The dynamics of turbulence near a wall according to a linear model

1967 ◽  
Vol 29 (1) ◽  
pp. 113-135 ◽  
Author(s):  
Gerald Schubert ◽  
G. M. Corcos
Keyword(s):  
Boundary Layer ◽  
Amplitude Ratio ◽  
Equations Of Motion ◽  
Pressure Fluctuations ◽  
Homogeneous System ◽  
Viscous Sublayer ◽  
Spanwise Direction ◽  
Mean Velocity ◽  
Normal Fluctuations

The dynamics of turbulent velocity fluctuations in and somewhat outside the viscous sublayer are examined by linearizing the equations of motion around the known mean velocity profile. The rest of the boundary layer is assumed to drive the motion in the layer by means of a fluctuating pressure which is independent of distance from the wall. The equations, which are boundary-layer approximations to the Orr-Sommerfeld equations, are thus treated as a non-homogeneous system and solved by convergent power series. The solutions which exhibit the strong role of viscosity throughout the layer considered provide a model endowed with many of the known features of turbulence near a wall. In particular, the phase angle between streamwise and normal fluctuations is found to be in plausible agreement with experiments. An important role is ascribed by the solutions to the displacement of the mean velocity by the normal fluctuations. The impedance of the layer is found to be anisotropic in that it favours fluctuations with a much larger scale in the streamwise than in the spanwise direction. For such disturbances, the ratio of turbulent intensity to the intensity of the pressure fluctuations approximates the experimental ratio. According to the solutions it is primarily the spanwise component of the pressure gradient which is responsible for the intense level of turbulence very near the wall. The model apparently underestimates the amplitude ratio of normal to streamwise components of the velocity.

‘Inactive’ motion and pressure fluctuations in turbulent boundary layers

1967 ◽  
Vol 30 (2) ◽  
pp. 241-258 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Pressure Fluctuations ◽  
Turbulent Energy ◽  
Viscous Sublayer ◽  
Wave Number ◽  
Noticeable Effect ◽  
Frequency Spectra ◽  
Active Motion ◽  
Order Of Magnitude

Townsend's (1961) hypothesis that the turbulent motion in the inner region of a boundary layer consists of (i) an ‘active’ part which produces the shear stress τ and whose statistical properties are universal functions of τ and y, and (ii) an ‘inactive’ and effectively irrotational part determined by the turbulence in the outer layer, is supported in the present paper by measurements of frequency spectra in a strongly retarded boundary layer, in which the ‘inactive’ motion is particularly intense. The only noticeable effect of the inactive motion is an increased dissipation of kinetic energy into heat in the viscous sublayer, supplied by turbulent energy diffusion from the outer layer towards the surface. The required diffusion is of the right order of magnitude to explain the non-universal values of the triple products measured near the surface, which can therefore be reconciled with universality of the ‘active’ motion.Dimensional analysis shows that the contribution of the ‘active’ inner layer motion to the one-dimensional wave-number spectrum of the surface pressure fluctuations varies as τ2w/k1 up to a wave-number inversely proportional to the thickness of the viscous sublayer. This result is strongly supported by the recent measurements of Hodgson (1967), made with a much smaller ratio of microphone diameter to boundary-layer thickness than has been achieved previously. The disagreement of the result with most other measurements is attributed to inadequate transducer resolution in the other experiments.

scholarly journals Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer

2021 ◽  
Vol 118 (34) ◽  
pp. e2111144118 ◽  
Author(s):  
Kevin Patrick Griffin ◽  
Lin Fu ◽  
Parviz Moin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Flows ◽  
Viscous Sublayer ◽  
Mean Velocity ◽  
General Transformation ◽  
Law Of The Wall ◽  
Velocity Transformation ◽  
Logarithmic Region ◽  
Logarithmic Layer

In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall, is proposed. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2,000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.

