Dynamics of Hyperbolically Symmetric Fluids

We study the general properties of dissipative fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. It is shown that the energy density is necessarily negative, and the central region cannot be attained by any fluid element. We describe this inner region by a vacuum cavity around the center. By assuming a causal transport equation some interesting thermodynamical properties of these fluids are found. Several exact analytical solutions, which evolve in the quasi–homologous regime and satisfy the vanishing complexity factor condition, are exhibited.

Testing the effect of resolution on gravitational fragmentation with Lagrangian hydrodynamic schemes

To study the resolution required for simulating gravitational fragmentation with newly developed Lagrangian hydrodynamic schemes, Meshless Finite Volume method (MFV) and Meshless Finite Mass method (MFM), we have performed a number of simulations of the Jeans test and compared the results with both the expected analytic solution and results from the more standard Lagrangian approach: Smoothed Particle Hydrodynamics (SPH). We find that the different schemes converge to the analytic solution when the diameter of a fluid element is smaller than a quarter of the Jeans wavelength, λJ. Among the three schemes, SPH/MFV shows the fastest/slowest convergence to the analytic solution. Unlike the well-known behaviour of Eulerian schemes, none of the Lagrangian schemes investigated displays artificial fragmentation when the perturbation wavelength, λ, is shorter than λJ, even at low numerical resolution. For larger wavelengths (λ > λJ) the growth of the perturbation is delayed when it is not well resolved. Furthermore, with poor resolution, the fragmentation seen with the MFV scheme proceeds very differently compared to the converged solution. All these results suggest that, when unresolved, the ratio of the magnitude of hydrodynamic force to that of self-gravity at the sub-resolution scale is the largest/smallest in MFV/SPH, the reasons for which we discussed in detail. These tests are repeated to investigate the effect of kernels of higher-order than the fiducial cubic spline. Our results indicate that the standard deviation of the kernel is a more appropriate definition of the ‘size’ of a fluid element than its compact support radius.

Flow Classification and Its Application to Fluid Processing

Mathematically, the problem of flow field classification can be analyzed by the eigenanalysis of the deformation-rate tensor; however, such analysis technique have not been commonly applied in fluid processing. We derive a simplified objective flow classification scheme based on the invariants of the strain-rate tensor and the vorticity tensor. Multiaxiality of flow, which is related to the type of elongation, and converging/bifurcating flow, is characterized by the strain-rate tensor, while rotation contribution that protects fluid element from stretching is characterized by the relative intensity of an objective vorticity to the strain-rate. The spatial distributions of flow classification quantities offer an essential tool in understanding the flow pattern structure, and therefore can be useful to get insights into the connection between the geometry and the process performance.

Stokes drift in coral reefs with depth-varying permeability

In his famous paper of 1847 (Stokes GG. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8 , 441–455), Stokes introduced the drift effect of particles in a fluid that is undergoing wave motion. This effect, now known as Stokes drift, is the result of differences between the Lagrangian and Eulerian velocities of the fluid element and has been well-studied, both in the laboratory and as a mechanism of mass transport in the oceans. On a smaller scale, it is of vital importance to the hydrodynamics of coral reefs to understand drift effects arising from waves on the ocean surface, transporting nutrients and oxygen to the complex ecosystems within. A new model is proposed for a class of coral reefs in shallow seas, which have a permeable layer of depth-varying permeability. We then note that the behaviour of the waves above the reef is only affected by the permeability at the top of the porous layer, and not its properties within, which only affect flow inside the porous layer. This model is then used to describe two situations found in coral reefs; namely, algal layers overlying the reef itself and reef layers whose permeability decreases with depth. This article is part of the theme issue ‘Stokes at 200 (part 2)’.

Modeling and Verification of a RANCF Fluid Element Based on Cubic Rational Bezier Volume

This investigation is focused on developing a novel three-dimensional rational absolute nodal coordinate formulation (RANCF) fluid element based on cubic rational Bezier volume. The new fluid element can describe liquid columns with initially curved configurations precisely, performing better than the conventional absolute nodal coordinate formulation (ANCF) fluid element. A new kinematic description, which employs a different interpolation function to describe the displacement field, makes this element a true difference. The shape function is no longer calculated by an incomplete polynomial or nonrational B-spline function, replaced by the rational Bezier function. Dynamical model or governing equation of the RANCF fluid element is built based on the constitutive equation of fluid, momentum, and constraint equation. One liquid column with initially cylindrical configuration is established by the RANCF fluid element, the position vector of control points and their weights are calculated to achieve the specific initial configuration. A simulation of the cylindrical liquid column collapsing on a plane is implemented to verify the validity of the RANCF fluid element, and numerical results are in good agreement with those obtained in the literature. The convergence of the RANCF fluid element is also checked and proved not to be influenced by mesh size. Finally, the precise description ability of the RANCF fluid element is compared with that of the conventional ANCF fluid element, the former shows a great advantage.

