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In this paper, we investigate the regularity criterion of weak solutions to three-dimensional magneto-micropolar fluid equations with fractional dissipation. A regularity criterion is established via the third component of the velocity fields, the micro-rotational velocity fields, and the magnetic fields. [ABSTRACT FROM AUTHOR]

The use of additives, generally called DRAs (Drag Reducing Additives), has been proposed to re-duce the energy consumption in pressurized pipes. Although many research works have been conducted to analyze the effect of these additives, less attention have been devoted to the application of coatings to the pipe wall. This paper demonstrates that the application of a hydrophobic coating to the pipe can lead to a head loss reduction for a transition flow regime with moderate Reynolds number values (Re). For this purpose, an experiment was conducted to compare the performance of both coated and uncoated pipes by measuring the head losses and assessing the Drag Reduction Percentage (%DR) and the pipe friction factor (f). This was done for two Polyvinylchloride (PVC) pipes with different nominal diameters (PVC90 and PVC63). In addition, the flow velocity distribution was also measured in all these tests. The %DR decreased as the Re values increased, with the reduction being notably less pronounced for higher Re values. This could be explained by the fact that a partial slip condition is induced by the hydrophobic product. Its effect is significant for a transition regime where the effect of viscosity is important, but it becomes negligible for increasing levels of turbulence. No significant differences were observed in the flow distribution between coated and uncoated pipes, which seems to indicate that the velocity change could be limited to the near-wall viscous sublayer. The results of this work open an important research line aimed at reducing energy costs and the carbon footprint in pipe fluid distribution systems. [ABSTRACT FROM AUTHOR]

In the impinging region of opposing jets, strong mixing and significant energy dissipation are observed, but the mixing parameters invariably change with the opposed impinging strength (OIS). In this paper, the ratio of the turbulent kinetic energy (TKE) intensity at the theoretical impinging point to the nozzle exit is defined as the opposed impinging strength. To examine the mixing properties of opposed impinging jets (OIJs) in a limited field under various OIS, a renormalization group k-ε turbulence model is employed to calculate three-dimensional OIJs under various OIS. The nozzle exit diameter is set to 0.6 m, and the inlet velocity is between 0.08 and 8 m/s, so the simulations are performed at Re between 4.8 × 104 and 4.8 × 106. This work focuses on the radial and vertical jets produced after impinging as well as the distribution of the TKE, flow field, and vortices. A thorough investigation reveals that although the OIS of the jets is primarily determined by the degree of jet development, it increases with the Reynolds number. A low OIS results in less mixing in the surrounding water and relatively unconstrained jet generation; however, it also results in limited energy extraction from the fluid. Once the OIS is high, there is more mixing in the surrounding water, and more energy is also lost during impinging. The distribution of vortices in the vortex field is not only influenced by the OIS but is also very closely related to the scale of the limited mixing field. [ABSTRACT FROM AUTHOR]

In this paper, large-eddy simulation of the interaction between a shock wave and the hypersonic turbulent boundary layer in a compression corner with a fixed 34° deflection angle at Ma = 6 for different Reynolds number cases is conducted. For investigating the effects of the Reynolds number for hypersonic cases, three cases where the free-stream Reynolds numbers are 14000, 20000, and 30000/mm are selected. The averaged statistics, such as the mean velocity, the skin friction, the heat flux, and the wall pressure, are used in this paper. The flow structures in the compression ramp including the shock wave and interaction region are discussed. The decomposition of the mean skin-friction drag for the flat flow is extended to be used in the compression corner. In addition, the turbulent kinetic energy is studied through the decomposition of the mean skin-friction drag for the flat-plate region and the corner region. It is found that higher Reynolds numbers would increase the turbulent kinetic energy by turbulent dissipation at the interaction region, while higher Reynolds numbers would decrease the turbulent kinetic energy by turbulent dissipation after reattachment. In addition, it is also found that the turbulent kinetic energy is larger with a higher Reynolds number and higher turbulent kinetic energy inhibits the movement from the separation point to the inflection point (x = 0 mm), which deduces larger separation bubbles. [ABSTRACT FROM AUTHOR]

This paper presents a modal and non-modal stability analysis of the boundary layer developed on a hot plate. A liquid-type temperature-dependent viscosity model has been considered to account for the viscosity variation in the boundary layer region. The base flow is uniform and parallel to the surface at the leading edge. The base flow solution is obtained using an open-source finite volume source code. The Reynolds number (Re) is defined based on the displacement thickness (δ*) at the inlet of the computation domain. The spectral collocation method is used for spatial discretization of governing stability equations. The formulated generalized eigenvalue problem (EVP) is solved using Arnoldi's iterative algorithm with the shift and invert strategy. The global temporal eigenmodes are calculated for the sensitivity parameter β from 1 to 7, Re = 135, 270, and 405, and the span wise wave-number N from 0 to 1. The modal and non-modal stability analysis have been performed to study the least stable eigenmodes and the optimal initial conditions and perturbations (using mode superposition), respectively. The global temporal eigenmodes are found more stable for β > 0 at a given value of N. Thus, heating the boundary layer within the considered range of β (0 < β ≤ 7) leads to the stabilization of flow. The optimal energy growth increases with the β due to reducing the perturbation energy loss. Tilted elongated structures of the optimal perturbations are found near the outflow boundary. However, the length scale of the elongated cellular mode structure reduces with increase in β. The same qualitative structure of the optimal perturbations has been found at a given value of N. [ABSTRACT FROM AUTHOR]

