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Natural convection has been extensively studied due to its presence in many engineering applications. It is one of the most important modes of heat transfer and arises due to buoyancy-induced flows resulting from temperature differences. This review presents a detailed summary of numerical and experimental studies related to laminar natural convection in enclosures with and without internal bodies. Square, circular, and elliptical cylinders are mostly considered as internal bodies. The presence of internal bodies makes significant changes in the flow characteristics within the enclosure. The effects on the flow regime and thermal fields of various parameters have been discussed in detail, including the Rayleigh number, aspect ratio, position of internal bodies, number of internal bodies, and inclination angle. The different flow regimes depending on the input parameters are categorized based on observations made from flow and thermal patterns. This review discusses various methodologies used by a large group of researchers to improve the hydrodynamic and thermal behavior for buoyancy-driven flows within an enclosure.

This study reports on an experimental investigation of the effect of mass ratio on the transverse flow-induced vibration (FIV) response of an elastically mounted square cylinder placed at three different incidence angles: two symmetric with respect to the centreplane, α = 0 ° and 45 ° ; and one asymmetric at 20 ° . These three angles display different dominant FIV phenomena: transverse galloping and combined vortex-induced vibration (VIV) and galloping for α = 0 ° , VIV for α = 45 ° , and higher branch subharmonic (period-doubled) VIV for α = 20 ° (Nemes et al., 2012). The mass ratio is defined as the ratio of the total oscillating mass ( m ) to the displaced fluid mass ( m d ), m ∗ = m ∕ m d . The present results show that the mass ratio ( m ∗ = 2 . 64 – 15.00) has a significant influence on the structural vibration response for all FIV phenomena, and can dictate whether two of these modes exist at all. Three primary observations are presented: for the α = 0 ° case, the combined VIV–galloping response is diminished as the mass ratio is increased, and it ceases to exist for m ∗ ⩾ 11 . 31 ; for the α = 45 ° case, the peak values of the normalised oscillation amplitude during VIV are only reduced marginally with increasing m ∗ , however the body oscillation amplitude in the desynchronised regions is significantly attenuated; for the α = 20 ° case, there exists a critical mass ratio ( m crit ∗ ≃ 3 . 50 ) above which the higher branch subharmonic VIV does not persist.

Fluid dynamics and heat transfer behaviour are studied past side-by-side square cylinders at incidence in vertical flow arrangement numerically considering laminar, Newtonian, steady, incompressible and two-dimensional flow using Finite Volume Method based ANSYS Fluent solver. Using air (Pr = 0.7) as the working fluid, computations are performed at a representative value of Re = 100. The angle of incidence (alpha) is varied from 0 degrees to 45 degrees in the step of 5 degrees, whereas, the lateral distance between the cylinders is kept constant. To consider all possibilities, cylinders are rotated either clockwise or counter-clockwise, simultaneously or individually, which generates thirty-four different orientations. Buoyancy assisting phenomenon is created by changing the Richardson number (Ri) from 0 to 1 in step of 0.25. Due to the variation of the angle of incidence and its orientations, vortex generation is observed in the buoyancy assisting case at a critical value of Ri. To study heat transfer characteristics, time average and the local Nusselt number are analysed. For a fixed lateral distance between the cylinders, maximum heat transfer is found to occur at an incident angle of 45 degrees. Other important parameters, such as drag coefficient (C-D), lift coefficient (C-L), Strouhal number (St) are also studied. (C) 2018 Elsevier Ltd. All rights reserved.

The natural ocean/river currents energy can be harvested using Flow Induced Motion (FIM) phenomena. The effect of damping-ratio and mass-ratio on Flow Induced Motion energy harnessing of a square cylinder are numerically investigated for Reynolds number 15500

Many previous studies have been conducted to investigate wind-induced galloping of slender structures or structural members. While some recent studies have examined the particular problem of galloping involving coupling between vibration components about the principal axes, few occurrences of such vibrations of full-scale structures have been reported. This paper presents a comprehensive investigation that incorporates full-scale and wind tunnel experiments and an analytical formulation to study the galloping oscillation of a type of slender tower. The full-scale and wind tunnel experiments were conducted to assess the characteristics of the oscillations, their correlation with the wind characteristics, as well as the core parameters that influence the interaction between the tower and the wind. Based on the results from the experiments, a state-space model for coupled galloping of slender towers is formulated. This model enables the prediction of the susceptibility of a slender tower to galloping instability through an evaluation of the net damping resulting from the wind-structure interaction. The tower subjected to monitoring in the full-scale study is used as an example structure in an illustrative application of the analytical model.

