Table of contents

The Landau–Lifshitz frame has been widely used to represent the macroscopic quantities of relativistic hydrodynamics in the presence of the dissipative process. In this paper, we derive the Landau–Lifshitz frame in the near-equilibrium regime under self-contained assumptions that do not require comparison with the Eckart frame. And then we revisit the relativistic BGK model proposed by Anderson and Witting to provide an application example of the Landau–Lifshitz frame.

This paper assesses the prediction of inert tracer gas dispersion within a cavity of height (H) 1.0 m, and unity aspect ratio, using large Eddy simulation (LES). The flow Reynolds number was 67 000, based on the freestream velocity and cavity height. The flow upstream of the cavity was laminar, producing a cavity shear layer which underwent a transition to turbulence over the cavity. Three distinct meshes are used, with grid spacings of $H / 100$ (coarse), $H / 200$ (intermediate), and $H / 400$ (fine) respectively. The Smagorinsky, WALE, and Germano-Lilly subgrid-scale models are used on each grid to quantify the effects of subgrid-scale modelling on the simulated flow. Coarsening the grid led to small changes in the predicted velocity field, and to substantial over-prediction of the tracer gas concentration statistics. Quantitative metric analysis of the tracer gas statistics showed that the coarse grid simulations yielded results outside of acceptable tolerances, while the intermediate and fine grids produced acceptable output. Interrogation of the fluid dynamics present in each simulation showed that the evolution of the cavity shear layer is heavily influenced by the grid and subgrid scale model. On the coarse and intermediate grids the development of the shear layer is delayed, inhibiting the entrainment and mixing of the tracer gas into the shear layer, reducing the removal of the tracer gas from the cavity. On the fine grid, the shear layer developed more rapidly, resulting in enhanced removal of the tracer gas from the cavity. Concentration probability density functions showed that the fine grid simulations accurately predicted the range, and the most probable value, of the tracer gas concentration towards both walls of the cavity. The results presented in this paper show that the WALE and Germano-Lilly models may be advantageous over the standard Smagorinsky model for simulations of pollutant dispersion in the urban environment.

We have constructed an energy-conserving 16 mode dynamical system to model hexagonal pattern in Rayleigh-Bénard convection of Boussinesq fluids with symmetric stress-free thermally conducting boundaries. The model shows stable roll pattern at the onset of convection. Hexagon is found to appear in the system via sausage and (or) stationary rhombus patterns. Both up and down hexagons arise periodically or chaotically with roll, sausage and rhombus patterns. Hexagonal pattern exists for all values of the Prandtl number, $1 \leq Pr \leq 5$ explored here. However, the pattern is more prominent for small Pr and $k {\lt} k_c$, where k denotes the wave number. The plot of Nusselt number matches with previous theoretical result. In dissipationless limit, the total energy and the unavailable energy are constants though the kinetic energy, the potential energy and the available energy vary with time. The derived model does not diverge for large values of Rayleigh number Ra.

We present a novel computationally efficient approach for investigating the effect of surface roughness on the fluid flow in small discrete fracture networks at low Reynolds number. The effect of parallel and series fracture arrangements on the flow rate and hydraulic resistance was studied numerically by patching Hele-Shaw (HS) cells to represent the network. In this analysis, the impact of surface roughness was studied in different arrangements of the network. For this aim, four models with different sequences of fracture connections were studied. The validity of the models was assessed by comparing the results with solutions of the full Navier–Stokes equations (NSE). The approximate hydraulic resistance and flow rate calculated by the HS method were found to be in good agreement with the NSE (less than 7% deviation). Results suggest a quadratic relationship between the network hydraulic resistance and the joint roughness coefficient (JRC). Notably, an increase in surface roughness caused a growth in hydraulic resistance and a fall in flow rate. Further insight was provided by drawing an analogy between resistors in electrical circuits and fractures in networks.

