Inhomogeneous Flow Research Articles

Large eddy simulations of turbulent planar jets of viscoelastic fluids

Direct numerical simulations and large-eddy simulations of turbulent planar jets are used to assess the distortion similarity (DSIM) model, recently developed by Ferreira et al. [“Large-eddy simulations of forced isotropic turbulence with viscoelastic fluids described by the finitely extensible nonlinear elastic rheological model with Peterlin's closure model,” Phys. Fluids 28, 125104 (2016)] for homogeneous turbulence, in the simulation of turbulent viscoelastic planar jets. Both a priori and a posteriori tests of the DSIM model are used and show that the several assumptions used in the development of the DSIM model hold well in inhomogeneous free turbulent viscoelastic flows, e.g., (i) the scale similarity of the subgrid-scale (SGS) polymer stretching and (ii) the local equilibrium of the elastic energy production and dissipation. The DSIM model for the SGS polymer stretching term, together with the dynamic Smagorinsky model, is able to reproduce well the flow structures and the classical one-point statistics of turbulent viscoelastic planar jets. The model should be equally able to simulate other free shear flows of viscoelastic fluids, e.g., wakes and mixing layers.

Exact solutions of the Navier–Stokes equations for describing an isobaric one-directional vertical vortex flow of a fluid

The article proposes a family of exact solutions to the Navier–Stokes equations for describing isobaric inhomogeneous unidirectional fluid motions. Due to the incompressibility equation, the velocity of the inhomogeneous Couette flow depends on two coordinates and time. The expression for the velocity field has a wide functional arbitrariness. This exact solution is obtained by the method of separation of variables, and both algebraic operations (additivity and multiplicativity) are used to substantiate the importance of modifying the classical Couette flow. The article contains extensive bibliographic information that makes it possible to trace a change in the exact Couette solution for various areas of the hydrodynamics of a Newtonian incompressible fluid. The fluid flow is described by a polynomial depending on one variable (horizontal coordinate). The coefficients of the polynomial functionally depend on the second (vertical) coordinate and time; they are determined by a chain of the simplest homogeneous and inhomogeneous partial differential parabolic-type equations. The chain of equations is obtained by the method of undetermined coefficients after substituting the exact solution into the Navier–Stokes equation. An algorithm for integrating a system of ordinary differential equations for studying the steady motion of a viscous fluid is presented. In this case, all the functions defining velocity are polynomials. It is shown that the topology of the vorticity vector and shear stresses has a complex structure even without convective mixing (creeping flow).

The Biermann Battery Driven by a Streaming Plasma

Abstract The Biermann battery is a promising generation mechanism of a seed magnetic field in the universe. We propose a new driving mechanism for the Biermann battery in an inhomogeneous plasma with a beam component. An inhomogeneous electron flow induced by the return current can make an electron pressure gradient that is not parallel to the density gradient. As a result, the magnetic field is generated by the Biermann battery. We demonstrate the new generation mechanism of the magnetic field by conducting three-fluid plasma simulations. By this mechanism, the first cosmic rays can generate the seed magnetic field with astrophysical scales at redshift around 20.

Response of shear in bulk orientations of charged DNA rods: Taylor- and gradient-banding

Shear-induced instabilities leading to various kinds of inhomogeneous flow profiles play an important role in the processing of complex fluids, ranging from polymeric materials to various types of biological systems. In previously studied systems, either Taylor banding, or gradient banding, or fracture is observed. In the present work we study a system for which all instabilities occur in orientation textures (OTs), and where Taylor banding occurs simultaneously with gradient banding. The system here consists of crowded suspensions of long and thin DNA-based rods (at a low ionic strength of 0.16 mM salt), where the applied shear rate is systematically varied, for concentrations well below and above the glass-transition concentration (12.4 mg ml−1). To simultaneously measure the velocity profile along the gradient direction, in fracture and gradient banding, the optical cell is placed in a specially designed heterodyne light scattering set up, where the scattering volume can be scanned across the cell gap. The results confirm that Taylor bands and gradient banding occur in the concentration of DNA rods and applied shear-rates (35–80 s−1). Taylor bands clearly show the flow access in vorticity-direction, while the gradient banding is rearranged as thick rolling flows of OTs, at the middle shear-rate (50 s−1). The observations can be then useful to facilitate other biological complex fluids and the glass-forming liquids.

Analyzing the impact of intake structure on the flow at low pressure SHPP

AbstractThe structural parts of intake structures directly affect the flow velocity distribution in the turbine intake of small hydropower plants, where inhomogeneous flow leads to uneven load of the turbine units causing operational problems. A 2D numerical flow modeling was used for investigations of the flow in an intake structure of a low-head small hydropower plant. The effects of shape changes of the intake structure on the flow velocity distribution in the turbine intakes were investigated and assessed proving significant effect of the shapes of the intake structure on the flow homogeneity in turbine intakes.