Proper EMA-balance (balance of kinetic energy, linear momentum and angular momentum), pressure-robustness and Re-semi-robustness (Re: Reynolds number) are three important properties of Navier–Stokes simulations with exactly divergence-free elements. This EMA-balance makes a method conserve kinetic energy, linear momentum and angular momentum in an appropriate sense; pressure-robustness means that the velocity errors are independent of the pressure; Re-semi-robustness means that the constants appearing in the error bounds of kinetic and dissipation energies do not explicitly depend on inverse powers of the viscosity. In this paper, based on the pressure-robust reconstruction framework and certain suggested reconstruction operators in Linke and Merdon [Comput. Methods Appl. Mech. Eng.311 (2016) 304–326], we propose a reconstruction method for a class of non-divergence-free simplicial elements which admits almost all the above properties. The only exception is the energy balance, where kinetic energy should be replaced by a suitably redefined discrete energy. The lowest order case is the Bernardi–Raugel element on general shape-regular meshes. Some numerical comparisons with exactly divergence-free methods, the original pressure-robust reconstruction methods and the EMAC method are provided to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

A lot of studies have shown that the hydraulic characteristics of orifice plate are mainly controlled by its contraction ratio, but the thickness of square-edged orifice plate also has many impacts on energy loss characteristics. The primary objective of this study was to investigated the effects of square-edged orifice plate thickness on energy loss characteristics. In this paper, the effects of square-edged orifice plate thickness on energy loss characteristics are investigated by numerical simulation using CFD. Orifice plate discharge tunnel is axial symmetric, two dimensional numerical simulations of orifice plate discharge tunnel flow was used. The equation (9) for calculating energy loss coefficient of square-edged orifice plate energy dissipater considering the influence of thickness is proposed. The results of the present research demonstrate that energy loss coefficient decreases with increase of the orifice plate thickness. The results of model experiment are consistence with the results calculated by using rectified equation in present paper. The CFD simulations and Model experiment for the flow through an orifice plate are carried out. For square-edged orifice plate energy dissipater, the relative orifice plate thickness T/D has remarkable impacts on its energy loss coefficient ξ. The Traditional equation (8) is corrected by numerical results. The equation (9) for calculating energy loss coefficient of square-edged orifice plate energy dissipater considering the influence of thickness is proposed and this equation is available in the condition of d/D = 0.4–0.8, T/D = 0.05–0.25, and Re > 105(Re is Reynolds number). Comparing with the physical model experimental data, the relative errors of equation (9) is smaller than 15%. [ABSTRACT FROM AUTHOR]

The object of this paper is to apply spectral geometry methods to predicting pressure losses in mildly curved pipes at high Reynolds numbers. The obtained formula for the pressure losses is theoretically justified and provides good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

This paper studies the interaction of two droplets splashing on a stationary film. A source term is included in the large-density-ratio pseudopotential lattice Boltzmann method to achieve tuneable surface tension. This model offers excellent numerical accuracy and stability for droplet impacts on liquid films. The influence of the Reynolds number, Weber number, film thickness, and horizontal/vertical distance between the droplets on the crown geometry evolution is investigated. The energy loss during the impact process and the velocity discontinuity in the liquid film are the two key factors affecting the stability and evolution process of the crown. A smaller Reynolds number or thicker liquid film enhances the energy loss and decreases the velocity discontinuity, leading to more stable side and central jets. An increase in the horizontal distance between the droplets reduces the velocity discontinuity, causing the central jet height to decrease. An increase in the Weber number does not affect the energy loss or velocity discontinuity, but the lower surface tension leads to a dramatic deformation in both the central and side jets. A vertical distance between the two droplets causes an asymmetrical evolution of the crown geometry, and postpones the breakup time of the central jet. [ABSTRACT FROM AUTHOR]

