Calm Fluid Research Articles

Fluid structure interaction analysis: vortex shedding induced vibrations

Fluid Structure Interaction (FSI) numerical modelling requires an efficient workflow to properly capture the physics involved. Computational Structural Mechanics (CSM) and Computation Fluid Dynamics (CFD) have to be coupled and at the moment there is a lack of monolithic solvers capable to tackle industrial applications that involves high fidelity models which mesh can be comprised of hundred millions of cells. This paper shows an efficient approach based on standard commercial tools. The FEM solver ANSYS® Mechanical™ is used to extract a given number of eigenmodes. Then the modal shapes are imported in the CFD solver Fluent® using the Add On RBF Morph™. Updating the modal coordinates it is possible to adapt the shape of the model by taking into account the elasticity of the CFD model. Transient analysis is faced using a time marching solution by updating the shape of the mesh at each time step (weak coupling, evaluated as single DOF systems and integrating modal forces over the CFD grid). Numerical performances and solution accuracy of this approach are analyzed on a practical application (NACA0009 Hydrofoil) for which experimental data are available. A comparison between proposed method and experiment is provided. Transient coupled solver is used for the computation of eigenvalues in water by post processing the free vibration response in calm fluid.

Numerical analysis of Sakiadis flow problem considering Maxwell nanofluid

This article investigates the flow of Maxwell nanofluid over a moving plate in a calm fluid. Novel aspects of Brownian motion and thermophoresis are taken into consideration. Revised model for passive control of nanoparticle volume fraction at the plate is used in this study. The formulated differential system is solved numerically by employing shooting approach together with fourth-fifth-order-Runge-Kutta integration procedure and Newton?s method. The solutions are greatly influenced with the variation of embedded parameters which include the local Deborah number, the Brownian motion parameter, the thermophoresis parameter, the Prandtl number, and the Schmidt number. We found that the variation in velocity distribution with an increase in local Deborah number is non-monotonic. Moreover, the reduced Nusselt number has a linear and direct relationship with the local Deborah number.

Numerical solution for Sakiadis flow of upper-convected Maxwell fluid using Cattaneo-Christov heat flux model

Present work studies the well-known Sakiadis flow of Maxwell fluid along a moving plate in a calm fluid by considering the Cattaneo-Christov heat flux model. This recently developed model has the tendency to describe the characteristics of relaxation time for heat flux. Some numerical local similarity solutions of the associated problem are computed by two approaches namely (i) the shooting method and (ii) the Keller-box method. The solution is dependent on some interesting parameters which include the viscoelastic fluid parameter β, the dimensionless thermal relaxation time γ and the Prandtl number Pr. Our simulations indicate that variation in the temperature distribution with an increase in local Deborah number γ is non-monotonic. The results for the Fourier’s heat conduction law can be obtained as special cases of the present study.

Harmonic oscillations of laminae in non-Newtonian fluids: A lattice Boltzmann-Immersed Boundary approach

In this paper, the fluid dynamics induced by a rigid lamina undergoing harmonic oscillations in a non-Newtonian calm fluid is investigated. The fluid is modelled through the lattice Boltzmann method and the flow is assumed to be nearly incompressible. An iterative viscosity-correction based procedure is proposed to properly account for the non-Newtonian fluid feature and its accuracy is evaluated. In order to handle the mutual interaction between the lamina and the encompassing fluid, the Immersed Boundary method is adopted. A numerical campaign is performed. In particular, the effect of the non-Newtonian feature is highlighted by investigating the fluid forces acting on a harmonically oscillating lamina for different values of the Reynolds number. The findings prove that the non-Newtonian feature can drastically influence the behaviour of the fluid and, as a consequence, the forces acting upon the lamina. Several considerations are carried out on the time history of the drag coefficient and the results are used to compute the added mass through the hydrodynamic function. Moreover, the computational cost involved in the numerical simulations is discussed. Finally, two applications concerning water resources are investigated: the flow through an obstructed channel and the particle sedimentation. Present findings highlight a strong coupling between the body shape, the Reynolds number, and the flow behaviour index.

