Theory Of Turbulent Flow Research Articles

A mathematical introduction to complex dynamical systems

This work proposes an investigation of the theory of dynamic systems, focusing on the analysis of entropy in its classical and topological manifestations. Initially, the fundamental concepts of dynamical systems theory are presented, with an emphasis on topological dynamical systems (TDS). Next, definitions of discrete topological entropy and its relationship to dynamical systems are discussed, followed by the introduction of topological entropy pressure as a weighted form of topological entropy. Subsequently, some applications of topological entropy in dynamic systems are examined, highlighting its role in the analysis of chaotic systems and in ergodic theory. Furthermore, we present a new theory, called Topological Ergodic Entropy Theory (TEET), which offers an innovative approach to the analysis of ergodic dynamical systems. Finally, the Ergodic Theory of Turbulent Flow (ETTF) is introduced, exploring the relationship between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. The results presented contribute to a deeper understanding of the complexity of dynamical systems and their applications in various areas of mathematics and physics. The investigation of topological entropy and its applications in dynamical systems offers new insights into the chaotic and stochastic behavior of these systems, while the introduction of new theories, such as ETTF, provides a new perspective for the analysis and modeling of turbulent phenomena.

Evolution of small-scale turbulence at large Richardson numbers

Abstract. The theory of stratified turbulent flow developed earlier by the authors is applied to data from different areas of the ocean. It is shown that turbulence can be amplified and supported even at large gradient Richardson numbers. The cause of that is the exchange between kinetic and potential energies of turbulence. Using the profiles of Brunt–Väisälä frequency and vertical current shear given in Forryan et al. (2013), the profiles of the kinetic energy dissipation rate are calculated. The results are in reasonable agreement with the experimental data.

Immersion in Complex Dynamical Systems with Ergodicity

This work delves into the theory of dynamic systems, focusing on the analysis of entropy in both classical and topological contexts. Beginning with an exposition of fundamental concepts in dynamical systems theory, particular attention is given to topological dynamical systems (TDS). The discussion progresses to explore discrete topological entropy and its significance within dynamical systems, culminating in the introduction of topological entropy pressure as a nuanced form of this concept. The study then investigates various applications of topological entropy within dynamic systems, emphasizing its utility in understanding chaotic systems and its role in ergodic theory. A novel theory, termed Topological Ergodic Entropy Theory (TEET), is presented, offering a fresh perspective on the analysis of ergodic dynamical systems. Furthermore, the work introduces the Ergodic Theory of Turbulent Flow (ETTF), which probes the interplay between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. Through these explorations, the findings contribute significantly to the comprehension of the intricate nature of dynamical systems and their diverse applications across mathematics and physics. By scrutinizing topological entropy and its implications in dynamical systems, this research offers novel insights into the chaotic and stochastic behaviors exhibited by these systems. Additionally, the introduction of pioneering theories like ETTF opens up new avenues for understanding and modeling turbulent phenomena, thereby enriching our understanding of complex dynamical processes.

The similarity theory of free turbulent shear flows of viscoelastic fluids

A new theory is formulated for the description of the conformation state of the polymer chains in free turbulent shear flows of viscoelastic fluids. Using self-similarity arguments and new scaling relations for the turbulent flux of conformation tensor we show the existence of minimum and maximum solvent dissipation reduction asymptotes, and four different polymer deformation regimes. The similarities with the maximum drag reduction asymptote of turbulent pipe flow is discussed and new scaling laws are obtained for all components of the mean conformation tensor at each deformation regime. Analytical solutions for the self-similar transverse profiles of the conformation tensor components are also obtained, providing the complete solution for the mean flow problem at the far field. The analysis is developed for both planar jets and wakes and covers the two limits of shear flows, with large and small velocity differences, respectively. Comparisons of the new theoretical results with several direct numerical simulations employing the FENE-P rheological model show excellent agreement.

Turbulent Transport in a Stratified Shear Flow

Within the framework of the theory of unsteady turbulent flows in a stratified fluid, a new parameterization of the turbulent Prandtl number is proposed. The parameterization is included in the k-ε-closure and used within the three-dimensional model of thermohydrodynamics of an enclosed water body where density distribution includes pycnocline. This allows us to describe turbulence in a stratified shear flow without the restrictions associated with the gradient Richardson number and justify the choice of closure constants. Numerical experiments, where the downward penetration of turbulence was considered, confirm the advantage of the developed approach in describing the effects neglected in the classical closures.

