8 results
Inviscid flow analysis of a circular cylinder traversing across an unbounded uniform-shear stream
- A. M. Naguib, M. M. Koochesfahani
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- Journal:
- Journal of Fluid Mechanics / Volume 882 / 10 January 2020
- Published online by Cambridge University Press:
- 11 November 2019, A21
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The present study is focused on obtaining the inviscid flow solution for a circular cylinder traversing steadily across an unbounded uniform-shear flow. The work is motivated by understanding the aerodynamics of bodies traversing across a shear flow, as well as by developing an understanding of fundamental concepts that are well understood for uniform free stream but not in the presence of shear. The results show that, in general, the presence of shear makes it impossible to define a unique approach-stream incidence angle $\unicode[STIX]{x1D6FC}$ relative to the cylinder. However, in the limit of, what we have termed ‘quasi-uniform’ flow, such an angle can be defined. We show that in this limit, the flow is also quasi-steady, and the static-cylinder solution can be used to solve for the moving-cylinder problem with good accuracy. This ‘quasi-uniform and quasi-steady’ (QUS) condition is attained when a single unsteadiness parameter $\dot{U}_{o}^{+}$ approaches zero. For small values of the cylinder-to-free-stream velocity ratio $V_{r}$, $\dot{U}_{o}^{+}\approx K_{eff}V_{r}$, where $K_{eff}$ is the effective non-dimensional shear rate. Away from the QUS flow limit, the flow field and the surface pressure distribution are significantly different between the moving and the static cylinders. However, a surprising result is that regardless of whether QUS conditions hold, the force acting on the moving cylinder in a Galilean frame of reference is always the same as that on a static cylinder in uniform-shear free stream but with non-dimensional shear rate and incidence angle equal to the moving cylinder’s instantaneous $K_{eff}$ and $\tan ^{-1}(V_{r})$, respectively.
High-fidelity measurements in channel flow with polymer wall injection
- John R. Elsnab, Jason P. Monty, Christopher M. White, Manoochehr M. Koochesfahani, Joseph C. Klewicki
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- Journal:
- Journal of Fluid Mechanics / Volume 859 / 25 January 2019
- Published online by Cambridge University Press:
- 26 November 2018, pp. 851-886
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Streamwise velocity profiles and their wall-normal derivatives were used to investigate the properties of turbulent channel flow in the low polymer drag reduction $(DR)$ regime ($DR=6.5\,\%$ to $26\,\%$), as realized via polymer injection at the channel surface. Streamwise velocity data were obtained over a friction Reynolds number ranging from $650$ to $1800$ using the single-velocity-component version of molecular tagging velocimetry (1c-MTV). This adaptation of the MTV technique has the ability to accurately capture instantaneous profiles at very high spatial resolution (${\gtrsim}850$ data points per wall-normal profile), and thus generate well-resolved derivative information as well. Owing to this ability, the present study is able to build upon and extend the recent numerical simulation analysis of White et al. (J. Fluid Mech., vol. 834, 2018, pp. 409–433) that examined the mean dynamical structure of polymer drag-reduced channel flow at friction Reynolds numbers up to $1000$. Consistently, the present mean velocity profiles indicate that the extent of the logarithmic region diminishes with increasing polymer concentration, while statistically significant increases in the logarithmic profile slope begin to occur for drag reductions less than $15\,\%$. Profiles of the r.m.s. streamwise velocity indicate that the maximum moves farther from the wall and increases in magnitude with reductions in drag. Similarly, with increasing drag reduction, the profile of the combined Reynolds and polymer shear stress exhibits a decrease in its maximum value that also moves farther from the wall. Correlations are presented that estimate the location and value of the maximum r.m.s. streamwise velocity and combined Reynolds and polymer shear stress. Over the range of $DR$ investigated, these effects consistently exhibit approximately linear trends as a function of $DR$. The present measurements allow reconstruction of the mean momentum balance (MMB) for channel flow, which provides further insights regarding the physics described in the study by White et al. In particular, the present findings support a physical scenario in which the self-similar properties on the inertial domain identified from the leading-order structure of the MMB begin to detectably and continuously vary for drag reductions less than $10\,\%$.
