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- Title:
Extending the Logarithmic Velocity Profile in Turbulent Channel Flow
- Document type:
- Konferenzbeitrag
- Contribution type:
- Textbeitrag / Aufsatz
- Author(s):
- Youije Xu*, Steffen J. Schmidt, Nikolaus A. Adams
- Abstract:
- The logarithmic law of the mean velocity profile is a key feature of wall-bounded turbulence. For compressible flows, similar profile can be achieved through suitable transformations, such as Van Driest and Trettel & Larsson transformations. Many equilibrium wall models are based on the logarithmic law, and the matching point in these models is typically located in the logarithmic region. However, the limited range of the logarithmic region introduces the risk of misplacing the matching point beyond the logarithmic profile. This motivates us to investigate the methods to artificially extend the logarithmic profile. By revisiting the relation between mixing length and logarithmic law, we demonstrate that the logarithmic velocity profile emerges where the mixing length model for lm overlaps with its true value. Extending this overlap region for lm correspondingly broadens the logarithmic profile. Based on this principle, we propose a revised mixing length model that exhibits a wider overlap region compared to existing models. It is integrated into existing velocity transformations through a new parameter \beta, leading to the revised versions of these transformations: U^+_\{IC,\beta} , U^+_\{VD,\beta} , and U^+_\{TL, \beta} , respectively. The performance of the revised mixing length model and corresponding transformations are validated using Direct Numerical Simulations data for both incompressible and compressible turbulent channel flows across a wide range of Mach and Reynolds numbers. The revised model’s lm closely tracks the true value throughout the outer layer. The logarithmic velocity profiles under the revised transformations extend deep into the channel center, with deviations in the diagnostic function remaining within ±7% of the reference value. Compared to conventional logarithmic and velocity-defect laws, the extended logarithmic profile gives a more consistent description of velocity distribution across the outer layer. Meanwhile, it reduces the risk of misplacing the matching point outside the logarithmic profile in wall models based on the logarithmic law.
- Keywords:
- Logarithmic law, Compressible flows, Velocity transformation, Turbulent boundary layer flow
- Dewey Decimal Classification:
- 620 Ingenieurwissenschaften
- Book / Congress title:
- 2nd European Fluid Dynamics Conference, Dublin, Ireland, 26th - 29th August 2025.
- Congress city:
- Dublin, Ireland
- Date of congress:
- 26th - 29th August 2025
- Year:
- 2025
- Language:
- en
- WWW:
- https://www.efdc2.com/
- Notes:
- Acknowledgement: The first author gratefully acknowledges financial support from the China Scholarship Council (No.202006320042).
- TUM Institution:
- Lehrstuhl für Aerodynamik und Strömungsmechanik
BibTeX
Occurrences:
- mediaTUM GesamtbestandHochschulbibliographie2025SchoolsTUM School of Engineering and DesignLehrstuhl für Aerodynamik und Strömungsmechanik (Prof. Adams)