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Browsing by Subject "Turbulent boundary layer"

Now showing 1 - 3 of 3
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    Evolution of eddies and packets in turbulent boundary layers.
    (2011-03) Gao, Qi
    The objective of this study was to improve understanding of the population distribution and evolution of eddies and eddy packets in turbulent boundary layers using experimental methods. To effectively identify vortical structures, an advanced vortex identification algorithm was developed based on swirl strength, and the real eigenvector of the velocity gradient tensor as an indicator of eddy orientation. The new method applied on the streamwise/spanwise plane had a good performance on vortex identification, which was tested by two Direct Numerical Simulation (DNS) of channel flow at Re#28; = 590 and 934, and one Dual-Plane Particle Image Velocimetry (PIV) data set of boundary layer at Re#28; = 2480. The effect of spatial resolution was studied. Although it was found that relatively coarse resolution of 24.5 wall units (Dual-Plane PIV) caused underestimation of velocity gradients, which resulted in underestimated magnitudes of several derived variables, such as swirl strength, vorticity and circulation, the statistical results of vortex population distribution had a good agreement between DNS and Dual-Plane PIV data sets. A new method of scaling the swirl was proposed based on the invariants of the characteristic equation of the velocity gradient tensor, which could minimize the effects of data resolution among different data sets. A volumetric PIV technique, Tomographic PIV (TPIV), was applied to investigate vortical structures. Although the TPIV resolution was too coarse to resolve the smallest eddies accurately, it worked very well for identifying larger eddies and packets. Population distributions of eddy orientation, size, circulation and convection velocity in the logarithmic region were obtained from both numerical and experimental data. It was found that the elevation angle and size of eddies increased with increasing wall-normal distance, while the eddy circulation decreased with increasing wall-normal distance. The mean convection velocity of eddies was normally #24;97% of the local mean. Joint PDFs of eddy radius and circulation yielded a peak fitting curve of an exponential function a(r+)b. The exponent b was found equal to 2.2 for all data sets in the logarithmic region, while the coefficient a was proportional to the mean magnitude of vorticity which was dependent on the resolution. The difference between vorticity vector and the real eigenvector was documented, and this was thought to be caused by the local shear motion. The volumetric data from TPIV gave strong support for the local shear hypothesis showing that the eigenvector is a better indicator of eddy orientation. Eddy packets and flow evolution were studied using flying TPIV data in the lower (z+ = 100 #24; 300) and upper (z+ = 300 #24; 500) logarithmic region for Re#28; = 2480. Long slow regions (> 0:6#14;) surrounded by eddy pairs were often seen in both locations (#24;10% of all instantaneous fields). The width of the long slow regions was #24;400-500 viscous units (#24;0.16-0.2#14;) at z+ #25; 200 and #24;650- 750 viscous units (#24;0.26-0.3#14;) at z+ #25; 400. Pairs of hairpin legs propagated mostly at velocity of 0.92U+ for both wall-normal locations. The streamwise spacing of vortex pairs in the packets was about 300 viscous units at z+ #25; 200 and 150 viscous units at z+ #25; 400. The spanwise spacing of two long slow regions was typically larger than 0.5#14;. One case at the lower wall-normal location showed that a long slow region stably lasted at least #1;t+ #25; 2300 and traveled about 15.5#14;, while one long slow region lasted #1;t+ #25; 1500 and traveled about 11.5#14; at the upper location. Deforming, meandering, merging, and breaking of these long slow regions was observed. Interaction of neighboring eddies was also observed. Oscillation of hairpin legs in the spanwise direction showed that, whenever they became closer, they appeared to become stronger, and vice versa. Eddies with strong circulation showed greater stability over time. The eddies with less than 10% circulation variation over #1;t+ = 78 had mean circulation of 500 at the lower location and 350 at the upper location.
