Reynolds Number Ratio Research Articles

Experimental Investigation of the Dynamics of Methane-Oxygen Diffusion Flame Stabilized Over Swirl Coaxial Injector

ABSTRACT The combustion dynamics of methane-oxygen inverse diffusion flames stabilized over a swirl coaxial injector are investigated in detail. Mapping of different regimes of flame dynamics was carried out by classifying the flame into stable flames, oscillating flames, and unstable flames. The dominant frequency of the acoustics associated with different flame characteristics was determined from a free-field microphone measurement of combustion noise, and the respective flame morphology was studied by high-speed imaging of OH* chemiluminescence. Experiments were conducted for different oxidizer jet Reynolds numbers corresponding to each of the three different fuel jet Reynolds numbers. For all three power levels, flame transition from stable to unstable was observed as the oxidizer Reynolds number and equivalence ratio increased from fuel-rich to oxidizer-rich conditions. Strong acoustic-combustion heat release rate coupling was observed in the unstable flames. Modal decomposition techniques were employed to study the spatio-temporal evolution of the flame. The energetic coherent modes corresponding to the frequency of oscillation reveal two different modes of flame oscillation: longitudinal and transverse. All three fuel Reynolds numbers under investigation showed a predominant longitudinal mode of oscillation, while only the highest fuel flow conditions, corresponding to a fuel jet Reynolds number of 765 showed a transverse mode flame oscillation, as the oxidizer Reynolds number increased above 8000.

Numerical study of fluid-structure interaction for enhanced heat transfer in microchannels with an oscillating elastic wall

The present numerical study explores the performance of fluid-structure interaction (FSI) in a microchannel with an oscillating elastic wall. A two-dimensional (2D) Computational Fluid Dynamics (CFD) simulation was performed to investigate the influence of the elastic wall's frequency and amplitude on fluid flow behavior, pressure drop, and heat transfer enhancement. The FSI governing equations were solved using the Arbitrary Lagrangian-Eulerian (ALE) method. The results indicated that the Nusselt number (Nu) decreases as oscillation frequency increases. In contrast, the Nu increased linearly with the oscillation amplitude. Additionally, the Prandtl number (Pr) showed an insignificant influence on the Nu number for the studied operating range. An optimal operating condition was identified for the microchannel with an oscillating wall, achieving a spatial average Nu number of 16.796 compared to 14.577 for a simple microchannel channel, representing a 15.23 %% enhancement in heat transfer. A correlation is derived for the spatial average Nu number as a function of the Reynolds number (Re), Strouhal number (St), Pr, and vibration amplitude ratio, providing a valuable tool for designing and optimizing microchannel systems with FSI. Finally, the Maxwell boundary conditions are incorporated into the simulation of a microchannel with a vibrating upper wall to evaluate the slip conditions.

Experimental and numerical investigation of a three-blade horizontal axis hydrokinetic water turbine (HAHWT) in high blockage conditions

Horizontal-axis hydrokinetic water turbines (HAHWT) represent a cost-effective and low-maintenance opportunity for hydropower generation in low-velocity channels. To enhance understanding of the potentiality of an original HAHWT prototype working at high blockage operations (e.g. tidal channels, man-made water infrastructure, offshore energy platforms), an experimental and numerical investigation was carried out to assess its performance curves under sub-critical flow conditions.The dependence of the turbine efficiency on the Froude Number (Fr), Reynolds Number (Re) and Blockage Ratio (Br) was thus investigated, showing their relevance for the overall turbine assessment. The overall energy exploitation was strictly dependent on the contribution of the potential head, thus showing the significant reduction of the turbine efficiency for partially submerged operations.

Immiscible non-Newtonian displacement flows in stationary and axially rotating pipes

