Stationary Circular Cylinder Research Articles

Струйный эффект при возникновении присоединенной каверны от системы импульсивных давлений

We consider the plane problem of the emergence of an attached cavity caused by the sudden action of impulsive pressures at some initial time. It is assumed that these pressures are distributed on the upper part of the boundary of a stationary circular cylinder immersed in liquid. A problem with unilateral constraints is formulated, on the basis of which the flow of liquid at the initial moment of time and the initial zone of separation of liquid particles are determined. At the next moments of time, an attached cavity is formed, the shape of which is determined based on the solution of the dynamic initial-boundary value problem of the theory of potential flows of an ideal incompressible fluid with free boundaries. The main unknowns in it are the velocity potential, the shape of the cavity, the dynamics of the separation points, and the perturbation of the external free boundary of the liquid. It is required to study the posed problem at short times, focusing on the behavior of the internal free boundary of the liquid near the separation points. When studying this problem, pressure in the cavern, which is created artificially, plays an important role. At low pressures, the internal free boundary of the liquid near the separation point is located on opposite sides of this point. In this case, the end part of the cavity resembles a stream of gas directed along the boundary of the cylinder towards the liquid.

Binary interactions between stationary circular and non-circular cylinders in steady unbounded flow

Binary interactions between stationary circular and non-circular cylinders in steady unbounded flow

Predicting pressure fields from incomplete velocity fields based on deep convolutional neural network

Acquisition of an instantaneous pressure field in a flow field is essential for experimental fluid dynamics research because pressure is associated with various flow phenomena. Machine learning has performed well in various fluid mechanics studies in recent years due to its nonlinearity. In this paper, we use the machine learning method to predict the pressure fields from incomplete velocity fields while reconstructing the missing velocity information, as exemplified by the stationary circular cylinder flow and circular cylinder undergoing forced oscillating problems, in which the incompleteness of the velocity field is caused by the optical path occlusion in experiments. We propose a network model based on convolutional neural networks. The experimental results show that the error of machine learning methods is around 4%, and even if the resolution of the training set is reduced, it does not affect the prediction accuracy of the network. For statistical averaging of prediction results, the network has high accuracy in predicting first-order quantities, but its ability to predict second-order quantities is limited. We also explore the effects of the amount of noise on the performance of networks. When applying the model to the forced oscillating cylinder problem, we use transfer learning to train the network given the similarity of the two problems, and the training error yields faster convergence and more minor convergence results. In addition to this, we use flow field data with a single vibration frequency to construct a single dataset, and flow field data with multiple vibration frequencies to construct a mixed dataset, and study the effect of different datasets on the prediction accuracy, which shows that it is difficult for neural networks to achieve both accuracy and generalization.

Wake interference effects on flow-induced vibration of flexible membrane wings

This work investigates the effect of wake interference on the nonlinear coupled dynamics and aerodynamic performance of flexible membrane wings at a moderate Reynolds number. A high-fidelity computational aeroelastic framework is employed to simulate the flow-induced vibration of flexible membrane wings in response to unsteady vortex wake flows produced by an upstream stationary circular cylinder. The coupled dynamics of the downstream membrane are investigated at different gap ratios, aeroelastic numbers, and offset distances. The variations in flow features, membrane responses, and frequency characteristics are analyzed to understand the wake interference effect on membrane aeroelasticity. The results indicate that the aerodynamic performance and flight stability of the downstream membrane are degraded under the wake interference effect. Four distinct flow regimes are classified for the cylinder–membrane configuration, namely (i) single body flow, (ii) co-shedding I, (iii) co-shedding II, and (iv) detached vortex-dominated vibration, respectively. The mode transition is found to build new frequency synchronization between the flexible membrane and its own surrounding flows, or the wake flows of the cylinder, to adjust the aerodynamic performance and membrane vibration. This study sheds new light on membrane aeroelasticity in response to wake flows and enhances understanding of the fluid–membrane coupling mechanism. These findings can facilitate the development of next-generation bio-inspired drones that have high flight efficiency and robust flight stability in gusty flows.