The numerical simulation was carried out to investigate mechanism of the heat transfer enhancement in the fin-and-tube heat exchangers. As known, the vortex generators (VGs) were widely used to improve the thermal performance with bad flow resistance characteristics and led to bad comprehensive performance. This paper aims to expound the mechanism of thermal hydraulic characteristics and explore the effect of VGs position on the comprehensive performance. Three types of fins (type 1, type 2, and type 3) were discussed in this paper. The j factor, f factor, and performance evaluation (PEC) of three types of VGs in different positions were discussed and compared. Based on the numerical results, a detailed description of the effect of three types of VGs on the heat transfer performance and flow resistance characteristics was presented at different Reynolds number in the range between 1300 and 2000. In addition, local velocity distribution, local temperature distribution, and local pressure drop distribution were analyzed and discussed. And the effect of VG angle on the thermal performance and flow resistance was presented. It can be concluded that the main heat transfer occurred in the region before the tube, and the wake region behind the tube was harmful to improve the thermal performance and reduce the flow resistance. Besides, VG in the wake region was obviously beneficial to the enhancement of the thermal performance with less energy loss. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study on the effects of the Reynolds number (Resj = 300, 600, and 900) and porosity (ϕ = 20%–85%) on synthetic jet vortex rings impinging onto a porous wall. Laser-induced fluorescence and particle image velocimetry are used to acquire flow information qualitatively and quantitatively. When Resj is low (Resj = 300), ϕ plays a key role in determining the formation of transmitted vortex rings downstream. For the first time, a row of individual small-scale vortex rings that form at the lowest porosity (ϕ = 20%) have been observed in the synthetic jet/porous wall interaction. As Resj increases to 900, the triggered Kelvin–Helmholtz instability promotes the vorticity cancellation at a low porosity (ϕ = 30%), and thus contributes to the formation of a transmitted vortex ring. It is concluded that the vorticity cancellation is the dominant factor affecting the generation of a transmitted vortex ring. Time-averaged characteristics indicate that for a low Resj, the incoherence of the vortex ring is mainly due to the viscous effects. However, for a high Resj, it is the transition that leads to a significant enhancement in the turbulent kinetic energy. Measurements of flow macroscopic parameters show that the loss of the momentum flux exhibits a linear relationship with ϕ for all Resj, while the loss of the kinetic energy transport is nonlinearly dependent on ϕ. Incorporating ϕ, this study presents a more comprehensive similarity parameter, ϕln(Resj2 d h * 3 ), to characterize the synthetic jet/porous wall interaction. [ABSTRACT FROM AUTHOR]

Hydrofoil is widely used in hydraulic machinery, the complex shear flow and wake vortex with it can cause energy dissipation of system, affecting the stable operation of the unit. This paper takes the guide vane of a Francis turbine as the research object, and adopts the SST k − ω turbulence model to simulate the complex unsteady flow in a three-dimensional hydrofoil-channel. Entropy production theory is introduced to evaluate the energy dissipation. The effects of attack angle, gap ratio and Reynolds number on the flow loss are studied. The results show that: (1) In the hydrofoil-channel, the dissipation caused by the velocity gradient always dominates the irregular flow of fluid field. So the loss caused by the turbulent dissipation term is the main source of the loss in mainstream zone, accounting for more than 95%, while the loss caused by the viscous dissipation term accounts for only about 2% of the total loss, which can be almost ignored; (2) Changing the attack angle have a significant effect on the flow separation of the suction surface and the shear effect in the wake vortex zone, causing the energy loss to fluctuate accordingly. And 2.5° is the optimal attack angle. On this working condition, the loss decreases to the minimum value of 2.2714W/K and 0.1432 m, a decrease of 57% compared to the initial value; (3) The bottom boundary of channel suppress the development of wing tip vortex, reducing gap ratio will reduce the loss caused by wake vortex to some extent. Among them, S = 0.3 is the optimal gap ratio. Under this operating condition, the loss is 2.2941W/K and 0.1447m, a decrease of 56% compared to the initial value; (4) Affected by flow separation and wake vortexes, more than 80% of energy loss occurs in the middle and downstream zones. The effects of attack angle, gap ratio and Reynolds number on the fluid field are different. Increasing attack angle and flow velocity significantly exacerbate the flow separation and shear flow, while reducing gap ratio would inhibit the adverse flow in downstream wing tip vortex zone. • Applying entropy production theory to energy dissipation in hydrofoil fluid fields. • Discovering the dominant role of velocity fluctuations in turbulence. • The effects of attack angle, gap ratio, Reynolds number on vortex structure and energy loss are discussed, and the optimal conditions are given. [ABSTRACT FROM AUTHOR]

Rotor–stator mixers are characterized by a set of rotors moving at high speed surrounded closely by a set of stationary stators which produces high local energy dissipation. Rotor–stator mixers are therefore widely used in the process industries including the manufacture of many food, cosmetic and health care products, fine chemicals, and pharmaceuticals. This paper presents data demonstrating scale-up rules for the key power parameters; laminar power constant, Metzner–Otto constant, and Turbulent power number; for Silverson Batch rotor–stator mixers. Part 2 of this paper explores mixing times, surface aeration, and equilibrium drop sizes. These rules will allow processes involving rotor–stator mixers to be scaled up from around 1 l to over 600 l directly. [ABSTRACT FROM AUTHOR]

