Theory Of Turbulent Flow Research Articles

Potential landscape and flux field theory for turbulence and nonequilibrium fluid systems

Turbulence is a paradigm for far-from-equilibrium systems without time reversal symmetry. To capture the nonequilibrium irreversible nature of turbulence and investigate its implications, we develop a potential landscape and flux field theory for turbulent flow and more general nonequilibrium fluid systems governed by stochastic Navier–Stokes equations. We find that equilibrium fluid systems with time reversibility are characterized by a detailed balance constraint that quantifies the detailed balance condition. In nonequilibrium fluid systems with nonequilibrium steady states, detailed balance breaking leads directly to a pair of interconnected consequences, namely, the non-Gaussian potential landscape and the irreversible probability flux, forming a ‘nonequilibrium trinity’. The nonequilibrium trinity characterizes the nonequilibrium irreversible essence of fluid systems with intrinsic time irreversibility and is manifested in various aspects of these systems. The nonequilibrium stochastic dynamics of fluid systems including turbulence with detailed balance breaking is shown to be driven by both the non-Gaussian potential landscape gradient and the irreversible probability flux, together with the reversible convective force and the stochastic stirring force. We reveal an underlying connection of the energy flux essential for turbulence energy cascade to the irreversible probability flux and the non-Gaussian potential landscape generated by detailed balance breaking. Using the energy flux as a center of connection, we demonstrate that the four-fifths law in fully developed turbulence is a consequence and reflection of the nonequilibrium trinity. We also show how the nonequilibrium trinity can affect the scaling laws in turbulence.

Research on the jet characteristics of the deflector–jet mechanism of the servo valve**Project supported by the International Science and Technology Cooperation Program of China (Grant No. 2012DFG71490).

In view of the complicated structure of the deflector–jet mechanism, a mathematical model based on the turbulent jet flow theory in the deflector–jet amplifier is proposed. Considering the energy transformation and momentum variation, an equation of the flow velocity distribution at the key fluid region is established to describe the morphological changes of the fluid when it passes through the deflector and jets into the receiver. Moreover, the process is segmented into four stages. According to the research results, the oil enters the deflector and impinges with the side wall. Then one part of the oil’s flow velocity decreases and a high pressure zone is formed by the oil accumulation, the other part of the oil reverses out of the deflector along the side wall. Prior to entering the receiver, the flow is a kind of plane impinging jet. Virtually, the working pressure of the receiver is generated by the impact force, while the high speed fluid flows out of the receiver and forms a violent vortex, which generates negative pressure and causes the oil to be gasified. Compared with the numerical simulation results, the turbulent jet model that can effectively describe the characteristics of the deflector–jet mechanism is accurate. In addition, the calculation results of the prestage pressure characteristic have been verified by experiments.

Influence of Plasma Pressure Fluctuation on RF Wave Propagation**supported by the National Basic Research Program of China (No. 2014CB340205) and National Natural Science Foundation of China (No. 61301173)

Pressure fluctuations in the plasma sheath from spacecraft reentry affect radio-frequency (RF) wave propagation. The influence of these fluctuations on wave propagation and wave properties is studied using methods derived by synthesizing the compressible turbulent flow theory, plasma theory, and electromagnetic wave theory. We study these influences on wave propagation at GPS and Ka frequencies during typical reentry by adopting stratified modeling. We analyzed the variations in reflection and transmission properties induced by pressure fluctuations. Our results show that, at the GPS frequency, if the waves are not totally reflected then the pressure fluctuations can remarkably affect reflection, transmission, and absorption properties. In extreme situations, the fluctuations can even cause blackout. At the Ka frequency, the influences are obvious when the waves are not totally transmitted. The influences are more pronounced at the GPS frequency than at the Ka frequency. This suggests that the latter can mitigate blackout by reducing both the reflection and the absorption of waves, as well as the influences of plasma fluctuations on wave propagation. Given that communication links with the reentry vehicles are susceptible to plasma pressure fluctuations, the influences on link budgets should be taken into consideration.

