Journal articles on the topic 'Constant speed flows'
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1
Holyoake, Alex J., and Jim N. McElwaine. "High-speed granular chute flows." Journal of Fluid Mechanics 710 (August 31, 2012): 35–71. http://dx.doi.org/10.1017/jfm.2012.331.
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AbstractThis paper reports experimental findings on the flow of sand down a steep chute. Nearly all granular flow models have a maximum value for the friction and therefore predict that flows on steep slopes will accelerate at a constant rate until the interaction with the ambient fluid becomes important. This prediction has not been tested by previous work, which has focused on relatively low slope angles where steady, fully developed flows occur after short distances. We test this by investigating flows over a much greater range of slope angles (30–50${}^{\ensuremath{\circ} } $) and flow depths (4–130 particle diameters). We examine flows with two basal conditions, one flat and frictional, the other bumpy. The latter imposes a no-slip condition for slow, deep flows, but permits some degree of slip for high flow velocities. The data suggests that friction can be much larger than theories such as the $\ensuremath{\mu} (I)$ rheology proposed by Jop, Forterre & Pouliquen (Nature, vol. 441, 2006) suggest and that there may be constant velocity states above the angle of vanishing ${h}_{\mathit{stop}} $. Although these flows do not vary in time, all but the flows on the bumpy base at low inclinations accelerate down the slope. A recirculation mechanism sustains flows with a maximum mass flux of $20~\mathrm{kg} ~{\mathrm{s} }^{\ensuremath{-} 1} $, allowing observations to be made at multiple points for each flow for an indefinite period. Flows with Froude number in the range 0.1–25 and bulk inertial number 0.1–2.7 were observed in the dense regime, with surface velocities in the range 0.2–5.6 $\mathrm{m} ~{\mathrm{s} }^{\ensuremath{-} 1} $. Previous studies have focused on $I\lessapprox 0. 5$. We show that a numerical implementation of the $\ensuremath{\mu} (I)$ rheology does not fully capture the accelerating dynamics or the transverse velocity profile on the bumpy base. We also observe the transverse separation of the flow into a dense core flanked by dilute regions and the formation of longitudinal vortices.
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Huang, Yangyang, Monika Nitsche, and Eva Kanso. "Hovering in oscillatory flows." Journal of Fluid Mechanics 804 (September 9, 2016): 531–49. http://dx.doi.org/10.1017/jfm.2016.535.
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We investigate the hovering dynamics of rigid bodies with up-down asymmetry placed in oscillating background flows. Recent experiments on inanimate pyramid-shaped objects in oscillating flows with zero mean component demonstrate that the resulting aerodynamic forces are sufficient to keep the object aloft. The mechanisms responsible for this lift production are fundamentally unsteady and depend on the shed vorticity. Here, we consider a model system of a two-dimensional flyer and compute the unsteady, two-way coupling between the flyer and the surrounding fluid in the context of the vortex sheet model. We examine in detail the flow properties (frequency and speed) required for hovering and their dependence on the flyer’s characteristics (mass and geometry). We find that, at low oscillation frequencies, a flyer of a fixed mass and shape requires a constant amount of flow acceleration to hover, irrespective of the frequency and speed of the oscillating flow. Meanwhile, at high oscillation frequencies, the flow speed required to hover is constant. In either case, the aerodynamic requirements to hover (flow acceleration or flow speed) are an intrinsic property of the flyer itself. This physical insight could potentially have significant implications on the design of unmanned air vehicles as well as on understanding active hovering of live organisms that can manipulate their flapping motion to favour a larger oscillation amplitude or frequency.
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Flack, Ronald D., Steven B. Ainley, Klaus Brun, and Leonard Whitehead. "Laser Velocimeter Measurements in the Pump of an Automotive Torque Converter Part II – Effect of Pump Speed and Oil Viscosity." International Journal of Rotating Machinery 6, no. 3 (2000): 181–90. http://dx.doi.org/10.1155/s1023621x00000178.
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The velocity field inside a torque converter pump was studied for two separate effects: variable pump rotational speed and variable oil viscosity. Three-dimensional velocity measurements were taken using a laser velocimeter for both the pump mid- and exit planes. The effect ofvariable pump rotational speed was studied by running the pump at two different speeds and holding speed ratio (pump rotational speed]turbine rotational speed) constant. Similarly, the effect of viscosity on the pump flow field was studied by varying the temperature and]or using two different viscosity oils as the working fluid in the pump. Threedimensional velocity vector plots, through-flow contour plots, and secondary flow profiles were obtained for both pump planes and all test conditions. Results showed that torque converter mass flows increased approximately linearly with increasing pump rotational speed (and fixed speed ratio) but that the flow was not directly proportional to pump rotational speed. However, mass flows were seen to decrease as the oil viscosity was decreased with a resulting increased Reynolds number; for these conditions the high velocity regions were seen to decrease in size and low velocity regions were seen to increase in size. In the pump mid-plane strong counter-clockwise secondary flows and in the exit plane strong clockwise secondary flows were observed. The vorticities and slip factors were calculated from the experimental results and are presented. The torque core-to-shell and blade-to-blade torque distributions were calculated for both planes. Finally, the flow fields were seen to demonstrate similitude when Reynolds numbers were matched.
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GARRETT, CHRIS, and FRANK GERDES. "Hydraulic control of homogeneous shear flows." Journal of Fluid Mechanics 475 (January 25, 2003): 163–72. http://dx.doi.org/10.1017/s0022112002002884.
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If a shear flow of a homogeneous fluid preserves the shape of its velocity profile, a standard formula for the condition for hydraulic control suggests that this is achieved when the depth-averaged flow speed is less than (gh)1/2. On the other hand, shallow-water waves have a speed relative to the mean flow of more than (gh)1/2, suggesting that information could propagate upstream. This apparent paradox is resolved by showing that the internal stress required to maintain a constant velocity profile depends on flow derivatives along the channel, thus altering the wave speed without introducing damping. By contrast, an inviscid shear flow does not maintain the same profile shape, but it can be shown that long waves are stationary at a position of hydraulic control.
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Wang, B. Y., and I. I. Glass. "Boundary layer flows behind constant speed shock waves moving into a dusty gas." Shock Waves 1, no. 2 (June 1991): 135–44. http://dx.doi.org/10.1007/bf01414908.
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BOWERSOX, RODNEY D. W. "Extension of equilibrium turbulent heat flux models to high-speed shear flows." Journal of Fluid Mechanics 633 (August 25, 2009): 61–70. http://dx.doi.org/10.1017/s0022112009007691.
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An algebraic heat flux truncation model was derived for high-speed gaseous shear flows. The model was developed for high-temperature gases with caloric imperfections. Fluctuating dilatation moments were modelled via conservation of mass truncations. The present model provided significant improvements, up to 20%, in the temperature predictions over the gradient diffusion model for a Mach number ranging from 0.02 to 11.8. Analyses also showed that the near-wall dependence of the algebraic model agreed with expected scaling, where the constant Prandtl number model did not. This led to a simple modification of the turbulent Prandtl number model. Compressibility led to an explicit pressure gradient dependency with the present model. Analyses of a governing parameter indicated that these terms are negligibly small for low speeds. However, they may be important for high-speed flow.
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Kim, YC, Y. Tamura, A. Yoshida, T. Ito, W. Shan, and Q. Yang. "Experimental investigation of aerodynamic vibrations of solar wing system." Advances in Structural Engineering 21, no. 15 (May 7, 2018): 2217–26. http://dx.doi.org/10.1177/1369433218770799.
