Investigation of hypersonic boundary layer stability �for a flat plate with sharp and blunt leading edge��4th SU2 Conference, Varenna/Italy: 23 – 25 October 2023
Urvi Sanjiv Mehta and Jayahar Sivasubramanian
Ramaiah University of Applied Sciences, Bengaluru, India
Outline
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Introduction
Boundary Layer is the characteristic property of Viscous flow and the type of boundary layer observed- Laminar or Turbulent depends mainly on the Reynolds' number. Due to the variation of Reynolds’ number along the length of the boundary layer, transition from laminar to turbulence is observed.
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Figure 1: Receptivity Analysis
Linear Stability Theory
Linear Stability Theory
Principles:
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Linear Stability Theory
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The instability region increases as the Reynolds number decreases or as viscosity increases. The analysis of stability of hypersonic boundary layers is challenging due to it being characterized with many types of instability;
The second mode instability is the most amplified in hypersonic BLs and it is recognized to be the dominant mode which induces transition in hypersonic BL. This project’s focus revolves around capturing the dominant second mode as the first mode is least amplified or absent in 2D boundary layers.
Figure 2: Instability
Factors Affecting Transition
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Objective
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Methods and Methodology
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SU2: Solver Setup and Flow Conditions:
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The base flow laminar simulations are carried out in Stanford University Unstructured SU2.
Mesh: Sharp Leading Edge and Boundary Conditions
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Figure 3: Generated Mesh
Figure 4: Colour Coded Boundary Condition
Mesh: Blunt Leading Edge
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Figure 5: Generated Mesh
Figure 6: Magnified
Generated Mesh
Boundary Conditions
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Figure 7: Colour Coded Boundary Condition
Contours: Mach Number
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Figure 9: Blunt Leading edge
(6e-5 m)
Figure 10: Blunt Leading edge
(1e-3 m)
Figure 8: Sharp Leading edge
Contours: Density
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Figure 11: Sharp Leading edge
Figure 12: Blunt Leading edge
(6e-5 m)
Figure 13: Blunt Leading edge
(1e-3 m)
Contours: Temperature
Figure 16: Blunt Leading edge
(1e-3 m)
Figure 15: Blunt Leading edge
(6e-5 m)
Figure 14: Sharp Leading edge
Velocity Profiles:
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Figure 17: Validation of velocity profiles at x=0.1 m
Figure 18: Validation of velocity profiles at x=0.3 m
Temperature Profiles:
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Figure 19: Validation of temperature profiles at x=0.1 m
Figure 20: Validation of temperature profiles at x=0.3 m
Velocity Profiles: Effect of leading edge radius
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The boundary layer profile is extracted at point 0.1 m from the leading edge.
Figure 21: y vs U/Ue
Figure 22: Magnified y vs U/Ue
Temperature Profiles: Effect of leading edge radius
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The boundary layer profile is extracted at point 0.1 m from the leading edge.
Figure 24: Magnified y vs T/Te
Figure 23: y vs T/Te
Velocity Profiles: Effect of leading edge radius
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The boundary layer profile is extracted at point 0.3 m from the leading edge.
Figure 25: y vs U/Ue
Figure 26: Magnified y vs U/Ue
Temperature Profiles: Effect of leading edge radius
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The boundary layer profile is extracted at point 0.3 m from the leading edge.
Figure 28: Magnified y vs T/Te
Figure 27: y vs T/Te
Velocity Profiles: Sharp and Blunt leading edge
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The boundary layer profile is extracted from the leading edge.
Figure 29: y vs U/Ue at 0.1 m
Figure 30: Magnified y vs U/Ue at 0.3 m
Velocity Profiles: Sharp and Blunt leading edge
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The boundary layer profile is extracted from the leading edge.
Figure 31: y vs U/Ue at 0.1 m
Figure 32: Magnified y vs U/Ue at 0.3 m
Eigen Value Spectrum:
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The velocity profiles extracted are fed into the Python code, and the input files for LST are obtained. The output of the LST solver is the Eigen value spectrum of the complex streamwise wavenumber. The spectrum represents the values of the streamwise wavenumber of all the possible disturbances or perturbations in the boundary layer. The spectrum is comprised of continuous and discrete spectra. The discrete spectra are the cause of instability in the BL. It is also unnecessary that all discrete spectra will cause instability in BL. If the complex component of the wavenumber of the discrete spectra is negative, such waves are called amplified waves, which induce instability in the BL.
Eigen Value Spectrum: Sharp Leading Edge
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Figure 33: Spectra with no unstable discrete mode CASE A
Figure 34: Spectra with second mode unstable discrete mode CASE B
Eigen Value Spectrum: Blunt Leading Edge
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Figure 35: Spectra with no unstable discrete mode
Figure 36: Spectra with an unstable discrete mode
Future Work
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Conclusions
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References
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THANK YOU!
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Urvi Mehta
urvimehta1504@gmail.com