Characteristic Reynolds Number Research Articles

On the generation of free-stream turbulence at low Reynolds number: A numerical study

We investigate the generation of free-stream perturbations at a relatively low characteristic Reynolds number of 1000 by means of direct numerical simulations using a synthetic turbulence generation method. This approach consists of generating turbulent fluctuations by means of digital filtering and a source term formulation in the Navier–Stokes equations. To assess its validity in the framework of decaying turbulence, we compare the results with those obtained with a physically-based, grid-induced turbulent flow in terms of spatial decay, evolution of characteristic length-scales and energy spectra. Also, we highlight relevant differences such as those in the streamwise development length and the anisotropy of the largest scales. Then, we characterize the generated perturbations when systematically varying the input parameters, namely the initial integral length-scale and turbulence intensity. Here, we notice differences in the streamwise decay of the turbulence intensity and the development length as we vary these parameters. By inspecting the evolution of the characteristic length-scales and the micro-scale Reynolds number, we also identify that the effective scale separation is highly sensitive to these variations.

Пульсации течения жидкого металла, генерируемые переменным магнитным полем

This paper studies numerically a vortex flow of liquid metal driven by an electromagnetic force, which is generated by the interaction of the alternating magnetic field of a short solenoid with the induced electrical current. A short solenoid is placed coaxially to a cylindrical cell at half of its height. The mathematical model used to describe the process is based on the equations of magnetic hydrodynamics in the induction-free approximation. Calculations, which are carried out by the control volume method using the ANSYS Fluent package, show that the average flow has the form of two toroidal vortices. The calculated velocity fields are indicative of the oscillatory behavior of vortices, accompanied by a change in their sizes. In the examined range of the force parameter, the predominant flow pattern is the single-mode oscillatory flow. The dependences of characteristic frequency and Reynolds number on the force parameter, are obtained using spectral analysis. It has been found that the oscillation period is close to the period of rotation of a large-scale vortex. It has been established that the oscillations are of quasi-periodic character, and a distinct oscillation frequency is observed only in the flow region near the solenoid. The effect of velocity fluctuations is strong and can be detected in laboratory conditions when using gallium eutectic. Such experiment is planned for the near future. The flow rate of gallium eutectic will be measured by an ultrasonic Doppler anemometer. The results of numerical modeling and their verifications can be useful in determining the ways of reducing the intensity of vortex flows during the electromagnetic separation of impurities, which is based on the induction mechanism responsible for the generation of electromagnetic force that displaces particles. The data on the oscillation frequency of the unsteady flow can be used in the development of a non-contact technique for estimating the average electrical conductivity of a two-phase medium, such as a liquid metal with undesirable impurities.

An analytical solution for convective heat transfer in conical gaps with either cone or disk rotating

This study is devoted to solving two problems of laminar fluid flow in a conical gap with small conicity angles up to 4°: cone rotation with a fixed disk, and disk rotation with a fixed cone. A new improved asymptotic expansion method for energy equation was used to obtain an approximate analytical solution to the convective heat transfer equation. The characteristic Reynolds number ranged from 0.001 to 1.0, the Prandtl number took values 0.71, 1, 5, and 10, and the exponent n* in the power-law for the disk temperature was 0 (constant disk temperature) or 2 (strongly radially increasing disk temperature). A novel model for the asymptotic expansion of the temperature profile and a novel expansion parameter Sv = Re2Pr, which is a new dimensionless number proposed for the first time in the known scientific literature, was developed. For the first time, new approximate analytical solutions were obtained for temperature profiles and Nusselt numbers on the disk and cone for both problems that agree well with the self-similar solution, if the Re and Pr numbers do not exceed threshold values. These analytical solutions are advantageous in analysis of experimental data and further development of one-dimensional models for gases, water, and aqueous solutions (Pr = 0.71–10).