Unsteady Dean flow between concentric circular cylinders in the presence of a uniform axial magnetic field

An analysis is carried out on the unsteady Dean flow of an incompressible electrically conducting viscous fluid between two concentric, stationary permeable circular cylinders in the presence of magnetic field of low intensity. The flow phenomenon is important in view of its biological as well as industrial applications, particularly in polymer industries for designing flows in cylindrical shaped pipes/tubes. The novelty of the study is to analyze the effect of electromagnetic body force which comes into play due to interaction of magnetic field with conducting fluid in flow. The cross flow due to suction/injection, azimuthal pressure gradient, and the Lorentz force (electromagnetic body force) are considered in the momentum transport equation. The mathematical model and the corresponding governing equations are solved in two methods; one is analytical using special function and another one is semi analytical approach, i.e. Laplace transform in conjuction with Riemann–Sum approximation for inversion. The study reveals the effects of magnetic parameter, suction/injection parameter and radii ratio of two concentric cylinders forming annular region. The striking outcomes which fulfills the design requirements are as follows. The applied radial magnetic field resulting electromagnetic body force on the flow, accelerates the circumferential velocity which energizes the industrial setup (flow model) to enhance faster productivity. Moreover, the curves of skin friction at R = λ posses critical points serving as benchmark for engendering flow instability.

Vortex-shedding and bistability in cylinder-flexible plate assembly in a channel

This study numerically investigates the fluid–structure interaction dynamics of a stationary circular cylinder with an attached flexible splitter plate in a confined fluid domain. We explore how variations in Reynolds number (Re), plate length, offset from the channel centerline, and blockage ratio influence the vortex-shedding and oscillatory behavior of the plates in laminar flow. Results indicate that at low Reynolds numbers (Re = 100), there are no vortex shedding or oscillations, while at higher Reynolds (Re = 200 to 300), the shorter plate exhibits first-mode oscillations and symmetry breaking, whereas the longer plate shows only transient second-mode oscillations at Re = 300 that diminish in amplitude, suggesting that increased plate length reduces vortex-induced forces. Dynamic Mode Decomposition (DMD) analysis confirms consistent primary flow structures across different Reynolds numbers, with initial modes encapsulating the majority of the system’s dynamics. In addition to determining the critical Re for vortex-shedding, vortex-induced oscillations and bistability, the study also examines the critical blockage ratios on the symmetry breaking phenomenon, and also shows that plate stability is influenced by domain asymmetry. These insights enhance understanding of the biomechanics of fish-like robots and inform the design and control of bioinspired flexible structures in fluid flows.

A novel vortex-induced vibration model for a circular cylinder in the vicinity of a plane wall

A novel vortex-induced vibration (VIV) model is proposed to predict the transverse responses of an elastically mounted circular cylinder in the proximity of the wall. Firstly, flow characteristics and hydrodynamic loads on a near-wall stationary circular cylinder are summarized and analyzed based on the existing experimental results, and then the Strouhal shedding frequency and the empirical correlations of the mean lift coefficient and oscillating lift coefficient are established. Subsequently, by introducing the empirical correlations of fluid loads to the equations of structure vibration, a novel VIV model for the near-wall circular cylinder is proposed to describe more precisely the effect of the plane wall. The accuracy, stability, and adaptability are validated by employing experimental VIV results. Compared to existing models, the novel model has advantages in achieving acceptable accuracy in various scenarios. Finally, using the proposed VIV model, the dynamic features of a near-wall circular cylinder to the reduced velocity and gap ratio are studied in detail, including the time-averaged displacements, lock-in regime, maximum amplitude, and dominant frequency. The results obtained are valuable for understanding the VIV characteristics of the near-wall cylinder, and the semi-empirical VIV model proposed could be applied in engineering prediction in the future.

