Transition Reynolds Number Research Articles

Turbulent flow around convex curved tandem cylinders

Turbulent flow around curved tandem cylinders has been studied for the first time, by means of direct numerical simulation. The convex configuration was used, with a nominal gap ratio of $L/D = 3$ and a Reynolds number of 3900. Along the span, the flow regimes vary from alternating overshoot/reattachment to co-shedding. Three distinct Strouhal numbers coexist in the flow that are tied directly to different tandem cylinder flow regimes. This result differs substantially from convex curved tandem cylinders at a transitional Reynolds number, where only a single dominant frequency is found. All regimes exhibit some degree of instability, so that the flow can be considered multistable. A mode switch from alternating overshoot/reattachment to symmetric reattachment is found. Complex interactions are observed between the primary instability, the shear layer instability and the flow mode alterations. As opposed to previous investigations with single and tandem straight cylinders in the subcritical flow regime, our results indicate that there may be direct feedback from the primary instability to the shear layer instability. The downdraft region in the gap exhibits slow meandering, and may travel upstream and amplify the shear layer instability, causing early transition in the gap shear layer. This downdraft is governed by the slow modulations of the vortex formation region in the lower gap, meaning that the vortex dynamics of this region may indirectly influence the shear layer instability higher up in the gap.

Experimental study on pressure drop and ice blockage characteristics of ice slurry flow in big-diameter pipes

Ice slurry utilization in district cooling brings about attractive reduction in both the storage volume and transportation power of the cold thermal energy. However, the ice slurry flow characteristics, particularly in big-diameter pipes, remains unclear, hindering the application of ice slurry in large-scale district cooling systems. This paper prepared the ice slurry from pure water without any additives to experimentally study its flow characteristics in big-diameter pipes, including DN50, DN80, DN100 and DN190 pipes. The normalized pressure drops and friction factors have been obtained at various velocities and ice fractions. Generally, the pressure drop characteristics did not conform to the Blasius correlation which could predict the single-phase flow until the Reynolds number exceeded a certain threshold, known as the transition Reynolds number. The transition Reynolds numbers were in the range of 3.91 × 104-6.77 × 104 depending on the ice volume fractions ranging from 5% to 21% in the present study. Some visualization measures have been employed to help to observe the flow pattern and confirm the occurrence of ice blockage which was found nowhere but in the branches and expansion. The ice blockage occurred intermittently in the branches, whereas it was irreversible in the expansion. The critical velocity at which the ice blockage began to occur was quantitatively determined, which increased with increasing the ice volume fraction. This study provides a guide for evaluating the pump power and transportation safety of the ice slurry flow in big-diameter pipes.

Modeling the unsteady wake of an impulsively started circular cylinder using refined potential flow theory

Cylindrical structures find usage in many engineering applications including tethered oil drums and engine canisters slung beneath helicopters in flight. The motion of air around such circular cylindrical structures and the helicopter presents interesting phenomena including flow separation, wakes and turbulence. The physics of these are enshrined in the continuity equation and the Navier–Stokes equations. Therefore, their studies are not only important in mathematics and physics, but they are also required for efficient helicopter operations. In practice, reduced-order models of these operations that take in aerodynamics models of the tethered loads are utilized for stability analysis, flight certification and pilot training because of the prohibitive cost of experimentation and computational analyses of these configurations. However, there is a dearth of realistic analytical models of finite cylinder flows because of the Navier–Stokes problem. Classical potential flow theory provides an avenue to develop such models, but the extant gaps in its predictions significantly preclude its usage for engineering applications. Attempting to bridge these gaps, this article introduces refined potential flow theory in which the governing equations and boundary conditions are satisfied. Viscous effects, fluctuations of the mean flow and three-dimensional effects are also incorporated. For characterization, refined potential flow theory is employed on an incompressible flow over an impulsively started circular cylinder for Reynolds numbers and non-dimensional times in the range 30<Re<104 and 0.2 ≤ T ≤ 77, 047 respectively. There is an excellent prediction of 0.209 for the Strouhal number at Re=3,900 . At this transitional Reynolds number, the harmonics of the Strouhal frequency are also captured, and the characteristic irregular fluctuations at sub-Strouhal frequencies are discernible in the velocity spectra. As the flow becomes more turbulent, these become more pronounced at Re=9,500 when the predicted Strouhal number is within 10% of experimental result. In the fully developed stage, spectra analyses of the wake velocity components at some downstream locations also display Kolmogorov's Five-Thirds law of homogeneous isotropic turbulence. The present model can thus aid the development of reduced-order models of helicopter operations that feature tethered cylindrical loads.