Two-dimensional space-time finite-element simulations are carried out to study the effect of oscillator mass ratio, m * on free in-line and transverse vibrations of a rigid square cylinder. The effect of viscous damping or resistance is not considered and thus cylinders of mass ratio 1, 5, 10 and 20 execute free undamped vibrations. Results are presented for 50≤ Re ≤250 where Re is the Reynolds number. For m * = 1, synchronization between cylinder oscillation and vortex-shedding is 1:1 (periodic flow). Thus, the C l -Y phase portraits must be single looped closed curves. For m * = 5-20, synchronization is 1:1 (periodic flow) prior to galloping. For m * = 5, the synchronization during galloping is quite different from 1:3. Along ‘increasing Re ’, the entire galloping branch of m * = 5 cylinder is quasi-periodic. However, along ‘decreasing Re ’, it is mostly quasi-periodic and it is periodic for Re ≤190. An 1:3 sub-harmonic synchronization is seen for the m * = 10 and 20 cylinders only in the periodic regime of galloping occurring at higher Re . For m * = 1, only one kink is seen in the response curve signifying transition from initial to lower branch. Two kinks are captured for m * = 5 cylinder. For m * = 10 and 20, an additional third kink is resolved in the galloping branch that signifies transition from quasi-periodic flow/body motion to periodic flow/body motion.

The FIV (Flow-Induced Vibration) responses of an elastically mounted square cylinder near a free surface are numerically investigated using 2-dimensional RANS equations in conjunction with SST k- ω turbulence model. In this work, the effect of submergence depth on the FIV response and energy conversion is studied. The flow field behavior for flow velocities between 0.2 m/s and 2.5 m/s (1.61 × 104

This paper presents a numerical study of the effect of spring stiffness and mass ratio on flow-induced vibration (FIV) of a square cylinder placed at four different incidence angles: α = 0 ∘ , 10 ∘ , 22 . 5 ∘ , 45 ∘ . The FIV is dominated by vortex-induced vibration (VIV), while another common form of FIV, galloping, is only found at α = 0 ∘ . A period-doubled mode which has a half of the shedding frequency of a fix body frequency component is found in all incidence angles except 0 ∘ . For these cases of α = 22. 5 ∘ ,4 5 ∘ , there exists a limiting mass ratio beyond which period-doubled does not exist. However, all mass ratio has a period-doubled mode at α = 10 ∘ due to its high asymmetry. The parameter of effective elasticity k e f f 1 ∗ combined by mass ratio and spring stiffness is introduced in this paper. For the period-double mode and galloping, another effective elasticity k e f f 0.5 ∗ related to half of the frequency of a fix body is needed. The results show that the different flow regimes is a function of the effective elasticity rather than the reduce velocity with the change of mass ratio and spring stiffness. By using the effective elasticity, the limited mass ratio for occurrence of galloping can be determined.

The vortical structures around a yawed square cylinder oscillating in quiescent water are investigated using the particle image velocimetry technique. Following a previous study on the hydrodynamics (Lou et al., 2017), the present experiments are performed at different yaw angles ( α ) and Keulegan-Carpenter (KC) numbers to correlate the independence principle (IP) to vortical flow structures. At KC = 6, the vortex pair shows no shedding. Similar vortex patterns at different yaw angles result in similar hydrodynamic behaviors, which validates the IP at small KC numbers. The single and double pairs of vortex shedding regimes are observed for α = 0° at KC = 11 and 19, respectively, and the vortex shedding process is determined by the movement of the cylinder as well as the interaction between vortices and shear layers. As α increases to 45°, the shear layers are stretched and show attachment to the upper and lower sides of the cylinder for most of the time within one oscillating cycle. The shedding is only observed at the end of each half cycle and the vortices are found to reattach to the cylinder body. The subsequent drag force behavior of the yawed cylinder displays significant differences from that at α = 0° and hence the IP is no longer applicable at KC = 11 and 19. When KC increases to 25, a three pairs of vortex shedding regime can be observed at both α = 0° and 45°. A similar flow feature, characterized by the shear layer attachment when the cylinder is at the neutral position and the vortex shedding at the end of each half cycle, has been found for both α = 0° and 45°. This result indicates that the IP becomes valid for the yawed square cylinder when the KC is sufficiently large until it is analogous to the steady flow.