Consequences of compliant walls for peristaltic transportation in a channel having porous medium and porous boundaries

2019 ◽  
Vol 97 (6) ◽  
pp. 599-608 ◽  
Author(s):  
Iqra Shahzadi ◽  
S. Nadeem
Keyword(s):  
Porous Medium ◽  
Distribution Function ◽  
Velocity Distribution ◽  
Amplitude Ratio ◽  
Equations Of Motion ◽  
Velocity Distribution Function ◽  
Driving Mechanism ◽  
Regular Perturbation ◽  
Mean Velocity ◽  
Porous Boundaries

The current communication addresses the two-dimensional peristaltic transport of viscous fluid in a channel having porous medium as well as porous boundaries. The walls of the channel are assumed to be compliant to represent the driving mechanism of the muscle. The equations of motion are considered for the deformable boundaries and the fluid to investigate the fluid–solid interaction problem. The zeroth-, first-, and second-order solutions of stream function for a small amplitude ratio are determined by using regular perturbation. Impact of related parameters on quantities D1, D2, mean velocity perturbation function, and mean velocity distribution function are interpreted graphically. One fundamental finding of the considered examination is that the increase in permeability parameter increases the amplitude of the velocity distribution function.

Investigation of Boundary Layer Flows Over a Flat Plate With Different-Size Transverse Square Grooves at s/w = 10

2007 ◽  
Author(s):  
Redha Wahidi ◽  
Walid Chakroun ◽  
Sami Al-Fahad
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Skin Friction ◽  
Turbulence Intensity ◽  
Viscous Sublayer ◽  
Velocity Profiles ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Uncertainty Range ◽  
The Mean

Turbulent boundary layer flows over a flat plate with multiple transverse square grooves spaced 10 element widths apart were investigated. Mean velocity profiles, turbulence intensity profiles, and the distributions of the skin-friction coefficients (Cf) and the integral parameters are presented for two grooved walls. The two transverse square groove sizes investigated are 5mm and 2.5mm. Laser-Doppler Anemometer (LDA) was used for the mean velocity and turbulence intensity measurements. The skin-friction coefficient was determined from the gradient of the mean velocity profiles in the viscous sublayer. Distribution of Cf in the first grooved-wall case (5mm) shows that Cf overshoots downstream of the groove and then oscillates within the uncertainty range and never shows the expected undershoot in Cf. The same overshoot is seen in the second grooved-wall case (2.5mm), however, Cf continues to oscillate above the uncertainty range and never returns to the smooth-wall value. The mean velocity profiles clearly represent the behavior of Cf where a downward shift is seen in the Cf overshoot region and no upward shift is seen in these profiles. The results show that the smaller grooves exhibit larger effects on Cf, however, the boundary layer responses to these effects in a slower rate than to those of the larger grooves.

scholarly journals Pressure fluctuations induced by a hypersonic turbulent boundary layer

2016 ◽  
Vol 804 ◽  
pp. 578-607 ◽  
Author(s):  
Lian Duan ◽  
Meelan M. Choudhari ◽  
Chao Zhang
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Surface Pressure ◽  
Free Stream ◽  
Spatial Scales ◽  
Pressure Fluctuations ◽  
Propagation Speed ◽  
Dominant Frequency ◽  
Mean Velocity ◽  
Taylor’S Hypothesis

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a spatially developed Mach 5.86 turbulent boundary layer. The unsteady pressure field is analysed at multiple wall-normal locations, including those at the wall, within the boundary layer (including inner layer, the log layer, and the outer layer), and in the free stream. The statistical and structural variations of pressure fluctuations as a function of wall-normal distance are highlighted. Computational predictions for mean-velocity profiles and surface pressure spectrum are in good agreement with experimental measurements, providing a first ever comparison of this type at hypersonic Mach numbers. The simulation shows that the dominant frequency of boundary-layer-induced pressure fluctuations shifts to lower frequencies as the location of interest moves away from the wall. The pressure wave propagates with a speed nearly equal to the local mean velocity within the boundary layer (except in the immediate vicinity of the wall) while the propagation speed deviates from Taylor’s hypothesis in the free stream. Compared with the surface pressure fluctuations, which are primarily vortical, the acoustic pressure fluctuations in the free stream exhibit a significantly lower dominant frequency, a greater spatial extent, and a smaller bulk propagation speed. The free-stream pressure structures are found to have similar Lagrangian time and spatial scales as the acoustic sources near the wall. As the Mach number increases, the free-stream acoustic fluctuations exhibit increased radiation intensity, enhanced energy content at high frequencies, shallower orientation of wave fronts with respect to the flow direction, and larger propagation velocity.

