Spectral Element Simulation of Flow in Grooved Channels: Cooling Chips with Tollmien-Schlichting Waves

The spectral element method is a high-order (p-type) finite element technique for the Navier-Stokes equations that combines the geometric flexibility of the finite element method with the rapid convergence and efficiency of spectral schemes. The method is applied here to steady and unsteady moderate Reynolds number flow and heat transfer in grooved channels. It is shown by direct numerical simulation that the least stable linear modes of the steady grooved- channel flow closely resemble Tollmien-Schlichting channel waves, forced by Kelvin-Helmholtz shear layer instability at the groove edge. For Reynolds numbers greater than a critical value, these modes become unstable and the flow takes the form of self-sustained oscillations. For Reynolds numbers less than this critical value, it is shown that oscillatory perturbation of the flow at the frequency of the least stable mode of the linearized system results in subcritical resonant excitation as the critical Reynolds number is approached. Application of this subcritical flow excitation to heat transfer enhancement and the cooling of chips (electronic components) is described.