Wavy Cylinder Research Articles

Forced convection heat transfer from an asymmetric wavy cylinder at a subcritical Reynolds number

The present study considered the asymmetric wavy (ASW) disturbance which has been confirmed as the passive control to modify the force coefficients Yoon et al. [25]. We evaluated the effect of the asymmetric wavy disturbance on the forced convection heat transfer. For the purpose of the comparison, the smooth (CY) and symmetric wavy (SW) cylinders are considered. Finally, the LES has been carried out to solve the momentum and energy equations governing the flow and thermal fields at the subcritical Reynolds number of 3000. The validation of the present numerical methods were successively done by comparing the force coefficients and the Nusselt number with the previous results. The ASW cylinder provided the smallest mean and fluctuation of the time-and total surface-averaged Nusselt number than the CY and SW cylinders. This dependence of the Nusselt number on the cylinder shape is correlated to the force coefficients. The time-and local spanwise surface averaged Nusselt number of the SW cylinder shows the regional dependent behaviors of an invariant region and an increasing region. The ASW cylinder shows the increasing and decreasing behaviors in the short and long wavelength parts. The double wavy formation of the temperature isosurface in the wake for the ASW cylinder is consistent with the 3D vortical structures. The most significant variation of the time-averaged local Nusselt Number appears in the upstream surface of the SW and ASW cylinders which induce the spanwise dependent incoming flow.

Numerical study of flow past a transversely oscillating wavy cylinder at Re=5000

In order to shed some light upon the mechanism for the free vibrations of the wavy cylinder reported previously (Zhang et al., 2017), we numerically investigate the effect of external forcing on the flow around a wavy cylinder at Re=5000. The forcing takes the form of sinusoidal transverse motion with the amplitude fixed at Ae/Dm = 0.2 and the frequency spanning from feDm/U∞=0.1 to 0.3. Even though the wavy cylinder is optimally designed to annihilate the Kármán vortex shedding in the fixed configuration, the Strouhal frequency is found to resurrect in the forced vibration cases, leading to very similar responses between the normal and wavy cylinders, especially at high forcing frequencies. By sectional analysis it is revealed that the sectional distribution of the force coefficients undergoes significant changes with the increase of the forcing frequency. Statistical tools such as the correlation and coherence reveals further spanwise features of the force coefficients. In addition, the instantaneous three-dimensional vortical structures are visualized by the spanwise voriticity isosurfaces to collaborate the previous discussions. The cessation of the flow control efficacy in the forced vibration is explained by the recession of the mean streamwise vorticity contours. The results presented in the work imply that the vortex-induced vibration of the wavy cylinder might be ascribed to the typical wake-structure interaction as the normal cylinder, although the mechanism for the initial growth of the oscillations still warrants further investigations.

Large eddy simulation of forced convection heat transfer from wavy cylinders with different wavelengths

Large eddy simulation was carried out to investigate the forced convection around a wavy cylinder at a Reynolds number of 3000 in the subcritical regime and a Prandtl number of 0.7. This is initial research to find the effect of the wavelength (λ/Dm) on the forced convection at a subcritical Reynolds number. A wide wavelength range of 1.136⩽λ/Dm⩽6.06 is considered, and the results are compared with those of a smooth cylinder. The local peaks of the time- and total surface-averaged Nusselt numbers for different wavelengths occur at the optimum wavelengths where the minimum and maximum drag occurs. Therefore, the variation of the time- and total surface-averaged Nusselt numbers along the wavelength correlates with the force coefficients on the wavy cylinder. The bifurcation of the location of the maximum Nusselt number from the node to the saddle occurs at the critical wavelength, which is the short optimal wavelength where the maximum drag reduction and suppression of the lift fluctuation appear. The position of the minimum Nusselt number moves from the middle toward the node with increasing wavelength and eventually saturates at the node. These variations of the local Nusselt number are supported by the isotherm distribution, which is strongly governed by wake structures based on shear layer separation.