A dynamic-mode-decomposition-based acceleration method for unsteady adjoint equations at low Reynolds numbers

The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic optimization. In this letter, the solution of unsteady adjoint equations is accelerated by dynamic mode decomposition (DMD). The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system. Thereafter, DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching. First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step. Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example, the efficiency of solving unsteady adjoint equations is significantly improved. Results show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics, and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors, which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.

The effect of transverse inclination angle on hydrodynamic characteristics of two tandem circular cylinders in an X arrangement

A numerical investigation of the flow around two stationary circular cylinders in an X arrangement, with a Reynolds number of Re = 3900 and a spacing ratio of L/D = 4.0, is conducted using Large-Eddy Simulation. Eight different transverse inclination angles (α = 0°–30°) are considered to investigate their effects on several aspects, including the time-averaged drag coefficient (Cd-ave), root-mean-square lift coefficient (Cl-rms), Strouhal number (St), instantaneous flow structure, and time-averaged pressure distribution. The numerical results demonstrate that when the inclination angle exceeds a critical value of αc = 12.5°–15°, the flow pattern in the gap between two cylinders transitions from the reattachment regime to the co-shedding regime. This flow transition indicates that the wake vortex periodically detaches from the upstream cylinder and impinges on the downstream cylinder, resulting in a sharp increase in force coefficients, especially for the downstream one. When compared with α = 15°–30°, the force coefficients for both cylinders at α = 0°–12.5° are reduced, which is favorable to the structural stability. Furthermore, an increase in α leads to a monotonic rise in Cd-ave for the downstream cylinder. This can be primarily attributed to the amplified pressure coefficient on the front face of the downstream cylinder, which is caused by the reduced shielding effect from the upstream one.

A spectral force representation and its physical implication for vortex shedding past a stationary or an oscillating circular cylinder at low Reynolds number

Vortex shedding is an ubiquitous phenomenon behind a bluff body (such as circular cylinder) and becomes more complicated when the body is also in oscillation. It is apparent that periodic behavior must be accompanied by the time-varying force, such as lift and drag (coefficients) with known distinguished cases (say, at Re=200) of low-frequency modulation (LFM), sub-harmonic synchronization (SHS), and normal harmonic synchronization (NHS). In a classical analysis, the force spectrum is often analyzed by the Fourier transform or some more recent methods, and typically, a quite complex frequency spectrum is obtained owing to the inherent nonlinearity in the flow system. In the present study, we extend the principal frequency analysis [Lu et al., “An EMD-based principal frequency analysis with applications to nonlinear mechanics,” Mech. Syst. Signal Process. 150, 107300 (2021)] to the principal spectrum analysis (PSA) with both its amplitude and phase in a composite functional form and provide a spectral representation (SR) of the force coefficients only in terms of the characteristic frequencies. In particular, we consider the unsteady laminar flow past a stationary circular cylinder or an oscillating circular cylinder (with frequency f0), while the resulting vortex shedding frequency is denoted by fVS. The spectral representation via the proposed PSA can reveal nonlinear interactions of the two characteristic frequencies (f0 and fVS) in influencing the force coefficients and distinguish direct and interactive modes in which f0 and fVS interact with each other. As a matter of fact, the successively shed vortices are not identical in the strength (amplitude) nor in the phase function. The spectral representation further enables us to identify complicated vorticity activity near around the bluff body: the periodicity of the strength of the shed vortices and the phase shift in the successive vortex shedding—all at the integer multiples of the greatest common-divisor (gcd) of the (two) characteristic frequencies. The gcd frequency of ⟨f0, fVS⟩ is identified as the genuine (slow, long-term) frequency of the entire vortex shedding process in contrast to the (fast, short-term) vortex shedding frequency. It turns out in this scheme of classification by the PSA-SR that all the distinguished types of the above-mentioned LFM, SHS, and NHS can be considered to be gcd-frequency synchronization.

