Experimental and Numerical Investigation of Turbulent Heat Transfer due to Rectangular Impinging Jets

by Dogruoz, Mehmet Baris.

Due to their efficient heat and mass transfer potential, impinging jets have received attention in various applications. Heat transfer and flow characteristics of rectangular turbulent impinging jets issued from a 24:1 aspect ratio and 24:1 contraction ratio nozzle were investigated experimentally and numerically. In the heat transfer measurements; a thin stainless-steel foil was utilized to obtain iso-flux boundary conditions on the impingement surface. The target plate was free to translate in the lateral direction and the heat transfer distributions were determined at 0 ? x/W ? 20 with the micro-thermocouples placed underneath the foil. The measurements were conducted for Rej = 8900 ? 48600 at nozzle-to-target spacing of 0.5 ? H/W ? 12.0. Both semi and fully confined jets were investigated. Heat transfer coefficients at Rej = 28100, 36800, 45600 and H/W = 4.0 were determined by using adiabatic-wall temperatures and the distributions were compared with those of the wall shear stress. Off-center peaks were observed at high Rej and low H/W. Since the wall distributions are susceptible to nozzle-exit conditions, velocity and turbulence profiles at the nozzle-exit were measured for the velocity range of interest. Additionally, near-wall mean velocity and turbulence profiles were determined at Rej = 21500 and 36800 at H/W = 4.0 to have a better understanding of the secondary peaks in the wall distributions. Numerical computations were performed by using several different turbulence models (k ? ?, k ? ?, V 2F and Reynolds stress models). In wall-bounded turbulent flows, near-wall modeling is crucial. Therefore, the turbulence models eliminating wall functions such as the k ? ? and V 2F models may be superior for modeling impingement flows. The numerical results showed reasonable agreement with the ex- 24 perimental data for local heat transfer and skin friction coefficient distributions. The occurrence of the secondary peaks was predicted by the k ? ? and V 2F models, and for a few cases with the low-Re-k ? ? models. Near-wall measurements along with the computed profiles were used to describe the “secondary peak” phenomena. It was shown that the increase in turbulence production in the wall-streamwise direction enhances turbulent momentum and heat transport in the wall-normal direction which lead to secondary peaks in the wall distributions. The possibility of improving surface heat transfer with fully-developed jets was also explored numerically as a case study. 25 Nomenclature cf cp e skin friction factor specific heat (J/kg·K) total energy per unit mass (J/kg) fi damping functions (i = 1, 2, µ) f22 h H I elliptic relaxation function heat transfer coefficient (W/m2·K) nozzle-to-plate spacing (m) current (A) k turbulence kinetic energy per unit mass (m2/s2) kf ? Nu P Ps P ? Pr thermal conductivity (W/m·K) mixing length or turbulence length scale (m) local Nusselt number pressure (Pa) stagnation pressure (Pa) non-dimensional pressure or pressure coefficient Prandtl number Prt turbulent Prandtl number, Eq. 2.23 q r R Re Sij heat transfer rate (W) radial coordinate (m) resistance (?) Reynolds number mean strain tensor (1/s) 26 t T u Um x X v V w W y time (s) temperature (K) velocity, velocity in the x-direction (m/s) maximum velocity at a cross-section in the x direction (m/s) lateral coordinate (m) non-dimensional x-coordinate (x/W) velocity in the y-direction (m/s) voltage (V) velocity in the z-direction (m/s) nozzle width (m) perpendicular distance from the wall, wall-normal coordinate (m) y1/2 y coordinate where u = 0.5Um (m) ym yne y+ y? Y z Z y coordinate where u = Um (m) axial distance from the nozzle exit (H ? y) (m) turbulence wall coordinate turbulence wall coordinate non-dimensional y-coordinate (y/W) longitudinal coordinate (m) non-dimensional z-coordinate (z/W) 27 Greek Symbols: ? thermal diffusivity (m2/s) ? uncertainty ? turbulence dissipation rate (m2/ s3) ? ? ? blending function von Karman constant blending function µ absolute viscosity (Pa·s) ? ?t ? ? momentum diffusivity (or kinematic viscosity)(m2/s) turbulent (eddy) viscosity (m2/s) specific turbulence dissipation rate (1/s) vorticity (1/s) ? density (kg/m3) ? ? ? ?? shear stress (Pa) stream function per unit depth (kg/s·m) mean turbulence parameter fluctuating turbulence parameter ? visocus dissipation (W/m2) ? ? power (W) non-dimensional stream function 28 Subscripts and Superscripts: a ambient c conduction D nozzle diameter e effective i index-i = 1, 2, 3 j nozzle exit or jet, index-j = 1, 2, 3 k index-k = 1, 2, 3 l loss m maximum P point r radiation st stagnation t turbulent w wall W nozzle width 2W nozzle hydraulic diameter ?? flux 29