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We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the 'dynamo problem', i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., 'broken ergodicity'. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the 'dynamo problem'. [ABSTRACT FROM AUTHOR]

The impact of particle addition jets on the flow field in natural gas pipelines was investigated, and the structural information of the flow field at different flow velocities in a symmetric jet flow was analyzed via numerical simulation. The results of coherent structures in the high-pressure natural gas pipeline reveal vortex structures of varying sizes both upstream and downstream of the jet flow. To determine the spatial distribution of the main vortex structures in the flow field, proper orthogonal decomposition (POD) mode analysis was performed on the unsteady numerical results. Moreover, the detailed spatial characteristics of the coherent vortex structures represented by each mode were obtained. The results indicate that the large-scale vortex structures within the pipeline are balanced and stable, with their energy increasing as the jet flow velocity increases. Additionally, higher-order modes exhibit significant shedding of small-scale vortex structures downstream of the jet flow. In this research, coherent structures present in symmetric particle addition jets are provided, offering theoretical support for future investigations on the distribution of particle image velocimetry (PIV) flowmeters. [ABSTRACT FROM AUTHOR]

The effects of the coolant pulsation and the plasma aerodynamic actuation (PAA) on the film cooling are herein explored via large eddy simulations. The electrohydrodynamic force derived from the PAA was solved through the phenomenological plasma model. The Strouhal number of the sinusoidal coolant pulsation and the averaged pulsation blowing ratio were 0.25 and 1.0, respectively. Comprehensive analyses were carried out on the time-averaged flow fields, and the results reveal that the pulsed cooling jet might cause a deeper penetration into the crossflow, and this phenomenon could be remarkably mitigated by the downward force of the PAA. Comparing steady film cooling to pulsed film cooling revealed a modest 15.1% reduction in efficiency, while the application of the dielectric barrier discharge plasma actuator (DBDPA) substantially enhanced the pulsed film cooling efficiency by 42.1%. Moreover, the counter-rotating vortex pair (CRVP) was enlarged and lifted off from the wall more poorly due to the coolant pulsation, and the PAA weakened the detrimental lift-off effect and entrainment of the CRVP. Then, the spatial–temporal development of the coherent structures was figured out by the alterations in the centerline temperature, reflecting the formation of the intermittent coherent structures rather than hairpin vortices due to the coolant pulsation, and their size and upcast behaviors were reduced by the PAA; thus, the turbulent integration of the coolant with the crossflow was suppressed fundamentally. Finally, the three-dimensional streamlines confirmed that the coherent structure dynamic behaviors were significantly regulated by the PAA for alleviating the adverse influences of the coolant pulsation. In summary, the PAA can effectively improve the pulsed film cooling efficiency by controlling the spatial–temporal development of the dominant coherent structures. [ABSTRACT FROM AUTHOR]

In order to study the evolution principle of the coherent structure in the low flow rate runaway condition, the pump turbine of a certain pumped storage power plant was employed. The transient dynamic stress of the runner was numerically simulated and examined in this study in order to analyze the coherent structure of the vortex and the stability of the grid connection during the transition process. Based on the realizable k-ε turbulent model, the unsteady flow of the whole pump turbine channels was calculated. The results show that the flow in the runner channels presents with a turbulence state, and with many different scales vortices. These vortex structures are mainly distributed in the inlet region of the blade, the area of the blade trailing edge and the middle section of the runner channels. These vortex structures affect the distribution of the blade pressure load. Moreover, the vortex structure at the inlet of the runner depends on the change in the attack angle. In the flow region formed at the outlet of the blade near the suction surface and the runner cone, the blade has a limited effect on the fluid; thus, the vortex structure depends on the Coriolis force and the centrifugal force joint action. The evolution of these vortex structures will have a greater impact on the grid connection of the power station. During the operation of the power station, it is necessary to reduce the time of transitional conditions so that the power station can operate efficiently. [ABSTRACT FROM AUTHOR]

