Finite Volume Model Research Articles

Numerical investigation on the effect of solder paste rheological behaviour and printing speed on stencil printing

PurposeThe purpose of this paper is to investigate the effect of different viscosity models (Cross and Al-Ma’aiteh) and different printing speeds on the numerical results (e.g. pressure over stencil) of a numerical model regarding stencil printing.Design/methodology/approachA finite volume model was established for describing the printing process. Two types of viscosity models for non-Newtonian fluid properties were compared. The Cross model was fitted to the measurement results in the initial state of a lead-free solder paste, and the parameters of a Al-Ma’aiteh material model were fitted in the stabilised state of the same paste. Four different printing speeds were also investigated from 20 to 200 mm/s.FindingsNoteworthy differences were found in the pressure between utilising the Cross model and the Al-Ma’aiteh viscosity model. The difference in pressure reached 33-34% for both printing speeds of 20 and 70 mm/s and reached 31% and 27% for the printing speed of 120 and 200 mm/s. The variation in the difference was explained by the increase in the rates of shear by increasing printing speeds.Originality/valueParameters of viscosity model should be determined for the stabilised state of the solder paste. Neglecting the thixotropic paste nature in the modelling of printing can cause a calculation error of even approximately 30%. By using the Al-Ma’aiteh viscosity model over the stabilised state of solder pastes can provide more accurate results in the modelling of printing, which is necessary for the effective optimisation of this process, and for eliminating soldering failures in highly integrated electronic devices.

Water transport in foam concrete: visualisation and numerical modelling

Most problems concerning the durability and functional degradation of foam concrete are intimately related to water transfer. The water transfer behaviour in foam concrete under capillary absorption and full submersion conditions is studied in this paper. To overcome the low resolution between water and cement paste in in-situ X-ray computed tomography (XCT) tests, caesium chloride (CsCl; 6 wt%) was used as a contrast-enhancement agent. The dynamic changes to the wetting head and water distribution in foam concrete were successfully visualised in two and three dimensions. The multiscale pore structure of foam concrete was quantitatively characterised by a combination of mercury intrusion porosimetry (micropore <10 μm) and XCT (macropore >10 μm). The results show that the microporosity governs a large part of the capillary suction of water due to the high capillary force in these micropores. However, for macropores, they are partially connected and can hold water under pressure and simultaneously hinder capillary rise due to the blocking of the capillary network and prolonged transfer tortuosity. Finally, a numerical finite-volume model was used to simulate the dynamic water transfer process directly based on the XCT binary images. The modelling results agreed well with the experimental results.

A 2D HLL-based weakly coupled model for transient flows on mobile beds

Abstract We propose a finite-volume model that aims at improving the ability of 2D numerical models to accurately predict the morphological evolution of sandy beds when subjected to transient flows like dam-breaks. This model solves shallow water and Exner equations with a weakly coupled approach while the fluxes at the interfaces of the cells are calculated thanks to a lateralized HLLC flux scheme. Besides describing the model, we ran it for four different test cases: a steady flow on an inclined bed leading to aggradation or degradation, a dam-break leading to high interaction between the flow and the bed, a dam-break with a symmetrical enlargement close to the gate and a dam-break in a channel with a 90° bend. The gathered results are discussed and compared to an existing fully coupled approach based on HLLC fluxes. Although both models equally perform regarding water levels, the weakly coupled model looks to better predict the bed evolution for the four test cases. In particular, its results are not affected by an excessive numerical diffusion encountered by the coupled model. Moreover, it usually better estimates the amplitudes of the maximum deposits and scours. It is also more stable when subject to high bed–flow interaction.

A tool to minimize the need of Monte Carlo ray tracing code for 3D finite volume modelling of a standard parabolic trough collector receiver under a realistic solar flux profile