Direct numerical simulation of transition under free-stream turbulence and the influence of large integral length scales

Under the action of free-stream turbulence (FST), elongated streamwise streaky structures are generated inside the boundary layer, and their amplitude and wavelength are crucial for the transition onset. While turbulence intensity is strongly correlated with the transitional Reynolds number, characteristic length scales of the FST are often considered to have a slight impact on the transition location. However, a recent experiment by Fransson and Shahinfar [J. Fluid Mech. 899, A23 (2020)] shows significant effects of FST scales. They found that, for higher free-stream turbulence levels and larger integral length scales, an increase in the length scale postpones transition, contrary to established literature. Here, by performing well-resolved numerical simulations, we aim at understanding why the FST integral length scale affects the transition location differently at low- and high turbulence levels. We found that the integral length scales in Fransson and Shahinfar's experiment are so large that the introduced wide streaks have substantially lower growth in the laminar region, upstream of the transition to turbulence, than the streaks induced by smaller integral length scales. The energy in the boundary layer subsequently propagate to smaller spanwise scales as a result of the nonlinear interaction. When the energy has reached smaller spanwise scales, larger amplitude streaks results in regions where the streak growth are larger. It takes longer for the energy from wider streaks to propagate to the spanwise scales associated with the breakdown to turbulence, than for those with smaller spanwise scales. Thus, there is a faster transition for FST with lower integral length scales in this case.

Attenuation of boundary-layer instabilities for natural laminar flow design on supersonic highly swept wings

To meet the challenge of drag reduction for next-generation supersonic transport aircraft, increasing attention has been focused on Natural Laminar Flow (NLF) technology. However, the highly swept wings and high-Reynolds-number conditions of such aircraft dramatically amplify Crossflow (CF) instabilities inside boundary layers, making it difficult to maintain a large laminar flow region. To explore novel NLF designs on supersonic wings, this article investigates the mechanisms underlying the attenuation of Tollmien–Schlichting (TS) and CF instabilities by modifying pressure distributions. The evolution of TS and CF instabilities are evaluated under typical pressure distributions with different leading-edge flow acceleration region lengths, pressure coefficient slopes and pressure coefficient deviations. The results show that shortening the leading-edge flow acceleration region and using a flat pressure distribution are favorable for suppressing CF instabilities, and keeping a balance of disturbance growth between positive and negative wave angles is favorable for attenuating TS instabilities. Based on the uncovered mechanisms, a strategy of supersonic NLF design is proposed. Examination of the proposed strategy at a 60° sweep angle and Ma = 2 presents potential to exceed the conventional NLF limit and achieve a transition Reynolds number of 17.6 million, which can provide guidance for NLF design on supersonic highly swept wings.

The Spatial Development Characteristics of High-Pressure Methane Jet Impinging on Methane Lean-Burn Premixed Flame

This work investigated the effect of high-pressure (10 MPa) methane gas jet impinging on the methane lean-burn premixed flame (equivalent ratio of 0.7) based on a three-dimensional numerical simulation by CONVERGE software. The results show that laminar premixed flame is accelerated to develop into a stable turbulent flame under the action of the methane jet, the whole process of flame front development is divided into three stages: laminar (Reynolds number maintains stable, 1–1.3 ms), transition (Reynolds number shows an increasing trend, 1.4–8 ms), and turbulent (Reynolds number tends to stabilize at a high value, 1.9–3 ms). The effect of high-pressure jet on flame development along jet direction (Z axis) is greater than that on vertical direction (Y axis). During turbulence stage, the momentum and kinetic energy of Z axis are 2.7 and 6.3 times greater than that of Y axis, respectively. The high-pressure methane jet causes a change in heat distribution, resulting in local flameout. The rate of change in the local flameout area is greater than that in the flame area, causing a temperature drop in Z axis. This temperature drop increases with the increase in equivalence ratio and with the decrease in distance between cross-section position and ignition center.

