# Non-Adiabatic Surface Effects on Step-Induced Boundary-Layer Transition

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## Abstract

The effect on step-induced boundary-layer transition of surface temperatures different from the adiabatic-wall temperature was investigated for a (quasi-) two-dimensional flow at large Reynolds numbers and at both low and high subsonic Mach numbers. Sharp forward-facing steps were mounted on a flat plate and transition was studied non-intrusively by means of the temperature-sensitive paint technique. The experiments were conducted in the Cryogenic Ludwieg-Tube Göttingen with various streamwise pressure gradients and temperature differences between flow and model surface. A reduction of the ratio between surface and adiabatic-wall temperatures had a favorable influence on step-induced transition up to moderate values of the step Reynolds number and of the step height relative to the boundary-layer displacement thickness, leading to larger transition Reynolds numbers. However, at larger values of the non-dimensional step parameters, the increase in transition Reynolds number for a given reduction in the wall temperature ratio became smaller. Transition was found to be insensitive to changes in the wall temperature ratio for step Reynolds numbers above a certain value. Up to this limiting value, the relation between the relative change in transition location (with respect to its value for a smooth surface) and the non-dimensional step parameter was essentially unaffected by variations in the wall temperature ratio. The present choice of non-dimensional parameters allows the effect of the steps on transition to be isolated from the influence of variations in the other factors, provided that both transition locations on the step and smooth configurations are measured at the same conditions.

## Keywords

Transition Step Non-adiabatic surface Temperature-sensitive paint Boundary layer Surface imperfection Natural laminar flow TSP## Notes

### Acknowledgments

The authors would like to thank: S. Hein (DLR) for the support during the definition of the tests and the analysis of the results, and for the modification of COCO to account for the thermal boundary condition at the model surface; W. H. Beck (DLR) for the productive discussion of the results and for the help during the drafting of this work; S. Koch (DLR) for the assistance during the experimental campaign and the wind tunnel data evaluation; C. Fuchs and T. Kleindienst (DLR) for the support during the preparation of the model; U. Henne and W. E. Sachs (DLR) for the help in the TSP data analysis; V. Ondrus (University of Hohenheim) for the chemical development of the temperature-sensitive paint; R. Kahle, M. Aschoff and S. Hucke (DNW-KRG) for the support during the whole test campaign; L. Koop and H. Rosemann (DLR) for the constant advice during the definition and conduction of this project; W. Schröder (RWTH Aachen), A. Dillmann (DLR), W. Kühn and S. Schaber (Airbus) for their invaluable advice.

### Compliance with Ethical Standards

### **Conflict of interests**

The authors declare that they have no conflict of interest.

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