Abstracts:In this article the Homann stagnation-point flow of a micropolar fluid over a spiraling disk is considered. A spiraling motion is produced due to uniform rotation and linear radial stretching of the disk. The coupled ordinary differential equations are obtained through the similarity reduction of the governing flow equations of micropolar fluid. A numerical technique known as the shooting method is implemented for obtaining the numerical results. Important features of the flow are investigated for various values of the spiral angle, spiraling parameter and material parameters.

Abstracts:Many studies have shown that low-density jets exhibit self-excited varicose oscillations. We use direct numerical simulation of the low Mach number Navier–Stokes equations to perform a linear global stability analysis of a helium jet at the threshold of onset of these oscillations. We calculate the direct and adjoint global modes and overlap these to obtain the structural sensitivity. We find that the structural sensitivity has high magnitudes in the shear layer downstream of the entrance plane, where the flow is absolutely unstable. We use the direct and adjoint global modes to calculate the effect of a control force on the growth rate and frequency of the unstable mode. We produce maps of the regions of the flow that are most sensitive to localized open loop steady forcing in the form of a body force and a heat source. We find that the most sensitive location for open loop steady forcing is the area around the shear layer, around 2 jet diameters downstream of the exit plane, and that the influence of steady forcing and heat injection is advected by the flow outside the jet. We use these maps to calculate the influence of a ring placed in the flow. When the ring is at the same temperature as the flow, it influences the flow through its drag. The ring has most influence when placed in the inner edge of the shear layer. When the ring is heated, it also influences the flow through the density reduction caused by heat input. In this case, the ring has most influence when placed in the outer edge of the shear layer. It is also influential when placed outside the jet because the expanded gas is advected towards the jet. In both these cases, the influence of the steady change to the base flow is significantly greater than the influence of an unsteady feedback force caused by the ring.

Abstracts:The present work proposes to investigate the impact of a turbulent round jet on a disk. The disk diameter is one order of magnitude larger than the jet diameter but small enough to avoid the formation of a circular hydraulic jump. The case of a smooth disk is first studied as the reference case. We then report results obtained with a disk engraved along its circumference by a number $N$ of radial grooves. The grooves are used to split the liquid sheet into multiple jets. According to the incoming flow rate $Q$ and to the geometry of the groove, the number of jets $n$ can be stable and corresponds to 2$N$ jets and $N$ jets, or variable, i.e. merged jets (mixed zone). Phase diagrams ($Q,n$) are deduced from measurements for different lengths of the groove. Finally, the obtained droplets are characterized in terms of diameters and velocities.

Abstracts:Nonlinear and viscous contributions in the equation of a vorticity evolution in three-dimensional flow are represented in the divergent form. The concept ”vorticity transfer tensor” which describes transference of the vorticity in a flow is introduced. The vortex flux for all the flow points and from the body surface are defined (the vortex flux from the body surface in general case is not the same as the boundary vorticity flux used in the literature). Exact expressions of force and moment via the vortex flux from the body surface for non stationary viscous incompressible flow under the no-slip boundary condition are derived directly from Navier–Stokes equations without applying the conservation law in the whole flow region. The expressions contain only surface integrals, and are valid for calculating force and moment for each body of the system in infinite or bounded space. They are most useful when meshless vortex methods are applied for the flow simulation. That is demonstrated in the numerical example of the flow around the sphere. The formulas obtained can also be useful for checking the accuracy of the computations which are performed in natural variables.

Abstracts:This paper extends the recent work by Weidman (2015) on the steady axisymmetric rotational stagnation-point flow impinging on a rotating disk to the case of a permeable stretching/shrinking rotating disk. Similarity variables are used to convert the Navier–Stokes equations to a pair of coupled ordinary differential equations governed by a dimensionless rotation rate $\alpha$, the velocity of the wall relative to the outer flow $\lambda$ and the wall transfer rate $S$. These equations are then solved numerically using the bvp4c function from MATLAB software. The skin friction coefficients or shear stress in both the radial and azimuthal directions are determined. It is found that, for given parameter values, up to three solutions can exist. Asymptotic expressions are derived for large stretching rates $\lambda$ and for strong fluid withdrawal and injection as well as for rapid rotation rates $\alpha$, these being compared with the numerically determined values.

Abstracts:A novel theoretical model for solving the cavities in axisymmetric supercavitating flow past a slender conical body in subsonic fluid has been established in the present paper based on the slender body theory. The fluid compressibility has been taken into consideration in the present model. The nonlinear integral differential equation is derived for solving subsonic supercavitating flow. The numerical discrete method and the iterative process to solve the equation are presented in this paper. The critical Mach number are obtained to describe the subsonic flow. The results of supercavity shapes and the hydrodynamic coefficients obtained by the present theoretical model are compared with the results of other literatures, which verifies the present model have theoretical accuracy and broad application. Finally we discuss the compressibility effects on cavity shape, surface pressure distribution and drag coefficient in the subsonic liquid flow.

Abstracts:The structure of planar shock wave propagating through a helium–argon mixture is modeledby the direct simulation Monte Carlo (DSMC) method based on ab initio potentials for a wide range of the Mach number and for various molar fractions. The use of ab initio potentials allows us to carry out the simulation without any adjustable parameter usually extracted from experimental data. As a result, the density, temperature, molar fraction, diffusion velocity, pressure tensor and heat flow profiles inside of the shock wave are calculated. The temperature overshoot phenomenon is discussed in details. The slopes of density are calculated with the numerical error less than 0.5 %. It is pointed out that the slopes for mixture are always smaller than those for a single gas.

Abstracts:The transient wave sloshing in the square-base tank horizontally shaken in a circular orbit is numerically studied. The liquid sloshing is simulated by the boundary element method (BEM) based on the fully-nonlinear potential-flow theory. The tank is firstly excited at the first odd natural sloshing frequency. Resonant swirling waves are observed travelling along the tank sides, when the even sloshing mode is aroused. Then, the tank is excited at half of the first even natural frequency. Techniques of the FFT filter and wavelet analysis are applied to distinct the wave components from the wave elevation histories, through which the occurrence of the secondary resonance is identified. During the secondary resonance, three typical wave motion patterns are observed, i.e. swirling waves, standing waves and double-peak travelling waves. Effects of the excitation amplitude and the liquid depth on the secondary resonance are investigated. Further, the secondary resonance by oscillating the tank at the difference of the first even and first odd natural frequency is studied. The first odd sloshing mode is found to contribute to the dominance of the even mode wave component during the secondary resonance.

Abstracts:The flow structure of perforated circular cylinders was thoroughly scrutinized by using the technique of high-image-density Particle Image Velocimetry (PIV). The perforated circular cylinder diameter ($D=100$ mm), was kept constant during the experimental investigation and corresponding Reynolds number was $Re=10000$ based on the cylinder diameter. Turbulent statistics e.g., planar turbulent kinetic energy, stream-wise Reynolds normal stress, transverse Reynolds normal stress and Reynolds shear stress were computed in the wake region in order to reveal the differences among various porosities in the range of $0.25\le \beta \le 0.80$. It would be noted that by increasing porosity, $\beta$ the flow fluctuations are substantially reduced in the wake region according to the PIV results. As a result, the prevention of Karman Vortex Street was accomplished by the use of perforated cylinders because of elongated and fragmented shear layers and reduced magnitudes of vortices.