low-Reynolds Turbulence Model Research Articles

Numerical investigation on the effects of non-uniform azimuthal heating in natural convection airflow within a vertical tube

Airflows established by buoyancy forces within vertical tubes with circular cross-section are analyzed. Obtained (finite-volume) numerical results cover the complete laminar-turbulent range (modified Rayleigh number from 10−3 to 109), through a low-Reynolds turbulence model. Both uniform and non-uniform heating conditions are regarded. Three different types of non-uniform heating along the azimuthal direction are considered, which constitutes an advance in the knowledge of the flow behavior, since it has not sufficiently addressed in the literature. Specifically, two modes of continuous non-uniform heating are proposed (temperature fixed at wall, and heat flux fixed at wall), and another mode through discrete heaters (for heat flux condition). The circumstances under which non-uniform azimuthal heating can be beneficial or detrimental with respect to thermal and dynamic performance are investigated. It is encountered that disrupting effect of discrete heat sources can induce, under given conditions, an improvement in the thermohydraulic performance.

Enhancing the Performance of a Rooftop Solar Chimney Through Flow Disturbers

Abstract Enhancing the performance of passive solar chimneys constitutes a key point for successful applications in bioclimatic architecture. Present work assesses applications of several kinds of flow disturbers in a rooftop solar chimney, under isoflux heating and windless conditions, and including surface radiative effects. Systematic numerical calculations are conducted aiming a comprehensive analysis, by means of a low-Reynolds turbulence model, being the range of Rayleigh number considered 2.170 × 1012 − 2.170 × 1013. Effect of different geometrical parameters is analyzed, although main attention is posed on the influence of disturbers elements on the thermohydraulic behavior of the established airflow, for obtaining best performance conditions. Some obstacles cause a clear decrease in the efficiency of the system, but given disturbers appropriately located produce valuable enhancements in the thermal or dynamic efficiency. Insertion of intermediate plates proves to be the best option, achieving maximum increases of even approximately 50% in the ventilation capacity.

Evaluation of novel wall function approach for supersonic flow problems involving separations induced by geometry and shocks

Supersonic combustion ramjet engine involves complex flow physics including shock-turbulent boundary layer interaction (STBLI) and shock-induced separations. The general approach while using an averaged Navier-Stokes equations to capture these flow separation, due to the flow physics and/or geometry accurately, is to use a low-Reynolds turbulence model. This requires the placement of first grid point in the viscous sublayer ( y + ≃ 1 ), which implies a need of finer mesh near the wall leading to an overall increase in number of cells in the computational domain and thus an increase in overall computational time. The wall-function method is a substitute to this approach which allows for the use of a coarser mesh in the region near to the wall. However, the standard wall-function methods are generally not very successful in capturing flow separations. In this work, we have employed a generalized wall function approach which incorporates the effect of both pressure gradient and compressibility in its formulation and have evaluated its performance for complex supersonic flow cases involving shock-turbulence boundary layer interactions (STBLI) and shock induced separations, which have not been done previously. We have shown that this method captures the flow physics accurately even with much coarser meshes near the wall. Further, insensitivity of the method to the placement of first grid point has also been demonstrated.

Numerical simulation of the transient turbulent natural convection in an inclined rectangular shaped solar air heater

Due to high energy demand and adverse effect of global warming, improving the performance of solar thermal systems is of great importance. In this respect, the transient flow and thermal behavior of turbulent naturally ventilated airflow in a flat plate solar air heater (SAH) are investigated numerically. To achieve this aim, conservation of mass, momentum, and energy equations are solved for the turbulent airflow concurrently with the conduction equation inside the solid element using finite element method (FEM). The low Reynolds turbulence model is applied in the calculation of turbulent stress and heat flux, and the Boussinesq approximation is applied for computing buoyancy forces associated with the density gradient. The surface radiation is also considered explicitly in the calculations to obtain more accurate and reliable results. It is found that although based on the considered location the maximum incident radiation occurs at the optimum angle of 30°, the maximum flow rate reach to its peak when the inclination angle is 60°, in which the total increase of incident radiation is nearly 17%. It is also found that the rate of heat transfer is a decreasing function of the inclination angle (30⩽θ⩽90), such that the overall rate of heat transfer reduction is around 50%. Further, investigation of the impacts of solar radiation and air duct width on thermal performance showed that by increasing both parameter the rate of heat transfer and air flow increase by about 35% and 100% respectively. The exclusive analysis of the effects of sudden climate change on the SAH’s behavior revealed that a short time climate change leads to zero incident radiation, and considerable fluctuations in outlet temperature and flow rate.

