Multiple Reference Frame Approach Research Articles

Effects of Flow Baffles on Flow Profile, Pressure Drop and Classification Performance in Classifiers

This paper presents a study of the use of flow baffles inside a centrifugal air classifier. An air classifier belongs to the most widely used classification devices in mills in the mineral industry, which is why there is a great interest in optimizing the process flow and pressure loss. Using Computational Fluid Dynamics (CFD), the flow profile in a classifier without and with flow baffles is systematically compared. In the simulations, turbulence effects are modeled with the realizable k–ε model, and the Multiple Reference Frame approach (MRF) is used to represent the rotation of the classifier wheel. The discrete phase model is used to predict the collection efficiency. The effects on the pressure loss and the classification efficiency of the classifier are considered for two operating conditions. In addition, a comparison with experimental data is performed. Firstly, the simulations and experiments show good agreement. Furthermore, the investigations show that the use of flow baffles is suitable for optimizing the flow behavior in the classifier, especially in reducing the pressure loss and therefore energy costs. Moreover, the flow baffles have an impact on the classification performance. The impact depends on the operation conditions, especially the classifier speed. At low classifier speeds, the classifier without flow baffles separates more efficiently; as the speed increases, the classification performance of the classifier with flow baffles improves.

Investigation of Tire Rotating Modeling Techniques Using Computational Fluid Dynamics

Abstract Fuel efficiency becomes very important for new vehicles. Therefore, improving the aerodynamics of tires has started to receive increasing interest. While the experimental approaches are time consuming and costly, numerical methods have been employed to investigate the air flow around tires. Rotating boundary and contact patch are important challenges in the modeling of tire aerodynamics. Therefore, majority of the current modelling approaches are simplified by neglecting the tire deformation and contact patch. In this study, a baseline CFD model is created for a tire with contact patch. To generate mesh efficiently, a hybrid mesh, which combines hex elements and polyhedral elements, is used. Then, three modeling approaches (rotating wall, multiple reference frame and sliding mesh) are compared for the modeling of tire rotation. Additionally, three different tire designs are investigated, including smooth tire, grooved tire and grooved tire with open rim. The predicted results of the baseline model agree well with the measured data. Additionally, the hybrid mesh show to be efficient and to generate accurate results. The CFD model tends to over predict the drag of a rotating tire with contact patch. Sliding mesh approach generated more accurate predictions than the rotating wall and multiple reference frame approaches. For different tire designs, tire with open rim has the highest drag. It is believed that the methodology presented in this study will help in designing new tires with high aerodynamic performance.

CFD Study on Impeller Effect on Mixing in Miniature Stirred Tank Reactor

Mixing of fluid can happen in existence or absence of impeller which will affect the mixing performance. The hydrodynamics behavior of fluid has a strong effect on the mixing. The design of mixing systems and operation using the agitated tanks is complicated because it is difficult to obtain accurate information for turbulence’s impeller induced. Computational Fluid Dynamics can be used to provide a detailed comprehension of those systems. This paper describes the effect of various designs of impeller in miniature stirred tank reactor towards the mixing of the calcium alginate beads with the milk using Computational Fluid Dynamics (CFD) software, ANSYS Fluent 19.2. The four different type of impellers are edge beater, 5-turbine blade, t-shape, and paddle. The impeller was simulated at different speeds of 150 rpm, 250 rpm, and 300 rpm. K-epsilon turbulence model was employed to simulate the flow distribution pattern of calcium alginate beads and the Multiple Reference Frame approach was used for the impeller rotation’s simulation. The simulation results obtained have a good agreement with the experimental results in term of vortex formation. The simulation results obtained for contour plots were fitted well with the experimental results as well as with pattern of impeller flow which was also studied. As a result, an optimal design of the impeller that is able to produce good mixing can be achieved using CFD analysis. The results obtained after performing the simulation proved that edge beater blade outperformed the other impellers and took the least time to fully distribute the calcium alginate beads in the tank at 250 rpm compared to 150 and 300 rpm. It can also be concluded that the edge beater blade is the best for the mixing of two-phase fluid and also produces mixed pattern flow. The obtained results from CFD can also be used to scale up the mixing process in larger systems.

