Convective heat transfer predictions in an axisymmetric jet impinging onto a flat plate using an improved k-ω model

The paper shows the results of the convective heat transfer prediction in turbulent axisymmetric jets impinging onto a flat plate using the newest version (2006) of the k-ω turbulence model of Wilcox [1]. Improvements to the heat transfer predictions are obtained in the strongly strained flow regions with the impingement invariant proposed by Manceau [2] together with the F1 function proposed by Menter (1993). As an alternative, a modification based on the von Karman length scale is also discussed. The heat transfer rates predicted by the new version of the k-ω model are closer to the experimental data than with earlier versions due to a stress limiter reducing production of turbulent kinetic energy in stagnation flow regions. In order to further improve heat transfer predictions in stagnation flow regions even stronger damping of the turbulent viscosity is required, especially when the impingement plate is placed within the stress-free core of the jet. In the present simulations, the turbulent viscosity νt in the k-ω model is modified multiplying the limiter in Eq. (1) by the impingement function Fimp ω ν ~ k t = , ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ∗ β ω ω ij ij imp S S F C 2 , max ~ lim (1) where β=0.09, Clim=7/8. The impingement function Fimp is norm imp imp P F A F 1 1+ = where ( ) 2 2 ,0 3 2 norm MIN P P η ⎡ ⎤ ⎣ ⎦ = , { } P = SM , { } 2 η = S (2) where {.} denotes the trace of the tensor, S is the mean strain rate tensor and the components of the tensor M are Mij=ninj -1/3δij, where ni is the i-th component of the unit vector normal to the wall. This unit vector also has to be defined in the interior of the flow. The value of the constant Aimp in (2) was set to Aimp=2.0 by tuning it for one of the test cases in order to obtain good agreement with the experimental value of the Nusselt number in the stagnation flow region. On the other hand, a correction to the length scale is proposed defining the turbulent viscosity by