Wall turbulence without walls

AbstractWe perform direct numerical simulations of turbulent channels whose inner layer is replaced by an off-wall boundary condition synthesized from a rescaled interior flow plane. The boundary condition is applied within the logarithmic layer, and mimics the linear dependence of the length scales of the velocity fluctuations with respect to the distance to the wall. The logarithmic profile of the mean streamwise velocity is recovered, but only if the virtual wall is shifted to a position different from the location assumed by the boundary condition. In those shifted coordinates, most flow properties are within 5–10 % of full simulations, including the Kármán constant, the fluctuation intensities, the energy budgets and the velocity spectra and correlations. On the other hand, buffer-layer structures do not form, including the near-wall energy maximum, and the velocity fluctuation profiles are logarithmic, strongly suggesting that the logarithmic layer is essentially independent of the near-wall dynamics. The same agreement holds when the technique is applied to large-eddy simulations. The different errors are analysed, especially the reasons for the shifted origin, and remedies are proposed. It is also shown that the length rescaling is required for a stationary logarithmic-like layer. Otherwise, the flow evolves into a state resembling uniformly sheared turbulence.

Download Full-text

Spatio-temporal spectra in the logarithmic layer of wall turbulence: large-eddy simulations and simple models

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.116 ◽

2015 ◽

Vol 769 ◽

Cited By ~ 32

Author(s):

Michael Wilczek ◽

Richard J. A. M. Stevens ◽

Charles Meneveau

Keyword(s):

Large Scale ◽

Temporal Structure ◽

Streamwise Velocity ◽

Wall Turbulence ◽

Mean Flow ◽

Frequency Spectra ◽

Eddy Simulation ◽

Large Eddy ◽

Spatio Temporal ◽

Logarithmic Layer

Motivated by the need to characterize the spatio-temporal structure of turbulence in wall-bounded flows, we study wavenumber–frequency spectra of the streamwise velocity component based on large-eddy simulation (LES) data. The LES data are used to measure spectra as a function of the two wall-parallel wavenumbers and the frequency in the equilibrium (logarithmic) layer. We then reformulate one of the simplest models that is able to reproduce the observations: the random sweeping model with a Gaussian large-scale fluctuating velocity and with additional mean flow. Comparison with LES data shows that the model captures the observed temporal decorrelation, which is related to the Doppler broadening of frequencies. We furthermore introduce a parameterization for the entire wavenumber–frequency spectrum $E_{11}(k_{1},k_{2},{\it\omega};z)$, where $k_{1}$, $k_{2}$ are the streamwise and spanwise wavenumbers, ${\it\omega}$ is the frequency and $z$ is the distance to the wall. The results are found to be in good agreement with LES data.

Download Full-text

The logarithmic variance of streamwise velocity and conundrum in wall turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.1057 ◽

2021 ◽

Vol 933 ◽

Author(s):

Yongyun Hwang ◽

Nicholas Hutchins ◽

Ivan Marusic

Keyword(s):

Turbulence Intensity ◽

Streamwise Velocity ◽

Early Observation ◽

Wall Turbulence ◽

Inviscid Limit ◽

Necessary Condition ◽

Outer Length ◽

Power Spectral ◽

Parallel Direction ◽

Logarithmic Layer

The logarithmic dependence of streamwise turbulence intensity has been observed repeatedly in recent experimental and direct numerical simulation data. However, its spectral counterpart, a well-developed $k^{-1}$ spectrum ( $k$ is the spatial wavenumber in a wall-parallel direction), has not been convincingly observed from the same data. In the present study, we revisit the spectrum-based attached eddy model of Perry and co-workers, who proposed the emergence of a $k^{-1}$ spectrum in the inviscid limit, for small but finite $z/\delta$ and for finite Reynolds numbers ( $z$ is the wall-normal coordinate, and $\delta$ is the outer length scale). In the upper logarithmic layer (or inertial sublayer), a reexamination reveals that the intensity of the spectrum must vary with the wall-normal location at order of $z/\delta$ , consistent with the early observation argued with ‘incomplete similarity’. The streamwise turbulence intensity is subsequently calculated, demonstrating that the existence of a well-developed $k^{-1}$ spectrum is not a necessary condition for the approximate logarithmic wall-normal dependence of turbulence intensity – a more general condition is the existence of a premultiplied power-spectral intensity of $O(1)$ for $O(1/\delta ) < k < O(1/z)$ . Furthermore, it is shown that the Townsend–Perry constant must be weakly dependent on the Reynolds number. Finally, the analysis is semi-empirically extended to the lower logarithmic layer (or mesolayer), and a near-wall correction for the turbulence intensity is subsequently proposed. All the predictions of the proposed model and the related analyses/assumptions are validated with high-fidelity experimental data (Samie et al., J. Fluid Mech., vol. 851, 2018, pp. 391–415).

