| dc.description.abstract | Current numerical methods solving the Navier-Stokes equations such as, the subject matter of this project, the parabolized stability equations (PSE) have proven to be costly for industrial applications. In particular, improving upon cost effective numerical methods for hypersonic regimes has been a topic of interest. The Hypersonic Vehicle Simulation Institute aims to study the process of transition for hypersonic boundary layers by extending the amplification factor transport (AFT) model to these flow regimes. The work done in this paper will provide developers of the AFT model with accurate stability results calculated by LPSE for comparison and relate the growth rates of the instability to energy contributions within the system.
The geometry chosen for this study is a straight cone with an angle of incidence. The cross-flow instability is identified with a max N-factor of 14.5 at an azimuthal angle of 148.6◦ and a wavenumber of 81.9. In its current form, the AFT model only reports instability near the leeward plane and does not capture the crossflow mechanisms in the regions reported by LPSE.
An energy-perturbation budget analysis shows large Reynolds-flux production counteracted by pressure work and dissipation for highly unstable conditions. The balancing of these energy pro-duction values results in the growth rate. The largest energy contribution factors are the Reynolds heat-flux and the temperature-perturbation dissipation. Using these two terms, the neutral point is approximated with low relative error compared to the growth rate neutral point (≤ 10% for regions of interest) as well as large linear correlation to the development of the growth rate in the streamwise direction.
Another topic of interest for aerospace engineers is the reduction of drag on commercial air-craft. The National Aeronautics and Space Administration (NASA) University Leadership Initiative (ULI) has developed an airfoil with the slotted-natural-laminar-flow concept (SNLF). Stability characteristics for the bottom side of this airfoil, which includes the slotted region, are generated using linear (LPSE) and nonlinear (NPSE) parabolized stability equations. The development of in-stability mechanisms described for portions upstream of the slot, near the slot entrance, and within the slotted region of the airfoil for varying sweep angles 0◦ ≤ Λ ≤ 35◦.
The instability mechanisms are defined as the crossflow instability for swept cases and the Görtler mechanism in the concave region of the slot. Using LPSE, a large Görtler amplification is found in the slot (N = 13) for the steady and unsteady equivalent of the disturbance. This amplification is stabilized by the presence of crossflow within the slot. At Λ = 35◦, the N-factor is approximately 8.5 and 7.5 for the unsteady and steady disturbance, respectively.
For large sweep angles (Λ ≥ 20◦) a destabilized crossflow instability is present in the upstream portion of the airfoil. This amplification is quickly dampened by the convex surface curvature resulting in a stable flow at the slot entrance indicating little to no upstream influence of the crossflow instability.
A nonlinear study indicates the highly distorted Görtler instability within the vicinity of the slot. The largest initial amplitude allowing convergence is A(0,1) = 10−2. The neutral point for the nonlinear case remains consistently at a location slightly downstream of the slot entrance regardless of sweep. A more pronounced sweep angle results in nonlinear saturation occurring further down-stream. The crossflow velocity component causes a smearing effect primarily in regions where the velocity has upwelled further into the freestream. | |
