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Ghosh, Bikramaditya, Krishna M.C., Shrikanth Rao, Emira Kozarević, and Rahul Kumar Pandey. "Predictability and herding of bourse volatility: an econophysics analogue." Investment Management and Financial Innovations 15, no. 2 (June 25, 2018): 317–26. http://dx.doi.org/10.21511/imfi.15(2).2018.28.
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Financial Reynolds number works as a proxy for volatility in stock markets. This piece of work helps to identify the predictability and herd behavior embedded in the financial Reynolds number (time series) series for both CNX Nifty Regular and CNX Nifty High Frequency Trading domains. Hurst exponent and fractal dimension have been used to carry out this work. Results confirm conclusive evidence of predictability and herd behavior for both the indices. However, it has been observed that CNX Nifty High Frequency Trading domain (represented by its corresponding financial Reynolds number) is more predictable and has traces of significant herd behavior. The pattern of the predictability has been found to follow a quadratic equation.
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de Roode, Stephan R., Peter G. Duynkerke, and A. Pier Siebesma. "Analogies between Mass-Flux and Reynolds-Averaged Equations." Journal of the Atmospheric Sciences 57, no. 10 (May 2000): 1585–98. http://dx.doi.org/10.1175/1520-0469(2000)057<1585:abmfar>2.0.co;2.
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Deckelman, Steven, Jennifer Graetz, and Tyler Russell. "A multiplicative analogue of the Reynolds operator and construction of invariants." Rocky Mountain Journal of Mathematics 45, no. 4 (August 2015): 1107–18. http://dx.doi.org/10.1216/rmj-2015-45-4-1107.
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Gaviglio, J. "Reynolds analogies and experimental study of heat transfer in the supersonic boundary layer." International Journal of Heat and Mass Transfer 30, no. 5 (May 1987): 911–26. http://dx.doi.org/10.1016/0017-9310(87)90010-x.
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McKeon, B. J., and J. F. Morrison. "Asymptotic scaling in turbulent pipe flow." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 365, no. 1852 (January 16, 2007): 771–87. http://dx.doi.org/10.1098/rsta.2006.1945.
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The streamwise velocity component in turbulent pipe flow is assessed to determine whether it exhibits asymptotic behaviour that is indicative of high Reynolds numbers. The asymptotic behaviour of both the mean velocity (in the form of the log law) and that of the second moment of the streamwise component of velocity in the outer and overlap regions is consistent with the development of spectral regions which indicate inertial scaling. It is shown that an ‘inertial sublayer’ in physical space may be considered as a spatial analogue of the inertial subrange in the velocity spectrum and such behaviour only appears for Reynolds numbers R + >5×10 3 , approximately, much higher than was generally thought.
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Radkevich, E. V., E. A. Lukashev, and O. A. Vasil’eva. "Hydrodynamic instabilities and nonequilibrium phase transitions." Доклады Академии наук 486, no. 5 (June 20, 2019): 537–42. http://dx.doi.org/10.31857/s0869-56524865537-542.
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For laminar-turbulent transition model is built reconstruction of the initial stage of instability as a nonequilibrium phase transition, the mechanism of which is diffusion stratification. It is shown that the Gibbs free energy deviations from the homogeneous state (relative to the instability under consideration) is an analogue Ginzburg-Landau potentials. Numerical experiments were performed. Self-excitation of a homogeneous state by edge control condition of increasing speed. Under external influence (increase in speed at the input), there is a transition to chaos through bifurcations of period doubling, when the internal control parameter (analogue of the Reynolds number) changes, like the Feigenbaum period doubling cascade.
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CHILDRESS, STEPHEN, SAVERIO E. SPAGNOLIE, and TADASHI TOKIEDA. "A bug on a raft: recoil locomotion in a viscous fluid." Journal of Fluid Mechanics 669 (January 12, 2011): 527–56. http://dx.doi.org/10.1017/s002211201000515x.
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The locomotion of a body through an inviscid incompressible fluid, such that the flow remains irrotational everywhere, is known to depend on inertial forces and on both the shape and the mass distribution of the body. In this paper we consider the influence of fluid viscosity on such inertial modes of locomotion. In particular we consider a free body of variable shape and study the centre-of-mass and centre-of-volume variations caused by a shifting mass distribution. We call this recoil locomotion. Numerical solutions of a finite body indicate that the mechanism is ineffective in Stokes flow but that viscosity can significantly increase the swimming speed above the inviscid value once Reynolds numbers are in the intermediate range 50–300. To study the problem analytically, a model which is an analogue of Taylor's swimming sheet is introduced. The model admits analysis at fixed, arbitrarily large Reynolds number for deformations of sufficiently small amplitude. The analysis confirms the significant increase of swimming velocity above the inviscid value at intermediate Reynolds numbers.
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Zhao, Shuo, Xiaoping Chen, Yuting Yang, and Dengsong Huang. "Effects of Viscosity Law on High-Temperature Supersonic Turbulent Channel Flow for Chemical Equilibrium." Processes 12, no. 2 (January 24, 2024): 256. http://dx.doi.org/10.3390/pr12020256.
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Direct numerical simulations of temporally evolving high-temperature supersonic turbulent channel flow for chemical equilibrium were conducted with a Mach number of 3.0, a Reynolds number of 4880, and a wall temperature of 1733.2 K to investigate the influence of the viscosity law. The mean and fluctuating viscosity for the mixture rule is higher than that for Sutherland’s law, whereas an opposite trend is observed in the mean temperature, mean pressure, and dissociation degree. The Trettel and Larsson transformed mean velocity, the Reynolds shear stress, the turbulent kinetic energy budget, and the turbulent Prandtl number are insensitive to the viscosity law. The semilocal scaling that take into account local variation of fluid characteristics better collapses the turbulent kinetic energy budget. The modified strong Reynolds analogies provide reasonably good results for the mixture rule, which are better than those for Sutherland’s law. The streamwise and spanwise coherencies for the mixture rule are stronger and weaker than those for Sutherland’s law, respectively. The relationship between viscosity and species components can help to identify the traveling wave packet.
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Yim, Eunok, and Paul Billant. "Analogies and differences between the stability of an isolated pancake vortex and a columnar vortex in stratified fluid." Journal of Fluid Mechanics 796 (May 11, 2016): 732–66. http://dx.doi.org/10.1017/jfm.2016.248.
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In order to understand the dynamics of pancake shaped vortices in stably stratified fluids, we perform a linear stability analysis of an axisymmetric vortex with Gaussian angular velocity in both the radial and axial directions with an aspect ratio of ${\it\alpha}$. The results are compared to those for a columnar vortex (${\it\alpha}=\infty$) in order to identify the instabilities. Centrifugal instability occurs when $\mathscr{R}>c(m)$ where $\mathscr{R}=ReF_{h}^{2}$ is the buoyancy Reynolds number, $F_{h}$ the Froude number, $Re$ the Reynolds number and $c(m)$ a constant which differs for the three unstable azimuthal wavenumbers $m=0,1,2$. The maximum growth rate depends mostly on $\mathscr{R}$ and is almost independent of the aspect ratio ${\it\alpha}$. For sufficiently large buoyancy Reynolds number, the axisymmetric mode is the most unstable centrifugal mode whereas for moderate $\mathscr{R}$, the mode $m=1$ is the most unstable. Shear instability for $m=2$ develops only when $F_{h}\leqslant 0.5{\it\alpha}$. By considering the characteristics of shear instability for a columnar vortex with the same parameters, this condition is shown to be such that the vortex is taller than the minimum wavelength of shear instability in the columnar case. For larger Froude number $F_{h}\geqslant 1.5{\it\alpha}$, the isopycnals overturn and gravitational instability can operate. Just below this threshold, the azimuthal wavenumbers $m=1,2,3$ are unstable to baroclinic instability. A simple model shows that baroclinic instability develops only above a critical vertical Froude number $F_{h}/{\it\alpha}$ because of confinement effects.
