Turbulent Stress Research Articles

Validation of a numerical model for hot-spot detection on the surface of a rotor pole using a scale model of a hydroelectric generator

To meet the ever-increasing demand for electricity, Hydro-Québec is investigating the viability of running its existing hydroelectric generators at higher power levels than their current operating limits. To assist in this investigation, numerical models capable of simulating the conjugate turbulent air flow and heat transfer phenomena in these generators were formulated and then validated, by using them to predict these phenomena within a scale model of a hydroelectric generator available at Hydro-Québec’s Research Institute and comparing the results to complementary experimental data. Reynolds-averaged governing equations were used, with turbulent stresses and heat fluxes approximated using eddy-viscosity and eddy-diffusivity approaches, in conjunction with the standard k − ɛ and a k − ω shear-stress-transport models, constant turbulent Prandtl number, and specialized treatments of the near-wall regions. Variable- and constant-fluid-property formulations (with coupled and decoupled solutions of the fluid flow and heat transfer) were assessed. The discretization of the complex geometry and the governing equations, and solutions of the discretized equations, were done using commercial codes. These numerical models gave favorable and comparable results, with predictions of global flow quantities (such as windage losses and overall mass flow rates) lying within 4%, and average and maximum temperatures of the pole surface within 5 °C and 3 °C, respectively, of the corresponding experimental data when using the constant-property, coupled, standard k − ɛ model with specialized wall functions. However, the equivalent decoupled model, which was the least computationally intensive, was also adequate for the task at hand. Numerical assessments of two alternate ventilation configurations in the scale model were also undertaken. They showed that increasing the surface area of the spider arms reduced the maximum temperature of the pole by 2.6 °C; and restricting the rotor inlet area reduced the windage losses and the maximum temperature of the pole by 4.7% and 1.5 °C, respectively. • 3D Conjugate heat transfer simulations of a hydroelectric generator scale model. • Validation of flow and temperature distributions by way of experimental measurements. • In contrast with design assumptions, flow across the rotor rim ducts is non-uniform. • Numerical predictions of hot-spots on the scale model’s rotor to within 2.7 °C. • Proposed modifications to the rotor design to reduce rotor pole hot-spot temperatures.

How Do Planetary Boundary Layer Schemes Perform in Hurricane Conditions: A Comparison With Large‐Eddy Simulations

AbstractParameterizations of turbulent processes in planetary boundary layer (PBL) schemes impact tropical cyclone (TC) forecasts. Existing PBL schemes are mostly designed for low‐wind conditions, and assessing their uncertainties in hurricane conditions remains challenging, mostly due to very scarce observations. Using a recently developed framework based on large‐eddy simulations (LES), this study evaluates K‐profile parameterization (KPP) and high‐order PBL schemes in hurricane conditions. Among KPP PBL schemes, the Global Forecast System (GFS) scheme tends to produce excessively deep inflow layers with large values of eddy viscosity (Km). Opposite results are found for the Yonsei University (YSU) scheme. Using LES results as a benchmark, the performance of YSU and GFS schemes is improved by modifying the “shape parameter” such that Km is maximized closer to the surface, and by using a new definition of boundary layer height tailored to high‐wind conditions. The LES results also suggest an asymptotic mixing length of ∼40 m can improve the Louis‐type parameterizations of the YSU scheme that operates above the boundary layer. Among high‐order PBL schemes, the Mellor–Yamada–Nakanishi–Niino (MYNN) scheme produces reasonably accurate vertical profiles of eddy viscosity, turbulent stress, and boundary layer winds under different high‐wind conditions. Further analysis of MYNN supports a “three‐layer” strategy for the mixing length parameterization for TCs that represents different types of turbulent regimes. In contrast, the high‐order eddy‐diffusivity mass‐flux scheme produces excessive boundary‐layer vertical mixing and a deeper inflow layer, partly attributable to a notable overestimation of the maximum allowable mixing length in the PBL code.

