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Experimental investigations have been carried out on opposing mixed convective flows of water induced around a horizontal rectangular cylinder in the range of the Reynolds and modified Rayleigh numbers, ReD =500-3000 and RaD*=7x107-1010. The flow and temperature fields around the cylinder were first visualized with dye and liquid crystal thermometry. The results showed that longitudinal vortices of which axes parallel to the flow direction appear over the upper surface of the cylinder when the buoyancy force beyond critical. The flow along the upper surface, then, separates at the edges of the cylinder. Thus, the side and bottom surfaces of the cylinder are covered by separation bubbles and wake. The local and overall heat transfer coefficients from the cylinder were subsequently measured. The coefficients from the upper and side surfaces showed marked increase with the buoyancy force. This yields higher overall Nusselt numbers than those of the forced convections. It was also found that the non-dimensional parameter (GrD*/ReD2.5) well correlates the present overall Nusselt numbers.

The aim of this study is to investigate on the flow behavior in the wake behind a circular cylinder by induced jet using dielectric barrier discharge (DBD) plasma. The plasma was created using a wave form with bipolar voltage of 4 kVpp and frequency of 10 kHz, and the plasma actuators were mounted on the circular cylinder. The forward and backward jets for the main flow direction were induced by electrode arrangements of the plasma actuators. The flow field was visualized using a high-speed video camera, and the streamwise and vertical velocities ware calculated by dynamics PIV method at Reynolds number of 1.0×103. We discussed that the vortex motion around the cylinder, Reynolds stress profiles and the half width of wakes by the forward and backward jets. Also, the characteristic frequency of vortex shedding was confirmed from the continuous photographs.

To clarify the mechanism of observed violent vibration of a brace adjacent to a high circular stack, an experimental study was performed. The experimental apparatus consists of a vertical elastic rod placed close to a large solid cylinder. Accordingly, airflow makes the rod whirl at its first natural angular frequency. Whirling motion grows as airflow velocity increases. Whirling direction depends on the relative location to the cylinder and not on airflow velocity. Further, analytical study was done by assuming the flow past cylinder is frictionless, irrotational and incompressible. Analytical results show fairly good agreement with experimental ones as well as the actual brace vibration.

The wake oscillation of a circular cylinder, which is placed near a rigid plane boundary, with tangential blowing from a surface slot is investigated experimentally under the condition of Re=2.7 ×104. The time-mean surface pressure measurements on the circular cylinder, flow visualizations and velocity fluctuation measurements were carried out for various momentum coefficient Cμ and clearances between the circular cylinder and the rigid plane boundary changed. Based on these experiments it is found that periodic velocity fluctuation, which is associated with vortex shedding (Karman vortices), is suppressed by the tangential blowing. However, in the case of the cylinder placed near the rigid plane boundary, the reverse flow occurs in the clearance between the cylinder and the boundary, in particular Cμ increases. The level of flow unsteadiness naturally increases. Moreover, velocity fluctuation measurements revealed that the velocity fluctuation classified into two cases, one being the velocity fluctuation occurring Periodically (H/D>0.1) and the other occurring non-periodically (H/D=0.1).

The flow around a circular cylinder is a traditional problem of fluid dynamics, knowledge of which is essential for basic understanding as well as for technical applications, such as large buildings, bridges, standpipes, heat exchanger tubes, rods, transport pipelines, poles and cables, all of which attracted widespread attention. A circular cylinder usually experiences boundary layer separation. In certain Reynolds number range, a periodic flow motion develops in the wake as a result of boundary layer vortices being shed alternatively from either side of the cylinder leading to unwanted structural vibrations. In order to calculate the cylinder response to the flow, a computational method to solve the flow around the body and its resultant vibration using Fluent® is previously developed and validated. The present study details the extension and verification using the same method by incorporating flow turbulence through its modeling. The incoming free stream flow is uniform with Reynolds number based on diameter of 3.8 and 12.7mm. Results for the unsteady shedding flow behind a circular cylinder and its vibration are presented with experimental comparisons, along with a comparison of two-dimensional laminar as well as turbulent models of the flow for fully coupled interaction. The Strouhal number and structural displacements are in good comparison with the experimental data of [2] showing the capability of FSI method using Fluent® to tackle laminar as well as turbulent flows.