Experimental and numerical investigation of the effects of buoyancy and flow acceleration on the heat transfer of hexamethyldisiloxane (MM) at supercritical pressures

The hexamethyldisiloxane (MM) has relatively higher thermostability and lower critical parameters than other organic working fluids, making it suitable for the medium/high temperature supercritical ORC system. However, the fluid at supercritical pressures experiences sharp variation of thermophysical properties near the pseudo-critical temperature which results in the abnormal heat transfer phenomenon, so the heat transfer design becomes one of the challenges for supercritical ORC system. Most of the extant researches believe that the abnormal heat transfer of supercritical fluid is caused by the effects of buoyancy and flow acceleration induced by the dramatic change of fluid density, but it is still necessary to further improve the understanding of its physical mechanism and prediction of heat transfer characteristics. Based on experimental and numerical data, the present work analyses the distributions of key parameters to reveal the main causes of abnormal heat transfer. Then, the dimensionless parameters of the buoyancy and flow acceleration and their thresholds are obtained in combination of the in-tube turbulent flow theory. The results show that the effects of buoyancy and flow acceleration can reduce the local turbulence intensity. The affected positions are respectively the near-wall area after the wall temperature reaching the pseudo-critical point and the mainstream area where the fluid temperature reaches the pseudo-critical point. For this reason, the thermophysical reference temperature in the dimensionless boundary layer thickness for the buoyancy parameter (Bu) and flow acceleration parameter (Ac) are set as the wall temperature and bulk temperature respectively. The corresponding thresholds where the buoyancy and flow acceleration have large influence on the heat transfer are 3.9 × 10−6 and 9.8 × 10−7, which can well predict the initial position of heat transfer deterioration (HTD).

Numerical simulation of planar hydraulic fracture propagation with consideration to transition from turbulence to laminar flow regime

Turbulent flow in fluid-driven fractures exerts important effects on the hydraulic fracture extension, fracture geometry, and proppant transport. Based on linear elastic fracture mechanics, the implicit level set algorithm, laminar flow theory, and turbulent flow theory, this study established planar fracture propagation models of permeable and impermeable reservoirs with consideration the flow regime transition from turbulent to laminar flow when the Reynolds number is larger than the critical Reynolds number. Additionally, the frictional behavior of the fluid in the turbulent flow regime was approximated based on the MDR asymptote and Blasius correlation. The influence of the turbulent flow effect on the hydraulic fracture propagation was theoretically and numerically analyzed. The results reveal that the turbulent flow regime exerts a significant effect within the first few minutes of fracture propagation. Compared with the fully-laminar-flow model, the turbulent-laminar flow model predicted a shorter fracture radius, larger maximum fracture width, and fluid net pressure. This indicates that the fracturing process requires greater pumping power than that predicted by the laminar flow models under the influence of turbulent flow to achieve the desired design parameters. Compared with impermeable rock, the turbulent flow in the fracture is enhanced by fluid leak-off. Slickwater can transition from turbulent to laminar flow at a lower critical Reynolds number compared with pure water. The normalized fracture parameters indicate that the fracture radius corresponding to pure water is smaller, and the maximum width of fracture and maximum net pressure are larger than those of slickwater. The threshold time of turbulent flow for different fracture parameters varies depending on the injected fluid properties and reservoir parameters. Our study contributes toward a deeper understanding of the real physical behavior of hydraulic fracture propagation at large injection rates.

Minichannel and minigap classification criteria based on the aspect ratio of the minigeometry: A numerical study

A detailed numerical investigation has been carried out to analyze the diabatic flow distribution and velocity profile in 18 minigeometries with various aspect ratios for V-type and I-type flow configurations (for 36 cases) assuming ethanol as a working fluid. The aim of the study is to distinguish the value of the aspect ratio for which the flow in minigeometry starts to be two-dimensional (minigap). Cases with a constant Reynolds number of 4167 (variable mass flow rate) were compared. The normalized velocity profiles over the normalized width of the minigeometry acquired from the simulation have been compared with the theoretically calculated profiles based on the one-seventh power-law and turbulent flow theory. The results show that the one-seventh power-law velocity profiles are not consistent with the profiles simulated at an aspect ratio greater than 7. A new correlation for normalized velocity profile incorporating aspect ratio of the minigeometry for minigaps has been proposed. The conclusions are independent of the geometry depth, working fluid, and flow configuration.

Analysis of magnetohydrodynamic channel flow through complex network analysis.

