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Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth

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A special issue of Fluids (ISSN 2311-5521). This special issue belongs to the section "Turbulence".

Deadline for manuscript submissions: closed (31 March 2022) | Viewed by 34075

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Special Issue Editor

Prof. Dr. Timothy Wei

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Guest Editor

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
Interests: swimming; vascular flows; bacterial biofilms; cerebral-spinal flows; phonation; papermaking; turbulent boundary layers; drag reduction; wake flows

Special Issue Information

Dear Colleagues,

Bill Willmarth, or W3, was a pioneer in near wall turbulent boundary layer measurements. He was one of the first to make highly resolved measurements of wall pressure fluctuations. He also made hot-wire and LDV measurements with a resolution smaller than a viscous length. Much of what is known about about coherent structures in TBLs finds its roots in work from this era. He later extended his scope to turbulence at free surfaces.

This special issue honors Bill’s legacy by focusing on advances in the structure and dynamics of bounded turbulent shear flows into the 21st century. With invited contributions from premier researchers in the field, the goal of this issue is to show how wide and rich the field continues to be. Submissions are solicited that will highlight the state-of-the-art and chart future directions in the field. Papers broadly related turbulence generated at a solid or free surface boundary are welcome.

Prof. Dr. Timothy Wei
Guest Editor

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

turbulence
boundary layers
coherent structures
shear flows
free surface
vorticity
drag
mixing

Published Papers (15 papers)

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Research

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19 pages, 1486 KiB

Open AccessArticle

Advances in the Prediction of the Statistical Properties of Wall-Pressure Fluctuations under Turbulent Boundary Layers

by Gabriele Grasso, Michel Roger and Stéphane Moreau

Fluids 2022, 7(5), 161; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7050161 - 05 May 2022

Cited by 3 | Viewed by 2619

Abstract

Analytical or empirical models of the wall-pressure power spectral density under a turbulent boundary layer are often validated on test cases in an incompressible flow regime. In this work, an analytical model based on the compressible Poisson equation for the unsteady pressure in a turbulent boundary layer is developed. The Large Eddy Simulation of the flow over a controlled-diffusion airfoil at Mach 0.5 is used to validate the assumptions made on the statistical properties of the boundary layer turbulence and to validate the prediction of the statistics of the wall-pressure fluctuations. The predicted wall-pressure spectrum also compares favorably with experimental data. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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22 pages, 11901 KiB

Open AccessArticle

Secondary Flow in Smooth and Rough Turbulent Circular Pipes: Turbulence Kinetic Energy Budgets

by Paolo Orlandi and Sergio Pirozzoli

Fluids 2021, 6(12), 448; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6120448 - 10 Dec 2021

Cited by 6 | Viewed by 2056

Abstract

Direct Numerical Simulations have been performed for turbulent flow in circular pipes with smooth and corrugated walls. The numerical method, based on second-order finite discretization together with the immersed boundary technique, was validated and applied to various types of flows. The analysis is focused on the turbulence kinetic energy and its budget. Large differences have been found in the near-wall region at low Reynolds number. The change in the near-wall turbulent structures is responsible for increase of drag and turbulence kinetic energy. To investigatselinae the effects of wall corrugations, the velocity fields have been decomposed so as to isolate coherent and incoherent motions. For corrugated walls, we find that coherent motions are strongest for walls covered with square bars aligned with the flow direction. In particular, the coherent contribution is substantial when the bars are spaced apart by a distance larger than their height. Detailed analysis of the turbulence kinetic energy budget shows for this set-up a very different behavior than for the other types of corrugations. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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9 pages, 1795 KiB

Open AccessArticle

Vortex Formation Times in the Glottal Jet, Measured in a Scaled-Up Model

by Michael Krane

Fluids 2021, 6(11), 412; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6110412 - 15 Nov 2021