Impacts of Instrumented Bottom Frame on Flow and Turbulence Measurements

Abstract A series of laboratory experiments are carried out to demonstrate the impacts of instrumented bottom frame legs on flow and turbulence. The magnitudes of vertical velocity, turbulent kinetic energy, dissipation, and shear stress induced by the frame legs depend on several factors, including the diameter and number of the frame legs, distances between the legs and the observational location, and the magnitude of the incoming flow and its direction with respect to the layout of the frame. In situ observations were carried out near the mouth of the Yellow River using two acoustic Doppler velocimeters mounted on a bottom frame. The estimated vertical velocity and turbulent kinetic energy dissipation rate show a significant asymmetry with flood and ebb tidal flows. This asymmetry can be partly explained by the influences of the bottom frame legs. Finally, the design and deployment principles of bottom frames are discussed for the purpose of reducing the impacts of the frame legs. Significance Statement Instrumented bottom frames are widely used for observations in the oceanic bottom boundary layer and above. However, the impacts of frame legs on the observed flow and turbulence have rarely been investigated. A series of laboratory experiments demonstrate that frame legs can induce vertical flow and enhanced turbulence, and the magnitudes of these influences vary with the size and layout of the frame legs and the magnitude and direction of the background flow. The results of the laboratory experiments can partially explain an “asymmetry” behavior of the vertical flow and turbulent kinetic energy with the flood and ebb tidal flows, derived from in situ observations near the mouth of the Yellow River.

Trapping (sub-)Neptunes similar to TOI-216b at the inner disk rim

Context. The occurrence rate of observed sub-Neptunes has a break at 0.1 au, which is often attributed to a migration trap at the inner rim of protoplanetary disks where a positive co-rotation torque prevents inward migration. Aims. We argue that conditions in inner disk regions are such that sub-Neptunes are likely to open gaps, lose the support of the co-rotation torque as their co-rotation regions become depleted, and the trapping efficiency then becomes uncertain. We study what it takes to trap such gap-opening planets at the inner disk rim. Methods. We performed 2D locally isothermal and non-isothermal hydrodynamic simulations of planet migration. A viscosity transition was introduced in the disk to (i) create a density drop and (ii) mimic the viscosity increase as the planet migrated from a dead zone towards a region with active magneto-rotational instability (MRI). We chose TOI-216b as a Neptune-like upper-limit test case, but we also explored different planetary masses, both on fixed and evolving orbits. Results. For planet-to-star mass ratios q ≃ (4–8) × 10−5, the density drop at the disk rim becomes reshaped due to a gap opening and is often replaced with a small density bump centred on the planet's co-rotation. Trapping is possible only if the bump retains enough gas mass and if the co-rotation region becomes azimuthally asymmetric, with an island of librating streamlines that accumulate a gas overdensity ahead of the planet. The overdensity exerts a positive torque that can counteract the negative torque of spiral arms. Under suitable conditions, the overdensity turns into a Rossby vortex. In our model, efficient trapping depends on the a viscosity and its contrast across the viscosity transition. In order to trap TOI-216b, αDZ = 10−3 in the dead zone requires αMRI ≳ 5 × 10−2 in the MRI-active zone. If αDZ = 5 × 10−4, αMRI ≳ 7.5 × 10−2 is needed. Conclusions. We describe a new regime of a migration trap relevant for massive (sub-)Neptunes that puts valuable constraints on the levels of turbulent stress in the inner part of their natal disks.

MRI turbulence in accretion discs at large magnetic Prandtl numbers

ABSTRACT The effect of large magnetic Prandtl number Pm (the ratio of viscosity to resistivity) on the turbulent transport and energetics of the magnetorotational instability (MRI) is poorly understood, despite the realization of this regime in astrophysical environments as disparate as discs from binary neutron star (BNS) mergers, the inner regions of low-mass X-ray binaries and active galactic nuclei, and the interiors of protoneutron stars. We investigate the MRI dynamo and associated turbulence in the regime Pm > 1 by carrying out fully compressible, 3D MHD-shearing box simulations using the finite-volume code pluto, focusing mostly on the case of Keplerian shear relevant to accretion discs. We find that when the magnetic Reynolds number is kept fixed, the turbulent transport (as parameterized by α, the ratio of stress to thermal pressure) scales with the magnetic Prandtl number as α ∼ Pmδ, with δ ∼ 0.5−0.7 up to Pm ∼ 128. However, this scaling weakens as the magnetic Reynolds number is increased. Importantly, compared to previous studies, we find a new effect at very large Pm – the turbulent energy and stress begin to plateau, no longer depending on Pm. To understand these results we have carried out a detailed analysis of the turbulent dynamics in Fourier space, focusing on the effect of increasing Pm on the transverse cascade – a key non-linear process induced by the disc shear flow that is responsible for the sustenance of MRI turbulence. Finally, we find that α–Pm scaling is sensitive to the box vertical-to-radial aspect ratio, as well as to the background shear.

