Turbulent Kinetic Energy Equation Research Articles

A Generalized Mixing Length Closure for Eddy‐Diffusivity Mass‐Flux Schemes of Turbulence and Convection

AbstractBecause of their limited spatial resolution, numerical weather prediction and climate models have to rely on parameterizations to represent atmospheric turbulence and convection. Historically, largely independent approaches have been used to represent boundary layer turbulence and convection, neglecting important interactions at the subgrid scale. Here we build on an eddy‐diffusivity mass‐flux (EDMF) scheme that represents all subgrid‐scale mixing in a unified manner, partitioning subgrid‐scale fluctuations into contributions from local diffusive mixing and coherent advective structures and allowing them to interact within a single framework. The EDMF scheme requires closures for the interaction between the turbulent environment and the plumes and for local mixing. A second‐order equation for turbulence kinetic energy (TKE) provides one ingredient for the diffusive local mixing closure, leaving a mixing length to be parameterized. Here, we propose a new mixing length formulation, based on constraints derived from the TKE balance. It expresses local mixing in terms of the same physical processes in all regimes of boundary layer flow. The formulation is tested at a range of resolutions and across a wide range of boundary layer regimes, including a stably stratified boundary layer, a stratocumulus‐topped marine boundary layer, and dry convection. Comparison with large eddy simulations (LES) shows that the EDMF scheme with this diffusive mixing parameterization accurately captures the structure of the boundary layer and clouds in all cases considered.

A local correlation-based zero-equation transition model

In this work, the local correlation-based one-equation transition model (Menter, F.R., Smirnov, P.E., Liu, T. and Avancha, R., A one-equation local correlation-based transition model. Flow, Turbulence and Combustion, vol. 95, no. 4, pp. 583–619, 2015.) is transformed into a zero-equation transition model. The new model provides an attractive choice in terms of quick implementation of a transition model in existing turbulent flow solvers with Menter’s shear-stress transport (SST) turbulence model, as it only introduces three extra source terms in the transport equation of turbulent kinetic energy. The model is validated against a set of benchmark flat-plate test cases: T3 series and SK, and also subsonic flows past two different airfoils: Aerospatiale A-airfoil (Re=2.1 million) and E387 (Re=0.2 million), and finally applied to a transonic flow over 3D DLR-F5 wing (Re=1.5 million). Results show that the proposed model produces similar transition prediction as the one-equation transition model, with a reduced computational effort. The computations are performed with an in-house finite-volume solver for compressible turbulent flows on block-structured grids.

New insight on large-eddy simulation of flow past a circular cylinder at subcritical Reynolds number 3900

Flow past a circular cylinder at the subcritical Reynolds number of 3900 is numerically investigated based on large-eddy simulations (LESs) via the open-source toolbox OpenFOAM. Good grid convergence property is achieved for the present LESs with different subgrid-scale models as far as the near-wake statistics are concerned. On the intermediate-resolution grid, current LES data in terms of mean flow and turbulence quantities are in good agreement with the benchmark experimental results. A comparison study on the Smagorinsky model manifests that increasing the model coefficient results in a longer recirculation length and smaller drag and lift coefficients. The budget analysis of the turbulent kinetic energy (TKE) equation suggests that the main source in the wake area is the TKE production, which is transported downstream mainly through the advection by mean flow and further moved upward and downward through the transport terms. The flow patterns indicate that the weak production rates induced by the shear layers delay the downward movement of the mean flow, resulting in a longer recirculation region. This dynamic picture provides a reliable explanation for the differences in the recirculation length and mean flow profiles observed in the near-wake area from different experimental and numerical studies.

Assessment of IEC Normal Turbulence Model and Modelling of the Wind Turbulence Intensity for Small Wind Turbine Design in Tropical Area: Case of the Coastal Region of Benin

