Rohit Deshmukh

Characterization of structural response to hypersonic boundary-layer transition

The inherent relationship between boundary-layer stability, aerodynamic heating, and surface conditions makes the potential for interaction between the structural response and boundary-layer transition an important and challenging area of study in high-speed flows. This paper phenomenologically explores this interaction using a fundamental two-dimensional aerothermoelastic model under the assumption of an aluminum panel with simple supports. Specifically, an existing model is extended to examine the impact of transition onset location, transition length, and transitional overshoot in heat flux and fluctuating pressure on the structural response of surface panels. Transitional flow conditions are found to yield significantly increased thermal gradients, and they can result in higher maximum panel temperatures compared to turbulent flow. Results indicate that overshoot in heat flux and fluctuating pressure reduces the flutter onset time and increases the strain energy accumulated in the panel. Furthermore, ...

Reduced Order Modeling of Turbulent Flows using Sparse Coding

Basis identification is a critical step in the construction of accurate reduced order models using Galerkin projection. This is particularly challenging for turbulent flow fields due to the presence of multi-scale phenomena that cannot be ignored when building a reduced order model. The ubiquitous proper orthogonal decomposition approach seeks to truncate the basis spanning an observed data set into a small set of dominant modes, leading to loss of small scale information in turbulent flow fields. Ignoring the small scale information results in under-resolved rate of dissipation of energy, and consequentially, over-prediction of kinetic energy by constructed reduced order models. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. The sparse coding approach seeks the best compact basis to span the entire data set, and capture the multi-scale features present in the turbulent flows. These approaches are demonstrated for a canonical problem of an incompressible flow inside a 2-D lid-driven cavity. Results indicate that Galerkin reduction of the governing equations using only a few sparse modes produces reasonably accurate predictions of second order statistics of the fluid flow. Additionally, the sparse modes based models are found to maintain balance between the production and dissipation of energy. Whereas, models constructed using the same numbers of proper orthogonal decomposition modes are found to perform poorly.

Basis Identification for Reduced Order Modeling of Unsteady Flows Using Sparse Coding

Basis identification is a critical step in the construction of accurate reduced order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored, and are not well captured using the ubiquitous Proper Orthogonal Decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared to Proper Orthogonal Decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding seeks a compact basis that best spans the entire data set. Thus, the resulting bases are inherently multi-scale, enabling improved reduced order modeling of unsteady flow fields. The approach is demonstrated for two canonical problems — a 2-D incompressible flow past a moving cylinder, and an incompressible flow inside a 2-D lid-driven cavity. Results indicate that a set of sparse modes generalize better to unseen flow compared to a truncated set of the traditional proper orthogonal modes. Furthermore, Galerkin reduction of the governing equations using sparse modes yields significantly improved fluid predictions.

Basis Identification for Nonlinear Dynamical Systems Using Sparse Coding

Basis identification is a critical step in the construction of accurate reduced order models using Galerkin projection. This is particularly challenging in unsteady nonlinear flow fields due to the presence of multi-scale phenomena that cannot be ignored and are not well captured using the ubiquitous Proper Orthogonal Decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared to Proper Orthogonal Decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to select a compact basis that best spans the entire data set. Thus, the resulting bases are inherently multi-scale, enabling improved reduced order modeling of unsteady flow fields. The approach is demonstrated for a canonical problem of an incompressible flow inside a 2-D lid-driven cavity. Results indicate that Galerkin reduction of the governing equations using sparse modes yields significantly improved fluid predictions.