Flow structures and downstream wake behind two identical tandem flat plates and a square cylinder has been studied at high Reynolds number and similarities and dissimilarities in coherent and incoherent structures have been identified. It was found that the square cylinder produces higher coherent turbulence kinetic energy (TKE) with peaks up to seven times higher than the flat plates in tandem. Also, turbulence kinetic energy production contours revealed that while the turbulent peak occurs mainly at the edges of the normal flat plates in tandem, it develops at centreline in the wake of the square cylinder. Interestingly, it was observed that the square cylinder exhibits two alternative shedding frequencies along centreline in the wake region.

Numerical analysis of two dimensional steady flows over a triangular extended solid (thorn) attached to square cylinder positioned at front stagnation point and at rear stagnation point separately is reported at low Reynolds number ( Re = 40). The variation of thorn length ( l ′ = 0.2, 0.4 & 0.6) & inclination angle ( Θ = 5°, 10°, 15° & 20°) and its effect on the drag, pressure, shear stress, boundary layer as well as on the inertia force and viscous force are of interest. There is comparatively large variation on drag when the thorn is placed at the front side instead of placing at rear. The recirculation length is remained constant by varying the length and inclination of the thorn irrespective of its position. The variation of drag is comparatively less by changing thorn inclination. It is found that the drag is minimized by 2–3% compared to square model.

A new kind of parallel finite-difference time-domain (FDTD) method is used to calculate and analyze the transmission properties of photonic crystal. The effectiveness and the accuracy of parallel FDTD method were proved by the typical two-dimensional sine wave. The result shows that parallel FDTD method, which can save time effectively in electromagnetic problems with large size and long time, performs as accurate as the series one. This method, whose results shows that the photonic band gap normalized frequency moves to the low-frequency direction with the enlargement of the section area of the square cylinder and that the band gap gets thinner, is applied to simulate and analyze the two-dimensional photonic crystal and gives calculating method and analyzing accordance to calculate and analyze large-sized photonic crystal structure.

The flow past a square cylinder attracts extensive interests in the past decades. It also has been used for the drag reduction research of flow past a bluff body. The present study performs Very-Large Eddy Simulation (VLES) of passive drag reduction for a square cylinder based on the open-source CFD (Computational Fluid Dynamics) toolbox, OpenFOAM. The newly developed VLES method is implemented in OpenFOAM and also assessed in the complex flow control simulations. For the drag reduction, a passive flow control method is used, i.e. cutting the corners at the front edge of the square cylinder. Firstly, a control method from previous studies (referred as to CM-1, i.e. control method 1) is adopted and numerical investigations are performed. Based on that, a new control method, i.e. cutting the corners with an extra cut (referred as to CM-2, i.e. control method 2) is proposed and the performance of the new control method for drag reduction is examined. The results show that, firstly, the reliability and accuracy of the VLES turbulence method is verified by the simulations, and also it is confirmed that the VLES method can give satisfactory predictions using a relatively coarse computational grid. Then, it is found that both the control methods of CM-1 and CM-2 can give significant drag reduction, up to 48% and 61% drag reductions compared with the original square cylinder. Also, the new proposed control method generally works better than the previous control method. The results can benefit to the high-fidelity numerical simulation and also the drag reduction studies for general bluff body flows which is widely encountered in ocean engineering applications.