Some properties of sink-flow turbulent boundary layers

1972 ◽  
Vol 56 (2) ◽  
pp. 337-351 ◽  
Author(s):  
W. P. Jones ◽  
B. E. Launder
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
High Reynolds Number ◽  
Viscous Sublayer ◽  
Turbulent Boundary Layers ◽  
Inertial Subrange ◽  
Mean Velocity ◽  
Acceleration Parameter ◽  
Power Spectral ◽  
High Reynolds

An experimental study of asymptotic sink-flow turbulent boundary layers is reported. Three levels of acceleration corresponding to values of the acceleration parameter K of 1·5 × 10−6, 2·5 × 10×6 and 3·0 × 10×6 have been examined. In addition to mean velocity profiles, measurements have been obtained of the profiles of longitudinal turbulence intensity, and, for the lowest value of K, of the lateral and transverse components as well. Measurements at selected positions in the boundary layer of the power spectral density indicate that none of the boundary layers exhibit an inertial subrange; for the steepest acceleration, in particular, throughout the boundary layer the spectrum shapes are similar in form to those reported within the viscous sublayer of a high Reynolds number turbulent flow.

scholarly journals Pressure fluctuations beneath instability wavepackets and turbulent spots in a hypersonic boundary layer

2014 ◽  
Vol 756 ◽  
pp. 1058-1091 ◽  
Author(s):  
Katya M. Casper ◽  
Steven J. Beresh ◽  
Steven P. Schneider
Keyword(s):  
Boundary Layer ◽  
Pressure Fluctuation ◽  
Electrical Breakdown ◽  
Pressure Fluctuations ◽  
Spanwise Direction ◽  
Hypersonic Boundary Layer ◽  
Nozzle Wall ◽  
Turbulent Spots ◽  
Fluctuation Field ◽  
Second Mode

AbstractTo investigate the pressure-fluctuation field beneath turbulent spots in a hypersonic boundary layer, a study was conducted on the nozzle wall of the Boeing/AFOSR Mach-6 Quiet Tunnel. Controlled disturbances were created by pulsed-glow perturbations based on the electrical breakdown of air. Under quiet-flow conditions, the nozzle-wall boundary layer remains laminar and grows very thick over the long nozzle length. This allows the development of large disturbances that can be well-resolved with high-frequency pressure transducers. A disturbance first grows into a second-mode instability wavepacket that is concentrated near its own centreline. Weaker disturbances are seen spreading from the centre. The waves grow and become nonlinear before breaking down to turbulence. The breakdown begins in the core of the packets where the wave amplitudes are largest. Second-mode waves are still evident in front of and behind the breakdown point and can be seen propagating in the spanwise direction. The turbulent core grows downstream, resulting in a spot with a classical arrowhead shape. Behind the spot, a low-pressure calmed region develops. However, the spot is not merely a localized patch of turbulence; instability waves remain an integral part. Limited measurements of naturally occurring disturbances show many similar characteristics. From the controlled disturbance measurements, the convection velocity, spanwise spreading angle, and typical pressure-fluctuation field were obtained.

scholarly journals Turbulent boundary layers and channels at moderate Reynolds numbers

2010 ◽  
Vol 657 ◽  
pp. 335-360 ◽  
Author(s):  
JAVIER JIMÉNEZ ◽  
SERGIO HOYAS ◽  
MARK P. SIMENS ◽  
YOSHINORI MIZUNO
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Flows ◽  
Pressure Fluctuations ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Rotational Flow ◽  
Mean Velocity ◽  
The Mean ◽  
External Flows

