# NUMERICAL STUDY ON THREE-DIMENSIONAL FLOW AND HEAT TRANSFER CHARACTERISTICS OF TURBULENT FLOWS OVER A BACKWARD-FACING STEP IN A RECTANGULAR DUCT

**Hiroshi Iwai**

Department of Mechanical Engineering, Department of Aeronautics and Astronautics, Kyoto University, Nishikyo-ku, Kyoto 615-8540, Japan

**Eng Chong Neo **

Department of Mechanical Engineering Kyoto University, Kyoto 606-8501, Japan

**Kenjiro Suzuki**

Department of Mechanical Engineering, Kyoto University, Kyoto; Department of Machinery and Control Systems, Shibaura Institute of Technology, 307 Fukasaku, Saitama, 337-8570, Japan

## Abstract

Two- and three-dimensional numerical simulations were carried out for turbulent flows over a backward-facing step in a rectangular duct and related heat transfer employing a non-linear eddy viscosity model proposed by the UMIST group (Craft, Launder and Suga). Reynolds number and the expansion ratio were kept constant at *Re*=5,200 and *ER*=2, respectively. The wall downstream of the step was heated at a constant heat flux and the other walls were treated to be adiabatic. The computations were carried out for two different aspect ratios in the 3-D simulations. The objectives of the present study include the comparison of 2-D and 3-D computational results. Examination is also made for the effects of the duct sidewalls on the flow and thermal fields. It is found that the statistical quantities calculated in the centerplane in the case of *AR*=12 agree satisfactory with the results obtained by 2-D simulations. Two-dimensional region however is not observed around the duct center region in the case of *AR*=4. Calculated results also indicate significant differences of characteristic values on the heated wall in the spanwise direction. Transverse counter rotating eddies are observed in the relatively low velocity region right after the step, resulting the highly three-dimensional flow and thermal fields in the recirculation region. This three-dimensionality is more prominent for the smaller aspect ratio (*AR*=4).