In this study, a numerical experiment of flow around a self-oscillating circular cylinder with whirling limitation was performed using the boundary element method combined with the vortex method. The flow feature of vortex shedding and the characteristics of vibration due to the fluid force were simulated about various initial setting position of circular cylinder at the Reynolds number Re=1×105, the mass ratio M=5.15, the damping factor C=0.0 and the reduced velocities Vr=1.8 and Vr=2.4. As a result of calculation, in the case of coaxial setting, the flow feature and the characteristics of cylinder vibration due to the fluid force were as same as a result of self-oscillating case, however, in the case of not coaxial setting, the frequency of cylinder's motion was changed and the flow features were changed from the twin type vortex shedding pattern to the Karman type vortex shedding pattern. It was shown that the characteristic of cylinder vibration frequency depended on both of the distance and the direction between the circular cylinder and the wall of pit.

The flow around a circular cylinder, which is placed near a rigid plane boundary, with tangential blowing is investigated experimentally under the condition of Re=2.7×104. The time-mean surface pressure measurements on the circular cylinder and flow visualizations were carried out for various momentum coefficient Cμ and clearances between the circular cylinder and the rigid plane boundary. The fluid force on the circular cylinder was calculated from these surface pressure distributions. The results of experiment show that the lift reaches the maximum value at certain Cμ and then starts decreasing, and this tendency has never been observed for the cylinder placed in the open flow field. It is considered that the phenomenon is attributed to change in the flow pattern around the circular cylinder, more specifically, due to the occurrence of reverse flow in the gap. In addition, the characteristics of the lift forces can be represented by newly defined nominal jet coefficient C'μ and nominal lift coefficient C'L.

Experiments have been performed for a turbulent channel flow obstructed with a triangular cylinder. Two kinds of triangular cylinders with different front edge angle are used. Three clearances between the wall and the triangular cylinder of 1, 2 and 5 mm are tested. The local heat transfer coefficient, the wall static pressure and the wall shear stress are measured. The particle image velocimetry (PIV) has been applied to measure the fluid flow around the triangular cylinder. When the flow field is unsteady because of the existence of the periodically shed vortices, a phase-averaged measurement is carried out. When the clearance is small, the reattachment flow effectively enhances the heat transfer. On the other hand, at large clearance the heat transfer coefficient takes a high value in the location where a large periodic fluctuating motion appears.

Omnidirectional reductions in drag and fluctuating forces were achieved for a circular cylinder subjected to cross-flow by attaching cylindrical rings along its span at an interval of several diameters. The Reynolds number based on the cylinder diameter, d , ranged from Re d = 3000 to 38000 for the experiments. The aspect ratio of the cylinder, L / d , was approximately 20. The addition of the rings reduced the drag force for Re d ≥ 20000, even though the projected area increased. This was attributed to the formation of separation bubbles on both sides of the ring, which led to pressure recovery on the rear of the cylinder. The optimum ring configuration for drag reduction was found to be D / d = 1.3, W / d = 1.0, and P / d = 6 at Re d ≈ 30000, where D is the ring diameter, W is the spanwise width of the ring, and P is the spanwise pitch of the ring. This configuration reduced the drag force by 15%. In addition, the fluctuating lift, which was estimated from the fluctuating surface pressures, was weakened for all Reynolds numbers due to the suppression of vortex shedding.

Influence of adding cationic surfactant (Ethoquard O12) with a consentration of 50 ppm on water flow around a cylinder in a range of Reynolds number Res between from 64 to 600 was investigated by using LDV and PIV. At Res =300, the flow with the surfactant formed a stagnant zone, which appeared periodically, in front of the cylinder expanding along the axial direction. The period of the appearance was about 120 [s]. The periodic flow structure was visualized by the measurements of velocity fluctuation. The development of the stagnant zone in front of the cylinder induced the expansion of a low speed flow area near the side of the cylinder.

A gas-liquid two-phase flow through vertical sudden contraction pipe is an area that still little is known and has been studied experimentally, visually and numerically. In this study, the flow characteristics of vertical upward gas-liquid two-phase flow through a sudden contraction pipe are examined experimentally and numerically, and a new simple method of flow control to reduce the flow fluctuation and resistance is shown. When mounting a ring-shaped step before the contraction, vortex formation at the contraction was reduced. That is, the flow is suggested by mounting a ring-shaped small obstacle before the contraction to lead to stabilized flow and drag reduction. The effects of Reynolds number, volumetric flow rate ratio of air to water and the ring position were examined. Numerical analysis using an incompressible tow-fluid model was conducted in order to understand the flow pattern well.