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The general characteristics of aerodynamic vibrations of a solar wing system were investigated through wind tunnel tests using an aeroelastic model under four oncoming flows. In total, 12 solar panels were suspended by cables and orientated horizontally. Distances between panels were set constant. Tests showed that the fluctuating displacement increases proportionally to the square of the mean wind speed for all wind directions in boundary-layer flows. Larger fluctuating displacements were found for boundary-layer flows with larger power-law indices. Under low-turbulence flow, the fluctuating displacement increased proportionally to the square of the mean wind speed for wind directions between 0° and 30°, but an instability vibration was observed at high mean wind speed for wind directions larger than 40°. And when the wind direction was larger than 60°, a limited vibration was observed at low mean wind speed and the instability vibration was also observed at high mean wind speed. Fluctuating displacements under grid-generated flow showed a similar trend to that of the boundary-layer flows, although the values became much smaller.
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Venkateswaran, S. "Experimental Study of Casing Boundary Layers in a Multistage Axial Compressor." Journal of Fluids Engineering 113, no. 2 (June 1, 1991): 240–44. http://dx.doi.org/10.1115/1.2909486.
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Measurements of the casing boundary layers were obtained in a four-stage, low speed axial flow compressor, to verify the ‘law of the wall’ applicability to these complex flows. Some of the available shear stress models of the two-dimensional flows have been examined towards the quantitative assessment of skin friction. The shear stress prediction obtained from the Ludwieg-Tillmann relation applied to the streamwise or untwisted profile agreed closely with the measured shear stress by the hot wire. The skin friction was fairly constant for rotor and stator flows and was close to the flat plate values. The boundary layer profiles exhibited a well pronounced semi-logarithmic region with the universal constants of the law of the wall far removed from the standard two dimensional values, especially for rotor flows. Stator flows showed signs of similarity to two dimensional flows.
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WYLIE, JONATHAN J., and HUAXIONG HUANG. "Extensional flows with viscous heating." Journal of Fluid Mechanics 571 (January 4, 2007): 359–70. http://dx.doi.org/10.1017/s0022112006003338.
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In this paper we investigate the role played by viscous heating in extensional flows of viscous threads with temperature-dependent viscosity. We show that there exists an interesting interplay between the effects of viscous heating, which accelerates thinning, and inertia, which prevents pinch-off. We first consider steady drawing of a thread that is fed through a fixed aperture at given speed and pulled with a constant force at a fixed downstream location. For pulling forces above a critical value, we show that inertialess solutions cannot exist and inertia is crucial in controlling the dynamics. We also consider the unsteady stretching of a thread that is fixed at one end and pulled with a constant force at the other end. In contrast to the case in which inertia is neglected, the thread will always pinch at the end where the force is applied. Our results show that viscous heating can have a profound effect on the final shape and total extension at pinching.
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ZHU, DAVID Z., and GREGORY A. LAWRENCE. "Holmboe's instability in exchange flows." Journal of Fluid Mechanics 429 (February 25, 2001): 391–409. http://dx.doi.org/10.1017/s002211200000286x.
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A laboratory study of the exchange of two fluids of different density through a constant-width channel with an underwater sill has enabled us to study Holmboe's instability in greater detail than has been possible in mixing-layer experiments. The internal hydraulics of the exchange flow are such that we have been able to observe the initiation of instability, the development and behaviour of both symmetric and asymmetric Holmboe instabilities, and the suppression of the instability at bulk Richardson numbers above about 0.7. A number of stability criteria resulting from previous numerical investigations have been verified experimentally. Our laboratory measurements are consistent with theoretical predictions of wave speed and wavenumber.
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Ardalan, K., D. I. Meiron, and D. I. Pullin. "Steady compressible vortex flows: the hollow-core vortex array." Journal of Fluid Mechanics 301 (October 25, 1995): 1–17. http://dx.doi.org/10.1017/s0022112095003764.
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We examine the effects of compressiblity on the structure of a single row of hollowcore, constant-pressure vortices. The problem is formulated and solved in the hodograph plane. The transformation from the physical plane to the hodograph plane results in a linear problem that is solved numerically. The numerical solution is checked via a Rayleigh-Janzen expansion. It is observed that for an appropriate choice of the parameters M∞ = q∞/c∞, and the speed ratio, a = q∞/qv, where qv is the speed on the vortex boundary, transonic shock-free flow exists. Also, for a given fixed speed ratio, a, the vortices shrink in size and get closer as the Mach number at infinity, M∞, is increased. In the limit of an evacuated vortex core, we find that all such solutions exhibit cuspidal behaviour corresponding to the onset of limit lines.
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Wang, Shuai, Jianping Tan, and Zheqin Yu. "Shear Stress and Hemolysis Analysis of Blood Pump under Constant and Pulsation Speed Based on a Multiscale Coupling Model." Mathematical Problems in Engineering 2020 (July 14, 2020): 1–14. http://dx.doi.org/10.1155/2020/8341827.
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Current researches show that the constant speed mode adopted by the existing commercial blood pump may cause damage to the body. The way to solve this problem is to produce pulsating flow by changing the speed of the blood pump’s impeller. But at present, the flow field of the blood pump is not clear, when it changes speed, and the coupling between blood pump and body has not been considered in the simulation of the flow field. A multiscale coupling model combining hemodynamics (0D) and Computational Fluid Dynamics (3D) was established in this paper to solve the problem, and a speed change curve consistent with the ventricular motion was selected. The hemodynamics, shear stress, and hemolysis changes of 6000 rpm at different amplitude (2000, 3000, and 4000 rpm) were simulated, analyzed, and compared with the constant speed (7000 rpm). The results show that the pressure difference obtained by simulation is consistent with the experimental results, and the flow generated by the natural heart still flows through the blood pump, thus changing the working point of the blood pump. When the blood pump works at the changing speed, it could produce more pulsation, and the shear stress and hemolysis in the blood pump increase with the rising of speed and flow. But according to the hemolysis score of a single cardiac cycle, the hemolysis value of the changing speed model at an amplitude of 4000 rpm is only 11.71% higher than that of constant speed at 7000 rpm.
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Keady, G. "Asymptotic estimates for symmetric vortex streets." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 26, no. 4 (April 1985): 487–502. http://dx.doi.org/10.1017/s0334270000004677.
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AbstractSteady plane inviscid symmetric vortex streets are flows defined in the stripR× (0,b) and periodic inxwith period 2ain which the flow in (−a,a) × (0,b) is irrotational outside a vortex core on which the vorticity takes a prescribed constant value. A family of such vortex street flows, characterised by a variational principle in which the area |Aα| and the centroidycof the vortex coreAαare fixed, will be considered. For such a family, indexed by a parameter α, suppose that the coresAαbecome small in the sense thatAsymptotic estimates on functionals such as flux constant and speed are obtained.
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Martin, Calin Iulian. "On periodic geophysical water flows with discontinuous vorticity in the equatorial f -plane approximation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2111 (December 11, 2017): 20170096. http://dx.doi.org/10.1098/rsta.2017.0096.
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We are concerned here with geophysical water waves arising as the free surface of water flows governed by the f -plane approximation. Allowing for an arbitrary bounded discontinuous vorticity, we prove the existence of steady periodic two-dimensional waves of small amplitude. We illustrate the local bifurcation result by means of an analysis of the dispersion relation for a two-layered fluid consisting of a layer of constant non-zero vorticity γ 1 adjacent to the surface situated above another layer of constant non-zero vorticity γ 2 ≠ γ 1 adjacent to the bed. For certain vorticities γ 1 , γ 2 , we also provide estimates for the wave speed c in terms of the speed at the surface of the bifurcation inducing laminar flows. This article is part of the theme issue ‘Nonlinear water waves’.