Viewed by 1409

Abstract

In this paper, the timing of vortex formation on the glottal jet is studied using previously published velocity measurements of flow through a scaled-up model of the human vocal folds. The relative timing of the pulsatile glottal jet and the instability vortices are acoustically important since they determine the harmonic and broadband content of the voice signal. Glottis exit jet velocity time series were extracted from time-resolved planar DPIV measurements. These measurements were acquired at four glottal flow speeds (u_SS = 16.1–38 cm/s) and four glottis open times (T_o = 5.67–23.7 s), providing a Reynolds number range Re = 4100–9700 and reduced vibration frequency f* = 0.01−0.06. Exit velocity waveforms showed temporal behavior on two time scales, one that correlates to the period of vibration and another characterized by short, sharp velocity peaks (which correlate to the passage of instability vortices through the glottis exit plane). The vortex formation time, estimated by computing the time difference between subsequent peaks, was shown to be not well-correlated from one vibration cycle to the next. The principal finding is that vortex formation time depends not only on cycle phase, but varies strongly with reduced frequency of vibration. In all cases, a strong high-frequency burst of vortex motion occurs near the end of the cycle, consistent with perceptual studies using synthesized speech. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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14 pages, 3123 KiB

Open AccessArticle

Experiments and Simulations of Free-Surface Flow behind a Finite Height Rigid Vertical Cylinder

by Valentin Ageorges, Jorge Peixinho, Gaële Perret, Ghislain Lartigue and Vincent Moureau

Fluids 2021, 6(10), 367; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6100367 - 18 Oct 2021

Cited by 5 | Viewed by 2216

Abstract

We present the results of a combined experimental and numerical study of the free-surface flow behind a finite height rigid vertical cylinder. The experiments measure the drag and the wake angle on cylinders of different diameters for a range of velocities corresponding to [...] Read more.

< R e <

200,000 and

0.2 < F r < 2

where the Reynolds and Froude numbers are based on the diameter. The three-dimensional large eddy simulations use a conservative level-set method for the air-water interface, thus predicting the pressure, the vorticity, the free-surface elevation and the onset of air entrainment. The deep flow looks like single phase turbulent flow past a cylinder, but close to the free-surface, the interaction between the wall, the free-surface and the flow is taking place, leading to a reduced cylinder drag and the appearance of V-shaped surface wave patterns. For large velocities, vortex shedding is suppressed in a layer region behind the cylinder below the free surface. The wave patterns mostly follow the capillary-gravity theory, which predicts the crest lines cusps. Interestingly, it also indicates the regions of strong elevation fluctuations and the location of air entrainment observed in the experiments. Overall, these new simulation results, drag, wake angle and onset of air entrainment, compare quantitatively with experiments. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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14 pages, 3823 KiB

Open AccessArticle

Asymmetrical Order in Wall-Bounded Turbulent Flows

by T.-W. Lee

Fluids 2021, 6(9), 329; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6090329 - 14 Sep 2021

Viewed by 1188

Abstract

Scaling of turbulent wall-bounded flows is revealed in the gradient structures, for each of the Reynolds stress components. Within the “dissipation” structure, an asymmetrical order exists, which we can deploy to unify the scaling and transport dynamics within and across these flows. There are subtle differences in the outer boundary conditions between channel and flat-plate boundary-layer flows, which modify the turbulence structure far from the wall. The self-similarity exhibited in the gradient space and corresponding transport dynamics establish capabilities and encompassing knowledge of wall-bounded turbulent flows. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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13 pages, 4569 KiB

Open AccessFeature PaperArticle

Numerical Studies of Disperse Three-Phase Fluid Flows

by Lei Zeng, Daniel Velez, Jiacai Lu and Gretar Tryggvason

Fluids 2021, 6(9), 317; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6090317 - 06 Sep 2021

Cited by 5 | Viewed by 1750

Abstract

The dynamics of a three-phase gas–liquid–liquid multiphase system is examined by direct numerical simulations. The system consists of a continuous liquid phase, buoyant gas bubbles, and smaller heavy drops that fall relative to the continuous liquid. The computational domain is fully periodic, and a force equal to the weight of the mixture is added to keep it in place. The governing parameters are selected so that the terminal Reynolds numbers of the bubbles and the drops are moderate; while the effect of bubble deformability is examined by changing its surface tension, the surface tension for the drops is sufficiently high so they do not deform. One bubble in a “unit cell” and eight freely interacting bubbles are examined. The dependency of the slip velocities, the velocity fluctuations, and the distribution of the dispersed phases on the volume fraction of each phase are examined. It is found that while the distribution of drops around a single bubble in a “unit cell” is uneven and depends on its deformability, the distribution of drops around freely interacting bubbles is relatively uniform for the parameters examined in this study. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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13 pages, 1865 KiB

