Evaluation of transition in flight tests using nonlinear parabolized stability equation analysis

Schrauf, G.; Herbert, Thorwald; Stuckert, Greg

doi:10.2514/3.46980

Cited by 13 publications

(12 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A compressible and incompressible linear stability analysis was carried out and the critical N-factors were determined. It was shown, in agreement with earlier findings (Schrauf 1994(Schrauf , 2000(Schrauf , 2005Schrauf et al 1996Schrauf et al , 1998, that the exclusive incorporation of compressibility into linear stability analysis leads to a larger deviation in the determined critical N-factors as compared to incompressible stability analysis. However, when not only compressibility but also the varying influence of the spectral level of total pressure fluctuations on the initial T-S wave amplitude is incorporated in the N-factor analysis, the correlation of compressible critical N-factors is equally good or even better than in the incompressible case.…”

Section: Resultssupporting

confidence: 90%

“…In general, it should be emphasized that the scatter of the found N-factors is smaller than in most previous investigations conducted at high Reynolds numbers (Schrauf 1994(Schrauf , 2000(Schrauf , 2005Schrauf et al 1996Schrauf et al , 1998.…”

Section: Uncertainties In the Critical N-factor Analysismentioning

confidence: 54%

“…23: the compressible critical N-factors decrease with increasing Mach number, which agrees with findings by Schrauf (2000). At first sight, the observed decrease of compressible critical N-factors with M appears to be contradictory to what one would expect physically: as the compressible N-factor analysis also captures the stabilizing effect of compressibility on the boundary layer, a smaller variation with Mach number would be expected (Arnal and Vermeersch 2011;Schrauf et al 1996). However, it is very likely that the stabilizing effect of compressibility is compensated by a destabilizing effect of increasing flow disturbances with Mach number (Arnal 1989), which may explain the better correlation of the determined incompressible critical N-factors.…”

Section: Mach Number Influence On Compressible and Incompressible Crimentioning

confidence: 81%

“…The e N -method is based on linear stability theory (Schlichting and Gersten 2000) and was first published in 1956 (van Ingen 1956;Smith and Gamberoni 1956). Since then, it has been widely used for transition prediction on aircraft surfaces (Hue et al 2015(Hue et al , 2018Schrauf 1994Schrauf , 2000Schrauf , 2005Schrauf et al 1996Schrauf et al , 1998Streit et al 2011;van Ingen 2008;Voogt 1996). The N-factor method uses growth rates of T-S waves in a laminar boundary layer calculated by linear stability theory and assumes that transition takes place where the most unstable disturbances are amplified by a factor of e N , where N is assumed to be a universal constant.…”

Section: Transition Prediction By the E N -Methods And Correction Of Dmentioning

confidence: 99%

“…The N-factor method is a widely used method for transition prediction on two-dimensional boundary layers (van Ingen 2008). However, large discrepancies have been found in the determined critical N-factors (Schrauf 1994(Schrauf , 2000(Schrauf , 2005Schrauf et al 1996Schrauf et al , 1998. In the first part of this section, the results of compressible and incompressible critical N-factors are compared and the influences of unit Reynolds number, Mach number and shape factor on Re ⋆ tr are discussed (Sects.…”

Section: Calculation and Correction Of The Critical N-factormentioning

confidence: 99%

See 4 more Smart Citations

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

et al. 2018

View full text Add to dashboard Cite

The influence of unit Reynolds number (Re 1 = 17.5 × 10 6-80 × 10 6 m −1), Mach number (M = 0.35-0.77) and incompressible shape factor (H 12 = 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 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 attained in earlier measurements. It was found that for the modified PaLASTra model the transition Reynolds number (Re tr) exhibits a linear dependence on the pressure gradient, characterized by H 12. Due to this linear relation it was possible to quantify the so-called 'unit Reynolds number effect', which is an increase of Re tr with Re 1. By a systematic variation of M, Re 1 and H 12 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, Re 1 and H 12. 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 H 12 decreased, leading to an average critical N-factor of about 9.5 with a standard deviation of ≈ 0.8.

show abstract