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Hao, Y., and Z. Q. Wu. "Random Flutter of Multi-Stable Airfoils Excited Parametrically in Steady Flows." Journal of Mechanics 35, no. 3 (July 2, 2018): 419–26. http://dx.doi.org/10.1017/jmech.2018.19.
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ABSTRACTIn this article, random flutter of multi-stable airfoils in steady flow is investigated by means of the analytical method for stochastic P-bifurcation, where the effect of the stochastic disturbance in the generalized flow speed on the airfoils is considered. The results show that under constant stochastic disturbance intensity, the coherence resonance could be induced by the variation of generalized flow speed. In addition, if the generalized flow speed keeps unchanged and its stochastic disturbance is sufficiently large, the response of the system will tend to be a stable equilibrium. It indicates that the parametric stochastic disturbance is effective to maintain system stability. Moreover, it is shown in this paper that the analytical method for stochastic P-bifurcation can be extended to study stochastic P-bifurcations in other high-dimensional systems.
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van Kuik, Gijs A. M. "On the velocity at wind turbine and propeller actuator discs." Wind Energy Science 5, no. 3 (July 7, 2020): 855–65. http://dx.doi.org/10.5194/wes-5-855-2020.
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Abstract. The first version of the actuator disc momentum theory is more than 100 years old. The extension towards very low rotational speeds with high torque for discs with a constant circulation became available only recently. This theory gives the performance data like the power coefficient and average velocity at the disc. Potential flow calculations have added flow properties like the distribution of this velocity. The present paper addresses the comparison of actuator discs representing propellers and wind turbines, with emphasis on the velocity at the disc. At a low rotational speed, propeller discs have an expanding wake while still energy is put into the wake. The high angular momentum of the wake, due to the high torque, creates a pressure deficit which is supplemented by the pressure added by the disc thrust. This results in a positive energy balance while the wake axial velocity has lowered. In the propeller and wind turbine flow regime the velocity at the disc is 0 for a certain minimum but non-zero rotational speed. At the disc, the distribution of the axial velocity component is non-uniform in all actuator disc flows. However, the distribution of the velocity in the plane containing the axis, the meridian plane, is practically uniform (deviation <0.2 %) for wind turbine disc flows with tip speed ratio λ>5, almost uniform (deviation ≈2 %) for wind turbine disc flows with λ=1 and propeller flows with advance ratio J=π, and non-uniform (deviation 5 %) for the propeller disc flow with wake expansion at J=2π. These differences in uniformity are caused by the different strengths of the singularity in the wake boundary vorticity strength at its leading edge.
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KIM, DONGJOO, and HAECHEON CHOI. "Laminar flow past a sphere rotating in the streamwise direction." Journal of Fluid Mechanics 461 (June 25, 2002): 365–86. http://dx.doi.org/10.1017/s0022112002008509.
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Numerical simulations are conducted for laminar flow past a sphere rotating in the streamwise direction, in order to investigate the effect of the rotation on the characteristics of flow over the sphere. The Reynolds numbers considered are Re = 100, 250 and 300 based on the free-stream velocity and sphere diameter, and the rotational speeds are in the range of 0 [les ] ω* [les ] 1, where ω* is the maximum azimuthal velocity on the sphere surface normalized by the free-stream velocity. At ω* = 0 (without rotation), the flow past the sphere is steady axisymmetric, steady planar-symmetric, and unsteady planar-symmetric, respectively, at Re = 100, 250 and 300. Thus, the time-averaged lift forces exerted on the stationary sphere are not zero at Re = 250 and 300. When the rotational speed increases, the time-averaged drag force increases for the Reynolds numbers investigated, whereas the time-averaged lift force is zero for all ω* > 0. On the other hand, the lift force fluctuations show a non-monotonic behaviour with respect to the rotational speed. At Re = 100, the flow past the sphere is steady axisymmetric for all the rotational speeds considered and thus the lift force fluctuation is zero. At Re = 250 and 300, however, the flows are unsteady with rotation and the lift force fluctuations first decrease and then increase with increasing rotational speed, showing a local minimum at a specific rotational speed. The vortical structures behind the sphere are also significantly modified by the rotation. For example, at Re = 300, the flows become ‘frozen’ at ω* = 0.5 and 0.6, i.e. the vortical structures in the wake simply rotate without temporal variation of their strength and the magnitude of the instantaneous lift force is constant in time. It is shown that the flow becomes frozen at higher rotational speed with increasing Reynolds number. The rotation speed of the vortical structures is shown to be slower than that of the sphere.
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Campos, L. M. B. C., and M. H. Kobayashi. "On the Propagation of Sound in a High-Speed Non-Isothermal Shear Flow." International Journal of Aeroacoustics 8, no. 3 (May 2009): 199–230. http://dx.doi.org/10.1260/147547208786940035.
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The propagation of sound in shear flows is relevant to the acoustics of wall and duct boundary layers, and to jet shear layers. The acoustic wave equation in a shear flow has been solved exactly only for a plane unidirectional homentropic mean shear flow, in the case of three velocity profiles: linear, exponential and hyperbolic tangent. The assumption of homentropic mean flow restricts application to isothermal shear flows. In the present paper the wave equation in an plane unidirectional shear flow with a linear velocity profile is solved in an isentropic non-homentropic case, which allows for the presence of transverse temperature gradients associated with the ***non-uniform sound speed. The sound speed profile is specified by the condition of constant enthalpy, i.e. homenergetic shear flow. In this case the acoustic wave equation has three singularities at finite distance (besides the point at infinity), viz. the critical layer where the Doppler shifted frequency vanishes, and the critical flow points where the sound speed vanishes. By matching pairs of solutions around the singular and regular points, the amplitude and phase of the acoustic pressure in calculated and plotted for several combinations of wavelength and wave frequency, mean flow vorticity and sound speed, demonstrating, among others, some cases of sound suppression at the critical layer.
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Ainley, Steven B., Ronald D. Flack, Klaus Brun, and Tony J. Rovello. "Laser Velocimeter Measurements in the Pump of an Automotive Torque Converter Part I – Effect of Speed Ratio." International Journal of Rotating Machinery 6, no. 3 (2000): 167–80. http://dx.doi.org/10.1155/s1023621x00000166.
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A torque converter was tested at four turbine/pump rotational speed ratios (0.200, 0.400, 0.600, and 0.800) all with a constant pump rotational speed in order to determine the effect of speed ratio on the torque converter pump flow field. Laser velocimetry was used to measure three components of velocity within the pump and a shaft encoder was employed to record the instantaneous pump angular position. Shaft encoder information was correlated with measured velocities to develop flow field blade-to-blade profiles and vector plots. Measurements were obtained in both the pump mid- and exit planes for all four speed ratios. Results showed large separation regions and jet/wake flows throughout the pump. The midplane flow was found to have strong counter-clockwise secondary components and the exit plane flow had strong clockwise secondary components. Mass flows were calculated from the velocity data and were found to decrease as the speed ratio was increased. Also, the vorticity and slip factors were calculated from the experimental data and are included. The mid-plane slip factors compare favorably to those for conventional centrifugal pumps but less slip was present in the exit plane than the mid-plane. Neither the slip factor nor the vorticity were seen to be strongly affected by the speed ratio. Finally, the torque core-to-shell and blade-to-blade torque distributions are presented for both planes.
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Papangelou, A. "Vortex shedding from slender cones at low Reynolds numbers." Journal of Fluid Mechanics 242 (September 1992): 299–321. http://dx.doi.org/10.1017/s0022112092002386.
