Damping of Water Waves by Grid Geometry

The drag force exerted on a body moving in a fluid is empirically known to follow a linear drag law at low Reynolds numbers and a quadratic drag law at very high Reynolds numbers. The major challenge with the empirical description of the drag lies in the uncertainty of the description of the drag coefficient as a function of velocity. If the function is precisely known, it may be possible to find a general formula for the drag, which would, in principle, be applicable for all Reynolds numbers. The general law can consequently be tested using the linear and quadratic drag laws within their validity regimes to confirm its reliability and validity. The current absence of such a general law implies that the prediction of the dynamics of a body moving under drag forces in the intermediate regime of the Reynolds number can only be approximate and inaccurate since it is not guided by any valid law. In this study, we derive a general relation for the drag force, which may be applicable in all the Reynolds number regimes. We achieve this through a simple transformation of Newton’s second equation for uniformly decelerated motion. It turns out that our general relation is a modification of the linear drag law. The effect of the introduced correction term in the dynamics of a projectile is evidently promising, as can be seen in the more realistic results generated.

An analysis of particle concentrations formed in direct numerical simulations of forced three-dimensional (3-D) turbulence is described. Up to 48 million particles responding passively to the flow with response times ranging from 0.2 to 6 times the dissipation time of the fluid were evolved together until the concentration field reached a statistical stationary state. The Stokes number (St), defined at the dissipation time scale, was the sole parameter used to characterize the particle–fluid coupling in the regime where particles preferentially concentrate. Concentrations resulting from three simulations equilibrating at the Taylor microscale Reynolds numbers (Reλ) 40, 80, and 140 were studied. We present several new results for concentration measures utilized in previous studies as well as measures introduced in this paper. The measures are compared and contrasted on a finer St grid than presented in previous work and are analyzed as functions of Reλ and spatial binning scale. The measures are based on (a) deviations of the concentration PDF (probability density function) from the PDF of a uniform particle field, (b) the correlation dimension (D2) for both 3-D and two-dimensional concentrations, and (c) the relative St-dependent concentrations contained in a localized region of space. Measure (c) is motivated by the observation that the total and St-dependent concentrations are linearly correlated. The concentration measures reveal St dependencies that are insensitive to the Reynolds number of the flow with each measure having its own characteristic shape. The widths and maxima of St functions for measures explicitly constructed on a single spatial binning scale showed a very weak dependence on bin sizes ranging from 2 to 6 times the Kolmogorov length scale. We conclude that the measures studied in this paper reveal a universality that may persist to much higher Reynolds numbers.

This paper aims to employ the Stokes number to mark aerodynamic penalties of airfoils caused by particles, which is crucial to implement their scaling experiments in a gas-solid flow. Each Stokes number is associated with a series of approximate aerodynamic penalties which are obtained at the same Reynolds number with different chord lengths. In the process, two phenomena which go against the mark are discussed and their mechanisms are revealed. The results show they occur at smaller and larger ranges of Stokes number, respectively. The effect of gravity is the leading cause and a larger chord length or diameter particle can strength its effect. The application scope of the mark, meanwhile, is ascertained. A chord length smaller than 1.5 m is advised at Re = 1.00 × 106 and those at other Reynolds numbers are also presented. As Stokes number decreases from 3, the aerodynamic penalty increases exponentially first at the advised chord length and reaches up to their peak values at the Stokes number of 0.050. In addition, the change of the aerodynamic penalty with Stokes number is dominated by the momentum exchange in the direction of gravity in the region between the particle injection plane and the airfoil.

