Fluid Mechanics

Abstract:  The three dimensional (3D) flight of a golf ball at taking into account the Magnus effect is studied in the paper. For this purpose it is composed a system of six nonlinear differential equations. To determine the 3D orientation of the ball the rotations around all three axes are given by the so-called Cardan angles instead of classical Euler ones. The high nonlinear system differential equations are solved numerically by a special program created in the MatLab-Simulink environment. It is founded the laws of motion, velocities and accelerations on all six coordinates, as well as the projections of trajectory on the three coordinate planes. The presented analytical base and numerical results in the paper increasing and expanding the knowledge in the theory of general motion of spherical solid and leads to new more extensive research in this complicated area.

—A submarine is a clandestine platform of watercraft for independent operation beneath water. In order to surpass under water she must obey some ground laws specially Archimedes principle with taking consideration of its flexible and economic structure and propulsion systems design. The main purpose of this research is to design and fabricate a prototype submarine to make experimentally available. The need for economic innovative design to ensure smart structure, propulsion, diving system and efficient power system has focused in the implemented prototype. The propulsion and power systems are provided by motor and battery. Depth rating comparison with other resplendent submarine makes the prototype unique in some cases. To submerge hydrostatically this research on designing basically implies Archimedes principle and buoyancy force, where negative buoyancy exerted either by increasing its own weight or decreasing its displacement of water.

The small-scale structure of grid turbulence is studied primarily using data obtained with a transverse vorticity (ω3) probe for values of the Taylor-microscale Reynolds number Rλ in the range 27–100. The measured spectra of the transverse vorticity component agree within ±10% with those calculated using the isotropic relation over nearly all wavenumbers. Scaling-range exponents of transverse velocity increments are appreciably smaller than exponents of longitudinal velocity increments. Only a small fraction of this difference can be attributed to the difference in intermittency between the locally averaged energy dissipation rate and enstrophy fluctuations. The anisotropy of turbulence structures in the scaling range, which reflects the small values of Rλ, is more likely to account for most of the difference. All four fourth-order rotational invariants Iα (α = 1 to 4) proposed by Siggia (1981) were evaluated. For any particular value of α, the magnitude of the ratio Iα / I1 is appr...

The entrainment experiments of Kato & Phillips (1969) and Kantha, Phillips & Azad (1977) (hereafter KP and KPA) are analysed to demonstrate a more general and effective scaling of the entrainment observations. The preferred scaling is \[ V^{-1} dh/dt = E(R_v), \] where h is the mixed-layer depth, V is the mean velocity of the mixed layer, Rv = B/V2 and B is the total mixed-layer buoyancy. This scaling effectively collapses entrainment data taken at various h/L, where L is the tank width, and in cases in which the interior is density stratified (KP) or homogeneous (KPA). The entrainment law E(Rv) is computed from the KP and KPA observations using the conservation equations for mean momentum and buoyancy. A side-wall drag term is included in the momentum conservation equation. In the range 0·5 < Rv < 1·0, which includes nearly all of the KP, KPA data, E ≃ 5 × 10−4R−4v. This is very similar to the entrainment law followed by a surface half-jet (Ellison & Turner 1959) and by the w...

Analytical expressions correlating the volumetric flow rate to the inlet and outlet pressures are derived for the time-independent flow of Newtonian fluids in cylindrically-shaped elastic tubes using a one-dimensional Navier-Stokes flow model with two pressure-area constitutive relations. These expressions for elastic tubes are the equivalent of Poiseuille and Poiseuille-type expressions for rigid tubes which were previously derived for the flow of Newtonian and non-Newtonian fluids under various flow conditions. Formulae and procedures for identifying the pressure field and tube geometric profile are also presented. The results are validated by a finite element method implementation. Sensible trends in the analytical and numerical results are observed and documented.

A conceptual framework for analysing the energetics of density-stratified Boussinesq fluid flows is discussed. The concept of gravitational available potential energy is used to formulate an energy budget in which the evolution of the background potential energy, i.e. the minimum potential energy attainable through adiabatic motions, can be explicitly examined. For closed systems, the background potential energy can change only due to diabatic processes. The rate of change of background potential energy is proportional to the molecular diffusivity. Changes in the background potential energy provide a direct measure of the potential energy changes due to irreversible diapycnal mixing. For open systems, background potential energy can also change due to boundary fluxes, which can be explicitly measured. The analysis is particularly appropriate for evaluation of diabatic mixing rates in numerical simulations of turbulent flows. The energetics of a shear driven mixing layer is used to i...