Stagnation-point flow of an aqueous titania-copper hybrid nanofluid toward a wavy cylinder

PurposeThe purpose of this paper is to investigate analytically the steady general three-dimensional stagnation-point flow of an aqueous titania-copper hybrid nanofluid past a circular cylinder that has a sinusoidal radius variation.Design/methodology/approachFirst, the analytic modeling of hybrid nanofluid is presented, and using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved by the well-known function bvp4c from MATLAB.FindingsThe current solution demonstrates good agreement with those of the previously published studies in the special cases of regular fluid and nanofluids. Graphical results are presented to investigate the influences of the titania and copper nanoparticle volume fractions and also the nodal/saddle indicative parameter on flow and heat transfer characteristics. Here, the thermal characteristics of hybrid nanofluid are found to be higher in comparison to the base fluid and fluid containing single nanoparticles. An important point to note is that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluids.Originality/valueAnalytic modeling of hybrid nanofluid is the important originality of present study. Hybrid nanofluids are potential fluids that offer better heat transfer performance and thermophysical properties than convectional heat transfer fluids (oil, water and ethylene glycol) and nanofluids with single nanoparticles. In this investigation, titania (TiO2, 50 nm), copper (Cu, 20 nm) and the hybrid of these two are separately dispersed into the water as the base fluid and analyzed.

Numerical study of unsteady flows past a rotating wavy cylinder

In the present paper, three-dimensional unsteady flows past a rotating wavy cylinder have been studied through numerical simulations. The behavior of the lift forces acting on a rotating wavy cylinder and a rotating straight cylinder is compared, respectively. The results suggest that the rotation rate of the wavy cylinder has to be about two times that of a straight rotating cylinder in order to obtain the same value of the mean lift. The pressure distribution and the vortex structures in the wake of the rotating wavy cylinder at various rotation rates are also demonstrated and analyzed in this work. As rotation rate of the cylinder increases, the vortex formation length increases and the periodic shedding of the Karman vortex is suppressed. Three-dimensional vortex structures in the wavy cylinder wake are visualized at various rotation rates. Due to the surface rotation effect, a distinct difference exists in the vortex structures between a rotating wavy cylinder and a stationary wavy cylinder.

Large eddy simulation of flow over inclined wavy cylinders

The wavy cylinders have been proven effective in suppressing the Kármán vortex shedding and mitigating the aerodynamic forces. As yet their performance in the inclined incoming flow has not been well understood. In the current work, large eddy simulations are carried out to unveil the aerodynamics of the flow around inclined wavy cylinders at the Reynolds number of 5000. Three inclination angles, 0°, 30° and 45°, together with 2 × 2 combinations of shape parameters, namely λ∕Dm=2 and 6, a∕Dm=0.1 and 0.15, have been taken into consideration. Firstly, the aerodynamic force coefficients in terms of both the span-wise averaged and sectional values are discussed at length. It is revealed that the growing inclination angle invites not only a surge in their span-wise averaged values, but also an enlargement in the sectional difference of the force coefficients. The span-wise correlation of the lift force is found to be enhanced for the wavy cylinders with the increase of inclination angle, while the opposite is true for the normal cylinders. By examining the mean wake properties, it is disclosed that the increase in the span-wise averaged drag force coefficients is closely related to the shrinkage in the vortex formation length and the regression of the base pressure, whereas the sectional distribution of the drag coefficients is largely affected by the stagnation pressure. The mean wall shear stress fields are exploited to shed light on the flow topology of the cylinder surfaces. It is discovered that the wavy cylinders, especially the short-wavelength one, exhibit significant span-wise variation in the separation structure in the inclined flow. Besides, the chaotic surface flow in the rear side of the non-inclined cylinders could be regulated to maintain symmetry by the secondary axial flow in the near wake of the inclined cylinders. The instantaneous three-dimensional vortical structures are visualized by the Q isosurfaces at last to collaborate the previous discussions. A preliminary mechanism for the cessation of flow control efficacy for the wavy cylinders in inclined flow is also presented.

A diffuse interface immersed boundary method for complex moving boundary problems