Numerical analysis of the hydrodynamics induced by rotating ring electrode using κ-ε models

The dynamic rotating rings electrode (RRE) has proven to be an efficient configuration for removing contaminants. The flow induced by the complex geometry of the RRE was analyzed by computational fluid dynamics (CFD) and the multiple reference frame approach (MRF), rotational speed in the range of 75–500 rpm. Assessment of the three κ-ε type models (standard, renormalization group theory (RNG) and realizable) to solve the turbulent flow was performed. The results show that the realizable model provides a more adequate physical description of the flow than the other models. The global flow was analyzed using integral parameters such as the average flow, circulation time, pumping number, and power number. The local flow was examined qualitatively through velocity profiles and streamlines. The effect of simulating two different positions (0° and 45°) of the RRE moving walls concerning the baffles when using the MRF approach was evaluated. The flow pattern is predominantly radial because the electrode external bars propel the fluid to the lateral tank wall. Besides, the external bars promote regions of high deformation in the fluid that produce vortices. It was found that the result at 0° is in good agreement with the experimental results of mixing time.

CFD modeling of the [formula omitted] capture by range hood in a full-scale kitchen

Air quality criteria in residential houses are increasing continuously. Multiple studies tend to use commercial CFD software in order to predict and optimize the flow conditions in range hoods. Most of them modeled the range hood without considering the rotating fan. In the present work, a new open-source solver was developed using the OpenFoam libraries. It is based on a buoyancy Boussinesq solver and a turbulent passive scalar transport equation accounting for the heated CO2 extraction by the rotating fan, fully modeled using the Multiple reference frame (MRF) approach. The new solver is carefully validated against experimental results for three benchmark cases: a CO2 plume, a differential heated cavity and the performance curve of a rotating fan. The model has been confidently used to model the CO2 extraction in a realistic residential kitchen considering one to four burners on. An improvement of 30% in the capture efficiency is reached by increasing the extraction flowrate of the fan from 100 to 300 cfm. An extraction efficiency of 100% is observed for flowrates above 330 cfm.

CFD Research on the Influence of 45° Disk Turbine Agitator Blade Diameter on the Solid–Liquid Mixing Characteristics of the Cone-Bottom Stirred Tank

A numerical simulation of a solid–liquid mixture concentration field in a cone-bottom stirred tank (diameter D = 150 mm) was conducted using computational fluid dynamics (CFD). The influence of the 45° disk turbine impeller diameter on the mixing time number of solid–liquid mixture, mixing energy per unit volume, concentration standard deviation, turbulence energy and turbulent dissipation rate as well as solid just-suspended impeller speed was analyzed. The Eulerian two-fluid model was employed along with the standard k–e turbulence model to simulate the turbulent solid–liquid flow in the cone-bottom stirred tank. A multiple reference frame approach was used to simulate the impeller rotation in a fully baffled reactor. The Fluent® 14.5 commercial CFD software was employed for the transient simulation. The radial and tangential velocities at the outer edge of the impeller along the blade width were compared with the experimental data of Wu and Patterson (Chem Eng Sci 44:2207–2221, 1989), Mahouast et al. (Entropy 133:7–17, 1987) and Kemoun et al. (IChemE Symp Ser 136:399–406, 1994). The further extended computational model could well predict the influence of impeller diameter on the solid–liquid mixing characteristics.

Experimental and numerical evaluation of the performance of the electrochemical reactor operated with static and dynamic electrodes in the reduction of hexavalent chromium

In this work, we assess two electrochemical reactor designs to reduce hexavalent chromium diluted in rinsing waters from the electroplating industry. One reactor has a dynamic electrode composed of rotating rings electrodes (RRE), and the other is a novel design that has static electrodes (SE) with two pitched blade turbines (PBT). The SE, named “Electro-Baffles”, disrupts the tangential flow induced by impellers and promotes the electrochemical reactions. The hydrodynamic behavior of both designs was assessed by Computational Fluid Dynamic using the multiple reference frame approach. Experimental measurements of the mixing and treatment times to validate the results were performed. The rotational velocity of the RRE was150 rpm, the optimum rpm reported, while for the impellers of the other design, two speeds were tested; one, operated at the same rpm as for RRE and the other, at 362 rpm, to operate it at the same Reynolds Number (Re) as the RRE. The pumping effectiveness (ηQ) using SE increased up to 86% in comparison with the RRE design, due to the enhancement in the axial circulation generated by the impellers and the flow interactions with the “Electro-Baffles”. Hydraulic SE system improvements reduced the mixing time by 16% with the PBT rotating at 150 rpm, while at the same Re, the reduction was 47%. The total specific energy had a reduction of 39% when the two PBT rotated at 362 rpm, whereas by about 21% at 150 rpm.