We examine immiscible displacement flows in stationary and rotating pipes, at a fixed inclination angle in a density-unstable configuration, using a viscoplastic fluid to displace a less viscous Newtonian fluid. We employ non-intrusive experimental methods, such as camera imaging, planar laser-induced fluorescence (PLIF), and ultrasound Doppler velocimetry (UDV). We analyze the impact of key dimensionless numbers, including the imposed Reynolds numbers (Re, Re*), rotational Reynolds number (Rer), capillary number (Ca), and viscosity ratio (M), on flow patterns, regime classifications, regime transition boundaries, interfacial instabilities, and displacement efficiency. Our experiments demonstrate distinct immiscible displacement flow patterns in stationary and rotating pipes. In stationary pipes, heavier fluids slump underneath lighter ones, resulting in lift-head and wavy interface stratified flows, driven by gravity. Decreasing M slows the interface evolution and reduces its front velocity, while increasing Re* shortens the thin layer of the interface tail. In rotating pipes, the interplay between viscous, rotational, and capillary forces generates swirling slug flows with stable, elongated, and chaotic sub-regimes. Progressively, decreasing M leads to swirling dispersed droplet flow, swirling fragmented flow, and, eventually, swirling bulk flow. The interface dynamics, such as wave formations and velocity profiles, is influenced by rotational forces and inertial effects, with Fourier analysis showing the dependence of the interfacial front velocity's dominant frequency on Re and Rer. Finally, UDV measurements reveal the existence/absence of countercurrent flows in stationary/rotating pipes, while PLIF results provide further insight into droplet formation and concentration field behavior at the pipe center plane.

Flow topology and mixing in alveolar edema: Unsteady flow in interconnected cavities with moving walls

The study of alveolar fluid mechanics is critical for comprehending respiratory function and lung diseases, particularly in cases of alveolar lesions that result in significant structural and fluid dynamic changes. This study investigates the flow topology and chaotic mixing within both normal and edematous alveoli, where the alveoli in the edematous model are interconnected by pores. To numerically simulate alveolar flow, a mathematical model is developed to ascertain the key parameters of Reynolds number (Re) and alveolar expansion ratio. Subsequently, the flow fields are analyzed to determine wall shear stress (WSS) and to identify WSS critical points and critical points of velocity vector, with a thorough presentation of the various flow topologies corresponding to these critical points. Moreover, a dynamic mode decomposition-based method is introduced to track particle trajectories, and the exploration of chaotic mixing is conducted through tracer advection, Poincare map, and the calculation of finite-time Lyapunov exponents. Results indicate that the edematous model exhibits a higher Re and higher WSS due to the fluid properties. Within the alveoli, high WSS is usually localized at the pores. The pores increase critical points and alter flow topologies, significantly changing chaotic mixing. Additionally, Re and alveolar locations also affect mixing patterns. These findings are crucial for understanding alveolar physiology and designing inhaled drugs for lung diseases, considering the role of chaos in particle transport in the lung acini.

Study on Turbulent Taylor-Couette Flow with High Reynolds Number and Large Radius Ratio in High-Speed Canned Motor Pump Internals

Abstract The Taylor-Couette flow, a prevalent flow pattern in fluid machinery. This study investigates turbulent Taylor-Couette flow within the internal flow of a shield pump through numerical simulations. The study encompasses a range of radius ratios (0.934 to 0.977) and inner cylinder frequencies (50 to 383 Hz). Our findings reveal a significant positive correlation between torque magnitude and radius ratio within the studied parameter range. Additionally, an exponential relationship between non-dimensional torque and Taylor number was identified through fitting. Moreover, the study elucidates that larger radius ratios lead to an earlier transition to the final turbulent region with increasing Taylor numbers. Furthermore, detailed analysis of the flow field vortex structure demonstrates the profound influence of radius ratio on the number of Taylor vortices.

Numerical investigation on a novel milli-sized heat sink equipped by twisted elliptical tubes

Thermal management in some small chemical reactors is essential to achieve a final high-quality product and heat sinks can play a remarkable role in dissipating heat from such systems. In this regard, this study attends to evaluate the conjugate heat transfer problem in a heat sink equipped by twisted elliptical tubes (TETs). The effects of significant parameters such as Reynolds number (Re = 250, 350, 500, 700 and 950) and twist ratio (TR = 2.5, 5 and 10) on hydrothermal and thermodynamics performance of the novel heat sink are investigated. The swirling flow is the main reason of fluid particles migration from hot surface to cold one and vice versa, leading a better heat transfer occurs at the expense of not significant pressure loss augmentation. The results revealed that the TETs are responsible of more wall temperature uniformity and avoids generating hot spots. Compared with plain elliptical tubes, the presence of TETs inside heat sink improves the heat transfer rate and enlarges the pressure drop by 1.08–2.03 times and by 1.02–1.92 times, respectively. In addition, the TETs decrease the entropy generation rate inside heat sink and the best value of second law efficiency is about 35 %, detected at TR = 2.5 and Re = 250.