Open AccessArticle

Correlation between Large-Scale Streamwise Velocity Features and the Height of Coherent Vortices in a Turbulent Boundary Layer

by Shaurya Shrivastava and Theresa Saxton-Fox

Fluids 2021, 6(8), 286; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6080286 - 16 Aug 2021

Cited by 1 | Viewed by 2386

Abstract

The preferential organisation of coherent vortices in a turbulent boundary layer in relation to local large-scale streamwise velocity features was investigated. Coherent vortices were identified in the wake region using the Triple Decomposition Method (originally proposed by Kolář) from 2D particle image velocimetry (PIV) data of a canonical turbulent boundary layer. Two different approaches, based on conditional averaging and quantitative statistical analysis, were used to analyze the data. The large-scale streamwise velocity field was first conditionally averaged on the height of the detected coherent vortices and a change in the sign of the average large scale streamwise fluctuating velocity was seen depending on the height of the vortex core. A correlation coefficient was then defined to quantify this relationship between the height of coherent vortices and local large-scale streamwise fluctuating velocity. Both of these results indicated a strong negative correlation in the wake region of the boundary layer between vortex height and large-scale velocity. The relationship between vortex height and full large-scale velocity isocontours was also studied and a conceptual model based on the findings of the study was proposed. The results served to relate the hairpin vortex model of Adrian et al. to the scale interaction results reported by Mathis et al., and Chung and McKeon. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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Graphical abstract

17 pages, 1678 KiB

Open AccessArticle

Comparison of Semi-Empirical Single Point Wall Pressure Spectrum Models with Experimental Data

by Nicholas Thomson and Joana Rocha

Fluids 2021, 6(8), 270; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6080270 - 31 Jul 2021

Cited by 8 | Viewed by 2291

Abstract

This study presents an evaluation of semi-empirical single-point wall pressure spectrum models by comparing model predictions with wind tunnel and flight test data. The mean squared error was used to compare the power spectral density of the wall pressure fluctuations predicted by semi-empirical models with a large amount of experimental data. Results show that the models proposed by Goody and Smol’yakov have the lowest mean squared error when predicting the power spectral density for wind tunnel experiments and the Rackl and Weston model has the lowest mean squared error when predicting the power spectral density for flight test data. In addition, although current studies of the power spectra obtained in the wind tunnel are similar, they are not generally an accurate representation of flight test experiments. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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16 pages, 3025 KiB

Open AccessArticle

Perspective on the Response of Turbulent Pipe Flows to Strong Perturbations

by Liuyang Ding, Tyler Van Buren, Ian E. Gunady and Alexander J. Smits

Fluids 2021, 6(6), 208; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6060208 - 04 Jun 2021

Cited by 2 | Viewed by 2713

Abstract

Pipe flow responds to strong perturbations in ways that are fundamentally different from the response exhibited by boundary layers undergoing a similar perturbation, primarily because of the confinement offered by the pipe wall, and the need to satisfy continuity. We review such differences by examining previous literature, with a particular focus on the response of pipe flow to three different kinds of disturbances: the abrupt change in surface condition from rough to smooth, the obstruction due to presence of a single square bar roughness elements of different sizes, and the flow downstream of a streamlined body-of-revolution placed on the centerline of the pipe. In each case, the initial response is strongly influenced by the pipe geometry, but far downstream all three flows display a common feature, which is the very slow, second-order recovery that can be explained using a model based on the Reynolds stress equations. Some future directions for research are also given. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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10 pages, 1525 KiB

Open AccessArticle

On the Comparison of Flow Physics between Minimal and Extended Flow Units in Turbulent Channels

by Ethan A. Davis, Siamak Mirfendereski and Jae Sung Park

Fluids 2021, 6(5), 192; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6050192 - 20 May 2021

Cited by 2 | Viewed by 2166

Abstract

Direct numerical simulations were performed to study the effects of the domain size of a minimal flow unit (MFU) and its inherent periodic boundary conditions on flow physics of a turbulent channel flow in a range of [...] Read more.

