Developing Compressible Turbulent Flow and Heat Transfer in Circular Tube with Uniform Injection or Suction

Abstract

In the present work , a numerical study has been made for the developing compressible turbulent flow and heat transfer in circular tube with uniform injection or suction. The study included the numerical solution of the continuity, momentum and energy equations together with the two equations of the (k-ε) turbulence model, by using the Finite Difference Method (FDM). The air was used as the working fluid, and the circular passage was composed of tube with diameter (20.0) cm , and the length was 130 (hydraulic diameter) .The Reynolds number of the flow was (Re=1.78x106), and the Mach number (M=0.44) the ratio of the transverse velocity at the wall (vw) to the axial velocity at inlet (Uin), Ω=(vw/Uin), for suction equal(0.001) and for injection (-0.001).. The wall of the tube was heated with constant wall temperature (Tw) and in other case with constant heat flux (Qw) as a thermal boundary condition. The development of both hydrodynamic and thermal boundary layers occurs simultaneously. The computational algorithm is capable of calculating the hydrodynamic parameters such as the velocities , friction factor , turbulence structure which includes the Reynolds stress and the turbulent kinetic energy and eddy viscosity. Besides, the thermal parameters are also predicted, such as the temperature, Nusselt number, and the turbulent heat fluxes.The Results showed that the hydrodynamic and thermal entrance length is increased with the increasing of Reynolds number. The suction caused a flatten for the velocity profile and thus decreasing the hydrodynamic entrance length, and caused an increase in the Nusselt number and decreasing the local coefficient of friction, but injection caused a steeping of the velocity profile , and thus increasing the entrance hydrodynamic length and caused a decrease in the Nusselt number and increase the local coefficient of friction. Turbulent kinetic energy and turbulent heat flux are decreased with suction and increased with injection .Predictions have been obtained which are in good agreement with results obtained by past experimental and theoretical work