Numerical investigation of air entrainment and outlet temperature characteristics of an infrared suppression device with obstacles

Infrared suppression devices (IRS) are crucial for stealth capabilities of modern naval ships and fighter jets. This study numerically investigates the air entrainment and outlet temperature characteristics of an IRS device with conical and spherical obstacles using finite volume method, to solve continuity, momentum, energy, and eddy viscosity-based k-ε equations. We vary Reynolds number (Ren), blockage volume ratio (Vob/Vmf), funnel-overlap height (Hov/Dn), and the nozzle inlet temperature (Tin/Tinf) within the ranges of 3.23×105 to 1.914×106, 0 to 0.106, 0 to 0.653, and 1.243 to 2.577, respectively, to analyze their impacts on enhancement in air entrainment and attenuation in outlet temperature. We observed that the dimensional air entrainment rate monotonously increases with the Reynolds number, and the obstacles further improve air ingestion. The conical obstacle entrains 28.96% more air than the spherical obstacle at a same Reynolds number (Ren=3.225×105) and blockage ratio. The blockage ratio positively impacts on the air ingress; and the maximum air ingestion occurs at a blockage ratio of 0.0266. An IRS with the higher positive overlap-height of funnels promotes air ingress to suppress the outlet temperature. Within the studied overlap height range (0–0.49), air ingress is enhanced by 50% and 85.9%, respectively at Ren=3.225×105 and 1.914×106. At Ren=1.914×106, the IRS exhibits 1.67 times more air entrainment rate at Tin/Tinf=1.91 than at Tin/Tinf=1.2438.

Effects of different momentum ratios and Reynolds number in a T-junction with an upstream elbow

This study focuses on analysing thermal mixing in T-junctions with varying momentum and Reynolds number ratios, utilizing computational fluid dynamics (CFD) simulations. The T-junction is a critical component of the primary nuclear thermal–hydraulic circuit within a pressurized water-cooled reactor (PWR). The T-junction connects the pressurizer (PRZ) with the steam generator (SG) and the reactor pressure vessel (RPV). Water from the PRZ and the SG are at different temperatures and incomplete thermal mixing occurs when these two fluid streams meet at the T-junction. This incomplete thermal mixing can induce thermal stratification of the water within the T-junction as well as thermal striping phenomena. Thermal striping phenomena can lead to fluctuations of the temperature at the inner pipe wall of the T-junction. Thermal stratification and thermal striping phenomena can induce thermo-mechanical fatigue and eventual pipe failure which can affect the safety of the reactor. Therefore, a high-fidelity, mechanistic understanding of the turbulent thermo-fluid mixing within T-junctions of PWRs might lead to improvements in component reliability and safety within nuclear power plants (NPPs).The primary aim of the research, presented in this paper, is to understand and quantify the effect of variations in the momentum ratio on the turbulent fluid flow within T-junctions. This is achieved by either varying the branch pipe diameter while keeping the inlet velocity constant (part one) or by adjusting the branch pipe inlet velocity while maintaining a constant diameter (part two). Despite the different variations in momentum ratios, the specific momentum ratios under consideration in both parts of the study remain consistent (namely 98 and 66.4). It is also noteworthy that the momentum ratios considered in the paper can be classified as wall-jet and impinging-jet, according to the definition in (Hosseini, Yuki, & Hashizume, 2008). It should be noted that the momentum ratio is manipulated by adjusting the flow parameters, leading to variations in the Reynolds number ratio between the main pipe inlet and the upstream branch pipe at the T-junction. The turbulent flows in the cases that are considered are simulated using the Improved delayed detached eddy simulation (IDDES-SST) model. The numerical results from these simulations indicate, for the considered momentum ratios, that maintaining the same momentum ratio does not produce similar mean flow behaviour and turbulent quantities of interest (QoI). For instance, the size of the flow recirculation zone is more likely linked to the diameter of the branch pipe. Moreover, the turbulent QoI and temperature fluctuations at the determined locations are likely affected by the changed flow recirculation zone as well as the Reynolds number of the branch pipe flow.

