Heat Transfer and Surface Friction Downstream of a Dual Array of Dimples of a Different Shape

Abstract

The wide experimental program was carried out in the Institute for Engineering Thermophysics (Kiev, Ukraine) to study heat transfer and surface friction downstream of the dual array of dimples. The test section is the rectangular channel 34 mm height, 290 mm wide and 125 mm long. The unheated dual array of dimples was placed on the channel floor (bottom) wall upstream of the electrically heated test section. Inserts with dimples of spherical, cylindrical and square shape were tested at their relative depth h/D of 0.20 and 0.30. Projected (surface) diameter of dimples is 25.0 mm; the second row was placed in the staggered fashion with the downstream pitch Sx/D of 0.64. The span-wise spacing Sz/D is of 2.0 providing the second row exactly fills in the open span-wise gap between dimples in the first row. The inlet air speed was from 4.1 to 16.6 m/c, Reynolds number Re2H, based on the equivalent (hydraulic) channel diameter varied from 17,400 to 71,800, the inlet boundary layer thickness did not exceed 1.0 mm. According to shape factor measurements the turbulent flow existed in front of dimples for all flow conditions tested. Heat transfer measurements were performed over the center line downstream of the representative dimple placed in the first or second row. The Reynolds number Rex based on the downstream distance was ranged from 3,000 to 105,000. Based on measurements, the conclusion was made that immediately after dimple array (at Rex>3,000) heat transfer corresponds to the turbulent flow data for a smooth flat plate extended into the low Reynolds number area. The downstream heat transfer ratio Nux/Nu0 weakly depends on the dimple shape and depth. The downstream surface friction τw was measured over the central line beyond the dimple placed in the first or second row. The tube-in-flow technique was employed in these measurements. At low probe distances (x/D = 1.2–2.4) the surface friction coefficients locate between classic correlations for the laminar and turbulent flow (extended into the low Reynolds number area) for a smooth flat plate. At high probe distances (x/D > 4.16) the surface friction data agrees well with the classic turbulent flow correlation for the smooth flat plate. Close to the dimple downstream edge (x/D < 2.4) the Reynolds analogy factor is over the unity for all dimple depths and geometries, thus confirming the greater heat transfer increases compared with pressure drop growth. At higher distances, the Reynolds analogy factor is above or below the Reynolds analogy line (RAF = 1.0) depending on the dimple shape and depth. Comparisons on the Reynolds analogy factor magnitude were made in terms of the downstream distances from the dimple back edge.