Transitions to different kinds of turbulence in a channel with soft walls

2017 ◽  
Vol 822 ◽  
pp. 267-306 ◽  
Author(s):  
S. S. Srinivas ◽  
V. Kumaran
Keyword(s):  
Reynolds Number ◽  
Travelling Waves ◽  
Fluid Velocity ◽  
Rectangular Channel ◽  
Wall Turbulence ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Wall Displacement ◽  
Experimental Resolution ◽  
Soft Wall

The flow in a rectangular channel with walls made of polyacrylamide gel is experimentally studied to examine the effect of soft walls on transition and turbulence. The bottom wall is fixed to a substrate and the top wall is unrestrained. As the Reynolds number increases, two different flow regimes are observed. The first is the ‘soft-wall turbulence’ (Srinivas & Kumaran,J. Fluid Mech., vol. 780, 2015, pp. 649–686). There is a large increase in the magnitudes of the velocity fluctuations after transition and the fluid velocity fluctuations appear to be non-zero at the soft walls, although higher resolution measurements are required to establish the nature of the boundary dynamics. The fluid velocity fluctuations are symmetric about the centreline of the channel, and they show relatively little downstream variation. The wall displacement measurements indicate that there is no observable motion perpendicular to the surface to within the experimental resolution, but displacement fluctuations parallel to the surface are observed after transition. As the Reynolds number is further increased, there is a second ‘wall-flutter’ transition, which involves visible downstream travelling waves in the top (unrestrained) wall alone. Wall displacement fluctuations of frequency less than approximately$500~\text{rad}~\text{s}^{-1}$are observed both parallel and perpendicular to the wall. The mean velocity profiles and turbulence intensities are asymmetric, with much larger turbulence intensities near the top wall. The transitions are observed in sequence from a laminar flow at Reynolds number less than 1000 for a channel of height 0.6 mm and from a turbulent flow at a Reynolds number greater than 1000 for a channel of height 1.8 mm.

Effect of viscoelasticity on the soft-wall transition and turbulence in a microchannel

2017 ◽  
Vol 812 ◽  
pp. 1076-1118 ◽  
Author(s):  
S. S. Srinivas ◽  
V. Kumaran
Keyword(s):  
Molecular Weight ◽  
Reynolds Number ◽  
Reynolds Stress ◽  
Mass Fraction ◽  
Rectangular Cross Section ◽  
Pure Water ◽  
Polymer Concentration ◽  
Wall Turbulence ◽  
Solution Viscosity ◽  
Soft Wall

The modification of soft-wall turbulence in a microchannel due to small amounts of polymer dissolved in water is experimentally studied. The microchannels are of rectangular cross-section with height ${\sim}$160 $\unicode[STIX]{x03BC}\text{m}$, width ${\sim}$1.5 mm and length ${\sim}$3 cm, with three walls made of hard polydimethylsiloxane (PDMS) gel, and one wall made of soft PDMS gel with an elasticity modulus of ${\sim}$18 kPa. Solutions of polyacrylamide of molecular weight $5\times 10^{6}$ and mass fraction up to 50 ppm, and of molecular weight $4\times 10^{4}$ and mass fraction up to 1500 ppm, are used in the experiments. In all cases, the solutions are in the dilute limit below the critical overlap concentration, and the solution viscosity does not exceed that of water by more than 10 %. Two distinct types of flow modifications are observed below and above a threshold mass fraction for the polymer, $w_{t}$, which is ${\sim}$1 ppm and 500 ppm for the solutions of polyacrylamide with molecular weights $5\times 10^{6}$ and $4\times 10^{4}$, respectively. At or below $w_{t}$, there is no change in the transition Reynolds number, but there is significant turbulence attenuation, by up to a factor of 2 in the root-mean-square velocities and a factor of 4 in the Reynolds stress. When the polymer concentration increases beyond $w_{t}$, there is a decrease in the transition Reynolds number and in the intensity of the turbulent fluctuations. The lowest transition Reynolds number is ${\sim}$35 for the solution of polyacrylamide with molecular weight $5\times 10^{6}$ and mass fraction 50 ppm (in contrast to 260–290 for pure water). The fluctuating velocities in the streamwise and cross-stream directions are lower by a factor of 5, and the Reynolds stress is lower by a factor of 10, in comparison to pure water.