Role of saltmarsh systems in estuarine trapping of microplastics

Saltmarshes are important natural ecosystems along many temperate (and other) coastlines. They stabilize sediments and act as biofilters for a range of industrial pollutants and, potentially, microplastics. Accumulation of microplastics along estuarine coastlines may be enhanced by the presence of saltmarsh species, as they offer better particle trapping efficiency than adjacent intertidal mudflats under prevailing flood and ebb tidal currents. However, the trapping efficiency of entire saltmarsh systems under varying flow conditions has not been widely assessed. While the effects of saltmarsh systems on water flow, and on sediment transport and trapping, have been relatively well studied, little is known about the contributions of saltmarsh halophytes, resident organisms and the associated saltmarsh sediments to the trapping of microplastics. To address this, a series of flume experiments were undertaken to examine transport and accumulation of Bakelite particles (~ 500 µm) and PVC nurdles (~ 5 mm) as model plastics in sub-sampled saltmarsh and intertidal mudflat monoliths. The results showed that saltmarsh systems influenced the hydrodynamics within and above the canopy, enhancing turbulence and shear stresses. With increasing flow velocities (≤ 0.51 m s−1), negligible quantities (2 times 10−4 mg L−1) of sediments and Bakelite particles were eroded and resuspended. The algal biogenic roughness from the mudflat, and the vegetative roughness from the Spartina plants on the saltmarsh, inhibited the transportation of the microplastics within the tested systems. Resident burrowing crabs (Carcinus maenas) promoted the burial, release and transport of microplastics. The results of this study provide evidence of the contributory roles of saltmarsh systems in the sequestration of microplastics and sediment stabilization. Estuarine saltmarsh systems can act as sinks for microplastics with enhanced burial from burrowing crabs under favourable flow conditions.

Large Eddy Simulation of trenched cylindrical film hole with backward compound angles

Many previous studies have demonstrated that both transverse trench and backward cooling injection are capable of improving jet lift-off problem of traditional cylindrical film hole at high blowing ratios. However, few studies have attempted to combine the above two cooling schemes to further alleviate the cooling deterioration phenomenon. This paper proposed two trenched film holes with different backward compound angles of β = 180° and 135°, and used highly-resolved Large Eddy Simulation method to explore in detail their unsteady flow fields including vortex structures, level of velocity fluctuation, turbulent shear stress, distributions of vorticity and adiabatic wall cooling effectiveness. The results are compared against those of the benchmark trenched film hole with β = 0°. The simulations were carried out under blowing ratio of 1.5, and the coolant to mainstream density ratio of 2.0.The detrimental symmetric counter-rotating vortex pair shown in the trench with β = 0° hole is replaced by an asymmetric vortex pair in the trench with β = 180° hole and only a single asymmetric vortex in the trench with β = 135° hole. Inside the trench, hairpin-like vortices are the dominant vortex structures for the trench with backward film holes. In the region downstream of the trench, the trench with β = 180° hole obtains the highest level of three velocity components fluctuations in the central region because of the direct intense collision between the coolant and mainstream, while the trench with β = 135° hole shows a highest level of lateral velocity component fluctuation in the lateral sides and a highest level of turbulent shear stress in the near wall region due to the significantly enhanced lateral motion of the coolant. The trenches with β = 180° and 135° holes significantly improve the lateral uniformity of the coolant, and respectively provide constantly high levels of 0.21 and 0.3 in laterally averaged cooling effectiveness on the wall downstream of the trench, compared to the trench with β = 0° hole with a low level of less than 0.2.

