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Unit Reynolds number, Mach number and pressure gradient effects on laminar–turbulent transition in two-dimensional boundary layers

Risius, Steffen and Costantini, Marco and Koch, Stefan and Hein, Stefan and Klein, Christian (2018) Unit Reynolds number, Mach number and pressure gradient effects on laminar–turbulent transition in two-dimensional boundary layers. Experiments in Fluids, 59 (5), pp. 1-29. Springer. doi: 10.1007/s00348-018-2538-8. ISSN 0723-4864.

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Official URL: https://doi.org/10.1007/s00348-018-2538-8


The influence of unit Reynolds number (Re1=17.5E6/m to 80E6/m), Mach number (M=0.35-0.77) and incompressible shape factor (H12=2.50-2.66) on laminar-turbulent boundary layer transition was systematically investigated in the Cryogenic Ludwieg-Tube Göttingen (DNW-KRG). For this investigation the existing two-dimensional wind tunnel model, PaLASTra, which offers a quasi-uniform streamwise pressure gradient, was modified in order to reduce the size of the flow separation region at its trailing edge. The streamwise temperature distribution and the location of laminar-turbulent transition were measured by means of temperature-sensitive paint (TSP) with a higher accuracy than in earlier measurements. It was found that for the modified PaLASTra model the transition Reynolds number (Retr) exhibits a linear dependence on the pressure gradient, characterized by H12. Due to this linear relation it was possible to quantify the so-called ‘unit Reynolds number effect’, which is an increase of Retr with Re1. By a systematic variation of M, Re1 and H12 in combination with a spectral analysis of freestream disturbances, a stabilizing effect of compressibility on boundary layer transition, as predicted by linear stability theory, was detected (‘Mach number effect’). Furthermore, two expressions were derived which can be used to calculate the transition Reynolds number as a function of the amplitude of total pressure fluctuations, Re1 and H12. In order to determine critical N-factors, the measured transition locations were correlated with amplification rates, calculated by incompressible and compressible linear stability theory. By taking into account the spectral level of total pressure fluctuations at the frequency of the most amplified Tollmien-Schlichting wave at transition location, the scatter in the determined critical N-factors was reduced. Furthermore, the receptivity coefficients dependence on incidence angle of acoustic waves was used to correct the determined critical N-factors. Thereby, a found dependency of the determined critical N-factors on H12 decreased, leading to an average critical N-factor of about 9.5 with a standard deviation of 0.8.

Item URL in elib:https://elib.dlr.de/122349/
Document Type:Article
Additional Information:First Online: 07 May 2018; Online ISSN: 1432-1114; Article: 86
Title:Unit Reynolds number, Mach number and pressure gradient effects on laminar–turbulent transition in two-dimensional boundary layers
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Risius, Steffensteffen.risius (at) dlr.dehttps://orcid.org/0000-0002-5530-9609
Costantini, MarcoMarco.Costantini (at) dlr.dehttps://orcid.org/0000-0003-0642-0199
Koch, StefanStefan.Koch (at) dlr.deUNSPECIFIED
Hein, Stefanstefan.hein (at) dlr.deUNSPECIFIED
Klein, Christianchristian.klein (at) dlr.deUNSPECIFIED
Date:May 2018
Journal or Publication Title:Experiments in Fluids
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
DOI :10.1007/s00348-018-2538-8
Page Range:pp. 1-29
Series Name:Springer Berlin Heidelberg
Keywords:boundary layer transition, COCO, compressibility effect, critical N-factor, Cryogenic Ludwieg-Tube Göttingen (DNW-KRG), freestream pressure fluctuations, laminar-turbulent transition, LILO, linear stability analysis, Mach number effect, PaLASTra, receptivity, unit Reynolds number effect, temperature-sensitive paint (TSP), Tollmien-Schlichting, transonic wind tunnel
Institution:Deutsches Zentrum für Luft- und Raumfahrt e.V.
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation and Validation (old)
Location: Göttingen
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > Experimental Methods, GO
Institute for Aerodynamics and Flow Technology > High Speed Configurations, GO
Deposited By: Micknaus, Ilka
Deposited On:05 Dec 2018 11:33
Last Modified:06 Sep 2019 15:25

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