Sakiadis flow with nonlinear Rosseland thermal radiation

In a recent paper by Cortell (2008 Chin. Phys. Lett.25 1340–2) the effect of radiation on the classical Sakiadis flow along a moving plate in a calm fluid was considered. The results in that paper have been produced using a linearized Rosseland approximation, which is valid only for small temperature differences between the plate and the ambient fluid. In the present work, we extend the above work to a nonlinear Rosseland approximation, which is valid for both small and large temperature differences.

FURTHER RESULTS ON HYDROMAGNETIC BOUNDARY-LAYER FLOW OF A NON-NEWTONIAN POWER-LAW FLUID OVER A CONTINUOUSLY MOVING SURFACE WITH SUCTION

The flow of a non-Newtonian, power-law conducting fluid under the effect of a constant transverse magnetic field is considered. The flow is produced by a plate moving with constant velocity in a calm fluid. The plate is porous and fluid can either be sucked or injected through it. The boundary layer equations are transformed into a nondimensional form and are solved with a finite difference method. Part of this problem has been investigated in the past but only for suction and pseudo-plastic fluids. However, all flows of the present work reach an asymptotic state and exact analytical solutions exist for Newtonian fluids. In the present work we extend the investigation to both pseudo-plastic Newtonian and dilatant fluids in both suction and injection cases.

Oscillating cylinder in viscous fluid: calculation of flow patterns and forces

Laminar and large-eddy-simulation (LES) calculations with the dynamic Smagorinsky model evaluate the flow and force on an oscillating cylinder of diameter D = 2R in otherwise calm fluid, for β = D 2/νT in the range 197–61400 and Keulegan–Carpenter number K = U m T/D in the range 0.5–8 (ν kinematic viscosity, T oscillation period, U m maximal velocity). Calculations resolving the streakline patterns of the Honji instability exemplify the local flow structures in the cylinder boundary layer (β ~ 197–300, K ~ 2) but show that the drag and inertia force are not affected by the instability. The present force calculations conform with the classical Stokes–Wang solution for all cases below flow separation corresponding to K < 2 (with β < 61400). The LES calculations of flow separation and vortical flow resolve the flow physics containing a large range of motion scales; it is shown that the energy in the temporal turbulent fluctuations (in fixed points) are resolved. Accurate calculation of the flow separation occurring for K > 2 has strong implication for the force on the cylinder. Present calculations of the force coefficients for K up to 4 and β = 11240 are in agreement with experiments by Otter (Appl Ocean Res 12:153–155, 1990). Drag coeffients when flow separation occurs are smaller than found in U-tube experiments. Inertia coefficients show strong decline for large K (up to 8) and moderate β = 1035 but is close to unity for K = 4 and β = 11240. The finest grid has 2.2 × 106 cells, finest radial Δr/R = 0.0002, number of points along the cylinder circumference of 180, Δz/R = 0.044 and a time step of 0.0005T.

Experiments on the spreading of shear-free turbulence under the influence of confinement and rotation

From Lie-group (symmetry) analysis of the multi-point correlation equation Oberlack and Gunther (Fluid Dyn Res 33:453-476, 2003) found three different solutions for the behavior of shear-free turbulence: (i) a diffusion like solution, in which turbulence diffuses freely into the adjacent calm fluid, (ii) a deceleration wave like solution when there is an upper bound for the integral length scale and (iii) a finite domain solution for the case when rotation is applied to the system. This paper deals with the experimental validation of the theory. We use an oscillating grid to generate turbulence in a water tank and Particle Image Velocimetry (PIV) to determine the two-dimensional velocity and out-of-plane vorticity components. The whole setup is placed on a rotating table. After the forcing is initiated, a turbulent layer develops which is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/non-turbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid. We measure the propagation of the TNTI and find quantitative agreement with the predicted spreading laws for case one and two. For case three (system rotation), we observe that there is a sharp transition between a 3D turbulent flow close to the source of energy and a more 2D-like wavy flow further away. We measure that the separation depth becomes constant and in this sense, we confirm the theoretical finite domain solution.