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JIMÉNEZ, JAVIER, SERGIO HOYAS, MARK P. SIMENS, and YOSHINORI MIZUNO. "Turbulent boundary layers and channels at moderate Reynolds numbers." Journal of Fluid Mechanics 657 (June 2, 2010): 335–60. http://dx.doi.org/10.1017/s0022112010001370.
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The behaviour of the velocity and pressure fluctuations in the outer layers of wall-bounded turbulent flows is analysed by comparing a new simulation of the zero-pressure-gradient boundary layer with older simulations of channels. The 99 % boundary-layer thickness is used as a reasonable analogue of the channel half-width, but the two flows are found to be too different for the analogy to be complete. In agreement with previous results, it is found that the fluctuations of the transverse velocities and of the pressure are stronger in the boundary layer, and this is traced to the pressure fluctuations induced in the outer intermittent layer by the differences between the potential and rotational flow regions. The same effect is also shown to be responsible for the stronger wake component of the mean velocity profile in external flows, whose increased energy production is the ultimate reason for the stronger fluctuations. Contrary to some previous results by our group, and by others, the streamwise velocity fluctuations are also found to be higher in boundary layers, although the effect is weaker. Within the limitations of the non-parallel nature of the boundary layer, the wall-parallel scales of all the fluctuations are similar in both the flows, suggesting that the scale-selection mechanism resides just below the intermittent region, y/δ = 0.3–0.5. This is also the location of the largest differences in the intensities, although the limited Reynolds number of the boundary-layer simulation (Reθ ≈ 2000) prevents firm conclusions on the scaling of this location. The statistics of the new boundary layer are available from http://torroja.dmt.upm.es/ftp/blayers/.
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HALL, PHILIP, and SPENCER SHERWIN. "Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures." Journal of Fluid Mechanics 661 (August 16, 2010): 178–205. http://dx.doi.org/10.1017/s0022112010002892.
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The relationship between asymptotic descriptions of vortex–wave interactions and more recent work on ‘exact coherent structures’ is investigated. In recent years immense interest has been focused on so-called self-sustained processes in turbulent shear flows where the importance of waves interacting with streamwise vortex flows has been elucidated in a number of papers. In this paper, it is shown that the so-called ‘lower branch’ state which has been shown to play a crucial role in these self-sustained processes is a finite Reynolds number analogue of a Rayleigh vortex–wave interaction with scales appropriately modified from those for external flows to Couette flow, the flow of interest here. Remarkable agreement between the asymptotic theory and numerical solutions of the Navier–Stokes equations is found even down to relatively small Reynolds numbers, thereby suggesting the possible importance of vortex–wave interaction theory in turbulent shear flows. The relevance of the work to more general shear flows is also discussed.
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MYDLARSKI, L. "Mixed velocity–passive scalar statistics in high-Reynolds-number turbulence." Journal of Fluid Mechanics 475 (January 25, 2003): 173–203. http://dx.doi.org/10.1017/s0022112002002756.
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Statistics of the mixed velocity–passive scalar field and its Reynolds number dependence are studied in quasi-isotropic decaying grid turbulence with an imposed mean temperature gradient. The turbulent Reynolds number (using the Taylor microscale as the length scale), Rλ, is varied over the range 85 [les ] Rλ [les ] 582. The passive scalar under consideration is temperature in air. The turbulence is generated by means of an active grid and the temperature fluctuations result from the action of the turbulence on the mean temperature gradient. The latter is created by differentially heating elements at the entrance to the wind tunnel plenum chamber. The mixed velocity–passive scalar field evolves slowly with Reynolds number. Inertial-range scaling exponents of the co-spectra of transverse velocity and temperature, Evθ(k1), and its real-space analogue, the ‘heat flux structure function,’ 〈Δv(r)Δθ(r)〉, show a slow evolution towards their theoretical predictions of −7/3 and 4/3, respectively. The sixth-order longitudinal mixed structure functions, 〈(Δu(r))2(Δθ(r))4〉, exhibit inertial-range structure function exponents of 1.36–1.52. However, discrepancies still exist with respect to the various methods used to estimate the scaling exponents, the value of the scalar intermittency exponent, μθ, and the effects of large-scale phenomena (namely shear, decay and turbulent production of 〈θ2〉) on 〈(Δu(r))2(Δθ(r))4〉. All the measured fine-scale statistics required to be zero in a locally isotropic flow are, or tend towards, zero in the limit of large Reynolds numbers. The probability density functions (PDFs) of Δv(r)Δθ(r) exhibit roughly exponential tails for large separations and super-exponential tails for small separations, thus displaying the effects of internal intermittency. As the Reynolds number increases, the PDFs become symmetric at the smallest scales – in accordance with local isotropy. The expectation of the transverse velocity fluctuation conditioned on the scalar fluctuation is linear for all Reynolds numbers, with slope equal to the correlation coefficient between v and θ. The expectation of (a surrogate of) the Laplacian of the scalar reveals a Reynolds number dependence when conditioned on the transverse velocity fluctuation (but displays no such dependence when conditioned on the scalar fluctuation). This former Reynolds number dependence is consistent with Taylor’s diffusivity independence hypothesis. Lastly, for the statistics measured, no violations of local isotropy were observed.
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Nyandeni, Zamashobane, and Tiri Chinyoka. "Computational aeroacoustic modeling using hybrid Reynolds averaged Navier–Stokes/large‐eddy simulations methods with modified acoustic analogies." International Journal for Numerical Methods in Fluids 93, no. 8 (April 26, 2021): 2611–36. http://dx.doi.org/10.1002/fld.4990.
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Bayada, Guy, and Grzegorz Łkaszewicz. "On micropolar fluids in the theory of lubrication. Rigorous derivation of an analogue of the reynolds equation." International Journal of Engineering Science 34, no. 13 (October 1996): 1477–90. http://dx.doi.org/10.1016/0020-7225(96)00031-6.
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Colagrossi, Andrea, Emanuele Rossi, Salvatore Marrone, and David Le Touzé. "Particle Methods for Viscous Flows: Analogies and Differences Between the SPH and DVH Methods." Communications in Computational Physics 20, no. 3 (August 31, 2016): 660–88. http://dx.doi.org/10.4208/cicp.150915.170316a.
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AbstractIn this work two particle methods are studied in the context of viscous flows. The first one is a Vortex Particle Method, called Diffused Vortex Hydrodynamics (DVH), recently developed to simulate complex viscous flows at medium and high Reynolds regimes. This method presents some similarities with the SPH model and its Lagrangian meshless nature, even if it is based on a different numerical approach. Advantages and drawbacks of the two methods have been previously studied in Colagrossi et al. [1] from a theoretical point of view and in Rossi et al. [2], where these particle methods have been tested on selected benchmarks. Further investigations are presented in this article highlighting analogies and differences between the two particle models.
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Litvinenko, Yuri E. "Plasma Flows in Solar Filaments as Electromagnetically Driven Vortical Flows." Physics 3, no. 4 (November 10, 2021): 1046–50. http://dx.doi.org/10.3390/physics3040065.
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Electromagnetic expulsion acts on a body suspended in a conducting fluid or plasma, which is subject to the influence of electric and magnetic fields. Physically, the effect is a magnetohydrodynamic analogue of the buoyancy (Archimedean) force, which is caused by the nonequal electric conductivities inside and outside the body. It is suggested that electromagnetic expulsion can drive the observed plasma counter-streaming flows in solar filaments. Exact analytical solutions and scaling arguments for a characteristic plasma flow speed are reviewed, and their applicability in the limit of large magnetic Reynolds numbers, relevant in the solar corona, is discussed.
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Banerjee, I., M. E. Rosti, T. Kumar, L. Brandt, and A. Russom. "Analogue tuning of particle focusing in elasto-inertial flow." Meccanica 56, no. 7 (March 23, 2021): 1739–49. http://dx.doi.org/10.1007/s11012-021-01329-z.