The dynamics of the air cavity created by vertical water entry of a three-dimensional body is investigated theoretically, computationally and experimentally. The study is focused in the range of relatively low Froude numbers, Fr ≡ V(gD)−1/2 ≤ O(10) (where V is the dropping velocity of the body, D its characteristic dimension and g the gravitational acceleration), when the inertia and gravity effects are comparable. To understand the physical processes involved in the evolution of cavity, we conduct laboratory experiments of water entry of freely dropping spheres. A matched asymptotic theory for the description of the cavity dynamics is developed based on the slender-body theory in the context of potential flow. Direct comparisons with experimental data show that the asymptotic theory properly captures the key physical effects involved in the development of the cavity, and in particular gives a reasonable prediction of the maximum size of the cavity and the time of cavity closure. Du...

The stability of an immiscible layer of fluid bounded by two other fluids of different viscosities and migrating through a porous medium is analysed, both theoretically and experimentally. Linear stability analyses for both one-dimensional and radial flows are presented, with particular emphasis upon the behaviour when one of the interfaces is highly stable and the other is unstable. For one-dimensional motion, it is found that owing to the unstable interface, the intermediate layer of fluid eventually breaks up into drops.However, in the case of radial flow, both surface tension and the continuous thinning of the intermediate layer as it moves outward may stabilize the system. We investigate both of these stabilization mechanisms and quantify their effects in the relevant parameter space. When the outer interface is strongly unstable, there is a window of instability for an intermediate range of radial positions of the annulus. In this region, as the basic state evolves to larger r...

The multiscale dynamics of a shock–droplet interaction is crucial in understanding the atomisation of droplets due to external airflow. The interaction phenomena are classified into wave dynamics (stage I) and droplet breakup dynamics (stage II). Stage I involves the formation of different wave structures after an incident shock impacts the droplet surface. These waves momentarily change the droplet's ambient conditions, while in later times they are mainly influenced by shock-induced airflow. Stage II involves induced airflow interaction with the droplet that leads to its deformation and breakup. Primarily, two modes of droplet breakup, i.e. shear-induced entrainment and Rayleigh–Taylor piercing (RTP) (based on the modes of surface instabilities) were observed for the studied range of Weber numbers $(We\sim 30\text{--}15\,000)$ . A criterion for the transition between two breakup modes is obtained, which successfully explains the observation of RTP mode of droplet breakup at hi...

The stability of the oscillatory Stokes layers is examined using two quasi-static linear theories and an integration of the full time-dependent linearized disturbance equations. The full theory predicts absolute stability within the investigated range and perhaps for all the Reynolds numbers. A given wavenumber disturbance of a Stokes layer is found to be more stable than that of the motionless state (zero Reynolds number). The quasi-static theories predict strong inflexional instabilities. The failure of the quasi-static theories is discussed.

The objective of this study is the development of an efficient high-order compact scheme for unsteady incompressible viscous flows. The scheme is constructed on a staggered Cartesian grid system in order to avoid spurious oscillations in the pressure field. Navier-Stokes equations are advanced in time with the second order Adams-Bashford method without considering the pressure terms in the predictor step, the velocity field is then corrected such that discrete mass continuity equations satisfied through pressure Poisson equation. Since the efficiency of the fractional step method depends on the Poisson solver, a V-cycle multigrid acceleration with compact Mehrstellen discretization based iterative method is implemented in the pressure Poisson equation to enhance the computational efficiency. The efficiency and accuracy of iterative Poisson solvers (pseudo-time, Jacobi, Gauss-Seidel) are also tested within the multigrid framework. The method is then validated by the simulations of the Taylor-Green vortex decaying problem. Results show that the fractional-step compact scheme with multigrid acceleration has high resolving efficiency that drastically reduces computational time and high-order accuracy making the method applicable for simulation of incompressible viscous flows.

Coherent structures of turbulent open-channel flow in the wall region of a channel bed were examined quantitatively using experimental data obtained by flow visualization. Successive pictures of flow patterns in two horizontal cross-sections at different levels near the channel bed were taken, and then were digitized and analysed by a computer.This method of flow visualization and picture processing enabled us to calculate the distributions of the three components of the velocity vectors. The distributions of velocities, streamlines, two-dimensional divergence and three components of vorticity could be calculated and are displayed as graphical output. In our numerical analyses, the idea of a two-dimensional correlation coefficient is introduced, through which the degree of similarity of turbulence structures can be better estimated than with the usual one-dimensional coefficient. Use of the data was based on the premise that the essential element in a turbulence structure is vortex ...