scholarly journals Wall-attached structures of velocity fluctuations in a turbulent boundary layer

2018 ◽  
Vol 856 ◽  
pp. 958-983 ◽  
Author(s):  
Jinyul Hwang ◽  
Hyung Jin Sung
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Wall Turbulence ◽  
Velocity Fluctuations ◽  
Moderate Reynolds Number ◽  
Wide Range ◽  
Logarithmic Region ◽  
High Reynolds ◽  
Attached Eddies

Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence arises in most practical flows, and is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviours of turbulence, the presence of coherent structures that contribute to the logarithmic behaviours has not been observed in instantaneous flow fields. Here, we demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ($u_{i}$) through the direct numerical simulation of a moderate-Reynolds-number boundary layer ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). The wall-attached structures are self-similar with respect to their heights ($l_{y}$), and in particular the population density of the streamwise component ($u$) scales inversely with $l_{y}$, reminiscent of the hierarchy of attached eddies. The turbulence intensities contained within the wall-parallel components ($u$ and $w$) exhibit the logarithmic behaviour. The tall attached structures ($l_{y}^{+}>100$) of $u$ are composed of multiple uniform momentum zones (UMZs) with long streamwise extents, whereas those of the cross-stream components ($v$ and $w$) are relatively short with a comparable width, suggesting the presence of tall vortical structures associated with multiple UMZs. The magnitude of the near-wall peak observed in the streamwise turbulent intensity increases with increasing $l_{y}$, reflecting the nested hierarchies of the attached $u$ structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.

scholarly journals Natural logarithms

2013 ◽  
Vol 718 ◽  
pp. 1-4 ◽  
Author(s):  
B. J. McKeon
Keyword(s):  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Significant Advance ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Logarithmic Scaling ◽  
The Mean ◽  
High Reynolds

AbstractMarusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis.

Computation of Flow and Heat Transfer in Rotating Rectangular Channels (AR=4:1) With Pin-Fins by a Reynolds Stress Turbulence Model

2006 ◽  
Vol 129 (6) ◽  
pp. 685-696 ◽  
Author(s):  
Guoguang Su ◽  
Hamn-Ching Chen ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Rotation Number ◽  
Rectangular Channel ◽  
Density Ratio ◽  
Three Dimensional ◽  
Diameter Ratio ◽  
Mean Velocity ◽  
Flow And Heat Transfer ◽  
Pin Fins

Computations with multi-block chimera grids were performed to study the three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with staggered arrays of pin-fins. The channel aspect ratio (AR) is 4:1, the pin length to diameter ratio (H∕D) is 2.0, and the pin spacing to diameter ratio is 2.0 in both the stream-wise (S1∕D) and span-wise (S2∕D) directions. A total of six calculations have been performed with various combinations of rotation number, Reynolds number, and coolant-to-wall density ratio. The rotation number and inlet coolant-to-wall density ratio varied from 0.0 to 0.28 and from 0.122 to 0.20, respectively, while the Reynolds number varied from 10,000 to 100,000. For the rotating cases, the rectangular channel was oriented at 150deg with respect to the plane of rotation to be consistent with the configuration of the gas turbine blade. A Reynolds-averaged Navier-Stokes (RANS) method was employed in conjunction with a near-wall second-moment turbulence closure for detailed predictions of mean velocity, mean temperature, and heat transfer coefficient distributions.

scholarly journals Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160077 ◽  
Author(s):  
W. J. Baars ◽  
N. Hutchins ◽  
I. Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Wall Turbulence ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Scale Interaction ◽  
High Reynolds ◽  
Near Wall

