Predicting Boundary-Layer Transition over Backward-Facing Steps via Linear Stability Analysis

Hildebrand, Nathaniel; Choudhari, Meelan M.; Paredes, Pedro

doi:10.2514/1.j059713

Cited by 21 publications

(30 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The forward movement of transition for moderate step heights is linked to a destabilization effect on the TS waves in the neighbourhood of the step (Klebanoff & Tidstrom, 1972). This enhanced growth has been investigated numerically for different flow conditions (see for example Edelmann & Rist, 2015;Hildebrand, Choudhari, & Paredes, 2020;Nayfeh, 1992;Perraud & Séraudie, 2000). The calculated change in the linear growth factor n(x) at some downstream position (where transition is observed or assumed to occur) can be correlated to the transition movement.…”

Section: Introductionmentioning

confidence: 99%

Characterizing surface-gap effects on boundary-layer transition dominated by Tollmien–Schlichting instability

Crouch

Kosorygin

Sutanto

et al. 2022

Flow

View full text Add to dashboard Cite

Effects of gaps (rectangular surface cavities) on boundary-layer transition are investigated using a combination of linear stability theory and experiments, for boundary layers where the smooth-surface transition results from Tollmien–Schlichting (TS) instability. Results are presented for a wide range of gap characteristics, with the associated transition locations ranging from the smooth-surface location all the way forward to the gap location. The transition movement is well described by a variable $N$ -factor, which links the gap characteristics to the level of instability amplification $e^N$ leading to transition. The gap effects on TS-wave transition are characterized by two limiting behaviours. For shallow gaps $d/w < 0.017$ , the reduction in $N$ -factor is a function of the gap depth $d$ and is independent of the gap width $w$ . For deep gaps $d/w > 0.028$ , the reduction in $N$ -factor is a function of the gap width and is independent of the gap depth. When both the gap width and depth are sufficiently large relative to the displacement thickness $\delta ^*$ , the TS-wave transition is bypassed, resulting in transition at the gap location. These behaviours are mapped out in terms of ( $w/ \delta ^*$ , $d/ \delta ^*$ ), providing a predictive model for gap effects on transition.

show abstract

Section: Introductionmentioning

confidence: 99%

Characterizing surface-gap effects on boundary-layer transition dominated by Tollmien–Schlichting instability

Crouch

Kosorygin

Sutanto

et al. 2022

Flow

View full text Add to dashboard Cite

show abstract

“…More recent work by Hildebrand et al. (2020) resulted in better agreement with experimental results across a broad range of parameters by computing the -factor envelope for the basic state distorted by the BFS.…”

Section: Introductionmentioning

confidence: 77%

“…2013; Hu, Hickel & Van Oudheusden 2020), though typically these studies were performed for relatively large BFS heights (). It is also well known that a BFS can cause the destabilization of already-existent boundary-layer instabilities, in particular, Tollmien–Schlichting (TS) waves (Wang & Gaster 2005; Crouch, Kosorygin & Ng 2006; Hildebrand, Choudhari & Paredes 2020). In fact, this forms the basis for a semi-empirical transition prediction method known as the method (Wörner, Rist & Wagner 2002; Crouch et al.…”

Section: Introductionmentioning

confidence: 99%

Mechanisms of instability growth, interaction and breakdown induced by a backward-facing step in a swept-wing flow

Eppink

2021

J. Fluid Mech.

View full text Add to dashboard Cite

Time-resolved particle image velocimetry measurements were performed downstream of a swept backward-facing step. The measurements allow detailed analysis of the interactions between the unsteady instabilities and the stationary crossflow vortices. Different mechanisms are identified that lead to the modulation of the different families of unsteady instabilities that occur downstream of the step. For the low-frequency spanwise-travelling mode, the modulation occurs due to a redistribution of momentum when the instability encounters regions of large spanwise shear of the wall-normal and streamwise velocity. However, the higher-frequency streamwise-travelling instabilities undergo the familiar ‘lift-up’ mechanism when they encounter the regions of large vertical velocity due to the presence of the stationary crossflow vortices. The process leading to large velocity spikes, and ultimately to a laminar breakdown to turbulence, is identified as a constructive interaction between the different unsteady instabilities, coupled with an interaction with the stationary crossflow vortices when the phases align properly.

show abstract

“…11 shows the development of the displacement thickness δ * and the momentum loss thickness θ for the laminar boundary layer for one given flow case as an example, which is an immediate result of the boundary layer solution from COCO. The data is shown here for the sake of completeness, since the ∆N -models from Crouch et al (2006), Perraud et al (2014) and Hildebrand et al (2020) are based on the relation of the step height h to the local boundary layer thicknesses, either δ * or θ. Also shown is the resulting shape factor H k .…”

Section: Stability Analysis and Validationmentioning

confidence: 99%

“…The ∆N -values from Wie and Malik (1998) differ especially for small h/δ * , since they are not linear in this region. Finally, the correlations from Hildebrand et al (2020) are designed to give a better fit, while still including the data from Crouch et al (2006). Their version is:…”

Section: Introductionmentioning

confidence: 99%

Measurements on the Effect of Steps on the Transition of Laminar Boundary Layers

Heintz

Scholz

2022

Preprint

View full text Add to dashboard Cite

The effects of steps on the transition of laminar boundary layers were measured on a flat plate for low Reynolds numbers with critical and subcritical step heights. The transition position was measured by determining the intermittency distribution in streamwise direction, including the characteristic length of the transitional region. The results are compared with formulations of a critical step Reynolds number Reh, i.e. the step height that will instantly trigger transition at the step position, and--for subcritical step heights--with δN-formulations from literature. For backward facing steps the concept of a step Reynolds number can be used to distinguish between subcritical and critical step heights, whereas for forward facing steps there seems not to be one unique Reh. Furthermore, for subcritical backward facing steps the concept of a δN-approximation gives a reasonable description of the experimental observations. Again in contrast, for forward facing steps a δN-approach scattered a lot and no clear dependency was found between the reduction of the critical N-Factor of transition and the relative step height.

show abstract

Predicting Boundary-Layer Transition over Backward-Facing Steps via Linear Stability Analysis

Cited by 21 publications

References 27 publications

Characterizing surface-gap effects on boundary-layer transition dominated by Tollmien–Schlichting instability

Characterizing surface-gap effects on boundary-layer transition dominated by Tollmien–Schlichting instability

Mechanisms of instability growth, interaction and breakdown induced by a backward-facing step in a swept-wing flow

Measurements on the Effect of Steps on the Transition of Laminar Boundary Layers

Contact Info

Product

Resources

About