AbstractThe energy collection element of a parabolic trough collector includes a selective coated metallic receiver tube inside an evacuated glass tube. Perpendicularly incident sun light on the parabolic trough mirror aperture is concentrated on the receiver tube highly nonuniformly along its circular direction. This solar energy is collected as thermal energy circulating a suitable heat transfer fluid (HTF) through the tube. This conjugate heat transfer phenomenon under nonuniform heat flux boundary condition is computationally studied applying 3D finite volume (FV) modelling technique of computational fluid dynamics coupled with Monte Carlo ray tracing (MCRT) optical data. The MCRT model simulates the actual flux profile around the receiver tube. Apart from a FV model, this coupled study requires expertise in, and access to, a suitable MCRT code. A combination of polynomial correlations and user‐defined function (UDF) is introduced in this article in order to minimize the need of MCRT codes from subsequent FV modelling of the receiver tube of the Luz Solar 2 (LS2) collector. The correlations are developed from a verified 3D MCRT model, which is equivalent to the local irradiation data as a function of receiver circular location. The UDF includes two algorithms: one to develop solar flux profile from the correlations around the receiver, and the other to calculate heat loss from the receiver. Interpreting the UDF into ANSYS Fluent, a 3D FV model of the LS2 receiver is developed and validated with experimental results. The effectiveness of the UDF as an alternative to MCRT code is verified. The FV model is capable to investigate the heat transfer characteristics of the LS2 collector receiver at different solar irradiation level, optical properties of the collector components, glass tube conditions, HTFs, inserts or swirl generators, collector length, and internal diameter of the tube.

Coupling pore network and finite element methods for rapid modelling of deformation

Numerical modelling of deformation in hydromechanical systems can be time-consuming using fully coupled classical numerical methods for large representative porous media samples. In this paper, we present a new two-way coupled partitioned fluid–solid system. The coupled system is applied for simulating geomechanical processes at the pore-scale. We track the deformation of the solid resulting from the drainage of resident fluids in the pores, as well as the evolution of fluid properties from dynamic loading. The finite element method is responsible for capturing the structural deformation in the coupled system while the dynamic pore network is used for modelling multiphase flow in the fluid subsystem. A fictitious fluid–solid interface is created at each pore network-finite element node junction via convex hulling, followed by data exchange using linear interpolation. The results show good agreement with a pre-existing coupled finite volume model and the computations are completed in much less time.

Numerical simulations of high frequency transverse pulsed jet injection into a supersonic crossflow

The design of scramjet engines includes the investigation of minimally intrusive fuel delivery mechanisms which maximize jet fuel penetration and mixing. In subsonic crossflows it has been shown that pulsation of gaseous jets can improve jet penetration and mixing in comparison to unforced (steady) jets. Extensive investigations have already explored subsonic flow regimes for pulsed injection; however, only a limited number of experimental and numerical studies have been performed which investigate pulsed jets in a supersonic crossflow. This study presents fully three-dimensional (3D) scale-resolving simulations of steady and a sinusoidally pulsed jet (f = 16 kHz) using a wall modeled large eddy simulation approach to capture large-scale vortical structures in turbulent jet in supersonic crossflow and pulsed jet in supersonic crossflow. A block-structured, fully 3D turbulent scale resolving finite volume model was used to explore physics simulations of steady and pulsed jets in a supersonic crossflow. The results of the simulations presented show that sinusoidal pulsation of a gaseous hydrogen jet improves penetration and mixing over the steady jet when the momentum flux ratios are equivalent.

Numerical simulations of arc plasma under external magnetic field-assisted gas metal arc welding

The arc plasma behavior for gas metal arc welding (GMAW) with an external compound magnetic field was numerically investigated. A three-dimensional finite element model for the external magnetic field (EMF) and a three-dimensional finite volume model for the arc plasma were established. The effects of the EMF on the redistribution of the temperature, fluid flow, pressure, and electromagnetic force in the arc plasma were compared with traditional GMAW under the same welding parameters. The control mechanism of the external compound magnetic field on the arc plasma behavior was analyzed. The results show that the magnitude of the additional electromagnetic force was much lower than that of the self-induced electromagnetic force, but it caused forward inclination and periodic swinging of the arc plasma. When an EMF was applied, the peak temperature decreased, and the temperature distribution was more uniform. The peak pressure was also much smaller than that without an applied EMF.

Assessment of subgrid method in a finite-volume model

We present an implementation of a subgrid finite-volume model based on a nonlinear semi-implicit solver originally proposed by Casulli (2009), but with different approaches for constructing the tangential velocity as required by all Arakawa C-grid models. The model is carefully benchmarked through a few revealing test cases that consist of a theoretical nonlinear inundation case and a field application to San Francisco Bay. Through these tests, we seek to answer a critical science question, i.e. whether a structured grid with the help from a subgrid representation of underlying bathymetry can produce comparable results to an unstructured grid. Results suggest that comparable results for surface elevation can be achieved provided that the resolution of the base cell is sufficient fine; on the other hand, use of subgrid does not significantly improve the velocity results. The latter is attributed to the assumption that the surface elevation is assumed to be constant at the base cell. Future research priorities for this type of models should focus on improving the subgrid representations of the elevation and velocity.