Small-scale velocity fluctuations in turbulent boundary layers are often coupled with the larger-scale motions. Studying the nature and extent of this scale interaction allows for a statistically representative description of the small scales over a time scale of the larger, coherent scales. In this study, we consider temporal data from hot-wire anemometry at Reynolds numbers ranging from Re τ ≈2800 to 22 800, in order to reveal how the scale interaction varies with Reynolds number. Large-scale conditional views of the representative amplitude and frequency of the small-scale turbulence, relative to the large-scale features, complement the existing consensus on large-scale modulation of the small-scale dynamics in the near-wall region. Modulation is a type of scale interaction, where the amplitude of the small-scale fluctuations is continuously proportional to the near-wall footprint of the large-scale velocity fluctuations. Aside from this amplitude modulation phenomenon, we reveal the influence of the large-scale motions on the characteristic frequency of the small scales, known as frequency modulation. From the wall-normal trends in the conditional averages of the small-scale properties, it is revealed how the near-wall modulation transitions to an intermittent-type scale arrangement in the log-region. On average, the amplitude of the small-scale velocity fluctuations only deviates from its mean value in a confined temporal domain, the duration of which is fixed in terms of the local Taylor time scale. These concentrated temporal regions are centred on the internal shear layers of the large-scale uniform momentum zones, which exhibit regions of positive and negative streamwise velocity fluctuations. With an increasing scale separation at high Reynolds numbers, this interaction pattern encompasses the features found in studies on internal shear layers and concentrated vorticity fluctuations in high-Reynolds-number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Heavy hydroelastic travelling waves

2007 ◽  
Vol 463 (2085) ◽  
pp. 2371-2397 ◽  
Author(s):  
J.F Toland
Keyword(s):  
Harmonic Function ◽  
Travelling Waves ◽  
Fluid Velocity ◽  
Saddle Point Problem ◽  
Elastic Response ◽  
Moving Frame ◽  
Point Problem ◽  
Gravitational Acceleration ◽  
Mean Velocity ◽  
Elastic Sheet

This is a mathematical study of steady two-dimensional waves of prescribed period which propagate without change of form on the surface of an infinitely deep expanse of fluid that is moving under gravity and bounded above by heavy, frictionless, thin elastic sheet. The flow, which is supposed irrotational, is at rest at infinite depth and its velocity is stationary relative to a frame moving with the wave. In that frame, the elastic sheet coincides with the zero streamline and its material points move according to the equations of hyperelasticity. From the mechanics of the surface material, the pressure on a point of the sheet in the moving frame is shown to be a function of its height, its slope and derivatives with respect to arc length of these quantities. Independently, according to classical fluid mechanics, the pressure in the fluid at the same point is determined by its height and the fluid velocity tangent to the zero streamline. Therefore, this is a free-boundary problem: to find a non-self-intersecting curve in the plane which is the zero contour of a harmonic function (the stream function) and at which the normal derivative of the same harmonic function is a prescribed function of the shape of the curve. With the wavelength fixed, the parameters are the density ρ of the undeformed sheet, the wave velocity c 0 , the mean velocity c of the surface sheet relative to the wave and the gravitational acceleration g . The case of a weightless sheet, in which ρ =0 and c does not appear, is a special case. Under quite general hypotheses on the elastic response of the sheet, the existence of rapidly propagating or very slow (depending on parameter values) steady waves is established by finding a critical point of the Lagrangian. This is a saddle-point problem in the calculus of variations.

After transition in a soft-walled microchannel

2015 ◽  
Vol 780 ◽  
pp. 649-686 ◽  
Author(s):  
S. S. Srinivas ◽  
V. Kumaran
Keyword(s):  
Velocity Profile ◽  
Root Mean Square ◽  
Reynolds Stress ◽  
Fluid Velocity ◽  
Maximum Velocity ◽  
Reynolds Numbers ◽  
Dynamical Instability ◽  
Mean Square ◽  
Velocity Fluctuations ◽  
Soft Wall

