European Journal of Mechanics B-fluids最新文献

Linear stability analysis of the steady flow past elliptic cylinders of different aspect ratio ($Ar$) has been conducted for the flow Reynolds number ($Re$) in the range 30–200. A new unstable mode, which we refer as tertiary wake mode, has been discovered. Two other unstable modes (the primary wake mode and the secondary wake mode), already reported in the literature, are also found. The critical $Re$ for the onset of instability of these modes and the corresponding Strouhal number ($St$) have been reported. Modes that have large growth rates tend to come close to the cylinder surface, and the extent to which they spread downstream in the wake is less compared to the weaker modes. The size of the vortical structures in a mode is inversely related to its $St$. The change in the characteristics of these modes with respect to change in $Ar$ and $Re$, as well as their evolution leading to the fully developed flow, has been studied. Selective suppression of the unstable modes is effected using a slip-plate placed on the wake centerline. For $Re$ = 150, it is shown that selective suppression of the unstable modes leads to different fully developed unsteady flows.

Exact radial-coordinate dependent Beltrami coefficients for unsteady axially symmetric viscous Beltrami vortices under external forces are sought in cylindrical coordinate system. Two types of solutions are presented. One breaks the scaling invariance and decays temporally exponentially. The other one keeps the scaling invariance and asymptotically exhibits a power-law decay. As a byproduct, the exact generalized Beltrami vortex solutions are found and are shown to have lower energy densities.

Using the Kazhikhov–Smagulov model, the linear stability of incompressible mixing layers and jets entailing large density variation is addressed analytically. The classical theorems of Squire, Rayleigh and Fjørtoft are extended to variable-density flows. It is shown that the bidimensional configuration is still the most unstable one, but the inflexion point is no longer a necessary condition for instability. Instead, a non trivial condition involving density and velocity gradient is identified. Dispersion relations are obtained for small wavenumbers as well as for piecewise linear base flow profiles. Additionally, an estimation of the threshold wavenumber that stabilises the flow is obtained. It is demonstrated that density variations modify the growth rate of the instability as well as the wavelength associated with the most unstable mode and the unstable wavenumber range. These results are in good agreement with numerical computations. Finally, it is observed that viscous effects are purely stabilising while molecular diffusion does not affect the stability.

The Rayleigh-Taylor instability (RTI) between a heavier Newtonian liquid and a lighter thixotropic liquid is studied in this paper by weakly compressible smoothed particles (WC-SPH). It is assumed that the thixotropic liquid obeys the Moore rheological model. First, the developed code is verified against available Newtonian RTI cases. Then, it is applied to thixotropic RTI cases to investigate the effects of the different non-dimensional parameters, including the thixotropic number (destruction-to-rebuild ratio), Reynolds number, Bond number, and Deborah number. It is shown that Bo is the most paramount non-dimensional parameter (i.e., it determines whether the two-phase boundary is stable or unstable), while Re, De, and thixotropic numbers have secondary influences on RTI. Based on the obtained results, the behavior of the thixotropic case is similar to the Newtonian high viscous counterpart at initial times; however, it is different at long times. It is demonstrated that the value of the thixotropic number determines when the transition between the short-time and long-time phenomena occurs.

In a remarkable paper, Cox and Mortell (1986) (A.A. Cox, M.P. Mortell 1986. J. Fluid Mech. 162, pp. 99-116) showed that for an oscillating water tank, the evolution of small-amplitude, long-wavelength, resonantly forced waves follow a forced Korteweg–de Vries (fKdV) equation. The solutions of this model agree well with experimental results by Chester and Bones (1968) (W. Chester and J.A. Bones 1968. Proc. Roy. Soc. A, 306, 23 (Part II)). We compare the fKdV solutions with a number of channel flows with different geometry that have been studied experimentally and numerically. When sweeping the selected wide parameter range, extreme cases of the fKdV equation are covered: single soliton solutions as well as multiple solitons with a rather short wavelength challenging the long-wave fKdV assumption. The transition of solutions with a different number of solitons is rather abrupt and we show that the parameter values for transitions from single soliton towards multi-soliton solutions can be predicted and follow a simple exponential relation. In particular, we compare the fKdV model with solutions from a fully nonlinear Navier–Stokes model. We further consider a case for which the 2D assumption of the fKdV equation is strictly speaking violated.