Improved asymptotic expansion method for laminar fluid flow and heat transfer in conical gaps with disks rotating

PurposeThe purpose of this paper was to study laminar fluid flow and convective heat transfer in a conical gap at small conicity angles up to 4° for the case of disk rotation with a fixed cone.Design/methodology/approachIn this paper, the improved asymptotic expansion method developed by the author was applied to the self-similar Navier–Stokes equations. The characteristic Reynolds number ranged from 0.001 to 2.0, and the Prandtl numbers ranged from 0.71 to 10.FindingsCompared to previous approaches, the improved asymptotic expansion method has an accuracy like the self-similar solution in a significantly wider range of Reynolds and Prandtl numbers. Including radial thermal conductivity in the energy equation at small conicity angle leads to insignificant deviations of the Nusselt number (maximum 1.23%).Practical implicationsThis problem has applications in rheometry to experimentally determine viscosity of liquids, as well as in bioengineering and medicine, where cone-and-disk devices serve as an incubator for nurturing endothelial cells.Social implicationsThe study can help design more effective devices to nurture endothelial cells, which regulate exchanges between the bloodstream and the surrounding tissues.Originality/valueTo the best of the authors’ knowledge, for the first time, novel approximate analytical solutions were obtained for the radial, tangential and axial velocity components, flow swirl angle on the disk, tangential stresses on both surfaces, as well as static pressure, which varies not only with the Reynolds number but also across the gap. These solutions are in excellent agreement with the self-similar solution.

Experimental study on convective heat transfer of hybrid impingement configuration by square-array continuous jets and a center-positioned synthetic jet

An experimental investigation is performed to illustrate the heat transfer characteristics for a specific hybrid-jet impingement configuration that is comprised of a square-layout continuous-jet array and a center-positioned loudspeaker-driven synthetic-jet actuator. Herein four continuous-jet Reynolds numbers (ranging from Re=3000 to Re=10,000), three hole-to-hole pitches (X/d = Y/d = 4. 5 and 6), and a series of impinging distances (H/d = 2–10) are considered while the central synthetic jet is operated at f = 250 Hz with a characteristic Reynolds number of about Re0=4500. It is identified that the integration of central synthetic jet in the array-jet unit is indeed an effective means to enhance the overall heat transfer performance, which is more suitable for the practical applications wherein the synthetic jet Reynolds number is greater than or equivalent to the array-jet Reynolds number. By the integration of central synthetic jet, a significant localized heat transfer augment is achieved at the central zone of array-jet unit, especially under small and moderate array-jet Reynolds numbers. In terms of the spatially-averaged Nusselt number, an increase of more than 100% could be achieved by the central synthetic jet integration at H/d ≥ 6 under Re=3000. The benefit of the central synthetic jet integration is also clearly demonstrated under Re=5000, wherein the spatially-averaged Nusselt number could be increased by 30%-60%, taking a monotonous increasing trend along with the impinging distance generally. Under Re=7000, a relative increase among 10%-30% still remains. When the array-jet Reynolds number is increased up to 10,000, only in the sparse continuous-jet array (X/d = Y/d = 6) the benefit of the central synthetic jet integration could behave, with a limited relative increase of less than 20%.

A Co‐Spectral Budget Model Links Turbulent Eddies to Suspended Sediment Concentration in Channel Flows

AbstractThe vertical distribution of suspended sediment concentration remains a subject of active research given its relevance to a plethora of problems in hydraulics, hydrology, ecology, and water quality control. Many of the classical theories developed over the course of 90 years represent the effects of turbulence on suspended sediments (SS) using an effective mixing length or eddy diffusivity without explicitly accounting for the energetics of turbulent eddies across scales. To address this gap, the turbulent flux of sediments is derived using a co‐spectral budget (CSB) model that can be imminently used in SS and other fine particle transport models. The CSB closes the pressure‐redistribution effect using a spectral linear Rotta scheme modified to include isotropization of production and interactions between turbulent eddies and sediment grains through a modified scale‐dependent de‐correlation time. The result is a formulation similar in complexity to the widely used Rouse's equation but with all characteristic scales, Reynolds number, and Schmidt number effects derived from well‐established spectral shapes of the vertical velocity and accepted constants from turbulence models. Finally, the proposed CSB model can recover Prandtl's and Rouse's equations under restricted conditions.

Effects of actuator-substrate ratio on hydrodynamic and propulsion performances of underwater oscillating flexible structure actuated by macro fiber composites