Download Full-text

Experimental study of wall boundary conditions for large-eddy simulation

Journal of Fluid Mechanics ◽

10.1017/s0022112001005924 ◽

2001 ◽

Vol 446 ◽

pp. 309-320 ◽

Cited By ~ 51

Author(s):

IVAN MARUSIC ◽

GARY J. KUNKEL ◽

FERNANDO PORTÉ-AGEL

Keyword(s):

Boundary Layer ◽

Boundary Condition ◽

Shear Stress ◽

Wall Shear Stress ◽

Large Eddy Simulation ◽

Boundary Conditions ◽

Streamwise Velocity ◽

New Model ◽

Eddy Simulation ◽

Large Eddy

An experimental investigation was conducted to study the wall boundary condition for large-eddy simulation (LES) of a turbulent boundary layer at Rθ = 3500. Most boundary condition formulations for LES require the specification of the instantaneous filtered wall shear stress field based upon the filtered velocity field at the closest grid point above the wall. Three conventional boundary conditions are tested using simultaneously obtained filtered wall shear stress and streamwise and wall-normal velocities, at locations nominally within the log region of the flow. This was done using arrays of hot-film sensors and X-wire probes. The results indicate that models based on streamwise velocity perform better than those using the wall-normal velocity, but overall significant discrepancies were found for all three models. A new model is proposed which gives better agreement with the shear stress measured at the wall. The new model is also based on the streamwise velocity but is formulated so as to be consistent with ‘outer-flow’ scaling similarity of the streamwise velocity spectra. It is therefore expected to be more generally applicable over a larger range of Reynolds numbers at any first-grid position within the log region of the boundary layer.

Download Full-text

Direct numerical simulation of turbulence in injection-driven three-dimensional cylindrical flows

Journal of Fluid Mechanics ◽

10.1017/s0022112010005215 ◽

2011 ◽

Vol 670 ◽

pp. 176-203 ◽

Cited By ~ 4

Author(s):

JU ZHANG ◽

THOMAS L. JACKSON

Keyword(s):

Reynolds Number ◽

Root Mean Square ◽

Streamwise Velocity ◽

Wall Turbulence ◽

Wall Friction ◽

Mean Square ◽

The Mean ◽

Wall Shear ◽

Strong Injection ◽

Near Wall

Incompressible turbulent flow in a periodic circular pipe with strong injection is studied as a simplified model for the core flow in a solid-propellant rocket motor and other injection-driven internal flows. The model is based on a multi-scale asymptotic approach. The intended application of the current study is erosive burning of solid propellants. Relevant analysis for easily accessible parameters for this application, such as the magnitudes, main frequencies and wavelengths associated with the near-wall shear, and the assessment of near-wall turbulence viscosity is focused on. It is found that, unlike flows with weak or no injection, the near-wall shear is dominated by the root mean square of the streamwise velocity which is a function of the Reynolds number, while the mean streamwise velocity is only weakly dependent on the Reynolds number. As a result, a new wall-friction velocity $$u_\tau{\,=\,}\sqrt{\tau_w/\rho}$$, based on the shear stress derived from the sum of the mean and the root mean square, i.e. $$\tau_{w,inj} {\,=\,} \mu |{\partial (\bar{u}+u_{rms})}/{\partial r}|_w$$, is proposed for the scaling of turbulent viscosity for turbulent flows with strong injection. We also show that the mean streamwise velocity profile has an inflection point near the injecting surface.