Computational analyses of heat flux of wall Y+ in supercritical fluid using star – Ccm+ Cfd code

Theoretical modeling techniques on resolving turbulent heat flows in a nondimensionalcircular tube mounted obstacle using the wall Y+ as guidance in selecting the appropriate grid configuration and corresponding turbulence models are investigated using CFD Code. The results obtained shows that the heat fluxes of 20, 23, 30 and 40 kW/m2, increases as the Y+wall profile moves away from the near – wall region, this is due to the effect of viscosity, buoyance, acceleration and the friction of the turbulence modification.The results also indicates that the low Y+wall treatment is suitable only for low Reynolds turbulence models in which it is assumed that the viscous sub-layer is properly resolved. The simulated results obtained in this research are in good agreements with the experimental results in the literature,even though they over predicted the observed heat transfer deterioration both quantitatively and qualitatively.
 Keywords: Wall Y+ , Turbulence, Supercritical fluid, Heat flux

Повышение качества проектных расчетов вязкого потока в малорасходных ступенях центробежного компрессора методами вычислительной газодинамики за счет обоснованного применения различных моделей турбулентности

The paper considers the issue of improving the quality of the numerical experiment in the calculation of viscous gas in the flowing part of a low-flow centrifugal compressor stage. The choice of turbulence model in creating a calculation model for calculations by methods of computational fluid dynamics is substantiated. As object of research is chosen low-flow stage with conditional flow coefficient Ф=0,008 and relative width at impeller outlet b2 /D2 =0,0133. The issue of qualitative modeling of friction losses in low-flow stages is of fundamental importance and is directly related to the choice of turbulence model. It is shown that the choice of low-Reynolds turbulence models in the case of unloaded and discontinuous low-flow stages can be made from the main common models (SpalartAllmaras, SST, k-ω) based on the economy of calculations, speed of convergence, solution stability and adequacy of the obtained results. For models with wall functions, the quality of the mesh model and the observance of the dimensionless distance to the wall y+ throughout the calculation domain are particularly important. For highReynolds turbulence models, at values of y+=25...50 on all friction surfaces of the computational domain in the optimal mode of operation, the grid independence of the solution for the entire gas-dynamic characteristic is ensured. It is unacceptable for y+ to fall into the transition region of 4...15 between the viscous sublayer and the region of the logarithmic velocity profile

Assessment and Evaluation of the Thermal Performance of Various Working Fluids in Parabolic Trough Collectors of Solar Thermal Power Plants under Non-Uniform Heat Flux Distribution Conditions

Changing the heat transfer fluid (HTF) is a viable approach to study the corresponding effect on the thermal and hydraulic performances of parabolic trough collectors (PTC). Three categorized-types of pure fluids are used in this study; water, Therminol® VP-1 and molten salt. The parametric comparison between pure fluids is also studied considering the effect of various inlet fluid temperatures and different Reynolds ( R e ) numbers on the thermal performance. Two low-Reynolds turbulence models are used; Launder and Sharma (LS) k-epsilon and Shear Stress Transport (SST) k-omega models. In order to assess the performance of each fluid, a number of parameters are analyzed including average Nusselt ( N u ) number, specific pressure drop distributions, thermal losses, thermal stresses and overall thermal efficiency of the PTC system. Results confirmed that changing the working fluid in the PTC enhances the overall heat transfer thereby improving thermal efficiency. For a temperature-range of (320–500) K, the Therminol® VP-1 performed better than water, resulting in higher N u numbers, lower thermal stresses and higher thermal efficiencies. On the other hand, for the common temperature-range, both Therminol® VP-1 and molten salt preformed more or less the same with Therminol® VP-1 case depicting lower thermal stresses. The molten salt is thus the best choice for high operating temperatures (up to 873 K) as it does not depict any significant reduction in the overall thermal efficiency at high temperatures; this leads to a better performance for the Rankine cycle. For the highest tested Reynolds number for an inlet fluid temperature of 320 K, a comparison of heat transfer performance (Nusselt number) and the overall thermal efficiency between Therminol® VP-1 and water showed that Therminol® VP-1 is the best candidate, whereas the molten salt is the best choice for a higher inlet temperature of 600 K. For example, at an inlet temperature of 320 K, the Nusselt number and overall thermal efficiency of therminol VP-1 were 910 and 49% respectively as opposed to 443 and 38% for water. On the other hand, at the higher inlet temperature of 600 K, these two parameters (Nusselt number and overall thermal efficiency) were recorded as 614 and 41 % for molten salt and 500 and 39 % for Therminol® VP-1.