Design of Multi-Stage Axial Flow Compressor and Validation using Numerical Simulations

The optimum yield of gas turbine engines has so far been driven on and around the operational efficiency of the compressor and in essence around the efficiency of the compressor blade. The efficacy of a compressor is ascertained substantially by the smoothness of the air flowing through it. In this present work, a multi-stage axial compressor in the Turbojet engine with an application for propulsion is designed based on thermodynamic calculations. The calculations were carried out employing the principles of thermodynamics, and aerodynamics along the mean streamline based on the technique of a velocity triangle in the lack of inlet guide vanes. The coordinates for the blade profile has been calculated on and around the premise of the calibrated blade base profile. The model for the seven-stage axial flow compressors based on thermodynamic calculations was devised and analyzed utilizing computational fluid dynamics methodology. The multiple reference frame approach was used to represent the impact of both rotating and stationary components and the simulation for the first stage was conducted using a periodic approach. For the intent of the verification, a comparison was made between the analytical values and the simulated values and the variation between these values was found to be 16.7%. Validation results demonstrate that the proposed method is valid and can be used for multi-stage axial compressor design and performance evaluation.

Effects of root Gurney flaps on the aerodynamic performance of a horizontal axis wind turbine

This paper presents a computational investigation on the effects of Gurney flaps on the aerodynamic performance of a horizontal axis wind turbine, which is part of the EU FP7 AVATAR project. The research investigates two configurations of Gurney flaps applied at the inboard part of the blade (r/R=0.30∼0.46) at 85% chord location on the pressure surface. The computational method applied in the investigation solves the Reynold-Averaged Navier-Stokes (RANS) equations with multiple reference frame (MRF) approach, which models the rotating turbulent flow over the wind turbine rotor. Numerical simulations are performed for the wind turbine rotor with and without Gurney flap at the tip speed ratios λ=4.59 and 6.35. Comparison of the numerical results with experimental measurements shows that the deployment of Gurney flaps effectively increases the power coefficients of the rotor by 21% at λ=6.35. Gurney flaps have a considerable 3D effect on spanwise thrust and torque coefficients distribution. The performance of two Gurney flaps configurations is compared. It is shown that the larger Gurney flap reduces the effect on the power generated due to protruding out of the local boundary layer of the flow. The numerical results are in good agreement with the experimental results in terms of total thrust and power within 14.1% difference, and complement the experimental database.

Evaluation of the Multiple Reference Frame Approach for the Modelling of an Axial Cooling Fan

The modelling of rotating parts, such as axial fans, is one of the main challenges of current CFD simulations of industrial applications. Different methods are available, but the most commonly used is the multiple reference frame (MRF) method. This paper investigates how different flow properties, such as temperature, pressure and velocity, develop when passing through the MRF domain. The results are compared to the more physical rigid body motion (RBM) approach. It is found that the MRF method transports the upstream properties with the streamlines of the relative velocity from the upstream to the downstream interface. This leads to a non-physical rotation by an angle that is dependent on the length of the domain and the ratio between axial and tangential velocity in the MRF region. The temperature field is more affected than the flow field, since wake structures from upstream obstacles are destroyed due to the wake of the blades. Downstream structures affect the flow in the upstream region by an increase in static pressure, which causes the streamlines in the MRF zone to slow down. Depending on the size of the obstacle, this can cause substantial distortions in the upstream and downstream flow field.

Numerical Validation of a Pressurized Batch Reactor for In-Situ Transesterification

