Instability of streaks in wall turbulence with adverse pressure gradient

2011 ◽  
Vol 681 ◽  
pp. 205-240 ◽  
Author(s):  
MATTHIEU MARQUILLIE ◽  
UWE EHRENSTEIN ◽  
JEAN-PHILIPPE LAVAL
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Gradient Flow ◽  
Adverse Pressure Gradient ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Instability Modes ◽  
Weak Pressure Gradient

A direct numerical simulation of a turbulent channel flow with a lower curved wall is performed at Reynolds number Reτ ≈ 600. Low-speed streak structures are extracted from the turbulent flow field using methods known as skeletonization in image processing. Individual streaks in the wall-normal plane averaged in time and superimposed to the mean streamwise velocity profile are used as basic states for a linear stability analysis. Instability modes are computed at positions along the lower and upper wall and the instability onset is shown to coincide with the strong production peaks of turbulent kinetic energy near the maximum of pressure gradient on both the curved and the flat walls. The instability modes are spanwise-symmetric (varicose) for the adverse pressure gradient streak base flows with wall-normal inflection points, when the total average of the detected streaks is considered. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation. Conditional averages of streaks have also been computed and the distance of the streak's centre from the wall is shown to be an essential parameter. For the upper-wall weak pressure gradient flow, spanwise-antisymmetric (sinuous) instability modes become unstable when sets of highest streaks are considered, whereas varicose modes dominate for the streaks closest to the wall.

scholarly journals Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation

2017 ◽  
Vol 829 ◽  
pp. 392-419 ◽  
Author(s):  
V. Kitsios ◽  
A. Sekimoto ◽  
C. Atkinson ◽  
J. A. Sillero ◽  
G. Borrell ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Streamwise Velocity ◽  
Far Field ◽  
Self Similar ◽  
The Mean

The statistical properties are presented for the direct numerical simulation of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation. The APG TBL has a momentum thickness-based Reynolds number range from $Re_{\unicode[STIX]{x1D6FF}_{2}}=570$ to 13 800, with a self-similar region from $Re_{\unicode[STIX]{x1D6FF}_{2}}=10\,000$ to 12 300. Within this domain the average non-dimensional pressure gradient parameter $\unicode[STIX]{x1D6FD}=39$, where for a unit density $\unicode[STIX]{x1D6FD}=\unicode[STIX]{x1D6FF}_{1}P_{\!e}^{\prime }/\unicode[STIX]{x1D70F}_{w}$, with $\unicode[STIX]{x1D6FF}_{1}$ the displacement thickness, $\unicode[STIX]{x1D70F}_{w}$ the mean shear stress at the wall and $P_{\!e}^{\prime }$ the far-field pressure gradient. This flow is compared with previous zero pressure gradient and mild APG TBL ($\unicode[STIX]{x1D6FD}=1$) results of similar Reynolds number. All flows are generated via the direct numerical simulation of a TBL on a flat surface with far-field boundary conditions tailored to apply the desired pressure gradient. The conditions for self-similarity, and the appropriate length and velocity scales, are derived. The mean and Reynolds stress profiles are shown to collapse when non-dimensionalised on the basis of these length and velocity scales. As the pressure gradient increases, the extent of the wake region in the mean streamwise velocity profiles increases, whilst the extent of the log-layer and viscous sublayer decreases. The Reynolds stress, production and dissipation profiles of the APG TBL cases exhibit a second outer peak, which becomes more pronounced and more spatially localised with increasing pressure gradient. This outer peak is located at the point of inflection of the mean velocity profiles, and is suggestive of the presence of a shear flow instability. The maximum streamwise velocity variance is located at a wall normal position of $\unicode[STIX]{x1D6FF}_{1}$ of spanwise wavelength of $2\unicode[STIX]{x1D6FF}_{1}$. In summary as the pressure gradient increases the flow has properties less like a zero pressure gradient TBL and more akin to a free shear layer.

Direct numerical simulation of turbulent channel flow up to

2015 ◽  
Vol 774 ◽  
pp. 395-415 ◽  
Author(s):  
Myoungkyu Lee ◽  
Robert D. Moser
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Mean Velocity ◽  
Layer Structures ◽  
High Reynolds

A direct numerical simulation of incompressible channel flow at a friction Reynolds number ($\mathit{Re}_{{\it\tau}}$) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant ${\it\kappa}=0.384\pm 0.004$. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in wavenumber $(k)$. Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.