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AbstractWe report a unique tuneable analogue trend in particle focusing in the laminar and weak viscoelastic regime of elasto-inertial flows. We observe experimentally that particles in circular cross-section microchannels can be tuned to any focusing bandwidths that lie between the “Segre-Silberberg annulus” and the centre of a circular microcapillary. We use direct numerical simulations to investigate this phenomenon and to understand how minute amounts of elasticity affect the focussing of particles at increasing flow rates. An Immersed Boundary Method is used to account for the presence of the particles and a FENE-P model is used to simulate the presence of polymers in a Non-Newtonian fluid. The numerical simulations study the dynamics and stability of finite size particles and are further used to analyse the particle behaviour at Reynolds numbers higher than what is allowed by the experimental setup. In particular, we are able to report the entire migration trajectories of the particles as they reach their final focussing positions and extend our predictions to other geometries such as the square cross section. We believe complex effects originate due to a combination of inertia and elasticity in the weakly viscoelastic regime, where neither inertia nor elasticity are able to mask each other’s effect completely, leading to a number of intermediate focusing positions. The present study provides a fundamental new understanding of particle focusing in weakly elastic and strongly inertial flows, whose findings can be exploited for potentially multiple microfluidics-based biological sorting applications.
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Madden, J., and J. Vermeer. "Lindelöf locales and realcompactness." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 3 (May 1986): 473–80. http://dx.doi.org/10.1017/s0305004100064410.
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We show that a locale possesses the localic analogue of the property of realcompactness if and only if it is regular Lindelöf. Thus, the localic version of the Hewitt real-compactification, originally defined by G.Reynolds using σ-frames, is the regular Lindelöf reflection. An immediate consequence is that a space is realcompact if and only if it is the point space of a regular Lindelöf local (3·2). We point out a nice analogy between a theorem of Reynolds and Stone's classical representation theorem for boolean algebras. Finally, we show that the quasi-F cover of a compact Hausdorff space is the Stone–čech compactifications of the smallest dense Lindelöf sublocale.
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SI, J., and K. ZHU. "NUMERICAL STUDY ON AERODYNAMIC CHARACTERISTICS OF BUNDLE CONDUCTOR FOR UHV BASED ON ALE METHOD." Latin American Applied Research - An international journal 44, no. 3 (July 31, 2014): 237–45. http://dx.doi.org/10.52292/j.laar.2014.447.
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The bundle conductor is often threatened by the wind-excited or wake-induced vibration generated by vortex shedding. So as to simulate the common fluid–structure nonlinear interaction problems in Ultra-High Voltage (UHV) transmission lines, the N-S equations of incompressible viscous fluid with the ALE description has been adopted to formulate the fluid-solid governing equations in the analogue computation and the 2-bundle and 6bundle sectional models, as well as the deduced finite element discretization scheme of conductor displacement are introduced in the algorithm. Wind tunnel experimental studies are carried out based on the single stranded model, 6-bundle stranded and 6bundle circle model for the focus of aerodynamic characteristics and the difference between stranded cable and circle cable. Results show that solution of numerical model agrees favorably with experimental results. The aerodynamic coefficients decrease significantly within the expected critical range of wind speed or Reynolds numbers and the cables roughness is not the principle factor to the aerodynamic coefficient when the Reynolds numbers belong to the critical region. However, the interference effect of the bundle conductor widely influenced the wind load applied on the surface of each cable.
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Kerswell, R. R., and A. Davey. "On the linear instability of elliptic pipe flow." Journal of Fluid Mechanics 316 (June 10, 1996): 307–24. http://dx.doi.org/10.1017/s0022112096000559.
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The linear stability of elliptic pipe flow is considered for finite aspect ratios thereby bridging the gap between the small-aspect-ratio analysis of Davey & Salwen (1994) and the large-aspect-ratio asymptotics of Hocking (1977). The flow is found to become linearly unstable above an aspect ratio of about 10.4 to the spanwise-modulated analogue of the Orr-Sommerfeld mode to which plane Poiseuille flow first loses stability. This disturbance is found to possess a series of intense vortices along its critical layer at lateral stations far removed from the central minor axis. The critical Reynolds number appears to fall from infinity as the aspect ratio increases above 10.4, ultimately approaching Hocking's (1977) asymptotic result at much larger aspect ratios.
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GONZÁLEZ, L. M., M. AHMED, J. KÜHNEN, H. C. KUHLMANN, and V. THEOFILIS. "Three-dimensional flow instability in a lid-driven isosceles triangular cavity." Journal of Fluid Mechanics 675 (March 22, 2011): 369–96. http://dx.doi.org/10.1017/s002211201100022x.
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Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.
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Manikantan, Harishankar, and Todd M. Squires. "Irreversible particle motion in surfactant-laden interfaces due to pressure-dependent surface viscosity." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2205 (September 2017): 20170346. http://dx.doi.org/10.1098/rspa.2017.0346.
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The surface shear viscosity of an insoluble surfactant monolayer often depends strongly on its surface pressure. Here, we show that a particle moving within a bounded monolayer breaks the kinematic reversibility of low-Reynolds-number flows. The Lorentz reciprocal theorem allows such irreversibilities to be computed without solving the full nonlinear equations, giving the leading-order contribution of surface pressure-dependent surface viscosity. In particular, we show that a disc translating or rotating near an interfacial boundary experiences a force in the direction perpendicular to that boundary. In unbounded monolayers, coupled modes of motion can also lead to non-intuitive trajectories, which we illustrate using an interfacial analogue of the Magnus effect. This perturbative approach can be extended to more complex geometries, and to two-dimensional suspensions more generally.
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Марзаева, В. И. "Математическое моделирование распространения верховых лесных пожаров при наличии противопожарных разрывов и заслонов." Журнал технической физики 89, no. 8 (2019): 1141. http://dx.doi.org/10.21883/jtf.2019.08.47883.392-18.
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Using the method of mathematical modeling, the process of spreading forest fires in the presence of fire breaks and barriers consisting of hardwood trees was studied. Mathematically, this problem is reduced to solving the Reynolds equations for turbulent flow, taking into account chemical reactions. To obtain a discrete analogue, the control volume method was used. Using numerical calculations, we obtained the distributions of the fields of velocity, temperature, oxygen concentrations, volatile products of pyrolysis, combustion and volume fractions of the condensed phase. The model allowed us to obtain contours of the spread of forest fires, which depend on the stock and type of forest combustible materials, moisture content, velocity and direction of wind, etc. It was also possible to determine the dependence of the sizes of fire breaks and barriers on the above parameters, at which the crown fire stops spreading.
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Gourdain, Nicolas, Jéromine Dumon, Yannick Bury, and Pascal Molton. "Transonic buffet of a space launcher aileron: Fanno and Rayleigh flows analogies." International Journal of Numerical Methods for Heat & Fluid Flow 32, no. 4 (October 18, 2021): 1255–80. http://dx.doi.org/10.1108/hff-07-2021-0506.
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Purpose The transonic buffet is a complex aerodynamics phenomenon that imposes severe constraints on the design of high-speed vehicles, including for aircraft and space launchers. The origin of buffet is still debated in the literature, and the control of this phenomenon remains difficult. This paper aims to propose an original scenario to explain the origin of buffet, which in turn opens promising perspectives for its alleviation and attenuation. Design/methodology/approach This work relies on the use of numerical simulations, with the idea to reproduce the buffet phenomenon in a transonic aileron designed for small space launchers. Two numerical approaches are tested: unsteady Reynolds averaged Navier–Stokes (URANS) and large-eddy simulation (LES). The numerical predictions are first validated against available experimental data, before to be analysed in detail to identify the origin of buffet on the studied configuration. A complementary numerical study is then conducted to assess the possibility to delay the onset of buffet. Findings The buffet control strategy is based on wall cooling. By adequately choosing the wall temperature, this work shows that it is feasible to delay the emergence of buffet. More precisely, this paper highlights the crucial role of the subsonic flow inside the boundary layer, showing the existence of upstream travelling pressure waves that are responsible for the flow coupling between both sides of the airfoil, at the origin of the buffet phenomenon. Originality/value This paper proposes a new scenario to explain the origin of buffet, based on the use of a Fanno and Rayleigh flow analogies. This approach is used to design a control solution based on a modification of the wall temperature, showing very promising results.