Two- and three-dimensional wake transitions of a NACA0012 airfoil

Flow transitions are an important fluid-dynamic phenomena for many reasons, including the direct effect on the aerodynamic forces acting on the body. In the present study, two-dimensional (2-D) and three-dimensional (3-D) wake transitions of a NACA0012 airfoil are studied for angles of attack in the range $0^\circ \leq \alpha \leq 20^\circ$ and Reynolds numbers $500 \leq {\textit {Re}} \leq 5000$ . The study uses water-channel experiments and 2-D and 3-D numerical simulations based on the nodal spectral-element method, level-set function-based immersed-interface method and Floquet stability analysis. The different wake states are categorised based on the time-instantaneous wake structure, non-dimensional frequency and aerodynamic force coefficients. The wake states and transition boundaries are summarised in a wake regime map. The critical angle of attack and Reynolds number for the supercritical Hopf bifurcation (i.e. steady to periodic wake transition) varies as $\alpha _1 {\sim} {\textit {Re}}^{-0.65}$ , while the critical angle of attack for the onset of three dimensionality varies as $\alpha _{3D} {\sim} {\textit {Re}}^{-0.5}$ . Over the entire Reynolds number range, the transition to 3-D flow occurs through a mode C (subharmonic) transition. Beyond this initial transition, further instabilities of the 2-D periodic base flow arise and are investigated. For instance, at $ {\textit {Re}}=2000$ and $\alpha _{3D,2}=11.0^\circ$ , mode C coexists together with modes related to modes A and QP seen in a stationary circular cylinder wake. In contrast, at $ {\textit {Re}}=5000$ and $\alpha _{3D,2}=8.0^\circ$ , the dominant mode C coexists with mode QP. Three-dimensional simulations well beyond critical angles indicate that 2-D vortex-street transitions are approximately maintained in the fully saturated 3-D wakes in a spanwise-averaged sense.

Impacts of Unsteady Flow Environments on the Propulsive Performance of Oscillating Foils

A numerical study is conducted to understand the impact of an unsteady freestream on the aerodynamic performance of an oscillating airfoil. The unsteady flow environment is generated by placing a stationary inline circular cylinder array upstream of the oscillating airfoil. The dependence of thrust with variation of Reynolds numbers and Strouhal numbers is investigated, and it is revealed that the unsteady flow environment enhances thrust production of a pitching airfoil. This increased thrust production was related to an effective increase in the Reynolds number experienced by the airfoil. With airfoil–vortex interaction analysis, the increase in average thrust coefficient was shown to be caused by constructive interaction of freestream vortex structures and the oscillating airfoil. Drag-inducing interactions were also observed but were less common than thrust-increasing events, resulting in a higher average thrust. A simple scaling law is expanded to include the effects of unsteadiness, where thrust is found to be linearly dependent on turbulence intensity. It is demonstrated that the thrust generated by the pitching airfoil when operating in highly unsteady flow environments is more accurately represented as a function of Reynolds number, Strouhal number, and turbulence intensity.

A hybrid Cartesian-meshless method for the simulation of thermal flows with complex immersed objects

In this study, a hybrid Cartesian-meshless method is first extended to deal with the thermal flows with complex immersed objects. The temperature and flow fields are governed by energy conservation equations and Navier–Stokes equations with the Boussinesq approximation, respectively. The governing equations are solved by a conventional finite difference scheme on a Cartesian grid and generalized finite difference (GFD) with singular value decomposition (SVD) approximation on meshless nodes, with second-order accuracy. The present thermal SVD–GFD method is applied to simulate the following seven numerical examples over a wide range of governing parameters, including that with the high Prandtl number: (1) forced convection around a circular cylinder; (2) mixed convection around a stationary circular cylinder in a lid-driven cavity; (3) mixed convection involving a moving boundary in a cavity with two rotating circular cylinders; (4) sedimentation of a cold circular particle in a long channel; (5) freely falling of a sphere in viscous fluid with thermal buoyancy; (6) sedimentation of a torus with thermal convection; and (7) flow over a heated circular cylinder. The excellent agreement between the published data and the present numerical results demonstrate the good capability of the thermal SVD–GFD method to simulate the thermal flows with complex immersed objects, especially those involving fluid–structure interaction and the high Prandtl number.

