R.M.C. So

Free vibrations of two side-by-side cylinders in a cross-flow

Free vibrations of two side-by-side cylinders with fixed support (no rotation and displacement) at both ends placed in a cross-flow were experimentally investigated. Two fibre-optic Bragg grating sensors were used to measure the dynamic strain, while a hot wire and flow visualization were employed to examine the flow field around the cylinders. Three T / d ratios, 3.00, 1.70 and 1.13, were investigated, where T is the centre-to-centre cylinder spacing and d is the diameter; they give rise to three different flow regimes. The investigation throws new light on the shed vortices and their evolution. A new interpretation is proposed for the two different dominant frequencies, which are associated with the narrow and the wide wake when the gap between the cylinders is between 1.5 and 2.0 as reported in the literature. The structural vibration behaviour is closely linked to the flow characteristics. At T / d = 3:00, the cross-flow root-mean-square strain distribution shows a very prominent peak at the reduced velocity U r ≈ 26 when the vortex shedding frequency f s , coincides with the third-mode natural frequency of the combined fluid–cylinder system. When T / d < 3:00, this peak is not evident and the vibration is suppressed because of the weakening strength of the vortices. The characteristics of the system modal damping ratios, including both structural and fluid damping, and natural frequencies are also investigated. It is found that both parameters depend on T / d . Furthermore, they vary slowly with U r , except near resonance where a sharp variation occurs. The sharp variation in the natural frequencies of the combined system is dictated by the vortex shedding frequency, in contrast with the lock-in phenomenon, where the forced vibration of a structure modifies the vortex shedding frequency. This behaviour of the system natural frequencies persists even in the case of the single cylinder and does not seem to depend on the interference between cylinders. A linear analysis of an isolated cylinder in a cross-flow has been carried out. The linear model prediction is qualitatively consistent with the experimental observation of the system damping ratios and natural frequencies, thus providing valuable insight into the physics of fluid–structure interactions.

Reynolds number effects on the flow structure behind two side-by-side cylinders

The wake structure of two side-by-side cylinders was experimentally investigated using the laser-induced fluorescence flow visualization, particle image velocimetry and hot-wire techniques. The investigation was focused on the asymmetrical flow regime, i.e., T/d=1.2–1.6, where T is the center-to-center cylinder spacing and d is the cylinder diameter. Experiments were conducted in both the water tunnel and the wind tunnel at a Reynolds number (Re) range of 150–14 300. It has been found that, as Re increases, the flow structure behind the cylinders may change from one single vortex street to two streets with one narrow and one wide for the same T/d. The one-street flow structure is dominated by one frequency f0*=f0d/U∞≈0.09, where f0 is the dominant frequency and U∞ is the free-stream velocity. On the other hand, two frequencies, f0*≈0.3 and 0.09, characterized the two-street flow structure. These are associated with the narrow and wide street, respectively. It is further observed that the critical Re, at w...

Near-wall modeling of the dissipation rate equation

Near-wall modeling of the dissipation rate equation is investigated and its asymptotic behavior is studied in detail using a k-epsilon model. It is found that all existing modeled dissipation rate equations predict an incorrect behavior for the dissipation rate near a wall. An improvement is proposed and the resulting near-wall dissipation rate distribution is found to be similar to that given by numerical simulation data. To further validate the improved k-epsilon model, it is used to calculate flat-plate turbulent boundary-layer flows at high- as well as low-turbulence Reynolds numbers, and the results are compared with measurements, numerical simulation data, and the calculations of three different two-equation models. These comparisons show that all the models tested give essentially the same flow properties away from the wall; significant differences only occur in a region very close to the wall. In this region, the calculations of the improved k-epsilon model are in better agreement with measurements and numerical simulation data. In particular, the modeled distribution of the dissipation rate is significantly improved and a maximum is predicted at the wall instead of away from the wall. Furthermore, the improved k-epsilon model is found to be the most asymptotically consistent among the four different two-equation models examined.

A turbulence velocity scale for curved shear flows

Assuming the turbulence length scale to be unaffected by streamline curvature, a turbulence velocity scale for curved shear flows is derived from the Reynoldsstress equations. Closure of the equations is obtained by using the scheme of Mellor & Herring (1973), and the Reynolds-stress equations are simplified by invoking the two-dimensional boundary-layer approximations and assuming that production of turbulent energy balances viscous dissipation. The resulting formula for the velocity scale has one free parameter, but this can be determined from data for non-rotating unstratified plane flows. Consequently there is no free constant in the derived expression. A single value of the constant is found to give good agreement between calculated and measured values of the velocity scale for a wide variety of curved shear flows. The result is also applied to test the validity and extent of the analogy between the effects of buoyancy and streamline curvature. This is done by comparing the present result with that obtained by Mellor (1973). Excellent agreement is obtainedfor therange - 0.21 < Ri, < 0.21. Therefore the present result provides direct evidence in support of the use of a Monin-Oboukhov (1 954) formula for curved shear flows as proposed by Bradshaw (1969).