Lift on a steady 2-D symmetric airfoil in viscous uniform shear flow
- Patrick R. Hammer, Miguel R. Visbal, Ahmed M. Naguib, Manoochehr M. Koochesfahani
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- Journal:
- Journal of Fluid Mechanics / Volume 837 / 25 February 2018
- Published online by Cambridge University Press:
- 28 December 2017, R2
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We present an investigation into the influence of upstream shear on the viscous flow around a steady two-dimensional (2-D) symmetric airfoil at zero angle of attack, and the corresponding loads. In this computational study, we consider the NACA 0012 airfoil at a chord Reynolds number $1.2\times 10^{4}$ in an approach flow with uniform positive shear with non-dimensional shear rate varying in the range 0.0–1.0. Results show that the lift force is negative, in the opposite direction to the prediction from Tsien’s inviscid theory for lift generation in the presence of positive shear. A hypothesis is presented to explain the observed sign of the lift force on the basis of the asymmetry in boundary layer development on the upper and lower surfaces of the airfoil, which creates an effective airfoil shape with negative camber. The resulting scaling of the viscous effect with shear rate and Reynolds number is provided. The location of the leading edge stagnation point moves increasingly farther back along the airfoil’s upper surface with increased shear rate, a behaviour consistent with a negatively cambered airfoil. Furthermore, the symmetry in the location of the boundary layer separation point on the airfoil’s upper and lower surfaces in uniform flow is broken under the imposed shear, and the wake vortical structures exhibit more asymmetry with increasing shear rate.
Effect of finite sampling time on estimation of Brownian fluctuation
- Shahram Pouya, Di Liu, Manoochehr M. Koochesfahani
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- Journal:
- Journal of Fluid Mechanics / Volume 767 / 25 March 2015
- Published online by Cambridge University Press:
- 12 February 2015, pp. 65-84
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We present a study of the effect of finite detector integration/exposure time $E$, in relation to interrogation time interval ${\rm\Delta}t$, on analysis of Brownian motion of small particles using numerical simulation of the Langevin equation for both free diffusion and hindered diffusion near a solid wall. The simulation result for free diffusion recovers the known scaling law for the dependence of estimated diffusion coefficient on $E/{\rm\Delta}t$, i.e. for $0\leqslant E/{\rm\Delta}t\leqslant 1$ the estimated diffusion coefficient scales linearly as $1-(E/{\rm\Delta}t)/3$. Extending the analysis to the parameter range $E/{\rm\Delta}t\geqslant 1$, we find a new nonlinear scaling behaviour given by $(E/{\rm\Delta}t)^{-1}[1-((E/{\rm\Delta}t)^{-1})/3]$, for which we also provide an exact analytical solution. The simulation of near-wall diffusion shows that hindered diffusion of particles parallel to a solid wall, when normalized appropriately, follows with a high degree of accuracy the same form of scaling laws given above for free diffusion. Specifically, the scaling laws in this case are well represented by $1-((1+{\it\epsilon})(E/{\rm\Delta}t))/3$, for $E/{\rm\Delta}t\leqslant 1$, and $(E/{\rm\Delta}t)^{-1}[1-((1+{\it\epsilon})(E/{\rm\Delta}t)^{-1})/3]$, for $E/{\rm\Delta}t\geqslant 1$, where the small parameter ${\it\epsilon}$ depends on the size of the near-wall domain used in the estimation of the diffusion coefficient and value of $E$. For the range of parameters reported in the literature, we estimate ${\it\epsilon}<0.03$. The near-wall simulations also show a bias in the estimated diffusion coefficient parallel to the wall even in the limit $E=0$, indicating an overestimation which increases with increasing time delay ${\rm\Delta}t$. This diffusion-induced overestimation is caused by the same underlying mechanism responsible for the previously reported overestimation of mean velocity in near-wall velocimetry.