The mixed convective flow stability of nanofluids past a square cylinder is investigated by Dynamic Mode Decomposition (DMD). The energy content in the individual modes for Cu–water nanofluids is found to be higher than that of Al2O3–water nanofluids. DMD results showed the fact that Cu–water nanofluids have more small-scale structures of higher frequency modes compared to that of Al2O3–water nanofluids. The most dominant temporal dynamic mode corresponds to the lower-frequency eigenvalue λ = ( 0.99374 , ± 0.1117 ) for Al2O3–water nanofluids and λ = ( 0.99451 , ± 0.10464 ) for Cu–water nanofluids. Energy content in the mean flow of the base fluid at Richardson number of −0.5 is found to be maximum compared to that of nanofluids.

A numerical study of the alteration of a square cylinder wake using a detached downstream thin flat plate is presented. The wake is generated by a uniform flow of Reynolds number 150 based on the side length of the cylinder, D. The sensitivity of the near wake structure to the downstream position of the plate is investigated by varying the gap distance (G) along the wake centerline in the range 0

In regards to the defect of respectively handling three conditions, this paper puts forward a new unified expression fitting for different boundary conditions. It also obtains the parameter values of expression in different boundary conditions. Take the infinite square cylinder putting into cold liquor as an example, it works out a program using the improved new boundary treatment to simulate cylinder temperature field. This paper gets distributions of temperature field at four different times. The results of simulation not only meet the physical situation, but also have high precision compared with the theoretical solutions. Since being easy to deal with complex boundary conditions, the new way makes the FEM useful again in engineering calculation and research.

The effects of blockage on the hydrodynamic, thermal and mass transfer characteristics of a circular cylinder (CC) and their association with each other are investigated numerically, by considering the influence of blockage (beta=0.333-0.800) on the flow and heat transfer mechanisms in conjunction with moisture diffusivity (D=1 x 10(-8)-1 x 10(-5) m(2)/s) to show how much mass transfer behavior and phenomena are affected. As some comprehensive ANSYS-CFX runs are performed in the hydrodynamic and thermal fields around the CC, the moisture distributions within the CC are evaluated by Alternating Direction implicit method. It is determined that blockage causes thinner hydrodynamic and thermal boundary layers, rises the frictional and thermal activities, and shifts the separation locations (theta(s)) downstream to theta(s)=50.20 degrees, 41.98 degrees and 37.30 degrees for beta=0.333, 0.571 and 0.800. In the complete blockage scenario set, stagnation point heat transfer values are evaluated to be above those of the back-face, signifying the superior heat transfer enhancing capability of the stagnation point momentum activity when compared with the impact of downstream vortex system. The influence of moisture diffusivity on the overall drying times is determined to advance with stronger blockage. As the back face mass transfer coefficients (h(m-bf)) rise with a high beta, the contrary is valid for front face values (h(m-ff)), with the interpreting ratios of (h) over bar (m-bf)/(h) over bar (m)=0.51 and 0.57 and (h) over bar (m-ff)/(h) over bar (m)=1.49 and 1.43 for beta=0.333 and 0.800.

The possibility of transverse galloping of a square cylinder at low Reynolds numbers (Re≤200Re≤200, so that the flow is presumably laminar) is analysed. Transverse galloping is here considered as a one-degree-of-freedom oscillator subjected to fluid forces, which are described by using the quasi-steady hypothesis (time-averaged data are extracted from previous numerical simulations). Approximate solutions are obtained by means of the method of Krylov-Bogoliubov, with two major conclusions: (i) a square cylinder cannot gallop below a Reynolds number of 159 and (ii) in the range 159≤Re≤200159≤Re≤200 the response exhibits no hysteresis.

The structure of confined wakes behind a square cylinder in a channel subject to a locally uniform suction or blowing at both the channel walls is presented. A pressure based finite-difference technique has been used to solve the unsteady Navier–Stokes equations. It is observed that the amplitude of the lift coefficient decreases with increase in the blowing velocity. Coefficients of drag also decrease for the application of uniform blowing and for a suitable value of the blowing parameter, the flow becomes steady and symmetric. The amplitude of the lift coefficients increases up to a certain limit of suction velocity and after that it suddenly decreases and flow becomes steady. Coefficients of drag also gives the same feature. Effects of the suction and blowing on the vortex-shedding region are analyzed in detail and presented graphically.

