Using similarity analysis, the scales and similarity constraints for a favorable pressure gradient (FPG) turbulent boundary layer with eventual quasilaminarization are obtained. In order to achieve equilibrium in the boundary layer, the pressure parameter must be a constant; thus, a power relation between the boundary layer thickness and the free-stream velocity exists. Consequently, the power is given by the pressure parameter as . Through an analysis using the pressure parameter, two quadrants are found: quadrant I describes FPG turbulent flows and quadrant II corresponds to quasilaminar flows. Moreover, a horizontal line exists for zero pressure gradient flows. Different values of the pressure parameter are found for equilibrium FPG flows, contrary to the findings of Castillo and George [“Similarity analysis for turbulent boundary layer with pressure gradient: Outer flow,” AIAA J. 39, 41 (2001)]. In the case of strong FPG flows with quasilaminarization, the pressure parameter reaches a maximum value of 0.47. At this point, a sudden reduction in the skin friction of about 57% is observed and a redistribution of the Reynolds stresses throughout the boundary layer is achieved. The mean velocity deficit profiles are also found to be attenuated when scaled using the free-stream velocity or . For flows in quadrant II, a reduction in the outer flow of the component of the Reynolds stress is observed, whereas the and components nearly vanish impending quasilaminarization. Due to the presence of the component in the boundary layer, the flow never reaches a full laminar state and a more uniform redistribution of the component is observed as the skin friction decreases due to the imposed FPG. Furthermore, the shape of the profile remains the same until a quasilaminar state is reached, where the profile no longer shows high values of the stress on the proximity to the wall. In addition, the production term is nearly zero for flows in quadrant II. Also, the boundary layer parameters such as the shape factor and the ratio of the displacement thickness to the boundary layer thickness, , increase as the flow achieves a quasilaminar state.
Skip Nav Destination
Article navigation
October 2008
Research Article|
October 31 2008
Similarity analysis of favorable pressure gradient turbulent boundary layers with eventual quasilaminarization
Raúl Bayoán Cal;
Raúl Bayoán Cal
a)
1Department of Mechanical and Materials Engineering,
Portland State University
, Portland, Oregon 97207, USA
and Department of Mechanical Engineering, The Johns Hopkins University
, Baltimore, Maryland 21218, USA
Search for other works by this author on:
Luciano Castillo
Luciano Castillo
2Department of Mechanical, Aeronautical and Nuclear Engineering,
Rensselaer Polytechnic Institute
, Troy, New York 12180, USA
Search for other works by this author on:
a)
Electronic mail: bayoan.cal@jhu.edu.
Physics of Fluids 20, 105106 (2008)
Article history
Received:
March 27 2008
Accepted:
September 03 2008
Citation
Raúl Bayoán Cal, Luciano Castillo; Similarity analysis of favorable pressure gradient turbulent boundary layers with eventual quasilaminarization. Physics of Fluids 1 October 2008; 20 (10): 105106. https://doi.org/10.1063/1.2991433
Download citation file:
Sign in
Don't already have an account? Register
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Pay-Per-View Access
$40.00
Citing articles via
On Oreology, the fracture and flow of “milk's favorite cookie®”
Crystal E. Owens, Max R. Fan (范瑞), et al.
A unified theory for bubble dynamics
A-Man Zhang (张阿漫), 张阿漫, et al.
Fluid–structure interaction on vibrating square prisms considering interference effects
Zengshun Chen (陈增顺), 陈增顺, et al.
Related Content
Analytical and numerical investigations of laminar and turbulent Poiseuille–Ekman flow at different rotation rates
Physics of Fluids (October 2010)
Numerical simulations of spatially developing, accelerating boundary layers
Physics of Fluids (October 2013)
Theoretical prediction of turbulent skin friction on geometrically complex surfaces
Physics of Fluids (October 2009)
A wall-layer model for large-eddy simulations of turbulent flows with/out pressure gradient
Physics of Fluids (January 2011)
Low Reynolds number effects on rotating turbulent Poiseuille flow
Physics of Fluids (August 2010)