Thermal effects on the wake of a heated circular cylinder operating in mixed convection regime
- H. Hu, M. M. Koochesfahani
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- Journal:
- Journal of Fluid Mechanics / Volume 685 / 25 October 2011
- Published online by Cambridge University Press:
- 06 October 2011, pp. 235-270
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The thermal effects on the wake flow behind a heated circular cylinder operating in the mixed convection regime were investigated experimentally in the present study. The experiments were conducted in a vertical water channel with the heated cylinder placed horizontally and the flow approaching the cylinder downwards. With such a flow arrangement, the direction of the thermally induced buoyancy force acting on the fluid surrounding the heated cylinder would be opposite to the approach flow. During the experiments, the temperature and Reynolds number of the approach flow were held constant. By adjusting the surface temperature of the heated cylinder, the corresponding Richardson number () was varied between 0.0 (unheated) and 1.04, resulting in a change in the heat transfer process from forced convection to mixed convection. A novel flow diagnostic technique, molecular tagging velocimetry and thermometry (MTV&T), was used for qualitative flow visualization of thermally induced flow structures and quantitative, simultaneous measurements of flow velocity and temperature distributions in the wake of the heated cylinder. With increasing temperature of the heated cylinder (i.e. Richardson number), significant modifications of the wake flow pattern and wake vortex shedding process were clearly revealed. When the Richardson number was relatively small (), the vortex shedding process in the wake of the heated cylinder was found to be quite similar to that of an unheated cylinder. As the Richardson number increased to , the wake vortex shedding process was found to be ‘delayed’, with the wake vortex structures beginning to shed much further downstream. As the Richardson number approached unity (), instead of having ‘Kármán’ vortices shedding alternately at the two sides of the heated cylinder, concurrent shedding of smaller vortex structures was observed in the near wake of the heated cylinder. The smaller vortex structures were found to behave more like ‘Kelvin–Helmholtz’ vortices than ‘Kármán’ vortices, and adjacent small vortices would merge to form larger vortex structures further downstream. It was also found that the shedding frequency of the wake vortex structures decreased with increasing Richardson number. The wake closure length and the drag coefficient of the heated cylinder were found initially to decrease slightly when the Richardson number was relatively small (), and then to increase monotonically with increasing Richardson number as the Richardson number became relatively large (). The average Nusselt number () of the heated cylinder was found to decrease almost linearly with increasing Richardson number.
MTV measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency
- DOUGLAS G. BOHL, MANOOCHEHR M. KOOCHESFAHANI
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- Journal:
- Journal of Fluid Mechanics / Volume 620 / 10 February 2009
- Published online by Cambridge University Press:
- 10 February 2009, pp. 63-88
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We present an experimental investigation of the flow structure and vorticity field in the wake of a NACA-0012 airfoil pitching sinusoidally at small amplitude and high reduced frequencies. Molecular tagging velocimetry is used to quantify the characteristics of the vortex array (circulation, peak vorticity, core size, spatial arrangement) and its downstream evolution over the first chord length as a function of reduced frequency. The measured mean and fluctuating velocity fields are used to estimate the mean force on the airfoil and explore the connection between flow structure and thrust generation.
Results show that strong concentrated vortices form very rapidly within the first wavelength of oscillation and exhibit interesting dynamics that depend on oscillation frequency. With increasing reduced frequency the transverse alignment of the vortex array changes from an orientation corresponding to velocity deficit (wake profile) to one with velocity excess (reverse Kármán street with jet profile). It is found, however, that the switch in the vortex array orientation does not coincide with the condition for crossover from drag to thrust. The mean force is estimated from a more complete control volume analysis, which takes into account the streamwise velocity fluctuations and the pressure term. Results clearly show that neglecting these terms can lead to a large overestimation of the mean force in strongly fluctuating velocity fields that are characteristic of airfoils executing highly unsteady motions. Our measurements show a decrease in the peak vorticity, as the vortices convect downstream, by an amount that is more than can be attributed to viscous diffusion. It is found that the presence of small levels of axial velocity gradients within the vortex cores, levels that can be difficult to measure experimentally, can lead to a measurable decrease in the peak vorticity even at the centre of the flow facility in a flow that is expected to be primarily two-dimensional.