The wind turbulence intensity observed on a site have an influence the wind turbine energy production and the lifetime of the blades. It is therefore primordial to master this parameter for the optimization of the production. So therefore, this study is interested on the modelling of the wind turbulence intensity at 10 m above the ground on the coast of Benin. Four years of wind data measured on the site of Cotonou Port Authority (PAC) from 2011 to 2014 and recorded with a temporal resolution of 10 min were used. From the transport equation of turbulent kinetic energy followed by a numerical simulation based on the Nelder-Mead algorithm developed under the Matlab software, we proposed five new models for estimating the wind turbulence intensity. The results of the different simulations reveal that four of proposed models and based on the roughness, the speed of friction and the length of Obukhov better fit the data, during the periods of January, April, June, July, August, September and December. The estimators of the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) vary from (0.02; 0.01) in December to (0.09; 0.07) in August. As for the model which is a function of roughness and the wind shear coefficient (expressed only according to the wind speed), it gives better performance whatever the time of the year and the atmosphere stability conditions. The estimations errors are included between (0.02; 0.01) obtained in December and (0.08; 0.06) observed in March. A comparative study between the existing models in the literature and the best model proposed in this study showed that only this model gives the best adjustment with the data. It can therefore be used on the sites where turbulence is influenced by the roughness and the atmosphere stability. Finally, from this model a new wind turbine design class has been proposed for the site of Cotonou. It takes into account the actual levels of turbulence observed and thus allow to optimize the energy production.

Turbulent kinetic energy transfer and dissipation in thermoviscous fluid flow

Turbulent flow of thermoviscous liquid is studied in a three-dimensional region with periodicity in two directions. Flow characteristics are described in the terms of equation for turbulent kinetic energy: this allows to differentiate contributions from different components related to generation, transport, and dissipation of turbulent kinetic energy. Those terms can be calculated from averaging the moments of different order. The previous studies demonstrated that thermoviscous liquid flow occurs through several stages of evolution, including the unsteady turbulence. This allows discussing the problem of mathematical rigorous statement and applicability of different methods for averaging. Existence of spatial periodicity allow using a combined spatial-time averaging for different values on the interval of steady turbulence. Results are presented as a set of Z—t-diagrams. Besides, the paper presents analysis of flow development on the basis of direct visualization of velocity and temperature.

Analysis of turbulence characteristics in a temporal dense gas compressible mixing layer using direct numerical simulation

This study investigates the effects of a Bethe–Zel’dovich–Thompson (BZT) dense gas (FC-70) on the development of a turbulent compressible mixing layer at a convective Mach number . Three-dimensional direct numerical simulations are performed with both FC-70 and air. The initial thermodynamic state for FC-70 lies inside the inversion region where the fundamental derivative of gas dynamics ( ) becomes negative. The complex Martin–Hou thermodynamic equation of state is used to reproduce thermodynamic peculiarities of the BZT dense gas (DG). The unstable growth phase in the mixing layer development shows an increase of -turbulent stress tensors in DG compared to perfect gas (PG). The following self-similar period has been carefully defined from the time evolution of the integrated streamwise production and transport terms. During the self-similar stage, DG and PG mixing layers at display close values of the momentum thickness growth rate, which seems similarly affected by the well-known compressibility-related reduction for PG. The same mechanisms are at stake, related to the reduction of pressure–strain terms. Turbulent kinetic energy (TKE) spectra show a slower decrease of TKE at small scales for DG compared with PG. The filtered kinetic energy equation balance developed by Aluie (Physica D, vol. 247 (1), 2013, pp. 54–65) is applied for the first time to a compressible mixing layer. The equation is reshaped to better account for TKE transport across the mixing layer. This new formulation brings out the role played by , the pressure strengths power. A detailed comparison of the contributions to the filtered TKE equation is provided for both PG and DG mixing layers.

An urban trees parameterization for modeling microclimatic variables and thermal comfort conditions at street level with the Town Energy Balance model (TEB-SURFEX v8.0)

Abstract. The Town Energy Balance (TEB) urban climate model has recently been improved to more realistically address the radiative effects of trees within the urban canopy. These processes necessarily have an impact on the energy balance that needs to be taken into account. This is why a new method for calculating the turbulent fluxes for sensible and latent heat has been implemented. This method remains consistent with the “bigleaf” approach of the Interaction Soil–Biosphere–Atmosphere (ISBA) model, which deals with energy exchanges between vegetation and atmosphere within TEB. Nonetheless, the turbulent fluxes can now be dissociated between ground-based natural covers and the tree stratum above (knowing the vertical leaf density profile), which can modify the vertical profile in air temperature and humidity in the urban canopy. In addition, the aeraulic effect of trees is added, parameterized as a drag term and an energy dissipation term in the evolution equations of momentum and turbulent kinetic energy, respectively. This set of modifications relating to the explicit representation of the tree stratum in TEB is evaluated on an experimental case study. The model results are compared to micrometeorological and surface temperature measurements collected in a semi-open courtyard with trees and bordered by buildings. The new parameterizations improve the modeling of surface temperatures of walls and pavements, thanks to taking into account radiation absorption by trees, and of air temperature. The effect of wind speed being strongly slowed down by trees is also much more realistic. The universal thermal climate index diagnosed in TEB from inside-canyon environmental variables is highly dependent and sensitive to these variations in wind speed and radiation. This demonstrates the importance of properly modeling interactions between buildings and trees in urban environments, especially for climate-sensitive design issues.