Oscillating flexible structures driven by smart actuators are promising thrust-producing components for underwater bionic vehicles. In this study, the hydrodynamic and propulsion performances of an oscillating flexible structure driven by macro fiber composites (MFCs) are investigated at varying actuator-substrate ratios. Numerical and experimental results demonstrate that the underwater resonant frequency increases approximately linearly with increasing actuator-substrate ratio. Moreover, the ratios of the in-air and underwater resonant frequencies vary with differing actuator-substrate ratios, and are mainly determined by the equivalent mass density. The effects of the actuator-substrate ratios on several characteristic parameters related to the propulsion performance are investigated and compared. The results suggest the generated mean thrust of the fully actuated case is the largest, but the power efficiency is the lowest among all the actuator-substrate ratios investigated, because this case has the lowest characteristic velocity and Reynolds number. In contrast, the highest power efficiency and lowest generated thrust are observed in the longest substrate case with the smallest actuator-substrate ratio. An optimal balance between the power efficiency and generated thrust is achieved when the actuator-substrate ratio approaches 0.6, in which case the characteristic parameters of propulsion performance are the highest among all the cases. These findings can provide useful guidelines for the design of efficient underwater bionic devices propelled by flexible fins driven by MFCs and other smart actuators.

Vortex-induced vibrations of a cylinder in inelastic shear-thinning and shear-thickening fluids

Vortex-induced vibrations (VIV) of a cylinder in a Newtonian fluid is a model problem in fluid–structure interactions and has been studied extensively. In this work, we study the influence of shear-thinning and shear-thickening fluids on the VIV response of a one-degree-of-freedom flexibly-mounted cylinder. We consider a system with a mass ratio of $m^*=2$ and zero structural damping in shear-thinning and shear-thickening power-law fluids at $Re_0 = 15$ and $Re_0 = 200$ , respectively, defined based on the zero-shear-rate viscosity of the fluids. We investigate how the VIV amplitude and frequency, flow forces, and the vorticity contours change as the reduced velocity, $U^*$ , and fluid's time constant, $\lambda$ , change. When the results are compared based on $Re_0$ , shear-thinning fluids enhance the oscillations while shear-thickening fluids suppress them. If, however, we define a characteristic Reynolds number, $Re_{char}$ , based on a viscosity evaluated at the characteristic shear rate, $\dot {\gamma } = U/D$ , then at a constant $Re_{char}$ , the amplitude of response stays very similar for the shear-thinning, shear-thickening and Newtonian fluids. Despite this similarity, the observed far wake is different: shear thinning amplifies the generation of vorticity and reduces the extent of the wake, whereas shear thickening limits the generation of vorticity and extends the wake. Our findings show that the local apparent viscosity observed close to the cylinder placed in shear-thinning or shear-thickening fluids governs the VIV response of the cylinder.

Flow Control for Unmanned Air Vehicles

The pervasiveness of unmanned air vehicles (UAVs), from insect to airplane scales, combined with active flow control maturity, has set the scene for vehicles that differ markedly from present-day configurations. Nano and micro air vehicles, with characteristic Reynolds numbers typically less than 105, rely on periodically generated leading-edge vortices for lift generation, propulsion, and maneuvering. This is most commonly achieved by mechanical flapping or pulsed plasma actuation. On larger UAVs, with Reynolds numbers greater than 105, externally driven and autonomous fluidic systems continue to dominate. These include traditional circulation control techniques, autonomous synthetic jets, and discrete sweeping jets. Plasma actuators have also shown increased technological maturity. Energy efficiency is a major challenge, whether it be batteries and power electronics on nano and micro air vehicles or acceptably low compressor bleed on larger UAVs. Further challenges involve the development of aerodynamic models based on experiments or numerical simulations, as well as flight dynamics models.

Magnetic Resonance Imaging measurements of scalar dispersion for a scaled urban transient release

Atmospheric dispersion in urban environments is highly complex, and a fundamental understanding requires a combination of field tests, laboratory experiments, and simulations. In this study, a transient release dispersion experiment was performed involving a scaled model of Oklahoma City, with the intention of being relevant for Joint Urban 2003 (JU2003) related studies. Flow over the city model was fully turbulent and housed in a water channel, with a characteristic building Reynolds number of 6200. The transient release was achieved by injecting a passive scalar at street level following a square waveform with a frequency of 1 Hz. Magnetic Resonance Imaging (MRI) techniques were leveraged to obtain phase-averaged velocity and concentration measurements over 12 intervals throughout the transient release cycle, with average uncertainties of 5.4% and 2.2% of the bulk velocity and injected concentration, respectively. Velocity and concentration measurements are obtained on three-dimensional grids of roughly 2 million data points each. An investigation of three-dimensional flow and dispersion features is presented, and a control volume encompassing an intersection within the city model is analyzed by applying the scalar transport equation to the experimental data. The phase-averaged measurements enable the calculation of scalar flux time series as well as the transient storage term. Scalar flux and transient storage indicate complex dispersion characteristics, and can potentially be used to infer the turbulent diffusion of contaminant. The MRI datasets can provide a reference for other atmospheric dispersion modelers and experimentalists, and the corresponding analyses demonstrate particular advantages of MRI data for model evaluation.