Mixing and chemical reactions in a turbulent liquid mixing layer
- M. M. Koochesfahani, P. E. Dimotakis
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- Journal:
- Journal of Fluid Mechanics / Volume 170 / September 1986
- Published online by Cambridge University Press:
- 21 April 2006, pp. 83-112
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An experimental investigation of entrainment and mixing in reacting and non-reacting turbulent mixing layers at large Schmidt number is presented. In non-reacting cases, a passive scalar is used to measure the probability density function (p.d.f.) of the composition field. Chemically reacting experiments employ a diffusion-limited acid–base reaction to directly measure the extent of molecular mixing. The measurements make use of laser-induced fluorescence diagnostics and high-speed, real-time digital image-acquisition techniques.
Our results show that the vortical structures in the mixing layer initially roll-up with a large excess of fluid from the high-speed stream entrapped in the cores. During the mixing transition, not only does the amount of mixed fluid increase, but its composition also changes. It is found that the range of compositions of the mixed fluid, above the mixing transition and also throughout the transition region, is essentially uniform across the entire transverse extent of the layer. Our measurements indicate that the probability of finding unmixed fluid in the centre of the layer, above the mixing transition, can be as high as 0.45. In addition, the mean concentration of mixed fluid across the layer is found to be approximately constant at a value corresponding to the entrainment ratio. Comparisons with gas-phase data show that the normalized amount of chemical product formed in the liquid layer, at high Reynolds number, is 50% less than the corresponding quantity measured in the gas-phase case. We therefore conclude that Schmidt number plays a role in turbulent mixing of high-Reynolds-number flows.
1 - Jets and mixing layers
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- By M. M. Koochesfahani, P. E. Dimotakis, M. Gharib, P. Derango, E. Villermaux, H. Rehab, E. J. Hopfinger, D. E. Parekh, W. C. Reynolds, M. G. Mungal, T. Loiseleux, J.-M. Chomaz, T. F. Fric, A. Roshko, S. P. Gogineni, M. M. Whitaker, L. P. Goss, W. M. Roquemore, S. Wernz, H. F. Fasel, S. Gogineni, C. Shih, A. Krothapalli
- M. Samimy, Ohio State University, K. S. Breuer, Brown University, Rhode Island, L. G. Leal, University of California, Santa Barbara, P. H. Steen, Cornell University, New York
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- Book:
- A Gallery of Fluid Motion
- Published online:
- 25 January 2010
- Print publication:
- 12 January 2004, pp 1-10
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Summary
Laser-induced fluorescence (LIF) diagnostics and highspeed, real-time digital image acquisition techniques are combined to map the composition field in a water mixing layer. A fluorescent dye, which is premixed with the lowspeed freestream fluid and dilutes by mixing with the highspeed fluid, is used to monitor the relative concentration of high-speed to low-speed fluid in the layer.
The three digital LIF pictures shown here were obtained by imaging the laser-induced fluorescence originating from a collimated argon ion laser beam, extending across the transverse dimension of the shear layer, onto a 512–element linear photodiode array. Each picture represents 384 contiguous scans, each at 400 points across the layer, for a total of 153 600 point measurements of concentration. The vertical axis maps onto 40 mm of the transverse coordinate of the shear layer, and the horizontal axis is time increasing from right to left for a total flow real time of 307 msec. The pseudocolor assignment is linear in the mixture fraction (ξ) and is arranged as follows: red-unmixed fluid from the low-speed stream (ξ=0); blue-unmixed fluid from the high-speed stream (ξ=1); and the rest of the spectrum corresponds to intermediate compositions.
Figures 1 and 2, a single vortex and pairing vortices, respectively, show the composition field before the mixing transition. The Reynolds number based on the local visual thickness of the layer and the velocity difference across the layer is Re=1750 with U2/U1=0.46 and U1=13 cm/sec. Note the large excess of high-speed stream fluid in the cores of the structures.