A diffuse interface immersed boundary method is proposed for problems with arbitrarily moving complex rigid bodies. The solid-fluid interface is replaced by fluid–fluid Lagrangian boundary. A universal equation that combines the momentum conservation and rigid body velocity through the volume fraction is solved in the entire domain. The ever changing volume fraction field is accurately computed locating the object boundary. As the desired boundary conditions are only enforced directly in a volume average sense scope of it spreads over a computing cell. Thus, by reducing size of the computing cell the proposed method approaches the conventional sharp interface methods though it eliminates the spurious force oscillations. Owing to the single universal equation on a fixed Eulerian Cartesian mesh the proposed method retains the simplicity, robustness and versatility of the original Cartesian grid simulation. Convergence study of the transverse oscillation of a cylinder shows second-order convergence with refinement of numerical parameters and significantly diminished force oscillation. The proposed method is parallelized on a mixed shared and distributed memory notions in order to facilitate large scale 2D and 3D simulations. A range of test cases have been carefully chosen to check the quality of prediction of the proposed technique for forced and induced motions of multiple objects. They include in-line, transverse and rotational forced motion of a circular cylinder, motion of a hovering thin wing, vortex induced vibration (VIB) of multiple circular and square cylinder, angular VIB of multiple objects, particle sedimentation, instability driven fluttering of a freely falling plate, settling of a sphere in a quiescent medium, 3D VIB of two cylinders, wake transition due to pitching of a large aspect ratio thin plate and turbulent wake behind a wavy cylinder.

Vortex-induced vibration of a wavy elliptic cylinder

This paper shows that three-dimensional separation lines on a wavy cylinder may be correlated by the lateral movement of the body responding to flow-induced excitations. Vortex-induced vibration (VIV) of a wavy elliptic cylinder is investigated by mean of experiments in a water channel in the range of Reynold number between 1,500 to 15,000. Results are compared with those for a plain circular cylinder of equivalent diameter with a combined mass–damping parameter of 0.018. Curves of displacement and frequency of vibration showed that the hydroelastic mechanism that drives the wavy cylinder into VIV is not different from that of a plain cylinder. Detailed decomposition of the fluid forces supports this conclusion. The reason for such similar behaviour is the correlation of the sinuous separation lines as the wavy cylinder starts to oscillate. Flow visualization reveals that the three-dimensional surface of the wavy cylinder affects the formation of vortices in the near wake, generating streamwise and cross-flow vorticity associated with the wavelength of the surface. However, once the cylinder is free to respond to VIV, moving in the cross-flow direction, coherent vortex filaments once more dominate the near wake.

Novel characteristics of wavy cylinder in supersonic turbulent flow

Supersonic flow past a wavy cylinder has been investigated numerically using scale-adaptive simulation technique. The free-stream Reynolds number and Mach number for this supersonic flow are chosen as 2×105 and 1.7, respectively. For the sake of comparison and discussion, a corresponding circular cylinder for the same computational parameters also has been calculated. Unlike the subsonic operating condition, drag reduction and fluctuating lift suppression of wavy cylinder in supersonic flow are less dramatic. Results indicate that wavy surface as a flow control technique is invalid for supersonic flow over a circular cylinder. This is because the existence of bow shock-wave and no large-scale vortex shedding in the flow field of circular cylinder. Further, two different flow states have been found in the near wake of wavy cylinder. One is a quasi-steady flow state behind the nodal position with converged wake, and the other is an unsteady flow state behind the saddle position with obvious vortex street. Based on the analyses of flow patterns, pressure power spectral densities, and proper orthogonal decomposition of pressure fields, some novel characteristics of wavy cylinder in supersonic flow are systematically investigated.

Large eddy simulation and proper orthogonality decomposition of turbulent flow around a vibrissa-shaped cylinder

The flow dynamics over a vibrissa-shaped cylinder at the sub-critical Reynolds number of 1.8 × 104 are comparatively investigated using the large eddy simulation (LES) approach, with particular emphasis on the wake structure and self-induced force. Three reference configurations with the same hydrodynamic diameters, i.e., a circular cylinder, an elliptical cylinder and a wavy cylinder, are compared with the vibrissa-shaped cylinder configuration. The results demonstrate that the fluctuation of lift force for the vibrissa-shaped cylinder is reduced by approximately 79.2% compared with that for the circular cylinder, and the predicted RMS magnitudes for the four configurations agree reasonably well with the experimental data. For the vibrissa-shaped cylinder, only one sharp peak with relatively low magnitude is observed at the characteristic frequency fD/U0=0.20, and the wake shedding does not dominate the dynamics, while the vortex structures show significantly three-dimensional features. Meanwhile, the separation line of the recirculation zone shows a remarkable wavy structure that corresponds to the trailing geometrical surface with a spanwise shift of approximately a half-period of undulation. A proper orthogonal decomposition (POD) analysis is performed to explore the three-dimensional structures in the wake behind the vibrissa-shaped cylinder. The POD modes reveal a completely three-dimensional and periodically staggered arrangement along both the spanwise and streamwise directions. The spectra of the first two time coefficients reveal that the wake shedding processes on the nodal and saddle planes are not synchronous. Finally, the phase-averaging results show sequential processes of vortex shedding in the wake behind the vibrissa-shaped cylinder, and demonstrate marked differences between this and the other cylinders. Two symmetrical vortices are attached closely to the backward side of the vibrissa-shaped cylinder, resulting in smaller fluctuations of velocity and wall pressure, which in turn contribute to reducing the vortex-induced force and suppressing its vibrations.