The behaviour of the velocity and pressure fluctuations in the outer layers of wall-bounded turbulent flows is analysed by comparing a new simulation of the zero-pressure-gradient boundary layer with older simulations of channels. The 99 % boundary-layer thickness is used as a reasonable analogue of the channel half-width, but the two flows are found to be too different for the analogy to be complete. In agreement with previous results, it is found that the fluctuations of the transverse velocities and of the pressure are stronger in the boundary layer, and this is traced to the pressure fluctuations induced in the outer intermittent layer by the differences between the potential and rotational flow regions. The same effect is also shown to be responsible for the stronger wake component of the mean velocity profile in external flows, whose increased energy production is the ultimate reason for the stronger fluctuations. Contrary to some previous results by our group, and by others, the streamwise velocity fluctuations are also found to be higher in boundary layers, although the effect is weaker. Within the limitations of the non-parallel nature of the boundary layer, the wall-parallel scales of all the fluctuations are similar in both the flows, suggesting that the scale-selection mechanism resides just below the intermittent region, y/δ = 0.3–0.5. This is also the location of the largest differences in the intensities, although the limited Reynolds number of the boundary-layer simulation (Reθ ≈ 2000) prevents firm conclusions on the scaling of this location. The statistics of the new boundary layer are available from http://torroja.dmt.upm.es/ftp/blayers/.

On the Tendency to Self-Preservation in Axisymmetric Ducted Jets

1964 ◽  
Vol 86 (4) ◽  
pp. 765-771 ◽  
Author(s):  
R. Curtet ◽  
F. P. Ricou
Keyword(s):  
Boundary Layer ◽  
Equations Of Motion ◽  
Form Factors ◽  
Velocity Profiles ◽  
Stream Velocity ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Air Jet ◽  
The Mean ◽  
Secondary Stream

If it is assumed that the mean-velocity profiles of a ducted jet are similar in form sufficiently for downstream of the orifice it is possible, as shown in earlier papers [1, 2, 3], to integrate the equations of motion using the boundary-layer approximation and assuming a constant-energy secondary stream. It is necessary to know when and how this limiting profile is reached, and whether a similar tendency to self-preservation of the components of the velocity fluctuations is observed before the jet reaches the duct-wall boundary layer. Measurements have been made in an axisymmetric ducted air jet of the mean and fluctuating velocities, jet width, secondary-stream velocity, ductwall static pressure, and the boundary layer thickness. Results are compared with values predicted by the approximate jet theory. The authors define form factors calculated from measured profiles of mean velocities, of radial and longitudinal components of the velocity fluctuations, and of the shear stress. The variation of these form factors indicates a definite tendency to similarity for the mean velocity profiles; however, departures from similarity persist for the velocity fluctuations to the limit of measurements, about three duct diameters (40 nozzle diameters).

scholarly journals Effect of wall compliance on peristaltic transport of a Newtonian fluid in an asymmetric channel

2006 ◽  
Vol 2006 ◽  
pp. 1-19 ◽  
Author(s):  
Mohamed H. Haroun
Keyword(s):  
Amplitude Ratio ◽  
Wave Train ◽  
Equations Of Motion ◽  
Peristaltic Transport ◽  
Driving Mechanism ◽  
Mean Flow ◽  
Mean Velocity ◽  
Symmetric Channel ◽  
Reversal Flow ◽  
Wall Compliance

Peristaltic transport of an incompressible viscous fluid in an asymmetric compliant channel is studied. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phases. The fluid-solid interaction problem is investigated by considering equations of motion of both the fluid and the deformable boundaries. The driving mechanism of the muscle is represented by assuming the channel walls to be compliant. The phenomenon of the “mean flow reversal” is discussed. The effect of wave amplitude ratio, width of the channel, phase difference, wall elastance, wall tension, and wall damping on mean-velocity and reversal flow has been investigated. The results reveal that the reversal flow occurs near the boundaries which is not possible in the elastic symmetric channel case.

Sign in / Sign up

Export Citation Format

Share Document