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    Large Eddy Simulation of complex flow over submerged bodies
    (2018-02) Kumar, Praveen
    Predicting the complex flow over a submerged marine vessel in maneuver has two major challenges: the hull boundary layer and the flow due to the propeller. Large eddy simulation (LES) using the dynamic Smagorinsky model (DSM) (Germano \textit{et al.} 1991, Lilly 1992) and discrete kinetic energy conserving numerical method of Mahesh \textit{et al.} (2004) has successfully predicted complex flows in the past. This dissertation discusses four advancements towards reliably using LES to predict and understand the complex flows encountered during maneuvers of submerged marine vessels: (1) understanding skin-friction in axisymmetric boundary layers evolving under pressure gradients, (2) simulating attached flow over axisymmetric hulls and wake evolution, (3) assessing the dependence of the stern flow and axisymmetric wake on hull boundary layer characteristics, and (4) simulating flow through a propeller at design operating condition. Axisymmetric boundary layers are studied using integral analysis of the governing equations for axial flow over a circular cylinder. The analysis includes the effect of pressure gradient and focuses on the effect of transverse curvature on boundary layer parameters such as shape factor ($H$) and skin-friction coefficient ($C_f$), defined as $H = \delta^*/\theta$ and $C_f = \tau_w/(0.5\rho U_e^2)$ respectively, where $\delta^*$ is displacement thickness, $\theta$ is momentum thickness, $\tau_w$ is the shear stress at the wall, $\rho$ is density and $U_e$ is the streamwise velocity at the edge of the boundary layer. Useful relations are obtained relating the mean wall-normal velocity at the edge of the boundary layer ($V_e$) and $C_f$ to the boundary layer and pressure gradient parameters. The analytical relations reduce to established results for planar boundary layers in the limit of infinite radius of curvature. The relations are used to obtain $C_f$ which shows good agreement with the data reported in the literature. The analytical results are used to discuss different flow regimes of axisymmetric boundary layers in the presence of pressure gradients. Wall-resolved LES is used to simulate flow over an axisymmetric body of revolution at a Reynolds number, $Re=1.1 \times 10^6$, based on freestream velocity and the length of the body. The geometry used in the present work is an idealized submarine hull (DARPA SUBOFF without appendages) at zero angle of pitch and yaw. The computational domain is chosen to avoid confinement effects and capture the wake up to fifteen diameters downstream of the body. The unstructured computational grid is designed to capture the fine near-wall structures as well as the wake. LES results show good agreement with the available experimental data. The axisymmetric turbulent boundary layer has higher skin-friction and higher radial decay of turbulence away from the wall, compared to a planar turbulent boundary layer under similar conditions. The mean streamwise velocity exhibits self-similarity, but the turbulent intensities are not self-similar over the length of the simulated wake, consistent with previous studies reported in the literature. The axisymmetric wake transitions from high-$Re$ to low-$Re$ equilibrium self-similar solutions, as theoretically proposed and observed for axisymmetric wakes in the past. The recycle-rescale method of \citet{Lund} is first implemented for unstructured grids and massively parallel platforms and then extended to spatially developing thin axisymmetric turbulent boundary layers. LES of flow over the stern portion of the hull is performed with a prescribed turbulent inflow at a momentum thickness $\theta/a=0.078$ and a momentum thickness-based Reynolds number $Re_{\theta}=2000$, where $a$ is the radius of curvature, to understand the dependence of the flow field in the stern region and the wake, on hull boundary layer characteristics. Additional simulations are performed to study the effect of $Re_\theta$ and $\theta/a$ at the inflow. The turbulent inflows needed for the simulations are generated from auxiliary simulations employing the recycle-rescale methodology. Results are compared to past studies, and used to describe the effect of incoming TBL on the overall flow field. The pressure coefficient on the body is largely insensitive to the incoming boundary layer characteristics, except in the vicinity of flow separation, where it is more sensitive to $\theta/a$. Skin-friction on the other hand, is very sensitive to the boundary layer characteristics. The boundary layer characteristics determine the location of flow separation and hence, the flow field in the stern region and the wake. The wake of the body is more sensitive to $Re_{\theta}$ compared to $\theta/a$. The wake of a five-bladed marine propeller at design operating condition is studied using LES. The mean loads and phase-averaged flow field show good agreement with experiments. Phase-averaged and azimuthal-averaged flow fields are analyzed in detail to examine the mechanisms of wake instability. The propeller wake consisting of tip and hub vortices undergoes streamtube contraction, which is followed by the onset of instabilities as evident from the oscillations of the tip vortices. Simulation results reveal a mutual induction mechanism of instability where instead of the tip vortices interacting among themselves, they interact with the smaller vortices generated by the roll-up of the blade trailing edge wake in the near wake. It is argued that although the mutual-inductance mode is the dominant mode of instability in propellers, the actual mechanism depends on the propeller geometry and the operating conditions. The axial evolution of the propeller wake from near to far field is discussed. Once the propeller wake becomes unstable, the coherent vortical structures break up and evolve into the far wake composed of a fluid mass swirling around an oscillating hub vortex. The hub vortex remains coherent over the length of the computational domain.