Computational methods for pore-scale simulation of rarefied gas flow

Direct simulation at the pore-scale is crucial to unravel rarefaction effect on gas transport in tight porous media. To satisfy the dual demands on modeling accuracy and computation effort, an appropriate method must be chosen. This work, therefore, evaluates four numerical methods for pore-scale rarefied gas flows in a two-dimensional (2D) model porous media over a wide range of rarefaction. These methods are the incompressible Navier-Stokes equation with the first-order velocity-slip boundary condition, and three gas-kinetic solvers i.e. a finite-difference (FD) iterative solver for the linearized Bhatnagar, Gross and Crook (BGK) model kinetic equation, a finite-volume (FV) solver for the non-linear Shakhov model, and an open-source direct simulation Monte Carlos (DSMC) solver. The benchmark cases cover the characteristic Knudsen number ranging from 0.0231 to 4.62 while the characteristic Reynolds numbers are kept to be less than 1.0. All the solvers are developed in OpenFOAM, except the FD solver, allowing us to investigate the effect of local grid refinements using the automatic Cartesian grid generator in OpenFOAM. The flow fields and the apparent permeabilities predicted by all the solvers have been compared in detail. Besides, the computational time of these solvers is measured and analyzed to demonstrate the relative cost of the three kinetic solvers. It is found that the FD solver is the most efficient one and gives accurate results over the whole range of Knudsen number. Finally, this study also evaluates the feasibility of the recently developed discrete unified gas-kinetic scheme (DUGKS), the algorithm in the aforementioned non-linear Shakhov model equation solver, for pore-scale rarefied gas flow. It is found the results predicted by this solver agree well with the other two kinetic solvers.

Mitigation of the aerodynamic noise of small axial wind turbines - methods and experimental validation

Although the characteristic Reynolds number of small horizontal axis wind turbines is only in the order of 100,000, their noise emissions can be annoying. Three different modifications of the blades aiming at attenuating the aerodynamic noise mechanisms are investigated: (i) Optimization of the blade profile, (ii) application of boundary layer tripping and (iii) addition of serrations to the trailing edges of the blades. All modifications were designed using either a novel optimization method or state-of-the-art design rules. They were tested on a three-bladed research wind turbine with 3 m diameter, which was placed on a large flat roof of an isolated tall building. Shaft and sound power were measured during substantial time periods, statistically analyzed and compared. Depending on the type and thickness of the blade profile, both, tripping and trailing edge serrations, were found to reduce noise but always degraded the turbine shaft power. The model-based optimization of the 15 % thick baseline profile S834 resulted in a new 10 % thick profile with a novel shape of the pressure and suction sides. Blades made from this profile, without trips but with trailing edge serrations, provided the best compromise between noise reduction and degradation of the aerodynamic turbine performance.

Energy exchange in a compressible turbulent mixing layer

Asymptotic methods have been used to study a turbulent flat mixing layer comprising a viscous compressible gas flow descending from the trailing edge of a body and a gas at rest having the same chemical composition but a different temperature. In contrast to the existing methods for analysing turbulent flows using the Reynolds-averaged Navier-Stokes (RANS) equations, with some closure hypotheses, this paper considers the Navier-Stokes equations using known classic assumptions and facts. The characteristic Reynolds number of the flow is considered large, the thickness of the mixing layer is small, and the Mach numbers are limited within the range of ‘0–5’. The method of multiple scales allows a stationary (secondary) flow inside the turbulent mixing layer to be found and investigated as a principal part of the fluctuating solution. It is shown that the self-induced entrainment of gas from the external flow into the mixing layer is the main stationary flow that ensures the supply of kinetic energy from the zone of maximum speed to the turbulence generation area. It is also discovered that heat diffusion and the inflow of high-velocity gas from the external flow together determine the properties of the mixing layer. The Kolmogorov-scale and turbulence generation regions do not influence the stationary solution in the main approximation.