The Okubo (1970 Deep Sea Res.17 445)–Weiss (1991 Physica D 48 273) criterion, has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo–Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo–Weiss criterion and show the Okubo–Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the vorticity manifold. The Okubo–Weiss criterion is then reformulated in polar coordinates, and is validated for several examples including the Lamb–Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi-geostrophic (QG) flows. The Okubo–Weiss parameter is shown to remain robust under the β-plane approximation to the Coriolis parameter. The Okubo–Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo–Weiss type criterion is formulate for 3D axisymmetric slows, and is validated via application to the round Landau–Squire Laminar jet flow.

This work presents the numerical solution for different velocity profiles and friction factors on a rectangular porous microchannel fully saturated by the flow of a nanofluid introducing different viscosity models, including one nanofluid density model. The Darcy-Brinkman-Forchheimer equation was used to solve the momentum equation in the porous medium. The results show that the relative density of the fluid, the nanoparticle diameters and their volumetric concentration have a direct influence on the velocity profiles only when the inertial effects caused by the presence of the porous matrix are important. Finally, it was found that only viscosity models that depend on temperature and nanoparticle diameter reduce the friction factor by seventy percent compared to a base fluid without nanoparticles; furthermore, these models show a velocity reduction of even ten percent along the symmetry axis of the microchannel.

The main emphasis of this article is to compare the heat transfer performance of two different nanofluids i.e. carboxy-methyl-cellulose (CMC) + water-based molybdenum dioxide (MoS₂) nanofluid and kerosene oil-based molybdenum dioxide nanofluid during the fluid flow through a symmetric microchannel which is pumped by the mechanism of peristalsis and electroosmosis. The energy dissipated by Joule heating and viscous dissipation is also taken into account. An analysis of volumetric entropy generation is also conducted. Rabinowitsch fluid model is employed to characterize the shear-thinning behavior of CMC + water solution and Newtonian fluid properties of kerosene oil. The mathematical model for the problem is formulated by the Navier–Stokes, energy equation, and Buongiorno fluid model in combination with the Corcione model for thermal conductivity and viscosity of the nanofluid. Further, the Poisson–Boltzmann equation is utilized to compute the potential generated across the electric double layer. The homotopy perturbation technique is employed to compute the approximate solutions for temperature and nanoparticle volume fraction and exact solutions are obtained for velocity and the stream function. Salient features of the fluid flow are illustrated with the aid of graphical results. Contour plots for stream function are prepared for flow visualization. A comparison of heat transfer performance and entropy generation between both working fluids is presented. It is observed that aqueous solution modified by CMC and nanoparticles possess a higher heat transfer tendency and less entropy is generated in this case when compared with other nanofluid i.e. MoS₂/kerosene oil nanofluid under the same physical conditions. It is further noted that fluid flow can be controlled by the strength of the applied electric field. Upon increasing electroosmotic parameters, there is a very minute rise in volumetric entropy generation in the case of MoS₂/CMC + water nanofluid. However, there is a substantial rise in entropy generation for MoS₂/kerosene oil nanofluid.

Control of flow separation is a great issue to deal with a moving body to ensure its proper aerodynamic characteristics. To achieve this, various methods including active and passive control are suggested depends upon the flow characteristics and the surface in which control is necessary. To make the better use of both active and passive method of flow control this article proposed a new type of double sided plasma actuator (DSPVG) to overcome the drag penalty of conventional vortex generators (VGs) that commonly used in controlling flow and to use actively control. In this regard, the effectiveness of DSPVG has been numerically and experimentally investigated in a separated flow region of a 20° diffuser of an open type tunnel. DSPVG is placed at the upstream of separation location normal to the surface as like as conventional VG except zero angle with flow direction. Both numerical and experimental results of DSPVG are compared with that of VG and baseline flow and better agreements are found. Moreover, DSPVG has shown better separation suppression ability than conventional VGs due to its dual vortices. It is found that DSPVG significantly delay the separation. A freestream flow of 4 m s⁻¹ is used for experiments and numerical computations.