A new mean‐field plasma edge transport model based on turbulent kinetic energy and enstrophy

AbstractThe predictive capabilities of mean‐field plasma edge transport codes are significantly reduced by the empirically determined radial diffusion coefficients commonly used to account for the turbulent transport. This paper aims to assess a two‐equation model including both turbulent kinetic energy and turbulent enstrophy for an improved description of the mean‐field turbulent transport. A turbulent enstrophy equation is analytically derived for isothermal, electrostatic, two‐dimensional, interchange‐dominated ExB turbulence in the scrape‐off layer. Evaluation of this equation shows that interchange is the dominant source, while the sheath loss and viscous terms provide the main sinks of turbulent enstrophy. Transport effects turn out to be of minor importance. A model for the combined turbulent kinetic energy and enstrophy equations and the particle transport is constructed starting from a one‐equation model for the turbulent kinetic energy. The resulting two‐equation model is shown to retain the dominant dynamics of the latter while improving its scalings.

Performance of the k-kL model for aerodynamics applications

PurposeThe purpose of this paper is to study the predictability of the recently proposed length scale-based two-equation k-kL model for external aerodynamic flows such as those also encountered in the high-lift devices.Design/methodology/approachThe two-equation k-kL model solves the transport equations of turbulent kinetic energy (TKE) and the product of TKE and the integral length scale to obtain the effect of turbulence on the mean flow field. In theory, the use of governing equation for length scale (kL) along with the TKE promises applicability in a wide range of applications in both free-shear and wall-bounded flows with eddy-resolving capability.FindingsThe model is implemented in the in-house unstructured grid computational fluid dynamics solver to investigate its performance for airfoils in difficult-to-predict situations, including stalling and separation. The numerical findings show the good capability of the model in handling the complex flow physics in the external aerodynamic computations.Originality/valueThe model performance is studied for stationary turbulent external aerodynamic flows, using five different airfoils, including two multi-element airfoils in high-lift configurations which, in the knowledge of the authors, have not been simulated with k-kL model until now.

Flow modulation by a few fixed spherical particles in a turbulent channel flow

Current understanding of turbulence modulation by solid particles is incomplete as making reliable predictions on the nature and level of modulation remains a challenging task. Multiple modulation mechanisms may be simultaneously induced by particles, but the lack of reliable methods to identify these mechanisms and quantify their effects hinders a complete understanding of turbulence modulation. In this work, we present a full analysis of the turbulent kinetic energy (TKE) equation for a turbulent channel flow laden with a few fixed particles near the channel walls, in order to investigate how the wall generated turbulence interacts with the particles and how, as a result, the global turbulence statistics are modified. All terms in the budget equations of total and component-wise TKEs are explicitly computed using the data from direct numerical simulations. Particles are found to modify turbulence by two competing mechanisms: the reduction of the intrinsic turbulence production associated with a reduced mean shear due to the resistance imposed by solid particles (the first mechanism), and an additional TKE production mechanism by displacing incoming fluid (the second mechanism). The distribution of TKE in the wall-normal direction is also made more homogeneous due to the significantly enhanced pressure transport of TKE. Finally, the budget analysis of component-wise TKE reveals an enhanced inter-component TKE transfer due to the presence of particles, which leads to a more isotropic distribution of TKE among three velocity components.