Numerical analysis on flow and heat transfer of supercritical CO<sub>2</sub> in horizontal tube

In the present study, the three-dimensional steady-state numerical simulation has been performed by using ANSYS Fluent15.0 with SST <i>k-ω</i> low Reynolds turbulence model to study flow and heat transfer characteristics for supercritical CO<sub>2</sub> in the horizontal straight tube with inner diameter <i>d</i><sub>i</sub> = 22.14 mm and heating length <i>L</i><sub>h</sub> = 2440 mm under heating condition. The reliability and accuracy of the numerical model was verified by the experimental data of flow and heat transfer of supercritical CO<sub>2</sub> in horizontal tube. Firstly, flow and heat transfer characteristics of supercritical CO<sub>2</sub> was studied in horizontal tube. Based on the assumption that the supercritical CO<sub>2</sub> will undergoes “phase transition” between liquid-like and vapor-like at pseudocritical temperature <i>T</i><sub>pc</sub>, the differences between top generatrix and bottom generatrix of horizontal tube at flow and heat transfer behaviors were revealed. The results show flow and heat transfer characteristics of supercritical CO<sub>2</sub> in horizontal tube are similar to those under subcritical pressure. Then, the influences of heat flux <i>q</i><sub>w</sub> and mass flux <i>G</i> on flow and heat transfer of supercritical CO<sub>2</sub> were analyzed. The higher heat flux <i>q</i><sub>w</sub> is or the smaller mass flux <i>G</i> is, the higher inner wall temperature <i>T</i><sub>w,i</sub> at top generatrix is. The reasons for difference in the distribution of inner wall temperature <i>T</i><sub>w,i</sub> at top generatrix under different heat flux <i>q</i><sub>w</sub> and mass flux <i>G</i> were explained by capturing detailed information about thermophysical properties distribution including specific heat at constant pressure <i>c</i><sub>p</sub> and thermal conductivity <i>λ</i>, axial velocity distribution and turbulent kinetic energy distribution in the fluid domain. It is observed that vapor-like film thickness <i>δ</i>, vapor-like film property characterized by specific heat at constant pressure <i>c</i><sub>p</sub> and thermal conductivity <i>λ</i>, axial velocity <i>u</i> and turbulent kinetic energy <i>k</i> are the main factors affecting the difference in inner wall temperature distribution at top generatrix. The present work can provide a theoretical guidance for design and safe operation of heat exchanger for supercritical CO<sub>2</sub> Brayton cycle.

Numerical study of a laminar hydrogen diffusion flame based on the non-premixed finite-rate chemistry model; thermal NOx assessment

The present study examines thermal NOx formation on a laminar hydrogen diffusion flame based on a patented multi-flame diffusion burner installed in a domestic boiler. The analysis is performed through CFD modeling by means of ANSYS-FLUENT 19.0. Detailed chemical, thermal, and transport parameters are implemented, in order to obtain accurate results using finite-rate chemistry together with laminar and low-Reynolds turbulence models. The Damköhler number is calculated using a Matlab code developed in-house. The chemical kinetics of the thermal NOx route are analyzed for several inlet flame power levels, so as to demonstrate the effectiveness of the flame-splitting method at reducing the formation of thermal NOx. The numerical results are contrasted through measurements from literature for validation purposes. In the present work, the flame power is varied from 0.05 kW up to 0.8 kW. In contrast to turbulent non-premixed hydrogen flames, the numerical results provide a quasi-constant trend in thermal NOx formation at higher power levels (0.4–0.8 kW). The heat exchange rate between the flame and the combustion chamber and its influence on thermal NOx formation are all carefully analyzed.