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Wind-tunnel experiments on the flows created by a number of slightly tapered models of circular cross-section have shown the presence of spanwise cells (regions of constant shedding frequency) at Reynolds numbers of the order of 100. The experiments have also shown a number of other interesting features of these flows: the cellular flow configuration is dependent on the base Reynolds number and independent of the tip Reynolds number, the frequency jump between adjacent cells is a function of flow speed, taper angle and kinematic viscosity, but is constant along a cone's span, and the unsteady hot-wire anemometer signal is both amplitude and phase modulated. A mathematical model is proposed based on the complex Landau—Stuart equation with a spanwise diffusive coupling term. Numerical solutions of this equation have shown many of the qualitative features observed in the experiments.
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Moore, D. W., and D. I. Pullin. "The compressible vortex pair." Journal of Fluid Mechanics 185 (December 1987): 171–204. http://dx.doi.org/10.1017/s0022112087003136.
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We consider the steady self-propagation with respect to the fluid at infinity of two equal symmetrically shaped vortices in a compressible fluid. Each vortex core is modelled by a region of stagnant constant-pressure fluid bounded by closed constant-pressure, constant-speed streamlines of unknown shape. The external flow is assumed to be irrotational inviscid isentropic flow of a perfect gas. The flow is therefore shock free but may be locally supersonic. The nonlinear free-boundary problem for the vortex-pair flow is formulated in the hodograph plane of compressible-flow theory, and a numerical solution method based on finite differences is described. Specific results are presented for a range of parameters which control the flow, namely the Mach number of the pair translational motion and the fluid speed on each vortex bounding streamline. Perturbation-theory predictions are developed, valid for vortices of small core radius when the pair Mach number is much less than unity. These are in good agreement with the hodograph-plane calculations. The numerical and the perturbation-theory results together confirm the recently discovered (Barsony-Nagy, Er-El & Yungster 1987) existence of continuous shock-free transonic compressible flows with embedded vortices. For the vortex-pair geometry studied, solution branches corresponding to physically acceptable flows that could be calculated using the present hodograph-plane numerical method were found to be terminated when either the flow on the streamline of symmetry separating the vortiqes tends to become superonic or when limiting lines appear in the hodograph plane giving a locally multivalued mapping to the physical plane.
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McC. HOGG, A., K. B. WINTERS, and G. N. IVEY. "Linear internal waves and the control of stratified exchange flows." Journal of Fluid Mechanics 447 (October 30, 2001): 357–75. http://dx.doi.org/10.1017/s0022112001006048.
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Internal hydraulic theory is often used to describe idealized bi-directional exchange flow through a constricted channel. This approach is formally applicable to layered flows in which velocity and density are represented by discontinuous functions that are constant within discrete layers. The theory relies on the determination of flow conditions at points of hydraulic control, where long interfacial waves have zero phase speed. In this paper, we consider hydraulic control in continuously stratified exchange flows. Such flows occur, for example, in channels connecting stratified reservoirs and between homogeneous basins when interfacial mixing is significant. Our focus here is on the propagation characteristics of the gravest vertical-mode internal waves within a laterally contracting channel.Two approaches are used to determine the behaviour of waves propagating through a steady, continuously sheared and stratified exchange flow. In the first, waves are mechanically excited at discrete locations within a numerically simulated bi-directional exchange flow and allowed to evolve under linear dynamics. These waves are then tracked in space and time to determine propagation speeds. A second approach, based on the stability theory of parallel shear flows and examination of solutions to a sixth-order eigenvalue problem, is used to interpret the direct excitation experiments. Two types of gravest mode eigensolutions are identified: vorticity modes, with eigenfunction maxima centred above and below the region of maximum density gradient, and density modes with maxima centred on the strongly stratified layer. Density modes have phase speeds that change sign within the channel and are analogous to the interfacial waves in hydraulic theory. Vorticity modes have finite propagation speed throughout the channel but undergo a transition in form: upwind of the transition point the vorticity mode is trapped in one layer. It is argued that modes trapped in one layer are not capable of communicating interfacial information, and therefore that the transition points are analogous to control points. The location of transition points are identified and used to generalize the notion of hydraulic control in continuously stratified flows.
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Korda, David, and Michal Švanda. "Combined helioseismic inversions for 3D vector flows and sound-speed perturbations." Astronomy & Astrophysics 622 (February 2019): A163. http://dx.doi.org/10.1051/0004-6361/201833000.
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Context. Time–distance helioseismology is the method of the study of the propagation of waves through the solar interior via the travel times of those waves. The travel times of wave packets contain information about the conditions in the interior integrated along the propagation path of the wave. The travel times are sensitive to perturbations of a variety of quantities. The usual task is to invert for the vector of plasma flows or the sound–speed perturbations separately. The separate inversions may be polluted by systematic bias, for instance, originating in the leakage of vector flows into the sound–speed perturbations and vice versa (called a cross-talk). Information about the cross-talk is necessary for a proper interpretation of results. Aims. We introduce an improved methodology of the time-distance helioseismology which allows us to invert for a full 3D vector of plasma flows and the sound–speed perturbations at once. Using this methodology one can also derive the mean value of the vertical component of plasma flows and the cross-talk between the plasma flows and the sound–speed perturbations. Methods. We used the Subtractive Optimally Localised Averaging method with a minimisation of the cross-talk as a tool for inverse modelling. In the forward model, we use Born approximation travel-time sensitivity kernels with the Model S as a background. The methodology was validated using forward-modelled travel times with both mean and difference point-to-annulus averaging geometries applied to a snapshot of fully self-consistent simulation of the convection. Results. We tested the methodology on synthetic data. We demonstrate that we are able to recover flows and sound–speed perturbations in the near-surface layers. We have taken the advantage of the sensitivity of our methodology to entire vertical velocity, and not only to its variations as in other available methodologies. The cross-talk from both the vertical flow component and the sound–speed perturbation has only a negligible effect for inversions for the horizontal flow components. Furthermore, this cross-talk can be minimised if needed. The inversions for the vertical component of the vector flows or for the sound–speed perturbations are affected by the cross-talk from the horizontal components, which needs to be minimised in order to provide valid results. It seems that there is a nearly constant cross-talk between the vertical component of the vector flows and the sound–speed perturbations.
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Yadav, Navneet K., and Arnab Samanta. "The stability of compressible swirling pipe flows with density stratification." Journal of Fluid Mechanics 823 (June 23, 2017): 689–715. http://dx.doi.org/10.1017/jfm.2017.335.
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We investigate the spatial stability of compressible, viscous pipe flows with radius-dependent mean density profiles, subjected to solid body rotations. For a fixed Rossby number $\unicode[STIX]{x1D716}$ (inverse of the rotational speed), as the Reynolds number $Re$ is increased, the flow transitions from being stable to convectively unstable, usually leading to absolute instability. If flow compressibility is unimportant and $Re$ is held constant, there appears to be a maximum $Re$ below which the flow remains stable irrespective of any rotational speed, or a minimum azimuthal Reynolds number $Re_{\unicode[STIX]{x1D703}}$ $(=Re/\unicode[STIX]{x1D716})$ is required for any occurrence of absolute instabilities. Once compressible forces are significant, the effect of pressure–density coupling is found to be more severe below a critical $Re$, where as rotational speeds are raised, a stable flow almost directly transitions to an absolutely unstable state. This happens at a critical $Re_{\unicode[STIX]{x1D703}}$ which reduces with increased flow Mach number, pointing to compressibility aiding in the instability at these lower Reynolds numbers. However, at higher $Re$, above the critical value, the traditional stabilizing role of compressibility is recovered if mean density stratification exists, where the gradients of density play an equally important role, more so at the higher azimuthal modes. A total disturbance energy-based formulation is used to obtain mechanistic understanding at these stability states, where we find the entropic energy perturbations to dominate as the primary instability mechanism, in sharp contrast to the energy due to axial shear, known to play a leading role in incompressible swirling flows.