Two Way Coupled Analysis of Fluid Force in the Annular Plain Seal and Vibration of the Rotor System Using Shooting Method

In turbomachinery, the rotor dynamic (RD) fluid force generated in a fluid element is one of the causes of shaft vibration. RD fluid force is caused by the interaction between shaft vibration and fluid force, and its precise prediction for various rotor’s orbit is difficult. This study performs a two-way coupled analysis of the fluid flow in the annular plain seal and shaft vibration using the shooting method. The frequency response is obtained and compared with that obtained from a direct numerical simulation of the coupled system, and the validity of the analysis is confirmed. The onset speed of instability is effectively and accurately obtained using the two-way coupled analysis with the shooting method, and the effects of the parameters on it are investigated.

Definitions of vortex vector and vortex

Although the vortex is ubiquitous in nature, its definition is somewhat ambiguous in the field of fluid dynamics. In this absence of a rigorous mathematical definition, considerable confusion appears to exist in visualizing and understanding the coherent vortical structures in turbulence. Cited in the previous studies, a vortex cannot be fully described by vorticity, and vorticity should be further decomposed into a rotational and a non-rotational part to represent the rotation and the shear, respectively. In this paper, we introduce several new concepts, including local fluid rotation at a point and the direction of the local fluid rotation axis. The direction and the strength of local fluid rotation are examined by investigating the kinematics of the fluid element in two- and three-dimensional flows. A new vector quantity, which is called the vortex vector in this paper, is defined to describe the local fluid rotation and it is the rotational part of the vorticity. This can be understood as that the direction of the vortex vector is equivalent to the direction of the local fluid rotation axis, and the magnitude of vortex vector is the strength of the location fluid rotation. With these new revelations, a vortex is defined as a connected region where the vortex vector is not zero. In addition, through direct numerical simulation (DNS) and large eddy simulation (LES) examples, it is demonstrated that the newly defined vortex vector can fully describe the complex vertical structures of turbulence.

Decoupling Method of Sloshing Water in PCCWST of Large-Scale Advanced Passive PWR Nuclear Power Plant

Modeling water in passive containment cooling water storage tank (PCCWST) using fluid element will result in large amount of calculation when conducting seismic analysis of shield building or NI. Thus, it is necessary to simplify the modal of water so as to reduce the difficulty of seismic analysis under condition that the error is slight enough to be ignored. By formula deduction and analysis, on the one hand, this paper proofs that modeling “sloshing mass” as fixed mass on structure is unreasonable. On the other hand, this paper proposes that the reasonable simplified approach is to decouple “sloshing mass” totally from the structure system. Furthermore, conditions of utilizing decoupling method are illustrated.

Impact of the spatial structure of the hydraulic conductivity field on vorticity in three-dimensional flows

A material fluid element within a porous medium experiences deformations due to the disordered spatial distribution of the Darcy scale velocity field, caused by the heterogeneity of hydraulic conductivity. A physical consequence of this heterogeneity is the presence of localized kinematical features such as straining, shearing and vorticity in the fluid element. These kinematical features will influence the shape of solute clouds and their fate. Studies on the deformation of material surfaces highlighted the importance of stretching and shearing, whereas vorticity received so far less attention, though it determines folding, a deformation associated with the local rotation of the velocity field. We study vorticity in a three-dimensional porous formation exploring how its fluctuations are influenced by the spatial structure of the porous media, obtained by immersing spheroidal inclusions into a matrix of constant hydraulic conductivity. By comparing porous formations with the same spatial statistics, we analyse how vorticity is affected by the different shape and arrangement of inclusions, defined as the medium ‘microstructure’. We conclude that, as microstructure has a significant impact on vorticity fluctuations, the usual second-order statistical description of the conductivity field is unable to capture local deformations of the plume.