Asymmetric disturbance effect on the flow over a wavy cylinder at a subcritical Reynolds number

A new geometric disturbance giving the reductions of the drag and lift fluctuations for bluff body flows has been proposed by applying the asymmetry to a symmetric wavy (SW) geometry. This asymmetric wavy (ASW) disturbance is applied on a circular cylinder to identify its effect on the flow control, forming the asymmetric wavy (ASW) cylinder. The turbulent flow over an ASW cylinder is investigated at a subcritical Reynolds number of 3000 using large eddy simulation based on the finite volume method. The findings of the present study identify that the ASW disturbance achieves more reductions in the mean drag and the lift fluctuation than the optimal wavy cylinder. The branch-like formation of the additional streamwise and transverse vorticities observed in the ASW cylinder are dissipated farther upstream than the symmetric wavy (SW) cylinder, resulting in wider regions of the zero vorticities in the near-wake. The ASW cylinder formed the asymmetric distribution of flow and the extent of the coherent flow farther downstream. The vortex formation length of the ASW cylinder reveals the asymmetric distribution along the span and is much longer than that of the smooth and SW cylinders. This comparison of the vortex formation length also proves the capacity of the ASW geometric disturbance to reduce the drag and lift fluctuation than the SW cylinder.

Preconditioned characteristic boundary conditions based on artificial compressibility method for solution of incompressible flows

The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.

Numerical simulation of vortex induced vibrations of a flexibly mounted wavy cylinder at subcritical Reynolds number

Wavy cylinders have been proven effective in controlling the flow and reducing the fluid induced forces. However, the hydro-elastic behavior of a flexibly mounted wavy cylinder remains unclear. The current paper endeavours to present a systematic study of the flow around a spring mounted wavy cylinder mainly at a moderate Reynolds number of 5000, the results of which are compared with a normal cylinder with the same fluid and structural attributions. It is discovered that the wavy cylinder, although almost eliminates the Kármán vortices in the fixed configuration, shows only limited efficacy on the mitigation of the flow induced vibration in the case of zero structural damping, and the typical initial-upper-lower type response curve is manifested. The hydrodynamic forces of the wavy cylinder also magnify significantly in the flexibly mounted cases during synchronization. Moreover, the phase lag between the lift coefficient and the displacement displays a clear change from 0° at the initial branch to 180° at the lower branch. The association of the 2S and 2P vortex shedding modes to the different branches is also similar to that of the normal cylinder, in which the 2S mode corresponds to the initial branch and the 2P to the lower branch. In general, despite the absence of the primary shedding frequency in the fixed configuration, the flexibly mounted wavy cylinder exhibits many features that is also found in the normal cylinder. This implies that the vortex induced vibration may not be initiated by the Kármán vortex shedding, and thus may defy the conventional view on the mechanism of the vortex induced vibrations. Additional simulations are performed with non-zero structural damping. It is disclosed that with sufficiently high structural damping, the vibration of the wavy cylinder could be reduced more efficiently than the normal cylinder.

Finite element based large eddy simulation of flow over bluff bodies

Large eddy simulation (LES) of bluff body flows is performed using a finite element based formulation which employs a combined subgrid-scale model. The combined model uses the residual based variational multiscale (RBVMS) approach along with the dynamic Smagorinsky eddy viscosity model. Specifically, the RBVMS model is used to represent the cross-stress terms while the dynamic eddy viscosity model is used for the Reynolds stresses. The dynamic procedure is based on a localized version of the variational Germano identity. Two sets of cases are considered: flow over straight and wavy circular cylinders at ReDm=3000, and flow over a straight square cylinder at ReD=22,000. For the straight circular cylinder case, we compare LES predictions based on the RBVMS model and the combined subgrid-scale model against the experimental data. The combined model provides better predictions (for both force data and centerline profiles in the wake) and we select it in the rest of the cases. For the wavy circular cylinder case, LES predictions (based on the combined model) shows a good agreement with the experimental data including mean velocity profiles in the wake. It accurately captures the elongation of the recirculation region. In the square cylinder case too, LES predictions (based on the combined model) show a very good agreement with the direct numerical simulation and multiple experimental datasets.