Hybrid turbulence models for flows around a stationary smooth circular cylinder

The aim of this paper is to evaluate the accuracy, stability and efficiency of the different hybrid turbulence models via the benchmark computations of flows around a stationary smooth circular cylinder. The hybrid turbulence models have been validated and applied a lot in turbine flow, combustion, aerodynamic and aeroacoustic problems, while not much in hydrodynamic problems. In order to verify the simulation performance of the newly proposed hybrid strategies, this paper uses the SST-PANS, SST-SAS and SST-IDDES to compare the numerical simulation of the large separation flow problem. The model performance is assessed by a detailed comparison of predictions regarding the turbulence characteristics, the hydrodynamic characteristics, and the distribution of eddy-viscosity. The self-developed CFD solver, vim-FOAM-SJTU, is used in the present simulations. From the assessment, it is confirmed that the hybrid models have the abilities to calculate the small-scale motions, and all models can be employed to predict the unsteady characteristics of wake vortices advantageously. Both the SST-PANS and SST-IDDES models can capture complex flow structures and physics mechanism. The SAS model using the Lvk scale with features of local-adaptive and grid-independent can predict the eddy-viscosity reasonable. When the constant Cs = 0.11 contained in the Lvk limiter is modified to be Cs = 0.08, SST-SAS is also able to achieve better performance in the same mesh. The hybrid model can calculate and simulate the 3D vortex structure well, which is closer to the real physical phenomenon. And SST-IDDES has the best simulation results. The numerical results from SST-IDDES show its comparable capabilities for simulation of massively separated hydrodynamic flows and its potential application in the prediction of industrial turbulent flows for vortex-induced motions (VIM).

Study on energy extraction of Kármán gait hydrofoils from passing vortices

How swimming fish extract energy from environmental vortices is still an open question. In this work, fish swimming in unsteady flow is numerically investigated by using the immersed boundary lattice Boltzmann method. The swimming fish is modeled as a forced Kármán gait hydrofoil, and the vortical flow is generated by a stationary circular cylinder. We calculate the Fourier spectra of hydrodynamic forces on the hydrofoil surface and found that there is a coupling between lateral force and drag, which results from a nonlinear wave interaction. The Kármán gait hydrofoil adjusts the lateral force by applying lateral excitation to the vortical flow and improves the drag/thrust through nonlinear wave interaction. We find that suppressing the harmonic energy of the viscous mode is the key ingredient to extract energy from the passing vortex. In turn, the downstream distance LN and foil-vortex phase φ determine whether the viscous harmonic energy can be suppressed. If the viscous mode harmonic is strong, the interaction between the vortex shedding mode and the viscous mode leads to a series of combined modes, which extract energy from the fundamental mode. These combined modes that appear in the fluid force spectra reduce the efficiency of energy extraction.

Laminar flow-induced vibration of a three-degree-of-freedom circular cylinder with an attached splitter plate