A mesoscopic modelling approach for direct numerical simulations of transition to turbulence in hypersonic flow with transpiration cooling

A rescaling methodology is developed for high-fidelity, cost-efficient direct numerical simulations (DNS) of flow through porous media, modelled at mesoscopic scale, in a hypersonic freestream. The simulations consider a Mach 5 hypersonic flow over a flat plate with coolant injection from a porous layer with 42 % porosity. The porous layer is designed using a configuration studied in the literature, consisting of a staggered arrangement of cylinder/sphere elements. A characteristic Reynolds number Rec of the flow in a pore cell unit is first used to impose aerodynamic similarity between different porous layers with the same porosity, ∊, but different pore size. A relation between the pressure drop and the Reynolds number is derived to allow a controlled rescaling of the pore size from the realistic micrometre scales to higher and more affordable scales. Results of simulations carried out for higher cylinder diameters, namely 24 μm, 48 μm and 96 μm, demonstrate that an equivalent Darcy-Forchheimer behaviour to the reference experimental microstructure is obtained at the different pore sizes. The approach of a porous layer with staggered spheres is applied to a 3D domain case of porous injection in the Darcy limit over a flat plate, to study the transition mechanism and the associated cooling performance, in comparison with a reference case of slot injection. Results of the direct numerical simulations show that porous injection in an unstable boundary layer leads to a more rapid transition process, compared to slot injection. On the other hand, the mixing of coolant within the boundary layer is enhanced in the porous injection case, both in the immediate outer region of the porous layer and in the turbulent region. This has the beneficial effect of increasing the cooling performance by reducing the temperature near the wall, which provides a higher cooling effectiveness, compared to the slot injection case, even with an earlier transition to turbulence.

Global thermodynamic, transport-property and dynamic characteristics of the Venus lower atmosphere below the cloud layer

This study investigates the global characteristics of the Venus lower atmosphere below the cloud layer. Starting from available data regarding species composition, temperature and pressure, the general thermodynamic and transport properties of the Venus lower atmosphere are first computed at altitudes below the cloud layer. The thermodynamic and transport properties are validated with known data. A thermodynamic stability analysis for a variety of potentially existing mixtures is conducted to highlight the sensitivity of the thermodynamic regime to the variation of the species molar fractions. The limits of thermodynamic stability are represented in the thermodynamic phase diagram of the mixture, and thus regions of phase stability and instability are determined. It is found that the Venus lower-atmosphere thermodynamic regime is located in the stable, single-phase regime, with supercritical conditions occurring in the lower few kilometers, thereby validating ad-hoc expectations which have never envisaged the existence of a two-phase regime at those altitudes. Using thermodynamic and transport-property information thus computed, several non-dimensional numbers are calculated. The Prandtl number is first evaluated. Then, the characteristic Reynolds number is estimated for different assumed length scales, showing that, independent of the length scale, the entire lower atmosphere below the cloud deck is in a fully-turbulent flow regime. Finally, the speed of sound and the Mach number are computed as function of altitude. The information obtained from all these calculations fills a scientific void, and may be crucial for the design of landers on the Venus surface.

Efficiency limits of fans

The purpose of this work is to identify upper efficiency limits of industrial fans such as axial rotor-only fans, axial with guide vanes, centrifugal rotor-only and centrifugal with volute. The efficiency limit is always a function of the class, the design point within the class and the definition of efficiency (total-to-static and total-to-total). The characteristic Reynolds number is another relevant parameter. First, based on analytical and empirical loss models, a theoretical efficiency limit is estimated. A set of idealizing assumptions in the loss models yields efficiencies which are assumed to be an insuperable limit but may be unrealistically high. Second, more realistic efficiency limits are estimated using a computational fluid dynamics-based optimization scheme, seeking for the best designs and hence the maximum achievable efficiencies in all classes. Given the self-imposed constraints in the geometrical parameter space considered, the thus-obtained practical efficiency limits can only be exceeded by admitting more complex geometries of the fans.

Sand-turbulence interaction in a high-Reynolds-number turbulent boundary layer under net sedimentation conditions