The flow-induced vibration of a circular cylinder is simulated numerically. The finite element method is used to solve the three-dimensional incompressible Navier-Stokes equations, and the flow field is coupled with the cylinder motion. The oscillation of the cylinder in the in-line direction is shown when the reduced velocity, Ur, is smaller than 4.0. Symmetric vortices are seen for Ur≤2.5 and alternative vortices appear for Ur≥2.9, while the cylinder motion is damped at around Ur=2.6. It is found that the cross-flow oscillation of the cylinder is dominant under the alternative vortex condition. The drag and lift coefficients increase and the vortex field become finer both in space and time by the cross-flow oscillation.

To clarify the effect of flow orientation on the gas-liquid interfacial structure and frictional pressure gradient in a narrow rectangular channel, simultaneous measurements of pressure gradients and spatio-temporal characteristics of gas-liquid interface are conducted for three different flow orientations ; vertical upward flow (V flow), horizontal flow between horizontal plates (H-H flow) and horizontal flow between vertical plates (H-V flow). The velocity field in the liquid flow with interfacial waves is also measured by the PIV and LIF methods. The interfacial structure at low gas and low liquid flow rates is greatly affected by the flow orientation, and the complicated interfacial structure is observed in V flow. To predict the frictional pressure gradient, the wave model which takes account of the wall shear stress for the wave propagation and base film flow is presented. From the comparison of experimental results with predictions by the present model, it is found that the difference in the frictional pressure gradient between the three flow orientations is closely related to the characteristics of interfacial waves as well as the average liquid velocity.

In this study, the flow features of vortex shedding from a self-oscillating circular cylinder and the characteristics of fluid force were examined using a vortex method simulation combined with boundary layer calculation in a uniform flow at high Reynolds number in order to investigate validity and applicability to the analysis of the flow-induced vibration problems. The calculations were performed for the parameters of the mass ratio M (=1.78, 5.15), the damping factor C (=0.0, 0.0153) and the reduced velocity Vr (=1.38-4.13) at the Reynolds number Re=1×105 based on the uniform flow velocity U and the cylinder diameter D. As a result of the calculations, two typical patterns of vortex shedding were observed, one of which is symmetric twin vortex shedding and the other is antisymmetric twin vortex shedding. It was confirmed that the calculated flow patterns and the free-oscillation motions of the cylinder, were in reasonable agreement with experimental results. The relationship between the fluid force and the resultant cylinder's displacement was investigated.

In the flow around a circular cylinder, the sudden decrease in the drag force occurs at a high Reynolds number, but the same phenomenon occurs at a lower Reynolds number in the case where there exist grooves or roughness on the circular cylinder surface. In this paper, in order to make clear the flow characteristics around a circular cylinder with triangular grooves, drag coefficient, pressure distribution and Strouhal number were measured. Moreover the flow was analyzed by applying the RNG k-e turbulent model and the surface flow pattern was investigated using oil-film technique. Consequently, it is made clear that the reattachment point changes position in each groove and the drag coefficient of a circular cylinder with triangular grooves decreases compared with a circular cylinder with arc grooves.

The flow around a circular cylinder in surfactant solution was investigated in the Reynolds number range of 6000 to 50000 in several ways : by measuring the pressure around the cylinder, by visualizing flow and by measuring the velocity profiles in the wake. The test fluids were aqueous of the surfactant Oreyl-bishydroxyethyl-methyl-ammonium (trade name : Ethoquad O/12) with sodium salicylate added as a counterion. The pressure coefficient of surfactant solutions at the back of the cylinder was larger than that of tap water for Reynolds number above 6000. The separation point of surfactant solutions moves downstream, and the angle increases with surfactant concentration. The width of the velocity defect in the wake of surfactant solutions was less than that of tap water. For Reynolds number above 6000, a maximum drag reduction approximately 35% occurred with the surfactant solutions.

In this investigation, confined vortex shedding past a square cylinder with a planar jet is numerically studied. Flow and scalar-transport simulations are presented for various cases including both laminar and turbulent flow situations. It is shown that the ratio of jet velocity to uniform inlet velocity significantly affects the overall flow structures and thus scalar transport downstream of the cylinder. Especially, when the ratio is large enough, the jet penetrates the main vortices shed from the cylinder, resulting in significant changes in the flow and scalar fields. In the case of laminar flow, regions of intense scalar are formed along the streamlines from the jet exit, and the oscillation of the force on the cylinder eventually disappears as the jet velocity is close to the inlet velocity. Large Eddy Simulation of turbulent flow also reveals complex flow structures and intense mixing depending on the velocity ratio; regions of intense scalar coincide with those of high turbulence intensity. The results obtained exhibit fuel-air mixing characteristics observed in a planar combustor where the square cylinder plays the role of a flame-holder.