Numerical study on the effect of shape modification to the flow around circular cylinders

Shape modification has been one of the effective ways of manipulating the flow past bluff bodies. Aiming at exploration of the flow control mechanisms of shape modified circular cylinders, a series of numerical simulations are conducted at the Reynolds number of 5000. The modifications adopted in the current paper could be divided into two categories, the 2-dimensional cross-sectional modifications (polygonal and ridged) and 3-dimensional span-wise modifications (linear wavy, sinusoidal wavy and O-ringed). By exploiting the numerical data obtained from the Large Eddy Simulations, several aspects, including the wake flow properties, the aerodynamic forces, the flow instabilities and span-wise correlations are compared in detail. The two wavy cylinders are found to modify the flow wake significantly, leading to considerable reduction in aerodynamic forces. The polygonal and ridged cylinders, however, are of no such effect in aerodynamic force mitigation. The O-rings only have slight effect on the flow wake and the forces. As for the flow instabilities, the modifications adopted in this paper barely affects the Kármán vortex shedding frequency. The shear layer frequency, however, differs from case to case. Particularly, in the cases of the two wavy cylinders, disparity exists in the shear layer frequency at the node and saddle. This is explained by the boundary layer properties at separation. While recognizing the insufficiency in the span-wise length of the cylinders, the span-wise correlations of the aerodynamic forces are inspected. It is found that the lift forces of the 3-dimensional cylinders are generally less correlated than that of the 2-dimensional ones.

Wake dynamics behind a seal-vibrissa-shaped cylinder: a comparative study by time-resolved particle velocimetry measurements

The wake dynamics behind a seal-vibrissa-shaped cylinder, which are closely related to the seal’s extraordinary ability to faithfully track the hydrodynamic trails of its upstream prey, were extensively studied by using time-resolved particle image velocity. Four cylindrical configurations that shared the same hydrodynamic diameter (i.e., a circular cylinder, an elliptical cylinder, a wavy cylinder, and a vibrissa-shaped cylinder) were chosen for the comparative study at the Reynolds number 1.8 × 103. The instantaneous flow fields behind the cylinders were measured along their vertical and horizontal planes. The distinct global differences between the wakes were determined from the streamline patterns, the reverse-flow intermittences, and both the streamwise and longitudinal velocity fluctuation intensities. Compared to the other three systems tested, the vibrissa-shaped cylinder system was characterized by a considerably reduced recirculation zone in the nodal plane, the existence of a very stably reversed flow, and substantial reductions in the streamwise and longitudinal velocity fluctuation intensities. Further cross-correlation of the fluctuating longitudinal velocities showed that the unsteady events behind the vibrissa-shaped cylinder were poorly organized by sequence and considerably constrained in their spatial extent. Finally, a dynamic mode decomposition (DMD) was performed on the instantaneously varying wake flows. In the wavy cylinder system, a single dominant DMD mode at St = 0.2 (corresponding to Karman vortex street) was detected in both the saddle and nodal planes. Although the dominant DMD modes at St = 0.23 and 0.3 were determined in the saddle and nodal planes of the vibrissa-shaped cylinder system, respectively, the spatial pattern of these two DMD modes showed resolved vortical structures that were highly distorted and constrained to an extremely limited space. These DMD modes had much less energy than those in the other three systems. The phase-dependent variations of the wake flows disclosed that the complex unsteady behavior at distinctly different frequencies in the saddle and nodal planes disrupted the regular vortex shedding process, suppressing the vortex-induced vibration of the vibrissa-shaped cylinder.