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DUAN, RENJUN. "GLOBAL SMOOTH FLOWS FOR THE COMPRESSIBLE EULER–MAXWELL SYSTEM: THE RELAXATION CASE." Journal of Hyperbolic Differential Equations 08, no. 02 (June 2011): 375–413. http://dx.doi.org/10.1142/s0219891611002421.
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The Euler–Maxwell system regarded as a hydrodynamic model for plasma physics describes the dynamics of 'compressible electrons' in a constant, charged, non-moving ion background. A global smooth flow with small amplitude is constructed here in three space dimensions when the electron velocity relaxation is taken into account. The speed of the electron flow tending to a uniform equilibrium, and the pointwise behavior of solutions to the linearized homogeneous system in the frequency space are investigated in detail.
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VANNESTE, J., and J. G. BYATT-SMITH. "Fast scalar decay in a shear flow: modes and pseudomodes." Journal of Fluid Mechanics 572 (January 23, 2007): 219–29. http://dx.doi.org/10.1017/s0022112006003661.
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The decay of a passive scalar in a sinusoidal shear flow translating in the cross-stream direction at a constant speed u is studied in the limit of small diffusivity κ. The decay rate, obtained by solving an eigenvalue problem, is found to tend to a non-zero constant as κ→0 when u is of order κ1/2. This result, establishing that fast decay is possible in shear flows, is fragile however: because of the existence of pseudomodes, the addition of a small noise leads to decay rates that decrease to zero with κ as κ2/5.
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Chien, S. Y., and M. S. Cramer. "Load and loss for high-speed lubrication flows of pressurized gases between non-concentric cylinders." Journal of Fluid Mechanics 867 (March 20, 2019): 1–25. http://dx.doi.org/10.1017/jfm.2019.113.
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We examine the high-speed flow of pressurized gases between non-concentric cylinders where the inner cylinder rotates at constant speed while the outer cylinder is stationary. The flow is taken to be steady, two-dimensional, compressible, laminar, single phase and governed by a Reynolds lubrication equation. Approximations for the lubricating force and friction loss are derived using a perturbation expansion for large speed numbers. The present theory is valid for general Navier–Stokes fluids at nearly all states corresponding to ideal, dense and supercritical gases. Results of interest include the observation that pressurization gives rise to large increases in the lubricating force and decreases in the fluid friction. The lubrication force is found to scale with the bulk modulus. Within the context of the Reynolds equation an exact relation between total heat transfer and power loss is developed.
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GUO, ZHENGGUANG, PETER WITTWER, and YONG ZHOU. "LEADING ORDER ASYMPTOTICS OF STATIONARY NAVIER–STOKES FLOWS IN THE PRESENCE OF A WALL." Mathematical Models and Methods in Applied Sciences 22, no. 03 (March 2012): 1150018. http://dx.doi.org/10.1142/s0218202511500187.
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We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. We give a detailed description of the asymptotic behavior on the fluid flow in a half-space using as a starting point the theory of existence of solutions which is obtained by interpreting the coordinate perpendicular to the wall as time variable.
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Noblesse, Francis, Gérard Delhommeau, and Chi Yang. "Practical Evaluation of Steady Flow Resulting from a Free-Surface Pressure Patch." Journal of Ship Research 53, no. 03 (September 1, 2009): 137–50. http://dx.doi.org/10.5957/jsr.2009.53.3.137.
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The linearized potential flow resulting from a distribution of pressure that advances at constant speed along a straight path at the free surface of calm water, of effectively infinite depth and lateral extent, is considered. A practical method for evaluating the free-surface elevation caused by the moving free-surface pressure patch—which can be used to model steady flows of air-cushion vehicles, high-speed planing boats, surface-effect ships, and some types of hybrid ships—is given. The key ingredient of this method is a highly simplified analytical approximation to the local-flow component in the expression for the Green function associated with the classic Michell-Kelvin linearized free-surface boundary condition.
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Webber, Mark. "Instability of thread-annular flow with small characteristic length to three-dimensional disturbances." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2091 (January 8, 2008): 673–90. http://dx.doi.org/10.1098/rspa.2007.1907.
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We present a linear stability analysis of viscous, pressure-driven flow in an annular pipe with a moving core. The core moves with constant speed along its axis and rotates with constant angular frequency. At both boundaries the fluid obeys slip boundary conditions. Our numerical results highlight the important role of asymmetric perturbations in the instability of the system. Boundary slip is seen to be stabilizing, as has been observed for other types of parallel flows. We show that motion of the solid core with respect to the outer cylinder causes the neutral curve to split into two distinct curves. In particular, we show that rotation has a surprising destabilizing effect.
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Papaioannou, Nick, Felix CP Leach, Martin H. Davy, Adam Weall, and Brian Cooper. "Evaluation of exhaust gas recirculation techniques on a high-speed direct injection diesel engine using first law analysis." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 233, no. 3 (January 23, 2018): 710–26. http://dx.doi.org/10.1177/0954407017749110.
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The effects of different exhaust gas recirculation (EGR) strategies on engine efficiency and the resulting energy flows at two speed/load conditions (1500 r/min/6.8 bar net indicated mean effective pressure (nIMEP) and 1750 r/min/13.5 bar nIMEP) were studied using a first law analysis approach. The EGR strategies tested were as follows: cooled high-pressure exhaust gas recirculation (baseline), the application of exhaust gas recirculation with the swirl flap closed and the use of exhaust gas recirculation under constant λ conditions. The closed swirl flap exhaust gas recirculation strategy reduced brake efficiency under high load conditions and increased heat transfer to the coolant for both load cases. Soot and CO emissions increased at high load, however, with an increase in NOx relative to the baseline case. The constant λ exhaust gas recirculation strategy reduced brake efficiency under low load, as well as the heat flow to the coolant for both load cases. The constant λ exhaust gas recirculation strategy benefited smoke emissions and increased combustion exhaust gas recirculation tolerance, albeit with a penalty in NOx emission.
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Forbes, Lawrence K., and Graeme C. Hocking. "The bath-plug vortex." Journal of Fluid Mechanics 284 (February 10, 1995): 43–62. http://dx.doi.org/10.1017/s0022112095000267.
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Steady flow with constant circulation into a vertical drain is considered. The precise details of the outflow are simplified by assuming that the drain is equivalent to a distributed volume sink, into which the fluid flows with uniform downward speed. It is shown that a maximum outflow rate exists, corresponding to no fluid circulation and vertical entry into the drain hole. Numerical solutions to the full nonlinear problem are computed, using the method of fundamental solutions. An approximate analysis, based on the use of the shallow-water equations, is presented for flows in which the free surface enters the drain. There is, in addition, a second type of solution, having a stagnation point at the free surface and no fluid circulation. These flows are also computed numerically, and results are presented.
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Grotberg, J. B., and N. Gavriely. "Flutter in collapsible tubes: a theoretical model of wheezes." Journal of Applied Physiology 66, no. 5 (May 1, 1989): 2262–73. http://dx.doi.org/10.1152/jappl.1989.66.5.2262.
