Three-dimensional laser doppler velocimeter studies of flow in a 90ℓ̊Curved duct : having a square cross-section

Measured values of the three velocity components and the associated turbulent fluctuations are presented for the flow of air in a 90° bend of 10 X 10 in (25.40 x 25.40 cm) cross-section duct; The bend had a mean radius of 23.0 in (58.42 cm) and was located downstream of 40.0 in (101.60 cm) and upstream of 10.0 in (25.40 cm) straight sections. The experiments were carried out at two Reynolds numbers, based on the hydraulic diameter and bulk mean flow velocity, of 99400 and 332000, corresponding to Dean numbers of 46300 and 155000, respectively. A three-dimensional, tri-orthogonal and Bragg-diffracted (vectorized) laser Doppler velocimeter system was used to measure the flow velocity at nine successive streamwise locations. Extensive laser-light-screen smoke flow-visualization was performed to identify qualitatively the characteristics of the flow. In addition, a Navier-Stokes computer code based on the Beam-Warming implicit, alternating-direction scheme was used as a numerical model in this study.

Experimental and computational results indicate that the flow patterns are complex and highly three-dimensional due to the formation of corner vortices. High streamwise velocities at a cross section are found to occur on the inner-radius wall at the bend entry and on the outer-radius wall at the bend exit under the influence of the duct axial pressure gradients. Normal-stress-driven secondary velocities of up to 6% of the bulk mean vlocity at the bend entry and pressure-driven secondary velocities of up to 33% of the bulk mean velocity at the bend exit are measured. In the downstream tangent of the bend, a pressure loss of about 0.3 ρU_b² for both flow cases is measured and is found to be greatly affected by the presence of a strong secondary motion of the Prandtl's First Kind at the bend exit. The effect of the growing boundary layer on the flow, distortion of the primary flow as a result of the secondary flow, stagnation point of the cross-stream flow and comparison of experimental results with computational results are discussed in detail and presented for the flow in a 90° curved duct having a square cross-section.