The in-line vibrations of an elastically supported circular cylinder subjected to cross flow were experimentally investigated, where velocity fluctuations in the cylinder wake were measured by two probes of a hot-wire anemometer symmetrically set up. Typical in-line vibrations were observed in two flow velocity ranges, one in the reduced flow velocity of 1.3-2.5, and the other in 2.5-3.5. In higher velocity range, out-of-phase velocity fluctuations were measured, which shows alternative vortex-shedding. In lower velocity range, in-phase velocity fluctuations were observed, which shows symmetrical vortex-shedding. Flow visualization confirmed the periodical formation and shedding of symmetrical vortices. It is concluded that the in-line vibration in low flow range is a kind of hard self-excited vibrations due to the interaction between the cylinder vibration and the symmetric vortex formation by the cylinder vibration itself.

This paper is the second report of the experimental study concerning the heat transfer in the separated flow behind a circular cylinder for Reynolds numbers from 120 to 30 000. In this report, unsteady and three-dimensional characteristics are described. Instantaneous temperature distribution and its fluctuating pattern on the cylinder surface were measured by an infrared camera. It was found that the pair of streamwise vortices formed in the near wake enhances the heat transfer around the rear stagnation of the cylinder. In particular, the streamwise vortices of 'mode-A', which is formed around Re = 200, effectively enhances the heat transfer around the rear stagnation. For 3 000

A standing wave with a peak line toward downstream appears on the surface of a liquid film flowing around a horizontal circular cylinder. The amplitude of the wave grows in the downward direction and finally a part of the wave separates from the film at certain position on the cylinder. A theoretical model was proposed to explain the physical mechanism of separation. The wave peak would separate when the resultant of the centrifugal force, gravitational force, surface tension and negative pressure acting on the wave root is not sufficient to supply the flow rate necessary to maintain the wave amplification. The points of separation on the cylinder were theoretically calculated from the above condition for three kinds of test liquids, i. e., water, ethanol and glycerin solutions. The results agree with those from experiments for various flow rates of the film flow.

A study was performed to characterize the behavior of the flow moving past an oscillating circular cylinder and the interactions between the flow velocity fluctuation and the cylinder oscillation. The oscillations of the cylinder had three distinct regions : two instability regions separated by a stability region. The flow velocity fluctuation was measured using built-in electromagnetic flow meters. The velocity data showed that the flow velocity fluctuations : a) had two frequency components in both the stability region and the second instability region ; the first dominant frequency matched the dominant frequency of the in-line oscillation and the second dominant frequency was induced by the alternate vortices. b) had phase estimations that : 1) indicated the effect of the alternate vortices on the cylinder gave different timings for the stability region and the second instability region. 2) confirmed the energy transfer between the flow and the cylinder occurred at the dominant frequency of the in-line cylinder oscillations. 3) indicated the flow velocity fluctuations induced by the alternate vortices were the antiphase at the opposite of the cylinder and 4) showed the flow velocity fluctuation at the dominant frequency of the in-line oscillation was stable for the two instability regions and unstable for the stability region.

This paper describes the results of an experimental study on characteristics of flow and fluid forces acting on two parallel circular cylinders. The Reynolds number was 5.5 × 104 on the bases of a single cylinder. For the spacing T/D

The surfactant used in this study is well known as an additive for drag reduction in straight (non-swirling) pipe flow. This paper deals with swirling flow characteristics of a surfactant solution. We investigated the effects of surfactant concentration and Reynolds number on flow characteristics. It is shown that the drag reducing effect is less than in straight pipe flow, and that the surfactant solution must be highly concentrated with great elasticity in order to produce a drag reduction. As the results of velocity measurement by LDV and wall pressure measurement in the axial direction, it is expected that the swirl intensity of the drag reducing swirling flow with a surfactant decays more quickly as the flow progresses downstream. And we propose that this mechanism helps create the drag reduction in swirling flow. For the velocity profiles of drag reducing swirling flow, only the forced-vortex type is observed in this experiment. This suggests that the velocity profiles of drag reducing swirling flow change more quickly to a forced-vortex type from a Rankin's combined vortex type. It is also reported that turbulence intensity of drag reducing swirling flow is smaller than turbulence intensity of a solvent.