A comprehensive framework to enhance numerical simulations in the spectral-element code Nek5000

A framework is presented for the spectral-element code Nek5000, which has been, and still is, widely used in the computational fluid dynamics (CFD) community to perform high-fidelity numerical simulations of transitional and high Reynolds number flows. Despite the widespread usage, there is a deficiency in having a comprehensive set of tools specifically designed for conducting simulations using Nek5000. To address this issue, we have created a unique framework that allows, inter alia, to perform stability analysis and compute statistics of a turbulent flow. The framework encapsulates modules that provide tools, run-time parameters and memory structures, defining interfaces and performing different tasks. First, the framework architecture is described, showing its non-intrusive approach. Then, the modules are presented, explaining the main tools that have been implemented and describing some of the test cases. The code is open-source and available online, with proper documentation, to-run instructions and related examples.

INFLUENCE OF THERMOCHEMICAL NONEQUILIBRIUM ON CHARACTERISTICS OF BOUNDARY LAYER AT FLIGHT IN THE MARTIAN ATMOSPHERE

In framework on the eN-method, comparative calculations of position beginning zone of laminar-turbulent transition completed for two points on landing trajectory of “Pathfinder” spacecraft on surface of the Mars. The calculations used a three-component model of a thermochemical nonequilibrium mixture CO2=CO=O. The set of frequencies of spatial disturbances is determined along neutral curves for first unstable modes of temporary disturbances. The transition Reynolds number Re T was determined from envelopes of families of the N-factor curves at NT=8. In hypersonic regime at M=12:6, taking into account the developed thermochemical nonequilibrium leads to a significant decrease in the static temperature of gas in the lower part of the boundary layer. As a result, beginning of the zone of laminar-turbulent transition shifts downstream by approximately 9% compared to case of a perfect gas.

Exploration of High-Frequency Actuation on Gust Response Using Large Eddy Simulation

Abstract Mitigation of gust-induced separation and aerodynamic loads using a high-frequency blowing/suction slot is demonstrated using high-order implicit large eddy simulation (LES). This approach was previously shown to be effective at alleviating dynamic stall on pitching wings. A NACA0012 wing section operating at a transitional chord-based Reynolds number of Rec=500,000, subsonic freestream Mach number of M∞=0.1, and angles of attack of α = 4 deg and 12 deg is subjected to discrete 1-cos transverse gusts. Gust-induced stall is demonstrated and then active flow control (AFC) is applied to cases vulnerable to gust-induced stall. The flow control strategy is shown to be effective at stall suppression during gust encounter, thereby providing partial alleviation of gust induced loads. This approach is most effective at attenuating pitching moment increment.

Dynamic Performance of Liquid Smooth Annular Seal Operating in the Transition Regime

Abstract This paper presents the experimental leakage and rotordynamic performance for a liquid smooth annular seal operating in the transition regime. The test conditions include pressure differentials up to 64 bars with 1∼2 bar increments for 6 rotor speeds (2.5, 3.8, 5, 7.5, 8.8, and 10 krpm), as well as nonrotating rotor case under zero preswirl condition. The rotordynamic coefficients for all the test conditions are obtained by pseudo-random excitation of the seal at multiple subsynchronous frequencies. By considering the transition Reynolds number (1000 &amp;lt; Re &amp;lt; 3000) and the Taylor Number (Ta) versus Axial Reynolds Number (Rez), the variations in the direct stiffness coefficients (K) can used as an indicator of the flow regime transition boundaries. The direct stiffness K resulting from the Lomakin and hydrodynamic effects significantly drops until Rez reaches ∼1500. For higher Rez, K increases mainly due to hydrodynamic effects. When K drops, the cross-coupled stiffness k, the direct damping C and the cross-coupled virtual mass m increase while the cross-coupled damping c and virtual mass M decrease. None of predictions based on either laminar or turbulent flow show the variations in rotordynamic coefficients obtained from experimental results. The leakage is not highly influenced by rotor speeds for low speed cases crossing laminar boundary as ΔP increases, however, results for higher speeds in the superlaminar region show reduced leakage rates as rotor speed increases.

Accelerated corrosion of low carbon steel by oscillatory acidic streams generated with a bio-inspired claw device.