Large-eddy simulation of helical- and straight-bladed vertical-axis wind turbines in boundary layer turbulence

Turbulent wake flows behind helical- and straight-bladed vertical axis wind turbines (VAWTs) in boundary layer turbulence are numerically studied using the large-eddy simulation (LES) method combined with the actuator line model. Based on the LES data, systematic statistical analyses are performed to explore the effects of blade geometry on the characteristics of the turbine wake. The time-averaged velocity fields show that the helical-bladed VAWT generates a mean vertical velocity along the center of the turbine wake, which causes a vertical inclination of the turbine wake and alters the vertical gradient of the mean streamwise velocity. Consequently, the intensities of the turbulent fluctuations and Reynolds shear stresses are also affected by the helical-shaped blades when compared with those in the straight-bladed VAWT case. The LES results also show that reversing the twist direction of the helical-bladed VAWT causes the spatial patterns of the turbulent wake flow statistics to be reversed in the vertical direction. Moreover, the mass and kinetic energy transports in the turbine wakes are directly visualized using the transport tube method, and the comparison between the helical- and straight-bladed VAWT cases show significant differences in the downstream evolution of the transport tubes.

The control mechanism of the soft trailing fringe on the flow characteristics over an airfoil

Inspired by the owl’s silent flight, we experimentally investigated the flow control mechanism of the soft trailing fringes (STFs) on the wake of the S833 airfoil at the Reynolds number of Re = 2 × 104. A high-speed Particle Image Velocimetry (PIV) system is employed to visualize and analyze the flow structures in the wake of the airfoil at different angles of attack (AOA). Furthermore, spectral proper orthogonal decomposition and bispectral mode decomposition are carried out to identify the coherent flow structures and reveal the control mechanism from the perspective of simplified models. PIV measurements’ results demonstrate that the STFs evidently suppress the turbulent quantities including turbulent kinetic energy and Reynolds shear stress in the airfoil wake. On the one hand, the STFs at low AOAs prevent the interaction between the upper and lower shear layers, and the leading- and trailing-edge vortices (TEVs) are significantly suppressed, thus destructing the von Karman vortex streets. On the other hand, the STFs at high AOAs divide the lower shear layer into two parts, markedly attenuating the TEVs and modifying the vortical structures in the wake. Besides, the quadrant analysis reveals that the STFs can mitigate the high-amplitude wall-pressure peaks, indicating that the STFs may manipulate the trailing-edge noise. However, the control effect is limited at median AOAs because the region with high triadic interactions moves upward in the interaction maps, which limits the impact of the STFs.

Numerical Simulations of Boundary-Layer Airflow Over Pitched-Roof Buildings

Arrays of buildings with pitched roofs are common in urban and suburban areas of European cities. Large-eddy simulations are performed to predict the boundary-layer flows over flat and pitched-roof cuboids to gain a greater understanding of the impact of pitched roofs on urban boundary layers. The simulation methodology is validated for an array of flat roof cuboids. Further simulations show that changes in the type of grid conformity have a negligible effect on the mean flow field and turbulent stresses, while having a visible, but small, effect on the dispersive stresses for a given packing density. Comparisons are made for flat and 45^circ pitched roof cuboid arrays at packing densities of 16.7% and 33.3%. The interactions between pitched-roof buildings and their effect on the urban boundary layer are considerably different to those of flat-roof buildings. The pitched roofs at a packing density of 33.3% leads to significant changes in the mean flow field, the Reynolds stresses, and the aerodynamic drag. Further work investigates the effects of changes in turbulence level and atmospheric thermal stratification in the approaching flow. Importantly, in comparison to a flat-roof array, the pitched-roof one at a packing density of 33.3% evidently increase the friction velocity and greatly reduces the effects of stable stratification conditions and changes in inflow turbulence level.

Numerical tripping of high-speed turbulent boundary layers

The influence of turbulence inflow generation on direct numerical simulations (DNS) of high-speed turbulent boundary layers at Mach numbers of 2 and 5.84 is investigated. Two main classes of inflow conditions are considered, based on the recycling/rescaling (RR) and the digital filtering (DF) approach, along with suitably modified versions. A series of DNS using very long streamwise domains is first carried out to provide reliable data for the subsequent investigation. A set of diagnostic parameters is then selected to verify achievement of an equilibrium state, and correlation laws for those quantities are obtained based on benchmark cases. Simulations using shorter domains, with extent comparable with that used in the current literature, are then carried out and compared with the benchmark data. Significant deviations from equilibrium conditions are found, to a different extent for the various flow properties, and depending on the inflow turbulence seeding. We find that the RR method yields superior performance in the evaluation of the inner-scaled wall pressure fluctuations and the turbulent shear stress. DF methods instead yield quicker adjustment and better accuracy in the prediction of wall friction and of the streamwise Reynolds stress in supersonic cases. Unrealistically high values of the wall pressure variance are obtained by the baseline DF method, while the proposed DF alternatives recover a closer agreement with respect to the benchmark. The hypersonic test case highlights that similar distribution of wall friction and heat transfer are obtained by both RR and DF baseline methods.Graphical abstract

