Turbulent heat transfer in channels with irregular roughness

Abstract

It is well known that rough surfaces affect turbulent flows significantly. How such surfaces affect turbulent heat transfer is less well understood. To gain more insight, we have performed a series of direct numerical simulations of turbulent heat transfer in a channel flow with grit-blasted surfaces. An immersed boundary method is used to account for the rough surface. A source term in the thermal energy balance is used to maximise the analogy between the transport of heat and the transport of streamwise momentum. The wall roughness size is varied from k
⁺
=15 to k
⁺
=120. Turbulence statistics like mean temperature profile, mean temperature fluctuations and heat fluxes are presented. The structure of the turbulent temperature field is analysed in detail. Recirculation zones, which are the result of an adverse pressure gradient, have a profound effect on heat transfer. This is important as it leads to the wall-scaled mean temperature profiles being of larger magnitude than the mean velocity profiles both inside and outside the roughness layer. This means that the temperature wall roughness function ΔΘ
⁺
(k
_s

⁺
,Pr) is different from the momentum wall roughness function ΔU
⁺
(k
_s

⁺
). Since the bulk temperature and velocity depend on ΔΘ
⁺
(k
_s

⁺
,Pr) and ΔU
⁺
(k
_s

⁺
), it was shown that the Stanton number and the skin friction factor directly depend on ΔΘ
⁺
(k
_s

⁺
,Pr) and ΔU
⁺
(k
_s

⁺
), respectively. Therefore, the failure of the Reynolds analogy in fully rough conditions can be directly related to the difference between ΔΘ
⁺
(k
_s

⁺
,Pr) and ΔU
⁺
(k
_s

⁺
).