In this work, we have analyzed the impact of polarization force, angle of obliqueness under the influence of nonadiabatic dust charge fluctuation on shock waves formation in magneto rotating plasma. The present plasma model is consisting of negatively charged dust grains, Maxwellian electrons, nonextensive ions. The dissipation is introduced in the system via nonadiabaticity, a new mechanism for the formation of shock waves. Using standard reductive perturbation method, nonlinear equation namely Korteweg–de Vries Burgers equation is derived and solution is obtained using the Tanh method. It is shown that dust charge fluctuation is the main source of dissipation. We have studied the various parameteric influences on such shock structure and also showed how the gradual variations of these parameter affect the generation and structure of the shocks in their respective domain. Much of experiments on dusty plasma with nonadiabatic dust charge fluctuation will benefit from the parametric study.

Based on the deep reinforcement learning (DRL) method, the active flow control strategy obtained from artificial neural networks (ANNs) is applied to reducing the drag force of various blunt bodies. The control strategy is realized by the agent described by ANNs model which maps appropriate environment sensing signals and control actions, and ANNs are constructed by exploring the controlled system through proximal policy optimization method. The drag reduction effect for ellipse, square, hexagon and diamond geometries under double- and triple-jets control is systematically studied, and the robustness of DRL jet control method is verified. The numerical results show that the drag reduction effect of triple-jets control is significantly better than that of double-jets control when Reynolds number is 80 and angle of attack is 0, and under the triple-jets control situation, the DRL agent can significantly reduce the drag by approximately 11.50%, 10.56%, 8.35%, and 2.78% for ellipse, square, hexagon and diamond model, respectively. In addition, based on the ellipse model, the drag reduction effect of the active control strategy under different AOA and different Reynolds numbers are further studied. When the AOA of ellipse configuration are 5°, 10°, 15° and 20° and the Reynolds number remains 80, the control strategies of DRL achieve the drag reduction of 5.44%, 0.59%, 11.67% and 0.28%, respectively. Meanwhile, when the AOA is 0, the drag reduction reaches 10.84% and 23.63% under the condition of the Reynolds number is 160 and 320, respectively. The significant control effect shows that the reinforcement learning method coupled with the ANNs shows a powerful ability to identical system when facing control problem with high-dimensional nonlinear characteristics. The ability to identify complex systems also shows that DRL methods can be further applied to active flow control under conditions of higher Reynolds number.

In the present paper, the spatio-temporal evolution of the vorticity field in the second wake instability, i.e. (pure) mode B is investigated to understand the wake vortex dynamics and sign relationships among the three vorticity components. Direct numerical simulation of the flow past a circular cylinder in the three-dimensional (3D) wake transition is performed, typically at a Reynolds number of 300. According to the time histories of fluid forces and frequency analysis, three different stages are identified. In the fully developed wake (FDW), the spanwise vortex core is almost two-dimensional, while the vortex braid is 3D due to the dominant streamwise interaction. However, streamwise and vertical vorticities owing to the intrinsic 3D instability are already generated first on cylinder surfaces early in the computational transition (CT). The evolution of additional vorticities with the same features as mode B shows that (pure) mode B could already be formed in the late CT. In the FDW, a special sign symmetry of these additional vorticities on the rear surface is observed, which is exactly opposite to that in (pure) mode B. Similarly, the two sign laws found in (pure) mode A are also verified in three typical regions, independent of the Reynolds number, for (pure) mode B. Particularly, the mechanism for the physical origin of streamwise and vertical vortices in the shear layers is the vortex generation on the wall first and then dominant vortex induction just near the wall. The entire process of the formation and shedding of vortices with three components of vorticity is first and completely illustrated. Other characteristics of the evolution of mode B are presented in detail.