SNN_flow: a shared nearest-neighbor-based clustering method for inhomogeneous origin-destination flows

ABSTRACT Identifying clusters from individual origin–destination (OD) flows is vital for investigating spatial interactions and flow mapping. However, detecting arbitrarily-shaped and non-uniform flow clusters from network-constrained OD flows continues to be a challenge. This study proposes a shared nearest-neighbor-based clustering method (SNN_flow) for inhomogeneous OD flows constrained by a road network. To reveal clusters of varying shapes and densities, a normalized density for each OD flow is defined based on the concept of shared nearest-neighbor, and flow clusters are constructed using the density-connectivity mechanism. To handle large amounts of disaggregated OD flows, an efficient method for searching the network-constrained k-nearest flows is developed based on a local road node distance matrix. The parameters of SNN_flow are statistically determined: the density threshold is modeled as a significance level of a significance test, and the number of nearest neighbors is estimated based on the variance of the kth nearest distance. SNN_flow is compared with three state-of-the-art methods using taxicab trip data in Beijing. The results show that SNN_flow outperforms existing methods in identifying flow clusters with irregular shapes and inhomogeneous distributions. The clusters identified by SNN_flow can reveal human mobility patterns in Beijing.

Hemodynamic Assessment of Hollow-Fiber Membrane Oxygenators Using Computational Fluid Dynamics in Heterogeneous Membrane Models.

Extracorporeal membrane oxygenation (ECMO) has been used clinically for more than 40 years as a bridge to transplantation, with hollow-fiber membrane (HFM) oxygenators gaining in popularity due to their high gas transfer and low flow resistance. In spite of the technological advances in ECMO devices, the inevitable contact of the perfused blood with the polymer hollow-fiber gas-exchange membrane, and the subsequent thrombus formation, limits their clinical usage to only 2-4 weeks. In addition, the inhomogeneous flow in the device can further enhance thrombus formation and limit gas-transport efficiency. Endothelialization of the blood contacting surfaces of ECMO devices offers a potential solution to their inherent thrombogenicity. However, abnormal shear stresses and inhomogeneous blood flow might affect the function and activation status of the seeded endothelial cells (ECs). In this study, the blood flow through two HFM oxygenators, including the commercially available iLA® MiniLung Petite Novalung (Xenios AG, Germany) and an experimental one for the rat animal model, was modeled using computational fluid dynamics (CFD), with a view to assessing the magnitude and distribution of the wall shear stress (WSS) on the hollow fibers and flow fields in the oxygenators. This work demonstrated significant inhomogeneity in the flow dynamics of both oxygenators, with regions of high hollow-fiber WSS and regions of stagnant flow, implying a variable flow-induced stimulation on seeded ECs and possible EC activation and damage in a biohybrid oxygenator setting.

Stratification and MHD Effects on Narrow Channel Problems

In this paper we analyze viscous oscillatory MHD inhomogeneous fluid flow through the channel which is narrow and rectangular with one wall being porous through which suction or injection is taken place with constant rate and the other wall being rigid. The equation pertaining to the motion of fluid are simplified by using narrow channel approximation and the simplified equation are solved using similarity transformation and the graphical representation are analyzed for velocity profiles. The results reveal that stratification and MHD effects are found predominantly at the centre of the channel while stratification suppresses the flow in vertical direction. For B 0=0 and N=0 the results are in accordance with that already available in literature.

A Study on Exponential and Linear Density Stratification on Rectangular Channel Problems

In this paper we analyze viscous oscillatory MHD inhomogeneous fluid flow through the rectangular channel with one wall being porous through which suction or injection is taken place with constant rate and the other wall being rigid. The density function in the equation of incompressibility are considered in first case as exponentially distributed and that in the second case as linearly distributed. The governing equation of motion in both cases are solved using similarity transformation and the graphical representation in both cases are analyzed and compared for velocity profiles. Further for second-degree approximation, the exponential stratification reduces to the results of linear stratification results, which are already available in the literature.

On small-scale and large-scale intermittency of Lagrangian statistics in canopy flow

Abstract

Deviations from Taylor\u2019s frozen hypothesis and scaling laws in inhomogeneous jet flows

Difficulties in studying turbulent flows stem, in part, from the lack of high-frequency, high-resolution measurements to interrogate small-scale structures and their rapid evolution. We present analysis of data from experiments employing a burst-mode laser system to capture both spatially resolved velocity fields and their dynamics using high-resolution particle image velocimetry measurements at 100 kHz. We show directly that velocity fluctuations in axisymmetric jet flows are inhomogeneous and anisotropic. The peak of the time-delayed cross correlation function decays exponentially in time and its velocity is smaller than the convection velocity; thus, Taylor’s frozen hypothesis fails to generalize for these inhomogeneous flows. Structure functions are isotropic only at small distances. They exhibit extended self-similarity, but no inertial range is found where the Kolmogorov frac{2}{3}-law is satisfied. Spectral-energy density of the flow, although anisotropic, is consistent with the Kolmogorov–Obukhov frac{5}{3}-law in the flow direction.