Finite Volume Modelling of Li-Ion Composite Cathodes Based on Micro-Scale X-Ray Computed Tomography

INTRODUCTION Mathematical models have been used to simulate the physical and electrochemical processes occurring inside batteries in order to aid understanding and design. Newman et al. developed one of the most popular lithium ion battery models based on the porous electrode and concentrated solution theory. Newman’s pseudo-2D (P2D) model assumes that the porous electrode is made of equally sized, isotropic, homogenous spherical particles. It has been shown that battery electrodes are actually very heterogeneous structures [1] and therefore more complex approaches are required in order to fully characterise the transport processes occurring within the battery. This work uses an open-source, data-driven, image-based modelling framework, OpenImpala, that is capable of modelling lithium-ion battery electrodes. METHODOLOGY A number of different imaging techniques are capable of providing electrode data, namely: scanning electron microscopy (SEM), focussed ion beam scanning (FIB) and x-ray computed tomography (CT). SEM techniques reach suitable resolutions (~0.5 nm) however they only provide 2D data, therefore they cannot capture the full 3D volume of the electrode. FIB scanning uses a beam of positively charged ions to mill away the surface of the target and so is a destructive method, therefore in-situ testing or re-testing of a battery would not be possible. State of the art CT scanners can achieve sub-micron resolutions whilst being a non-destructive method [2], for these reasons CT imaging was chosen.Finite element based models have been used extensively to simulate lithium-ion batteries [3] however they have been shown to be computationally expensive to mesh the image data. Finite difference/volume schemes use a regularly discretised mesh and are usually quicker to implement, as the voxel dataset can be used directly, but they can result in approximation errors. Adaptive mesh refinement (AMR) is a technique used in finite difference and volumes schemes to refine or coarsen the grid around regions of sensitivity, both spatially and temporally. This is a technique that allows for quick implementation of the mesh whilst retaining accuracy.The electrodes imaged were Lithium Iron Phosphate (LFP) samples on an aluminium foil substrate, originally made for a Lithium ion battery.Two scans were performed using the Zeiss 160 kVp Versa 510 at the University of Southampton. The first with a 15 s exposure time and 2401 projections across an image angle of ±180°, using a 20x optical magnification to capture a voxel size of 801 nm.The second with a 50 s exposure and 3201 projections, using a 40x optical magnification to capture a voxel size of 400 nm. Both used a voltage of 80 kV and a power of 6 W,the power was slightly higher than usual in order to better resolve the image. The two scans were both carried out on the same sample and using the same focal point, this is so they could be used as a direct comparison to see how porosity and tortuosity values changed with spatial resolution. RESULTS AND DISCUSSION It is found that the Bruggeman correlation significantly underestimates the tortuosity factor compared to the OpenImpala calculated results. It is also found that there is a larger stochastic variance in the 801 nm results, whereas the 400 nm results have a much smaller standard deviation. CONCLUSIONS AND FUTURE WORK This work has made use of a single-physics, image-driven computational model, OpenImpala. A comparison of resolution study was carried out to see how this affects results obtained, and these were then compared the Bruggeman relation. Work is ongoing to to fully expand the model to multi-physics simulations. REFERENCES 1. Tjaden, B., Cooper, S. J., Brett, D. J., Kramer, D., & Shearing, P. R. (2016). On the origin and application of the Bruggeman correlation for analysing transport phenomena in electrochemical systems. Current opinion in chemical engineering, 12, 44-51.2. Ojha, M., Le Houx, J., Mukkabla, R., Kramer, D., Wills, R. G. A., & Deepa, M. (2019). Lithium titanate/pyrenecarboxylic acid decorated carbon nanotubes hybrid-Alginate gel supercapacitor. Electrochimica Acta, 309, 253-263.3. Kashkooli, A. (2016) Multiscale Modeling of lithium-ion battery electrodes based on nano-scale X-ray computed tomography, Journal of Power Sources 307 496-509