Turbulent planar wakes of viscoelastic fluids analysed by direct numerical simulations

Direct numerical simulations employing the finitely extensible nonlinear elastic constitutive model closed with Peterlin's approximation (FENE-P) are used to investigate the far-field region of turbulent planar wakes of viscoelastic fluids and to develop the theory describing these flows. The theoretical results display excellent agreement with the simulations and provide new scaling laws for the evolution of the shear layer thickness $\delta (x) \sim x^{1/2}$ , mean velocity deficit ${\rm \Delta} U(x) \sim x^{-1/2}$ and, for very high Deborah numbers, of the maximum polymer shear stresses $\sigma ^{[p]}_c(x) \sim x^{-2}$ and averaged polymer chain extension $\textrm {tr}(\bar {C}(x) - \boldsymbol{\mathsf{I}}) \sim x^{-2}$ , where $x$ is the streamwise distance from the solid body generating the wake. The theory is able to show the existence of self-similarity for the profiles of mean velocity, mean polymer shear stress, averaged polymer chain extension and the conditions for similarity of the turbulent shear stress, and is very well supported by the numerical simulations. Similarly to the case of viscoelastic turbulent planar jets (Guimarães et al., J. Fluid Mech., vol. 899, 2020, p. A11), when the inlet Weissenberg and Deborah numbers are sufficiently large, turbulent viscoelastic wakes exhibit a considerable reduction of the spreading rate and of the normalised Reynolds stresses. However, for very large downstream locations the turbulent viscoelastic wake recovers the classical evolution laws observed for Newtonian turbulent planar wakes.

Thermal-hydraulic study in a wire-wrapped 19-rod bundle based on an isotropic four-equation model

The thermal–hydraulic performance of rod bundles with wire spacers is significant for studying Lead–Bismuth Eutectic (LBE) cooled fast reactor. The problem is that using the traditional constant turbulent Prandtl number of 0.85 ∼ 0.9, which is generally derived from the Reynolds analogy hypothesis suitable for conventional fluids, will greatly affect the numerical heat transfer accuracy of LBE having low Prandtl number properties. Thus, a great quantity of development work of four-equation models, which may improve the calculation accuracy of turbulent heat transfer in LBE flows, has been made by researchers, while no commercial code is available. The present work addresses an effort to study the thermal–hydraulic phenomenon in an LBE-cooled 19-rod bundle with wire spacers geometry on a self-compiled CFD solver (iso4eqnFoam), which is implemented by a standard finite volume method and C++ program and developed on OpenFOAM. In particular, the simulation aims to perform fully-developed turbulent stresses and turbulent heat fluxes by solving an isotropic four-equation model, which allows simple zero-fixed-value boundary conditions for turbulent variables and considers the difference between viscous and thermal boundary layer of LBE. The simulation results on a bare 19-rod bundle are first compared with heat transfer experimental data and other simulations to validate the effectiveness of the solver. Then, an LBE-cooled 19-rod bundle with wire spacers is presented with thermal–hydraulic simulations. The result shows that iso4eqnFoam can simulate the turbulent heat transfer of LBE under complex geometry. Finally, the distributions of temperature, temperature fluctuation, and turbulent Prandtl number in the channel of the wire-wrapped rod bundle are reported based on the isotropic four-equation model.