Assessment of performance of subgrid stress models for a LES technique for predicting suppression of turbulence and heat transfer in channel flows under the influence of body forces

The main purpose of this work was to assess the performance of subgrid stress models for large eddy simulation (LES) of the flow and heat transfer of a conductive liquid simulating a molten salt (Pr = 4.1) in a square duct under the influence of a transverse magnetic field and an upward flow of air in a vertical heated pipe under a strong influence of buoyancy. An analysis of these problems is important when choosing the most appropriate subgrid-scale LES model for calculating the flows of an electrically conductive liquid under the combined influence of a magnetic field and buoyancy forces. Four subgrid-scale (SGS) models were verified: the Smagorinsky model with damping function (SMP), a coherent structure model (CSM), a WALE model and a hybrid model based on the equation for turbulent kinetic energy (KDES). For magnetohydrodynamic (MHD) flow in the duct, computations were performed in a domain with periodic inlet-exit boundaries and in a domain corresponding to the entrance region of a duct with a transverse magnetic field. Mixed convection of the air in the vertical heated pipe was simulated only in the domain with periodic boundaries. The results are compared with available data of direct numerical simulations (DNS).For MHD flow in the duct, the best predictions of DNS data for the average and fluctuating velocity components at Ha=21.2 and Re=5602 were obtained with the CSM and WALE models. The skin-friction and heat transfer coefficients are well known to have a minimum as Ha increases due to turbulence suppression by the magnetic field. The SMP and KDES models predict a minimum at Hadip≈22, whereas the CSM and WALE models predict a minimum at Hadip≈30 for Re=5602. The DNS data marked these values as the lower and upper boundaries of the complete turbulence suppression region for the same Reynolds number.For mixed convection of the air upward flows in a circular heated pipe at Re=5300, the CSM and WALE models showed weaker suppression of turbulence due to buoyancy forces when compared to the DNS results. The results of calculations of skin-friction and heat transfer coefficients performed with the help of the SMP and KDES models are much more coincident with the DNS data.

Numerical prediction of interaction between turbulence structures and vortex cavitation

ABSTRACTA novel numerical method to perform direct numerical simulations (DNS) of turbulent flow was established to predict the characteristics of compressible gas–liquid two-phase flow. A cavitation model was introduced to reproduce the phase change in the cavitation phenomena, and a DNS of wall turbulence of water with cavitation was performed. Vortex cavitation was observed in the wall turbulence. The growing cavity in the core of the vortex changed the vortex intensity. After vortex cavitation finished, the friction coefficient for the cavitating flow became lower than that of non-cavitating flow. The variation tendency of turbulent statistics corresponded to that of experimental measurements. For a small friction coefficient of the cavitating flow, the redistribution term in the streamwise component of the turbulent kinetic energy equation was reduced owing to the vortex cavitation. Consequently, it was proved that the occurrence of vortex cavitation modified the redistribution term, resulting in turbulence modification.

Simple analytical solutions of one-equation modelling for steady/decaying homogeneous turbulence sensitized to small strain

This study presents a simple mathematical solution describing the turbulent kinetic energy in steady or decaying homogeneous turbulence sensitized to small strain. Small strain is found to have little effect on the anisotropy of decaying homogeneous turbulence, which is consistent with a previous experiment. The effect of small strain on dissipation in the governing equations of turbulent kinetic energy is examined using the standard k-ε model. Two temporal profiles, namely a constant profile and a linear profile, with small strain are used. The steady homogeneous turbulence is maintained by linear forcing, as previously reported. This study mainly focuses on the effects of small strain on the turbulence time scale. When the magnitude of the small strain is small, the effects on the turbulence time scale can be negligibly small, especially for a constant profile. Based on this result, the governing equations for steady or decaying homogeneous turbulence sensitized to small strain can be reduced to simple linear equations. The analytical solution of these equations, a simple exponential function, is the same for the two types of homogeneous turbulence.

Sensitivity of the Ocean Circulation Model to the k-ω Vertical Turbulence Parametrization

An ocean general circulation model (OGCM) of the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences with embedded k–ω vertical turbulent exchange model is developed based on the equations for turbulence kinetic energy k and energy dissipation frequency ω. The solution of the k–ω model equations depends on the frequencies of buoyancy and velocity shift simulated by the OGCM, and the coefficients of vertical turbulence depend on k and ω. The numerical algorithms of both models are based on the method of splitting by the physical processes. The k-ω model equations are split into two stages describing the three-dimensional transport-diffusion of the turbulence kinetic energy k and frequency ω and their local generation-dissipation. The system of ordinary differential equations, arising at the second stage, is solved analytically, which ensures algorithm efficiency. The analytical solution of the equation is also obtained for the vertical turbulence coefficient. The model is used to study the sensitivity of the model circulation of the North Atlantic–Arctic Ocean to variations in the parameters of vertical turbulence. The experiments show that varying the coefficients of the analytical solution of the k–ω model can improve the adequacy of the simulation. The preliminary comparison of the features of the k–ω and k–e turbulence models is presented using the method of splitting when they are employed in the OGCM.