Splitter plates are widely used for drag reduction and vibration control or enhancement of circular cylinders. The effects of a splitter plate on the vertical flow-induced vibrations of a circular cylinder have been well studied. However, its effects on the vertical-torsional coupled vibrations require further investigation. In this paper, the three-degree-of-freedom (TDoF) flow-induced vibrations of a circular cylinder with an attached splitter plate are numerically investigated at a Reynolds number of 100. The ratio between the torsional and vertical natural frequencies is varied within fθ,0/fh,0 = 6, 4, 3, 2, and 1. Numerical results show that the flow-induced vibrations of a TDoF cylinder-plate assembly, depending on the frequency ratio, may differ significantly from those of a single-degree-of-freedom (SDoF) vertical or torsional assembly. For cylinder-plate assemblies with fθ,0/fh,0 = 6–2, the vibrations can be divided into a vertical vibration-dominated branch (V branch), a torsional vibration-dominated branch (T branch), and a coupled vibration-dominated branch (C branch). The V branch vibration of a TDoF assembly is similar to that of an SDoF vertical assembly at the same reduced flow velocity, while the difference increases with decreasing the frequency ratio. The T branch vibration of a TDoF assembly is almost identical to the vibration of an SDoF torsional assembly at the same reduced flow velocity. The ratio between the torsional and vertical vibration amplitudes increases with decreasing the frequency ratio in the C branch. For the assembly with fθ,0/fh,0 = 1, vertical-torsional coupled vortex-induced vibrations are observed with the largest torsional amplitude as high as 46.3°. The vibrations of TDoF assemblies with all considered frequency ratios may be more severe than those of SDoF vertical and torsional assemblies within specific ranges of reduced flow velocities. The mean drag coefficients for the fθ,0/fh,0 = 6–2 assemblies are lower than a stationary circular cylinder but often higher than a stationary cylinder-plate assembly. The mean drag coefficients for the fθ,0/fh,0 = 1 assembly in the lock-in range are considerably larger than that of a stationary circular cylinder. For TDoF assemblies with fθ,0/fh,0 = 6–2, the V branch and C branch vibrations are mainly driven by the interaction between the assembly and the shear layers, while the T branch vibrations are excited by the typical 2S mode of vortex shedding. The 2S vortex shedding mode is also observed in the lock-in range of the fθ,0/fh,0 = 1 assembly.

Effect of frequency lock-in on the dynamic response and heat transfer from a circular cylinder at low Reynolds number

Numerical analyses are carried out to investigate the flow physics and heat transfer from an undamped freely oscillating circular cylinder at low Reynolds numbers, for an incompressible, constant property, Newtonian fluid. Mass ratio is fixed at 10, while the Prandtl number is 7. Natural frequency of the system is set equal to the vortex shedding frequency of a stationary circular cylinder at Reynolds number of 100. New results pertaining to the oscillation trajectory shapes, vortex formation length, influenced wake width and average Nusselt number in view of the pre lock-in, lock-in and post lock-in flow regimes are presented and discussed in detail. Recirculation bubble behind the cylinder disappears for large oscillation amplitudes during lock-in; while a pair of counter-rotating vortices, having opposite rotational directions to what might be expected, is observed behind the cylinder in the mean vorticity field, which alters the shape of the cylinder trajectory. Average drag coefficient is shown to be directly proportional to the vortex formation length while it is inversely related to the influenced wake width. Streamwise oscillations are noted to be more sensitive to the increasing Reynolds number during lock-in, as compared to the transverse oscillations. Progressively increasing space and time-averaged Nusselt number values comparably higher than stationary cylinder are observed as Reynolds number increases. The behavior of time-averaged-local Nusselt number varies with position around the surface of the cylinder. The maximum local Nusselt number on the surface of the cylinder is also seen to vary both in magnitude as well as location on the surface of the cylinder in a direct correspondence with the oscillation amplitudes of the cylinder. Moreover, a regression correlation is proposed which relates Reynolds number, root-mean-squared streamwise and transverse oscillation amplitudes and Strouhal number with the space and time-averaged Nusselt number.

Torsional vibration of a circular cylinder with an attached splitter plate in laminar flow