A new coupled model for the equivalent roughness heights of wind farms

Accurate parameterization of wind farms’ equivalent roughness heights is critical to meso-scale climate simulations as well as power predictions of wind turbines. A notable inadequacy of the existing models is that the results sensitively depend on sx/sy, where sx and sy are the dimensionless streamwise and spanwise spacing of the turbines. To understand the issue, we conduct large-eddy simulations (LESs) for three types of quasi-infinite wind farms with moderate, large, and small sx/sy. We find that the wind speed at the rotor is different from the horizontally averaged wind speed at the hub height, and this is particularly true for wind farms with small sx/sy. This flow inhomogeneity at the hub height plays an important role in determining wind farms’ equivalent roughness height but is often neglected in the existing models. Accounting for the flow inhomogeneity at the hub height, we propose a new coupled top-down/bottom-up model for the equivalent roughness heights of wind farms. Our model is compared with the existing models and our LESs. The results show that the proposed model is able to predict the equivalent roughness height of all types of wind farms irrespective of sx/sy’s value.

Effects of slot injection on detonation wavelet characteristics in a rotating detonation engine

Two-dimensional numerical simulations are performed to investigate the effects of spatially discrete slot injection of reactants on the features of detonation wavelets in a rotating detonation engine (RDE). The detonation dynamics is described by a model based on the reactive Euler equations coupled with two-step, induction-reaction kinetics. By varying injection conditions and the chemical sensitivity of the reactive mixture, a parametric study is carried out to examine the influence of the injection-slot area ratio α on the detonation wavelet patterns and different flow features inside an RDE combustion chamber. The simulation results demonstrate that the injection conditions, i.e., stagnation temperature and pressure, have a similar influence on slot-ozzle rotating detonation wavelets (RDWs) as compared with the mini-nozzle RDWs reported in a previous study. The corresponding mass flow rate and inhomogeneity generated due to the presence of slot injection, however, play a key factor in the self-sustained rotating detonation and its frontal structure.

Characteristics of drag due to streamwise inhomogeneous roughness

Characteristics of the skin friction due to streamwise inhomogeneous roughness are investigated by modeling it in a simplified manner using step changes in equivalent sand grain roughness height ks, denoted as P (ks = 81.25 μm), Q (ks = 325.00 μm) and R (ks = 568.75 μm). The selected ks values represent the common ship-hull roughness, i.e., from light slime to about small calcareous fouling. RANS simulations are performed to study the friction characteristics of various rough surfaces formed by a trio-combination of P, Q and R roughnesses on flat plates with streamwise lengths of 30, 60, 120 and 240 m. The three combinations of roughnesses form either homogeneous (PPP, QQQ or RRR) or inhomogeneous (PQR, PRQ, QPR, etc.) rough walled turbulent boundary layer flow. A step change in roughness height results in a sudden change of the local skin friction coefficient in the form of overshoot or undershoot, followed by a relaxation where the inhomogeneous local skin friction is slowly returning to the homogeneous local one. The sequence of roughness arrangement in a streamwise inhomogeneous roughness pattern plays a key role in the resulting overall skin friction with value increasing in the following order: PQR < PRQ < QPR < QRP < RPQ < RQP. The similarity laws hold for both homogeneous and inhomogeneous rough surfaces.

Effects of system rotation on diffusion of the disturbances in inhomogeneous strongly stratified flow

This study is an extension of our previous study [O. Iida, “Turbulent structure of stably stratified inhomogeneous flow,” Phys. Fluids 30, 045101 (2018)] where direct numerical simulations of a spectral method are performed for an inhomogeneous flow under stable density stratification by the inclusion of a fringe region where an artificial body force is imposed to make the flow locally disturbed, and thus, generated disturbances are horizontally diffused into the undisturbed laminar region. In this study, moreover, additional effects of system rotation on diffused disturbances are investigated in detail. As a result, we find that rotation makes the horizontally diffused disturbances anticyclonic vortices and that with a further increase in rotation, the horizontal diffusion is significantly attenuated, and their horizontal and vertical lengths decrease and increase, respectively. In addition, it is found that attenuating the energy cascade in the vertical direction simultaneously attenuates the horizontal enlargement of anticyclonic vortices.