Large eddy simulation of the tip-leakage cavitating flow with an insight on how cavitation influences vorticity and turbulence

• The tip-leakage cavitating flow is simulated by LES with Cartesian cut-cell mesh. • Three types of cavitating vortical flows, including TLV, TSV and IV, are analyzed from Euler/Lagrangian viewpoints. • Three stages for the spatial–temporal evolution of tip-leakage cavitating flow are discussed. • The physical mechanism for cavitation-turbulence interaction is clarified. Cavitation within a tip leakage flow remains a challenging issue in a variety of axial hydraulic machines. It is still not possible nowadays to predict cavitation occurrence in such a flow with acceptable accuracy. In the present study, we have carried out numerical simulations of a tip leakage cavitating flow, generated by a straight NACA0009 hydrofoil. We have used the LES method combined with the Schnerr–Sauer cavitation model. The numerical results agree well with experimental data. The evolution of the tip leakage cavitating flow, involving tip-leakage vortex (TLV), tip-separation vortex (TSV) and induced vortex (IV), is analyzed from Eulerian and Lagrangian viewpoints. The results show that the spatial evolution of the tip leakage cavitating flow can be divided into three stages: Stage Ⅰ, Independent development of the TLV and TSV; Stage Ⅱ, Fusion of the TLV and TSV; and Stage Ⅲ, Development of the IV and dissipation of the TLV. The Lagrangian coherent structures (LCSs) obtained from the numerical results indicate that the TLV cavitation significantly influence the local flow patterns. The vorticity transport equation was then used to further analyze the influence of the cavitation on the vortices. The results demonstrate that the stretching term dominates the TLV evolution and the dilatation term is responsible for the vorticity reduction inside the TLV cavity. The results also show how the cavitation influences the local turbulence and that the transport term in the turbulent kinetic energy equation influences the turbulence distribution near the TLV cavity.

A direct numerical investigation of two-way interactions in a particle-laden turbulent channel flow

Understanding the two-way interactions between finite-size solid particles and a wall-bounded turbulent flow is crucial in a variety of natural and engineering applications. Previous experimental measurements and particle-resolved direct numerical simulations revealed some interesting phenomena related to particle distribution and turbulence modulation, but their in-depth analyses are largely missing. In this study, turbulent channel flows laden with neutrally buoyant finite-size spherical particles are simulated using the lattice Boltzmann method. Two particle sizes are considered, with diameters equal to 14.45 and 28.9 wall units. To understand the roles played by the particle rotation, two additional simulations with the same particle sizes but no particle rotation are also presented for comparison. Particles of both sizes are found to form clusters. Under the Stokes lubrication corrections, small particles are found to have a stronger preference to form clusters, and their clusters orientate more in the streamwise direction. As a result, small particles reduce the mean flow velocity less than large particles. Particles are also found to result in a more homogeneous distribution of turbulent kinetic energy (TKE) in the wall-normal direction, as well as a more isotropic distribution of TKE among different spatial directions. To understand these turbulence modulation phenomena, we analyse in detail the total and component-wise volume-averaged budget equations of TKE with the simulation data. This budget analysis reveals several mechanisms through which the particles modulate local and global TKE in the particle-laden turbulent channel flow.

Turbulent mixing and dispersion mechanisms over flexible and dense vegetation

The present study investigates flow turbulence and dispersion processes in the presence of flexible and dense vegetation on the bed. The turbulent dispersion coefficients and the terms of the turbulent kinetic energy equation are determined by using data collected in a straight laboratory channel with living vegetation on the bed. Results show that the turbulent integral lengths assume an order of magnitude comparable to the stems’ characteristic dimension independently by the direction and the turbulence assumes an isotropic behavior. The coefficients of dispersion have a trend similar to that of the turbulent lengths and assume low values in the longitudinal, transversal and vertical directions. Results also show that, in the mixing layer, the shear and wake turbulence production terms balance the dissipation; the turbulent diffusion term also assumes low values and its sign varies along the vertical indicating a transport of turbulent energy both from the vegetation to the free surface and from the free surface to vegetation.

