E. J. Avital

Direct numerical simulation of sediment entrainment in turbulent channel flow

In this paper, the entrainment and movement of coarse particles on the bed of an open channel is numerically investigated. Rather than model the sediment transport using a concentration concept, this study treats the sediment as individual particles and investigates the interaction between turbulent coherent structures and particle entrainment. The applied methodology is a combination of the direct numerical simulation of turbulent flow, the combined finite-discrete element modeling of particle motion and collision, and the immersed boundary method for the fluid-solid interaction. In this study, flow over a water-worked rough-bed consisting of 2-3 layers of densely packed spheres is adopted and the Shields function is 0.065 which is just above the entrainment threshold to give a bed-load regime. Numerical results for turbulent flow, sediment entrainment statistics, hydrodynamic forces acting on the particles, and the interaction between turbulence coherent structures and particle entrainment are presented...

Large scale simulation of red blood cell aggregation in shear flows

Aggregation of highly deformable red blood cells (RBCs) significantly affects the blood flow in the human circulatory system. To investigate the effect of deformation and aggregation of RBCs in blood flow, a mathematical model has been established by coupling the interaction between the fluid and the deformable solids. The model includes a three-dimensional finite volume method solver for incompressible viscous flows, the combined finite-discrete element method for computing the deformation of the RBCs, a JKR model-Johnson, Kendall and Roberts (1964-1971) (Johnson et al., 1971) to take account of the adhesion forces between different RBCs and an iterative direct-forcing immersed boundary method to couple the fluid-solid interactions. The flow of 49,512 RBCs at 45% concentration under the influence of aggregating forces was examined, improving the existing knowledge on simulating flow and structural characteristics of blood at a large scale: previous studies on the particular issue were restricted to simulating the flow of 13,000 aggregative ellipsoidal particles at a 10% concentration. The results are in excellent agreement with experimental studies. More specifically, both the experimental and the simulation results show uniform RBC distributions under high shear rates (60-100/s) whereas large aggregation structures were observed under a lower shear rate of 10/s. The statistical analysis of the simulation data also shows that the shear rate has significant influence on both the flow velocity profiles and the frequency distribution of the RBC orientation angles.

Large Eddy Simulation of Flow Past Free Surface Piercing Circular Cylinders

Flows past a free surface piercing cylinder are studied numerically by large eddy simulation at Froude numbers up to FrD=3.0 and Reynolds numbers up to ReD=1×105. A two-phase volume of fluid technique is employed to simulate the air-water flow and a flux corrected transport algorithm for transport of the interface. The effect of the free surface on the vortex structure in the near wake is investigated in detail together with the loadings on the cylinder at various Reynolds and Froude numbers. The computational results show that the free surface inhibits the vortex generation in the near wake, and as a result, reduces the vorticity and vortex shedding. At higher Froude numbers, this effect is stronger and vortex structures exhibit a 3D feature. However, the free surface effect is attenuated as Reynolds number increases. The time-averaged drag force on the unit height of a cylinder is shown to vary along the cylinder and the variation depends largely on Froude number. For flows at ReD=2.7×104, a negative pressure zone is developed in both the air and water regions near the free surface leading to a significant increase of drag force on the cylinder in the vicinity of the free surface at about FrD=2.0. The mean value of the overall drag force on the cylinder increases with Reynolds number and decreases with Froude number but the reduction is very small for FrD=1.6–2.0. The dominant Strouhal number of the lift oscillation decreases with Reynolds number but increases with Froude number.

On three-dimensionality and control of incompressible cavity flow

The incompressible large eddy simulation technique, coupled with the Lighthill-Curle acoustic analogy, is used to investigate the oscillation mechanism and sound source of a two-dimensional cavity with a length-to-depth ratio of L∕D=4 and Reynolds number of ReD=5000. It is demonstrated that the development of the three-dimensional flow field, initiated by the introduction of a random inflow disturbance, is eventually accompanied by transition from the wake to the shear layer oscillation mode, regardless of the amplitude and shape of the inflow disturbance. Once the transition to the shear layer mode is accomplished, the amplitude and frequency of oscillations are not very sensitive to the particular shape of the inflow disturbance. The effectiveness of controlling the flow oscillations by applying simultaneous steady injection and suction through the front and rear cavity walls, respectively, is demonstrated. The results show that, for injection levels exceeding a certain threshold value, the oscillations...

Sound Generation by Vortex Pairing in Subsonic Axisymmetric Jets

Direct numerical simulation (DNS) and an acoustic analogy are used to investigate the sound generation by vortex pairing in idealized subsonic axisymmetric jets. The detailed sound source structure is provided by the DNS. The acoustic analogy is based on solving the nonlinearized Lilleys third-order wave equation in the time-space domain. A numerical algorithm for solving Lilleys equation is developed, in which the sound field is simulated simultaneously with the source field calculation. The computational domain includes both the near field and a portion of the acoustic far field. Effects of a coaxial secondary jet stream and the jet-to-ambient temperature ratio on the sound generation from an axisymmetric jet are investigated. It is shown that the sound source has a long axial distribution in the streamwise direction with the strongest source located near the end of the jet potential core where vortex pairing/merging occurs, and the radiated sound field is highly directive. It is also found that the secondary jet stream reduces the sound source size; therefore, the sound radiation from the coaxial jets is lower than that from the single jet. The hot jet simulation shows that increasing the jet-to-ambient temperature ratio leads to a smaller and weaker sound source, but does not lead to a weaker sound field. For the sound field a reasonable agreement is observed between the predictions from the axisymmetric Lilleys equation and the DNS results.