Rotor-stator mixers are characterized by a set of rotors moving at high speed surrounded closely by a set of stationary stators which produces high local energy dissipation. Rotor-stator mixers are therefore widely used in the process industries including the manufacture of many food, cosmetic and health care products, fine chemicals, and pharmaceuticals. This paper presents data demonstrating scale-up rules for the mixing times, surface aeration, and equilibrium drop size for Silverson batch rotor-stator mixers. Part 1 of this paper has already explored scale-up rules for the key power parameters. These rules will allow processes involving rotor-stator mixers to be scaled up from around 1 l to over 600 l directly avoiding problems such as surface aeration. [ABSTRACT FROM AUTHOR]

Abstract The heat transfer performance and friction loss of two-pass ribbed channels are highly influenced by the combined effect of rib orientation and bend shape. This paper, for the first time, numerically investigates this effect for four rib orientations, two rib angles and eight different bend shapes at Reynolds number of 30,000. The results show that the rib orientation determines the rotation direction and the transverse position of secondary flow in straight passages, while the bend shape determines the delivery of upstream secondary flow and the generation of local secondary flow. The key to heat transfer enhancement in the second passage is to promote local secondary flow using the energy from upstream secondary flow with the same rotation direction. The upstream secondary flow with the same rotation direction should be guided to a proper position, in order to enhance the dominant secondary flow in the second passage and reduce energy loss due to the undesirable secondary flow interaction. The impact of different bend shapes on the secondary flow has been summarized. The round inner corner for the bend is preferred for the significant friction loss reduction and the excellent secondary flow energy delivery capacity. Meanwhile, the secondary flow generated by the square outer corner can significantly enhance the cooling performance at the entrance of the second passage for some certain rib orientations. An optimized combination of 60° rib orientation and bend shape can either raise thermal performance factor by 10% in the second passage or reduce the friction loss by 22.3% in the whole channel, compared with the existing experimental design. By contrast, it is found cooling performance and pressure loss are not sensitive to bend shape for the rib angel of 45°. The optimized bend shape is inspired by an intuitive visualization of secondary flow evolution, which provides insight on the geometry optimization for heat and mass transfer applications. [ABSTRACT FROM AUTHOR]

Highlights • 2D RANS simulation sufficient to resolve turbulence in a stirred autoclave. • Simulation data can be used with a correlation function to predict the mean droplet size. • Minor modification to the stirred tank Reynolds Number improves correlation to pipes. • Simulation data can be used to improve the correlation between pipes and autoclaves. Abstract The prediction of droplet sizes in emulsions is important for fields ranging from the chemical process industry to emergency planning in the event of an underwater oil release. Typically scale models have needed to be built and the results scaled up, but as computational resources have grown and turbulence models have matured it has become possible to use computational fluid dynamics (CFD) to simulate the behaviour of the fluid/s. While direct simulation of multiphase breakup at high Reynolds number is currently computationally impractical, this paper looks into the use of CFD along with a correlation function based on maximum turbulent kinetic energy dissipation rate to predict the Sauter mean diameter of droplets in a 1 in. baffle-and-vane type autoclave. The results show that using a RNG-k ∊ turbulence model with a simplified 2D geometry gave droplet sizes within 26.2 μm of the Sauter mean diameter observed in experiments with no additional tuning of parameters. Correlating pipe and autoclave flows through the Reynolds number and the turbulent kinetic energy dissipation rate was also investigated. Using the traditional definitions of the Reynolds numbers the correlation is poor, the coefficient of determination of the linear fit to the log-log data is 0.64. The first modification replaced the diameter of the blade as characteristic length with the tip swept circumference which increased the coefficient of determination to 0.960. A further modification using data obtained from the turbulent fields of the simulation showed a significant improvement with the coefficient of determination increasing to 0.988. [ABSTRACT FROM AUTHOR]

This paper is devoted to the stability analysis of the Lamb-Oseen vortex in the regime of high circulation Reynolds numbers. When strongly localized perturbations are applied, it is shown that the vortex relaxes to axisymmetry in a time proportional to Re2/3, which is substantially shorter than the diffusion time scale given by the viscosity. This enhanced dissipation effect is due to the differential rotation inside the vortex core. Our result relies on a recent work by Li et al. (Pseudospectral and spectral bounds for the Oseen vortices operator, 2017, arXiv:1701.06269), where optimal resolvent estimates for the linearized operator at Oseen’s vortex are established. A comparison is made with the predictions that can be found in the physical literature, and with the rigorous results that were obtained for shear flows using different techniques. [ABSTRACT FROM AUTHOR]