In this paper, we describe the fluid force acting on a two-dimensional oscillating circular cylinder in a lock-in region. The experiment was carried out in an N. P. L blow-down wind tunnel with a working section of 500mm×500mm×2000mm and Reynolds number of 1.9×104. The cylinder was then forced to oscillate sinusoidally in the lift direction. The power spectrum of the fluctuating velocity in the wake behind the circular cylinder was measured to show the lock-in region in the present experiment. The time-mean pressure distribution and fluctuating pressure distribution on the circular cylinder were measured for the displacement in the oscillation. Consequently, it was found that the mean drag and fluctuating lift increase and become maximum in the lock-in region, while the base pressure at the rear surface (θ=180°) of the cylinder decreases and attains a minimum.

The Objective of the present study was to investigate the suppression of the fluid forces acting on a circular cylinder by passive control of the flow. The flow control was established by introducing a fine flat plate at the upstream of the circular cylinder. Measurements were carried out by varying the position and width of the flat plate. The time-averaged and fluctuating fluid forces, vortex shedding frequency and flow patterns were systematically examined. Furthermore, the controlled fluid forces and the behavior of the flow were discussed in detail. It was found that the maximum reduction of the time-averaged drag was 58%, and that of the fluctuating lift and drag was 61% and 46%, respectively, by using a 5 mm wide flat plate, which was considerably small compared to the circular cylinder diameter of 49 mm.

This paper treats transient low Reynolds number flows around (1) an impulsively started rotating circular cylinder and (2) an impulsively started and rotated circular cylinder. The main purpose of this paper is to discuss the difference between the two initial cases for large enough time and to know the asymptotic behavior of the transient flow to the steady flow as time to infinity. In the two-dimensional flow, the transient flow is determined uniquely by the initial condition, however, there are several initial flows, which are considered to approach the same steady flow as time to infinity. Thus, it is an interesting problem to know the asymptotic behaviors of the above mentioned two initial cases as time to infinity. The present paper shows that the convergence to the steady flow in the case (2) is, at most, of order of T-3/2 where T is the stretched time.

The flow around a rotating circular cylinder, which is placed near a moving plane wall, is investigated experimentally for high Reynolds number (Re=33000). The cylinder spanned the test section of a wind tunnel and was aligned with its axis parallel to the under wall of the test section and normal to a uniform flow. The wall of the test section under the cylinder was moved at the same speed as the uniform flow. Surface pressure measurements, velocity surveys and flow visualizations suggest the existence of three flow patterns in the near wake behind the cylinder by the change of the gap between the cylinder and the moving wall. The wake from the cylinder is characterized by the behavior of a jet passing through the gap. Furthermore, the behavior of the jet is sensitive to both the centrifugal force generated by the rotating cylinder and the inertial force of the jet.

The passive flow control was numerically studied for a two-dimensional rectangular cylinder. Several control means were proposed so far like a small obstacle placed in front of a rectangular cylinder. One of the present authors proposed to connect a front obstacle and a rectangular cylinder with a splitter plate. The controlled flow field was investigated by the Navier-Stokes equations with the modified LES turbulent model. The results were compared to a previous method and it was found that the improvements were achieved in the drag reduction.

A numerical method is developed to simulate a bubbly flow around a circular cylinder using a boundary-fitted coordinate system. In the present study, the number density model of a bubbly flow is employed, where the equations of conservation and the group motion of bubbles are solved directly. The three-dimensional simulations have been conducted under laminar flow conditions for the liquid Reynolds numbers from 100 to 2 000

A vortex element method based on Biot-Savalt law and the core spreading model was extended to analysis for unsteady heat transfer. Discrete heat elements were introduced into the flow field close to a wall surface in addition to nascent vortex elements. In this study, unsteady flow and heat transfer were calculated around a circular cylinder to a uniform flow in the range of Re=200a1000, and Pr=0.71. From the result of the present calculation, the mechanism of unsteady heat transfer in the separated flow region of the cylinder was clarified.