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A mathematical analysis of flow through a flexible channel is examined as a model of flow-induced flutter oscillations that pertain to the production of wheezing breath sounds. The model provides predictions for the critical fluid speed that will initiate flutter waves of the wall, as well as their frequency and wavelength. The mathematical results are separated into linear theory (small oscillations) and nonlinear theory (larger oscillations). Linear theory determines the onset of the flutter, whereas nonlinear theory determines the relationships between the fluid speed and both the wave amplitudes and frequencies. The linear theory predictions correlate well with data taken at the onset of flutter and flow limitation during experiments of airflow in thick-walled collapsible tubes. The nonlinear theory predictions correlate well with data taken as these flows are forced to higher velocities while keeping the flow rate constant. Particular ranges of the parameters are selected to investigate and discuss the applications to airway flows. According to this theory, the mechanism of generation of wheezes is based in the interactions of fluid forces and friction and wall elastic-restoring forces and damping. In particular, a phase delay between the fluid pressure and wall motion is necessary. The wave speed theory of flow limitation is discussed with respect to the specific data and the flutter model.
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Morenko, Konstantin S., and Sergey A. Morenko. "Power Model of a Small Wind Plant." Elektrotekhnologii i elektrooborudovanie v APK 67, no. 1 (March 28, 2020): 60–63. http://dx.doi.org/10.22314/2658-4859-2020-67-1-60-63.
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The production of small wind turbines requires constant modification of their designes. One of the main criteria for efficiency is the power of the wind farm. It makes it possible to evaluate the economic effect in simple categories and by simple means. (Research purpose) The research purpose is to develop a simplified scheme for estimating power flows in a wind farm to assess its main technical and economic indicators. (Materials and methods) The article describes the main operating modes of small wind power plant and correlates them with wind speeds. A small wind turbine with a capacity of 1.8 kilowatt with attack angle control with a nominal wind speed of 8 meters per second was used as the initial sample for testing. The dependence of the power of an operating small wind farm on the wind speed are presented in the article and was used for creating a mathematical model. (Results and discussion) It has been suggested that the efficiency at the nominal wind speed is maximum, but at the starting wind speed it is close to zero. The article presents a power model, the total power output of the installation, the static power loss dynamic power loss of power and aerodynamic limitations. In this case, the power of dynamic losses depends on the overall efficiency of the wind turbine, which is a function of the wind speed. The article presents graphical representation of these power flows. (Conclusions) The theoretical dependence of wind turbine capacity flows is a simple way to determine them in an existing wind turbine. The main characteristics of the model can be calculated from the dependence of power on wind speed, which significantly expands the possibilities of its application for further research. The model can be used in evaluating the effectiveness of the designed structure or changes in it.
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Colin de Verdière, A., and R. Tailleux. "The Interaction of a Baroclinic Mean Flow with Long Rossby Waves." Journal of Physical Oceanography 35, no. 5 (May 1, 2005): 865–79. http://dx.doi.org/10.1175/jpo2712.1.
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Abstract The effect of a baroclinic mean flow on long oceanic Rossby waves is studied using a combination of analytical and numerical solutions of the eigenvalue problem. The effect is summarized by the value of the nondimensional numberwhen the mean flow shear keeps a constant sign throughout the water column. Because previous studies have shown that no interaction occurs if the mean flow has the shape of the first unperturbed mode (the non–Doppler shift effect), an implicit assumption in the application of the present work to the real ocean is that the relative projections of the mean flow on the second and higher modes remain approximately constant. Because R2 is large at low latitudes between 10° and 30° (the southern branches of subtropical gyres or the regions of surface westward shear), the phase speed of the first mode is very slightly decreased from the no mean flow standard theory case. Between 30° and 40° latitudes (the northern branches of the subtropical gyres or the regions of surface eastward shear), R2 is O(10) and the westward phase speed can increase significantly (up to a factor of 2). At still higher latitudes when R2 is O(1) a critical transition occurs below which no discrete Rossby waves are found that might explain the absence of observations of zonal propagations at latitudes higher than 50°. Our case studies, chosen to represent the top-trapped and constant-sign shear profiles of observed mean flows, all show the importance of three main effects on the value of the first baroclinic mode Rossby wave speed: 1) the meridional gradient of the quantity N2/f (where N is the buoyancy frequency) rather than that of the potential vorticity fN2; 2) the curvature of the mean flow in the vertical direction, which appears particularly important to predict the sign of the phase speed correction to the no-mean-flow standard theory case: increase (decrease) of the westward phase speed when the surface-intensified mean flow is eastward (westward); and 3) a weighted vertical average of the mean flow velocity, acting as a Doppler-shift term, which is small in general but important to determine the precise value of the phase speed.
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MAURER, BENJAMIN D., DIOGO T. BOLSTER, and P. F. LINDEN. "Intrusive gravity currents between two stably stratified fluids." Journal of Fluid Mechanics 647 (March 18, 2010): 53–69. http://dx.doi.org/10.1017/s0022112009993752.
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We present an experimental and numerical study of one stratified fluid propagating into another. The two fluids are initially at rest in a horizontal channel and are separated by a vertical gate which is removed to start the flow. We consider the case in which the two fluids have the same mean densities but have different, constant, non-zero buoyancy frequencies. In this case the fluid with the smaller buoyancy frequency flows into the other fluid along the mid-depth of the channel in the form of an intrusion and two counter-flowing gravity currents of the fluid with the larger buoyancy frequency flow along the top and bottom boundaries of the channel. Working from the available potential energy of the system and measurements of the intrusion thickness, we develop an energy model to describe the speed of the intrusion in terms of the ratio of the two buoyancy frequencies. We examine the role of the stratification within the intrusion and the two gravity currents, and show that this stratification plays an important role in the internal structure of the flow, but has only a secondary effect on the speeds of the exchange flows.
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Goater, Alexander J. N., and Andrew J. Hogg. "Bounded dam-break flows with tailwaters." Journal of Fluid Mechanics 686 (September 27, 2011): 160–86. http://dx.doi.org/10.1017/jfm.2011.317.
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AbstractThe gravitationally driven collapse of a reservoir into an initially stationary layer of fluid, termed the tailwater, is studied using the nonlinear shallow water equations. The motion is tackled using the hodograph transformation of the governing equation which allows the solutions for velocity and depth of the shallow flowing layer to be constructed by analytical techniques. The front of the flow emerges as a bore across which the depth of the fluid jumps discontinuously to the tailwater depth. The speed of the front is initially constant, but progressively slows once the finite extent of the reservoir begins to influence the motion. There then emerges a variety of phenomena depending upon the depth of the tailwater relative to the initial depth of the reservoir. Provided that the tailwater is sufficiently deep, a region of quiescent fluid emerges adjacent to the rear wall of the reservoir, followed by a region within which the velocity is negative. Also it is shown that for non-vanishing tailwater depths, continuous solutions for the velocity and height of the flowing layer breakdown after a sufficient period and develop an interior bore, the location and time of inception of which are calculated directly from quasi-analytical solutions.
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Junevičius, Raimundas, and Marijonas Bogdevičius. "MATHEMATICAL MODELLING OF NETWORK TRAFFIC FLOW." TRANSPORT 24, no. 4 (December 31, 2009): 333–38. http://dx.doi.org/10.3846/1648-4142.2009.24.333-338.
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The article describes mathematical models of traffic flows to initiate different traffic flow processes. Separate elements of traffic flow models are made in a way to be connected together to get a single complex model. A model of straight road with different boundary conditions is presented as a separate part of the network traffic flow model. First testing is conducted in case the final point of the whole modelled traffic line is closed and no output from that point is possible. The second test is performed when a constant value of traffic flow speed and traffic flow rate is entered. Mathematical simulation is carried out and the obtained results are listed.
