scholarly journals Mean flow generation by three-dimensional nonlinear internal wave beams

2019 ◽  
Vol 864 ◽  
pp. 303-326 ◽  
Author(s):  
F. Beckebanze ◽  
K. J. Raja ◽  
L. R. M. Maas
Keyword(s):  
Internal Wave ◽  
Three Dimensional ◽  
Theoretical Expression ◽  
Mean Flow ◽  
Production Term ◽  
Nonlinear Internal Wave ◽  
Vertical Vorticity ◽  
Flow Generation ◽  
The Mean ◽  
Vorticity Production

We study the generation of resonantly growing mean flow by weakly nonlinear internal wave beams. With a perturbational expansion, we construct analytic solutions for three-dimensional internal wave beams, exact up to first-order accuracy in the viscosity parameter. We specifically focus on the subtleties of wave beam generation by oscillating boundaries, such as wave makers in laboratory set-ups. The exact solutions to the linearized equations allow us to derive an analytic expression for the mean vertical vorticity production term, which induces a horizontal mean flow. Whereas mean flow generation associated with viscous beam attenuation – known as streaming – has been described before, we are the first to also include a peculiar inviscid mean flow generation in the vicinity of the oscillating wall, resulting from line vortices at the lateral edges of the oscillating boundary. Our theoretical expression for the mean vertical vorticity production is in good agreement with earlier laboratory experiments, for which the previously unrecognized inviscid mean flow generation mechanism turns out to be significant.

Effect of background mean flow on PSI of internal wave beams

2019 ◽  
Vol 869 ◽  
Author(s):  
Boyu Fan ◽  
T. R. Akylas
Keyword(s):  
Internal Wave ◽  
Evolution Equations ◽  
Internal Gravity Wave ◽  
Necessary Condition ◽  
Finite Width ◽  
Asymptotic Model ◽  
Mean Flow ◽  
Short Scale ◽  
The Mean ◽  
Parametric Subharmonic Instability

An asymptotic model is developed for the parametric subharmonic instability (PSI) of finite-width nearly monochromatic internal gravity wave beams in the presence of a background constant horizontal mean flow. The subharmonic perturbations are taken to be short-scale wavepackets that may extract energy via resonant triad interactions while in contact with the underlying beam, and the mean flow is assumed to be small so that its advection effect on the perturbations is as important as dispersion, triad nonlinearity and viscous dissipation. In this ‘distinguished limit’, the perturbation dynamics are governed by the same evolution equations as those derived in Karimi & Akylas (J. Fluid Mech., vol. 757, 2014, pp. 381–402), except for a mean flow term that affects the group velocity of the perturbations and imposes an additional necessary condition for PSI, which stabilizes very short-scale perturbations. As a result, it is possible for a small amount of mean flow to weaken PSI dramatically.

Experimental Study of Flow Inside a Centrifugal Fan Using Magnetic Resonance Velocimetry

2019 ◽  
Author(s):  
Davis W. Hoffman ◽  
Laura Villafañe ◽  
Christopher J. Elkins ◽  
John K. Eaton
Keyword(s):  
Three Dimensional ◽  
Leading Edge ◽  
Suction Side ◽  
Reynolds Numbers ◽  
Centrifugal Fan ◽  
Mean Flow ◽  
Magnetic Resonance Velocimetry ◽  
Flow Features ◽  
Outlet Flow ◽  
The Mean

Abstract Three-dimensional, three-component time-averaged velocity fields have been measured within a low-speed centrifugal fan with forward curved blades. The model investigated is representative of fans commonly used in automotive HVAC applications. The flow was analyzed at two Reynolds numbers for the same ratio of blade rotational speed to outlet flow velocity. The flow patterns inside the volute were found to have weak sensitivity to Reynolds number. A pair of counter-rotating vortices evolve circumferentially within the volute with positive and negative helicity in the upper and lower regions, respectively. Measurements have been further extended to capture phase-resolved flow features by synchronizing the data acquisition with the blade passing frequency. The mean flow field through each blade passage is presented including the jet-wake structure extending from the blade and the separation zone on the suction side of the blade leading edge.

scholarly journals Three-dimensional spatial structure of the macro-pores and flow simulation in anthracite coal based on X-ray μ-CT scanning data

2020 ◽  
Vol 17 (5) ◽  
pp. 1221-1236
Author(s):  
Hui-Huang Fang ◽  
Shu-Xun Sang ◽  
Shi-Qi Liu
Keyword(s):  
Spatial Structure ◽  
Flow Velocity ◽  
Single Channel ◽  
Three Dimensional ◽  
Bedding Plane ◽  
Mean Flow ◽  
Equivalent Radius ◽  
Flow Pressure ◽  
The Mean ◽  
Mean Flow Velocity