Plasma-based flow control for low-pressure turbines at low-Reynolds-number

Purpose Reynolds number in small-size low-pressure turbines (LPT) can drop below 2.5 · 104 at high altitude cruise, which in turn can lead to laminar boundary layer separation on the suction surface of the blades. The purpose of this paper is to investigate the potential of an alternate current (AC)-driven Single Dielectric Barrier Discharge Plasma Actuator (AC-SDBDPA) for boundary layer control on the suction side of a LPT blade, operating at a Reynolds number of 2 · 104.Design/methodology/approach Experimental and numerical analyses were conducted. The experimental approach comprised the actuator testing over a curved plate with a shape designed to reproduce the suction surface of a LPT blade. A closed loop wind tunnel was employed. Sinusoidal voltage excitation was tested. Planar velocity measurements were performed by laser Doppler velocimetry (LDV) and particle image velocimetry (PIV). The device electrical power dissipation was also calculated. Computational fluid dynamics (CFD) simulations using OpenFOAM© were conducted, modelling the actuator effect as a body force calculated by the dual potential algebraic model. Unsteady RANS (Reynolds Averaged Navier-Stokes equations), also known as URANS approach, with the k-ε Lam-Bremhorst Low-Reynolds turbulence model was used.Findings The AC-SDBDPA operation brought to a reduction of the separation region; in particular, the boundary layer thickness and the negative velocity values decreased substantially. Moreover, the flow angle in both the main flow and in the boundary layer was reduced by the plasma control effect. The actuation brought to a reduction of the 17 per cent in the total pressure loss coefficient. The pressure coefficient and skin friction coefficient distributions indicated that under actuation the reattacnment point was displaced upstream, meaning that the flow separation was effectively controlled by the plasma actuation. Adopting slightly higher actuation parameters could bring to a full reattachment of the flow.Practical implications The work underlines the potentialities of an AC-SDBDPA to control separation in LPTs of aeroengines.Originality/value The present work sets a methodological framework, in which the validated procedure to obtain the body force model combined with CFD simulations can be used to study a configuration with multiple actuators allocated in array without requiring further experiments.

Radiation Effects on Turbulent Mixed Convection in an Asymmetrically Heated Vertical Channel

ABSTRACTThe purpose of present study is to numerically investigate the radiation effects on turbulent mixed convection flow between two differentially heated vertical parallel plates. Two flow situations known as aiding and opposing flow are considered. Frictional Reynolds number and Grashof number are assumed to be 150 and 1.6 × 106, respectively. Both hydrodynamically and thermally developing and fully developed regions in the channel are investigated. Three Reynolds-averaged Navier–Stokes-based low Reynolds turbulence models are evaluated and the model with better overall performance is applied to the simulations. The radiative transfer equation for the gray and participating fluid is solved using the discrete-ordinates method, adopting its eighth-order quadrature scheme. The effects of two radiative parameters, namely, wall emissivity and optical thickness, on the flow and thermal fields, Nusselt number, and friction factor are addressed. Present results indicate that the presence of thermal radiation has a significant influence on flow and thermal fields. With an increase in wall emissivity and optical thickness, influence of radiation on the mean velocity, mean temperature, and turbulence kinetic energy profiles grows in both aiding and opposing regions. This results in an increase in bulk temperature, centerline velocity, and Nusselt number and a decrease in friction factor on both sides.

Analysis of transitional flow in 3D geometries using a novel phenomenological model

A new phenomenological turbulence transition model is proposed. The model is based on the calculation of the pre-transitional u′v′‾ due to mean flow shear. This is used for analysis on the complex flow patterns over three-dimensional geometries. The tested 3D cases are the 6:1 prolate-spheroid under three flow conditions and the transonic DLR-F5 wing test case. The obtained results are compared with the low-Reynolds turbulence model of Spalart–Allmaras and the empirical transition model, γ-Reθ. These show that the developed transition model is able to capture the flow turbulence transition features experimentally recorded.

