ice‐water interface from equilibrium, and backward estimation of the freezing front. It also leads to an underestimation of water content in soils that were previously frozen by a rapid freezing rate, and an overestimation of water content in the rest of the soils.

Agent-based Model of Oxidation Reactions of Ferrous Ions

Molecules in comets are formed through chemical oxidation reactions induced by radiation. Thesereactions can be simulated in laboratory experiments applying gamma radiation to samples at low temperatures. The kinetics of the induced reactions can be modeled by a system of coupled non-linear ordinary differential equations describing the mass balance of all of the species involved. However, finding a traditional solution to this system is difficult because of the large number of reactions involved, the need to solve all of the equations simultaneously, and the strong dependence on the initial conditions due to the non-linear character of the equations. For each species, the mass-balance equation includes all of the reaction rates leading to production (source terms) and to destruction (sink terms). In this sense, each equation is analogous to the prey-predator model, with the sink terms consider to be the “prey” and the source terms as the “predators”. Due to this, we can use an agent-based model to follow the kinetics of the chemical reactions. In this paper, we present a code in Python for an agent-based model of the chemical oxidation of ferrous ions (Fe2+) induced by gamma radiation and in the presence of molecular oxygen. We compare the results that this code produces for molar concentrations of Fe3+over time with those obtained in the laboratory.

QMOM-based population balance model involving a fractal dimension for the flocculation of latex particles

An experimental and computational study of agglomeration and breakage processes for fully destabilized latex particles under turbulent flow conditions in a jar is presented. The particle size distribution (PSD) and the fractal dimension of flocs of latex particles were monitored using an on-line laser diffraction technique. A population balance equation (PBE) was adapted to our problem by including the fractal dimension in its formulation as well as in the aggregation and breakage kernels. The quadrature method of moments was used for the resolution. The adjustment of 4 model parameters was then conducted on the first 6 moments of the PSD for various mean shear rates. The model correctly predicts the evolution of the first 6 moments calculated from the experimental PSD. The experimental results were adequately simulated by a single set of adjusted parameters, proving the relevance of the dependency on the fractal dimension and mean shear rate. A sensitivity analysis was performed on two main adjusted parameters highlighting the major roles of (1) the power to which the mean shear rate is raised in the breakage kernel and (2) the sizes of the colliding aggregates in the collision efficiency model. Finally, analytical relations between the sink and source terms of the breakage or aggregation of the PBE were derived and discussed, highlighting interesting features of the PBE model.

Inactivation of airborne bacteria by cold plasma in air duct flow

This paper developed a numerical model for predicting bacteria inactivation by cold plasma tube. The bulk air velocity, ion mobility, electric field and ion diffusion were considered in the model to obtain the distribution of negative ions. The sink term appeared in the model was determined by a semi-empirical approach through experiment. A 9-m long, 200 mm square duct was used for carrying out experiments. Negative ion concentration along the duct and inactivation rate of E. coli was measured. Based on the inactivation rate, the sink term was estimated and fed to the model. Three different device installation scenarios were investigated: single plasma unit, two plasma tubes arranged in horizontal and finally two plasma arranged in vertical orientations. The simulation results were agreed well with site measurement of ion intensities as well as pathogen inactivation experiments, an application of cold plasma in a single hospital ward was discussed. The developed model can be applied to advanced disinfection technologies in HVAC systems, besides, the method for modeling the bacteria can be expanded to other microorganisms. Limitations of the model are also discussed.

Wind flow simulation over forested areas using a 3D RANS solver with a tree – scale approach

Wind flow over forested areas is simulated using a 3-D Reynolds Averaged Navier–Stokes solver, employing the Wilcox k–ω model modified for atmospheric flows. Each tree is simulated individually with a two-region approach considering the leaf area and the trunk area. Each area affects the surrounding flow acting as a momentum sink term in the RANS equations. Leaf area sink terms are computed via Leaf Area Density which is described by an empirical relation. Predictions are compared against measurements and simulation results of other methods. A good agreement with measurements is observed as a result of a more detailed simulation of the canopy in comparison to simpler methods. A parametric analysis investigates the effect of the forest density as well as of the type and shape of the trees on the surrounding flow. A reduction of wind speed deficit up to 25% is predicted when the tree shape changes from cylinder to cone.