Download Full-text

Evolution and dynamics of shear-layer structures in near-wall turbulence

Journal of Fluid Mechanics ◽

10.1017/s002211209100188x ◽

1991 ◽

Vol 224 ◽

pp. 579-599 ◽

Cited By ~ 96

Author(s):

Arne V. Johansson ◽

P. Henrik Alfredsson ◽

John Kim

Keyword(s):

Turbulent Channel Flow ◽

Wall Turbulence ◽

Turbulent Shear ◽

Spanwise Direction ◽

Wall Structures ◽

Layer Structures ◽

Turbulence Production ◽

Near Wall Turbulence ◽

Probe Measurements ◽

Near Wall

Near-wall flow structures in turbulent shear flows are analysed, with particular emphasis on the study of their space–time evolution and connection to turbulence production. The results are obtained from investigation of a database generated from direct numerical simulation of turbulent channel flow at a Reynolds number of 180 based on half-channel width and friction velocity. New light is shed on problems associated with conditional sampling techniques, together with methods to improve these techniques, for use both in physical and numerical experiments. The results clearly indicate that earlier conceptual models of the processes associated with near-wall turbulence production, based on flow visualization and probe measurements need to be modified. For instance, the development of asymmetry in the spanwise direction seems to be an important element in the evolution of near-wall structures in general, and for shear layers in particular. The inhibition of spanwise motion of the near-wall streaky pattern may be the primary reason for the ability of small longitudinal riblets to reduce turbulent skin friction below the value for a flat surface.

Download Full-text

Active control of near-wall turbulence by local oscillating blowing

Journal of Fluid Mechanics ◽

10.1017/s0022112001004542 ◽

2001 ◽

Vol 439 ◽

pp. 217-253 ◽

Cited By ~ 44

Author(s):

SEDAT F. TARDU

Keyword(s):

Isotropic Turbulence ◽

Structural Parameters ◽

Streamwise Velocity ◽

Wall Turbulence ◽

Injection Velocity ◽

Median Frequency ◽

Acceleration Phase ◽

Velocity Changes ◽

Near Wall Turbulence ◽

Near Wall

The effect of time-periodical blowing through a spanwise slot on the near-wall turbulence characteristics is investigated. The blowing velocity changes in a cyclic manner from 0 to 5 wall units. The frequency of the oscillations is nearly equal to the median frequency of the near-wall turbulence. The measurements of the wall shear stress and the streamwise velocity are reported and discussed. The flow field near the blowing slot is partly relaminarized during the acceleration phase of the injection velocity which extends 40 wall units downstream. The imposed unsteadiness is confined to the buffer layer, and the time-mean structural parameters under unsteady blowing are found to be close to those of isotropic turbulence in this region. The relaminarized phase is unstable and gives way to a coherent spanwise structure that increases the shear from 80 to 300 wall units downstream of the slot in a predictable way. This phenomenon is strongly imposed-frequency dependent.

Download Full-text

Tests of subgrid models in the near-wall region using represented velocity fields

Journal of Fluid Mechanics ◽

10.1017/s0022112083001652 ◽

1983 ◽

Vol 132 ◽

pp. 349-373 ◽

Cited By ~ 2

Author(s):

Y. Kaneda ◽

D. C. Leslie

Keyword(s):

Boundary Condition ◽

Velocity Fields ◽

Large Eddy Simulations ◽

Wall Region ◽

Dimensional Model ◽

Positive Side ◽

Turbulent Field ◽

Large Eddy ◽

Near Wall

The 2.5-dimensional model of the turbulent field near a wall, proposed by Hatziavramidis & Hanratty (1979) and modified by Chapman & Kuhn (1981), has been used to test the subgrid models of Schumann (1973, 1975) and Moin & Kim (1982). The results are disquieting, both trends and orders of magnitude sometimes being seriously in error. It also appears that the contribution of the subgrid energy to the pseudopressure calculated in large-eddy simulations can be large, although this contribution is usually neglected. On the positive side, Leonard's model for the Leonard stress is extremely good, and Schumann's synthetic boundary condition is also found to be reliable.These results must be taken with a grain of salt, since the tests reported in §5 show that the 2.5-dimensional model cannot reproduce important characteristics of the turbulence in the neighbourhood of y+ = 40.

Download Full-text