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    Resolving particle dynamics in turbulent wall-bounded flow
    (2021-10) Tee, Yi Hui
    Wall-bounded flows in the atmosphere, rivers and oceans are turbulent in nature and mixed with discrete particles. The particle length scale including the wake, can be important because it will affect whether a particle slides, rolls, lifts off or collides with the wall or bounding surface. To understand the transport of discrete particles due to particle-wall and particle-turbulence interactions, spheres extending into the logarithmic region with $d^+=56$ and 116 (when $Re_\tau=670$ and 1300 respectively) were considered. The mean fluid velocity statistics surrounding a fixed sphere on the wall with $Re_p=730$ and 1730 respectively were first investigated across the streamwise-wall-normal and wall-parallel planes. Then, spheres with specific gravities ranging from 1.006 (P1) to 1.152 (P3) were released individually from rest and allowed to propagate with the incoming fluid. Both sphere and fluid motions were tracked simultaneously via 3D particle tracking and stereoscopic particle image velocimetry over the streamwise-spanwise plane at multiple locations, respectively. The perturbations induced by a fixed sphere on the wall extend over a significant distance in both the streamwise ($x/\delta>1.6$; $x/d>17$) and spanwise ($|z|/\delta\sim0.3$; $|z|/d\sim3.3$) directions. When $Re_\tau$ increases, at $y/d=0.7$ ($y^+=40$ and 80 respectively), the vortex shedding increases the magnitude of the negative mean wall-normal velocity in the wake more significantly than the mean spanwise fluid velocity. By contrast, the streamwise velocity deficit downstream of the sphere recovers more rapidly when $Re_\tau$ increases. The presence of the sphere also leads to an increase in fluid velocity both upstream of and above the sphere. Hence, the particle length scale is important as it modulates the turbulence and the surrounding flow field. With sufficient mean shear, sphere P1 lifted off of the wall upon release before descending back towards the wall at both $Re_\tau$. These descents were prompted by a decrease in shear lift due to the surrounding slow-moving zone, downwash, and possibly upward tilting wake. While descending, the sphere either ascended again without returning to the wall or else contacted the wall and then slid before lifting off again. These subsequent lift-offs were prompted by upwash and/or instantaneous shear lift due to a passing high momentum region with large relative velocity. By contrast, the denser sphere P3 did not lift off upon release and mainly slid along the wall. At $Re_{{\tau}}=670$, the initial acceleration of the dense sphere P3 was significantly retarded by the opposing friction force, in contrast to the other spheres that accelerated steeply over a streamwise distance of $\delta$. Strong wake signatures were always observed downstream of this sphere, with loop-like vortices shedding off of the sphere. The streamwise velocities of both lifting and wall-interacting spheres correlated strongly with the fast- and slow-moving zones that approach and move over them. For the lifting sphere, the sphere streamwise velocity fluctuation within each run was also correlated with the sphere wall-normal positions. Meanwhile, the streamwise velocity fluctuation of the denser sphere was well correlated with the vortex shedding. As the denser sphere slid unsteadily downstream, it began to roll forward due to fluid torque induced by the wall-normal fluid motion as well as the shearing effect due to an approaching high momentum region. The sphere also accelerated to greater translational velocity due to an increase in angular velocity and/or the surrounding fast-moving zone. The forward rolling also induced small, repeated lift-off events due to Magnus lift. In all cases, the spheres migrated significantly in the spanwise direction, up to 12\% of the streamwise distance traveled. The sphere spanwise motion was prompted by the localized spanwise fluid motion, Magnus side-lift, and/or meandering of the coherent structures. Side force induced by spanwise gradients of streamwise velocity could be important especially when the relative velocity was large, as upon release. The spheres did not appear to migrate preferentially into the slow-moving zones. Instead, they traveled with either fast- and/or slow-moving zones throughout the observed trajectories based on the relative velocity and the spanwise forces.