Geometric Control of Turbulence in a Curved Pipe

Various studies have investigated the complex dynamics of furbulent flow in curved pipes. The curvature of the pipe generates a centrifugal force at the bend, resulting in a radial pressure gradient. This causes an acceleration on the outer wall and a deceleration on the inner wall. As a consequence of the velocity redistribution and skewing of the mean flow, a Prandtl's secondary flow of the first kind is generated. The skewing of the mean velocity and the emergence of the Dean vortices strongly influence the friction factor. Moreover, the nature of turbulence and its transition in curved pipes is known to be fundamentally different from straight pipes. The friction factor and the onset of the instabilities are dependent on both the curvature and the Reynolds number. Several experimental and numerical works show that the friction factor in curved pipes is not necessarily higher than in straight pipes at the same Reynolds number. For mildly curved pipes, the pressure loss could even be lower than the laminar correlation of the same curved pipe. Other studies found that the curvature effects can even lead to turbulence attenuation. This motivates the current work to explore the space of curvature and local Reynolds number using a free-form shape optimization method. Our optimization method allows a high-dimensional design space in which the curvature and the cross-section of the pipe can vary along its centerline axis. The optimization aims to achieve minimal total dissipation, thereby improving the friction factor and exploring the possibility of relaminarizing the flow. This was applied to a 180-degree bend with a curvature of 0.2 with a fully-developed turbulent inflow at ReD=10000. The optimized geometry shows a substantial increase in curvature of the centerline axis, and the cross-sectional profile tends to be oval-shaped. We validate the result of our optimization using high-resolution DNS and experiment using PIV. The DNS were performed at ReD=10,000 and 20,000 for both the baseline and the optimized designs, and they confirm that relaminarization is achieved for both Reynolds numbers. Furthermore, our experimental validation shows a consistent improvement in the pressure loss up to the maximum achievable Reynolds number of ~50,000, suggesting that the relaminarization effect is not limited only to lower Reynolds numbers.