Time‐dependent flows in grooved non‐isothermal channels

Abstract

A highly accurate and fully implicit algorithm for analyses of transient effects in heated grooved channels, including chaotic responses and transition to secondary states, has been developed. The algorithm can handle pattern interaction problems arising from combinations of geometric and heating patterns which are expected to be beneficial in the development of energy efficient stirring systems. The algorithm uses spectral spatial discretization and up to sixth‐order temporal discretization, providing the means to deliver machine accuracy. The spatial discretization relies on a combination of Chebyshev and Fourier expansions, guaranteeing very good resolution in the vicinity of the grooved walls. The enforcement of boundary conditions along the irregular boundaries is carried out using the immersed boundary conditions. The overall discretization leads to a gridless algorithm and provides the geometric flexibility required for efficient analyses of multitude of topography patterns. Extensive testing demonstrates that the algorithm achieves the theoretically predicted accuracy.

Accurate determination of stability characteristics of spatially modulated shear layers

“…The stability problem represents an initial-value problem that can be solved using DNS for any initial disturbance velocity and temperature fields set. The Fourier–Chebyshev expansions combined with IBC method provide the required high-accuracy discretization capable of handling complex geometry (Panday & Floryan 2020, 2021). The spectral element method described in Cantwell et al.…”

“…The following section briefly discusses the algorithm required for determining stationary states. This algorithm has been described elsewhere (Panday & Floryan 2020, 2021), so the presentation is limited to the basic concepts required to describe the stability algorithm.…”