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Kerstein, Alan R. "Linear-eddy modelling of turbulent transport. Part 6. Microstructure of diffusive scalar mixing fields." Journal of Fluid Mechanics 231 (October 1991): 361–94. http://dx.doi.org/10.1017/s0022112091003439.
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The linear-eddy approach for modelling molecular mixing in turbulent flow involves stochastic simulation on a one-dimensional domain with sufficient resolution to include all physically relevant lengthscales. In each realization, molecular diffusion is implemented deterministically, punctuated by a sequence of instantaneous, statistically independent ‘rearrangement events’ (measure-preserving maps) representing turbulent stirring. These events emulate the effect of compressive strain on the scalar field. An inertial-range similarity law is incorporated.The model reproduces key features of scalar power spectra, including dependences of spectra! amplitudes and transition wavenumbers on Reynolds and Schmidt numbers. Computed scaling exponents governing scalar power spectra, higher-order fluctuation statistics such as structure functions, and the spatial distribution of scalar level crossings are close to measured exponents. It is inferred that the characterization of stirring as a sequence of independent events (the model analogue of eddies) leads to a useful representation of mixing-field microstructure.
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MacDonald, M., N. Hutchins, and D. Chung. "Roughness effects in turbulent forced convection." Journal of Fluid Mechanics 861 (December 19, 2018): 138–62. http://dx.doi.org/10.1017/jfm.2018.900.
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We conducted direct numerical simulations of turbulent flow over three-dimensional sinusoidal roughness in a channel. A passive scalar is present in the flow with Prandtl number $Pr=0.7$, to study heat transfer by forced convection over this rough surface. The minimal-span channel is used to circumvent the high cost of simulating high-Reynolds-number flows, which enables a range of rough surfaces to be efficiently simulated. The near-wall temperature profile in the minimal-span channel agrees well with that of the conventional full-span channel, indicating that it can be readily used for heat-transfer studies at a much reduced cost compared to conventional direct numerical simulation. As the roughness Reynolds number, $k^{+}$, is increased, the Hama roughness function, $\unicode[STIX]{x0394}U^{+}$, increases in the transitionally rough regime before tending towards the fully rough asymptote of $\unicode[STIX]{x1D705}_{m}^{-1}\log (k^{+})+C$, where $C$ is a constant that depends on the particular roughness geometry and $\unicode[STIX]{x1D705}_{m}\approx 0.4$ is the von Kármán constant. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, $Re_{b}$. Meanwhile, the temperature difference between smooth- and rough-wall flows, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}^{+}$, appears to tend towards a constant value, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with $Re_{b}$ in the fully rough regime. Using shifted logarithmic velocity and temperature profiles, the heat-transfer law as described by the Stanton number in the fully rough regime can be derived once both the equivalent sand-grain roughness $k_{s}/k$ and the temperature difference $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$ are known. In meteorology, this corresponds to the ratio of momentum and heat-transfer roughness lengths, $z_{0m}/z_{0h}$, being linearly proportional to the inner-normalised momentum roughness length, $z_{0m}^{+}$, where the constant of proportionality is related to $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. While Reynolds analogy, or similarity between momentum and heat transfer, breaks down for the bulk skin-friction and heat-transfer coefficients, similar distribution patterns between the heat flux and viscous component of the wall shear stress are observed. Instantaneous visualisations of the temperature field show a thin thermal diffusive sublayer following the roughness geometry in the fully rough regime, resembling the viscous sublayer of a contorted smooth wall.
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Ganguli, Arijit, Viraj Bhatt, Anna Yagodnitsyna, Dipak Pinjari, and Aniruddha Pandit. "A Review of Pressure Drop and Mixing Characteristics in Passive Mixers Involving Miscible Liquids." Micromachines 15, no. 6 (May 24, 2024): 691. http://dx.doi.org/10.3390/mi15060691.
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The present review focuses on the recent studies carried out in passive micromixers for understanding the hydrodynamics and transport phenomena of miscible liquid–liquid (LL) systems in terms of pressure drop and mixing indices. First, the passive micromixers have been categorized based on the type of complexity in shape, size, and configuration. It is observed that the use of different aspect ratios of the microchannel width, presence of obstructions, flow and operating conditions, and fluid properties majorly affect the mixing characteristics and pressure drop in passive micromixers. A regime map for the micromixer selection based on optimization of mixing index (MI) and pressure drop has been identified based on the literature data for the Reynolds number (Re) range (1 ≤ Re ≤ 100). The map comprehensively summarizes the favorable, moderately favorable, or non-operable regimes of a micromixer. Further, regions for special applications of complex micromixer shapes and micromixers operating at low Re have been identified. Similarly, the operable limits for a micromixer based on pressure drop for Re range 0.1 < Re < 100,000 have been identified. A comparison of measured pressure drop with fundamentally derived analytical expressions show that Category 3 and 4 micromixers mostly have higher pressure drops, except for a few efficient ones. An MI regime map comprising diffusion, chaotic advection, and mixed advection-dominated zones has also been devised. An empirical correlation for pressure drop as a function of Reynolds number has been developed and a corresponding friction factor has been obtained. Predictions on heat and mass transfer based on analogies in micromixers have also been proposed.
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Tuominen, Ilkka, Maarit J. Korpi, Petri J. Käpylä, Marjaana Lindborg, and Ilya Ilyin. "Stellar nonlinear dynamos: observations and modelling." Proceedings of the International Astronomical Union 4, S259 (November 2008): 417–18. http://dx.doi.org/10.1017/s1743921309030944.
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AbstractRecent numerical modelling of mean-field stellar dynamos with induction and Reynolds' equations show that, with increasing rotation, field symmetry changes from an axisymmetric solar type to a nonaxymmetric one, where the so-called active longitudes in the same stellar hemisphere are predicted to be of opposite polarities. It was originally named Active star Hale rule in Tuominen et al. (2002), being an analogue to the famous bipolar sunspot polarity rule but different in scale and being a global phenomenon. In addition to long timeseries of temperature mapping and photometry, during the last few years we have been able to measure accurately polarization spectra of an active late-type star II Peg with the upgraded spectropolarimetric option of the high-resolution spectrograph SOFIN at the Nordic Optical Telescope, La Palma. The magnetic inversions (Carroll et al., Kochukhov et al.) can be compared to the dynamo models and the preliminary results show some resemblance to the dynamo solutions.
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DUAN, L., I. BEEKMAN, and M. P. MARTÍN. "Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature." Journal of Fluid Mechanics 655 (May 13, 2010): 419–45. http://dx.doi.org/10.1017/s0022112010000959.
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In this paper, we perform direct numerical simulation (DNS) of turbulent boundary layers at Mach 5 with the ratio of wall-to-edge temperature Tw/Tδ from 1.0 to 5.4 (Cases M5T1 to M5T5). The influence of wall cooling on Morkovin's scaling, Walz's equation, the standard and modified strong Reynolds analogies, turbulent kinetic energy budgets, compressibility effects and near-wall coherent structures is assessed. We find that many of the scaling relations used to express adiabatic compressible boundary-layer statistics in terms of incompressible boundary layers also hold for non-adiabatic cases. Compressibility effects are enhanced by wall cooling but remain insignificant, and the turbulence dissipation remains primarily solenoidal. Moreover, the variation of near-wall streaks, iso-surface of the swirl strength and hairpin packets with wall temperature demonstrates that cooling the wall increases the coherency of turbulent structures. We present the mechanism by which wall cooling enhances the coherence of turbulence structures, and we provide an explanation of why this mechanism does not represent an exception to the weakly compressible hypothesis.
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Swan, James W., and John F. Brady. "The hydrodynamics of confined dispersions." Journal of Fluid Mechanics 687 (October 17, 2011): 254–99. http://dx.doi.org/10.1017/jfm.2011.351.