About the three-dimensional behavior of the flow within a forest under unstable conditions

This paper describes three-dimensional aspects of the spatial turbulent structure within the Solling spruce forest, in Lower Saxony, Germany, which have been inferred by arranging and composing time-height cross sections of instantaneous velocity vectors, interpreting their statistics: scales, correlations and spectra, evaluating the distribution of sweep and ejection events by way of quadrant analysis and identifying with wavelet analysis the scales and time occurrence of the main turbulent structures. By means of published experimental data and the present results, the following picture describing aspects of the three-dimensional velocity field between the ground and intermediate heights was constructed: at z/ H=0.5 we conceive a layer of pairs of time dependent streamwise vortices promoting important vertical and lateral flow. In the region between vortices upward and downward flows occur. The upward flow raises nearly calm fluid from below generating adjacent low-velocity regions between and above the vortices. The downward flow pulls downward fluid from above. A possible mechanism of intermittent penetration events of mixing layer fluid within the canopy is presented. Near the ground we infer the existence of large cells containing slow horizontal forward, backward and lateral oscillating fluid. The results contribute to a more complete description of the three-dimensional fluid-dynamic structures that characterize the wind in forests.

A numerical model for the mixing of an inclined submerged heated plane water jet in calm fluid

The basic objective of this paper is the presentation of a numerical model for the mixing of an inclined submerged heated plane water jet in calm fluid, which has some improvements over similar models presented by various other investigators. The basic features of our model are: the conservation of heat flux instead of conservation of the buoyancy flux, the inclusion of the turbulent heat flux integrated across the jet, and the modification to include entrainment coefficient depending on the local Richardson number. This model predicts with reasonable accuracy experimental results regarding the axial dilution and the trajectory.

Closure to “Behavior of Buoyant Jet in Calm Fluid”

Closure to “Behavior of Buoyant Jet in Calm Fluid”

Closure to “Behavior of Buoyant Jet in Calm Fluid”

Closure to “Behavior of Buoyant Jet in Calm Fluid”

Discussion of “Behavior of Buoyant Jet in Calm Fluid”

Discussion of “Behavior of Buoyant Jet in Calm Fluid”

Discussion of “Behavior of Buoyant Jet in Calm Fluid”

Discussion of “Behavior of Buoyant Jet in Calm Fluid”

Behavior of Buoyant Jet in Calm Fluid

This investigation studied turbulent mixing which occurs when sewage is discharged into the sea from a deeply submerged outlet. The investigation was carried out by discharing fresh water, from circular nozzles of 1/2-in. and 1-in. diam, into quiescent ambient fluid of greater density. The ambient fluid was salt solution of uniform density. The motion in the rising plume is similar to convection over a heated source when the nozzle densimetric Froude number is low. The density at points in the plume was determined by measuring the concentration of the solution using an electrical conductivity probe. It was found that the density distribution across the plume is almost Gaussian.

On a cycle of eighteen years in the mean annual height of the barometer in the climate of London; and on a constant variation of the barometrical mean, according to the moon’s declination

For obtaining the general results communicated in the present paper, the author has followed the same method as that he had adopted in the two former papers laid before the Society on the connexion of the barometrical variation with the lunar phases and apsides. Tables are given of the barometrical averages on successive solar years, from 1815 to 1832, so constructed as to exhibit the variation of the moon’s influence according to her declination; and also of these averages on successive cycles of nine solar years, classed according to the moon’s place in declination, on either side of the equator. The results deduced from these comparisons are, first, that the barometrical mean in this climate is depressed by the moon’s declination being to the south of the equator; and, secondly, that this depression takes place gradually, commencing with the moon’s being in full north declination, and proceeding through her remaining positions to the time when she crosses the equator to resume the northern declination; at which season, the whole pressure that had been withdrawn from the atmosphere is suddenly restored. The author thinks there is evidence of a great tidal wave, or swell in the atmosphere, caused by the moon’s attraction, preceding her in her approach to, and following her slowly as she recedes from these latitudes; so that were the atmosphere a calm fluid ocean of air, of uniform temperature, this tide would be manifested with as great regularity as those of the ocean of waters. But the currents uniformly kept up by the sun’s varying influence effectually prevent this from taking place, and involve the problem in complexity. He finds that there is also manifested in the lunar influence a gradation of effect, which operates through a cycle of eighteen years. The mean pressure of the atmosphere during the first part of this period increases; and then, after preserving for a year its maximum amount, again decreases through the remaining years of the cycle, but exhibits, towards its minimum, some fluctuations before it again regularly increases.