A spatially accelerating turbulent flow with longitudinally contracting walls

This paper describes a study of spatially accelerating turbulent flow based on the direct numerical simulation of a flow with longitudinally accelerating moving walls to create a relative acceleration between the fluid and the wall without inducing streamline curvature. The results show a broad similarity to those of previous investigations of spatial acceleration, albeit with some differences. A new interpretation has been proposed considering this spatially accelerating flow to be characterised by the formation of a new boundary layer superimposed on the pre-existing turbulent flow. This is followed by the transition of the flow in response to the development of this new boundary layer. This can be seen as an extension of the transition theory for temporally accelerating turbulent flows (He & Seddighi, J. Fluid Mech., vol. 715, 2013, pp. 60–102). The existing turbulent structures act as disturbances for the new boundary layer similar to the role of free-stream turbulence in bypass transition. This boundary layer modulates the pre-existing near-wall structures, amplifying and elongating the streaks. Some streaks eventually become unstable in a sinuous mechanism reminiscent of streak breakdown in near-wall turbulence, resulting in the formation localised turbulent spots which spread until the entire wall is covered in new turbulence. This interpretation naturally splits the flow into a new boundary layer region and a core (or free-stream) flow with interactions between the two dominating a significant length of the flow development and potentially offers a new explanation for the slow evolution of the turbulent stresses observed previously.

Development Of A Turbulent Boundary Layer Over An Air Cavity

The turbulent boundary layer development over an air cavity is studied experimentally using planar Particle Image Velocimetry. An identification technique based on the gradient of correlation values was employed to detect the cavity interface which revealed a well-defined, asymmetric bump-like geometry at the spanwise-uniform region of the cavity. No separation was observed at the leeward side of the cavity, owing largely to the high boundary layer thickness to maximum cavity thickness ratio (δ/tmax ≈ 11.8). The shape of the cavity was found to dictate the turbulent boundary development by subjecting it to alternating streamwise pressure gradients: from an adverse to a favourable and back to an adverse, moving downstream along the cavity. Profiles o f mean s treamwise velocity and turbulent stresses show the alternate pressure gradients and air injection to be the dominant perturbations to the flow, with streamline curvature only having a minor influence, also based on previous observations.

GRMHD simulations of accreting neutron stars with non-dipole fields

ABSTRACT NASA’s NICER telescope has recently provided evidence for non-dipolar magnetic field structures in rotation-powered millisecond pulsars. These stars are assumed to have gone through a prolonged accretion spin-up phase, begging the question of what accretion flows on to stars with complex magnetic fields would look like. We present results from a suite of general relativistic magnetohydrodynamic simulations of accreting neutron stars for dipole, quadrupole, and quadrudipolar stellar field geometries. This is a first step towards simulating realistic hotspot shapes in a general relativistic framework to understand hotspot variability in accreting millisecond pulsars. We find that the location and size of the accretion columns resulting in hotspots changes significantly depending on initial stellar field strength and geometry. We also find that the strongest contributions to the stellar torque are from disc-connected field lines and the pulsar wind, leading to spin-down in almost the entire parameter regime explored here. We further analyse angular momentum transport in the accretion disc due to large-scale magnetic stresses, turbulent stresses, and wind and compressible effects which we identify with convective motions. The disc collimates the initial open stellar flux forming jets. For dipoles, the disc–magnetosphere interaction can either enhance or reduce jet power compared to the isolated case. However for quadrupoles, the disc always leads to an enhanced net open flux making the jet power comparable to the dipolar case. We discuss our results in the context of observed neutron star jets and provide a viable mechanism to explain radio power both in the low- and high-magnetic field case.

Maximizing the thermal performance index applying evolutionary multi-objective optimization approaches for double pipe heat exchanger

The thermal performance index (TPI) known as the efficiency parameter evaluates the highlight of the heat transfer for the same pumping power requirement. The optimum design of a heat exchanger with minimum pressure drops and efficient heat transfer is a big challenging task from an energy-saving point of view. One way to optimize this efficiency parameter is by changing the geometric parameters of the heat exchanger. For this purpose, the multi-objective reinforcement learner non-dominated sorting genetic algorithm (NSGA-RL) is employed maximizing TPI and Nusselt number and minimizing Fanning friction factor to the optimal design of a double pipe heat exchanger, with perforated baffles in the annulus side. Its performance is compared with a non-dominated sorting genetic algorithm - version II (NSGA-II), and a chaotic non-dominated sorting genetic algorithm (CNSGA). The calculations were carried out using the turbulent shear stress transport k-ω model. The multi-objective optimization techniques presented promising results in terms of the number of nondominated solutions, Euclidean distances to the origin point (reference point), and hypervolume indicators. However, in general, the results based on mean values indicate that the NSGA-RL outperforms the NSGA-II and CNSGA concerning the three performance indicators for the two double pipe heat exchanger evaluated cases. TPI increases 78% for case 1, and 108% for case 2 compared without baffles in a double pipe heat exchanger (DPHE). Numerical results revealed that DPHE employing internal perforated baffles improved heat transfer significantly with Nusselt number increased around 7.93–8.25 times and friction factor increased by 6.5–9.75 times compared with plain DPHE.