The hierarchical shell models of turbulence including a spatial dimension, namely, spatiotemporal tree models, reproduce the intermittent behavior of Navier-Stokes equations in both space and time dimensions corresponding to high Reynolds number turbulent flows. This model is used, for the first time in this paper, in a one-dimensional flow zone containing a dispersed-phase particle that can be used in the study of dispersed-phase flows. In this paper, a straightforward method has been used to introduce discrete phase into the spatiotemporal tree model that leads to an increased amount of turbulent energy dissipation rate in the vicinity of the discrete phase. The effects of particle insertion and particle size on the turbulent energy dissipation rate are demonstrated. Moreover, the space-scale behavior of the time-averaged turbulent energy dissipation rate in the presence of dispersed phase is demonstrated by means of continuous wavelet transform. [ABSTRACT FROM AUTHOR]

Anomalous enstrophy dissipation of incompressible ows in the inviscid limit is a significant property characterizing two-dimensional turbulence. It indicates that the investigation of nonsmooth incompressible and inviscid ows contributes to the theoretical understanding of turbulent phenomena. In the preceding study [J. Nonlinear Sci., 26 (2016), pp. 1525-1570], a unique global weak solution to the Euler-α equations, which is a regularized Euler equation, for point-vortex initial data is considered, and thereby it has been shown that, as α→ 0, the evolution of three point vortices converges to a self-similar collapsing orbit dissipating the enstrophy in the sense of distributions at the critical time. In the present paper, to elucidate whether this singular orbit can be constructed independently on the regularization method, we consider a functional generalization of the Euler-α equations, called the Euler-Poincaré models, in which the incompressible velocity field is dispersively regularized by a smoothing function. We provide a sufficient condition for the existence of the singular orbit, which is applicable to many smoothing functions. As examples, we confirm that the condition is satisfied with the Gaussian regularization and the vortex blob regularization that are both utilized in the numerical scheme solving the Euler equations. Consequently, the enstrophy dissipation via the collapse of three point vortices is a generic phenomenon that is not specific to the Euler-α equations but universal within the Euler-Poincaré models. [ABSTRACT FROM AUTHOR]

Low Kapitza liquids, such as mineral or vegetable oils, have a low surface tension and a high viscosity. In these liquids, capillary forces and extensional viscous dissipation play an equal role in damping interface deformation, resulting in a configuration which challenges the long wavelength assumption at the origin of low-dimensional models for falling films. This paper presents time-resolved 2D thickness measurements of a vertical falling film of Dipropilene Glycol ( Ka = 3.7 ± 2 % ) using the light absorption technique. The test cases are in the low Reynolds number regime ( Re = 1 – 6 ), with a flow rate pulsing at frequencies in the range f p = 12 – 24 Hz . Different liquid film responses to the perturbation are reported, including growing waves, fully developed traveling waves and sinusoidal waves under period doubling instability. For the fully developed waves, simple dimensionless correlations for wave celerity, wavelength and wave profiles are proposed using the Skhadov scaling. The wave characteristics are compared to those of 2D waves in high Kapitza liquid films, as described by Nosoko’s correlation (Nosoko et al., 1996). [ABSTRACT FROM AUTHOR]

While large-scale motions are most energetic in the logarithmic region of a high-Reynolds-number turbulent boundary layer, they also have an influence in the inner-region. In this paper we describe an experimental investigation of manipulating the large-scale motions and reveal how this affects the turbulence and skin-friction drag. A boundary layer with a friction Reynolds number of 14 400 is controlled using a spanwise array of nine wall-normal jets operated in an on/off mode and with an exit velocity that causes the jets in cross-flow to penetrate within the log-region. Each jet is triggered in real-time with an active controller, driven by a time-resolved footprint of the large-scale motions acquired upstream. Nominally, the controller injects air into large-scale zones with positive streamwise velocity fluctuations; these zones are associated with positive wall-shear stress fluctuations. This control scheme reduced the streamwise turbulence intensity in the log-region up to a downstream distance of more than five times the boundary layer thickness, δ , from the point of actuation. The highest reduction in spectral energy—more than 30%—was found for wavelengths larger than 5 δ in the log-region at 1.7 δ downstream of actuation, while scales larger than 2 δ still comprised more than 15% energy reduction in the near-wall region. In addition, a 3.2% reduction in mean skin-friction drag was achieved at 1.7 δ downstream of actuation. Our reductions of the streamwise turbulence intensity and mean skin-friction drag exceed a base line control-case, for which the jet actuators were operated with the same temporal pattern, but not synchronised with the incoming large-scale zones of positive fluctuating velocity. [ABSTRACT FROM AUTHOR]