Abstract The three-dimensional (3D) structures of pores directly affect the CH4 flow. Therefore, it is very important to analyze the 3D spatial structure of pores and to simulate the CH4 flow with the connected pores as the carrier. The result shows that the equivalent radius of pores and throats are 1–16 μm and 1.03–8.9 μm, respectively, and the throat length is 3.28–231.25 μm. The coordination number of pores concentrates around three, and the intersection point between the connectivity function and the X-axis is 3–4 μm, which indicate the macro-pores have good connectivity. During the single-channel flow, the pressure decreases along the direction of CH4 flow, and the flow velocity of CH4 decreases from the pore center to the wall. Under the dual-channel and the multi-channel flows, the pressure also decreases along the CH4 flow direction, while the velocity increases. The mean flow pressure gradually decreases with the increase of the distance from the inlet slice. The change of mean flow pressure is relatively stable in the direction horizontal to the bedding plane, while it is relatively large in the direction perpendicular to the bedding plane. The mean flow velocity in the direction horizontal to the bedding plane (Y-axis) is the largest, followed by that in the direction horizontal to the bedding plane (X-axis), and the mean flow velocity in the direction perpendicular to the bedding plane is the smallest.

Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser

2012 ◽  
Vol 699 ◽  
pp. 320-351 ◽  
Author(s):  
Johan Malm ◽  
Philipp Schlatter ◽  
Dan S. Henningson
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Low Frequency ◽  
Bulk Velocity ◽  
Time Signal ◽  
Mean Flow ◽  
The Mean ◽  
Dominant Frequencies

AbstractDominant frequencies and coherent structures are investigated in a turbulent, three-dimensional and separated diffuser flow at $\mathit{Re}= 10\hspace{0.167em} 000$ (based on bulk velocity and inflow-duct height), where mean flow characteristics were first studied experimentally by Cherry, Elkins and Eaton (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803–811) and later numerically by Ohlsson et al. (J. Fluid Mech., vol. 650, 2010, pp. 307–318). Coherent structures are educed by proper orthogonal decomposition (POD) of the flow, which together with time probes located in the flow domain are used to extract frequency information. The present study shows that the flow contains multiple phenomena, well separated in frequency space. Dominant large-scale frequencies in a narrow band $\mathit{St}\equiv fh/ {u}_{b} \in [0. 0092, 0. 014] $ (where $h$ is the inflow-duct height and ${u}_{b} $ is the bulk velocity), yielding time periods ${T}^{\ensuremath{\ast} } = T{u}_{b} / h\in [70, 110] $, are deduced from the time signal probes in the upper separated part of the diffuser. The associated structures identified by the POD are large streaks arising from a sinusoidal oscillating motion in the diffuser. Their individual contributions to the total kinetic energy, dominated by the mean flow, are, however, small. The reason for the oscillating movement in this low-frequency range is concluded to be the confinement of the flow in this particular geometric set-up in combination with the high Reynolds number and the large separated zone on the top diffuser wall. Based on this analysis, it is shown that the bulk of the streamwise root mean square (r.m.s.) value arises due to large-scale motion, which in turn can explain the appearance of two or more peaks in the streamwise r.m.s. value. The weak secondary flow present in the inflow duct is shown to survive into the diffuser, where it experiences an imbalance with respect to the upper expanding corners, thereby giving rise to the asymmetry of the mean separated region in the diffuser.

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

scholarly journals Flow Kinematics in Variable-Height Rotating Cylinder Arrays

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Anna E. Craig ◽  
John O. Dabiri ◽  
Jeffrey R. Koseff
Keyword(s):  
Power Output ◽  
Rotation Rate ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Streamwise Velocity ◽  
Vertical Flow ◽  
Mean Flow ◽  
Freestream Velocity ◽  
Cylinder Arrays ◽  
The Mean

Experimental data are presented for large arrays of rotating, variable-height cylinders in order to study the dependence of the three-dimensional mean flows on the height heterogeneity of the array. Elements in the examined arrays were spatially arranged in the same staggered paired configuration, and the heights of each element pair varied up to ±37.5% from the mean height (kept constant across all arrays), such that the arrays were vertically structured. Four vertical structuring configurations were examined at a nominal Reynolds number (based on freestream velocity and cylinder diameter) of 600 and nominal tip-speed ratios of 0, 2, and 4. It was found that the vertical structuring of the array could significantly alter the mean flow patterns. Most notably, a net vertical flow into the array from above was observed, which was augmented by the arrays' vertical structuring, showing a 75% increase from the lowest to highest vertical flows (as evaluated at the maximum element height, at a single rotation rate). This vertical flow into the arrays is of particular interest as it represents an additional mechanism by which high streamwise momentum can be transported from above the array down into the array. An evaluation of the streamwise momentum resource within the array indicates up to a 56% increase in the incoming streamwise velocity to the elements (from the lowest to highest ranking arrays, at a single rotation rate). These arrays of rotating cylinders may provide insight into the flow kinematics of arrays of vertical axis wind turbines (VAWTs). In a physical VAWT array, an increase in incoming streamwise flow velocity to a turbine corresponds to a (cubic) increase in the power output of the turbine. Thus, these results suggest a promising approach to increasing the power output of a VAWT array.