Two- and three-dimensional instabilities of the two-dimensional symmetric flow generated by a circular cylinder oscillating with simple harmonic motion in quiescent fluid, or, alternatively, by oscillatory flow past a stationary cylinder at low Keulegan-Carpenter and Stokes numbers are investigated via Floquet analysis and direct numerical simulation. Previous experimental visualization has found that the flows produced at low amplitudes and frequencies of motion can be grouped by their visual characteristics into a number of distinct regimes. At low values of Keulegan-Carpenter and Stokes numbers, the flow is two-dimensional and has a reflection symmetry about the axis of oscillation, in addition to a pair of spatio-temporal symmetries. This study isolates and classifies the symmetry-breaking instabilities from these two-dimensional basic states as functions of these control parameters. It is found that while the initial bifurcations produced by increasing the parameters can be to three-dimensional flows, much of the behaviour can be explained in terms of two-dimensional symmetry-breaking instabilities. These have two primary manifestations: at low Stokes numbers, the instability is synchronous with the imposed oscillation, and gives rise to a boomerang-shaped mode, while at higher Stokes numbers, the instability is quasi-periodic, with a well-defined second period, which becomes infinite as Stokes numbers are reduced along the marginal stability boundary, ‘freezing’ the quasi-periodic mode into a synchronous one. These two-dimensional modes are, with further small increase in control parameter, unstable to three-dimensional secondary instabilities, and these are the flows which have been reported in previous experimental studies. In contrast, the mode first reported by Honji (J. Fluid Mech. vol. 107, 1981, p. 509), which arises at high Stokes numbers, and lower Keulegan-Carpenter numbers than the two-dimensional quasi-periodic mode, has a three-dimensional primary instability arising directly from the symmetrical two-dimensional basic state.

Despite the ubiquity of turbulent flows in nature, a general solution to the governing equations of motion remain elusive. These equations are nonlinear and nonlocal, and they describe a chaotic system with multi-scale characteristics, making its theoretical analysis difficult. One viable way of investigating high Reynolds number turbulence is by experimental methods, either in laboratory conditions or environmental measurements. The latter, however, are difficult. In one hand, environmental flows have a high Taylor scale Reynolds number ( > 10000) with a high mean velocity flow. This demands a high temporal and spatial resolution anemometer in order to adequately observe the smaller scales. High resolution anemometers, however, require very specific conditions to operate or are very delicate, being able to break even if a sand particle collides with them. These characteristics are in direct opposition to the uncontrolled, particle laden environmental conditions usually found in several types of flows of interest (e.g. inside ice clouds and sandstorms). Laboratory setups offer a viable alternative, albeit at a reduced turbulence intensity. For example, the Max Planck Variable Density Turbulence Tunnel (VDTT) allows for turbulent flows of Taylor scale Reynolds number Reλ ~ 6000. This Reλ is generated by an active grid and kinematic viscosity tuning of the working gas achieved by changing the operating pressure. This allows great flexibility at modulating the turbulence over a wide and continuous range of Reλ values. This setup, in particular, offers the possibility of not only obtaining single point Eulerian statistics, but also to obtain high Re Lagrangian statistics via particle tracking, which cannot be easily performed on atmospheric conditions. This allows not only to complement and corroborate atmospheric Eulerian statistics with more controlled experiments in laboratory, but also to study Lagrangian statistics (which is a field with much less experimental data available) and to analyze certain properties of the VDTT, such as its isotropy. In this thesis, a novel hot-wire sensor which uses a carbon nanotube based material as its sensing element is developed and tested. This device shows a frequency response larger than 20kHz, as well as superior mechanical resistance when compared to conventional Pt-tungsten anemometers of similar dimensions. This would allow the acquisition of high resolution Eulerian statistics on a wide range of environmental flows previously inaccessible due to technological constraints. This thesis also shows, as a separate chapter, the improvements performed on the already existing Lagrangian particle tracking (LPT) setup on the VDTT. The system has been improved to have a Stokes number 4 times smaller than the previous iteration. This thesis also demonstrates, by two independent but complementary methods, that the particles in the system are not electrostatically charged, but inertial. By comparing the Eulerian statistics obtained from both LPT and a pre-existing hot-wire statistics database, it was found that the turbulence intensity from LPT is consistently lower than before, pointing to the existence of sampling biases. A measure of the anisotropy of the system is measured from the LPT statistics, and it is found that the flow is mostly isotropic, even at the inertial range.