We propose an approximation for the functional form of the slip length for two complementary lattice configurations of superhydrophobic texture. The first configuration consists of the square lattice of the superhydrophobic spots employed on the no-slip plane. The second configuration is an ‘inverse’ of the first one and consists of the same lattice but of the no-slip spots on the superhydrophobic base. We validate our analytical results by a numerical solution of Stokes equation.

This paper explores local absolute instability in the boundary layer flow over two distinct families of rotating spheroids (prolate and oblate). While convective instability was established in earlier work by Samad and Garrett [1], this study delves into the potential occurrence of local absolute instability. Some results of local convective instability under the assumption of stationary vortices are reproduced for a more comprehensive investigation. The analysis considers viscous and streamline curvature effects, demonstrating that the localized mean flow within the boundary layer over either family of the rotating spheroid is absolutely unstable for each fixed value of the eccentricity parameter $e\in [0,0.8]$. For certain combinations of Reynolds number $Re$ and azimuthal wave number $\beta$, a third branch (Branch 3) of the dispersion relation intersects Branch 1 at a pinch point, indicating absolute instability. Neutral curves depict regions that are absolutely unstable, while below critical Reynolds numbers, the region is either convectively unstable or stable. The paper also illustrates the effect of increasing eccentricity on spatial branches within both convectively and absolutely unstable regions. From lower to moderate latitudes, the stabilizing effect of $e$ on the onset of absolute instability is robust for the prolate family and almost negligible for the oblate family. At high latitudes of the prolate spheroid, the stabilizing effect of $e$ is fainter but persists until close to the equator. Conversely, at high latitudes of the oblate spheroid, the stabilizing effect of $e$ is more pronounced. The paper discusses the implications of the parallel flow assumption employed in the analyses.

Inhomogeneities in the wave field due to wave groups, currents, and shoaling among other ocean processes can affect the mean water level. In this work, the classical and unsolved problem of continuously computing the set-down and the following set-up induced by wave breaking on a shoal of constant finite slope is tackled. This is possible by using available theoretical knowledge on how to approximate the distribution of wave random phases in finite depth. Then, the non-homogeneous spectral analysis of the wave field allows the computation of the ensemble average by means of the phase distribution and the inversion of the integral of the second moment for the special case of a shoaling process with uniform phase distribution. In doing so, I am able to obtain a direct effect of the slope magnitude on the phases distribution. Therefore, an analytical and slope-dependent mean water level with continuity over the entire range of water depth is provided.

It is challenging to apply numerical simulations to accurately predict the stall behavior of aircraft equipped with high-lift devices. Simulations with Reynolds-Averaged NavierStokes (RANS) models suffer from lack of the reliability at high angles of attack with separated and reattached boundary layers, whereas wall-resolved Large Eddy Simulations (LES) of wall-bounded flows at high Reynolds numbers currently costs too much computational resources. A new unified hybrid turbulence modeling approach, denoted the Self-Adaptive Turbulence Eddy Simulation (SATES), is proposed and applied for complex turbulent flows combining with high-order numerical scheme of the Weighted Compact Nonlinear Scheme (WCNS) in the present study. It enables a seamless evolution from unsteady RANS to LES and finally approaches Direct Numerical Simulation (DNS) depending on the turbulent scales. In the framework of SATES, a new SATES-σ model with an adaptive model coefficient is developed by extending the underlying LES mode based on an enhanced sub-grid-scale model of the σ-model. The new SATES-σ is first examined in two benchmark cases of channel flow and flow past a square cylinder. Then, it is validated in supercritical flow past a circular cylinder to assess the performance of turbulent models. The results show significant improvements over the previous SATES and IDDES in the predictions of boundary layer flow. Finally, successful application is achieved in the accurate prediction of the stall of the MD-30P30N airfoil at a Reynolds number of 9×10⁶ with wide angles of attack. The simulation results show good agreement with experimental results for surface pressure even for the challenging cases of 21 and 23 deg angles of attack. Again, the SATES-σ shows better results than the previous SATES and IDDES. The presented method has considerable potential for the challenging stall predictions.