The DNSs of the incompressible flows around a circular cylinder are performed by using the Cartesian grid approach with virtual boundary method. In the virtual boundary method, the body surface is expressed by a set of plural points, and the velocity components on virtual boundary are feedbacked to the momentum equations as the additional forcing terms. As a validation of this method, the steady flows around a circular cylinder are computed in order to investigate the dependence of virtual boundary points on flow characteristics. Then, this method is applied to the unsteady flows. The results show that the present method is very promising for the DNSs of the incompressible complicated flow.

It is important to fluid mechanics and bio-fluid mechanics to understand an interaction among deformable surface, its surface, its surrounding flow field and hydrodynamical forces. In order to clarify this interaction by experiments, we have been using several cylinder models having an elasto-flexible surface in uniform water flow. The hydrodynamic forces were measured by a three-component force balance. The deformation of the surface and the flow field around it were visualized using a laser light sheet method simultaneously. The experimental results showed that the time-averaged hydrodynamical drag was approximately 20% lower than that of the rigid cylinder when the continuously occurring wave appeared on the surface. In the case of the drag reduction occurrence, the power spectra of the lift fluctuation were broadened and had several peaks. In particular, the prominent frequency of power spectrum was about 45% lower than the frequency in the cases of the rigid cylinder and of no drag reduction occurring. The visualization results suggested that the strength of the Karman vortex shed from the cylinder was decreased compared with that from the rigid cylinder and this decrease was responsible for the above mentioned drag reduction.

This paper describes the fluid force acting on the two-dimensional oscillating circular cylinder in the locking-in region. The experiment was carried out in an N. P. L, blow-down type wind-tunnel with a working section of 500 mm×500 mm×2000mm, and with the Reynolds number of 1.9×104. The cylinder was then forced to oscillate sinusoidally in the lift direction. The power spectrum of the fluctuating velocity in the wake behind a circular cylinder was measured to show the locking-in region in the present experiment. The time-mean pressure distribution and fluctuating pressure distribution on the circular cylinder were measured for the displacement in the vibration. Consequently it was found that the mean drag and fluctuating lift increase and become maximum in the locking-in region, while, the base pressure in the rear surface (θ=180°) of the cylinder becomes low and attains minimum.

An experiment showed a quite strong effect of inserting a circular cylinder into a unform rising bubbly flow. Size of the dffected zone was more than several times as that of the cylinder. The purpose of present study is to elucidate the mecahnism of generating the two-phase convection using a numerical analysis based on Elulerian-Lagrangian model by which the bubble's bpundary condition on the cylinder can be treated accurately. The numerical results showed a good agreement with the experimental results and revealed the dependency of the flow on the void fraction bubble radius, blockage ratio as well as the bubble's bouncing condition on the cylinder surface.

In this study, we propose a novel method to specify the added-mass coefficients of arbitrary two-dimensional bodies in an incompressible viscous fluid. This method is based on a discrete singularity method in which a fundamental solution of the Brinkman's equation is employed as a singularity. For computational examples, the following bodies are chosen : a circular cylinder in an infinite flow field and in cylindrical containers, an elliptic cylinder in an infinite flow field and a square-section cylinder in an infinite flow field. As a result, the effectivity of this method is confirmed.

Flow networks are abundant in the field of natural science and provides interesting phenomena with potential applications for heat transfer enhancement, flow control and others. An experimental study was performed on cross flow in the bundles of quadrilateral cylinders, including rectangular, diamond-shaped and cross-sectional geometry. Flow visualization by means of the particle tracing method, laser Doppler velocimetry (LDV) and pressure drop measurements using a piezometer were conducted in order to disclose the flow characteristics behind rows of the cylinder inside each bundle. Of most interesting is the finding of periodicity of timewise velocity variation in the vortex region behind each cylinder. The total pressure-loss coefficient is determined as a function of the Reynolds number.

For Taylor vortex flows developing between two concentric cylinders with finite length, the Reynolds number based on the rotation speed of the inner cylinder and the aspect ratio defined by the cylinder length and the gap between cylinders are dominant parameters which determine modes of flow patterns. In this study, the flow modes in decelerating flow are examined numerically. The finite difference method is used to solve unsteady axisymmetric Navier-Stokes equations. At a constant aspect ratio, the flow has three modes: primary mode, normal secondary mode and anomalous mode. The qualitative process of flow pattern exchange from the secondary mode to the primary mode is revealed and the Reynolds numbers at which flow modes change are determined. In the flow with anomalous cells, extra vortices near the end wall of cylinder merge and make the flow mode normal. The result shows good agreement with experimental observations.