This is a study of the interactions of solitary waves climbing up a circular island. A series of large-scale laboratory experiments with waves of different incident height-to-depth ratios and different crest lengths is described. Detailed two-dimensional run-up height measurements and time histories of surface elevations around the island are presented. A numerical model based on the two-dimensional shallow-water wave equations including runup calculations was developed. Numerical model predictions agreed very well with the laboratory data and the model was used to study wave trapping and the effect of slope. Under certain conditions, enhanced runup and wave trapping on the lee side of the island were observed, suggesting a possible explanation for the devastation reported by field surveys in Babi Island off Flores, Indonesia, and in Okushiri Island, Japan.

The study of sink flow turbulent boundary layers is of particular relevance to the problem of laminarization. The reason lies in the fact that the acceleration parameter which principally determines when a turbulent boundary layer will begin to revert towards laminar is, in these flows, constant from station to station. The paper presents theoretical solutions to this class of boundary layer by making use of the Prandtl mixing-length formula to relate the turbulent shear stress to the mean velocity gradient. Near the wall the Van Driest recommendation for mixing length is adopted and the Van Driest function, A+, is chosen such that the skin friction coefficient does not exceed a certain maximum value.The predicted solutions, which are in good agreement with available experimental data, display a plausible shift from the turbulent towards the laminar solution as the acceleration parameter is increased.

The bed entrainment rate in a gravity mass flow (GMF) is uniquely determined by the properties of the bed and the flow. In depth-averaging, however, critical information on the flow variables near the bed is lost and empirical assumptions usually are made instead. We study the interplay between bed and flow assuming a perfectly brittle bed, characterized by its shear strength ${\it\tau}_{c}$, and erosion along the bottom surface of the flow; frontal entrainment is neglected here. The brittleness assumption implies that the shear stress at the bed surface cannot exceed ${\it\tau}_{c}$. For quasi-stationary flows in a simplified setting, analytic solutions are found for Bingham and frictional–collisional (FC) fluids. Extending this theory to non-stationary flows requires some assumptions for the velocity profile. For the Bingham fluid, the profile of a ‘proxy’ quasi-stationary eroding flow is used; the rheological parameters are chosen to match the instantaneous velocity and shear-lay...

Magnus effect is a phenomenon where pressure difference is created according to Bernoulli's effect due to induced velocity changes caused by a rotating object in a fluid. Using this concept, the idea of delaying boundary layer separation on airfoil by providing moving surface boundary layer control has been developed. In order to analyze the influence of Magnus effect on the aerodynamic performance of an airfoil, there is no alternative of developing an experimental setup. This paper aims to develop such an experimental setup which will be capable of analyzing the influence of Magnus effect on both symmetric and asymmetric airfoils by placing a cylinder at the leading edge. To provide arrangements for a rotating cylinder at the leading edge of airfoil, necessary modifications and additions have been done in the test section of an AF100 subsonic wind tunnel.

En este trabajo se presenta el análisis llevado a cabo para determinar la potencia requerida por el corazón para enviar sangre a través de la aorta. El análisis se llevo a cabo desarrollando un modelo análogo al sistema circulatorio mediante tuberías y accesorios.
Debido a la amplitud y complejidad del sistema circulatorio el análisis llevado a cabo en este trabajo se limita a la aorta, y a las ramificaciones de los miembros superiores, (subclavial izquierda y derecha, axilar izquierda y derecha, braquial izquierda y derecha) que se consideran para efectos prácticos solo como extracciones de flujo .

Real-time holographic interferometry and shadowgraph visualization are used to study convection in the fluid between two concentric spheres when two distinct buoyancy forces are applied to the fluid. The heated inner sphere has a constant temperature that is greater than the constant temperature of the outer sphere by ΔT. In addition to the usual gravitational buoyancy from temperature induced density differences, another radial buoyancy is imposed by applying an a.c. voltage difference, ΔV between the inner and outer spheres. The resulting electric field gradient in this spherical capacitor produces a central polarization force. The temperature dependence of the dielectric constant results in the second buoyancy force that is especially large near the inner sphere. The normal buoyancy is always present and, within the parameter range explored in our experiment, always results in a large-scale cell that is axisymmetric about the vertical. We have found that this flow becomes unstabl...

In the Higgs mechanism, mediators of the weak force acquire masses by interacting with the Higgs condensate, leading to a vector boson mass matrix. On the other hand, a rigid body accelerated through an inviscid, incompressible and irrotational fluid feels an opposing force linearly related to its acceleration, via an added-mass tensor. We uncover a striking physical analogy between the two effects and propose a dictionary relating them. The correspondence turns the gauge Lie algebra into the space of directions in which the body can move, encodes the pattern of gauge symmetry breaking in the shape of an associated body and relates symmetries of the body to those of the scalar vacuum manifold. The new viewpoint is illustrated with numerous examples, and raises interesting questions, notably on the fluid analogues of the broken symmetry and Higgs particle, and the field-theoretic analogue of the added mass of a composite body.