Direct Numerical Simulation of Transonic Wake Propagation in the Presence of an Adverse Pressure Gradient and Streamline Curvature

2011 ◽  
Author(s):  
Jeffrey Gibson ◽  
Steven Gorrell
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Streamline Curvature

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.

scholarly journals Direct numerical simulation of a separated turbulent boundary layer

2002 ◽  
Vol 471 ◽  
pp. 107-136 ◽  
Author(s):  
MARTIN SKOTE ◽  
DAN S. HENNINGSON
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Scaling Laws ◽  
Separation Bubble ◽  
Turbulence Models ◽  
Adverse Pressure Gradient ◽  
Theoretical Work

Direct numerical simulation of two turbulent boundary layer flows has been performed. The boundary layers are both subject to a strong adverse pressure gradient. In one case a separation bubble is created while in the other the boundary layer is everywhere attached. The data from the simulations are used to investigate scaling laws near the wall, a crucial concept in turbulence models. Theoretical work concerning the inner region in a boundary layer under an adverse pressure gradient is reviewed and extended to the case of separation. Excellent agreement between theory and data from the direct numerical simulation is found in the viscous sub-layer, while a qualitative agreement is obtained for the overlap region.

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