A comprehensive knowledge of energy dissipation during the accelerations and decelerations in transient flow is essential to develop robust and accurate hydraulic transient solvers. Currently, most transient solvers are not accurate enough to describe the physical phenomenon, tending to underestimate observed energy dissipation. The current paper aims to contribute to a better understanding of transient flow by measuring instantaneous velocities using 2D particle image velocimetry (PIV) and discussing key features of the mean and of the turbulent flow. Measurements were carried out at the middle section of a coiled copper pipe for Reynolds and Dean numbers of 7,000 and 1,040, respectively. In steady-state flow, the time-averaged velocity profiles have shown a strong asymmetry, with maximum axial velocity in the outer bend region of the pipe, caused by the centrifugal force. During transient flow, the ensemble-averaged velocity profiles have clearly shown regions with strong gradients near the pipe wall and reverse flow. The direction of flow is firstly reversed in the inner bend region of the pipe. The unsteady wall shear stress is different for the outer and inner wall, and is lower than in the steady state, confirming that energy dissipation cannot be estimated based on steady-state formulae for the wall shear stress. [ABSTRACT FROM AUTHOR]

This paper presents a novel numerical model for incompressible flows on unstructured hybrid grids by combining the pressure-implicit with splitting of operator (PISO) algorithm and volume-integrated average and point value-based multimoment (VPM) method. Implementing the spatial discretization of VPM to the PISO solution procedure results in a novel formulation that is unconditionally stable and superior in numerical accuracy and robustness in comparison with the conventional finite volume method. The present VPM/PISO formulation provides a numerical framework of great practical significance that well balances the numerical accuracy and algorithmic complexity. Numerical verifications demonstrate that the present model can significantly improve numerical accuracy. Moreover, the numerical dissipation is effectively suppressed, which shows a great potential for simulations of high-Reynolds number flows. [ABSTRACT FROM PUBLISHER]

The phenomenon of emerging water jets from the holes of containers has been extensively studied; nevertheless, it continues to inspire researchers and teachers. The main aspects of the recent studies concern: the range of the jets trajectories; the extension of Bernoulli's equation, of which Torricelli's expression represents an ideal situation, to real fluids; and the measure of the jets' speed and the drainage time in dependence on the fluid system geometry and wetting conditions. The focus of this paper is to discuss Torricelli's relation between jet speed and hole depth in the case of a 19th-century glass bottle featuring three lateral holes. Measurements of the free water level displacements and jet speed from the holes have been carried out with 11th-grade students. [ABSTRACT FROM AUTHOR]

This paper describes the cryogenic chill-down experiments that are conducted on a 12.7 mm outer diameter, 1.25 mm wall thickness and 7 m long stainless steel horizontal pipe with liquid nitrogen (LN 2 ). The pipe is vacuum insulated during the experiment to minimize the heat leak from room temperature and to enable one to numerically simulate the process easily. The temperature and the pressure profiles of the chill-down line are obtained at the location which is 5.5 m in a distance from the pipe inlet. The mass flux range is approximately from 19 kg/m 2 s to 49 kg/m 2 s, which corresponds to the Reynolds numbers range from 1469 to 5240. The transient histories of temperature, pressure and mass flow rate during the line chill-down process are monitored, and the heat transfer coefficient and the heat flux are computed by an inverse problem solving method. The amplitude of the pressure oscillation and the oscillating period become larger and longer at higher pressure conditions. In the low mass flux conditions, the critical heat flux in horizontal pipes is not sensitive to mass flux, and is higher than that in vertical pipes. Kutateladze’s correlation with the constant coefficient, B = 0.029 , well matches the experimental data in the current work. In nucleate flow boiling regime, heat transfer coefficient, h , is proportional to ( q ″ ) n , and n is equal to 0.7. [ABSTRACT FROM AUTHOR]

Plug energy dissipater, as a kind of effective energy dissipater with economic characteristics, has become very popular. The energy loss coefficient and the minimum wall pressure coefficient of the plug are two important factors in the plug energy dissipater design. In this paper, the two coefficients and relative parameters, such as the contraction ratio of the plug diameter to the flood discharge tunnel diameter, the ratio of the plug thickness to the tunnel diameter, and the Reynolds number of the flow through the plug, were analysed by theoretical considerations, and their relationship expressions were obtained by numerical simulations and were verified by experimental data. It could be concluded that the two coefficients were mainly dominated by the contraction ratio of the plug. The lower contraction ratio of the plug is, the larger are the two coefficients. The research results demonstrate that effects of the Reynolds number on the two coefficients can be neglected when this number is greater than 105; the relative thickness of the plug has little impact on them and can be neglected. [ABSTRACT FROM AUTHOR]

In this paper, a Reynolds number increase transition from self-oscillations close to single-frequency ones to the temporally chaotic regime in the flow in a cylindrical channel driven by a spatially periodic force with four half-periods is experimentally investigated. The parameter ε proportional to the mean rate of the kinetic energy dissipation in unit mass per unit time associated with perturbations in the fluid is used as a basic characteristic of self-oscillations. The Reynolds number dependence ε(Re) for single frequency self-oscillations is considered theoretically. [ABSTRACT FROM AUTHOR]