An effective simulation scheme for the prediction of aerodynamic environment under hypersonic conditions characterized by NACA0012

Currently, aerodynamic environment prediction research into scramjet-propelled vehicles characterized by NACA0012 under hypersonic conditions is relatively sparse. Two-dimensional external flow field models are established, and then through validation tests, we perform a systematic investigation between simulation parameters and prediction accuracy, and an effective aerodynamic environment prediction simulation scheme under hypersonic conditions is proposed. Unlike under incompressible conditions, the maximum accuracy decline could be attributed to the inappropriate choice of the sharp trailing edge modeling method, but the definition formula is still preferred. In particular, for the two modeling data point sources, Airfoil tools and NACA4, the numerical performance of the latter is better than the former, and the calculation accuracy negatively correlates with the number of data points offered by both of them. Moreover, for the mesh cells near the shock, the cell Reynolds number and aspect ratio values should be no smaller than 16 and not exceed 380, respectively, and the recommended values for the far field distance, the turbulence model and flux type are 16L, Spalart-Allmaras, and ROE flux type. Under hypersonic conditions, the aerodynamic environment characterized by NACA0012 predicts a maximum temperature of approximately 1856.85 °C, with an average temperature change rate of 77 °C/s. Meanwhile, the top sound pressure level and the vibration acceleration could reach up to 145 dB and 182 g, respectively.

Effect of Flow Interference between Cylinders Subjected to a Cross Flow over a Cluster of Three Equally Spaced Cylinders

In this paper, flow over a cluster of three equally spaced circular cylinders was studied by numerical simulation based on the turbulence model k-kl-ω for two incidence angles β = 0° and 60°, at different Reynolds numbers, and flow interference pattern characteristics between cylinders, characteristics of force parameters, and Strouhal number of each cylinder with different spacing ratios ranging from 1.5 to 4 at Re 8 × 104, 2 × 105 and 2 × 106 were obtained. Analyzing the flow field around three cylinders, the following results have been obtained: (1) at incidence angle β = 0° and 60°, the wake was nearly symmetrical if S/D ≥ 2.0; (2) at β = 60°, S/D = 1.5, and Re = 2 × 105, an asymmetric periodic flow pattern occurred in the wake region which produced a significant effect on the surface mechanical parameters and Strouhal number, and this was observed for the first time. The periodic flow regime of the wake region also occurred at S/D = 1.35 and 1.5, without the same phenomenon at S/D = 1.7 and 2.0; this phenomenon is described for the first time in this paper; (3) the phenomenon of periodic flow regime in the wake region was intrinsic and related to Reynolds number and space ratio. In addition, the characteristics of force parameters of three cylinders were mainly affected by the interference between cylinders, at 1.5 < S/D < 4, which indicated that the drag coefficient of three cylinders reduces with different Reynolds numbers and increases with enlargement of the spacing ratio for upstream cylinders at incidence angle 0°. At incidence angle 60° and S/D = 1.5~4, the Strouhal number decreases with the enlargement of spacing ratio for the upstream cylinders, but the Strouhal number increases for the downstream cylinder, which is another prominent flow interference influence. The results indicated the effect of flow interference between cylinders subjected to a cross flow over a cluster of three equally spaced cylinders, considering the flow pattern, surface mechanical parameters and Strouhal number, which should be considered in the establishment of standard design codes in fields such as offshore wind turbine engineering for flow interference around groups of cylinders.

Stability of plane parallel flow revisited for particle-fluid suspensions

Abstract An alternative model is proposed for hydrodynamic stability of plane parallel flow of an incompressible Newtonian fluids with suspended solid particles. For heavy particle-laden dusty gases with negligible particle volume fraction, the effective complex-form mean velocity in the modified Orr-Sommerfeld equation derived by the present model is showed to be essentially identical to the well-known Saffman's classical results. In the limit cases of small or large Stokes number of particles, simple formulas are derived for the effective Reynolds number ratio of the particle-laden suspension to the clear fluid without particles under otherwise identical conditions. The derived formula for particles of finite particle-to-fluid density ratio and small Stokes number is verified by comparing predicted results with known data, although a comparison of the derived formula with known results for particles of finite density ratio and large Stokes number cannot be made here due to the lack of available data. It is hoped that the present work could offer a conceptually novel and relatively simplified model for hydrodynamics of solid particle-fluid suspensions.