Simultaneous two-phase particle image/tracking velocimetry (PIV/PTV) measurements are conducted on a particle-laden turbulent boundary layer (TBL) over a horizontal smooth-flat plate under net sedimentation conditions. Dilute desert sand grains with a median diameter of 203 μm and bulk volume fraction of O(10−5) are used as the discrete phase, and the characteristic Reynolds number of the TBL is relatively high (Reτ = 5500 based on the friction velocity uτ and boundary layer thickness δ). The two-dimensional velocity filed in the streamwise/wall-normal plane is measured by four CCD cameras aligned along the streamwise direction, which resolves a wide spectrum of the scales, ranging from small-scale energetic eddies to large-scale motions (LSMs) in the TBL. An improved phase separation algorithm and discrete particle matching method are developed for two-phase measurements. The results presented here provide new information concerning the effect of high-inertia particles with a dilute concentration on wall-bounded turbulence, especially at high Re. Analysis of the velocity spectrum of the gas phase reveals, for the first time, that the presence of sand grains with a size on the order of the Kolmogorov length scale attenuates turbulence fluctuation by suppressing small-scale sweep-ejection cycles in the near-wall region. A critical layer (y/δ = 0.12 or y+ = 670) is found to partition the streamwise evolution of both the local concentration and the streamwise mean velocity of the sand grains into a non-equilibrium near-wall region and a quasi-parallel outer region. In addition, a balance between the strength and probability between the sweep and ejection events of sand grains is reached at this layer. Such a critical layer might be a good indicator of the upper bound of the particle saltation process, in which LSMs are believed to play a significant role.

Analysis of inertial migration of neutrally buoyant particle suspensions in a planar Poiseuille flow with a coupled lattice Boltzmann method-discrete element method

In this study, a hybrid numerical framework for modelling solid-liquid multiphase flow is established with a single-relaxation-time lattice Boltzmann method and the discrete element method implemented with the Hertz contact theory. The numerical framework is then employed to systematically explore the effect of particle concentration on the inertial migration of neutrally buoyant particle suspensions in planar Poiseuille flow. The results show that the influence of particle concentration on the migration is primarily determined by the characteristic channel Reynolds number Re0. For relatively low Re0 (Re0 < 20), the migration behaviour can only be observed at a very low particle concentration (≤5%). However, when Re0 > 20 the migration behaviour can be observed at a high concentration (≥20%). Furthermore, a focusing number Fc is proposed to characterise the degree of inertial migration. It was found that the inertial migration can be classified into three regimes depending on two critical values of the focusing number, Fc+ and Fc−: (i) when Fc > Fc+, a full inertial migration occurs; (ii) when Fc < Fc−, particles are laterally unfocused; and (iii) when Fc− < Fc < Fc+, a partially inertial migration takes place.

Investigations on performance of valveless piezoelectric micropump with concave tuning diffuser/nozzle elements in transient flow

A diffuser/nozzle is one of the most frequently-used channels in a valveless piezoelectric micropump, but its efficiency has not been satisfactory. Hence, optimisation of the channel structure is of great significance. The concave tuning diffuser/nozzle element can obtain steady flow rectification under different Reynolds numbers, and its efficiency is much higher than the conventional diffuser/nozzle element whose diverging angle is >25°. Therefore, the application of concave tuning on the micropump is promising and worth anticipating. In this work, the experiment and numerical simulation were carried out under the conditions of voltage (50–250 vpp), excitation frequency (10–1000 Hz) and Rec (100–1000). The results show that the performance of a micropump with concave tuning is better than that with a straight sidewall, as the pump efficiency is improved significantly. The position and size of vortexes are of great significance to the pump efficiency of the micropumps. The distribution of pressure in the micropumps with concave tuning and straight sidewall was displayed. With the increase of characteristic Reynolds number, the adverse pressure gradient occurred. Compared with the straight sidewall, the concave tuning structure can better withstand adverse pressure gradient and delay the boundary layer separation in the channel.

Vortex-dynamical interpretation of anti-phase and in-phase flickering of dual buoyant diffusion flames

Anti-phase and in-phase flickering modes of dual buoyant diffusion flames were numerically investigated and theoretically analyzed in this study. Inspired by the flickering mechanism of a single buoyant diffusion flame, for which the deformation, stretching, or even pinch-off of the flame surface result from the formation and evolution of the toroidal vortices, we attempted to understand the anti-phase and in-phase flickering of dual buoyant diffusion flames from the perspective of vortex dynamics. The interaction between the inner-side shear layers of the two flames was identified to be responsible for the different flickering modes. Specifically, the transition between anti-phase and in-phase flickering modes can be predicted by a unified regime nomogram of the normalized flickering frequency versus a characteristic Reynolds number, which accounts for the viscous effect on vorticity diffusion between the two inner-side shear layers. Physically, the transition of the vortical structures from symmetric (in-phase) to staggered (anti-phase) in a dual-flame system can be interpreted as being similar to the mechanism causing flow transition in the wake of a bluff body and forming the Karman vortex street.