Subcritical in-situ transesterification is one of the more recently developed processes that consumes less energy and is more environmental friendly than conventional methods. Diving deeper into this process, the fluid dynamics of the liquid mixture is an area of interest not studied before due to the solid, thick metal enclosure of the reactor vessel. Previous studies observed that the mixing characteristics of the agitator being used influences biodiesel yield. As commercialization of this biofuel production process is of importance in order to contribute to biofuel demand in a nation-wide scale, this study considers a reactor vessel working volume of around 1.5L, which is relatively larger than typical laboratory batch-type sizes. A numerical validation study, through mesh analyses, was performed to produce a numerically accurate model for the study. Factoring in computational time and accuracy of the solution, a steady state, multiphase model running the standard k-∈ turbulence model was chosen. The Multiple Reference Frames approach was used for the steady state condition to be met. The validation model is of a 6.3L-volume cylinder with baffles. Glass beads served as the solids and water as the liquid in the system. The first mesh analysis was performed by comparing 11 unique mesh models. The model with a relevance of fine 30 was seen to have the closest data fit with the experimental data. It was seen that only when using the size function ‘proximity’ showed a slightly different velocity profile among the models. The second mesh analysis was conducted to check if the chosen mesh setting would affect this study’s smaller reactor geometry before the main study’s simulations are to be conducted. The model with baffle’s percent error at the specified point was at an acceptable 8.2%, and its resultant velocity profile’s is at 23.5% which is around the same range as that of the 1st mesh analysis’ models. With this, the numerical model developed was deemed to be applicable for the main study.

Improved Performance Prediction of Marine Propeller: Numerical Investigation and Experimental Verification

An approach was presented to improve the performance prediction of marine propeller through computational fluid dynamics (CFD). After a series of computations were conducted, it was found that the passage in the former study was too narrow, resulting in the unnecessary radial outer boundary effects. Hence, in this study, a fatter passage model was employed to avoid unnecessary effects, in which the diameter was the same as the length from the propeller to the downstream outlet and the diameter was larger than the previous study. The diameter and length of the passage were 5D and 8D, respectively. The propeller DTMB P5168 was used to evaluate the fat passage model. During simulation, the classical RANS model (standard k-ε) and the Multiple Reference Frame (MRF) approach were employed after accounting for other factors. The computational performance results were compared with the experimental values, which showed that they were in good agreement. The maximum errors of Kt and Kq were less than 5% and 3% on different advance coefficients J except 1.51, respectively, and that of η was less than 2.62%. Hence the new model obtains more accurate performance prediction compared with published literatures. The circumferentially averaged velocity components were also compared with the experimental results. The axial and tangential velocity components were also in good agreement with the experimental data. Specifically, the errors of the axial and tangential velocity components were less than 3%, when the r/R was not less than 3.4. When the J value was larger, the variation trends of radial velocity were consistent with the experimental data. In conclusion, the fat passage model proposed here was applicable to obtain the highly accurate predicted results.

Numerical Simulation of Gas-Liquid Dispersion in A Stirred Tank Agitated by Punched Rigid-Flexible Impeller

Abstract The hydrodynamics of gas-liquid dispersion process in a stirred tank with rigid impellers, rigid-flexible impellers, and punched rigid-flexible impellers were investigated using a combined computational fluid dynamics (CFD) and population balance model (PBM) approach. A classical Eulerian-Eulerian approach coupled with standard k-e turbulence model was employed to simulate gas-liquid turbulent flow in the stirred tank. The multiple reference frame (MRF) approach was used to simulate impeller rotation. The effects of impeller type, flexible connection piece length, aperture size/ratio, impeller speed and superficial gas velocity on the local gas holdup and bubble size distribution for the gas-liquid dispersion process were investigated. Results showed that a long flexible connection piece length was conductive to the gas-liquid dispersion process. The optimum aperture ratio and aperture diameter were 12 % and 8 mm, respectively, for the gas-liquid dispersion process. Punched rigid-flexible impeller could reduce the differential pressure ahead and behind the impeller blade, decrease the size of low-pressure zone, and improve the water shear strain rate compared with rigid impeller and rigid-flexible impeller at the same Pg,v. It was found that punched rigid-flexible impeller was more efficient in terms of gas dispersibility than rigid impeller and rigid-flexible impeller.