In comparison to the flow in a rigid channel, there is a multifold reduction in the transition Reynolds number for the flow in a microchannel when one of the walls is made sufficiently soft, due to a dynamical instability induced by the fluid–wall coupling, as shown by Verma & Kumaran (J. Fluid Mech., vol. 727, 2013, pp. 407–455). The flow after transition is characterised using particle image velocimetry in the $x{-}y$ plane, where $x$ is the streamwise direction and $y$ is the cross-stream coordinate along the small dimension of the channel of height 0.2–0.3 mm. The flow after transition is characterised by a mean velocity profile that is flatter at the centre and steeper at the walls in comparison to that for a laminar flow. The root mean square of the streamwise fluctuating velocity shows a characteristic sharp increase away from the wall and a maximum close to the wall, as observed in turbulent flows in rigid-walled channels. However, the profile is asymmetric, with a significantly higher maximum close to the soft wall in comparison to that close to the hard wall, and the Reynolds stress is found to be non-zero at the soft wall, indicating that there is a stress exerted by fluid velocity fluctuations on the wall. The maximum of the root mean square of the velocity fluctuations and the Reynolds stress (divided by the fluid density) in the soft-walled microchannel for Reynolds numbers in the range 250–400, when scaled by suitable powers of the maximum velocity, are comparable to those in a rigid channel at Reynolds numbers in the range 5000–20 000. The near-wall velocity profile shows no evidence of a viscous sublayer for $(yv_{\ast }/{\it\nu})$ as low as two, but there is a logarithmic layer for $(yv_{\ast }/{\it\nu})$ up to approximately 30, where the von Karman constants are very different from those for a rigid-walled channel. Here, $v_{\ast }$ is the friction velocity, ${\it\nu}$ is the kinematic viscosity and $y$ is the distance from the soft surface. The surface of the soft wall in contact with the fluid is marked with dye spots to monitor the deformation and motion along the fluid–wall interface. Low-frequency oscillations in the displacement of the surface are observed after transition in both the streamwise and spanwise directions, indicating that the velocity fluctuations are dynamically coupled to motion in the solid.

Computation of Flow and Heat Transfer in Rotating Rectangular Channels (AR=4:1) With Pin-Fins by a Reynolds Stress Turbulence Model

2005 ◽  
Author(s):  
Guoguang Su ◽  
Hamn-Ching Chen ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Rotation Number ◽  
Rectangular Channel ◽  
Density Ratio ◽  
Three Dimensional ◽  
Diameter Ratio ◽  
Mean Velocity ◽  
Flow And Heat Transfer ◽  
Pin Fins

Computations with multi-block chimera grids were performed to study the three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with staggered arrays of pin-fins. The channel aspect ratio (AR) is 4:1, the pin length to diameter ratio (H/D) is 2.0, and the pin spacing to diameter ratio is 2.0 in both the stream-wise (S1/D) and span-wise (S2/D) directions. A total of six calculations have been performed with various combinations of rotation number, Reynolds number, and coolant-to-wall density ratio. The rotation number and inlet coolant-to-wall density ratio varied from 0.0 to 0.28 and from 0.122 to 0.20, respectively, while the Reynolds number varied from 10,000 to 100,000. For the rotating cases, the rectangular channel was oriented at 150 deg with respect to the plane of rotation to be consistent with the configuration of the gas turbine blade. A Reynolds-Averaged Navier-Stokes (RANS) method was employed in conjunction with a near-wall second-moment turbulence closure for detailed predictions of mean velocity, mean temperature, and heat transfer coefficient distributions.

Computation of Flow and Heat Transfer in Rotating Rectangular Channels (AR = 4) With V-Shaped Ribs by a Reynolds Stress Turbulence Model

2003 ◽  
Author(s):  
Guoguang Su ◽  
Shuye Teng ◽  
Hamn-Ching Chen ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Rotation Number ◽  
Rectangular Channel ◽  
Density Ratio ◽  
Heat Fluxes ◽  
Reynolds Stresses ◽  
Transfer Coefficients ◽  
Mean Velocity ◽  
Flow And Heat Transfer

Computations were performed to study three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with 45° V-shaped ribs. The channel aspect ratio (AR) is 4:1, the rib height-to-hydraulic diameter ratio (e/Dh) is 0.078 and the rib-pitch-to-height ratio (P/e) is 10. A total of eight calculations have been performed with various combinations of rotation number, Reynolds number, coolant-to-wall density ratio, and channel orientation. The rotation number and inlet coolant-to-wall density ratio varied from 0.0 to 0.28 and from 0.122 to 0.40, respectively, while the Reynolds number varied from 10,000 to 500,000. Three channel orientations (90°, −135°, and 135° from the rotation direction) were also investigated. A multi-block Reynolds-Averaged Navier-Stokes (RANS) method was employed in conjunction with a near-wall second-moment turbulence closure for detailed predictions of mean velocity, mean temperature, turbulent Reynolds stresses, and heat fluxes and heat transfer coefficients.

Sign in / Sign up

Export Citation Format

Share Document