A methodology for including wall roughness effects in k-ɛ low-Reynolds turbulence models - Part I and Part II: Part I. Basis of the methodology

A model accounting for wall roughness effects in k-ɛ low-Reynolds turbulence models is described in the present paper. In particular, the introduction in the transport equations of k and ɛ of additional source terms related to roughness, based on simple assumptions and dimensional relationships, is proposed. An objective of the present paper, in addition to obtaining more realistic predictions of wall friction, is the application of the proposed model to the study of heat transfer to supercritical fluids.A first validation of the model is reported. The model shows the capability of predicting, at least qualitatively, some of the most important trends observed when dealing with rough pipes in very different flow conditions. Qualitative comparisons with some DNS data available in literature are also performed. Further analyses provided promising results concerning the ability of the model in reproducing the trend of friction factor when varying the flow conditions, though improvements are necessary for achieving better quantitative accuracy.First applications of the model in simulating heat transfer to supercritical fluids are also described, showing the capability of the model to affect the predictions of these heat transfer phenomena, in particular in the vicinity of the pseudo-critical conditions. A more extended application of the model to relevant deteriorated heat transfer conditions will clarify the usefulness of this modelling methodology in improving predictions of these difficult phenomena. Whatever the possible success in this particular application that motivated its development, this approach suggests a general methodology for accounting for wall roughness effects in low-Reynolds number turbulence models.

Low Reynolds turbulence model CFD simulation for complex electronic system: an industrial point of view

In electronic systems the presence of bluff bodies, sharp corners and bends are the cause of flow separation and large recirculation bubbles. Since the recirculation vortices develop they encapsulate the heat from an electronic component becoming one of the major contributors of malfunction. Going in depth in this, some numerical simulations of conjugate heat transfer for a heat wall-mounted cube have been performed using the commercial CFD code scSTREAM V11 by Software Cradle Co, Ltd. It is well known that the reliability of CFD analysis depends heavily on the turbulent model employed together with the wall functions implemented. The three low- Reynolds k – ϵ turbulent models developed by Abe-Nagano-Kondoh have been validated against experimental data consisting mainly of velocity profiles and surface temperature distributions provided in literature. The performed validation shows a satisfactory agreement between the measured and simulated data. The turbulent model chosen is then used for the CFD simulation of a complex electronic system.

Evaluation of Low Reynolds Number Turbulence Models for an Open-Channel Flow over a Rough Bed Using LES Data

There are quite a few studies investigating low Reynolds number turbulence models for predicting the near-wall flow over smooth walls. However, analogous work over rough walls is sparse despite the fact that many flows of practical interest, particularly in geophysical flows and hydraulic engineering, are over rough walls. This paper presents a priori and a posteriori evaluations of low Reynolds number Reynolds-averaged Navier-Stokes (RANS)–based modeling approaches for flows over rough walls with the help of high-resolution large-eddy simulation (LES) data. The LES data allow the calculation of the vertical distribution of the turbulent kinetic energy, the dissipation rate, the specific dissipation rate, and the turbulent eddy viscosity, so that the assumptions inherent of RANS-based turbulence models can be tested a priori. A posteriori testing of the models through RANS simulations showed that the three low Reynolds turbulence models evaluated in this paper provide a fairly accurate prediction of the velocity profile, turbulent eddy viscosity, and wall shear stress.

Prediction of Turbulent Convective Heat Transfer to Supercritical CH4/N2 in a Vertical Circular Tube

Cooling of supercritical CH4/N2 mixture is the most important heat transfer process during coalbed methane (CBM) liquefaction. In this paper, numerical studies of the turbulent convective heat transfer of supercritical CH4/N2 flowing inside a vertical circular tube have been conducted with Lam–Bremhorst low Reynolds turbulence model. The present numerical investigations focus on the effects of the nitrogen content, heat flux, and flow orientation. Results indicate that as nitrogen content increases, the maximum heat transfer coefficient gradually decreases and corresponds to lower temperature. Heat transfer coefficient is slightly affected by heat flux in the liquid-like region and increases with increasing heat flux in the gas-like region. Buoyancy effect gradually increases with decreasing bulk temperature, and reaches its maximum at the pseudo-critical point, and then drops as bulk temperature further decreases. It is significant in the liquid-like region and negligible in the gas-like region. At the same time, buoyancy effect enhances heat transfer in the upward flow and impairs it in the downward flow.

