Numerical analysis of laminar fluid flow characteristics past an elliptic cylinder: A parametric study
31 Jul 2014-International Journal of Numerical Methods for Heat & Fluid Flow (Emerald Group Publishing Limited)-Vol. 24, Iss: 7, pp 1570-1594
TL;DR: In this paper, the effects of Angle of Attack (AOA), Axis Ratio (AR) and Reynolds number (Re) on unsteady laminar flow over a stationary elliptic cylinder are studied numerically on a Cartesian grid using Projection method based Immersed Boundary technique.
Abstract: – 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. , – 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. , – 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. , – 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. , – 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.
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TL;DR: In this paper, the authors derived a heat transport model based on the vortex dynamics for two-dimensional elliptic cylinders by considering vorticity is acted by flow, which has shear and swirl.
Abstract: 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 Karman 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 Karman 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.
21 citations
Cites background or methods from "Numerical analysis of laminar fluid..."
...The onset of laminar separation and vortex shedding in an elliptic cylinder was studied by Paul et al. (2014b), while the critical Re at which the flow goes from 2-...
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...The value of the amplification rate (γ ) is calculated to be 0.01745, which matches well with the values obtained by Paul et al. (2014b)....
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TL;DR: In this article, the wake of an elliptical cylinder at low incident angles is investigated for different aspect ratio cylinders using stability analysis and direct simulations, and the two-and three-dimensional transitions are mapped for cylinders of aspect ratios between 1 and 4 using Floquet stability analysis.
Abstract: The wake of an elliptical cylinder at low incident angles is investigated for different aspect ratio ( ) cylinders using stability analysis and direct simulations. In particular, two- and three-dimensional transitions are mapped for cylinders of aspect ratios between 1 and 4 using Floquet stability analysis. The transition scenario for near-unity aspect ratio cylinders resembles that for a circular cylinder wake as Reynolds number is increased to ; first, with the transition from steady two-dimensional flow to unsteady two-dimensional flow, followed by the onset of three-dimensional flow via a long-wavelength instability (mode A), then, a short-wavelength instability (mode B) and, finally, an intermediary wavelength instability which is quasi-periodic in nature (mode QP). The effect of the incident angle on this transition scenario for the low-aspect-ratio cylinders is minimal. As the aspect ratio is increased towards 2, two synchronous modes, modes and , become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode persists for all incident angles investigated here, mode is found only to be unstable for incident angles up to . Surprisingly, for , the mode A instability observed at zero incident angle emerges as a quasi-periodic mode as the incident angle is increased even slightly. At higher incident angles, this quasi-periodic mode once again transforms to a real mode on increasing the Reynolds number. The parameter space maps for the various aspect ratios are presented in the Reynolds number–incident angle plane, and the three-dimensional modes are discussed in terms of similarities to and differences from existing modes. A key aim of the work is to map the different modes and various transition sequences as a simple body geometry is systematically changed and as the flow symmetry is systematically broken; thus, insight is provided on the overall path towards fully turbulent flow.
16 citations
TL;DR: In this article, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change.
Abstract: Purpose
In this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.
Design/methodology/approach
Even though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.
Findings
The numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.
Social implications
The present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.
Originality/value
For the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).
8 citations
TL;DR: In this article, the velocity field through fast Fourier transform in the near and far wake of an elliptic cylinder of axis ratio 0.4 whose major axis is kept perpendicular to the incoming flow is analyzed.
Abstract: Flow past any geometry contains structures of diverse sizes, albeit the shedding structure is the most prevalent. There are situations where the flow also has large-scale secondary dominant structures. This study attempts to provide the sources of such low frequency secondary structures in a laminar regime. To this end, we analyze the velocity field through fast Fourier transform in the near and far wake of an elliptic cylinder of axis ratio 0.4 whose major axis is kept perpendicular to the incoming flow. Numerical simulation is carried out for Reynolds number 130, where the flow is reported to be two-dimensional. This study reveals the presence of low-frequency structures besides the primary shedding structures in linear, transition, and saturation regions of temporal wake development. We show that the temporal source of the primary frequency is the saturated state of the wake development, while its physical source is the periodic nature of the saturation region, which inhibits the transmutation of the wavelength of flow structures. On the other hand, the secondary low frequency is embedded in the transitional developing stage of the wake and its physical source is the irregular behavior of the transition process, which aids transmutation of the wavelength of the structures.
8 citations
TL;DR: In this paper, the distinctive pitching of hinged splitters in the trailing edge of elliptic cylinders was experimentally studied at various angles of attack ( ) of the cylinder, Reynolds numbers, splitter lengths, aspect ratios, and freestream turbulence levels.