FSI - MRF Coupling Approach For Faster Turbocharger 3D Simulation

<div class="section abstract"><div class="htmlview paragraph">Fluid-Structure Interaction (FSI) simulation approach can be used to simulate a turbocharger. However, this predictive 3D simulation encounters the challenge of a long computational time. The impeller speed can be above 100,000 rpm, and generally a CFD solver limits the maximum movement of the impeller surface per time step. The maximum movement must be a fraction (~0.3) of the cell length, thus the time step will be very small. A Multiple Reference Frame (MRF) approach can reduce computational time by eliminating the need to regenerate the mesh at each time-step to accommodate the moving geometry. A static local reference zone encompassing the impeller is created and the impact of the impeller movement is modeled via a momentum source. However, the MRF approach is not a predictive simulation because the impeller speed must be given by the User. A new simulation approach was introduced that coupled the FSI and MRF approach. Like in the FSI approach, the total moment of the impeller was calculated based on the resultant force acting over the impeller surface. This calculation was conducted for each time-step and the resulted moment was returned back to the solver to update the MRF zone moment. With this coupling approach, the computational time is similar to the MRF approach while maintaining similar accuracy to the FSI predictive approach. The coupling approach was applied to simulate a turbocharger of 15 L diesel engine. The work done by the turbine on the compressor was adjusted to match the impeller speed with the test data. The calculated pressure upstream from the turbine showed a good agreement with test data. The new approach was also used to guide the design of the exhaust manifold for better turbocharger performance.</div></div>

A study on liquid‐liquid dispersions in a continuous mixer via computational fluid dynamics (CFD) simulation combined with population balance model (PBM)

AbstractLiquid‐liquid two‐phase flow in a mixer of mixer‐settler has been studied via a computational fluid dynamics (CFD) simulation combined with the population balance model (PBM) and verified with particle image velocimetry (PIV) experiments. The simulation was performed using the multiple reference frame (MRF) approach, the Eulerian‐Eulerian two‐fluid model, and the standard k‐ϵ model. The effects of impeller speed, flow ratio, and impeller type on flow field, droplet diameter, and dispersed phase holdup were investigated. The results showed that CFD simulation combined with PBM could predict droplet size distribution (DSD). The smaller droplets were mainly in the bottom region of the mixer, larger ones were in the top part of the mixer, and the largest droplets appeared in the impeller centre region. The DSD and holdup were more sensitive to impeller speed than to the organic/aqueous flow ratio. A dual‐impeller mixer configuration was designed to enhance the mixing performance. Compared with single‐impeller, the installation of dual‐impellers could effectively avoid the dispersed phase dead zone above the lower impeller. When hc /T = 0.3, the best dispersing effect, such as uniform DSD and high mixing chamber space utilization, could be obtained.

Bi-directional integral pumping devices for dual mechanical seals: Influence of mesh type on accuracy of numerical simulations

A numerical study is conducted to simulate the performance of barrier fluid flow through a bi-directional dual mechanical seal with an integral radial pumping ring. Standard K-ε model is implemented as a turbulence model. Multiple Reference Frame approach is implemented to model the rotation of the pumping ring. The present study is a sequel to a previous companion work done in the area of visualization of barrier fluid flow. Improvements to the previous work depended on two aspects. First, a multi-block hybrid (tetra, prism and hexa) mesh is used where it is aimed to reduce numerical false diffusion by orienting the cells to be aligned with flow direction as much as possible. Second, expanding model’s boundaries to include inboard sealing faces. The numerical results are validated against Q-ΔP curves produced from experimental tests where an experimental setup is constructed, and appropriate instrumentation is employed to measure the pressure, temperature, and flow rate of the barrier fluid.Moreover, implementation of two spatial discretization schemes is illustrated to verify the numerical performance of each method. Second order Upwind and QUICK (Quadratic Upstream Interpolation for Convective Kinematics) schemes are used for the discretization of convective terms. The validity of implementation of each method is investigated since higher-order methods are known to be more computationally expensive but their accuracy are higher. The results by the hybrid mesh indicate that the use of the Second-order scheme provides more accurate prediction of Q-ΔP curves than the previous companion work. Moreover, the impact of using the QUICK scheme is the increased computational time while providing slightly more accurate Q-H curve relative to the second-order scheme.Finally, expanding model’s boundaries to include inboard sealing faces revealed that closed barrier fluid circulation takes place in the vicinity of the inboard sealing faces indicating poor renewal of the barrier fluid contained within this zone compared to the outboard sealing faces.