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AbstractA method is proposed for computing the low-Reynolds-number hydrodynamic forces on particles comprising a suspension confined by two parallel, no-slip walls. This is constructed via the two-dimensional analogue of Hasimoto’s solution (J. Fluid Mech., vol. 5, 1959, pp. 317–328) for a periodic array of point forces in a viscous, incompressible fluid, and, like Hasimoto, the summation of interactions is accelerated by substitution and superposition of ‘Ewald-like’ forcing. This method is akin to the accelerated Stokesian dynamics technique (J. Fluid Mech., vol. 448, 2001, pp. 115–146) and models the suspension dynamics with log–linear computational scaling. The effectiveness of this approach is demonstrated with a calculation of the high-frequency dynamic viscosity of a colloidal dispersion as function of volume fraction and channel width. Similarly, the short-time self-diffusivity for and the sedimentation rate of spherical particles in a confined suspension are determined. The results demonstrate the influence of confining geometry on the transport of small particles, which is becoming increasingly important for micro- and biofluidics.
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Perminov, V. A., and K. O. Fryanova. "Mathematical modeling of the initiation and spread of forest fires and their impact on buildings and structures." Bulletin of the Karaganda University. "Physics" Series 99, no. 3 (September 30, 2020): 54–61. http://dx.doi.org/10.31489/2020ph3/54-61.
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Currently, methods of mathematical modeling are used to study processes in emergency situations. Forest fires are extremely complex and destructive natural phenomena which depend on availability of fuel, meteorological and other conditions. Mathematical model of forest fire is based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the theoretical study of the problems of crown forest fire spread in windy condition and their thermal impact on the wooden building were carried out. The research was based on numerical solution of two-dimensional Reynolds equations. The boundary-value problem is solved numerically using the method of splitting according to physical processes. A discrete analogue for the system of equations was obtained by means of the control volume method. A study of forest fire spreading made it possible to obtain a detailed picture of the change of the component concentration of gases and temperature fields in forest fire and on the wall of building with time. It let to determine the limiting distances between forest fire and building for possibility of wooden walls ignition for different meteorology conditions, size of building and intensity of fire impact.
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Mouza, Aikaterini, Olga Skordia, Ioannis Tzouganatos, and Spiros Paras. "A Simplified Model for Predicting Friction Factors of Laminar Blood Flow in Small-Caliber Vessels." Fluids 3, no. 4 (October 19, 2018): 75. http://dx.doi.org/10.3390/fluids3040075.
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The aim of this study was to provide scientists with a straightforward correlation that can be applied to the prediction of the Fanning friction factor and consequently the pressure drop that arises during blood flow in small-caliber vessels. Due to the small diameter of the conduit, the Reynolds numbers are low and thus the flow is laminar. This study has been conducted using Computational Fluid Dynamics (CFD) simulations validated with relevant experimental data, acquired using an appropriate experimental setup. The experiments relate to the pressure drop measurement during the flow of a blood analogue that follows the Casson model, i.e., an aqueous Glycerol solution that contains a small amount of Xanthan gum and exhibits similar behavior to blood, in a smooth, stainless steel microtube (L = 50 mm and D = 400 μm). The interpretation of the resulting numerical data led to the proposal of a simplified model that incorporates the effect of the blood flow rate, the hematocrit value (35–55%) and the vessel diameter (300–1800 μm) and predicts, with better than ±10% accuracy, the Fanning friction factor and consequently the pressure drop during laminar blood flow in healthy small-caliber vessels.
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Yu, Xiaoxi, Yuan Li, Yuquan Liu, Yuping Yang, and Yining Wu. "Flow Patterns of Viscoelastic Fracture Fluids in Porous Media: Influence of Pore-Throat Structures." Polymers 11, no. 8 (August 2, 2019): 1291. http://dx.doi.org/10.3390/polym11081291.
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Viscoelastic surfactant (VES) fluid and hydrolyzed polyacryamide (HPAM) solution are two of the most common fracturing fluids used in the hydraulic fracturing development of unconventional reservoirs. The filtration of fracturing fluids in porous media is mainly determined by the flow patterns in pore-throat structures. In this paper, three different microdevices analogue of porous media allow access to a large range of Deborah number (De) and concomitantly low Reynolds number (Re). Continuous pore-throat structures were applied to study the feedback effect of downstream structure on upstream flow of VES fluid and HPAM solution with Deborah (De) number from 1.11 to 146.4. In the infinite straight channel, flow patterns between VES fluids and HPAM solution were similar. However, as pore length shortened to 800 μm, flow field of VES fluid exhibited the triangle shape with double-peaks velocity patterns. The flow field of HPAM solution presented stable and centralized streamlines when Re was larger than 4.29 × 10−2. Additionally, when the pore length was further shortened to 400 μm, double-peaks velocity patterns were vanished for VES fluid and the stable convergent flow characteristic of HPAM solution was observed with all flow rates.
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Montenegro-Johnson, T. D., H. Gadêlha, and D. J. Smith. "Spermatozoa scattering by a microchannel feature: an elastohydrodynamic model." Royal Society Open Science 2, no. 3 (March 2015): 140475. http://dx.doi.org/10.1098/rsos.140475.
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Sperm traverse their microenvironment through viscous fluid by propagating flagellar waves; the waveform emerges as a consequence of elastic structure, internal active moments and low Reynolds number fluid dynamics. Engineered microchannels have recently been proposed as a method of sorting and manipulating motile cells; the interaction of cells with these artificial environments therefore warrants investigation. A numerical method is presented for large-amplitude elastohydrodynamic interaction of active swimmers with domain features. This method is employed to examine hydrodynamic scattering by a model microchannel backstep feature. Scattering is shown to depend on backstep height and the relative strength of viscous and elastic forces in the flagellum. In a ‘high viscosity’ parameter regime corresponding to human sperm in cervical mucus analogue, this hydrodynamic contribution to scattering is comparable in magnitude to recent data on contact effects, being of the order of 5°–10°. Scattering can be positive or negative depending on the relative strength of viscous and elastic effects, emphasizing the importance of viscosity on the interaction of sperm with their microenvironment. The modulation of scattering angle by viscosity is associated with variations in flagellar asymmetry induced by the elastohydrodynamic interaction with the boundary feature.
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Kleinhans, Maarten G., Maarten van der Vegt, Jasper Leuven, Lisanne Braat, Henk Markies, Arjan Simmelink, Chris Roosendaal, Arjan van Eijk, Paul Vrijbergen, and Marcel van Maarseveen. "Turning the tide: comparison of tidal flow by periodic sea level fluctuation and by periodic bed tilting in scaled landscape experiments of estuaries." Earth Surface Dynamics 5, no. 4 (November 28, 2017): 731–56. http://dx.doi.org/10.5194/esurf-5-731-2017.
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Abstract. Analogue models or scale experiments of estuaries and short tidal basins are notoriously difficult to create in the laboratory because of the difficulty to obtain currents strong enough to transport sand. Our recently discovered method to drive tidal currents by periodically tilting the entire flume leads to intense sediment transport in both the ebb and flood phase, causing dynamic channel and shoal patterns. However, it remains unclear whether tilting produces periodic flows with characteristic tidal properties that are sufficiently similar to those in nature for the purpose of landscape experiments. Moreover, it is not well understood why the flows driven by periodic sea level fluctuation, as in nature, are not sufficient for morphodynamic experiments. Here we compare for the first time the tidal currents driven by sea level fluctuations and by tilting. Experiments were run in a 20 × 3 m straight flume, the Metronome, for a range of tilting periods and with one or two boundaries open at constant head with free inflow and outflow. Also, experiments were run with flow driven by periodic sea level fluctuations. We recorded surface flow velocity along the flume with particle imaging velocimetry and measured water levels along the flume. We compared the results to a one-dimensional model with shallow flow equations for a rough bed, which was tested on the experiments and applied to a range of length scales bridging small experiments and large estuaries. We found that the Reynolds method results in negligible flows along the flume except for the first few metres, whereas flume tilting results in nearly uniform reversing flow velocities along the entire flume that are strong enough to move sand. Furthermore, tidal excursion length relative to basin length and the dominance of friction over inertia is similar in tidal experiments and reality. The sediment mobility converges between the Reynolds method and tilting for flumes hundreds of metres long, which is impractical. Smaller flumes of a few metres in length, on the other hand, are much more dominated by friction than natural systems, meaning that sediment suspension would be impossible in the resulting laminar flow on tidal flats. Where the Reynolds method is limited by small sediment mobility and high tidal range relative to water depth, the tilting method allows for independent control over the variables flow depth, velocity, sediment mobility, tidal period and excursion length, and tidal asymmetry. A periodically tilting flume thus opens up the possibility of systematic biogeomorphological experimentation with self-formed estuaries.