A unified theory for turbulent wake flows described by eddy viscosity

In this paper, we consider the conservation laws for the far downstream wake equations described by eddy viscosity. A basis of conserved vectors is constructed. The well-known conserved quantities for the turbulent classical wake and the turbulent wake of a self-propelled body are obtained by integrating the corresponding conservation law across the wake and imposing the boundary conditions. For the wake of a self-propelled body the additional condition that the drag on the body is zero and is required to obtain the conserved quantity. A third conservation law, which possibly belongs to another type of wake, is discovered. The Lie point symmetry associated with the conserved vector is used to obtain the invariant solution and a typical velocity profile for this wake is provided. This wake appears to have common properties with the other two well-known wakes. We then analyse the invariant solutions to all three wake problems and prove that a simple mathematical relationship exists between them thus unifying the theory for turbulent wake flows.

Comment on "Statistical symmetries of the Lundgren-Monin-Novikov hierarchy".

The article by M. Wacławczyk et al. [Phys. Rev. E 90, 013022 (2014)] proposes two new statistical symmetries in the classical theory for turbulent hydrodynamic flows. In this Comment, however, we show that both symmetries are unphysical due to violating the principle of causality. In addition, they must get broken in order to be consistent with all physical constraints naturally arising in the statistical Lundgren-Monin-Novikov (LMN) description of turbulence. As a result, we state that besides the well-known classical symmetries of the LMN equations no new statistical symmetries exist. Finally, we criticize the relation between intermittency and global symmetries as it is presented throughout that study.

Effects of Pressure Variation on Polarization Properties of Obliquely Incident RF Waves in Re-Entry Plasma Sheath

Synthesizing the compressible turbulent flow theory and plasma electromagnetic (EM) theory together, a novel method connecting pressure variation and relative permittivity of re-entry plasma sheath is developed. Using this method and transmission line analogy, effects of pressure variation on polarization properties of obliquely incident EM waves at GPS frequency and Ka frequency is studied. Numerical results indicate that effects in different conditions are various. When electron density is lower than $10^{18}~\text{m}^{\mathrm {-3}}$ , influences of pressure variation are obvious at GPS frequency, while Ka frequency is feeble. For GPS frequency, effects enlarge with the increase in incident angle, but reduce with the increase in collision frequency and electron density. Ka frequency has more advantages on mitigating the disturbances of pressure variations in this situation. While in the opposite situation, influences are more remarkable at Ka frequency. Considering that GPS wave rapidly attenuates in the sheath when electron density is higher than $10^{18}~\text{m}^{\mathrm {-3}}$ and Ka wave does not, Ka frequency is an effective way to mitigate the blackout during the re-entry process after its shortcomings on polarization alteration have been carefully considered.

Break-up of bubble clusters in turbulent flow—Theory

The behaviour of bubble clusters in turbulent conditions has been studied theoretically. The cluster behaviour was modelled based on concept drawn from the related field of bubble breakup. It was assumed that the bubbles were bridged by particles, so the cohesive strength was determined by the capillary force between the bubbles and the particles. Two different theories were investigated for the disruptive force from the turbulent liquid: the shear rate hypothesis of Camp and Stein (1943), and the turbulent fluctuation model arising from Kolmogorov's theory of isotropic turbulence (Kolmogorov, 1941). It was found that neither method is applicable in the fragmentation stage. However, in the equilibrium stage, an equation derived from Camp and Stein's theory was more realistic than that obtained using Kolmogorov's equation.

Floating Ring Balance Analysis of Journal Floating Ring Hybrid Bearing in Turbulent Regime

An externally pressurized deep/shallow pockets hybrid journal floating ring bearing compensated by flat capillary restrictor which can meet the need of high speed rotating machinery is presented in this paper. Bases on turbulent flow theory, the equations governing the flow of inner and outer fluid film in the journal floating ring bearing are established. The control equations together with the pressure boundary condition and the restrictor flow equation are solved by using the Finite Element Method. The balance of floating ring is achieved by adjusting ring-to-shaft speed ratio, inner film radial clearance and inner film eccentricity ratio. It can be seen from simulation results that the ring-to-shaft speed ratio and inner film clearance vary slightly and the floating ring can keep balance under different speed and eccentricity ratio. The variation of static and dynamic performance with eccentricity and rotational speed are calculated and analyzed based on floating ring balance.