Velocity time series of hydrodynamic and magnetohydrodynamic (MHD) turbulent flow are analyzed by means of complex network analysis in order to understand the mechanism of fluid patterns modification due to the external magnetic field. Direct numerical simulations of two cases are used, one for the plane hydrodynamic turbulent channel flow at the low Reynolds number of 180, based on the friction velocity, and the corresponding MHD flow with an external streamwise magnetic field with a magnetic interaction number of 0.1. By applying the visibility graph algorithm, we first transformed the time series into networks and then we evaluated the network topological properties. Results show that the proposed network analysis is not only able to identify and detect dynamical transitions in the system's behavior that identifies three distinct fluid areas in accordance with turbulent flow theory but also can quantify the effect of the magnetic field on the time series transitions. Moreover, we find that the topological measures of networks without a magnetic field and as compared to the one with a magnetic field are statistically different within a 95% confidence interval. These results provide a way to discriminate and characterize the influence of the magnetic field on the turbulent flows.

Rapid distortion theory of turbulent flow around a porous cylinder

Abstract

Longitudinal dispersion coefficients of submerged vegetation flow under the effect of surface wind.

The longitudinal dispersion coefficient is an important index for contaminant transports in rivers. Investigating it by using an analytical approach is conducive to obtain its expression with physical meanings and wide application ranges. However, the analytical solutions are extremely complex for subsequent derivations when many influencing factors, such as benthic vegetation and surface wind, are considered. This study combines turbulent flow theory and Biot's theory for poroelasticity into a two-layer flow model and acquires the analytical solutions of velocity. A database is generated from the analytical solutions to search a more concise expression of velocity through genetic programming. A formula for longitudinal dispersion coefficients of submerged vegetation flow under the effect of surface wind is deduced on the basis of this expression. Calculated coefficients from the formula are compared with the experimental coefficients from the model and real vegetation to show its validity. The formula indicates that the longitudinal dispersion coefficients are mainly affected by turbulent effect, vegetation height, and surface wind. The growth of vegetation height can weaken the influence of surface wind on longitudinal dispersion coefficient.

IMPROVEMENT OF APPROACHES AND METHODS OF TURBULENT FLOW THEORY IN THE PIPES

Abstract. The article consideres the analysis of the literature about the development of the water turbulent flow theory in the pipes. According to the results of analysis and theoretical studies, we obtained mathematical models. These models described the kinematic structure of the water turbulent flow in the pipes for different regions of turbulence. For the first time, the hypothesis was accepted that the dependence obtained from the Navier-Stokes differential equation for constructing the velocity profile in the laminar regime is suitable for calculating the average velocities in the turbulent regime of flow, but for this, it is necessary to replace the molecular kinematic viscosity with the total turbulent kinematic viscosity, which includes kinematic viscosity on the inner surface of the pipe and turbulent kinematic viscosity , which occurs due to the movement of masses from one layer into another, as recommended in J.V. Boussinesq. Based on experimental data I. Nikuradze and F.O. Shevelev, we obtained a distribution of the total kinematic viscosity in the pipes, including the kinematic viscosity on the pipe inner surface and the kinematic turbulent viscosity. For the first time, we used the kinematic viscosity distribution equation in the pipes and obtained the averaged velocity profile equation. This equation corresponds to the boundary conditions on the pipe inner surface and on the axis of the pipe. The equation of maximum averaged velocity, the equation of distance from the axis of the pipe to the points having average velocity, the equation of the ratio of maximum velocity to average velocity was obtained. For the first time, the equation of the tangent stresses components ( , ) and the tangent stresses equation in radial coordinates ( ) were obtained. The equation of the maximum value of the tangent stresses located on the inner surface of the pipe was obtained. The tangent stresses assume a zero value on the pipe axis. The equation of the vortex components ( , ) was obtained. We have shown that vortex lines are concentric circles whose centers are located on the pipe axis. The equation of angular velocity of flow particles rotation relative to the vortex lines was obtained. The maximum value of the particle rotation angular velocity on the pipe inner surface is determined. It decreases monotonically to zero on the axis of the pipeline. It is zero on the pipe axis. In this article, all equations reveal the kinematic structure of the water flow. We described these equations by the Reynolds number and the pipe friction factor. Such equations are adopted to show the dependencies between the regimes and the flow kinematic structure. These equations make it possible to calculate the distribution profile of the total kinematic viscosity, averaged velocity, tangential stresses and angular velocity of flow particle rotation.