We continue our study of the transition of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence from non-equilibrium initial conditions to equilibrium using long-time numerical simulations on a 128 3 periodic grid. A Fourier spectral transform method is used to numerically integrate the dynamical equations forward in time. The six runs that previously went to near equilibrium are here extended into equilibrium. As before, we neglect dissipation as we are primarily concerned with behavior at the largest scale where this behavior has been shown to be essentially the same for ideal and real (forced and dissipative) MHD turbulence. These six runs have various combinations of imposed rotation and mean magnetic field and represent the five cases of ideal, homogeneous, incompressible, and MHD turbulence: Case I (Run 1), with no rotation or mean field; Case II (Runs 2a and 2b), where only rotation is imposed; Case III (Run 3), which has only a mean magnetic field; Case IV (Run 4), where rotation vector and mean magnetic field direction are aligned; and Case V (Run 5), which has non-aligned rotation vector and mean field directions. Statistical mechanics predicts that dynamic Fourier coefficients are zero-mean random variables, but largest-scale coherent magnetic structures emerge and manifest themselves as Fourier coefficients with very large, quasi-steady, mean values compared to their standard deviations, i.e., there is 'broken ergodicity.' These magnetic coherent structures appeared in all cases during transition to near equilibrium. Here, we report that, as the runs were continued, these coherent structures remained quasi-steady and energetic only in Cases I and II, while Case IV maintained its coherent structure but at comparatively low energy. The coherent structures that appeared in transition in Cases III and V were seen to collapse as their associated runs extended into equilibrium. The creation of largest-scale, coherent magnetic structure appears to be a dynamo process inherent in ideal MHD turbulence, particularly in Cases I and II, i.e., those cases most pertinent to planets and stars. Furthermore, the statistical theory of ideal MHD turbulence has proven to apply at the largest scale, even when dissipation and forcing are included. This, along with the discovery and explanation of dynamically broken ergodicity, is essentially a solution to the 'dynamo problem'. [ABSTRACT FROM AUTHOR]

The fluid stress or flow-induced vibration of annular gap flow always has some influence on the stable working conditions of a hydraulic machine. A time-averaged analysis of flow may not have to explicitly acknowledge these factors. Accordingly, a finite-axial-length annular gap was measured via particle image velocimetry (PIV), with inner boundary motion and a stable outer boundary. As a statistic result regarding the fluid stress, the Reynolds stresses soared in the first region, were sustained in the middle region, but decreased at last. The flow had a higher convective transportation intensity in the radial direction than in other directions. Flow diagnostics were also performed by proper orthogonal decomposition (POD). As a result, the coherent structures were found. Then, the power spectrum density (PSD) functions were also calculated for finding the flow-induced vibration characteristics; the functions had high amplitude in the low-frequency domain and low amplitude in the high-frequency domain, with an order of magnitude between the two amplitudes of 10−1 to 10−2. In addition, the frequency was higher at a smaller gap width in the middle-frequency domain, but the condition was the opposite in the high-frequency domain. In conclusion, the fluid stresses were changeable and uneven along the flow direction, and flow-induced vibration obviously existed. Remarkably, the turbulence characteristics of the annular gap flow were not "laminar approximating," while the diameter ratio of the gap was 0.6 to 0.8. [ABSTRACT FROM AUTHOR]

In order to optimize the use of compact porous media as flow and heat transfer devices, it is imperative to understand those coherent structures of the associated flow that generate and sustain turbulence. Given the deficiency of data regarding this area in the literature, this study has been carried out to fill this need. To this end, a series of particle image velocimetry measurements were conducted to capture a turbulent flow field bounded by a model permeable medium of 85% porosity. The bulk Reynolds numbers based on the bulk velocity through the entire flow domain and the depth of flow over the permeable boundary are approximately 5.0 × 103 and 2.0 × 104. By applying velocity gradient eigenanalysis, quadrant decomposition, multi-point correlations, and proper orthogonal decomposition, requisite information about the coherent structures of the flow field is extracted. The results indicate the existence of spatial structures whose order, size, and orientation are dependent on the Reynolds number and location along the permeable boundary. While the largest scales are marked by sweeps, ejections, and high vortex activity, there is evidence of inward and outward interactive events at the upstream portions of the permeable boundary layer flow. This work helps to clarify some observations made on turbulent flow over the compact permeable boundary. [ABSTRACT FROM AUTHOR]