Modelling of surface tension force for free surface flows in ISPH method

PurposeThe purpose of this paper is to show how a surface tension model and an eddy viscosity based on the Smagorinsky sub‐grid scale model, which belongs to the Large‐Eddy Simulation (LES) theory for turbulent flow, have been introduced into ISPH (Incompressible smoothed particle hydrodynamics) method. In addition, a small modification in the source term of pressure Poisson equation has been introduced as a stabilizer for robust simulations. This stabilization generates a smoothed pressure distribution and keeps the total volume of fluid, and it is analogous to the recent modification in MPS.Design/methodology/approachThe surface tension force in free surface flow is evaluated without a direct modeling of surrounding air for decreasing computational costs. The proposed model was validated by calculating the surface tension force in the free surface interface for a cubic‐droplet under null‐gravity and the milk crown problem with different resolution models. Finally, effects of the eddy viscosity have been discussed with a fluid‐fluid interaction simulation.FindingsFrom the numerical tests, the surface tension model can handle free surface tension problems including high curvature without special treatments. The eddy viscosity has clear effects in adjusting the splashes and reduces the deformation of free surface in the interaction. Finally, the proposed stabilization appeared in the source term of pressure Poisson equation has an important role in the simulation to keep the total volume of fluid.Originality/valueAn incompressible smoothed particle hydrodynamics is developed to simulate milk crown problem using a surface tension model and the eddy viscosity.

SHARK-SKIN SURFACES FOR FLUID-DRAG REDUCTION IN TURBULENT FLOW: A REVIEW

The skin of fast-swimming sharks exhibits riblet structures aligned in the direction of flow that are known to reduce skin friction drag in the turbulent-flow regime. Structures have been fabricated for study and application that replicate and improve upon the natural shape of the shark-skin riblets, providing a maximum drag reduction of nearly 10 per cent. Mechanisms of fluid drag in turbulent flow and riblet-drag reduction theories from experiment and simulation are discussed. A review of riblet-performance studies is given, and optimal riblet geometries are defined. A survey of studies experimenting with riblet-topped shark-scale replicas is also given. A method for selecting optimal riblet dimensions based on fluid-flow characteristics is detailed, and current manufacturing techniques are outlined. Due to the presence of small amounts of mucus on the skin of a shark, it is expected that the localized application of hydrophobic materials will alter the flow field around the riblets in some way beneficial to the goals of increased drag reduction.

The Basis of an Industry-standard Aerodynamic Computation and its Theoretical Basis with Inferences and Applications

“The PNS method is in very widespread use; indeed, it forms the basis of an industry-standard computer program, which is used by virtually all major aerodynamics laboratories and companies.”(John D. Anderson Jr. American aerodynamicist 2006). Several PNS Eqs. With different slightly viscous terms and different name were suggested between the late 1960s and the late 1970s, in which the simplified NS Eqs. suggested by Z.Gao in 1967 was called by F.G.Zhuang(Academician, China) etal as first PNS. In early studies of PNS, it is not very clear what kind of basic flow is described by PNS Eqs., there is no basic fluid theory corresponding to PNS. The author presented a PNS's fluid basic theory: viscous/inviscid interacting shear flow (ISF) theory (including laminar, perturbed and turbulent flow theories). ISF consists of viscous shear layer and neighboring outer inviscid flow. Main points of ISF theory and inferences are as follows. Both the flow law and mathematical definition of ISF's viscous layer and ISF's governing Eqs. written in ISF's optimal coordinates, that is a fitted dividing flow surface orthogonal coordinates, are presented. The evolution laws of physical scales of ISF's viscous layer flow are solved, which do generate small scale structure and then do cause local sudden increase of several physical quantities(such as heat flux etc.). The PNS Eqs. can be simplified further on the dividing flow surface and the resultant Eqs. are called dividing flow surface criteria, whose two special cases are wall-surface criteria (WSC)for solutions of NS- and Euler Eqs. NS numerical solutions ought to satisfy WSC, which are proved numerically by some computations. People can obtain NS grid independent solution by operation of NS numerical solutions satisfying progressively the WSC. Especially, this criteria can evaluate the departure of NS numerical solutions from NS true solution by just one time NS calculation on one set of grid and are theoretical methods evaluating creditability of NS numerical solutions, and based on that some people suggest that the WSC method may be used as an ingenious substitute for the grid convergence analysis method in common use and that the WSC method and ISF theory are called Gao's criteria method and Gao's ISF theory, respectively. Some applications of ISF theory and its inferences to CFD are fruitful and creativeness and then research on this aspect is worth deepening and widening.