The results of spectral proper transformation (SPT) analyses applied to the pressure fluctuations on a square cylinder and on a bridge box deck are presented in this paper. The main objective of the paper is that of comparing the results obtained using SPT with those obtained through a covariance proper transformation (CPT) analysis, to understand whether additional information is provided by SPT with respect to CPT. The meaning of the frequency dependency of the spectral eigenvalues and eigenvectors is also investigated. It is observed that a correspondence between SPT and CPT modes can be found in some cases, if the phase shift between the components of the SPT complex modes is properly accounted for. It is also found that the frequency variation of the SPT eigenvalues is related to the characteristic frequencies of the different physical phenomena causing the pressure fluctuations.

Calculations are reported for the flow past a square cylinder at Re=22,000 placed at various distances from an adjacent wall, including the limiting case without wall influence. Experiments have indicated that unsteady vortex shedding is suppressed when the wall is relatively close to the cylinder. Two-dimensional (2-D) unsteady equations are solved which allow any periodic shedding motion to be resolved; the superimposed turbulent fluctuations are simulated with two versions of the k-e turbulence model: the standard k-e model and the modification attributable to Kato and Launder (1993), which eliminates the excessive turbulent kinetic energy production in stagnation regions produced by the standard model. Wall functions are used with both versions. The standard model was found to damp the shedding motion unrealistically so that shedding was suppressed at considerably larger gap widths than observed experimentally. The Kato-Launder modification yields reasonable predictions over the full range of gap widths; for G w D =0.75 a quantitative comparison is presented with the authors' phase-resolved experiments, which shows fairly good accord.

The unsteady turbulent flow past a square cylinder is calculated with the Baldwin-Lomax Model. The influence of the numerical schemes is studied. Comparisons with experimental data and with previous calculations using a Reynolds stress model and 3-D large eddy simulations are presented. It is shown that a good prediction is obtained with a Baldwin-Lomax model by using the recently proposed CPI discretization scheme.

This paper concerns an experimental investigation of the flow around and pressure forces on fixed (non-vibrating) rectangular cylinders at angles of attack 0°–90°. Pressure forces and moments for cylinders for cylinders with side ratios B A = 1, 1.62, 2.5 and 3 (shortest side A = 20 mm) were estimated from measurements of static pressure distributions at mid-span. Wake frequencies and associated Strouhal numbers were determined from hot wire measurements in the near-wake regions (A = 4 and 20 mm). With the smaller cylinders 12 side ratios within B A = 1–5 were investigated. The free stream turbulence intensity was less than 0.06%, blockages less than 5% and aspect ratios L A greater than 50. Reynolds numbers, based on A, ranged from about Re = 400 to Re = 3 × 104 (pressure measurements from about Re = 3 × 103). For the square cylinder, the measured pressure forces were used for calculations of quasi-steady galloping response in the plunging mode.

The unsteady flowfield past a two-dimensional(2D) square cylinder at Re=1.0 × 105 is predicted by Large Eddy Simulation(LES). Results of two-dimensional (2D) and three-dimensional(3D) computations are compared with results of previous experiments[1–4]. It is confirmed that the LES results based on 3D computation correspond very well with the experimental results, but the LES results based on 2D computation are different from those based on 3D computation as well as those based on experiments. Distributions of mean vorticity, vorticity fluctuations and turbulence terms in the mean vorticity equation are discussed in order to examine structural difference between the results of 2D and 3D LES computations.

The boundary layer wind tunnel was simulated numerically. The three-dimensional simulation method of turbulent boundary layer over rough surfaces using a refined κ-ϵ turbulence model was examined and its applicability is shown by comparing the numerical results with experimental data. Using the simulating method described here, wind characteristics over rough surfaces and effect of incident flow on the square cylinder were examined numerically. The good applicability of the simulation results indicate that these preliminary calculations could be a powerful tool in the design of actual wind tunnel tests.

The principles of aeroelastic and aerodynamic models are distinguished, and aeroelastic magnification is identified as a possible source of unacceptable error in the latter type of model. Past justifications of aerodynamic modelling have not clearly identified the relevant error-controlling parameters, or have not established quantitative limits required for valid results on the parameters studied. Results of new tests show that the reduced velocity, in conjunction with the mass-damping parameter, provide a good characterization of the aeroelastic magnification factor for an 8:11 square cylinder in a simulated suburban environment.