Inertial particle impaction on a cylinder in turbulent cross-flow at modest Reynolds numbers

To better understand the role of particle inertia on the heat transfer in the presence of a thermal inhomogeneity, Eulerian–Lagrangian direct numerical simulations (DNSs) have been carried out by using the point–particle model. By considering particles transported by a homogeneous and isotropic, statistically steady turbulent velocity field with a Taylor microscale Reynolds number from 37 to 124, we have investigated the role of particle inertia and thermal inertia in one- and two-way coupling collisionless regimes on the heat transfer between two regions at uniform temperature. A wide range of Stokes numbers, from 0.1 to 3 with a thermal Stokes-number-to-Stokes-number ratio equal to 0.5 to 4.43 has been simulated. It has been found that all moments always undergo a self-similar evolution in the interfacial region between the two uniform temperature zones, the thickness of which shows diffusive growth. We have determined that the maximum contribution of particles to the heat flux, relative to the convective heat transfer, is achieved at a Stokes number which increases with the ratio between thermal Stokes and Stokes number, approaching 1 for very large ratios. Furthermore, the maximum increases with the thermal Stokes-to-Stokes number ratio whereas it reduces for increasing Reynolds. In the two-way coupling regime, particle feedback tends to smooth temperature gradients by reducing the convective heat flux and to increase the particle turbulent heat flux, in particular at a high Stokes number. The impact of particle inertia reduces at very large Stokes numbers and at larger Reynolds numbers. The dependence of the Nusselt number on the relevant governing parameters is presented. The implications of these findings for turbulence modelling are also briefly discussed.

Study of the imposition of bulk flow pulsations on plane channel flow at moderate stokes numbers

Turbulent transition in impactor jets and its effects on impactor resolution

An experimental investigation of fluid loading on large smooth rectangular cylinders of five different aspect ratios was carried out at the Hydrodynamics Laboratory of the University of Glasgow. The cylinders were mounted vertically as surface piercing and horizontally submerged and were subjected to regular waves. The wave force coefficients corresponding to low Keulegan-Carpenter numbers were obtained. The results show that inertia and drag coefficients are dependent of Reynolds and Keulegan-Carpenter numbers and the frequency parameter. It is found that the drag coefficient exhibits large values as KC number approaches zero and then falls sharply as KC number increases within a small range. Inertia and drag coefficients are found to be strongly affected as the cylinders aspect ratios vary. Inertia and drag coefficients are found to be higher for vertical cylinders than those of corresponding horizontal cylinders. The calculated forces using Morison equation through the use of experimentally determined inertia and drag coefficients is found to be in good agreement with the meas-ired forces at low KC numbers. INTRODUCTION With the necessity of reducing the capital cost in exploring marginal fields, new offshore structure designs are emerging with non-circular cylindrical members. An offshore platform whose members made of rectangular cross-section cylinders is considered to be economically more viable than the conventional designs with circular cylindrical sections. New generation of semi-submersible drilling rigs and tension-leg platforms whose hulls and legs are conforming to rectangular geometry in cross-section are examples of these new designs. However, the circular cylindrical geometry has always been the sentre of attention in model tests when investigating the fluid loading. While a large amount of fluid loading data for circular cylinders have been accumulated over the years, relatively little is known about the loading on rectangular cylinders. The design of marine structures requires the prediction of wave & current induced forces. The inline force applied on a body immersed in an oscillating fluid is traditionally calculated using the well-known Morison equation. Since its introduction forty years ago, the Morison equation developed by Morison, O'Brien, Johnson and schaaf1 has become widely used and several experimental results have shown that it has enough accuracy for practical applications. The Morison equation gives the in-line force acting on a cylinder as a linear sum of the drag and inertia force components. The in-line force per unit length is expressed as (mathematical equation)(available in full paper) where the hydrodynamic coefficients CD & CM must be determined experimentally. Keulegan & carpenter2 were the pioneers in using the Morison equation to compute forces on submerged horizontal circular cylinders and flat plates placed in the node of a standing wave. They successfully correlated their experimentally determined CM & CD with a period parameter (herein referred as Keulegan-Carpenter KC number) defined as UmT/D. They did not find any significant dependence of these coefficients on Reynolds number. Later Sarpkaya3,4 using his well known Ushaped water oscillation tank generated a large amount of data giving inertia CM, drag CD and lift CL coefficients for circular cylinders. He found that these coefficients were dependent not only on Keulegan Carpenter number but on Reynolds number and roughness of the cylinders as well.

