Sensitivity of Second-Mode Linear Stability to Constitutive Models within Hypersonic Flow

Lyttle, Ian; Reed, Helen L.

doi:10.2514/6.2005-889

Cited by 17 publications

(10 citation statements)

References 15 publications

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“…Ref. 15 shows that the transport models of Stuckert and Blottner, predict approximately 10% and 25% difference in the magnitude of viscosity and thermal conductivity, respectively, at the peak boundary layer temperature of 2100 K. This difference results in an 8% variation in the peak growth rate prediction of the second mode instability. Similar results are reported for the M = 10 flat plate boundary layer in Ref.…”

Section: Introductionmentioning

confidence: 95%

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Linear stability of high-speed boundary layer flows at varying Prandtl numbers

Ramachandran

Saikia

Sinha

et al. 2015

45th AIAA Thermophysics Conference

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Accurate prediction of laminar to turbulent transition at hypersonic velocities is a challenging task. The high temperature and low pressure encountered in such applications can lead to large variations in physical and transport properties of the gas. This can result in significant changes in the effective Prandtl number. In this paper, we study the physical effects of Prandtl number on the stability of high Mach number boundary layer flows. Prandtl number values in the range of 0.3 to 1.2 are chosen and a temporal linear stability problem is formulated. The resulting eigenvalue problem is solved using Chebyshev spectral collocation method.We study the effect of Prandtl number on the eigenspectrum for a range of Mach number, Reynolds number and disturbance wave number. It is found that certain combinations of these parameters lead to synchronization between the fast and the slow modes, which can contribute to the peak growth rate. Two types of branching patterns are observed depending on the Prandtl number, where either the fast or the slow mode can be destabilized due to mode-synchronization. The stability diagrams plotted for a range of Reynolds number and wavenumber show a destabilizing role for increasing the Prandtl number, leading to larger regions of instability, and increased growth rates. This also leads to a significant reduction in the critical Reynolds number specifically at intermediate Mach numbers. High-speed flat plate boundary layer flow is thus found to be highly sensitive to slight changes in the Prandtl number.

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Section: Introductionmentioning

confidence: 95%

“…al. 15 consider a spherically blunted right circular cone at a Mach number of 13.5. The sensitivity of the second mode growth rate to the variation of constitutive models for reaction rate, specific heat and transport properties are studied.…”

Section: Introductionmentioning

confidence: 99%

Linear stability of high-speed boundary layer flows at varying Prandtl numbers

Ramachandran

Saikia

Sinha

et al. 2015

45th AIAA Thermophysics Conference

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“…The aforementioned investigations featured a wide variety of thermophysical models, because the mathematical description of high-temperature gas properties has remained a very active field of research over the past century; see the work of Chapman & Cowling (1939), Hirschfelder, Curtiss & Bird (1954, Blottner, Johnson & Ellis (1971), Gupta et al (1990), Fertig, Dohr & Frühauf (2001), McBride, Zehe & Gordon (2002, Magin & Degrez (2004), Scoggins (2017) or Clarey & Greendyke (2019). This motivated the investigations on the sensitivity of LST predictions to the thermophysical modelling by Lyttle & Reed (2005), Franko, MacCormack & Lele (2010) and, most thoroughly, by Miró Miró et al (2019a. The latter reported that second-mode instabilities were mostly affected by modelling inaccuracies that translated into a misestimation of the BL height.…”

Section: Introductionmentioning

confidence: 99%

Decoupling ablation effects on boundary-layer stability and transition

Miró

Pinna

2020

J. Fluid Mech.

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“…In addition, boundary conditions imposed on the vehicle surface, such as, cold/adiabatic, smooth/rough, catalytic/non-catalytic can delay or augment the transition process. The variation in thermodynamic and transport properties of the gas can also have a major influence on flow stability [6]- [7]. In the context of drag reduction, the role of transport property variation, mainly that of viscosity stratification, has been studied widely for incompressible as well as non-Newtonian flows and is well documented in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Stability studies of high-speed flows have reported that transport property effects can dominate over other thermodynamic and chemical reaction rate variations. Lyttle and Reed [7] consider a spherically blunted right circular cone at a Mach number of 13.5, and investigate the sensitivity of two different transport models (Stuckert and Blottner) on the second mode growth rate. They find that the peak growth rate of the second mode changes by around 8%, due to a 10% and 25% change in the viscosity and thermal conductivity values respectively.…”

Section: Introductionmentioning

confidence: 99%

Effects of viscosity and conductivity stratification on the linear stability and transient growth within compressible Couette flow

et al. 2017

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Accurate prediction of laminar to turbulent transition in compressible flows is a challenging task, as it can be affected by a combination of factors. Compressibility causes large variations in thermodynamic as well as transport properties of a gas, which in turn are known to affect flow stability. We study the stratification of individual transport properties, and their combined behavior. We also examine the effect of change in the magnitude of viscosity and conductivity on flow stability. The Couette flow of a perfect gas is our model problem and both modal and nonmodal analyses are carried out. We notice a large destabilizing role of increase in the conductivity value and a dramatic stabilizing effect of mean viscosity stratification, over a range of free-stream Mach number, Reynolds number, Prandtl number and disturbance wavenumber. In the combined case, the viscosity stratification plays a dominant role. We find this to be the case for finite-time transient growth in the parameter regime below linear instability as well as asymptotically at large time. A budget of the transient growth energy amplification is also shown to identify the effects of transport properties on the constituents of perturbation energy. The extensive results presented in this paper, we believe should motivate those studying more realistic flows to examine how these contrasting effects of stratification come together.

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Sensitivity of Second-Mode Linear Stability to Constitutive Models within Hypersonic Flow

Cited by 17 publications

References 15 publications

Linear stability of high-speed boundary layer flows at varying Prandtl numbers

Linear stability of high-speed boundary layer flows at varying Prandtl numbers

Decoupling ablation effects on boundary-layer stability and transition

Effects of viscosity and conductivity stratification on the linear stability and transient growth within compressible Couette flow

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