0894-1777/$ see front matter 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2013.04.004 DOI of original article: http://dx.doi.org/10.1016/j.expthermflusci.2012.12.007 ⇑ Corresponding author. Tel./fax: +86 21 34206869. E-mail address: yzliu@sjtu.edu.cn (Y. Liu). Fig. 12. Squared-strain distribution along the membrane length for the (a) present membrane at various Reynolds numbers and (b) membranes studied by Techet Shengxian Shi , T.H. New, Yingzheng Liu a,⇑

The extension of the enthalpy method to multi-dimensional Stefan problems is outlined. The method is applied to the numerical solution of a problem involving the solidification of a square cylinder of fluid when the surface temperature is lowered at a constant rate. One aim of this paper is to demonstrate that the numerical method successfully predicts the experimental results which have been published for this problem. The same technique is then applied to a similar problem, in which the surface temperature is lowered discontinuously at the initial instant, and the results compared with those obtained by other authors.

Pera and Gebhart [3] suggested that the usual expression “flow separation” was not an appropriate term for natural convection flows generated adjacent horizontal cylinders. The argument is applied to a horizontal square cylinder with sharp edges, in which the temperature inversions over the upper horizontal surface are observed unexpectedly in the interferograms with increment of Grashof numbers 2.77×104 to 2.19×105. These inversions can be interpreted in terms of twin vortex, which reveals the flow separation near the upper corners. Consequently, the argument should be extended to include that the flow separation may be developed in natural convection when caused by a body with edges such as the isothermal horizontal square cylinder.

Geometrical effects on the resonance integral of 238U are investigated by use of the RICM code, which calculates the resonance integrals in multi-region lattices and other various geometries. The geometries under consideration here are: (1) Various isolated lumps immersed in an infinite sea of moderator; a cylinder, plate, sphere and square cylinder. (2) Isolated systems having fuel or moderator regions within; a single annular, three region annular with a solid cylinder at its center, concentric double annular and tube-in-shell type fuel. (3) Lattices and clusters made up of regular hexagonal and square fuel rod arrangement. The resonance integrals of 221U for the fuel rods of U-metal, UO2 and UC are calculated by the RICM code and are compared with the experimental values of many researchers. Two assumptions in general use, i.e. the flat flux approximation in the fuel region and the 1/E flux assumption in the moderator, are further investigated. Temperature dependence of the resonance integrals are also calculated for the cases of the U-metal and UO2 fuel rods and the results are compared with the experimental ones. An equivalence of various isolated lumps to a cylinder has been established by introducing an effective surface area with a correction factor. By use of the RICM code, the resonance integrals of the annular and tube-in-shell type U02 fuel, lattices and clusters of the U02 rods are calculated. So as to minimize the difference between the above value and the one derived from the fitted formula for the resonance integral of the U02 rod, a value of the correction factor a in the expression of the effective surface area, introduced by LEVINE is determined to be 0·07. In the lattice and cluster calculations, the propriety of the NORDHEIM'S (or Bell's ) approximation for the fuel escape probability in a lattice is investigated and it turns out that his approximation is fairly good, so far as the systems are not quite compact. Finally, the RICM calculations are carried out for the experimental systems of the clusters used by Hellstrand, Pershagen and Amyot et al., and the resultant values are compared with their experimental ones. It is clear from all the comparisons shown here that the calculation is always in fairly good agreement with the experiment. This fact leads to the conclusion that the propriety of both the calculational method used in the RICM code and the adopted values of resonance parameters of 228U has been verified. The resonance parameters used throughout this report come from the recommendation made in BNL-325. New resonance data from ‘Petrel project’ give nearly same resonance integrals as the BNL-325 data.

This article deals with the effect of couple-stresses on thermal stress distribution in a square cylinder with a central circular hole under steady state temperature distribution. The analysis is developed by the point-matching technique. From our calculation, it may be concluded that stress concentration around a circular hole, taking couple-stress into account, results in lower values than those accepted heretofore.