Performance and wake characteristics of a tidal turbine under yaw

In tidal streams and rivers, the flow of water can be at yaw to the turbine rotor plane causing performance degradation and a skewed downstream wake. The current study aims to quantify the performance variation and associated wake behavior caused by a tidal turbine operating in a yawed inflow environment. A three-dimensional computational fluid dynamics study was carried out using multiple reference frame approach using κ-ω SST turbulence model with curvature correction. The computations were validated by comparison with experimental results on a 1:20 scale prototype for a 0° yaw case performed in a laboratory flume. The simulations were performed using a three-bladed, constant chord, untwisted tidal turbine operating at uniform inflow. Yaw effects were observed for angles ranging from 5° to 15°. An increase in yaw over this range caused a power coefficient deficit of 26% and a thrust coefficient deficit of about 8% at a tip speed ratio of 5 that corresponds to the maximum power coefficient for the tested turbine. In addition, wake propagation was studied up to a downstream distance of ten rotor radius, and skewness in the wake, proportional to yaw angle was observed. At higher yaw angles, the flow around the turbine rotor was found to cushion the tip vortices, accelerating the interaction between the tip vortices and the skewed wake, thereby facilitating a faster wake recovery. The center of the wake was tracked using a center of mass technique. The center of wake analysis was used to better quantify the deviation of the wake with increasing yaw angle. It was observed that with an increase in yaw angle, the recovery distance moved closer to the rotor plane. The wake was noticed to meander around the turbine centerline with increasing downstream distance and slightly deviate towards the free surface above the turbine centerline, magnitude of which varied depending on yaw.

EFECTO DEL TAMAÑO DEL MARCO DE REFERENCIA ROTATIVO PARA SIMULAR UN IMPULSOR DE MEZCLADO DE PALETAS RECTAS EN UN TANQUE CON BAFLES.

A computational fluid dynamics (CFD) study was performed to simulate the flow induced by a turbine of four flat blades in a stirred baffled-tank. The multiple reference frame approach is employed to model the impeller rotation. The work focuses specifically on investigating the influence of the surface position separating the rotating reference frame (RRF) and the static reference frame (SRF) regions over the numerical results reliability. Power number measurements were obtained to validate the CFD model. It was found that for laminar flow, the interface position between both regions does not have a substantial effect on numerical results. However, its position plays a substantial role as the flow regime increases; the higher this is, the larger the RRF must be. Finally, we employ the RRF-region dimensions obtained in turbulent conditions for reproducing satisfactorily experimental results of a published system.

Identifying dominant spatial and time characteristics of flow dynamics within free-surface baffled stirred-tanks from CFD simulations

In many chemical and biochemical processes, it is fundamental to accurately predict flow dynamics within reactors of different sizes and its influence on reactions and their kinetics. Computational Fluid Dynamics can provide detailed modeling about hydrodynamics. The objective of the present work is to assess the abilities of CFD to simulate free-surface turbulent flow within baffled stirred-tanks reactors. Transient simulations are carried out using a homogeneous Euler-Euler multiphase approach, the Volume-of-Fluid (VOF) method, with a Realizable k–ε turbulence model. Two methods are considered to account for the impeller motion, namely the Multiple Reference Frame (MRF) and Sliding Mesh (SM) approaches. Global and local results obtained by CFD are presented by means of statistical analysis, including the estimation of characteristic turbulent length scales. Instantaneous numerical data fields obtained with the SM model are then interpreted using modal decompositions methods, i.e. the Proper Orthogonal Decomposition (POD) and the Dynamic Mode Decomposition (DMD) in order to extract their dominant spatial structures with their time behavior. All simulations are discussed based on comparison with experimental data.

Investigating the Effect of Multiple Reference Frame Approach on the Modelling of an Oxidation Ditch

One of the common bioreactors in activated sludge process is oxidation ditch (OD). Since aeration and mixing are the main causes of alteration in flow field, study on hydrodynamics is essential for effective operation and optimization of an OD. Such study has become less-difficult and more cost-effective because computational fluid dynamics as a dominant tool to simulate the hydrodynamics has increasingly improved. Rotation of the impeller and mixer generates fluid flow, so selecting a model that outlines impeller rotation plays a vital role. Based on the proficiency of multiple reference frame (MRF) approach, the flow characteristics associated with several rotational parts can be investigated. However, in most of the previous studies on OD as a wastewater treatment equipment, there is no clear comment on the dimension of rotational zone required for the simulation; therefore, an exclusive investigation is essential and can be supportive for additional studies on processes with moving parts. In this paper, the influence of rotational zone proportions on the precision of OD simulation was analysed and four models were proposed and simulated by (or with) MRF approach. As a result of this investigation, the more the radius of rotating zone is, the greater the exactness of modelling is. Additionally, the semi-circle rotating zone in MRF approach is infeasible.