Distribution of turbidity in flow constrained by transverse dam

Construction of control structures in rivers allows to manage channel flow in required direction and artificially change its natural condition providing rational interaction of flow and channel. Redistribution of both liquid and solid flow occur under influence of control structures. The main goal of the given work is to set the distribution pattern of turbidity in flow constrained by transverse blind dam. For the first time the task is studied with the use of field research data from dam No.30 in Amudarya river. The location of section and verticals in choosing turbidity samples, the sections are set based on the hydraulic structure of deformed flow. Flow division scheme has been proposed for hydraulically homogeneous zones of weakly disturbed core, intensive turbulent mixing and backflow, as it is accepted in the theory of turbulent flow with mixture spreading in a confined space. For the verticals the samples were taken in two depth points 0.2H and 0.8H, and areas with shallow depth – at 0.6H. Turbidity distribution by depth in weakly disturbed core has the shape of a “boot” and μ 0,8H is 2-3 times higher than μ0,2H . The rest are close to logarithmic. The maximal turbidity at 0.8H is 3.6 kg/m3. Turbidity distribution in layout in the zone of intensive turbulent mixing is affine and comply with Shlihting-Abramovih’s theoretical relationship for starting point. The obtained results can be used in future to forecast interdam area sedimentation and new bank line borders.

Study of Convective Heat Transfer in Grinding Applied to Tool Carbide

Abstract The grinding temperature is of great importance for the quality and integrity of machined cemented carbide tool. Tool edge surfaces may be damaged by softening or being stressed, hardened, burned, or cracked. Former research on grinding temperature prediction often made assumptions to simplify heat convection due to the grinding fluid. However, these simplifying assumptions can sometimes undermine the mathematical relationships between grinding conditions and surface temperature, particularly in low-temperature grinding where fluid convection is most important. This paper is an attempt to provide an improved comprehensive thermal model for the prediction of contact temperatures and for monitoring and control of thermal damage. Based on previous thermal model research, this paper tackles a key element of the thermal model for temperature prediction. It proposes a convective heat transfer model based on the classic theory of turbulent flow passing a plate. Theoretical predictions from the thermal model of turbulent flow developed in this paper are compared with experimental values. Predictions are further compared with values from a previously published laminar flow model. And it is shown that the new model leads to a significant reduction in predicted temperatures. The results suggest that the thermal model for the turbulent flow provides a reasonable estimate of predicted temperature values within the region of the fluid boiling temperature. The estimates appear to be an improvement compared with the laminar flow thermal model. The turbulent flow thermal model is considered to improve estimates of background contact temperatures in grinding cemented carbide.

Thermal interactions in rolling bearings

Rolling bearing dynamics model, based on classical differential equations of motion of bearing elements coupled with thermal interactions, is presented. While churning and drag effects are based on classical laminar and turbulent flow theories, independently measured lubricant rheology, including shear dependence of viscosity, is used to model lubricant traction. The energy equation is integrated through the lubricant film to first compute Newtonian traction with thermal effects. Viscosity dependence on shear stress is then applied to model “shear-thinning” effects. At very high contact pressure and very low slide-to-roll ratios material creep effects, where the behavior of lubricated and dry contacts is similar, are implemented, while a shear stress limit is applied at very high slide-to-roll ratios. Traction predictions for a typical contact in a traction rig show good agreement with experimental traction data. Transient heat generations are time-averaged over thermal time step to compute time-varying temperature fields in the bearing, which alter properties of bearing materials, operating bearing geometry, and rheology of the lubricant. As the transient solutions converge to stable operating temperatures, bearing heat generation approaches the expected steady-state value. Heat generation predictions for both ball and rolling bearings are in good agreement with measured experimental data.

Instability characteristics analysis of a simply supported cylindrical shell subjected to swirling annular flow of viscous fluid

The instability characteristics of an out cylindrical shell subjected to an annular flow, where the fluid is flowing through the annulus between the inner shell and the outer shell, are investigated based on the zero-level contour method and the travelling wave solutions. The inviscid fluid-dynamic forces, related to shell vibrations, are determined by the potential flow theory. The time-mean Navier-Stokes equations are utilized to obtained steady viscous forces based on the fully developed turbulent flow theory. The Flügge's thin shell theory is used for shell motions. Adopting the zero-level contour method and the Galerkin's method, the behaviors of losing stability of the flow-shell system are given and physical reasons for the instability of the system are explained. Detailed studies are performed in order to elucidate quantificationally the effects of pre-loads related to the steady viscous forces, geometry parameters on the loss of stability. Especially, the influence of the swirl number on the instability characteristics of the system is discussed.