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Bavassano, B., R. Bruno, and H. Rosenbauer. "Compressive fluctuations in the solar wind and their polytropic index." Annales Geophysicae 14, no. 5 (May 31, 1996): 510–17. http://dx.doi.org/10.1007/s00585-996-0510-z.
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Abstract. Magnetohydrodynamic compressive fluctuations of the interplanetary plasma in the region from 0.3 to 1 AU have been characterized in terms of their polytropic index. Following Chandrasekhar's approach to polytropic fluids, this index has been determined through a fit of the observed variations of density and temperature. At least three different classes of fluctuations have been identified: (1) variations at constant thermal pressure, in low-speed solar wind and without a significant dependence on distance, (2) adiabatic variations, mainly close to 1 AU and without a relevant dependence on wind speed, and (3) variations at nearly constant density, in fast wind close to 0.3 AU. Variations at constant thermal pressure are probably a subset of the ensemble of total-pressure balanced structures, corresponding to cases in which the magnetic field magnitude does not vary appreciably throughout the structure. In this case the pressure equilibrium has to be assured by its thermal component only. The variations may be related to small flow-tubes with approximately the same magnetic-field intensity, convected by the wind in conditions of pressure equilibrium. This feature is mainly observed in low-velocity solar wind, in agreement with the magnetic topology (small open flow-tubes emerging through an ensemble of closed structures) expected for the source region of slow wind. Variations of adiabatic type may be related to magnetosonic waves excited by pressure imbalances between contiguous flow-tubes. Such imbalances are probably built up by interactions between wind flows with different speeds in the spiral geometry induced by the solar rotation. This may account for the fact that they are mainly found at a large distance from the sun. Temperature variations at almost constant density are mostly found in fast flows close to the sun. These are the solar wind regions with the best examples of incompressible behaviour. They are characterized by very stable values for particle density and magnetic intensity, and by fluctuations of Alfvénic type. It is likely that temperature fluctuations in these regions are a remnant of thermal features in the low solar atmosphere. In conclusion, the polytropic index appears to be a useful tool to understand the nature of the compressive turbulence in the interplanetary plasma, as far as the frozen-in magnetic field does not play a crucial role.
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Holzner, Markus, Baofang Song, Marc Avila, and Björn Hof. "Lagrangian approach to laminar–turbulent interfaces in transitional pipe flow." Journal of Fluid Mechanics 723 (April 16, 2013): 140–62. http://dx.doi.org/10.1017/jfm.2013.127.
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AbstractTransition in shear flows is characterized by localized turbulent regions embedded in the surrounding laminar flow. These so-called turbulent spots or puffs are observed in a variety of shear flows and in certain Reynolds-number regimes, and they are advected by the flow while keeping their characteristic length. We show here for the case of pipe flow that this seemingly passive advection of turbulent puffs involves continuous entrainment and relaminarization of laminar and turbulent fluid across strongly convoluted interfaces. Surprisingly, interface areas are almost two orders of magnitude larger than the pipe cross-section, while local entrainment velocities are much smaller than the mean speed. Even though these velocities were shown to be small and proportional to the Kolmogorov velocity scale (in agreement with a prediction by Corrsin) in a flow without mean shear before, we find that, in pipe flow, local entrainment velocities are about an order of magnitude smaller than this scale. The Lagrangian method used to study the dynamics of the laminar–turbulent interfaces allows accurate determination of the leading and trailing edge speeds. However, to resolve the highly complex interface dynamics requires much higher numerical resolutions than for ordinary turbulent flows. This method also reveals that the volume flux across the leading edge has the same radial dependence but the opposite sign as that across the trailing edge, and it is this symmetry that is responsible for the puff shape remaining constant.
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IAIA, J., and S. BETELU. "Solutions of the porous medium equation with degenerate interfaces." European Journal of Applied Mathematics 24, no. 3 (December 7, 2012): 315–41. http://dx.doi.org/10.1017/s0956792512000423.
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We prove the existence of a one-parameter family of solutions of the porous medium equation in which the interface is a half line whose end point advances at a constant speed. Then we prove the stability of the solutions under a suitable class of perturbations. We discuss the relevance of these solutions to gravity-driven flows of thin films, and show that some solutions develop a very thin triangular plateau in the direction of propagation and that the angle of the plateau and its thickness are decreasing functions of the speed.
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Gottlieb, James J. "An indirect method of measuring gas- and particulate-phase velocities of shock-induced dusty-gas flows." Canadian Journal of Physics 70, no. 2-3 (February 1, 1992): 122–33. http://dx.doi.org/10.1139/p92-016.
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A method of indirectly measuring the temporally varying velocities of both the particulate and gas phases in the nonequilibrium region of a shock wave moving at constant speed in a dusty-gas mixture is described. This method is implemented by using experimental data from shock-induced air flows containing glass beads 40 μm in diameter in a dusty-gas shock-tube facility featuring a large horizontal channel 197 mm high by 76 mm wide with a special dust-injection device. Simultaneous measurements of the shock-front speed with time-of-arrival gauges, particulate concentration by light extinctiometry, and combined particulate concentration and gas density by beta-ray absorption are used in conjunction with two mass conservation laws to provide these indirect two-phase velocity measurements. Direct measurements of the particulate-phase velocity by laser-Doppler velocimetry are also presented for comparison, and the capability of the indirect velocity-measurement method is assessed.
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GONZALEZ-JUEZ, E., and E. MEIBURG. "Shallow-water analysis of gravity-current flows past isolated obstacles." Journal of Fluid Mechanics 635 (September 10, 2009): 415–38. http://dx.doi.org/10.1017/s0022112009007678.
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The flow of a partial-depth lock-exchange gravity current past an isolated bottom-mounted obstacle is studied by means of two-dimensional direct numerical simulations and steady shallow-water theory. The simulations indicate that the flux of the current downstream of the obstacle is approximately constant in space and time. This information is employed to extend the shallow-water models of Rottman et al. (J. Hazard. Mater., vol. 11, 1985, pp. 325–340) and Lane-Serff, Beal & Hadfield (J. Fluid Mech., vol. 292, 1995, pp. 39–53), in order to predict the height and front speed of the downstream current as functions of the upstream Froude number and the ratio of obstacle to current height. The model predictions are found to agree closely with the simulation results. In addition, the shallow-water model provides an estimate for the maximum drag that lies within 10% of the simulation results for obstacles much larger than the boundary-layer thickness.
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Souza, F. A. de, V. D. Nguyen, and S. Tavoularis. "The structure of highly sheared turbulence." Journal of Fluid Mechanics 303 (November 25, 1995): 155–67. http://dx.doi.org/10.1017/s0022112095004216.
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Uniformly sheared flows have been generated in a high-speed wind tunnel at shear rates higher than previously achieved, in an effort to approach those in the inner turbulent boundary layer. As at lower shear rates, the turbulence structure was found to attain a self-similar state with approximately constant anisotropies and exponential kinetic energy growth. The normal Reynolds stress anisotropies showed no systematic dependence upon the mean shear within the examined range; however, the shear stress anisotropy was significantly lower than the low-shear values, in conformity with boundary layer measurements and direct numerical simulations of homogeneous shear flow.
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Chechina, Antonina, Natalia Churbanova, and Marina Trapeznikova. "Driver Behaviour Algorithms for the Cellular Automata-Based Mathematical Model of Traffic Flows." EPJ Web of Conferences 248 (2021): 02002. http://dx.doi.org/10.1051/epjconf/202124802002.