200 \leq R e_{τ} \leq 1000

. This was accomplished by comparing turbulent statistics with those computed in sub-domains (SD) of extended domain simulations. The dimensions of the MFU and SD were matched, and SD dynamics were set to minimize artificial periodicities. Streamwise and spanwise dimensions of healthy MFUs were found to increase linearly with Reynolds number. It was also found that both MFU and SD statistics and dynamics were healthy and in good agreement. This suggests that healthy MFU dynamics represent extended-domain dynamics well up to

R e_{τ} = 1000

, indicating a nearly negligible effect of periodic conditions on MFUs. However, there was a small deviation within the buffer layer for the MFU at

R e_{τ} = 200

, which manifested in an increased mean velocity and a tail in the Q2 quadrant of the

u^{'}

v^{'}

plane. Thus, it should be noted that when considering an MFU domain size, stricter criteria may need to be put in place to ensure healthy turbulent dynamics. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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21 pages, 2849 KiB

Open AccessArticle

Experiments and Modeling of a Compliant Wall Response to a Turbulent Boundary Layer with Dynamic Roughness Forcing

by David P. Huynh, Yuting Huang and Beverley J. McKeon

Fluids 2021, 6(5), 173; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6050173 - 26 Apr 2021

Cited by 4 | Viewed by 2153

Abstract

The response of a compliant surface in a turbulent boundary layer forced by a dynamic roughness is studied using experiments and resolvent analysis. Water tunnel experiments are carried out at a friction Reynolds number of

{Re}_{τ} \approx 410

, with flow and [...] Read more.

{Re}_{τ} \approx 410

, with flow and surface measurements taken with 2D particle image velocimetry (PIV) and stereo digital image correlation (DIC). The narrow band dynamic roughness forcing enables analysis of the flow and surface responses coherent with the forcing frequency, and the corresponding Fourier modes are extracted and compared with resolvent modes. The resolvent modes capture the structures of the experimental Fourier modes and the resolvent with eddy viscosity improves the matching. The comparison of smooth and compliant wall resolvent modes predicts a virtual wall feature in the wall normal velocity of the compliant wall case. The virtual wall is revealed in experimental data using a conditional average informed by the resolvent prediction. Finally, the change to the resolvent modes due to the influence of wall compliance is studied by modeling the compliant wall boundary condition as a deterministic forcing to the smooth wall resolvent framework. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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12 pages, 2712 KiB

Open AccessArticle

Static Pressure Distribution on Long Cylinders as a Function of the Yaw Angle and Reynolds Number

by William W. Willmarth and Timothy Wei

Fluids 2021, 6(5), 169; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6050169 - 22 Apr 2021

Cited by 2 | Viewed by 1973

Abstract

This paper addresses the challenges of pressure-based sensing using axisymmetric probes whose axes are at small angles to the mean flow. Mean pressure measurements around three yawed circular cylinders with aspect ratios of 28, 64, and 100 were made to determine the effect [...] Read more.

{\bar{C}}_{p N}

, and drag coefficient,

C_{D N}

. The existence of four distinct types of circumferential pressure distributions—subcritical, transitional, supercritical, and asymmetric—were confirmed, along with the appropriateness of scaling

{\bar{C}}_{p N}

and

C_{D N}

on a streamwise Reynolds number,

R e_{s w}

, based on the freestream velocity and the fluid path length along the cylinder in the streamwise direction. It was found that there was a distinct difference in the values of

C_{D N}

and

{\bar{C}}_{p N}

at identical

R e_{s w}

values for cylinders yawed between 5° and 30°, and for cylinders at greater than a 30° yaw. For γ < 5°, there did not appear to be any large-scale vortices in the near wake, and

C_{D N}

and

\bar{C}

_pN appeared to become independent of

R e_{s w}

. Over the range of 5° ≤ γ ≤ 30°, there was a complex interplay of freestream speed, yaw angle, and aspect ratio that affected the formation and shedding of Kármán-like vortices. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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17 pages, 1030 KiB

Open AccessEditor’s ChoiceArticle

Characterising Momentum Flux Events in High Reynolds Number Turbulent Boundary Layers

by Rahul Deshpande and Ivan Marusic

Fluids 2021, 6(4), 168; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6040168 - 20 Apr 2021

Cited by 9 | Viewed by 2547

Abstract

The momentum flux in a canonical turbulent boundary layer is known to have a time-series signature that is characterised by a highly intermittent variation, which includes very short periods of intense flux activity. Here, we study the variation in these flux signal characteristics [...] Read more.