A mechanical device inspired by the pistol shrimp snapper claw was developed. This technology features a claw characterized by a periodic opening/closing motion, at a controlled frequency, capable of producing oscillating flows at transitional Reynolds numbers. An innovative method was also proposed for determining the corrosion rate of carbon steel samples under oscillating acidic streams (aqueous solution of HCl). By employing very-thin carbon steel specimens (25 μm thickness), with one side coated with Zn and not exposed to the stream, it became possible to electrochemically sense the Zn surface once the steel sample was perforated, thus providing the average dissolution rate into the most relevant pit on the steel surface. Furthermore, a laser light positioned beneath the metallic sample, along with a camera programmed to periodically capture images of the steel surface, facilitated the accurate counting of the number of newly formed pits. The system consisting of the thin steel sample and the Zn coating can be seen as a type of corrosion sensor. Furthermore, the proposed laser illumination method allows corroborating the electrochemical detection of pits and also establishing their location. The techniques crafted in this study pave the way for developing alternative corrosion sensors that boast appealing attributes: affordability, compactness, and acceptable accuracy to detect in time and space localized damage.

Variations in gas temperature and average velocity during laminar-turbulent transition in high-speed gas flow through microtubes

The primary objective of this study is to investigate variations in gas temperature and average velocity during the laminar-turbulent transition of compressible flow. This investigation encompasses an exploration of the effect of Mach number on transitional Reynolds number. Experiments were conducted utilizing a pair of adiabatic stainless steel microtubes with a diameter (D) of 131.6 μm. The first microtube was dedicated to measuring local pressure to obtain friction factor, local Mach number, and bulk temperature. The second microtube was employed for measuring local wall temperature. Additionally, a stainless steel microtube with a diameter (D) of 124 μm and a rectangular microchannel with a hydraulic diameter (Dh) of 99.36 μm were incorporated in the study. Friction factor, Mach number, and bulk temperature were determined by measuring mass flow rate and local pressure near the outlet. The measured mass flow rate exhibited a slight increase that plateaued during the laminar-turbulent transition as the Reynolds number increased. In laminar flow, an increase in the Reynolds number resulted in an increase of the Mach number and a reduction in bulk temperature. Conversely, during the laminar-turbulent transition, the Mach number either remained constant or decreased, and the bulk temperature increased due to the conversion of kinetic energy to thermal energy. Experimental validation of this phenomenon was achieved by measuring the wall temperature of an adiabatic microtube.

Laminar to turbulent transitions of pipe flows by resonances of natural frequencies of components of test sections

This investigation analyses special papers and doctoral theses that treat transitions of pipe flows as a resonance phenomenon of wave frequencies. These frequencies are natural frequencies of pipe flows, of components of the test section and of vortex ring formations. Resonance conditions are derived that show how the critical Reynolds number, Rec , depends on the volume of the plenum chamber, the pipe diameter, the pipe length, etc. The derived resonance relations were verified experimentally using the experimental data of the third author, yielding R e c ∼ 1 / V ple , R e c ∼ 1 / ( L D ) and other interesting results. These findings suggest that the laminar-to-turbulent transition has various modes and transitive dependences. To understand this fully, it is necessary to take all components of the test section involved into account. The test section considered in this paper consists of a mass flow controller to supply the airflow and a plenum chamber, followed by the actual pipe of interest. It is shown that all the components can contribute to the measured value of the critical Reynolds number of pipe flow transition.

Experimental study on the transition modes of falling film between horizontal 3D finned tubes and their transitional Reynolds number prediction model

Abstract To investigate the effect of different falling film modes on the heat transfer performance of three-dimensional (3D) finned tubes in a falling film heat exchanger, the falling film transition modes are experimentally investigated by observing the flow modes on 3D finned tubes and determining the Reynolds numbers of flow transition modes. A test facility, which contains an array of three horizontal test tubes, is constructed to study the effect of tube spacing and fin structure on the falling film Reynolds number (Re). The results show that tube spacing and fin structure significantly affect the Re and observed mode. With the increase in tube spacing, the Re overall shows an increasing trend for the four transition modes, especially for the transition between the column and the column–sheet mode. With the increase in the ratio for fin structure parameters, the Re overall shows a downward trend, and this phenomenon is more evident with the increase in the tube spacing. Machine learning methods are utilized to predict the Re, considering the effects of tube spacing and fin structure. Both this method and the linear regression method are used to predict the Re of the literature and this experiment, and the results indicate that machine learning has a lower prediction deviation.