On the mean motion induced by internal gravity waves

1969 ◽  
Vol 36 (4) ◽  
pp. 785-803 ◽  
Author(s):  
Francis P. Bretherton
Keyword(s):  
Gravity Waves ◽  
Wave Energy ◽  
Wave Train ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Wave Number ◽  
Mean Flow ◽  
Mean Velocity ◽  
Mean Motion ◽  
The Mean

A train of internal gravity waves in a stratified liquid exerts a stress on the liquid and induces changes in the mean motion of second order in the wave amplitude. In those circumstances in which the concept of a slowly varying quasi-sinusoidal wave train is consistent, the mean velocity is almost horizontal and is determined to a first approximation irrespective of the vertical forces exerted by the waves. The sum of the mean flow kinetic energy and the wave energy is then conserved. The circulation around a horizontal circuit moving with the mean velocity is increased in the presence of waves according to a simple formula. The flow pattern is obtained around two- and three-dimensional wave packets propagating into a liquid at rest and the results are generalized for any basic state of motion in which the internal Froude number is small. Momentum can be associated with a wave packet equal to the horizontal wave-number times the wave energy divided by the intrinsic frequency.

A Transport Model for the Deterministic Stresses Associated With Turbomachinery Blade Row Interactions

2000 ◽  
Vol 122 (4) ◽  
pp. 593-603 ◽  
Author(s):  
Allan G. van de Wall ◽  
Jaikrishnan R. Kadambi ◽  
John J. Adamczyk
Keyword(s):  
Turbine Blade ◽  
Transport Model ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Two Dimensional ◽  
Mean Flow ◽  
Viscous Effects ◽  
Vortical Structures ◽  
Blade Row ◽  
The Mean

The unsteady process resulting from the interaction of upstream vortical structures with a downstream blade row in turbomachines can have a significant impact on the machine efficiency. The upstream vortical structures or disturbances are transported by the mean flow of the downstream blade row, redistributing the time-average unsteady kinetic energy (K) associated with the incoming disturbance. A transport model was developed to take this process into account in the computation of time-averaged multistage turbomachinery flows. The model was applied to compressor and turbine geometry. For compressors, the K associated with upstream two-dimensional wakes and three-dimensional tip clearance flows is reduced as a result of their interaction with a downstream blade row. This reduction results from inviscid effects as well as viscous effects and reduces the loss associated with the upstream disturbance. Any disturbance passing through a compressor blade row results in a smaller loss than if the disturbance was mixed-out prior to entering the blade row. For turbines, the K associated with upstream two-dimensional wakes and three-dimensional tip clearance flows are significantly amplified by inviscid effects as a result of the interaction with a downstream turbine blade row. Viscous effects act to reduce the amplification of the K by inviscid effects but result in a substantial loss. Two-dimensional wakes and three-dimensional tip clearance flows passing through a turbine blade row result in a larger loss than if these disturbances were mixed-out prior to entering the blade row. [S0889-504X(00)01804-3]

scholarly journals Analysis of Separated Flows Inside an Annular Compressor Cascade Using a Low-Re-Number k-ϵ and an Algebraic Reynolds-Stress-Model

1997 ◽  
Author(s):  
Jürgen R. Lücke ◽  
Heinz E. Gallus
Keyword(s):  
Flow Field ◽  
Reynolds Stress ◽  
Three Dimensional ◽  
Separated Flow ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Mean Flow ◽  
Compressor Cascade ◽  
Production Term ◽  
Algebraic Reynolds Stress Model

The flow field inside an annular compressor cascade is numerically investigated. The mean flow features are complex three-dimensional zones of turbulent separation at hub and shroud at high inflow angles. The flow field is investigated with an implicit three-dimensional Navier-Stokes code. To predict turbulent effects the flow solver includes two different variants of a Low-Re-number k-ϵ-model and an algebraic Reynolds-stress-model. Using the Low-Re-number model the structure of the regions of separated flow are fairly well predicted. However, intensity and size of these zones are too small compared with the experimental data. Better results are produced using the anisotropic algebraic Reynolds-stress-model combined with a stagnation point modification of the turbulent production term. Stucture and intensity of the vortex systems are simulated in more detail. Static pressure distributions and loss contours are in a very good agreement with the experiments.

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