Mathematical modeling and the study of exchange processes in disperse boundary layer control actions

A significant interest of researchers is attracted to the effective management and forecasting of exchange processes in the boundary layer, which are key for the implementation of effective and reliable equipment. Modeling of exchange processes occurring in a high-speed dispersed boundary layer with external influences is a very difficult task. Mathematical modeling allows us to develop reliable devices and engines for the fields of aircraft, energy, shipbuilding with minimal costs for its creation. Despite the interest of numerous groups of researchers around the scientific projects and a large number of works, the current theory of the boundary layer is imperfect. This may be due to several circumstances: firstly, the theory of single-phase turbulent flows of continuous media is far from being completed, secondly, turbulent flows with dispersed impurities in the form of particles greatly complicate the already intricate flow pattern. Interest in dispersed flows is particularly relevant due to the fact that almost all gas-dynamic flows contain a certain concentration of particles, and their impact can provoke significant changes in the structure of the boundary layer and affect the intensity of exchange processes. The article proposes a two-fluid mathematical model describing the motion of a high-speed dispersed boundary layer on a surface with hemispherical damping cavities. The use of hemispherical damping cavities allows to reduce turbulent exchange in the boundary layer, which makes it possible to control the intensity of metabolic processes. The possibility of a significant reduction of turbulent heat transfer and friction in the dispersed boundary layer is established. The proposed method of impact on the turbulent transport in the boundary layer will improve the equipment and installations, including GTU and GTE used in various industries of our country, such as energy, aircraft, shipbuilding.

On the Mechanism of Turbulent Shear Flows

As a result of our analysis of some facts of turbulent flows, whose explanation is beyond the scope of existing semiempirical theories, in particular, our estimate of the effective roughness height in pipes with distributed roughness characterized by two or more length scales, we present a version of the theory of turbulent flows in channels with smooth and rough walls with a unified mechanism of the dynamic interaction (friction mechanism) of a turbulent flow with its boundaries—the channel walls or external laminar flow. We have derived the expressions for a generalized law of friction that describe a turbulent flow at all admissible Reynolds numbers from the regime of flow with smooth walls to the regime with a complete manifestation of roughness elements and for sand roughness consistent with Nikuradse’s experimental data. One of the conclusions of the theory is the assertion that the only source of turbulence for turbulent flows in channels and jets are the vortices forming near the walls of channels and at the free boundaries of turbulent jets, and only through these vortices is the kinetic energy from the mean flow converted to the energy of turbulent pulsations. The difference between the mechanisms of the laminar and turbulent flow regimes can be clearly represented by Eq. (24).

Constitutive theory of inhomogeneous turbulent flow based on two-scale Lagrangian formalism

A self-consistent closure theory is developed for inhomogeneous turbulent flow, which enables systematic derivations of the turbulence constitutive relations without relying on any empirical parameters. The double Lagrangian approach based on the mean and fluctuation velocities allows us to describe a wide variety of correlations in a consistent manner with both Kolmogorov’s inertial-range scaling and general-covariance principle.

A numerical analysis and experimental investigation of three oil grooves sleeve bearing performance

PurposeThis paper aims to reveal the cavitation characteristics of three oil wedges sleeve bearing and set the theoretical and experimental basis for defining the oil film boundary condition.Design/methodology/approachComputational fluid dynamics model of three oil wedges sleeve bearings based on the Navier–Stokes equation is set using Fluent considering turbulent situation and two-phase flow theory. The cavitation characteristics of bearing is investigated by taking pictures of experiment.FindingsThe rupture region of oil film and the contours of air volume fraction increase distinctly with the increase of rotating speed and the decrease of input pressure. The critical rotating speed of cavitation occurrence and oil film pressure increases with the increase of input pressure. The change trend of experiment cavitation with the rotating speed and input pressure is consistent with theoretical cavitation in general.Originality/valueThe finite element model of three oil wedges sleeve bearings is established based on the Navier-Stokes calculation equation of the fluid, two-phase flow theory and turbulent model. Sleeve bearing is transparent, the pictures of cavitation can be easily taken by high-speed camera, the cavitation characteristics of bearing is studied by experiment. The cavitation performance of three oil wedges bearings is studied with the change of input pressure and rotating speed, the change trend is basically consistent for theory and experiment. The study on critical rotating speed of cavitation occurrence is benefit for defining the oil film boundary condition.