Predicting River Embankment Failure Caused by Toe Scour Considering 1D and 2D Hydraulic Models: A Case Study of Da-An River, Taiwan

Physically based numerical models can predict scour depth at embankments located in bend reaches. However, methodologies for utilizing these numerical models to assess the risk of reinforced concrete embankment failure are rarely investigated. Therefore, a new assessment methodology is proposed to predict the riverbank failure caused by bend scour. The methodology is primarily based on a bend scour simulation model that integrates a one-dimensional (1D) hydraulic model, a two-dimensional (2D) hydrodynamic finite-volume model, and an empirical equation of bend scour prediction. The model was first applied to the Shuiwei Embankment located in a river bend reach of Da-An River in Taiwan and verified against results from the 1D hydraulic model and field data. The model was then used to simulate 2D flow field and the temporal evolution of bend scour depth under different return period flood events to examine the relationships between river discharge, water level, shear stress, and bend scour depth. The influence of shear stress on the stability of toe protections was also investigated. The field data (from two events) and numerical solutions (four scenarios) were assessed to conceive two empirical equations for predicting shear stress and bend scour depth. A new assessment methodology was proposed using these two equations to predict the risk of river embankment failure during flood periods. The proposed methodology can be easily applied in other disaster-prone regions to mitigate the effects of disasters caused by bend scouring.

Finite volume modeling of coupled thermo-hydro-mechanical processes with application to brine migration in salt

The disposal of heat-generating nuclear waste in salt host rock generates a thermal gradient around the waste package that may cause brine inclusions in the salt grains to migrate toward the waste package. In this study, a dual-continuum model is developed to analyze such a phenomenon. In this model, fluid flow in terms of advective and diffusive fluxes in the interconnected pore space and diffusive and thermal-diffusive fluxes in the salt grains is considered. Due to the very distinct behavior of fluid flow in the interconnected pore space versus in the salt grains, this process is simulated based on a dual-continuum model. In the dual-continuum model, the mass balance of salt and water in the two continua is separately considered, and the coupling between the two continua is represented by flux associated with brine migration in one medium and out of another. The energy balance is simulated assuming thermal equilibrium among different components and phases in the whole system. For mechanical analysis, a new formulation (extended finite volume method, XFVM) is proposed and is applied with a Voronoi tessellated mesh. The coupling between the hydraulic and mechanical fields in terms of pore-volume effects is consistent with Biot’s theory, while thermal and mechanical fields are linked in terms of thermal expansion. The resulting fully coupled THM model is capable of modeling strongly nonlinear features, involving salt concentration effects on fluid mass associated with advection, and thermal effects on brine migration. A Newton-Raphson iteration formula is used to generate the linearized equations for this nonlinear problem. The model was verified step by step for each component of the coupling terms, including thermal-hydraulic (TH) and hydro-mechanical (HM) couplings, and was applied to analyze diffusion in single continuum and dual continua, small-scale brine migration, and large-scale brine migration induced by thermal gradient. The results show that the model is able to quantify brine under different conditions and thermal gradients, making it a valuable tool for performance assessment for nuclear waste disposal in salt.

A Rigorous Model Order Reduction Framework for Waste Heat Recovery Systems Based on Proper Orthogonal Decomposition and Galerkin Projection

A proper orthogonal decomposition (POD) and Galerkin projection-based model order reduction framework is developed for the evaporator heat exchanger in heavy-duty diesel engine organic Rankine cycle waste heat recovery system. The dynamics in the heat exchanger are first modeled by a finite-volume model, composed of highly nonlinear, coupled, partial differential equations, and then used to generate snapshots from which basis functions are defined. Reduced order models (ROMs) are then derived using the Galerkin projection approach. The accuracy and the execution time of different POD ROMs are evaluated against the high-fidelity finite-volume model. The results show that the POD ROM dimension can be selected based on the specific requirements of accuracy and computation time demanded by the intended model utilization. The proposed ROM framework can be utilized to generate ROMs with various dimensions for different purposes, such as estimator design, model-based control, and benchmark generation.