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Mériaux, Catherine A., and Cathy B. Kurz-Besson. "Sedimentation from binary suspensions in a turbulent gravity current along a V-shaped valley." Journal of Fluid Mechanics 712 (September 13, 2012): 624–45. http://dx.doi.org/10.1017/jfm.2012.389.
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AbstractWe present a study of bidispersed particulate gravity currents at high Reynolds numbers flowing along a V-shaped valley. The speed and width of the currents, the mass deposited by the currents and the density of the deposits were examined by both a box model and lock-exchange experiments in a 5 m long tank. Silicon carbide and glass beads were used for the bidispersed suspension models. The initial conditions of the currents were similar, except that the grain size of the glass beads was successively chosen to be 2, 2.5 and 4 times that of the silicon carbide. For all experiments a Stokes’ settling velocity model, assuming that both particles are spherical, gives a settling rate of the glass beads that is greater than that of the silicon carbide by a factor ranging from 1.6 to 16.5. When the ratio of the Stokes’ settling velocity of the glass beads to that of the silicon carbide is greater than ∼6, we find a complete agreement between the box model and the experiment. In particular, the deposit shows a substantial decline in the mass of the coarser glass beads in the first metre, so that it only contains the finer silicon carbide further downstream. By contrast, when the Stokes’ settling velocity ratio is less than ∼4, only the speed of the current and the total sedimented mass can be well described by the box model. The experimental deposit is otherwise characterized by a slightly increasing density, which the box model fails to match. There is no difference in the deposit density across the valley. For all experiments in the V-shaped valley, the width of the currents decreases with time $t$ according to ${t}^{\ensuremath{-} 2/ 7} $. Analogue experiments in a flat-bottom tank were also performed to assess the influence of the valley on the sedimentation dynamics described above. A similar behaviour with settling velocity ratios was found. This study eventually shows the need for considering particle interactions in even dilute gravity currents at high Reynolds numbers.
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Moreau, Stéphane. "Turbomachinery Noise Predictions: Present and Future." Acoustics 1, no. 1 (January 4, 2019): 92–116. http://dx.doi.org/10.3390/acoustics1010008.
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In future Ultra-High By-Pass Ratio turboengines, the turbomachinery noise (fan and turbine stages mainly) is expected to increase significantly. A review of analytical models and numerical methods to yield both tonal and broadband contributions of such noise sources is presented. The former rely on hybrid methods coupling gust response over very thin flat plates of finite chord length, either isolated or in cascade, and acoustic analogies in free-field and in a duct. The latter yields tonal noise with unsteady Reynolds-Averaged Navier–Stokes (u-RANS) simulations, and broadband noise with Large Eddy Simulations (LES). The analytical models are shown to provide good and fast first sound estimates at pre-design stages, and to easily separate the different noise sources. The u-RANS simulations are now able to give accurate estimates of tonal noise of the most complex asymmetric, heterogeneous fan-Outlet Guiding Vane (OGV) configurations. Wall-modeled LES on rescaled stage configurations have now been achieved on all components: a low-pressure compressor stage, a transonic high-pressure turbine stage and a fan-OGV configuration with good overall sound power level predictions for the latter. In this case, hybrid Lattice–Boltzmann/very large-eddy simulations also appear to be an excellent alternative to yield both contributions accurately at once.
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Ruschak, Kenneth J., and Steven J. Weinstein. "Laminar, Gravitationally Driven Flow of a Thin Film on a Curved Wall." Journal of Fluids Engineering 125, no. 1 (January 1, 2003): 10–17. http://dx.doi.org/10.1115/1.1522412.
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Gravitationally driven flow of a thin film down an arbitrarily curved wall is analyzed for moderate Reynolds number by generalizing equations previously developed for flow on a planar wall. In the analysis, the ratio of the characteristic film thickness to the characteristic dimension of the wall is presumed small, and terms estimated to be first order in this parameter are retained. Partial differential equations are reduced to ordinary differential equations by the method of von Ka´rma´n and Pohlhausen; namely, an expression for the velocity profile is assumed, and the equation for conservation of linear momentum is averaged across the film. The assumed velocity profile changes shape in the flow direction because a self-similar profile, one of fixed shape but variable magnitude, leads to an equation that typically fails under critical conditions. The resulting equations for film thickness routinely accommodate subcritical-to-supercritical transitions and supercritical-to-subcritical transitions as classified by the underlying wave propagation. The more severe supercritical-to-subcritical transition is manifested by a standing wave where the film noticeably thickens; this standing wave is a simple analogue of a hydraulic jump. Predictions of the film-thickness profile and variations in the velocity profile compare favorably with those from the Navier-Stokes equation obtained by the finite element method.
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Jardine, M. "Three-dimensional steady-state magnetic reconnection." Journal of Plasma Physics 51, no. 3 (June 1994): 399–422. http://dx.doi.org/10.1017/s0022377800017657.
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A family of three-dimensional models of reconnection is presented in which the different members of the family are characterized by the vorticity with which plasma flows towards the reconnection site. The nature of this inflow also determines the size and speed of the outflow jet that carries reconnected field lines away from the reconnection site, and the shape of the MHD shocks that bound it. Flows with positive vorticity are of a flux pile-up type, for which the outflow jet is fastest and narrowest. Among those with negative vorticity is the three-dimensional analogue of Petschek reconnection. Not all combinations of vorticity and reconnection rate are possible; for those solutions with negative vorticity, there is a maximum reconnection rate. As the magnetic Reynolds number Rme or the current density is increased, this maximum is reduced and the possible types of solution become more polarized towards the two extremes of flux pile-up and slow compression regimes. Given a distribution of vorticities and inflow speeds, these models give the corresponding distribution of possible steady-state reconnection rates. As an illustrative example, we take Gaussian distributions of both to show that the resulting distribution is dominated by the flux pile-up regime.
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Sow, Aliou, Ashwin Chinnayya, and Abdellah Hadjadj. "Mean structure of one-dimensional unstable detonations with friction." Journal of Fluid Mechanics 743 (March 6, 2014): 503–33. http://dx.doi.org/10.1017/jfm.2014.49.
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AbstractThis investigation deals with the study of the mean structure of a mildly unstable non-ideal detonation wave. The analysis is based on the integration of one-dimensional reactive Euler equations with friction forces using a third-order Runge–Kutta scheme and a fifth-order weighted essentially non-oscillatory (WENO5) spatial discretization. A one-step Arrhenius reaction mechanism is used for modelling the chemical reaction. When the frictional forces are active, the limit cycle based on the post-shock pressure reveals an enhanced pulsating behaviour of the downstream subsonic reaction zone compared to the ideal case. The results show that the detonation-velocity deficit increases as the mean reaction zone becomes thicker compared to the generalized ZND model. A new master equation, based on the Favre-averaged quantities, is derived and analysed along with new sonicity and thermicity conditions. The analysis of the species, momentum and energy balances reveals that the presence of mechanical fluctuations within the reaction zone constitutes another source of energy withdrawal, meaning that the detonation deviates from its laminar structure. Furthermore, the compressibility of the flow is analysed and the relationships between the fluctuations of temperature, velocity and reactive scalar are discussed in terms of strong Reynolds analogies.
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Augier, Pierre, Ashwin Vishnu Mohanan, and Erik Lindborg. "Shallow water wave turbulence." Journal of Fluid Mechanics 874 (July 15, 2019): 1169–96. http://dx.doi.org/10.1017/jfm.2019.375.