Lifting of Transversely Forced Turbulent Nonpremixed Coaxial Jet Flames

The lifting behavior of turbulent nonpremixed coaxial jet flames was investigated experimentally as a function of the center jet Reynolds number, annular-to-center jet velocity ratio, acoustic frequency, and acoustic amplitude, all with and without transverse acoustic disturbances acting on the flames situated at a pressure antinode. Global lifting regimes were mapped and consisted of attached flames, periodically lifted flames, and permanently lifted flames. With one exception, all flames were attached in the absence of acoustics and lifted only because of the applied acoustic excitation. The exception occurred at the highest Reynolds number and velocity ratio, where the flames were unconditionally lifted in all cases. Between these two extremes, a range of lifting regimes was observed. Lower applied frequencies and smaller amplitudes were found to generally promote attachment to the burner. Flow visualizations using high-speed Schlieren and OH* chemiluminescence imaging revealed a lateral spreading effect near the jet exit. The lateral spreading was hypothesized to be caused by an axially oriented counterflow collision between the downstream flowing jets and presumed local upstream portion of the acoustic velocity fluctuations. Physical mechanisms were hypothesized based on this observation, which appear to consistently explain most of the observed behavior.

Numerical investigation of the divergence-free constraint for the miscible fluids interaction in a lock-exchange arrangement

The present work scrutinizes the implementation of the divergence-free constraint in miscible fluids flow algorithms. In general, the flow solvers handling the interaction of the miscible fluid enforce the zero divergence condition, considering the fluids to be incompressible. In these algorithms, however, a convection-diffusion equation for the mass fraction, in conjunction with the Navier-Stokes equation, is solved for incorporating the mixing effects. This equation leads to a non-zero velocity field in the numerical modeling and the derived velocity divergence is a function of Reynolds and Schmidt numbers. Therefore, in this work, a quasi-incompressible formulation is presented for such flows wherein weak compressibility effects exist, but Mach numbers are very small. This novel approach is tested extensively in the classical lock-exchange setup where the effects of Reynolds and Schmidt numbers are analyzed. The role of density ratios is also investigated to realize whether the quasi-incompressible formulation generates a different mixing behavior or is similar to the conventional incompressible approach. The results demonstrate the convincing differences in these two formulations subjected to the specific combinations of Reynolds number, Schmidt number, and density ratio. A lenient criterion is also suggested by investigating the numerical tests carried out in this work, which may predict the possibilities of generating consistent results in both formulations.

Analyzing heat transfer behavior in two-dimensional Darcy–Forchheimer porous medium using magnetized nanoparticles

This study investigates the two-dimensional boundary layer flow and heat transfer of an incompressible fluid over a plate embedded in a Darcy–Forchheimer porous medium of magnetite ternary hybrid ferrofluid in the presence of suction or injection. It uniquely includes the effects of thermal radiation and viscous dissipation in the energy equation, offering a comprehensive analysis of the phenomena involved. The research focuses on three nanoparticle (NP) combinations of ferrofluid particles ( Fe 3 O 4 ) and metal oxide NPs ( CuO / TiO 2 ) dispersed in an aquatic base fluid with different volume fractions. The governing nonlinear partial differential equations are transformed into ordinary differential equations via similarity transformations and solved using the Runge–Kutta-based shooting technique. The study evaluates key physical quantities, such as the skin friction coefficient and Nusselt number, and examines the effects of dimensionless parameters, including the absorbent Reynolds number (Re), expansion ratio (α), Peclet number (Pe), Eckert number (Ec), NP volume fractions ( φ 1 , φ 2 , and φ 3 ) , porous medium parameter (r), and Darcy-porous medium parameter (F), on velocity and temperature profiles. The results indicate that increasing the porous medium parameters r and F leads to opposite shear stress effects in the dual-porosity medium. Higher Peclet number (Pe) and Eckert number (Ec) values enhance heat transfer rates within the thermal boundary layers. Moreover, elevated Reynolds number (Re) and expansion ratio (α) values result in opposing radial velocity profiles within the momentum boundary layers. This comprehensive analysis provides valuable insights into the complex interactions governing ternary ferrofluid flow and thermal performance in dual-porosity media, contributing to advancements in fluid system applications.

On the Nusselt number correlations of tandem surrogate firebrands on a flat surface

Through the heat-mass transfer analogy, naphthalene sublimation experiments were conducted in a heated-air wind tunnel to study the effects of aspect ratio and dimensionless separation distance on the convective heat transfer coefficients of three tandem naphthalene cylinders. Nusselt number correlations were presented for the individual naphthalene cylinders and the full configuration of three cylinders. In all the cases studied, the Reynolds number had the strongest effect on the Nusselt number followed by the aspect ratio and the dimensionless separation distance. Nusselt numbers were higher for the smaller aspect ratios. For a given Reynolds number and aspect ratio, the Nusselt number increases with the dimensionless separation distance.