Effect of Ply Orientation on the In-Depth Response of Carbon-Phenolic Ablative

The effect of ply orientation on the in-depth response of carbon-phenolic ablative, which is widely used for thermal protection of rocket motor nozzles and reentry capsules, is studied using a newly developed axisymmetric, unstructured, finite volume model. The numerical scheme for solving the conservation equations of solid mass, gas mass, and mixture energy, along with Darcy’s law for the flow of pyrolysis gases, is discussed. Carbon-phenolic decomposition model is developed using thermogravimetry studies. Arcjet tests are conducted on the specimens with different ply orientations, and the in-depth temperature response is compared with the predictions from the numerical model. The effect of ply orientation on the in-depth density and pore pressure is analyzed.

A finite-volume numerical model for temporal and spatial variability of methane oxidation in landfill covers

Abstract A multi-field model is proposed to study methane oxidation in landfill covers, especially its temporal and spatial variability. The proposed model consists of water-gas two-phase flow, multi-component gas flow, heat transfer, and biochemical reaction modules, and is solved using OpenFOAM based on the finite volume method. Applying this model, the coupled effect of gas diffusion, temperature and oxidation rate is studied, and the influence of water content on oxidation efficiency and capacity is quantified. The temporal variability of oxidation efficiency and capacity in landfill covers is illustrated by modelling a long-term field test. It is found that the CH4 removal rate can reach 40 g d−1 m−2 in the summers and drop to less than 10 g d−1 m−2 in the winters. A 3-D landfill cover cell with a cracked zone is applied to illustrate the spatial variability of oxidation, and a significant preferential flow can be observed when the cracked zone depth of a 1 m thick soil cover exceeds 0.8 m. The above studies demonstrate that the proposed model is able to predict temporal and spatial distributions of methane oxidation efficiency and capacity, and some results contribute to a better understanding of methane oxidation in landfill covers.

Study on mud discharge after emergency disconnection of deepwater drilling risers

Mud is often discharged into seawater after emergency disconnection of risers in offshore oil and gas drilling engineering. The discharged mud needs to be simulated accurately since it can produce a huge load on risers. Several mud discharge models have been proposed, such as Young's slug model, SFM model, WFC model and one-dimensional finite volume model. However, the mud is taken as a one-dimensional rigid body in existing mud discharge models. As a consequence, the radial velocity of mud, the mixing interface between mud and seawater, and mud discharge in complicated riser flow channels cannot be simulated. In this paper, a more accurate and applicable three-dimensional (3D) computational fluid dynamics (CFD) model is established to simulate the mud discharge process. The proposed method is demonstrated by its application to a case. It turns out that the actual mud discharge process can be simulated based on the 3D CFD model. Characteristics of the mud discharge including the radial velocity, axial velocity and the interface between two fluids are calculated based on the 3D CFD model, which improves the understanding of the mud discharge. Besides, the applicability of each mud discharge model is determined through model comparison. The influence of key factors including drill pipes with pipe joints, riser inner diameter, mud density and mud dynamic viscosity on the mud discharge is also analyzed based on the 3D CFD model.

Thermal performances of porous snow by a hydronic heating system at different weather conditions

The snow on the road in the cold regions is easy to cause slippery conditions, which are dangerous for vehicles and people. To remove the slippery conditions, the hydronic snow melting system has been applied to remove the snow on the road. This study proposed a transient finite volume model with snow porous characteristics, to analyze the snow melting performances by a hydronic heating system. Three primary environmental parameters (snow thickness, wind velocity, and air temperature) were selected to compare the average road surface temperature and snow melting ratio. Then, the snow melting performances using a hydronic road heating system were analyzed. The results showed that the snow melting ratio was rapidly dropped as the snow thickness was increased from 10 to 90 mm. The snow thickness had a slight influence on the average road surface temperature in the melting process, whereas it had a significant impact after the snow was completely cleared. When the wind velocity was increased to 5 m s−1, the critical melting ratio appeared at around 0.7. The wind velocity had a significant influence on average road surface temperature when the average road surface temperature increased more than 273.15 K. There is a critical air temperature existed between 263.15 and 258.15 K, which limits the snow melting process at current supplied fluid temperature (313.15 K), indicating that more energy was need to supply to overcome cold weather. This study offers a good reference for the design of a hydronic snow melting system in severely cold regions.