R e_{τ}

) by analysing datasets acquired using miniature cross-wire probes with matched spatial resolution. The analysis is facilitated by conditionally sampling the signal based on the quadrant (Qi; i = 1–4) and magnitude of the flux, revealing fractional cumulative contribution from Q4 to increase at a much faster rate than from Q2 with

R e_{τ}

. An episodic description of the flux signal is subsequently undertaken, which associates this rapid increase in Q4 contributions with the emergence of extreme and rare flux events with

R e_{τ}

. The same dataset is also used to test Townsend’s hypothesis on the active and inactive components of the momentum flux, which are obtained for the first time by implementing a spectral linear stochastic estimation-based decomposition methodology. While the active component is found to be the dominant contributor to the mean momentum flux consistent with Townsend’s hypothesis, the inactive component is found to be small but non-zero, owing to the non-linear interactions associated with the modulation phenomenon. Finally, an episodic description of the active and inactive momentum flux signal is undertaken to highlight the starkly different time series characteristics of the two flux components. The inactive flux signal is found to comprise individual statistically significant events associated with all four quadrants, leading to a small net contribution to the total flux. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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12 pages, 555 KiB

Open AccessEditor’s ChoiceArticle

Effect of Wall Boundary Conditions on a Wall-Modeled Large-Eddy Simulation in a Finite-Difference Framework

by H. Jane Bae and Adrián Lozano-Durán

Fluids 2021, 6(3), 112; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6030112 - 10 Mar 2021

Cited by 16 | Viewed by 2809

Abstract

We studied the effect of wall boundary conditions on the statistics in a wall-modeled large-eddy simulation (WMLES) of turbulent channel flows. Three different forms of the boundary condition based on the mean stress-balance equations were used to supply the correct mean wall shear stress for a wide range of Reynolds numbers and grid resolutions applicable to WMLES. In addition to the widely used Neumann boundary condition at the wall, we considered a case with a no-slip condition at the wall in which the wall stress was imposed by adjusting the value of the eddy viscosity at the wall. The results showed that the type of boundary condition utilized had an impact on the statistics (e.g., mean velocity profile and turbulence intensities) in the vicinity of the wall, especially at the first off-wall grid point. Augmenting the eddy viscosity at the wall resulted in improved predictions of statistics in the near-wall region, which should allow the use of information from the first off-wall grid point for wall models without additional spatial or temporal filtering. This boundary condition is easy to implement and provides a simple solution to the well-known log-layer mismatch in WMLES. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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Other

Jump to: Research

15 pages, 3683 KiB

Open AccessPerspective

Coupling Vortical Bulk Flows to the Air–Water Interface: From Putting Oil on Troubled Waters to Surfactants on Protein Solutions

by Amir H. Hirsa and Juan M. Lopez

Fluids 2021, 6(6), 198; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6060198 - 25 May 2021

Cited by 2 | Viewed by 2095

Abstract

The air–water interface in flowing systems remains a challenge to model, even in cases where the interface is essentially flat. This is because even though each side is governed by the Navier–Stokes equations, the stress balance which provides the boundary conditions for the equations involves properties associated with surfactants that are inevitably present at the air–water interface. Aside from challenges in measuring interfacial properties, either intrinsic or flow-dependent, the two-way coupling of bulk and interfacial flows is non-trivial, even for very simple flow geometries. Here, we present an overview of the physics associated with surfactant monolayers of flowing liquid and describe how the monolayer affects the bulk flow and how the monolayer is transported and deformed by the bulk flow. The emphasis is primarily on cylindrical flow geometries, and both Newtonian and non-Newtonian interfacial responses are considered. We consider interfacial flows that are solenoidal as well as those where the surface velocity is not divergence free. Full article

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)

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