Direct bed shear stress measurements in bore-driven swash

Abstract. This paper is the last in a series of three investigating the friction laws and their parametrisation in idealised gravity currents in a rotating frame. Results on the dynamics of a gravity current (Wirth, 2009) and on the estimation of friction laws by data assimilation (Wirth and Verron, 2008) are combined to estimate the friction parameters and discriminate between friction laws in non-hydrostatic numerical simulations of gravity current dynamics, using data assimilation and a reduced gravity shallow water model. I demonstrate, that friction parameters and laws in gravity currents can be estimated using data assimilation. The results clearly show that friction follows a linear Rayleigh law for small Reynolds numbers and the estimated value agrees well with the analytical value obtained for non-accelerating Ekman layers. A significant and sudden departure towards a quadratic drag law at an Ekman layer based Reynolds number of around 800 is shown, in agreement with classical laboratory experiments. The drag coefficient obtained compares well to friction values over smooth surfaces. I show that data assimilation can be used to determine friction parameters and discriminate between friction laws and that it is a powerful tool in systematically connecting models within a model hierarchy.

Flow instability of nanofuilds in jet

ABSTRACTAbrasive erosion at bend is a common issue in gas–solid pneumatic system. Vortex chamber design is one of the specialized designs that offers promising prospect at reducing erosion. The performance of design is still relatively unknown in the literature. The aim of this work is to study the effect of basic erosion variables such as the flow Reynolds number, the particle Stokes number, and the vortex chamber size. The results show that the vortex chamber always reduces the erosion in comparison to the common radius bend, and it is more effective at higher Reynolds number. Increasing the chamber size reduces the erosion but the most significant reduction happens when the chamber size to the pipe diameter ratio is increased from 1 to 1.25. The chamber size influences the erosion differently at different Reynolds number. Trends describing these effects were obtained through trial-and-error approach. The particle Stokes number has nonunique effect on erosion. Increasing Stokes number through increasing Re increases the erosion while increasing Stokes number through decreasing Rep decreases the erosion.

Modern electronics demand more powerful cooling systems due to an increase in heat dissipation. The traditional cooling techniques reached their limit and the synthetic jet impingement arises as a promising method for cooling of modern electronic systems. This paper presents the experimental studies on the heat transfer characteristics of a synthetic jet. The synthetic jet is driven by a piston actuator. The effects of dimensionless parameters like the distance between the orifice and heater plate (Z/D), the ratio of stroke length to diameter of orifice ( L/D), Stokes number, and Reynolds number are discussed. The effect of orifice geometry, number of orifices are also presented. The results indicate that the Z/D and Stokes number have a significant influence on the heat transfer rate. As the Stokes number increases the heat transfer increases due to an increase in axial momentum and turbulence in the flow direction. For circular orifice and at high Z/D, the L/D ratio should be higher for better heat transfer. Rectangular orifice performs better than square and circular geometries. When compared to single jet multiple jets have a higher heat transfer rate. Maximum and minimum values of normalized pressure ( P nr ) are achieved for high Stokes number and smaller areas of the orifice.