On mathematical analysis of complex fluids in active hydrodynamics

&lt;p style='text-indent:20px;'&gt;This is a survey article for this special issue providing a review of the recent results in the mathematical analysis of active hydrodynamics. Both the incompressible and compressible models are discussed for the active liquid crystals in the Landau-de Gennes Q-tensor framework. The mathematical results on the weak solutions, regularity, and weak-strong uniqueness are presented for the incompressible flows. The global existence of weak solution to the compressible flows is recalled. Other related results on the inhomogeneous flows, incompressible limits, and stochastic analysis are also reviewed.&lt;/p&gt;

Influence of the non-monotonic loading and short stops on the regularities of the jerky flow in the Al-Mg alloy

The aim of the paper is to investigate the influence of the non-monotonic loading and short stops on the spatial-time inhomogeneity due to the jerky flow in the Al-Mg alloy. Experimental study on the regularities of inhomogeneous deformation and the processes of macroscopic localization of the plastic flow due to the Portevin-Le Chatelier effect was carried out. Using the digital image correlation technique the data on the initiation and propagation of the strain bands were obtained. Experimental data were obtained that show the effect of short-term stops and non-monotonic loading on the regularities of inelastic deformation of the Al-Mg alloy when the PLC effect manifests itself. Short stops decrease the level of critical strain when the jerky flow starts. Non-monotonic tests led to a change in the type of the PLC effect and a change in the regularities of the spatial-time inhomogeneity of plastic flow.

Influence of the loading system stiffness on the jerky flow in Al-Mg alloy at inelastic and postcritical deformation stages

The work is devoted to studying the issues of experimental studies of the behavior of materials under conditions of inhomogeneous discontinuous flow at the stages of plastic and supercritical deformation (deformation softening). Obtaining reliable experimental data on the indicated stages of inelastic deformation of materials is important for understanding the physical processes occurring in materials during deformation and ultimately leading to fracture. The results of tests are presented, confirming the influence of the rigidity of the loading system in relation to the working part of the sample on the processes of intermittent plastic deformation. The tests were carried out on samples of Al-Mg alloy. The loading rigidity was varied using a rig with variable rigidity. Registration of displacement and deformation fields on the surface of the working part of the samples was carried out by a non-contact video system Vic-3D Correlated Solutions based on the digital image correlation (DIC) technique. The use of this system makes it possible to measure both deformation at the macro level and the distribution of its components in the working part of the specimen under conditions of inhomogeneous discontinuous deformation. As a result of tensile tests, deformation diagrams were obtained for Al-Mg alloy samples tested at different values ​​of the rigidity of the loading system: 120 MN/m (nominal value), 50 MN/m, 18 MN/m, and 5 MN/m. All the diagrams show discontinuous plastic deformation (the Portevin-Le Chatelier effect). A decrease in the rigidity of loading with respect to the working part of the specimen led to a change in the type of discontinuous yield and an increase in the magnitude of the stress drop at each tooth of the diagram. The indicated effects of inhomogeneous plastic deformation are observed both at the stage of strain hardening and at the stage of postcritical deformation.

Effects of rolling-cutting processing parameters on micro-grooved strips forming

High heat flux density in the micro-electronics field urges the demand for functional surface for heat transfer. Micro-grooved surface is the classical heat transfer surface because of the larger specific area and better inducement of turbulence. A novel micro-grooved surface manufacturing process, the rolling-cutting process, is proposed to produce micro-grooved strips. Experiments are conducted to analyze the influence of processing parameters on the strips forming. The optimal combination of processing parameters is given to attain the micro-grooved strips with higher fins height and thinner base thickness. Additionally, the obtained strips are of three-dimensional structures with serrated bulges at the top. The difference between the material flow of serrated bulges and strip base is discussed, and the forming of serrated bulges is mainly due to inhomogeneous sinuous material flow.

Точные решения уравнений Обербека – Буссинеска для сдвиговых течений вязкой бинарной жидкости с учетом эффекта Соре

The paper considers an exact solution to the equations of thermal diffusion of a viscous incompressible fluid in the Boussinesq approximation with neglect of the Dufour effect for a steady shear flow. It is shown that the reduced system of constitutive relations is nonlinear and overdetermined. A nontrivial exact solution of this system is sought in the Lin–Sidorov–Aristov class. The resulting family of exact solutions allows one to describe steady-state inhomogeneous shear flows. This class generalizes the classical Couette, Poiseuille, and Ostroumov–Birikh solutions. It is demonstrated that the system of ordinary differential equations reduced within this class retains the properties of nonlinearity and overdetermination. A theorem on solvability conditions for the overdetermined system is proved; it is reported that, when these conditions are met, the solution is unique. The overdetermined system is solvable owing to the algebraic identity relating the horizontal velocity gradients, which are linear functions of the vertical coordinate. The constructive proof of the computation of hydrodynamic fields consists in the successive integration of the polynomials, the polynomial degree being dependent on the values of the boundary parameters.