An algorithm for analysis of pressure losses in heated channels

Abstract

A spectrally accurate and very efficient algorithm suitable for prediction of pressure losses in heated grooved channels has been developed. Heating and topography patterns are used to create spatial flow modulations resulting in a pattern interaction problem. Search for combinations of patterns resulting in the reduction of pressure losses requires development of a very accurate and efficient algorithm. The proposed algorithm uses a combination of the Fourier expansions in the horizontal directions and the Chebyshev expansions in the vertical direction to provide a very good resolution of the near wall regions. The immersed boundary conditions (IBC) method is used to enforce flow boundary conditions at the geometrically irregular boundaries. The resulting gridless discretization can be easily adapted to handle a wide range of topography patterns. Various tests demonstrate that the algorithm delivers spectral accuracy and can provide machine level accuracy. Comparisons with the standard open‐source codes based either on the finite volume or on the spectral element discretization demonstrate several orders of magnitude better efficiency of the proposed algorithm.

Propulsion due to thermal streaming

“…The discretization process provided spectral accuracy with the absolute error controlled by the number of Chebyshev polynomials and Fourier modes used in the computations. Using 10 Fourier modes and 45 Chebyshev polynomials provided a minimum of five digits accuracy for all quantities of interest (Panday & Floryan 2021).…”

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. The spectral element method described in Cantwell et al (2015) represents an alternative, but its existing implementations provide only a low-order temporal discretization.…”

Time‐dependent flows in grooved non‐isothermal channels

“…Substitution of ( 19) and ( 22) into (44), expressing values of Chebyshev polynomials at the walls by the relevant Fourier expansions and execution of integrations result in…”

“…and all inner products < f (ŷ), g(ŷ) > can be found in. 44 The above algebraic system is supplemented with the boundary conditions (12c) which are discretized following method described in Section 4.1.1. The final form of the resulting boundary relations suitable for numerical implementation is as follows: and…”

“…The algorithm must provide acceptable resolution near the walls so that it can faithfully reproduce flow physics driven by small corrugations and must have high enough temporal resolution to capture various possible bifurcations and transition processes including the prediction of secondary states emerging from these transitions including Hopf bifurcations. The proposed algorithm relies on the spectral spatial discretization and high‐order temporal discretization and can be viewed as an extension of work on steady algorithms 44 —these algorithms are used to verify the results of time‐dependent computations in the proper limits. The time discretization is implemented in a fully implicit manner to take advantage of its superior stability characteristics.…”