Calculation of Basic Sound Radiation of Axisymmetric Jets by Direct Numerical Simulations

The basic radiation of sound from forced laminar axisymmetric jets (Re D = 6 × 10 2 to 1.5 × 10 3 ) is calculated by a hybrid approach, whereby the hydrodynamic field is calculated by an incompressible stream function-vorticity direct numerical simulation (DNS) and the sound field is calculated by the compact Lighthill and Mohring-Kambe formulations. It is shown that, because of the oscillatory behavior of the source as a wave packet, the acoustic results are more sensitive to numerical constraints such as the DNS hox size than are the hydrodynamic results. Lighthills formulation shows a strong sensitivity to the radial boundary condition imposed on the velocity in the DNS. A zero second-order radial derivative for the stream function behaves the best, and a zero radial velocity condition behaves the worst. The Mohring-Kambe formulation shows a strong dependence on the arbitrary location of the coordinate origin. A boundary correction developed to eliminate this dependence is shown to work well by achieving a good agreement between the two formulations in the dominant features of the sound radiation. The effects of the inflow momentum thickness and Reynolds numher are investigated with reference to the directivity and frequency spectrum of the emitted sound.

Stretched Cartesian grids for solution of the incompressible Navier-Stokes equations

Two Cartesian grid stretching functions are investigated for solving the unsteady incompressible Navier-Stokes equations using the pressure-velocity formulation. The first function is developed for the Fourier method and is a generalization of earlier work. This function concentrates more points at the centre of the computational box while allowing the box to remain finite. The second stretching function is for the second-order central finite difference scheme, which uses a staggered grid in the computational domain. This function is derived to allow a direct discretization of the Laplacian operator in the pressure equation while preserving the consistent behaviour exhibited by the uniform grid scheme. Both functions are analysed for their effects on the matrix of the discretized pressure equation. It is shown that while the second function does not spoil the matrix diagonal dominance, the first one can. Limits to stretching of the first method are derived for the cases of mappings in one and two directions. A limit is also derived for the second function in order to prevent a strong distortion of a sine wave. The performances of the two types of stretching are examined in simulations of periodic co-flowing jets and a time developing boundary layer.

Asymmetric instability of a viscid capillary jet in an inviscid media

The instability of asymmetric disturbances in a full circular viscid jet is investigated. It is found that asymmetric disturbances can be dominant for moderate modes and intermediate axial wave numbers for a low Weber number (≊10−5). But no asymmetric disturbance with maximum wave growth higher than the axisymmetric one was found.

NONLINEAR PROPAGATION OF SOUND EMITTED BY HIGH SPEED WAVE PACKETS

Jets sound-field emitted by a large scale source modeled as a wave packet is considered. Attention is given to nonlinear propagation effects caused by the sources supersonic Mach number and high amplitude. The approach of the Westervelt equation is adapted to derive a new set of weakly nonlinear sound propagation equations. An optimized Lax–Wendorff scheme is proposed for the newly derived equations. It is shown that these equations can be simulated using a time step close to the CFL limit even for high amplitudes unlike the conventional finite-difference simulation approach of the Westervelt equation. Two- and three-dimensional sound propagations were simulated for symmetric and asymmetric supersonic wave packets. It is seen that nonlinearity in the sound field is affected by the wave packet form, an effect that cannot be captured by a 1D propagation equation. High skewness in the pressure fluctuation and its time derivative were found near the Mach direction, showing crackle-like features. Pressure time history and frequency spectra are also investigated.

Computational aeroacoustics : The low speed jet

Low speed circular, elliptic and planar jets are investigated computationally for basic sound generation and hydrodynamics. The jets are assumed to be incompressible and are simulated using the large eddy simulation (LES) approach. The emitted sound is calculated using Lighthills acoustic analogy. Two formulations are used, Lighthills stress tensor formulation and Powells vortex sound formulation. A new boundary correction for Powells formulation is developed in order to account for the finite size of the computational domain. Low to moderate Reynolds number jets are simulated. Good agreement with known hydrodynamic results is achieved. This includes the nature of the transition process, e.g. enhanced mixing and axis switching in the elliptic jet and in some statistical results. The new boundary correction for Powells formulation proves to be vital in order to achieve good agreement with Lighthills formulation. Some success in high frequency prediction at least for the circular and elliptic jets is achieved in terms of getting the expected asymptotic behaviour. Both formulations show that the elliptic jet noise level is mildly lower than the circular jet noise level. Good to very good agreement is achieved in terms of directivities and frequency spectra with known results for the various jets.