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The work is devoted to the development of new algorithms describing the complex interaction of drivers for the parallel numerical implementation of the traffic flow model developed by the authors based on the cellular automata theory. As is known from observations, the behaviour of drivers largely determines how difficult it will be to pass a section with a bottleneck (a narrowing, a motionless obstacle, etc.) or even without it at the same flow values. In such conditions, cars can move in a synchronized flow at a more or less constant speed or go into “stop-and-go” mode. The authors have developed a set of algorithms for a large number of different road situations, which is featured in this article.
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Liang, Jun-Hong, Xiaoliang Wan, Kenneth A. Rose, Peter P. Sullivan, and James C. McWilliams. "Horizontal Dispersion of Buoyant Materials in the Ocean Surface Boundary Layer." Journal of Physical Oceanography 48, no. 9 (September 2018): 2103–25. http://dx.doi.org/10.1175/jpo-d-18-0020.1.
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ABSTRACTThe horizontal dispersion of materials with a constant rising speed under the exclusive influence of ocean surface boundary layer (OSBL) flows is investigated using both three-dimensional turbulence-resolving Lagrangian particle trajectories and the classical theory of dispersion in bounded shear currents generalized for buoyant materials. Dispersion in the OSBL is caused by the vertical shear of mean horizontal currents and by the turbulent velocity fluctuations. It reaches a diffusive regime when the equilibrium vertical material distribution is established. Diffusivity from the classical shear dispersion theory agrees reasonably well with that diagnosed using three-dimensional particle trajectories. For weakly buoyant materials that can be mixed into the boundary layer, shear dispersion dominates turbulent dispersion. For strongly buoyant materials that stay at the ocean surface, shear dispersion is negligible compared to turbulent dispersion. The effective horizontal diffusivity due to shear dispersion is controlled by multiple factors, including wind speed, wave conditions, vertical diffusivity, mixed layer depth, latitude, and buoyant rising speed. With all other meteorological and hydrographic conditions being equal, the effective horizontal diffusivity is larger in wind-driven Ekman flows than in wave-driven Ekman–Stokes flows for weakly buoyant materials and is smaller in Ekman flows than in Ekman–Stokes flows for strongly buoyant materials. The effective horizontal diffusivity is further reduced when enhanced mixing by breaking waves is included. Dispersion by OSBL flows is weaker than that by submesoscale currents at a scale larger than 100 m. The analytic framework will improve subgrid-scale modeling in realistic particle trajectory models using currents from operational ocean models.
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Iornumbe, SI, T. Tivde, and RA Chia. "A Mathematical Model of Stratified Geophysical Fluid Flows Over Variable Bottom Topography." NIGERIAN ANNALS OF PURE AND APPLIED SCIENCES 3, no. 3b (November 15, 2020): 112–37. http://dx.doi.org/10.46912/napas.202.
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In this paper, a mathematical model of stratified geophysical fluid flow over variable bottom topography was derived for shallow water. The equations are derived from the principles of conservation of mass and conservation of momentum. The force acting on the fluid is gravity, represented by the gravitational constant. A system of six nonlinear partial differential equations was obtained as the model equations. The solutions of these models were obtained using perturbation method. The presence of the coriolis force in the shallow water equations were shown as the causes of the deflection of fluid parcels in the direction of wave motion and causes gravity waves to disperse. As water depth decreases due to varied bottom topography, the wave amplitude were shown to increase while the wavelength and wave speed decreases resulting in overturning of the wave. The results are presented graphically.
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Guo, Hua, Haiqiao Wang, and Zhirong Wu. "Model and Experiment on Resistance Loss of Wet Chordal Grid with Spray Pressure and Structural Parameters." Mathematical Problems in Engineering 2021 (February 4, 2021): 1–10. http://dx.doi.org/10.1155/2021/6682988.
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To reduce the dedusting resistance of wet vibrating string grille precipitators during dedusting in mine ventilation roadways, we investigated the dedusting resistance characteristics of water fog and water film coupling and determined the relationship between dedusting resistance and spray pressure, vibrating grid filling rate, and wind speed. A mathematical resistance coefficient model is established using hydrodynamics theory and capillary mechanics. The theoretical relationship of dedusting resistance is deduced. The results show that when wind speed is constant, the spray pressure and dedusting resistance are higher and the resistance is smaller with a high filling rate compared with a low filling rate. Constant spray pressure allows faster wind speeds and reverse pressure gradient forces to increase when dust flows around the wet vibrating wire, which makes the pressure distribution asymmetrical around the steel wire and increases resistance. Dust removal resistance of the resonance chord with a high filling rate is substantially lower than that with a low filling rate under the same working conditions. On the basis of satisfying the dedusting efficiency, the resonance chord dedusting system does not affect normal production and resistance is low. The spray pressure is controlled at 0.3–0.7 MPa and the optimal wind speed is 3–4 m/s. According to the theoretical calculation and experimental data, the optimal filling rate of a vibrating string grid plate is 77.8%, spray pressure is 0.7 MPa, and wind speed is 3.5 m/s. Dust removal with low resistance and improved economic benefit can thus be obtained.
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Pegler, Samuel S. "The dynamics of confined extensional flows." Journal of Fluid Mechanics 804 (August 31, 2016): 24–57. http://dx.doi.org/10.1017/jfm.2016.516.
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I present a theoretical and experimental study of floating viscous fluid films introduced into a channel of finite length, motivated by the flow of glacial ice shelves. The dynamics are characterized by a mixture of viscous extensional stresses, transverse shear stresses and a driving buoyancy force. A theory based on a width-integrated model is developed and investigated using analytical, asymptotic and numerical methods. With fluid introduced at a constant rate, the flow is found to approach a steady state with two possible asymptotic forms depending on the length of the channel. For channel lengths less than half the width, the flow is similar to a purely extensional one-dimensional flow, characterized by concave surface profiles and being insensitive to the position of the channel exit (or calving front). Greater lengths result in a more complex asymptotic structure in which the flow adjusts over a short distance towards a prevailing flow of universal dimensionless form. In complete contrast to the extensional regime, the prevailing flow is controlled by the position of the channel exit. Data from a new laboratory experiment involving particle velocimetry of a floating fluid film compares well with the predicted along-channel velocity. Motivated by glaciological application, the analysis is generalized to power-law rheologies and the results used to classify the flow regimes of a selection of ice shelves. The prediction for the frontal speed is in good agreement with geophysical data, indicating that the universal profile predicted by the theory is common in nature.
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CLASEN, C., J. BICO, V. M. ENTOV, and G. H. McKINLEY. "‘Gobbling drops’: the jetting–dripping transition in flows of polymer solutions." Journal of Fluid Mechanics 636 (September 25, 2009): 5–40. http://dx.doi.org/10.1017/s0022112009008143.
Full textAbstract:
This paper discusses the breakup of capillary jets of dilute polymer solutions and the dynamics associated with the transition from dripping to jetting. High-speed digital video imaging reveals a new scenario of transition and breakup via periodic growth and detachment of large terminal drops. The underlying mechanism is discussed and a basic theory for the mechanism of breakup is also presented. The dynamics of the terminal drop growth and trajectory prove to be governed primarily by mass and momentum balances involving capillary, gravity and inertial forces, whilst the drop detachment event is controlled by the kinetics of the thinning process in the viscoelastic ligaments that connect the drops. This thinning process of the ligaments that are subjected to a constant axial force is driven by surface tension and resisted by the viscoelasticity of the dissolved polymeric molecules. Analysis of this transition provides a new experimental method to probe the rheological properties of solutions when minute concentrations of macromolecules have been added.