Splitter plates have been recognized as useful passive devices to reduce drag, mitigate flow-induced vibration, and enhance heat transfer efficiency of a circular cylinder. However, undesired torsional flow-induced vibrations due to splitter plate attachment require further investigation. This paper numerically studies the flow-induced torsional vibrations of an elastically mounted circular cylinder with an attached splitter plate in laminar flow with a Reynolds number of 100. A finite volume formulation is utilized to solve the incompressible two-dimensional fluid governing equations. Torsional vortex-induced vibrations (VIVs) are observed at lower reduced flow velocities, while a symmetry-breaking bifurcation occurs as the reduced flow velocity increases, after which the cylinder-plate assembly vibrates around a nonzero equilibrium angle. The numerical results show that the synchronization range of VIV extends, the peak VIV amplitude increases, and the critical reduced flow velocity for the bifurcation decreases with decreasing the moment of inertia. The symmetry-breaking bifurcation is due to a combined effect of the structural restoring moment and the flow-induced moment. The critical reduced velocity of the bifurcation and the nonzero equilibrium angle at any reduced velocity can be calculated based on the mean moment coefficients of the cylinder-plate assembly. The flow-induced moment is mainly induced by the pressure difference between the splitter plate's upper and lower surfaces. The phase difference between the torsional moment and displacement is 0° at lower reduced velocities, while the phase difference jumps to 180° at a reduced velocity of approximately 6.5. The mean drag coefficient of the vibrating cylinder-plate assembly is lower than the mean drag coefficient of a stationary circular cylinder but often higher than that of a stationary cylinder-plate assembly. The dominant frequency of the drag force is twice the vibration frequency before the symmetry-breaking bifurcation, while the dominant frequency becomes consistent with the vibration frequency after the bifurcation. The typical 2S mode of vortex shedding is identified for all considered moments of inertia and reduced flow velocities. However, the timing of a non-shedding vortex changes at the critical flow velocities for the phase jump and symmetry-breaking bifurcation. The observed torsional vibrations suggest that circular cylinders with splitter plate attachments may be competitive candidates for VIV-based energy harvesting, while they may not be good choices for heat exchangers.

Dynamics of flow in trapezoidal enclosure having a heated inner circular cylinder containing Casson nanofluid

In this article, simulation of the two-dimensional flow of natural convective transport in the partially heated lid-driven trapezoidal cavity was presented with finite element method using software called COMSOL Multiphysics®. Inside the cavity a stationary circular cylinder with a high temperature has been placed. The enclosure was filled with Cu−H2O nanofluid. The flow is assumed to be two-dimensional and has been examined when the parallel sides of the cavity are adiabatic. The temperature on non-parallel sides is assumed to be cold. The top wall of the cavity moves with a velocity η0 in the positive x-direction, and the considered fluid is a non-Newtonian Casson nanofluid. Computation has been done for the Rayleigh numbers 104,105 and 106, the Casson fluid parameter 0.1,0.5, and 1, and the nanofluid solid volume fraction 0 and 0.15. Prandtl number is kept fixed at Pr=6.2 throughout the calculations. Isotherms and streamlines were sketched to visualize the distribution of temperature and flow field in the cavity. The impacts of governing parameters such as Casson parameter, solid volume fraction, Rayleigh number on heat transfer, and flow field were numerically computed and analyzed. Average Nusselt number also exhibited in a tabular and graphical form to signify the rate of heat transfer in the cavity. It was found that the centers of the two larger circulations were observed to migrate towards the top wall of the cavity as the Rayleigh number increased. Furthermore, heat transport was enhanced as the concentration of nanoparticles increased.

On reducing lift and drag forces of a stationary circular cylinder using side-by-side pair of inward rotating cylinders

Effect of side-by-side pair of inwardly rotating circular cylinders on the nature of drag and lift forces of the stationary circular cylinder is numerically investigated for Reynolds number Re = 100. Non-dimensional rotation rates of cylinders in consideration are α = 0, 1, 3, and 5. Center to center gap spacing between rotating cylinders is taken as 6D (D is cylinder diameter), and the stationary cylinder is centrally placed in the gap. For the case of two side-by-side inward rotating cylinders, above a certain critical rotation rate, Chan et al. [1] reported the formation of a virtually elliptical body accompanied by vortex suppression. Drag on both the cylinders became almost zero after the formation of a virtually elliptical body. The present study aims to use the same concept of a virtually elliptical body to reduce the drag and lift forces on a stationary circular cylinder. At α = 3, complete suppression of vorticity is observed, followed by the formation of a virtual elliptical body at α = 5. With an increase in α from 0 onwards, the drag coefficient for the stationary cylinder reduces and becomes zero at α = 5.