One-Step Aeroacoustics Simulation Using Lattice Boltzmann Method

The lattice Boltzmann method (LBM) is a numerical simplification of the Boltzmann equation of the kinetic theory of gases that describes fluid motions by tracking the evolution of the particle velocity distribution function based on linear streaming with nonlinear collision. If the Bhatnagar‐Gross‐Krook (BGK) collision model is invoked, the velocity distribution function in this mesoscopic description of nonlinear fluid motions is essentially linear. This intrinsic feature of LBM can be exploited for convenient parallel programming, which makes itself particularly attractive for one-step aeroacoustics simulations. It is shown that the compressible Navier‐Stokes equations and the ideal gas equation of state can be correctly recovered by considering the translational and rotational degrees of freedom of diatomic gases in the internal energy and using a multiscale Chapman‐Enskog expansion. Assuming two relaxation times in the BGK model allows the temperature dependence of the first coefficient of viscosity of diatomic gases to be replicated. The modified LBM model is solved using a two-dimensional 9-discretized and a twodimensional 13-discretized velocity lattices. Three cases are selected to validate the one-step LBM aeroacoustics simulation. They are the one-dimensional acoustic pulse propagation, the circular acoustic pulse propagation, and the propagation of acoustic, vorticity, and entropy pulses in a uniform stream. The accuracy of the LBM is established by comparing with direct numerical simulation (DNS) results obtained by solving the governing equations using a finite difference scheme. The tests show that the proposed LBM and the DNS give identical results, thus suggesting that the LBM can be used to simulate aeroacoustics problems correctly.

Complex turbulent wakes generated by two and three side-by-side cylinders

Abstract Turbulent complex wakes generated by two and three cylinders in a side-by-side arrangement were investigated experimentally. In the present context, the complex wake refers to the flow formed by two or more simple wakes behind side-by-side cylinders. One cylinder was slightly heated; the temperature difference is about 1°C so that the temperature could be treated as a passive scalar. A combination of an X-wire and a cold wire was used to measure the velocity and temperature fluctuations. The present objective is to document the turbulence field of the complex wakes and examine the interactions between turbulent simple wakes and their effects on the momentum and heat transport phenomena. It is observed that the cross-stream distributions of the Reynolds normal stresses can be asymmetrical at a small spacing-to-diameter ratio. The Reynolds shear stress and its lateral transport distributions however remain symmetrical. This is explained in terms of the gap flow deflection behind side-by-side cylinders and the transport characteristics of vortical structures. The interactions between simple wakes do not seem to have any effect on the fine-scale turbulence, at least up to the scales in the inertial sub-range. On the other hand, the temperature spectra in the inertial sub-range have been affected; their slopes have been appreciably increased compared with the single-cylinder data. The gradient transport assumption is found to be valid for the turbulence field, but not for the temperature field. The heat flux and temperature gradient do not approach zero simultaneously near the centerlines of simple wakes, thus giving rise to a substantial variation in the heat transport. This leads to a significant drop in the turbulent Prandtl number. The superposition hypothesis, as proposed by Bradshaw and his co-workers, is also examined for the present complex wakes.

A near-wall two-equation model for compressible turbulent flows

Abstract : A near-wall two-equation turbulence model of the K - epsilon type is developed for the description of high-speed compressible flows. The Favre- averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K - omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper.

Flow pattern and velocity field distribution of cross-flow around four cylinders in a square configuration at a low Reynolds number

Abstract The flow around four cylinders in a square configuration with a spacing ratio of 4 and at a Reynolds number of 200 were investigated using laser-induced fluorescence (LIF) visualization and particle image velocimetry (PIV) for angles of incidence ranging from α=0° to 45° at a 5° interval. Several distinct flow patterns were observed. Dependent on α, the flow was classified into three basic flow regimes. Each regime has its own dominant flow pattern and could lead to different problems. Two distinct flow patterns, which could lead to strong flow-induced vibration, were observed in this experiment. One is the impingement of oncoming vortices on the cylinders directly. The other is the formation of a jet flow between the near wake (or alternatively known as stagnation wake) of the upstream cylinder and downstream cylinder and such a jet flow is most prominent at α=15°. These experimental results can be used to validate numerical simulation methods developed to investigate flows around cylinder arrays.

Low Reynolds number modeling of turbulent flows with and without wall transpiration

A full Reynolds-stress closure that is capable of describing the flow all the way to the wall is formulated. The closure is based on the conventional high Reynolds number form of the redistribution model, the inclusion of molecular diffusion, and a modified dissipation model to account for viscous effects near a wall. Two dissipation models are investigated along with two gradient diffusion and two redistribution models. Their respective effects on the calculated flow properties are assessed by comparing them with the data of fully developed turbulent flows and a developing pipe flow with wall transpiration. The near-wall behavior is very well predicted; however, the wall correction to the redistribution modeling is found to have little effect on the calculated results. The overall behavior of the fully developed turbulent flows is best described by a nonisotropic gradient diffusion model, a return-to-isotropy redistribution model, and a dissipation model that accounts for viscous behavior near a wall. This same closure also gives the best prediction of the axial pressure drop behavior along a pipe with a uniform wall suction. Furthermore, the near-wall behavior of such a flow is very well predicted by this closure.

A non-linear fluid force model for vortex-induced vibration of an elastic cylinder

Abstract Even under the assumption of a sinusoidal lift and drag force at a single frequency for a stationary cylinder in a cross flow, higher harmonics that represent non-linearity in the fluid–structure interaction process are present. This fact is considered in the formulation of a non-linear fluid force model for a freely vibrating cylinder in a cross flow. The force model is developed based on an iterative process and the modal analysis approach. The fluid force components in the model can be evaluated from measured vibration data with the help of the auto-regressive moving averaging (ARMA) technique. An example is used to illustrate that non-linear (higher order) force components are present at resonance, even for a case with relatively weak fluid–structure interaction. Further analysis reveals that the fluid force components are dependent on structural damping and mass ratio. The non-linear fluid force model is further modified by taking these considerations into account and is used to predict the dynamic characteristics of a freely vibrating cylinder over a range of Reynolds numbers, mass and structural damping ratios. On comparison with measurements obtained from four different experiments and predictions made by previous single-degree-of-freedom model, good agreement is found over a wide range of these parameters.