On the identification of cross-flow mode in three-dimensional boundary layers
Parametric zones are obtained where the cross-flow instability can be identified as a mode in the three-dimensional boundary layers with the Mach number ranging from 0 to 10. Although the term cross-flow mode is widely used in the investigations on boundary-layer instability, the previous work [Z. L...
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| Published in | AIP advances Vol. 13; no. 1; pp. 015203 - 015203-19 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Melville
American Institute of Physics
01.01.2023
AIP Publishing LLC |
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| Online Access | Get full text |
| ISSN | 2158-3226 2158-3226 |
| DOI | 10.1063/5.0135008 |
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| Abstract | Parametric zones are obtained where the cross-flow instability can be identified as a mode in the three-dimensional boundary layers with the Mach number ranging from 0 to 10. Although the term cross-flow mode is widely used in the investigations on boundary-layer instability, the previous work [Z. Liu, Phys. Fluids 34, 094110 (2022)] has demonstrated that a cross-flow mode cannot be designated in certain circumstances. The identification of the cross-flow mode is significant not only in the justifiable use of the term but also in judging whether a disturbance is more inclined to a cross-flow type or not. In this work, a criterion is built to identify the cross-flow mode based on the growth-rate peak and disturbance shape. By means of extensive calculations and identifications, parametric zones are presented for the unstable cross-flow mode. It is found that the cross-flow mode cannot be identified at large local sweep or at Mach numbers larger than 1.6. In parametric zones, the cross-flow mode can be distinguished from the Tollmien–Schlichting mode, or identified as the solely dominant mode. Based on the identifications, the maximum growth rates of the cross-flow mode, the Tollmien–Schlichting mode, and the Mack modes in the three-dimensional boundary layers are provided. The dominant mode can be determined at different Mach numbers. The cross-flow mode is revealed to dominate the boundary-layer instability at low Mach numbers. Under large cross-flow strengths, the second mode could not be the dominant mode in the hypersonic boundary layers, which contrasts sharply with the two-dimensional case. |
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| AbstractList | Parametric zones are obtained where the cross-flow instability can be identified as a mode in the three-dimensional boundary layers with the Mach number ranging from 0 to 10. Although the term cross-flow mode is widely used in the investigations on boundary-layer instability, the previous work [Z. Liu, Phys. Fluids 34, 094110 (2022)] has demonstrated that a cross-flow mode cannot be designated in certain circumstances. The identification of the cross-flow mode is significant not only in the justifiable use of the term but also in judging whether a disturbance is more inclined to a cross-flow type or not. In this work, a criterion is built to identify the cross-flow mode based on the growth-rate peak and disturbance shape. By means of extensive calculations and identifications, parametric zones are presented for the unstable cross-flow mode. It is found that the cross-flow mode cannot be identified at large local sweep or at Mach numbers larger than 1.6. In parametric zones, the cross-flow mode can be distinguished from the Tollmien–Schlichting mode, or identified as the solely dominant mode. Based on the identifications, the maximum growth rates of the cross-flow mode, the Tollmien–Schlichting mode, and the Mack modes in the three-dimensional boundary layers are provided. The dominant mode can be determined at different Mach numbers. The cross-flow mode is revealed to dominate the boundary-layer instability at low Mach numbers. Under large cross-flow strengths, the second mode could not be the dominant mode in the hypersonic boundary layers, which contrasts sharply with the two-dimensional case. |
| Author | Liu, Zhiyong |
| Author_xml | – sequence: 1 givenname: Zhiyong orcidid: 0000-0002-1366-2236 surname: Liu fullname: Liu, Zhiyong |
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| Title | On the identification of cross-flow mode in three-dimensional boundary layers |
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