Abstract: The distinctive pitching of hinged splitters in the trailing edge of elliptic cylinders was experimentally studied at various angles of attack ( ) of the cylinder, Reynolds numbers, splitter lengths, aspect ratios ( ) of the cylinder and freestream turbulence levels. High-resolution telemetry and hotwire anemometry were used to characterize and gain insight on the dynamics of splitters and wake flow. Results show that the motions of the splitters contain various dominating modes, e.g. and , which are induced by the mean flow and wake dynamics. High background turbulence dampens the coherence of the regular vortex shedding leading to negligible . For a sufficiently long splitter, namely twice the semimajor axis of the cylinder, dual vortex shedding mode exists close to the leading and trailing edges of the splitter. In general, the splitters oscillate around an equilibrium position nearly parallel to the mean direction of the flow; however, a skewed equilibrium is also possible with a strong recirculation region. This is the case with cylinders of low and high , where higher lift and drag occurs. Flow measurements at various transverse locations within the wake of the cylinder–splitter system indicate that the signature of the low-frequency splitter pitching is shifted in the wake in the cases with non-zero of the cylinder. Although the splitter pitching exhibits two dominant vortex shedding modes in various configurations, only the higher frequency is transmitted to the wake.
7 citations
References
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TL;DR: A review of wake vortex dynamics can be found in this article, with a focus on the three-dimensional aspects of nominally two-dimensional wake flows, as well as the discovery of several new phenomena in wakes.
Abstract: Since the review of periodic flow phenomena by Berger & Wille (1972) in this journal, over twenty years ago, there has been a surge of activity regarding bluff body wakes. Many of the questions regarding wake vortex dynamics from the earlier review have now been answered in the literature, and perhaps an essential key to our new understandings (and indeed to new questions) has been the recent focus, over the past eight years, on the three-dimensional aspects of nominally two-dimensional wake flows. New techniques in experiment, using laser-induced fluorescence and PIV (Particle-Image-Velocimetry), are vigorously being applied to wakes, but interestingly, several of the new discoveries have come from careful use of classical methods. There is no question that strides forward in understanding of the wake problem are being made possible by ongoing three- dimensional direct numerical simulations, as well as by the surprisingly successful use of analytical modeling in these flows, and by secondary stability analyses. These new developments, and the discoveries of several new phenomena in wakes, are presented in this review.
3,206 citations
TL;DR: The term immersed boundary (IB) method is used to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries.
Abstract: The term “immersed boundary method” was first used in reference to a method developed by Peskin (1972) to simulate cardiac mechanics and associated blood flow. The distinguishing feature of this method was that the entire simulation was carried out on a Cartesian grid, which did not conform to the geometry of the heart, and a novel procedure was formulated for imposing the effect of the immersed boundary (IB) on the flow. Since Peskin introduced this method, numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In addition, there is another class of methods, usually referred to as “Cartesian grid methods,” which were originally developed for simulating inviscid flows with complex embedded solid boundaries on Cartesian grids (Berger & Aftosmis 1998, Clarke et al. 1986, Zeeuw & Powell 1991). These methods have been extended to simulate unsteady viscous flows (Udaykumar et al. 1996, Ye et al. 1999) and thus have capabilities similar to those of IB methods. In this review, we use the term immersed boundary (IB) method to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries. Furthermore, this review focuses mainly on IB methods for flows with immersed solid boundaries. Application of these and related methods to problems with liquid-liquid and liquid-gas boundaries was covered in previous reviews by Anderson et al. (1998) and Scardovelli & Zaleski (1999). Consider the simulation of flow past a solid body shown in Figure 1a. The conventional approach to this would employ structured or unstructured grids that conform to the body. Generating these grids proceeds in two sequential steps. First, a surface grid covering the boundaries b is generated. This is then used as a boundary condition to generate a grid in the volume f occupied by the fluid. If a finite-difference method is employed on a structured grid, then the differential form of the governing equations is transformed to a curvilinear coordinate system aligned with the grid lines (Ferziger & Peric 1996). Because the grid conforms to the surface of the body, the transformed equations can then be discretized in the
3,184 citations
TL;DR: For R > 3.5 × 10^6, definite vortex shedding occurs, with Strouhal number 0.27 as discussed by the authors, while for R > 0.7, the vortex shedding rate becomes constant.
Abstract: Measurements on a large circular cylinder in a pressurized wind tunnel at Reynolds numbers from 10^6 to 10^7 reveal a high Reynolds number transition in which the drag coefficient increases from its low supercritical value to a value 0.7 at R = 3.5 × 10^6 and then becomes constant. Also, for R > 3.5 × 10^6, definite vortex shedding occurs, with Strouhal number 0.27.
1,226 citations
TL;DR: In this paper, a new immersed-boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source/sink as well as a momentum forcing.
1,090 citations
TL;DR: In this article, the authors describe measurements of the drag on circular cylinders, made by observing the bending of quartz fibres, in a stream with the Reynolds number range 0·5-100.
Abstract: Part I describes measurements of the drag on circular cylinders, made by observing the bending of quartz fibres, in a stream with the Reynolds number range 0·5-100. Comparisons are made with other experimental values (which cover only the upper part of this range) and with the various theoretical calculations.Part II advances experimental evidence for there being a transition in the mode of the vortex street in the wake of a cylinder at a Reynolds number around 90. Investigations of the nature of this transition and the differences between the flows on either side of it are described. The interpretation that the change is between a vortex street originating in the wake and one originating in the immediate vicinity of the cylinder is suggested.
1,075 citations