Phase transition to super-rotating atmospheres in a simple planetary model for a nonrotating massive planet: Exact solution

An energy-enstrophy model for the equilibrium statistical mechanics of barotropic flow on a massive nonrotating sphere is introduced and solved exactly for phase transitions to rotating solid-body atmospheres when the kinetic energy level is high. Unlike the Kraichnan theory which is a Gaussian model, we substitute a microcanonical enstrophy constraint for the usual canonical one, a step which is based on sound physical principles. This yields a spherical model with zero total circulation, microcanonical enstrophy constraint, and canonical constraint on energy, leaving angular momentum free as is required for any model whose objective is to predict super-rotation in planetary atmospheres. A closed-form solution of this spherical model, obtained by the Kac-Berlin method of steepest descent, provides critical temperatures and amplitudes of the symmetry-breaking rotating solid-body flows. The critical values depend linearly on the relative enstrophy, with proportionality constant derived from the spectrum of the Laplace-Beltrami operator on the sphere, as expected within an energy-enstrophy theory for macroscopic turbulent flows. This model and its results differ from previous solvable models for related phenomena in the sense that the model is not based on a mean-field assumption.

A Study on the Pier Scour and Seismic Capacity Assessment of Bridges

Climate changes in recent years have caused a trend of increasing rainfall in Taiwan. In addition, the rivers of Taiwan flow down steep slopes with rapid currents, and the flow is extremely turbulent in particular segments of the rivers, causing pile scours that affect the stability of bridges in the area. Based on turbulent flow theory, this paper establishes an estimation model for the pier scour depth limit of suitable bridges crossing rivers in Taiwan, according to the characteristics of the stagnation point and separation point of fluid mechanics. A bridge in northern Taiwan is analyzed according to measurements, confirming that the channel scour formula suggested in this paper demonstrates sufficient accuracy. Additionally, lateral pushover analysis is performed on the bridge to understand the seismic durability of the bridge structure following a scour.

The Matching of Flow Control and Structure Parameters for the Bitumen Foaming Technology

A new driving device is developed for precise flow control of bitumen foaming. Based on the theoretical studies like fluid dynamics, contact heat transfer, phase change, multiphase flow and turbulent flow theories, a reasonable control model for the bitumen foaming behavior is built. And the CFD simulation analysis of the model with the testing parameters is taken. The results show that the foamed bitumen outlet flow follows the quadratic curve control law with the new driving device.

Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere

The large-scale circulation of planetary atmospheres such as that of the Earth is traditionally thought of in a dynamical framework. Here we apply the statistical mechanics theory of turbulent flows to a simplified model of the global atmosphere, the quasigeostrophic model, leading to nontrivial equilibria. Depending on a few global parameters, the structure of the flow may be either a solid-body rotation (zonal flow) or a dipole. A second-order phase transition occurs between these two phases, with associated spontaneous symmetry breaking in the dipole phase. This model allows us to go beyond the general theory of marginal ensemble equivalence through the notion of Goldstone modes.

