Accurate but economical modeling of supersonic turbulent boundary layers is a standing challenge due to the intricate entanglement of temperature, density, and velocity fluctuations on top of the mean-field variation. Application of the van Driest transformation may describe well the mean state but cannot provide detailed flow information. This lack-in modeling coarse and fine-scale variability is addressed by the present study using a stochastic one-dimensional turbulence (ODT) model. ODT is a simulation methodology that represents the evolution of turbulent flow in a low-dimensional stochastic way. In this study, ODT is extended to fully compressible flows. An Eulerian framework and a conservative form of the governing equations serve as the basis of the compressible ODT model. Computational methods for statistical properties based on ODT realizations are also extended to compressible flows, and a comprehensive way of turbulent kinetic energy budget calculation based on compressible ODT is put forward for the first time. Two canonical direct numerical simulation cases of supersonic isothermal-wall channel flow at Mach numbers 1.5 and 3.0 with bulk Reynolds numbers 3000 and 4880, respectively, are used to validate the extended model. A rigorous numerical validation is presented, including the first-order mean statistics, the second-order root mean square statistics, and higher-order turbulent fluctuation statistics. In ODT results, both mean and root mean square profiles are accurately captured in the near-wall region. Near-wall temperature spectra reveal that temperature fluctuations are amplified at all turbulent scales as the effects of compressibility increase. This phenomenon is caused by intensified viscous heating at a higher Mach number, which is indicated by the steeper profiles of viscous turbulent kinetic energy budget terms in the very near-wall region. The low computational cost and predictive capabilities of ODT suggest that it is a promising approach for detailed modeling of highly turbulent compressible boundary layers. Furthermore, it is found that the ODT model requires a Mach-number-dependent increase in a viscous penalty parameter Z in wall-bounded turbulent flows to enable accurate capture of the buffer layer.
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March 2023
Research Article|
March 08 2023
One-dimensional turbulence modeling of compressible flows. I. Conservative Eulerian formulation and application to supersonic channel flow
Tianyun Gao (高天运)
;
Tianyun Gao (高天运)
(Conceptualization, Formal analysis, Investigation, Methodology, Validation, Writing – original draft)
1
Science and Technology on Scramjet Laboratory, National University of Defense Technology
, Changsha 410073, China
2
International Studies College, National University of Defense Technology
, Nanjing 210039, China
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Heiko Schmidt
;
Heiko Schmidt
(Conceptualization, Methodology, Supervision, Writing – review & editing)
3
Brandenburg Technical University Cottbus-Senftenberg
, Siemens-Halske-Ring 14, Cottbus 03046, Germany
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Marten Klein
;
Marten Klein
(Conceptualization, Methodology, Validation, Writing – review & editing)
3
Brandenburg Technical University Cottbus-Senftenberg
, Siemens-Halske-Ring 14, Cottbus 03046, Germany
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Jianhan Liang (梁剑寒)
;
Jianhan Liang (梁剑寒)
a)
(Conceptualization, Funding acquisition, Methodology, Supervision, Writing – review & editing)
1
Science and Technology on Scramjet Laboratory, National University of Defense Technology
, Changsha 410073, China
a)Authors to whom correspondence should be addressed: [email protected], [email protected], and [email protected]
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Mingbo Sun (孙明波)
;
Mingbo Sun (孙明波)
a)
(Funding acquisition, Methodology, Supervision)
1
Science and Technology on Scramjet Laboratory, National University of Defense Technology
, Changsha 410073, China
a)Authors to whom correspondence should be addressed: [email protected], [email protected], and [email protected]
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Chongpei Chen (陈崇沛)
;
Chongpei Chen (陈崇沛)
a)
(Investigation, Validation, Writing – review & editing)
1
Science and Technology on Scramjet Laboratory, National University of Defense Technology
, Changsha 410073, China
a)Authors to whom correspondence should be addressed: [email protected], [email protected], and [email protected]
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Qingdi Guan (关清帝)
Qingdi Guan (关清帝)
(Data curation, Validation)
1
Science and Technology on Scramjet Laboratory, National University of Defense Technology
, Changsha 410073, China
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Heiko Schmidt
3
Marten Klein
3
Qingdi Guan (关清帝)
1
1
Science and Technology on Scramjet Laboratory, National University of Defense Technology
, Changsha 410073, China
2
International Studies College, National University of Defense Technology
, Nanjing 210039, China
3
Brandenburg Technical University Cottbus-Senftenberg
, Siemens-Halske-Ring 14, Cottbus 03046, Germany
a)Authors to whom correspondence should be addressed: [email protected], [email protected], and [email protected]
Physics of Fluids 35, 035115 (2023)
Article history
Received:
September 12 2022
Accepted:
November 01 2022
Citation
Tianyun Gao, Heiko Schmidt, Marten Klein, Jianhan Liang, Mingbo Sun, Chongpei Chen, Qingdi Guan; One-dimensional turbulence modeling of compressible flows. I. Conservative Eulerian formulation and application to supersonic channel flow. Physics of Fluids 1 March 2023; 35 (3): 035115. https://doi.org/10.1063/5.0125514
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