This paper investigates the dynamics of velocity gradients for a spatially developing flow generated by a single square element of a fractal square grid at low inlet Reynolds number through direct numerical simulation. This square grid-element is also the fundamental block of a classical grid. The flow along the grid-element centreline is initially irrotational and becomes turbulent further downstream due to the lateral excursions of vortical turbulent wakes from the grid-element bars. We study the generation and evolution of the symmetric and anti-symmetric parts of the velocity gradient tensor for this spatially developing flow using the transport equations of mean strain product and mean enstrophy respectively. The choice of low inlet Reynolds number allows for fine spatial resolution and long simulations, both of which are conducive in balancing the budget equations of the above quantities. The budget analysis is carried out along the grid-element centreline and the bar centreline. The former is observed to consist of two subregions: one in the immediate lee of the grid-element which is dominated by irrotational strain, and one further downstream where both strain and vorticity coexist. In the demarcation area between these two subregions, where the turbulence is inhomogeneous and developing, the energy spectrum exhibits the best$-5/3$power-law slope. This is the same location where the experiments at much higher inlet Reynolds number show a well-defined$-5/3$spectrum over more than a decade of frequencies. Yet, the$Q{-}R$diagram, where$Q$and$R$are the second and third invariants of the velocity gradient tensor, remains undeveloped in the near-grid-element region, and both the intermediate and extensive strain-rate eigenvectors align with the vorticity vector. Along the grid-element centreline, the strain is the first velocity gradient quantity generated by the action of pressure Hessian. This strain is then transported downstream by fluctuations and strain self-amplification is activated a little later. Further downstream, vorticity from the bar wakes is brought towards the grid-element centreline, and, through the interaction with strain, leads to the production of enstrophy. The strain-rate tensor has a statistically axial stretching form in the production region, but a statistically biaxial stretching form in the decay region. The usual signatures of velocity gradients such as the shape of$Q{-}R$diagrams and the alignment of vorticity vector with the intermediate eigenvector are detected only in the decay region even though the local Reynolds number (based on the Taylor length scale) is only between 30 and 40.

Non-canonical wakes of two-dimensional elliptic cylinders are analysed numerically for their near- and far-wake characteristics. The governing equations are solved using an immersed boundary method based projection scheme. The wakes are then classified into three distinct types according to diverse flow and thermal properties. An unexpected mean temperature evolution along the centreline of the wake is observed for certain wake states. In order to explain this unusual variation, novel heat transport models are constructed based on the vortex dynamics. These models are derived by considering vorticity is acted by flow, which has shear and swirl. Mechanisms of the primary vortex street breakdown and formation of the secondary vortex street are also proposed based on these models. A new phenomenon namely ‘dual near-wall instantaneous recirculation’ is observed, and its appearance is found to be a function of length of the primary von Kármán vortex street. The same phenomenon is also found to be responsible for the secondary peak in the Nusselt number variation along the circumference of the cylinder. Despite varied differences between the wake types, it is observed that the transitions occur through a supercritical Hopf bifurcation in all of them, at least in the von Kármán region of the wake. Low-frequency unsteadiness observed in the far wakes is examined through a signal decomposition method. Our results show that the secondary low frequency is resulting from the transition region which has a negative instability slope. Finally, onset of the primary vortex street breakdown and its scale in terms of Reynolds number is computed.

This article presents the numerical studies on predicting onset of flow separation and vortex shedding in flow past unconfined two-dimensional elliptical cylinders for various Axis Ratios (AR) and a wide range of Angles of Attack (AOA). An efficient Cartesian grid technique based immersed boundary method is used for numerical simulations. The laminar separation Reynolds number (Res) that marks separation of flow from surface and the critical Reynolds number (Recr) which represents transition from steady to unsteady flow are determined using diverse methods. A stability analysis which uses Stuart-Landau equation is also performed for calculating Recr. The shedding frequency (Stcr) that corresponds to Recr is calculated using Landau constants. The simulated results for circular cylinder are found to be in good agreement with the literature. The effects of AR and AOA on Res, Recr, and Stcr are studied. It is observed that the Res, Recr, and Stcr exhibit a direct/inverse relationship with AR depending upon the given AOA. Correlations of Res, Recr, and Stcr with respect to AR and AOA are proposed with good accuracy.

The present direct numerical simulation (DNS) study, the first of its kind, explores the effect that the location of a cylinder, immersed in the turbulent wake of a grid-element, has on heat transfer. An insulated single square grid-element is used to generate the turbulent wake upstream of the heated circular cylinder. Due to fine-scale resolution requirements, the simulations are carried out for a low Reynolds number. Three locations downstream of the grid-element, inside the production, peak and decay regions, respectively, are considered. The turbulent flow in the production and peak regions is highly intermittent, non-Gaussian and inhomogeneous, while it is Gaussian, homogeneous and fully turbulent in the decay region. The turbulence intensities at the location of the cylinder in the production and decay regions are almost equal at 11 %, while the peak location has the highest turbulence intensity of 15 %. A baseline simulation of heat transfer from the cylinder without oncoming turbulence was also performed. Although the oncoming turbulent intensities are similar, the production region increases the stagnation point heat transfer by 63 %, while in the decay region it is enhanced by only 28 %. This difference cannot be explained only by the increased approaching velocity in the production region. The existing correlations for the stagnation point heat transfer coefficient are found invalid for the production and peak locations, while they are satisfied in the decay region. It is established that the flow in the production and peak regions is dominated by shedding events, in which the predominant vorticity component is in the azimuthal direction. This leads to increased heat transfer from the cylinder, even before vorticity is stretched by the accelerating boundary layer. The frequency of oncoming turbulence in production and peak cases also lies close to the range of frequencies that can penetrate the boundary layer developing on the cylinder, and therefore the latter is very responsive to the impinging disturbances. The highest Nusselt number along the circumference of the cylinder is shifted 45 degrees from the front stagnation point. This shift is due to the turbulence-generating grid-element bars that result in the prevalence of intense events at the point of maximum Nusselt number compared to the stagnation point.

Purpose – The purpose of this paper is to study the effects of Angle of Attack (AOA), Axis Ratio (AR) and Reynolds number (Re) on unsteady laminar flow over a stationary elliptic cylinder. Design/methodology/approach – The governing equations of fluid flow over the elliptic cylinder are solved numerically on a Cartesian grid using Projection method based Immersed Boundary technique. This numerical method is validated with the results available in open literature. This scheme eliminates the requirement of generating a new computational mesh upon varying any geometrical parameter such as AR or AOA, and thus reduces the computational time and cost. Findings – Different vortex shedding patterns behind the elliptic cylinder are identified and classified using time averaged centerline streamwise velocity profile, instantaneous vorticity contours and instantaneous streamline patterns. A parameter space graph is constructed in order to reveal the dependence of AR, AOA and Re on vortex shedding. Integral parameters of flow such as mean drag, mean lift coefficients and Strouhal number are calculated and the effect of AR, AOA and Re on them is studied using various pressure and streamline contours. Functional relationships of each of integral parameters with respect to AR, AOA and Re are proposed with minimum percentage error. Practical implications – The results obtained can be used to explain the characteristics of flow patterns behind slender to bluff elliptical cylinders which found applications in insect flight modeling, heat exchangers and energy conservation systems. The proposed functional relationships may be very useful for the practicing engineers in those fields. Originality/value – The results presented in this paper are important for the researchers in the area of bluff body flow. The dependence of AOA on vortex shedding and flow parameters was never reported in the literature. These results are original, new and important.