Thermal performance analysis of a new structured-core translucent vacuum insulation panel in comparison to vacuum glazing: Experimental and theoretically validated analyses

The notion at which, nowadays, building sector is being recognized to be nearly zero-energy buildings (NZEBs) relies partly on the thermal performance of its fabric insulation. Vacuum glazing (VG) technology attracted the research interest as an option to reduce heat loss through windows. However, the total glazing thermal transmittance (U-value) for VG increases with the use of smaller glazing area due to the edge-seal effects, due to the thermal short-circuit around the edges and the overall construction cost of VG leading to an unaffordable option to deal with energy conservation of buildings. Therefore, this study aims to propose a new structured core transparent vacuum insulation panel (TVIP) to accomplish insulation for the windows without edge sealing effect, with lower cost and can be easily retrofitted to the conventional windows of the existing buildings. To do this, VG and TVIP were constructed and their thermal conductivity were measured using heat flow meter apparatus. In addition, a 3D finite volume model considering the effect of surface to surface radiation, gas conduction, and thermal bridges through the spacer material and sealing material is developed. The model is validated with the experiments in this work and with the data for VG in the literature. The effect of vacuum pressure increase is simulated to mimic the vacuum deterioration problem and the effect of glazing size on the insulation performance of both VG and TVIP were investigated. The results indicate that for a smaller glazing area of less than 30 cm × 30 cm, the TVIP accomplished lower U-value compared with the VG at vacuum pressure of 0.1 Pa and 1 Pa. While, at a vacuum pressure of 10 Pa, the TVIP attained a lower U-value over the entire range of the investigated glazing sizes. Further, the edge-seal effect in the VG is diminished with the use of TVIP. Furthermore, the material cost per unit area of the TVIP is three times less than the cost of VG at laboratory scale. The results of the current study can guide vacuum window designers and researchers to further enhance the performance of TVIP based window to compete for the VG in the markets.

Computationally efficient optimization of wavy surface roughness in cooling channels using simulated annealing

This article reports a computationally efficient optimization for wavy surface roughness in cooling channels based on simulated annealing. Our approach rapidly calculates the performance metrics of cooling channels using closed-form models and approximates an optimum design via a random optimization technique, simulated annealing. The proposed method optimizes the wall roughness of cooling channels for maximizing the heat transfer rate while satisfying the pressure drop constraint. The channel wall smoothly converges and diverges throughout to locally modulate the heat transfer rate and the pressure drop. For a given pressure constraint and heat load distribution, the optimizer is able to compare more than 10,000 possible channel designs within a minute and generate a distinct channel design that achieves the optimization objective. The channel temperature predicted by the optimizer differs up to 10.9% to the estimations by a finite volume model. Lastly, optimized wavy channel designs are introduced that exhibit up to 2.7 times greater performance factor than a conventional channel geometry. This work demonstrates the potential of algorithm-based optimization techniques for designing efficient thermodynamic systems.

Numerical investigation on cooling performance of filter in a pyrotechnic gas generator

As a key part of the pyrotechnic gas generator, the filter not only removes the particulate matter but also cools the hot gas to a safe level. This paper aims to improve the understanding of the basic heat and flow phenomenon in the gas generator. The pyrotechnic gas generator is modelling by a simplified filter structure with fiber arrays. A finite-volume model of the heat and fluid flow is proposed to simulate the detailed multi-dimensional flow and energy conversion behaviors. Several verification results are in good agreement with data in different references. Simulation results demonstrate that the filter can not only absorb heat from the gas but also cause the high intensity enhancement of the heat transfer. The performance difference between inline and staggered arrays is also discussed. The findings of the study put a further prediction tool for the understanding and design of the filter system with fibers.

NUMERICAL SIMULATION OF DRILLING FLUID BEHAVIOR IN DIFFERENT DEPTHS OF AN OIL WELL

When drilling an oil well, a viscous fluid is injected to aid drilling. This fluid is also responsible for removing the cuttings and maintaining structural stability of well. The rheology of this drilling fluid has a direct influence on the cleaning of the well, on the dynamics of the fluid in pipe and annular areas. Linear mathematical extrapolations for high pressure and high temperature environments can lead to rheology errors up to 75%. In this study, a finite volume model was developed to simulate the flow of a water-based mud in annular and jetting environments in the drilling environment. Annulars were made by steel pipes and permeable formations. The fluids evaluated were developed empirically with xanthan gum and bentonite clay. The numerical results are consistent with literature and represent characteristics of a Yield Power Law fluid and a Bingham plastic. A comparison was made with water, allowing a correlation between rheological effects and fluid dynamics in annular and high vorticity regions.