Influence of deep gaps on laminar–turbulent transition in two-dimensional boundary layers at subsonic Mach numbers

Systematic experimental investigations on the influence of deep gaps on the location of laminar–turbulent transition are reported. The tests were conducted in the Cryogenic Ludwieg–Tube Göttingen, a blow-down wind tunnel with good flow quality, at eight different unit Reynolds numbers ranging from Re_1 = {17.5,,times 10^{6},mathrm{{m}^{-1}}} to 80,times,10^{6},mathrm{m}^{-1}, three Mach numbers, M= 0.35, 0.50 and 0.65, and various pressure gradients. A flat-plate configuration, the extended two-dimensional wind tunnel model PaLASTra was modified in order to allow the installation of gaps with nominal widths of 30 upmu m, 100 upmu m and 200 upmu m and a depth of d = {9,mathrm{mm}}. A maximum Reynolds number based on the gap width Re_{w} = Re_1 cdot w approx {16{,}000} was reached. Transition Reynolds numbers ranging from Re_{tr}approx 1 × 106 to 11 × 106 were measured, as a function of gap width, pressure gradient and Mach and Reynolds number. This systematic investigation facilitates a linear approximation of Re_{tr} dependent on the boundary layer shape factor H_{12} for various flow conditions and gap widths. It was therefore possible to conduct an investigation of Re_{tr} depending on Re_{1} and the relative change of the transition location depending on the gap width w. Incompressible linear stability analysis was used to calculate amplification rates of Tollmien–Schlichting waves and determine critical N-factors by correlation with measured transition locations. The change in the critical N-factor varDelta N by installation of the gap is investigated as a function of w and Re_w. It was found that a gap width of 30 upmu m reduces the critical N-factors in the range of varDelta N approx 0.5 pm 0.25, while gap widths of 100 upmu m and 200 upmu m reduce the critical N-factor in the range of varDelta N approx 1.5 pm 1. Interestingly, an increase in gap width from 100 to 200 upmu m was not found to induce smaller transition Reynolds numbers or reduced N-factors, which might be due to resonance effects.

Instability of MHD mixed convection flow of nanofluid in porous channel with thermal radiation, chemical reaction, Dufour and Soret effects

The present paper aims to investigate a stability analysis of the mixed convection of Al2O3/water nanofluid through an anisotropic porous channel heated from below and cooled from above. The effects of the magnetic field, thermal radiation, chemical reaction, mass transfer (Soret effect) and energy transfer (Dufour effect) are taken into consideration. The equations governing the motion of the nanofluid are converted by means of hydrodynamic stability theory into a system of eigenvalue equations which is then solved numerically by the spectral collocation method. The effects of Hartmann number, thermal radiation parameter, volume fraction of nanoparticles, permeability parameter, chemical reaction parameter, Dufour and Soret number are presented and analyzed. The results showed that in presence of nanoparticles the inertia of the working fluid increases, which dampens the disturbances and thus reduces their growth. The Hartman number attenuated the amplitude of the disturbances and thus has a stabilizing effect. The permeability parameter affected the stability of the flow and its growth prevented the redistribution of disturbances within the flow, which reflected its stabilizing character. The numbers of Soret and Dufour showed an important effect on the stability of the convective mixed flow. Their growth increased the transition Reynolds number for which there was a transition to instabilities, which prevented the transition to increasingly turbulent flows. On the other hand, the increase in the chemical reaction parameter decreased the values of transition Reynolds number, thus showing that the chemical reaction maintained the instabilities.

Effect of normal magnetic field on the exact coherent state of channel flow at large Reynolds number

Laminar-turbulent subcritical transition has been always a hot issue in fluid mechanics. Exact coherent states are important for predicting the path of transition and understanding the cycle of turbulent self-sustaining process. One of the most common methods of investigating subcritical transition is dynamical system method and many different forms of invariant solutions have been obtained in many shear flows. In order to study the effect of magnetic field on the exact coherent state of channel flow at large Reynolds number, the direct numerical simulation combined with bisection method is used to calculate the exact coherent state-periodic orbit solution with different magnetic field strength at Re ⩾ 9000, and the structure and morphology in the flow field are compared. The results show that the magnetic field strength does not change the structure and shape of the solution and the scaling law between the transition threshold and Reynolds number does not change significantly, which shows obviously self-similarity. As the magnetic field strength increases, the period of the exact coherent state decreases and the perturbation energy in each direction exhibits periodical oscillation changes. In addition the shape of the amplitude curve also changes due to the magnetic field effect. The above results show that the magnetic field has a certain inhibition effect on the disturbance at large Reynolds number, and the flow field remains relatively stable.