Ventilation bubble is widely used to reduce friction drag of object travelling in fluid. A large number of experimental studies are performed on the ventilation bubble in water tunnel, while little is known about it around vertically moving cylinder under reduced pressure. We aim to investigate dynamics of the ventilation bubble in vertically moving case. To support the study, a specialized experiment set-up is designed, based on which images of ventilation bubble around vertically moving cylinder under reduced ambient pressure can be captured and experiments are conducted to study the influence of velocities and flow rate on the ventilation bubble dynamics. In detail, we first describe the development of ventilation bubble and details of re-entrant jet. In addition to that, two types of re-entrant jets are observed, and the maximum velocity of re-entrant jet is obtained. Besides, four modes of development of ventilation bubbles' closure patterns are concluded. Finally, geometric features of ventilation bubble are obtained through image processing which are then described and analyzed in detail. The above results contribute to the research on the control of vertically moving cylinder through ventilation bubble.

This paper presents an investigation of the stability of a vortex with azimuthal velocity profile $\bar{V} = \left[1 - \left(1 - \varepsilon r^2 \right) e^{- r^2}\right]/r$. When ε = 0, the Lamb–Oseen vortex model is recovered. Although the Lamb–Oseen vortex supports propagating waves known as Kelvin waves, the flow is stable according to Rayleigh's circulation criterion. In this paper, on the other hand, the modified vortex profile admits linearly unstable disturbances for ε > 0 and we investigate their characteristics. These may be either axisymmetric or non-axisymmetric, but we find that the axisymmetric perturbations have the largest growth rates. When their growth rates are small, it becomes very difficult to solve the linear equation governing the axisymmetric perturbations because the eigenfunctions have a rapid exponential growth as one moves outward radially from the vortex center. To deal with such cases, a modified Riccati transformation was employed and found to be effective in solving the associated eigenvalue problem.

We have examined the effects caused on the motion and sedimentation of a free falling solid particle by the hydrodynamic forces acting on the particle's surface arising when particle is close to wall. Drag and lift coefficients for a settling particle inside a narrow domain are calculated. An Eulerian mesh is adopted for computing the motion of free moving solid particles through the domain. The combined particle and fluid mixture is treated with a fictitious boundary method approach. To avoid particle-wall collisions, an approach proposed by Singh, Glowinsk and coauthors is used to handle such interactions. The particulate flow is computed using multigrid finite element solver FEATFLOW (Finite element analysis tool for flow problems). Numerical experiments are performed by decreasing domain widths for a single falling particle. The size and density of the particle is varied to inspect the particle paths. The behavior of the particle and its interaction with wall while it is moving inside constricted domains is analyzed. Results for the drag and lift forces on the surface of particle are presented and compared with the reference values.

Cellular secondary flows are inevitably present in turbulent flows through ducts, natural or artificial channels, and compound channels. Secondary currents significantly modify the characteristics of turbulent quantities, the pattern of primary flow velocity by causing dip-phenomenon. To understand the detailed mechanism and hidden cause, modelling of secondary flow velocities is crucial. In this study, proper mathematical models of secondary flow velocities along vertical and transverse directions are proposed for steady and uniform turbulent flow through wide open channels with equal smooth and rough bed strips. Starting from the continuity and the Reynolds averaged Navier–Stokes equations, governing equation for secondary velocity is derived first and then using appropriate boundary conditions (no-slip boundary conditions at channel bottom and free surface, and maximum vertical velocity in magnitude at the interface of two cellular secondary cells and at mid-depth of the channel. All these conditions are consistent with several experimental observations). A new model of the streamwise Reynolds shear stress is proposed for the entire cross-sectional plane and using it, the analytical solutions are obtained. Proposed models include the effects of viscosity of the fluid and the eddy viscosity model of turbulence. All suggested models are validated with existing experimental data in rectangular open-channel flows, compound open channel flows, and duct flows, and satisfactory results are obtained. Furthermore, models are also compared with existing empirical models from literature to show the effectiveness and superiority of proposed models. Apart from these, the obtained results from this study are used to investigate the effects of vertical and transverse secondary flow velocities on the settling velocity vector in a cross-sectional plane. Effective alternative models for the settling velocity vector are suggested. The model of settling velocity vector is also compared with the existing model. Finally, all results are justified from physical viewpoints.