In this paper, an improved delayed detached eddy simulation method combined with shear-stress transport (SST) model was used to study the three-dimensional turbulent characteristics in a small rotary engine with a peripheral port. The turbulent characteristics including instantaneous velocity, turbulent fluctuation, coherent structure and velocity circulation were analysed based on a dynamic model of the small rotary engine. Three sets of conclusions on the basis of computational results were obtained. First, it was found that large-scale vortex structures with high intensity were distributed in the center of the chamber in the intake process and broke into lots of small vortex structures in the compression process. Second, flow stability in the X direction decreased from the leading to the trailing in the small rotary engine. The fluctuation velocity of the Y direction showed the paraboloid feature and its peak position moved from the mid-back to the middle of the chamber during the operation process. Third, during the intake process, two vortices occurred in the cross section parallel to the covers and were located at the leading and trailing of the cross section, respectively. Compared to the intake process, more vortices occur at cross sections which were far away from the central section during the compression process. [ABSTRACT FROM AUTHOR]

Pulsed waterjet can break rocks effectively by taking advantage of the water hammer effect, and is thus widely used in mining, petroleum, and natural gas fields. With the aim to further clarify the flow field characteristics of pulsed jets induced by a Helmholtz oscillator, large eddy simulation was conducted under different operating pressures. The velocity distribution, mean flow field, and the coherent structure were examined using the oscillators of different cavity lengths and diameters. The results clearly showed that the major frequency of jet pulsation gradually increased with the increase of operating pressure. A stable periodic velocity core was formed at the outlet of the Helmholtz oscillator, while the external flow field was subjected to periodic impact. As a result, the ambient fluid was strongly entrained into the jet beam. With the increase of the cavity length, the length of the core segment decreased while the energy loss caused by the cavity increased, which was also accompanied by a rapid attenuation of the axial velocity at the jet outlet. The coherent structure of the jet in the oscillator with small cavity diameter was more disordered near the nozzle outlet, and the vortex scale was larger. The effect of cavity diameter can be reflected in the feedback modulation of the jet in the cavity. Compared with the conical nozzle, the length of the core section of the jet was shorter, but the jet had better bunching, a smaller diffusion angle, and better mixing performance. These results provide a further understanding of the characteristics of pulsed water jet for better utilizations in the fields of energy exploitation. [ABSTRACT FROM AUTHOR]

Highlights from the article: Keywords: turbulence; statistical mechanics; intermittency; coherent structure; multi-scale problem; self-organisation; bifurcation; non-locality; scaling; multifractal Chliamovitch and Thorimbert [[2]] present a new method of dealing with non-locality of turbulence flows through the formulation of the bilocal kinetic equation for pairs of particles. Based on a maximum-entropy-based generalisation of Boltzmann's assumption of molecular chaos, they utilise the two-particle kinetic equations and derive the balance equations from the bilocal invariants to close their kinetic equations. By solving the population balance equation and CFD simulations, they elucidate the effects of the impeller type - six-blade Rushton turbine and three-blade high-efficiency impeller - and droplet breakage coalescence (dispersion) on drop size distribution.

The skin friction consumes some of the energy when a train is running, and the coherent structure plays an important role in the skin friction. In this paper, we focus on the coherent structure generated near the vent of a train. The intention is to investigate the effect of the vent on the generation of coherent structures. The ventilation system of a high-speed train is reasonably simplified as a T-junction duct with vertical blades. The velocity signal of the cross duct was measured in three different sections (upstream, mid-center and downstream), and then the coherent structure of the denoised signals was analyzed by continuous wavelet transform (CWT). The analysis indicates that the coherent structure frequencies become abundant and the energy peak decreases with the increase of the velocity ratio. As a result, we conclude that a higher velocity ratio is preferable to reduce the skin friction of the train. Besides, with the increase of velocity ratio, the dimensionless frequency St of the high-energy coherent structure does not change obviously and St = 3.09 × 10−4–4.51 × 10−4. [ABSTRACT FROM AUTHOR]