Influence of distributed hydrogen injection and combustion on supersonic boundary layer stability and transition

This theoretical study recorded the influence of the distributed injection of hydrogen through a permeable surface and its combustion on the stability and transition of a supersonic boundary layer (BL). The laminar base flow for a multicomponent flat-plate BL was computed using the computational fluid dynamics solver with finite-rate chemistry for free-stream Mach number (M) = 2. Linear stability theory (LST) equations for a reactive gas mixture were derived in the local parallel base flow approximation. Stability calculations based on the developed theory revealed the possibility of a decrease in the local spatial amplification rates of unstable perturbations. A double reversal in the maximal amplification rate magnitudes of perturbations was obtained, wherein at first, they increased, then decreased to zero, and then rose again. The influence of the distributed injection and combustion of hydrogen in the supersonic BL on the position of the laminar-turbulent transition was estimated using the LST-based eN-method. Calculated and experimentally obtained dependencies of the relative transition Reynolds number on the relative mass flow rate of injected hydrogen were compared. It was found that depending upon the flow conditions, the hydrogen diffusion flame could accelerate or decelerate the transition in the supersonic M = 2 BL, when compared to absence of hydrogen burning. Two counteracting effects compete: heat supply by combustion exerts stabilizing influence, while low-molecular-weight gas blowing from the surface exerts destabilizing influence. Depending on the interplay of these two factors, it would be possible to obtain acceleration or deceleration of transition.

Experimental study of flow field and transition characteristics in rod bundle channel

Utilizing the particle image velocimetry (PIV) technique, this study investigates the fully developed flow field and turbulence statistics in a 5×5 rod bundle across 22 cases, with Reynolds numbers ranging from 310 to 12296.Time-averaged, statistical, and spectral analyses were performed on the full field and instantaneous velocity vectors obtained through PIV measurements to examine the velocity distribution, turbulence characteristics, and spectral features in different subchannels under various Reynolds numbers. In conjunction with a differential pressure transmitter, the flow properties and fluid transitions were also explored.The experimental results reveal that the relative velocity gradient in the rod bundle channel is more significant at lower Reynolds numbers. As the Reynolds number increases, the relative velocity distribution becomes more uniform. A comparison of experimental results from different planes indicates that the fluctuation velocity in the gap subchannel is greater than that in the inner subchannel, suggesting that tightly arranged rods can generate higher turbulence intensity. Furthermore, the transition observed through the friction factor in the rod bundle channel is less distinct than those in pipes, with the transition Reynolds number being approximately 900. A low Reynolds number effect is present in the rod bundle channel, where the dimensionless fluctuation velocity decreases as the Reynolds number increases. Upon reaching the transition Reynolds number, the area-averaged dimensionless fluctuation velocity abruptly rises. By examining the turbulence intensity variations at different positions within the rod bundle, it becomes evident that the transition Reynolds numbers vary across different subchannel positions. Ultimately, the experimental data can be employed to validate the applicability of turbulence models for different Reynolds numbers.

Flow in a Taylor–Couette Reactor with Ribbed Rotors

This paper investigates the flow structure and flow pattern transition within a conical ribbed Taylor–Couette reactor (TCR), which is 4 mm in gap width and 200 mm in height, via particle image velocimetry (PIV) and numerical simulation methods. The effect of various parameters on the vortex structure and on flow transition, including the structural parameters of the ribs (rib spacing and rib width) and the operating parameters (Taylor number and axial Reynolds number), were investigated. Without axial flow, the ribbed TCR can control the flow structure while maintaining the symmetry of the flow field. Under certain conditions, a Taylor vortex pair can form between the ribs, with the down vortex rotating clockwise and the up vortex rotating counterclockwise. The axial dimension of the Taylor vortex can be controlled by adjusting the rib spacing, which can be summarized into four different conditions according to the size of the rib spacing. With axial flow, the axial Reynolds number greatly impacts the Taylor vortex structure within the ribbed TCR, and as the axial Reynolds number increases, the up vortex appears to be compressed and the down vortex appears to be stretched. The double vortex flow pattern between the ribs is eventually transformed into a single vortex. The critical axial Reynolds number for flow pattern transition is defined and correlated with the Taylor number and rib spacing. The results show that the critical axial Reynolds number is positively proportional to the Taylor number and is inversely proportional to rib spacing. The empirical correlation equation developed in this study shows strong predictive power and is validated using the experimental results. Overall, this study provides a comprehensive understanding of the flow structure and pattern transition within a ribbed TCR and lays the foundation for the further optimization of TCR design.