Pathways to the Production of Precipitating Hydrometeors and Tropical Cyclone Development

Abstract Pathways to the production of precipitation in two cloud microphysics schemes available in the Weather Research and Forecasting (WRF) Model are investigated in a scenario of tropical cyclone intensification. Comparisons of the results from the WRF Model simulations indicate that the variation in the simulated initial rapid intensification of an idealized tropical cyclone is due to the differences between the two cloud microphysics schemes in their representations of pathways to the formation and growth of precipitating hydrometeors. Diagnoses of the source and sink terms of the hydrometeor budget equations indicate that the major differences in the production of hydrometeors between the schemes are in the spectral definition of individual hydrometeor categories and spectrum-dependent microphysical processes, such as accretion growth and sedimentation. These differences lead to different horizontally averaged vertical profiles of net latent heating rate associated with significantly different horizontally averaged vertical distributions and production rates of hydrometeors in the simulated clouds. Results from this study also highlight the possibility that the advantage of double-moment formulations can be overshadowed by the uncertainties in the spectral definition of individual hydrometeor categories and spectrum-dependent microphysical processes.

Numerical study of wave–current–vegetation interaction in coastal waters

Research on interactions among wave, current, and vegetation has received increasing attention. An explicit depth-averaged hydrodynamic model coupled with a wave spectral model (CMS-wave) was proposed in this study in order to simulate the wave and wave-induced current in coastal waters. The hydrodynamic model was based on the finite volume method while the intercell flux was computed by employing the Harten–Lax–van Leer approximate Riemann solver to investigate the dry-to-wet interface, and the drag force of vegetation was modeled as the sink terms in the momentum equations. The CMS-wave model was used to investigate the non-breaking and the breaking random waves propagation in vegetation fields. Afterwards, an empirical wave energy dissipation term with plant effect was derived to represent the resistance induced by aquatic vegetation in the wave-action balance equation. The established model was calibrated and validated with both the experimental and field data. The results showed that the wave height decreased significantly along the wave propagation direction in the presence of vegetations. The sensitivity analysis for the plant density, the wave height, and the water depth were performed by comparing the numerical results for the wave height attenuation. In addition, wave and wave-induced current through a finite patch of vegetation in the surf zone were investigated as well. The strong radiation stress gradient could be produced due to the variation of the energy dissipation by vegetation effect in the nearshore zone, which impacted the direction and amplitude of the longshore current. The calculated results showed that the coupling model had good performance in predicting wave propagation and the current over vegetated water regions.

On the Dynamics of the Formation of the Kelvin Cat’s-Eye in Tropical Cyclogenesis. Part II: Numerical Simulation

Abstract A shallow-water model is used to study the role of critical layers in tropical cyclogenesis. Forced and unforced problems of disturbances on a parabolic jet associated with weak basic-state meridional potential vorticity (PV) gradients, leading to Kelvin cat’s-eye formation around the jet axis, are first investigated. Numerical simulations with various initial disturbance magnitudes and structures suggest that the results of previous studies can be extended to the next level of complexity toward the more realistic atmosphere. The model is therefore initialized using an observed jet profile obtained from the reanalysis data presented in Part I of this study. For this asymmetric marginally stable basic-state profile, unforced (free) and forced linear integrations show spatial contraction of the perturbation structures in the meridional direction, similar to what occurred in experiments on the parabolic jet. Nonlinear free simulations highlight the role of nonlinear processes in redistributing PV within the critical-layer region. However, they do not yield a realistic time scale for the formation of the cat’s-eye. By including diabatic heating as a mass sink term to represent convective PV generation, the nonlinear forced simulation is found to produce a realistic time scale for cat’s-eye formation, and confirms the analytical solution of τeτQ ~ O(ε−1) obtained in Part I. These results highlight the synergic role of the dynamical mechanisms, including wave breaking and PV redistribution within the nonlinear critical layer characterized by weak PV gradients and the thermodynamical mechanisms such as convectively generated PV anomalies in the cat’s-eye formation in tropical cyclogenesis.

Algorithms for the Haar wavelet based fast evaluation of aggregation integrals in population balance equations

In several production processes, the distribution of particles dispersed in an environmental phase may be mathematically described by the solution of population balance equations. We are concerned with the development of efficient numerical techniques for the aggregation process: It invokes an integral term that is usually numerically expensive to evaluate and often dominates the total simulation cost.We describe an approach on locally refined nested grids to evaluate both the source and the sink terms in almost linear complexity (instead of quadratic complexity resulting from a direct approach). The key is to switch from a nodal to a wavelet basis representation of the density function. We illustrate the numerical performance of this approach, both in comparison to a discretization of piecewise constant functions on a uniform grid as well as to the fixed pivot method on a geometric grid.