Over the past 30 years, the Eddy Dissipation Concept (EDC) has been widely applied in the industry for the numerical simulations of turbulent combustion problems. The success of the EDC is mainly due to its ability to incorporate detailed chemical mechanisms at an affordable computational cost compared to some other models. Detailed kinetic schemes are necessary in order to capture turbulent flames where there is strong coupling between the turbulence and chemical kinetics. Such flames are found in Moderate and Intense Low-oxygen Dilution (MILD) combustion, where chemical time scales are increased compared with conventional combustion, mainly because of slower reactions (due to the dilution of reactants). Recent modelling studies have highlighted limitations of the standard EDC model when applied to the simulation of MILD systems, noticeably a significant overestimation of temperature levels. Modifications of the model coefficients were proposed to account for the specific features of MILD combustion, i.e. an extension of the reaction region and the reduction of maximum temperatures. The purpose of the present paper is to provide functional expressions showing the dependency of the EDC coefficients on dimensionless flow parameters such as the Reynolds and Damköhler numbers, taking into account the specific features of the MILD combustion regime, where the presence of hot diluent and its influence on the flow and mixing fields impacts on the reaction rate and thermal field. The approach is validated using detailed experimental data from flames stabilized on the Adelaide Jet in Hot Co-flow (JHC) burner at different co-flow compositions (3%, 6% and 9% O 2 mass fraction) and fuel-jet Reynolds numbers (5000, 10,000 and 20,000). Results show promising improvement with respect to the standard EDC formulation, especially at diluted conditions and medium to low Reynolds numbers. [ABSTRACT FROM AUTHOR]

In this paper Reynolds transport theory is applied to obtain energy conservation equation (ECE). Depth integrated ECE is derived considering a control volume extended over water depth. It is demonstrated that mild slope equation (MSE) is derivable from depth integrated ECE for linear waves. Two equations are derived by separating real and imaginary parts of depth integrated ECE for multidirectional wave fields that can properly deal with reflecting waves. Geometrical optics equations, derived for non-reflecting waves, can be obtained from aforementioned equations as well. Depth integrated ECE is averaged over a wave period for monochromatic waves. The result is similar in form to energy transport equation (ETE) governing spectral wave models. The terms of energy density and energy flux, obtained here, are more accurate expressions, comparing to those of ETE. It should be mentioned that ETE is also obtained from ECE, the general form derived here. The strength of newly derived equations in dealing with reflective wave fields has been illustrated by simple numerical computations. In this research MSE has been derived by the new presented method. Besides, coupled equations for multidirectional waves as well as time averaged depth integrated ECE have also been obtained through mentioned new approach. [ABSTRACT FROM AUTHOR]

This article is a review of our work towards a parameter-free method for simulation of turbulent flow at high Reynolds numbers. In a series of papers we have developed a model for turbulent flow in the form of weak solutions of the Navier–Stokes equations, approximated by an adaptive finite element method, where: (i) viscous dissipation is assumed to be dominated by turbulent dissipation proportional to the residual of the equations, and (ii) skin friction at solid walls is assumed to be negligible compared to inertial effects. The result is a computational model without empirical data, where the only model parameter is the local size of the finite element mesh. Under adaptive refinement of the mesh based on a posteriori error estimation, output quantities of interest in the form of functionals of the finite element solution converge to become independent of the mesh resolution, and thus the resulting method has no adjustable parameters. No ad hoc design of the mesh is needed, instead the mesh is optimized based on solution features, in particular no boundary layer mesh is needed. We connect the computational method to the mathematical concept of a dissipative weak solution of the Euler equations, as a model of high Reynolds number turbulent flow, and we highlight a number of benchmark problems for which the method is validated. The purpose of the article is to present the computational framework in a concise form, to report on recent progress, and to discuss open problems that are subject to ongoing research. [ABSTRACT FROM AUTHOR]

The developments in nanocoating and nanospray technology have resulted in the increasing importance of the impact of micro-/nanoscale liquid droplets on solid surface. In this paper, the impact of a nanodroplet on a flat solid surface is examined using molecular dynamics simulations. The impact velocity ranges from 58 m/s to 1044 m/s, in accordance with theWeber number ranging from 0.62 to 200.02 and the Reynolds number ranging from 0.89 to 16.14. The obtained maximum spreading factors are compared with previous models in the literature. The predicted results from the previous models largely deviate from our simulation results, with mean relative errors up to 58.12%. The estimated viscous dissipation is refined to present a modified theoretical model, which reduces the mean relative error to 15.12% in predicting the maximum spreading factor for cases of nanodroplet impact. [ABSTRACT FROM AUTHOR]