Numerical study of energy consumption in spacer-filled feed channels through 3D inverse modeling and computational fluid dynamics

This project employs advanced Computational Fluid Dynamics (CFD) simulations to investigate the complex flow field dynamics within the channel of membrane module featuring a commercially available feed spacer. Utilizing Micro-CT scanning, the intricate three-dimensional (3D) structure of the spacer is accurately captured, enhancing the precision of the simulation models. The project focuses on the effects of varying Reynolds number (Re) and Aspect Ratio (AR) on the energy consumption within the feed channel of membrane module, analyzing streamline patterns, vorticity, and flow separation angles in detail. Findings indicate that the total enstrophy identification method effectively pinpoints areas of high energy consumption, especially at lower Re levels where flow separation significantly contributes to hydraulic losses. As Re increases, the separation vortex shifts rearward, resulting in a marked decrease in the energy consumption coefficient. Furthermore, the flow separation angle consistently declines with increasing Re, stabilizing at higher levels. Significantly, a reduction in AR from 1.015 to 0.725 more than doubles the decrease in flow separation angle, highlighting substantial potential energy savings through spacer design optimization. These insights are crucial for improving the design and efficiency of spiral wound membrane modules and for refining feed spacer configurations to enhance performance.

Multiple solution of MHD Casson fluid flow in porous channel with chemical reactions and thermal radiation effects

This study focused on evaluating the synergistic effects of magnetohydrodynamics, Casson fluid properties, thermal radiation, chemical reactions, and heat transfer mechanisms within a porous channel. Through the application of similarity transformation, nonlinear governing equations are converted into nonlinear ordinary differential equations. These modified equations were then numerically solved in MATLAB using the Runge–Kutta method alongside the shooting technique to ensure precise results. The investigation yielded various numerical solutions for the dimensionless velocity, temperature, concentration, skin friction coefficient, heat transfer coefficient, and Sherwood number, all of which are presented in both tabular and graphical formats. Three distinct solutions emerged from the analysis, differentiated by variations in the Reynolds number, Casson number, expansion or contraction ratio, and magnetic parameters. These solutions demonstrate differences in the parameters under investigation. Solutions within the ranges of γ[5,∞] and R[31.07,∞] are influenced by the specific values of the magnetic number M[0,2.0]. For each M value, there exists a unique set of solutions for γ and R that satisfy the established parameters. As the magnetic number varies, so does the range of feasible solutions, highlighting the sensitivity of the system to magnetic influence. The values of γ and R are adjusted according to the chosen M value.

Study on windage loss characteristics of supercritical CO2 Taylor-Couette-Poiseuille flows

Taylor-Couette-Poiseuille (TCP) flow is prevalent in rotating machinery, occurring extensively between a high-speed rotating shaft and its static case. This study employed a numerical simulation method to investigate the flow characteristics and windage loss in supercritical carbon dioxide (sCO2) TCP flow. The findings revealed that increasing the rotational Reynolds number and aspect ratio and decreasing the axial Reynolds number and radius ratio reduced the friction coefficient (Cf). Ultimately, a Cf correlation for sCO2 TCP flow was derived through fitting simulation results, exhibiting an average relative error within ± 2 %. These results established a theoretical foundation for the structural design of sCO2 rotating machinery.

Vortex-induced rotation of a square cylinder under the influence of Reynolds number and density ratio

Numerical simulations are carried out on the vortex-induced rotations of a freely rotatable rigid square cylinder in a two-dimensional uniform cross-flow. A range of Reynolds numbers between 40 and 150 and density ratios between 0.1 and 10 are considered. Results show eight different characteristic regimes, expanding the classification of Ryu & Iaccarino (J. Fluid Mech., vol. 813, 2017, pp. 482–507). New regimes include the transition and wavy rotation regimes; in the ${\rm \pi}$ -limited oscillation regime we observe multipeak subregimes. Moment-generating mechanisms of these regimes and subregimes are further elucidated. A phenomenon related to the influence of density ratio is the tooth-like shape of the ${\rm \pi} /2$ -limit oscillation regime observed in the regime map, which is explained as a result of the imbalance relation between the main frequencies of rotation response and the vortex shedding frequency. In addition, existence of multiple regimes and multistable states are discussed, indicating multiple stable attractive structures in phase space.