A Numerical Investigation of the Effect of Inlet Velocity Oscillation on Heat Transfer in a Two-Dimensional Laminar Jet Impinging on an Isothermal Surface

Abstract

Heat transfer in a laminar confined oscillating slot jet impinging on an isothermal surface is numerically investigated. A uniform inlet velocity profile, oscillating with an angle φ, is used at the jet exit. The angle φ changes in a sinusoidal form. The height-to-jet width ratio is fixed at 5. The working fluid is air with constant physical properties corresponding to Prandtl number, Pr, equal to 0.74 at ambient conditions. Reynolds number, Re, is defined based on the jet hydraulic diameter and is varied in the self-stable range between 100 and 400. Strouhal number, St, is also varied between 0.05 and 0.75. Oscillating the jet at Reynolds number equal to 100 showed no heat transfer improvement over the steady state case, regardless of the used Strouhal number values. The vortices generated by the oscillation were too weak and could barely reach the wall. The flow showed a high vulnerability to severe oscillations which drastically reduced the jet heat removal ability. The vorticity contours showed a perfect symmetry which resulted in instantaneous and average Nusselt number distributions that are symmetric about the center of the isothermal surface at x = 0. The average stagnation Nusselt number, Nu0, decreased by about 1.25% as Strouhal number is increased from 0.4 to 0.625 then dipped by 44.1% as St is further increased to 0.75, a fact that was attributed to reduction in the bulk momentum by the relatively high frequency. With Reynolds number at 250, the lowest two frequencies corresponding to St of 0.05 and 0.1, resulted in a flow field that is more developed to the right side of the channel, a phenomenon that was linked to the direction of the first jet swing. The corresponding average Nusselt number distributions were consequently asymmetric, with a significant shift to the right. This asymmetric behavior gradually disappeared as the frequency is increased. At St of 0.4 and 0.5, the average stagnation Nusselt number Nu0, showed a 2.2% increase over the steady jet case. As Strouhal number is further increased beyond 0.5, the average Nu0 gradually decreased, since the oscillation period became too short for a vortex to be strong enough to reach the wall. For Reynolds number set at 400, the oscillating condition at the inlet engaged the jet into flapping. The jet showed a tendency to a permanent lean towards one side of the channel, for all used frequencies. Flapping was more one-sided which led to a shift in the average Nusselt number distribution at low frequencies. As Strouhal number is increased to 0.75, flapping became more stable and the generated vortices were expectedly weaker due to the higher frequency. Also, at this Strouhal number value, the average Nu distribution showed the best symmetry with a 2.45% improvement of the average stagnation Nusselt number, over that of the steady state case.