A new boundary layer integral method based on the universal velocity profile

A recently developed mixing length model of the turbulent shearing stress in wall bounded flows has been used to formulate a universal velocity profile (UVP) that provides an effective replacement for the widely used Coles wall-wake formulation. Comparisons with both direct numerical simulation and experimental data demonstrate the ability of the profile to approximate a wide variety of wall-bounded flows. The UVP is uniformly valid from the wall to the boundary layer edge and for all Reynolds numbers from zero to infinity. There is no presumption of logarithmic dependence of the velocity profile outside the viscous wall layer so the profile can accurately approximate low Reynolds number turbulent boundary layers. The effect of a pressure gradient is included in the UVP through the introduction of a modified Clauser parameter that correlates well with the parameters that determine the wake portion of the velocity profile. The inherent dependence of the UVP on Reynolds number, extended to include the effect of pressure gradient, enables it to be used as the basis of a new method for integrating the von Kármán boundary layer integral equation for a wide variety of attached wall bounded flows. To illustrate its application, the UVP is used to determine the zero-lift drag coefficient of the Joukowsky 0012 and NACA (National Advisory Committee for Aeronautics) 0012 airfoils over a wide range of chord Reynolds numbers.

Combined dynamo of gravitational and magneto-rotational instability in irradiated accretion discs

Aims. We aim to assess whether magneto-rotational instability (MRI) can exist in a turbulent state generated by gravitational instability (GI). We investigated the magnetic field saturation and elucidated the ability of GI turbulence to act as a dynamo. Methods. The results were obtained by numerical simulations using the magnetohydrodynamics code Athena. A sub-routine to solve the Poisson equation for self-gravity using three-dimensional Fourier transforms was implemented for that purpose. A GI-turbulent state was then restarted, with a zero-net-flux type magnetic seed field being introduced. The seed field was chosen with β ≈ 1010 to make sure that the magnetic field of the stationary state is exclusively generated by the dynamo. Results. Shortly after introducing the magnetic seed field, a significant field amplification is observed, despite MRI not being active. This shows that GI acts as a kinematic dynamo. The growing magnetic field allows MRI to become active, which leads to the emergence of a butterfly diagram. The turbulent stress of the saturated state is found to be consistent with the superposition of GI stresses and MRI stresses. Moreover, the ratio of magnetic stress to magnetic pressure is found to lie in the 0.3−0.4 range, which is typical for MRI turbulence. Furthermore, it is found that the magnetic energy significantly decreases if self-gravity is turned off. This indicates, in accordance with the initial field amplification, that GI provides the dominant dynamo contribution and that MRI is not simply added but rather grows on the magnetic field provided by GI turbulence. Finally, it is shown that the combined GI-MRI-dynamo is consistent with an α − Ω model and that the observed oscillation frequency of the butterfly diagram roughly agrees with the model prediction.

Intensification of thickening processes during pulp dehydration by efficient mixing of suspensions with flocculant solutions

The efficiency of the process of thickening the products of enrichment of non-ferrous metal ores largely depends on the particle size in the pulp, therefore, flocculants are used to intensify the thickening of fine pulps. In the process of mixing, it is important to evenly distribute the flocculant solution over the entire volume of the pulp and not to destroy the formed flakes by excessive shear stresses of the mixer. The process of flocculation during mechanical mixing of the pulp with concentrated solutions of the flocculant is considered. The previously developed method, based on the semi-empirical Prandtl turbulence model, for selecting mixing devices, taking into account agitator`s geometry, was confirmed. It has been established that the choice of the optimal rotational speed of the agitator is related to the magnitude of turbulent friction stresses created by the agitator`s blades. The results of experimental studies on mixing a suspension with a high-molecular flocculant Greenlife K40 of cationic action using different types of mixing device are presented. The comparison was made between traditional turbine and three-bladed agitators, as well as the developed conical agitator with a new geometry. The efficiency of the mixing devices was determined by comparing the size of the formed flakes. It has been established that larger and stronger flakes are formed in the case of using a conical mixer.