In this paper, we study systematically the effects of forcing time scale in the largescale stochastic forcing scheme of Eswaran and Pope ["An examination of forcing in direct numerical simulations of turbulence," Comput. Fluids 16, 257 (1988)] on the simulated flow structures and statistics of forced turbulence. Using direct numerical simulations, we find that the forcing time scale affects the flow dissipation rate and flow Reynolds number. Other flow statistics can be predicted using the altered flow dissipation rate and flow Reynolds number, except when the forcing time scale is made unrealistically large to yield a Taylor microscale flow Reynolds number of 30 and less. We then study the effects of forcing time scale on the kinematic collision statistics of inertial particles. We show that the radial distribution function and the radial relative velocity may depend on the forcing time scale when it becomes comparable to the eddy turnover time. This dependence, however, can be largely explained in terms of altered flow Reynolds number and the changing range of flow length scales present in the turbulent flow. We argue that removing this dependence is important when studying the Reynolds number dependence of the turbulent collision statistics. The results are also compared to those based on a deterministic forcing scheme to better understand the role of large-scale forcing, relative to that of the small-scale turbulence, on turbulent collision of inertial particles. To further elucidate the correlation between the altered flow structures and dynamics of inertial particles, a conditional analysis has been performed, showing that the regions of higher collision rate of inertial particles are well correlated with the regions of lower vorticity. Regions of higher concentration of pairs at contact are found to be highly correlated with the region of high energy dissipation rate. [ABSTRACT FROM AUTHOR]

This paper investigates the universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and direct numerical simulations (DNS) of the Navier-Stokes equations. It shows that the numerical and experimental velocity structure functions up to order 9 follow a log-universality (Castaing et al. Phys. D Nonlinear Phenom. 1993); this leads to a collapse on a universal curve, when units including a logarithmic dependence on the Reynolds number are used. This paper then investigates the meaning and consequences of such log-universality, and shows that it is connected with the properties of a "multifractal free energy", based on an analogy between multifractal and thermodynamics. It shows that in such a framework, the existence of a fluctuating dissipation scale is associated with a phase transition describing the relaminarisation of rough velocity fields with different Hölder exponents. Such a phase transition has been already observed using the Lagrangian velocity structure functions, but was so far believed to be out of reach for the Eulerian data. [ABSTRACT FROM AUTHOR]

In this paper a numerical investigation on shell-and-tube heat exchanger (STHE) with three configurations of novel segmental curved baffles (convex core baffles/convex peripheral baffles (CB1), convex peripheral baffles/convex core baffles (CB2), and convex peripheral baffles/concave core baffles (CB3)) for thermohydralic performance analysis and enhancement is presented. STHE with conventional straight baffles (SB) is also numerically studied for comparison. Each baffle configuration was tested under different Reynolds number in shell side (Re c) (17693–30331) based on the overall heat transfer coefficient (U), effectiveness (ε), and number of transfer unit (NTU). Also, pressure loss across the shell side is calculated to estimate the energy loss from the system due to the suggested design. In addition, the influence the inlet cold fluid temperature, baffle cutting ratio, and baffle spacing are tested, analyzed and discussed. The results showed that CB3 configuration results in a significant augmentation of the heat exchanger performance compared with the others two configurations for all investigated cases. The enhancements in U , ε, NTU by using CB3 configuration compared to SB are 48.98%−51.31% and 22.92%–23.62% and 48.98%–51.31% respectively, with decreasing in pressure loss by 12.40%–11.22%. [ABSTRACT FROM AUTHOR]

Steady two‐dimensional turbulent free‐surface flow in a channel with mild baseline slope is considered. The shape of the channel bottom is assumed to be undular with a very small amplitude. Asymptotic expansions for large Reynolds numbers and Froude numbers slightly above the critical value 1, respectively, give for the surface elevation a differential equation of KdV‐type, with the additional terms representing turbulent dissipation and forcing due to the wavy bottom, respectively. No turbulence modelling is required. This asymptotic approach was used in [1] to describe stationary solitary waves in a channel with plain bottom and small variations in the bottom friction coefficient. It was shown recently [2,3] that there exist stationary single‐wave solutions of a different kind that are characterized by smaller wave amplitudes. In [4], both kinds of single stationary waves above single obstacles (bumps, ramps) are investigated theoretically and experimentally. In this paper, stationary space‐periodic surface waves for channel bottoms with undular shape are studied. First, a one‐parametric family of exact solutions for particular bottom shapes is derived. Remarkably, these particular solutions exist only in a narrow parameter range. The solutions are reproduced with a numerical solver to verify that the solver gives correct results. Secondly, a different type of asymptotic expansion is performed in order to describe solutions characterized by smaller wave amplitudes. The resulting linear differential equation is solved numerically. Both solutions are briefly discussed. [ABSTRACT FROM AUTHOR]

Onsager principle is the variational principle proposed by Onsager in his celebrated paper on the reciprocal relation. The principle has been shown to be useful in deriving many evolution equations in soft matter physics. Here the principle is shown to be useful in solving such equations approximately. Two examples are discussed: the diffusion dynamics and gel dynamics. Both examples show that the present method is novel and gives new results which capture the essential dynamics in the system. [ABSTRACT FROM AUTHOR]