Pseudospectrum in Rectangular Mini/Micro Channel Fluidics Linear Transition to Turbulence

Recent years have seen a significant increase in interest in rectangular mini/micro channels, such as those found in high-power research reactors with plate-type fuels, high-performance microelectronic cooling systems, photovoltaic panel cooling systems, fuel-cell powered vehicles, advanced propulsion systems, heat exchangers for cooling computer chips and biomedical micro fluidics. The laminar-to-turbulent transition is critical when studying single-phase thermal hydraulics in the above problems because the fluid properties in laminar flow differ dramatically from those in transition and turbulent flow. It’s important to understand the boundaries of laminar flow that cause instability for accurate design. Direct numerical simulation (DNS) presented itself as one high fidelity mathematical to resolve this challenge by full nonlinear simulations yet the computational needs, sensitivity to disturbances and related expertise is still very demanding for regular industrial applications. In the context of more accessible linear transition to turbulence, certain laminar flows are known to be linearly stable at all Reynolds numbers, Re, although in practice they always become turbulent for large Reynolds numbers. One resolution of this paradox is given by small finite perturbations that leads to transition. Trefethen has investigated the effects of small finite perturbations for Pipe Poiseuille flow. Rectangular duct flow of current study shows similarity to Pipe Poiseuille flow at aspect ratio one and at infinite aspect ratio it merges to Plane Poiseuille flow. A boundary satisfying Chebyshev-Collocation spectral method is employed for high-accuracy computation of linearized dynamics of incompressible flow in an infinite rectangular duct. The symmetries are exploited to reduce the high computational cost of the eigenvalue problem. The boundary satisfying basis are exploited for this cause. Systematic studies are conducted on the dependence of eigenvalue problem on the downstream wave numbers, aspect ratio and the Reynolds number. The linear non-normal mechanisms are observed to investigate the mechanisms of small finite perturbations that might lead to transition to decide on transition envelopes. Systematic studies of the dependence of non-normality of eigenvalues, transient growth factors and other quantities on axial wave number, aspect ratio and Reynolds numbers are presented for mini/micro rectangular channel’s design at low Reynolds number laminar flows that govern the physics of the design problems being investigated.