Self-Energy Closure for Inhomogeneous Turbulent Flows and Subgrid Modeling

A new statistical dynamical closure theory for general inhomogeneous turbulent flows and subgrid modeling is presented. This Self-Energy (SE) closure represents all eddy interactions through nonlinear dissipation or forcing ‘self-energy’ terms in the mean-field, covariance and response function equations. This makes the renormalization of the bare dissipation and forcing, and the subgrid modeling problem, transparent. The SE closure generalizes the quasi-diagonal direct interaction closure to allow for more complex interactions. The SE closure is applicable to flows in different geometries, is exact near maximum entropy states corresponding to canonical equilibrium, and provides a framework for deriving simpler realizable closures.

Instability Theory of Sand Ripples Formed by Turbulent Shear Flows

AbstractA theory of turbulent shear flow over a sand bed is developed, addressing the instability principle of the fluid-granular bed interface leading to the formation of ripples. The Reynolds-averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation are analyzed using a 1/7-power law of the time-averaged streamwise velocity and treating the curvilinear streamlines by the Boussinesq approximation. The integration of the RANS equations leads to a governing dynamical equation of flow over a mobile bed. A near-bed flow layer of 3.5 times the ripple height is considered being affected by the ripples. The dynamical equation of the mobile sand bed is based on the Exner’s sediment continuity equation in conjunction with the Meyer-Peter and Muller bed-load transport formula as modified to account for the effect of local bed slope attributable to bed forms. The coupled dynamical equations are then analyzed to estimate the parameters for the instability that results in the formation of ripp...

The effect of riblets in rectangular duct flow

Much is known about the benefits of surface structures which mimic the riblets found on the skin of fast swimming sharks. Structures have been fabricated for study and application which replicate and improve upon the natural shape of the shark skin riblets, providing a maximum drag reduction of nearly 10% in external turbulent fluid flow. Mechanisms of fluid drag in turbulent flow and riblet-drag reduction theories from experiment and simulation are discussed. A brief review of riblet performance studies is given, and optimal riblet geometries are defined for external flow. A discussion of the structure of internal turbulent fluid flow is provided, and existing data for riblet drag reduction benefit is presented. A flow cell for studying riblet effects in internal rectangular duct flow is discussed, and data collected using several riblet surfaces fabricated for the flow cell is presented and analyzed. A discussion of the effects of the riblets on fluid flow is given, and conclusions are drawn about the possible benefits of riblets in internal fluid flow.

A statistical theory for inhomogeneous turbulent flow formulated in the mean-Lagrangian coordinates

An analytical way for investigating the inhomogeneous turbulent flow has been proposed by introducing Lagrangian-like view. The present method is developed based on TSDIA (Two-Scale Direct Interaction Approximation) which is one of the few theoretical works for the inhomogeneous turbulent flow formulated in the Eulerian frame work and has fundamental inconsistency with the general covariance under the coordinate transformation. The present work reached certain success in the following two aspects. First, the algebraic representation for the Reynolds stress derived by the present method has been proved to be generally covariant. Second the algebraic Reynolds stress is in much better agreement with the result of a DNS of the channel flow.

Numerical simulation of sandy bed erosion by 2D vertical jet

A two-dimensional numerical model of vertical jet scour was developed based on the turbulent flow theory and jet scour mechanism. In this model, drag force acts as the main reference variable and the critical Shields number acts as the incipient motion criteria of sediment. The morphological change in the bed caused by bed-load transport is simulated using the moving mesh method and the suspended-load is not considered. An experiment investigating vertical clear water jet scour was conducted in the laboratory, and some effective experimental results, such as flow patterns and distribution characteristics of scour pits, were obtained. Numerical simulation of the 2D jet scour was conducted using the same parameters as were used in the flume experiment. The evolution process of the jet scour observed in the experiment was simulated by the new model; validation of the numerical model and the algorithm was conducted. Semi-empirical formulas of the characteristic length of the equilibrium scour hole were deduced based on the results of the experiment and simulation.