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The dynamics of irrotational shallow water wave turbulence forced at large scales and dissipated at small scales is investigated. First, we derive the shallow water analogue of the ‘four-fifths law’ of Kolmogorov turbulence for a third-order structure function involving velocity and displacement increments. Using this relation and assuming that the flow is dominated by shocks, we develop a simple model predicting that the shock amplitude scales as $(\unicode[STIX]{x1D716}d)^{1/3}$, where $\unicode[STIX]{x1D716}$ is the mean dissipation rate and $d$ the mean distance between the shocks, and that the $p$th-order displacement and velocity structure functions scale as $(\unicode[STIX]{x1D716}d)^{p/3}r/d$, where $r$ is the separation. Then we carry out a series of forced simulations with resolutions up to $7680^{2}$, varying the Froude number, $F_{f}=(\unicode[STIX]{x1D716}L_{f})^{1/3}/c$, where $L_{f}$ is the forcing length scale and $c$ is the wave speed. In all simulations a stationary state is reached in which there is a constant spectral energy flux and equipartition between kinetic and potential energy in the constant flux range. The third-order structure function relation is satisfied with a high degree of accuracy. Mean energy is found to scale approximately as $E\sim \sqrt{\unicode[STIX]{x1D716}L_{f}c}$, and is also dependent on resolution, indicating that shallow water wave turbulence does not fit into the paradigm of a Richardson–Kolmogorov cascade. In all simulations shocks develop, displayed as long thin bands of negative divergence in flow visualisations. The mean distance between the shocks is found to scale as $d\sim F_{f}^{1/2}L_{f}$. Structure functions of second and higher order are found to scale in good agreement with the model. We conclude that in the weak limit, $F_{f}\rightarrow 0$, shocks will become denser and weaker and finally disappear for a finite Reynolds number. On the other hand, for a given $F_{f}$, no matter how small, shocks will prevail if the Reynolds number is sufficiently large.
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Lai, Chris C. K., John J. Charonko, and Katherine Prestridge. "A Kármán–Howarth–Monin equation for variable-density turbulence." Journal of Fluid Mechanics 843 (March 27, 2018): 382–418. http://dx.doi.org/10.1017/jfm.2018.125.
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We present a generalisation of the Kármán–Howarth–Monin (K–H–M) equation to include variable-density (VD) effects. The derived equation (i) reduces to the original K–H–M equation when density is a constant and (ii) leads to a VD analogue of the $4/5$-law with the same value of constant ($=4/5$) appearing as the prefactor of the dissipation rate. The equation is employed to understand negative turbulent kinetic energy production in a $\text{SF}_{6}$ turbulent round jet with an initial density ratio of 4.2. From a Reynolds-averaged Navier–Stokes (RANS) perspective, negative production means that the mean flow is strengthened at the expense of the energy of turbulent fluctuations. We show that the associated energy transfer is accomplished by the deformation of smaller turbulent eddies into large ones in the development region of the jet and is captured by the linear scale-by-scale energy transfer term in the VD K–H–M equation. The nonlinear transfer term of the VD K–H–M equation depicts a conventional forward cascade for all eddies having a size less than the Eulerian integral length scale, regardless of their orientation. The net effect is a retarded energy cascade in the non-Boussinesq jet that has not been accounted for by existing turbulence theories. Implications of this observation for turbulence modelling are discussed.
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Andreev, Oleg, Yurii Kolesnikov, and André Thess. "Visualization of the Ludford column." Journal of Fluid Mechanics 721 (March 13, 2013): 438–53. http://dx.doi.org/10.1017/jfm.2013.76.
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AbstractWhen a liquid metal flows around a truncated cylinder in the presence of a magnetic field which is parallel to the axis of the cylinder, a stagnant region develops above the cylinder. We call this region a Ludford column. The Ludford column represents the magnetohydrodynamics (MHD) analogue of the well-known Taylor columns in rotating flows. Whereas Taylor columns can be easily visualized using dye, the visualization of Ludford columns has remained elusive up to now because liquid metals are opaque. We demonstrate that this fundamental limitation of experimental MHD can be overcome by using a superconducting 5 T magnet. This facility permits us to perform MHD experiments in which the opaque liquid metals are replaced with a transparent electrolyte while maintaining the key MHD effects. We report results of a series of flow experiments in which an aqueous solution of sulphuric acid flows around a bar with square cross-section (which for simplicity shall be referred to as a cylinder). We vary the Reynolds number in the range $5\lt Re\lt 100$ and the Hartmann number in the range $0\lt Ha\lt 14$. The experimental procedure involves flow visualizations using tracer particles as well as velocity measurements using particle image velocimetry (PIV). Our experiments provide direct access to the Ludford column for the first time and reveal the spatial structure of this basic feature of MHD flows.
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Sahu, Chunendra K., and M. R. Flynn. "Filling box flows in porous media." Journal of Fluid Mechanics 782 (October 9, 2015): 455–78. http://dx.doi.org/10.1017/jfm.2015.555.
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We report upon a theoretical and experimental investigation of a porous medium ‘filling box’ flow by specifically examining the details of the laminar descending plume and its outflow in a control volume having an impermeable bottom boundary and sidewalls. The plume outflow initially comprises a pair of oppositely directed gravity currents. The gravity currents propagate horizontally until they reach the lateral sidewalls at $y=\pm L$. The flow then becomes of filling box type, with a vertically ascending ‘first front’ separating discharged plume fluid below from ambient fluid above. The flow details are described analytically by first deriving a new similarity solution for Darcy plumes with $\mathit{Pe}>O(1)$, where $\mathit{Pe}$ is the Péclet number. From the similarity solution so obtained, we then derive expressions for the plume volume flux and mean reduced gravity as functions of the vertical distance from the source. Regarding the plume outflow, a similarity solution adopted from Huppert & Woods (J. Fluid Mech., vol. 292, 1995, pp. 55–69) describes the height and front speed of the gravity currents, whereas a semi-implicit finite difference scheme is used to predict the first front elevation versus time and horizontal distance. As with high-Reynolds-number filling box flows, that studied here is an example of a coupled problem: the gravity current source conditions are prescribed by the plume volume flux and mean reduced gravity. Conversely, discharged plume fluid may be re-entrained into the plume, be it soon or long after reaching the bottom impermeable boundary. To corroborate our model predictions, analogue laboratory experiments are performed with fresh water and salt water as the working fluids. Our experiments consider as independent variables the porous medium bead diameter and the plume source volume flux and reduced gravity. Predictions for the gravity current front position and height compare favourably against analogue measured data. Good agreement is likewise noted when considering either the mean elevation or the profile of the first front. Results from this study may be adopted in modelling geological plumes. For example, our equations can be used to predict the time required for discharged plume fluid to return to the point of injection in the case of aquifers closed on the sides and below by impermeable boundaries.
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HEWITT, RICHARD E., and PETER W. DUCK. "Pulsatile jets." Journal of Fluid Mechanics 670 (January 12, 2011): 240–59. http://dx.doi.org/10.1017/s0022112010005227.
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We consider the evolution of high-Reynolds-number, planar, pulsatile jets in an incompressible viscous fluid. The source of the jet flow comprises a mean-flow component with a superposed temporally periodic pulsation, and we address the spatiotemporal evolution of the resulting system. The analysis is presented for both a free symmetric jet and a wall jet. In both cases, pulsation of the source flow leads to a downstream short-wave linear instability, which triggers a breakdown of the boundary-layer structure in the nonlinear regime. We extend the work of Riley, Sánchez-Sans & Watson (J. Fluid Mech., vol. 638, 2009, p. 161) to show that the linear instability takes the form of a wave that propagates with the underlying jet flow, and may be viewed as a (spatially growing) weakly non-parallel analogue of the (temporally growing) short-wave modes identified by Cowley, Hocking & Tutty (Phys. Fluids, vol. 28, 1985, p. 441). The nonlinear evolution of the instability leads to wave steepening, and ultimately a singular breakdown of the jet is obtained at a critical downstream position. We speculate that the form of the breakdown is associated with the formation of a ‘pseudo-shock’ in the jet, indicating a failure of the (long-length scale) boundary-layer scaling. The numerical results that we present disagree with the recent results of Riley et al. (2009) in the case of a free jet, together with other previously published works in this area.
