Numerical simulation of controlled transition to developed turbulence in a zero-pressure-gradient flat-plate boundary layer [electronic resource]
Keywords: Mechanical Engineering

Laminar to turbulent transition has been a subject of intensive experimental, theoretical, and numerical research. The transition process causes flow parameters such as the skin friction coefficient and heat flux to increase rapidly from their laminar values and in some cases overshoot their nominal turbulent values during late transition. Therefore, predicting transition accurately is of interest in the design and performance analysis of engineering devices such as turbomachinery and flying vehicles. Direct numerical simulations (DNS) of Klebanoff (K-) type and Herbert (H-) type controlled transitions are performed for compressible (Ma = 0.2), zero-pressure-gradient flat plate boundary layers. Each calculation is carried out using approximately 1.1 billion grid points, required to directly resolve the small scale turbulent structures in the near-wall region of the flow. For H-type transition, the computational domain extends from Re_theta = 210, where laminar blowing and suction excites the most unstable fundamental wave and a pair of oblique waves, to fully turbulent stage at Re_theta = 1250. The computational domain for K-type transition extends to Re_theta = 1410. The evolutions of K-type and H-type disturbances are compared and contrasted across the entire transition process. In each case localized linear disturbance is amplified through weak non-linear instability that grows into Lambda-shaped vortices with harmonic wavelength. These two calculations serve as a benchmark to assess the performance of models in predicting transition. Several subgrid scale models including, constant coefficient Smagorinsky and Vreman models and their dynamic extensions, dynamic mixed scale-similarity, dynamic one-equation kinetic energy model, and global coefficient Vreman models are applied to these transitional scenarios. We assess the capability of each model to predict the location of transition and the skin friction throughout the transition process. The constant coefficient models fail to detect transition, but the dynamic procedure, by allowing for negligible turbulent viscosity in the early transition region, result in correct prediction of the point of transition. However, after secondary instabilities set in leading to the overshoot in the skin friction profile, all models (in coarse LES calculations) fail to produce sufficient subgrid scale shear stress required for the correct prediction of skin friction and the mean velocity profile. The same underprediction of skin friction persists into the turbulent region. Modes of dynamical importance in the transitional regime of the two controlled cases are then extracted using dynamic mode decomposition (DMD). The contribution of each mode to the total Reynolds shear stress is estimated by employing the triple mode decomposition methodology. It is shown that in both transitional cases a few modes provide a good estimate of the Reynolds shear stress gradient within the transitional region. As subgrid scale models fail to produce sufficient subgrid scale shear stress to compensate for the lack of resolution, these modes can potentially be used as a reduced order representation of the transitional regime.