Effects of large spanwise wavelength on the wake of a sinusoidal wavy cylinder

The wake of a sinusoidal wavy cylinder with a large spanwise wavelength λ/Dm (=3.79–7.57) and a constant wave amplitude a/Dm=0.152, where Dm is the mean diameter of the cylinder, is investigated using three dimensional (3D) large eddy simulation (LES) at a subcritical Reynolds number Re=3×103, based on incoming free-stream velocity (U∞) and Dm. Attention is paid to assimilating the effects of λ/Dm on the cylinder wake, including vortex shedding frequency, spanwise vortex formation length, streamwise velocity distribution, flow separation angle, 3D vortex structure, and turbulent kinetic energy (TKE) distribution. Based on the predominant role of λ/Dm in the near wake modification, three regimes are identified, i.e., regime I at λ/Dm<6.0, regime II at λ/Dm≈6.0 and regime III at λ/Dm>6.0. A dramatic decrease in fluid forces is observed at λ/Dm=6.06, about 16% and 93% reduction in time-averaged drag and fluctuating lift, respectively, compared to those of a smooth cylinder. We identified, for the first time, an optimum λ/Dm (=6.06) for the wavy cylinder with relatively large λ/Dm (>3.5) in the subcritical flow regime. The underlying mechanisms of force reduction are discussed, including the flow characteristics at the three λ/Dm regimes. A comparison is also made between the results of λ/Dm effects on the near wakes of a circular and a square cylinder.

Effect of Thermal Diffusion and Radiation on Unsteady Mixed Convective Heat and Mass Transfer Flow of a Viscous Fluid in a Vertical Wavy Cylinder

Effect of Thermal Diffusion and Radiation on Unsteady Mixed Convective Heat and Mass Transfer Flow of a Viscous Fluid in a Vertical Wavy Cylinder

Unsteady convective heat and mass transfer of a nanofluid in Howarth’s stagnation point by Buongiorno’s model

Purpose – The purpose of this paper is to do a comprehensive study on the unsteady general three-dimensional stagnation-point flow and heat transfer of a nanofluid by Buongiorno’s model. Design/methodology/approach – In this study, the convective transport equations include the effects of Brownian motion and thermophoresis. By introducing new similarity transformations for velocity, temperature and nanoparticle volume fraction, the basic equations governing the flow, heat and mass transfer are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved both analytically and numerically. Findings – The analysis shows that velocity, temperature and nanoparticle concentration profiles in the respective boundary layers depend on five parameters, namely unsteadiness parameter A, Brownian motion parameter Nb, thermophoresis parameter Nt, Prandtl number Pr and Lewis number Le. It is found that the thermal boundary layer thickens with a rise in both of the Brownian motion and the thermophoresis effects. Therefore, similar to the earlier reported results, the Nusselt number decreases as the Brownian motion and thermophoresis effects become stronger. A correlation for the Nusselt number has been developed based on a regression analysis of the data. This correlation predicts the numerical results with a maximum error of 9 percent for a usual domain of the physical parameters. Originality/value – The stagnation point flow toward a wavy cylinder (with nodal and saddle stagnation points) that a little attention has been given to it up to now. The examination of unsteadiness effect on the general three-dimensional stagnation-point flow. The application of an interesting and global model (Boungiorno’s model) for the nanofluid that incorporates the effects of Brownian motion and thermophoresis. The study of the effects of Brownian motion and thermophoresis on the nanofluid flow, heat and mass transfer characteristics. The prediction of correlation for the Nusselt number based on a regression analysis of the data. General speaking, we can tell the problem with this geometry, characteristics, the applied model, and comprehensive results, was Not studied and analyzed in literature up to now.

On the flow behaviour of confined finite-length wavy cylinders

Confined aspect-ratio of 6 wavy cylinders with a mean blockage-ratio of 0.5 were studied using time-resolved particle-image velocimetry at a sub-critical Reynolds number of 2700. Wavelengths and wave amplitudes of 2–4 and 0.1–0.3 mean diameters respectively were investigated. Results show that vortices are generally shed from the wavy cylinder and channel walls regularly, reminiscent of the unsteady symmetric flow configuration in confined non-wavy cylinders. Furthermore, vortex formation lengths for confined wavy cylinders are generally shorter than their unconfined counterparts, though their variations with respect to geometrical changes remain consistent with unconfined flow conditions. Gross cross-stream flow behaviour does not differ significantly between confined and unconfined wavy cylinders, indicating that finite-length effects are independent of the present confinement. Confined wavy cylinder wake regions are more sensitive towards geometrical changes and a combination of small wavelength and large wave amplitude leads to significant suppression of coherent cylinder and wall vortex-shedding. This is supported by phase-averaged flow reconstructions derived from Proper Orthogonal Decomposition analysis. Lastly, larger wave amplitudes lead to redistributions of dominant flow energy further downstream and to higher mode numbers, which suggests a causal link to the formation of stronger and more coherent streamwise vortices.