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Shaheen, Nighat, Saima Arzeen, and Sidra Batool. "Effect of Depression on Sleep Quality and Pain among Patients with Arthritis Disease." Journal of Peace, Development & Communication 07, no. 01 (January 29, 2023): 41–52. http://dx.doi.org/10.36968/jpdc-v07-i01-05.
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The major aim of the present study was to examine the effect of depression on sleep quality and pain among patients with arthritis. The sample included (N=30) arthritis female patients recruited from outpatients of three main hospitals of Peshawar using Convenient Sampling Technique. Age range of the sample was between 45 to 65 years (M=54.51 ± 5.24). The inclusion criteria consisted of patients having diagnosed with hip and/or knee arthritis since one year on the basis of X-rays reports and currently were under treatment. The control group consisted of (N=26) female outpatients in the same age range who visited the OPD of the same hospitals for their less severe diseases. The Siddiqui Shah Depression Scale (Siddiqui & Shah, 1997) was used to measure depression, the Pittsburgh Sleep Quality Index (Buysse, Reynolds, Monk, Berman, & Kupfer, 1989) was used to assess quality of sleep and the Visual Analogue Scale (Gracely, McGrath, Dubner, 1978) was used to obtain data on the severity of pain in participants. Results showed that participants having higher baseline depression obtained significantly higher mean scores on the SSDS, the PSQI, and the VAS scales compared to the control group. The results support all hypotheses of the study. The findings have critical implications in clinical setting by suggesting an utmost need of treatment of the depression in arthritis patients in order to overcome their problem of sleep and reducing intensity of pain. Key Words: Depression, Sleep Quality, Pain, Arthritis
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Michaelides, Efstathios E. "Hydrodynamic Force and Heat/Mass Transfer From Particles, Bubbles, and Drops—The Freeman Scholar Lecture." Journal of Fluids Engineering 125, no. 2 (March 1, 2003): 209–38. http://dx.doi.org/10.1115/1.1537258.
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Recent advances on the analytical form of the hydrodynamic force and heat/mass transfer from a particle, bubble, or drop are examined critically. Also some of the recent computational studies, which help strengthen or clarify our knowledge of the complex velocity and temperature fields associated with the momentum and heat/mass transfer processes are also mentioned in a succinct way. Whenever possible, the processes of energy/mass exchange and of momentum exchange from spheres and spheroids are examined simultaneously and any common results and possible analogies between these processes are pointed out. This approach results in a better comprehension of the transport processes, which are very similar in nature, as well as in the better understanding of the theoretical expressions that are currently used to model these processes. Of the various terms that appear in the transient equations, emphasis is given to the history terms, which are lesser known and more difficult to calculate. The origin, form, and method of computation of the history terms are pointed out as well as the effects of various parameters on them. Among the other topics examined here are the differences in the governing and derived equations resulting by finite Reynolds and Peclet numbers; the origin, theoretical validity and accuracy of the semi-empirical expressions; the effects of finite internal viscosity and conductivity of the sphere; the effects of small departures from the spherical shape; the effects of the finite concentration; and the transverse, or lift, components of the force on the sphere.
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Froitzheim, Andreas, Rodrigo Ezeta, Sander G. Huisman, Sebastian Merbold, Chao Sun, Detlef Lohse, and Christoph Egbers. "Statistics, plumes and azimuthally travelling waves in ultimate Taylor–Couette turbulent vortices." Journal of Fluid Mechanics 876 (August 6, 2019): 733–65. http://dx.doi.org/10.1017/jfm.2019.552.
Full textAbstract:
In this paper, we experimentally study the influence of large-scale Taylor rolls on the small-scale statistics and the flow organization in fully turbulent Taylor–Couette flow for Reynolds numbers up to $Re_{S}=3\times 10^{5}$. The velocity field in the gap confined by coaxial and independently rotating cylinders at a radius ratio of $\unicode[STIX]{x1D702}=0.714$ is measured using planar particle image velocimetry in horizontal planes at different cylinder heights. Flow regions with and without prominent Taylor vortices are compared. We show that the local angular momentum transport (expressed in terms of a Nusselt number) mainly takes place in the regions of the vortex in- and outflow, where the radial and azimuthal velocity components are highly correlated. The efficient momentum transfer is reflected in intermittent bursts, which becomes visible in the exponential tails of the probability density functions of the local Nusselt number. In addition, by calculating azimuthal energy co-spectra, small-scale plumes are revealed to be the underlying structure of these bursts. These flow features are very similar to the one observed in Rayleigh–Bénard convection, which emphasizes the analogies of these systems. By performing a complex proper orthogonal decomposition, we remarkably detect azimuthally travelling waves superimposed on the turbulent Taylor vortices, not only in the classical but also in the ultimate regime. This very large-scale flow pattern, which is most pronounced at the axial location of the vortex centre, is similar to the well-known wavy Taylor vortex flow, which has comparable wave speeds, but much larger azimuthal wavenumbers.
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Pringle, Chris C. T., Ashley P. Willis, and Rich R. Kerswell. "Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos." Journal of Fluid Mechanics 702 (May 29, 2012): 415–43. http://dx.doi.org/10.1017/jfm.2012.192.
Full textAbstract:
AbstractWe propose a general strategy for determining the minimal finite amplitude disturbance that triggers transition to turbulence in shear flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude which respect the boundary conditions, incompressibility and the Navier–Stokes equations, to maximize a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe flow. Our results indicate that the variational problem yields a smooth converged solution provided that the initial amplitude is below the threshold for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth optimal. At the critical threshold, the optimization seeks out a disturbance that is on the ‘edge’ of turbulence during the period. Above this threshold, when disturbances trigger turbulence by the end of the period, convergence is then practically impossible. The first disturbance found to trigger turbulence as the amplitude is increased identifies the ‘minimal seed’ for the given geometry and forcing (Reynolds number). We conjecture that it may be possible to select a functional such that the converged optimal below threshold smoothly converges to the minimal seed at threshold. Our choice of the energy growth functional is shown to come close to this for the pipe flow geometry investigated here.
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BUSH, JOHN W. M. "The anomalous wake accompanying bubbles rising in a thin gap: a mechanically forced Marangoni flow." Journal of Fluid Mechanics 352 (December 10, 1997): 283–303. http://dx.doi.org/10.1017/s0022112097007350.
Full textAbstract:
A novel wake structure, observed as penny-shaped air bubbles rise at moderate Reynolds number through a thin layer of water bound between parallel glass plates inclined at a shallow angle relative to the horizontal, is reported. The structure of the wake is revealed through tracking particles suspended in the water. The wake completely encircles the rising bubble, and is characterized by a reverse surface flow or ‘edge jet’ which transports fluid in a thin boundary layer along the bubble surface from the tail to the nose at speeds which are typically an order of magnitude larger than the bubble rise speed. A consistent physical explanation for the wake structure is proposed. The wake is revealed to be a manifestation of the three-dimensionality of the flow in the suspending fluid. The bubble surface advances through a rolling motion, thus generating regions of surface divergence and convergence at, respectively, the leading and trailing edges of the bubble. A nose-to-tail gradient in surfactant concentration is thus established, and the associated surface tension gradient drives the edge jet. The dependence of the wake structure on the suspending fluid is examined experimentally.Surfactants play an anomalous role in the reported flow, serving to promote rather than suppress surface motions. The wake structure is an example of a mechanically forced Marangoni flow, and so represents a mechanical analogue of that accompanying thermocapillary drop motion in microgravity. A theoretical model is developed which reproduces the salient features of the flow, and on the basis of which an estimate is made of the mechanically induced surface tension gradient along the bubble surface.