Validation of a CFD model for hydraulic seals

Optimization of seal geometries can reduce significantly the energetic losses in a hydraulic seal [1], especially for high head runner turbine. In the optimization process, a reliable prediction of the losses is needed and CFD is often used. This paper presents numerical experiments to determine an adequate CFD model for straight, labyrinth and stepped hydraulic seals used in Francis runners. The computation is performed with a finite volume commercial CFD code with a RANS low Reynolds turbulence model. As numerical computations in small radial clearances of hydraulic seals are not often encountered in the literature, the numerical results are validated with experimental data on straight seals and labyrinth seals. As the validation is satisfactory enough, geometrical optimization of hydraulic seals using CFD will be studied in future works.

Numerical prediction of wall-bounded flows with low-Reynolds k − ε turbulence models

In this paper, we present a numerical model for the simulation of turbulent flows. The numerics rely on a three-dimensional upwind compressible solver which applies to tetrahedrisations. The accuracy in boundary layers is increased by a new type of tetrahedrisation. The Reynolds-Averaged Navier-Stokes (RANS) equations are solved by using a mixed finite element-volume method for spatial discretisation. The linear low-Reynolds turbulence models of Goldberg et al., and a nonlinear extension, are implemented with this numerical technique. The computational results of both turbulent channel flow and a backward-facing step flow are compared to experimental data.

Simulating drag reduction phenomenon in turbulent pipe flows

Drag reduction using polymeric additives is an interesting phenomenon in turbulent pipe flows which was first discovered by Toms [Toms, B.A., 1948. Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proc. First Int. Cong. Rheol. 2, 135–141]. Due to its industrial importance, the phenomenon has been the subject of much study in the past, in both theoretical and experimental domains alike. As to the mechanisms involved, it has been argued that polymeric additives act through affecting the structure of turbulent bursts near the wall by boosting the extensional viscosity of the base fluid (see [Lumley, J.L., Blossey, P., 1998. Control of turbulence. Ann. Rev. Fluid Mech. 30, 311–327]). In practice, drag reduction as large as 90% has been achieved with concentration as low as 20 ppm of certain high-molecular-weight flexible polymers. Prediction of such huge drag reductions obtained using polymeric additives has not been possible in the past partly, because of the limitations of the computational facilities and also because of the inadequacies of the constitutive equations used for the simulations. Recently, Pinho [Pinho, F.T., 2003. A GNF framework for turbulent flow models of drag reducing fluids and proposal for a k– ε type closure. J. Non-Newtonian Fluid Mech. 114, 149–184] modified the generalized Newtonian fluid (GNF) model in such a way that it could take into account the extensional viscosity (a measure of the elastic behavior of a fluid) in addition to the shear viscosity (a measure of the viscous behavior of a fluid). Based on this idea, Pinho (2003) derived the first time-averaged turbulent flow formulations for viscoelastic fluids. These formulations were used by Cruz and Pinho [Cruz, D.O.A., Pinho, F.T., 2003. Turbulent pipe flow predictions with a low-Reynolds number k– ε model for drag reducing fluids. J. Non-Newtonian Fluid Mech. 114, 109–148] and Cruz et al. [Cruz, D.O.A., Pinho, F.T., Resende, P.R., 2004. Modeling the new stress for improved drag reduction predictions of viscoelastic pipe flow. J. Non-Newtonian Fluid Mech. 121, 127–141] by embedding the low-Reynolds turbulence model of Nagano–Hishida [Nagano, Y., Hishida, M., 1987. Improved form of the k– ε model for wall turbulent shear flows. J. Fluid Eng. 109–156]. They performed several simulations using this well-known turbulence model and showed that it can well predict the large drag reduction observed in practice for some polymeric additives. But for certain other polymers the prediction were found not to be so great. In this work, it will be shown that better predictions can be obtained for these polymers if use is made of another low-Reynolds number k– ε turbulence model called Launder–Sharma model [Launder, B.E., Sharma, B.I., 1974. Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfer 1, 131–138] for the simulations.

B212 環状流路反転部における流動挙動の数値的可視化

Flow visualization in a target for the accelerator driven system was analyzed numerically to obtain the fundamental flow characteristics under annular channel geometry with a reverse section. The analytical geometry simply simulates the experimental condition. The three-dimensional numerical computations were carried out using the SCRYU/Tetra code and the nonlinear low Reynolds turbulence model. Two kinds of channel end geometries were provided as a numerical parameter. From the present numerical study, the following conclusions were derived: an effect of the channel end geometry to the fluid flow behavior was clarified; and, detailed flow configurations inside the annular channel with a reverse section were predicted quantitatively.