Spatial direct numerical simulation of boundary-layer transition mechanisms: Validation of PSE theory

Joslin, Ronald D.; Streett, Craig L.; Chang, Chau‐Lyan

doi:10.1007/bf00418777

Cited by 168 publications

(66 citation statements)

References 40 publications

(39 reference statements)

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“…The results by the NavierStokes solver and by the parabolic stability equation solver agree remarkably well. This corresponds to the good agreement between the Navier-Stokes solver and the parabolic stability equation solver reported for the Blasius boundary layer mentioned above Bertolotti et al (1992); Joslin et al (1993). The results by the Orr-Sommerfeld solver on the other hand display an earlier growth of the Tollmien-Schlichting wave compared to the other two solvers.…”

Section: Linear Stability Of the Boundary Layer Flow Under A Solitarysupporting

confidence: 77%

“…As the amplitude of the perturbation is considered small, the parabolic stability equation solver and the Navier-Stokes solver are expected to produce similar results, since they both contain all the essential physics of the problem. This has been observed by Bertolotti et al (1992) and Joslin et al (1993) in their stability analysis of the Blasius boundary layer. Figure 10 shows three plots for the case = 0.4 and δ = 8 · 10 −4 .…”

Section: Linear Stability Of the Boundary Layer Flow Under A Solitarysupporting

confidence: 54%

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Linear stability of boundary layers under solitary waves

Verschaeve

Pedersen

2014

J. Fluid Mech.

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A theoretical and numerical analysis of the linear stability of the boundary layer flow under a solitary wave is presented. In the present work, the nonlinear boundary layer equations are solved. The result is compared to the linear boundary layer solution in Liu et al. (2007) revealing that both profiles are disagreeing more than has been found before. A change of frame of reference has been used to allow for a classical linear stability analysis without the need to redefine the notion of stability for this otherwise unsteady flow. For the linear stability the Orr-Sommerfeld equation and the parabolic stability equation were used. The results are compared to key results of inviscid stability theory and validated by means of a direct numerical simulation using a Legendre-Galerkin spectral element Navier-Stokes solver. Special care has been taken to ensure that the numerical results are valid. Linear stability predicts that the boundary layer flow is unstable for the entire parameter range considered, confirming qualitatively the results by Blondeaux et al. (2012). As a result of this analysis the stability of this flow cannot be described by a critical Reynolds number unlike what is atempted in previous publications. This apparent contradiction can be resolved by looking at the amplification factor responsible for the amplification of the perturbation. For lower Reynolds numbers, the boundary layer flow becomes unstable in the deceleration region of the flow. For higher Reynolds numbers, instability arises also in the acceleration region of the flow, confirming, albeit only qualitatively, an observation in the experiments by Sumer et al. (2010).

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Section: Linear Stability Of the Boundary Layer Flow Under A Solitarysupporting

confidence: 77%

Section: Linear Stability Of the Boundary Layer Flow Under A Solitarysupporting

confidence: 54%

Linear stability of boundary layers under solitary waves

Verschaeve

Pedersen

2014

J. Fluid Mech.

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“…Implicit Crank-Nicolson time-advancement is used for the wallnormal di usion terms and a three-stage Runge-Kutta scheme for the remaining terms. A code validation study was previously performed by Joslin et al 1992Joslin et al , 1993 .…”

Section: Methodsmentioning

confidence: 99%

Large-Eddy Simulation of Transition to Turbulence in Boundary Layers

Xiaoli

Ronald

Piomelli

1997

Theoretical and Computational Fluid Dynamics

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Large-eddy simulation results for laminar-to-turbulent transition in a spatially developing boundary layer are presented. The disturbances are ingested into a laminar ow through an unsteady suction-and-blowing strip. The ltered, three-dimensional timedependent N a vier-Stokes equations are integrated numerically using spectral, high-order nite-di erence, and three-stage low-storage Runge-Kutta methods. The bu er-domain technique is used for the out ow boundary condition. The localized dynamic model used to parameterize the subgrid-scale stresses begins to have a signi cant impact at the beginning of the nonlinear transition or intermittency region. The ow structures commonly found in experiments are also observed in the present simulation; the computed linear instability modes and secondary instability lambda-vortex structures are in agreement with the experiments, and the streak-like-structures and turbulent statistics compare with both the experiments and the theory. The physics captured in the present LES are consistent with the experiments and the full Navier-Stokes simulation DNS , at a signi cant fraction of the DNS cost. A comparison of the results obtained with several SGS models shows that the localized model gives accurate results both in a statistical sense and in terms of predicting the dynamics of the energy-carrying eddies, without ad hoc adjustments.

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“…A comparison between the PSE and DNS schemes had previously been considered by Joslin et al (21) who found excellent agreement between the two methods for the propagation of two-dimensional T-S waves on a semi-infinite flat plate. However, unlike Joslin et al (21) the PSE method of (19) considered in this paper allows the comparison of T-S wave streamwise velocity amplitudes rather than just growth rates.…”

Section: Introductionmentioning

confidence: 95%

Tollmien-schlichting wave amplitudes on a semi-infinite flat plate and a parabolic body: comparison of a parabolized stability equation method and direct numerical simulations

Turner

2012

The Quarterly Journal of Mechanics and Applied Mathematics

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SummaryIn this paper the interaction of free-stream acoustic waves with the leading edge of an aerodynamic body is investigated and we compare two different methods for analysing this interaction. Results are compared for a method which incorporates Orr-Sommerfeld calculations using the parabolized stability equation (PSE) to those of direct numerical simulations (DNS). By comparing the streamwise amplitude of the Tollmien-Schlichting (T-S) wave it is found that non-modal components of the boundary-layer response to an acoustic wave can persist some distance downstream of the lower branch. The effect of nose curvature on the persisting non-modal eigenmodes is also considered, with a larger nose radius allowing the non-modal eigenmodes to persist farther downstream.

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Spatial direct numerical simulation of boundary-layer transition mechanisms: Validation of PSE theory

Cited by 168 publications

References 40 publications

Linear stability of boundary layers under solitary waves

Linear stability of boundary layers under solitary waves

Large-Eddy Simulation of Transition to Turbulence in Boundary Layers

Tollmien-schlichting wave amplitudes on a semi-infinite flat plate and a parabolic body: comparison of a parabolized stability equation method and direct numerical simulations

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