Direct Numerical Simulation of Passive Scalar Field in a Turbulent Channel Flow

1992 ◽  
Vol 114 (3) ◽  
pp. 598-606 ◽  
Author(s):  
N. Kasagi ◽  
Y. Tomita ◽  
A. Kuroda
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Streamwise Velocity ◽  
Heat Fluxes ◽  
Wall Region ◽  
Turbulent Heat ◽  
Turbulent Heat Fluxes

A direct numerical simulation (DNS) of the fully developed thermal field in a two-dimensional turbulent channel flow of air was carried out. The isoflux condition was imposed on the two walls so that the local mean temperature increased linearly in the streamwise direction. With any buoyancy effect neglected, temperature was considered as a passive scalar. The computation was executed on 1,589,248 grid points by using a spectral method. The statistics obtained were root-mean-square temperature fluctuations, turbulent heat fluxes, turbulent Prandtl number, and dissipation time scales. They agreed fairly well with existing experimental and numerical simulation data. Each term in the budget equations of temperature variance, its dissipation rate, and turbulent heat fluxes was also calculated. It was found that the temperature fluctuation θ′ was closely correlated with the streamwise velocity fluctuation u′, particularly in the near-wall region. Hence, the distribution of budget terms for the streamwise and wall-normal heat fluxes, u′θ′ and v′θ′, were very similar to those for the two Reynolds stress components, u′u′ and u′v′.

Large-Eddy Simulation of Film Cooling in an Adverse Pressure Gradient Flow

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Martin Konopka ◽  
Wilhelm Jessen ◽  
Matthias Meinke ◽  
Wolfgang Schröder
Keyword(s):  
Pressure Gradient ◽  
Film Cooling ◽  
Gradient Flow ◽  
Adverse Pressure Gradient ◽  
Streamwise Velocity ◽  
Co2 Injection ◽  
Pressure Gradients ◽  
Cooling Effectiveness ◽  
Turbulent Schmidt Number ◽  
Large Eddy

In order to analyze the interaction of multiple rows of film cooling holes in flows at adverse pressure gradients, large-eddy simulations (LESs) are performed. The considered three-row cooling configuration consists of inclined cooling holes at an angle of 30 deg with a lateral pitch of p/D=3 and a streamwise spacing of l/D=6. The cooling holes possess a fan-shaped exit geometry with lateral and streamwise expansions. For each cooling row the complete internal flow is computed. Air and CO2 are injected in order to investigate the influence of an increased density ratio on the film cooling physics at adverse pressure gradients. The CO2 injected at the same blowing rate as air shows a higher magnitude of the Reynolds shear stress component and, thus, an enhanced mixing downstream of the cooling holes. The LES results of the air and CO2 configurations are compared to the corresponding particle-image velocimetry (PIV) measurements and show a convincing agreement in terms of the averaged streamwise velocity and streamwise velocity fluctuations. Furthermore, the cooling effectiveness is investigated for a zero and an adverse pressure gradient configuration with a temperature ratio at gas turbine conditions. For the adverse pressure gradient case, reduced temperature levels off the wall are observed. However, the cooling effectiveness shows only minor differences compared to the zero pressure gradient flow. The turbulent Schmidt number at CO2 injection shows large variations. Just downstream of the injection it attains low values, whereas high values are detected in the upper mixing zone of the cooling flow and the freestream at each film cooling row.

Large-Eddy Simulation of Film Cooling in an Adverse Pressure Gradient Flow

2012 ◽  
Author(s):  
Martin Konopka ◽  
Wilhelm Jessen ◽  
Matthias Meinke ◽  
Wolfgang Schröder
Keyword(s):  
Pressure Gradient ◽  
Film Cooling ◽  
Gradient Flow ◽  
Adverse Pressure Gradient ◽  
Streamwise Velocity ◽  
Co2 Injection ◽  
Pressure Gradients ◽  
Cooling Effectiveness ◽  
Turbulent Schmidt Number ◽  
Large Eddy

To analyze the interaction of multiple rows of film cooling holes in flows at adverse pressure gradients large-eddy simulations (LES) are performed. The considered three-row cooling configuration consists of inclined cooling holes at an angle of 30° with a lateral pitch p/D = 3 and a streamwise spacing l/D = 6. The cooling holes possess a fan-shaped exit geometry with lateral and streamwise expansions. For each cooling row the complete internal flow was computed. Air and CO2 are injected to investigate the influence of an increased density ratio on the film cooling physics at adverse pressure gradients. CO2 injected at the same blowing rate as air shows a higher magnitude of the Reynolds shear stress component and thus an enhanced mixing downstream of the cooling holes. The LES results of the air and CO2 configurations are compared to the corresponding particle-image velocimetry (PIV) measurements and show a convincing agreement in terms of averaged streamwise velocity and streamwise velocity fluctuations. Furthermore the cooling effectiveness is investigated for a zero and an adverse pressure gradient configuration with a temperature ratio at gas turbine conditions. For the adverse pressure gradient case reduced temperature levels off the wall are observed. However, the cooling effectiveness shows only minor differences compared to the zero pressure gradient flow. The turbulent Schmidt number at CO2 injection shows large variations. Just downstream of the injection it attains low values, whereas high values are detected in the upper mixing zone of the cooling flow and the freestream at each film cooling row.

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