Predicting macroturbulence energy and timescales for flow over a gravel bed: Experimental results and scaling laws

The fluvial science community lacks predictive equations for macroturbulence energy and timescales, which may serve useful for predicting sediment transport in rivers. Therefore, we investigated the systematic variation of macroturbulence scales by varying hydraulic parameters in an experimental facility, collecting velocimetry data and measuring macroturbulence scales with spectral analyses, and testing scaling laws for macroturbulence prediction that consider inner variables, outer variables, and turbulence kinetic energy. Experiments spanned across 11 energy gradients and aspect ratio combinations including 116 testing conditions each with 30 minute instantaneous turbulence time-series collected. Results showed velocimetry data and time-average turbulence parameters supported the presence of an equilibrium outer region and coherent double-layer assumed in the experimental design. Macroturbulence and bursting wavenumbers were constant in the outer region when scaled with the flow depth, and were independent of distance above the boundary, aspect ratio, energy gradient, Froude number, or Shields parameter. Data results agreed with the derivation herein and showed macroturbulence energy scales with the streamwise turbulence kinetic energy. Semi-theoretical equations for turbulence kinetic energy scaled macroturbulence energy reasonably well. A novel equation is presented for the macroturbulence period, and the equation's transferability is supported by consistency with past macroturbulence studies, bursting formula, and flow visualization studies. Novel equations are presented for macroturbulence energy, and transferability is supported on theoretical and empirical grounds; however open questions remain regarding a universal function for streamwise turbulence kinetic energy and the net contribution of macroturbulence to total turbulence energy. Results showed the macroturbulence wavenumber required a relatively long duration of data (i.e., 17 min) to stabilize. Results were used to formulate a time scale for minimum measurement length of turbulence data when information about macroturbulence is sought after. We discuss macroturbulence linkages with sediment transport, including, prediction of the sediment carrying capacity via macroturbulence formula as one application to help close the gap between turbulence and fluvial sediment transport.

Effect of the Spool Cone Angle on the Erosion of a Novel Inner Blowout Preventer

This paper presents a novel structure with reliable sealing property for the inner blowout preventer (BOP) device aiming at improving its safety and reliability during drilling process. Namely, the study of effects of flow rate and seat cone angle on the erosion wear rate of inner BOP is performed based on the numerical simulation analyses of inner flow field of inner BOP by means of computational fluid dynamics method with various models including RNG k–e model, discrete phase model and Tabakoff–Grant erosion model. The finite volume method is used for the discrete calculation, and the SIMPLE algorithm is applied for solving the continuity, momentum, energy and turbulent kinetic energy equations. The results reveal that some positions of the valve core are prone to erosion wear, and the optimal angle of the taper angle of the upper and lower valve seats for the inner BOP is 25°. Finally, the static stress analyses and leak tests validate the reliability of the inner BOP. These analyses provide the basis for structural design of the inner BOP.

Turbulence and interphase mass diffusion assumptions on the performance of secondary settling tanks.

Secondary settling tanks (SSTs), also known as secondary sedimentation tanks or secondary clarifiers, are a basic yet complicated process in a biological water resource recovery facility. In order to understand and improve SST performance, computational fluid dynamics methods have been employed over the last 30years. In the present investigation, a Fluent-based two-dimensional axisymmetric numerical model is applied to understand the effects of the buoyancy term (Gb ) in the turbulent kinetic energy (TKE) equation and two model parameters (the coefficient of buoyancy term (C3 ) in the turbulent dissipation rate equation and the turbulent Schmidt number (σc ) in the sludge transport equation) on the performance of an SST. The results show that the hydrodynamics can only be correctly predicted by buoyancy-coupled TKE equation, unless the mixed liquor suspended solids is low and sludge settling velocity is extremely high. When the field observations show the SST is operating well, the buoyancy-decoupled TKE equation predicts the correct result, but the buoyancy-decoupled TKE equation may predict failure. Care is required in selecting the correct modeling technique for various conditions. This study provides guidance on how to avoid modeling problems and increase rates of convergence. PRACTITIONER POINTS: C3 can be set to zero to improve rate of convergence and reduce computing time. σc can be used to adjust SBH, when ESS and RAS concentrations are well calibrated to the field data, but the SBH does not fit field observation.