Separations and secondary structures due to unsteady flow in a curved pipe

Abstract

Unsteady flows in highly curved geometries are of interest in many engineering applications and also in physiological flows. In this study, we use flow visualization and computational fluid dynamics to study unsteady flows in a highly curved tube ($\unicode[STIX]{x1D6FD}=0.3$) with square cross-section; here, $\unicode[STIX]{x1D6FD}$ is the ratio of the half edge length to the radius of curvature of the tube. To explore the combined effects of curvature and pulsatility, we use a single flow pulse of duration $T$ and peak area averaged axial velocity $U_{p(max)}$, which are independently varied to investigate a range of Dean and Womersley numbers. This range includes cases corresponding to flows in the ascending aorta. We observe radially inward moving secondary flows which have the structure of wall jets on the straight walls; their subsequent collision on the inner wall leads to a re-entrant radially outward moving jet. The wall jet arises due to an imbalance between the centrifugal force and the radial pressure gradient. During the deceleration phase, the low-axial-momentum fluid accumulated in the jet reverses direction and leads to flow separation near the inner wall. We use boundary layer equations to derive scales, which have not been reported earlier, for the secondary flow velocities, the wall shear stress components and the distance ($\hat{P}$) traversed by the secondary flow structures in the transverse plane. We show that $\hat{P}$ predicts the movement of vortical structures until collision. In the limit $\unicode[STIX]{x1D6FD}\rightarrow 0$, the Reynolds number based on this secondary flow velocity scale asymptotes to the secondary streaming Reynolds number proposed by Lyne (J. Fluid Mech., vol. 45 (01), 1971, pp. 13–31) in loosely curved pipes. The magnitude of the secondary flow velocity is high and ${\sim}40\,\%$ of $U_{p(max)}$ for physiological flow conditions. We show that the flow separation on the inner wall has origins in the secondary flow, which was reported in a few earlier studies, and is not due to the axial pressure gradient in the tube as proposed earlier. The wall shear stress components, hypothesized to be important in arterial mechanobiology, may be estimated using our scaling relations for geometries with different curvatures and varying pulsatilities.

Hydrodynamic stability study in a curved square duct by using the energy gradient method

“…Generation of counter-rotating vortex motion (i.e., Dean roll cells as main secondary flow) is related to the partial backtransfer of flow momentum. For θ > 108° at De > 590.62, peaks on velocity and total pressure profiles are representative of Dean hydrodynamic instability with additional Dean vortices which are also observed in Krishna et al [23] study. Figure 8 shows distribution of velocity contours on different computational sections (see Fig.…”

“…Their results show that the reason of flow separation is the secondary motion movement that is also observed by Helal et al [22]. Krishna et al [23] conducted experimental tests with computational fluid dynamics (CFD) analysis on unsteady pulsatility flow through the highly curved duct. Their results show that the secondary flow is the origin of flow separation through the highly curved square duct.…”

Numerical Investigation on the Transition of Fluid Flow Characteristics Through a Rotating Curved Duct

“…Almost the same study was carried out by Nazeer et al [8] for multiple staggered rows of square cylinders. Secondary structures due to the unsteady flow through a curved duct were investigated by Krishna et al [9]. The fluctuation of axial velocity with respect to time was analyzed by Hashemi et al [10] for both finite and infinite length curved pipes.…”

Formation and interaction of multiple secondary flow vortical structures in a curved pipe: transient and oscillatory flows

“…(2007) was pulsatile. Krishna, Gundiah & Arakeri (2017) performed dye flow visualization and Fluent simulations for flow in a curved square duct with a half-sine flow rate followed by a period of resting. They looked at the effect of different Reynolds and Womersley numbers on the flow features.…”

“…It should be noted that the flow in Sudo et al (1992) was purely oscillatory with a flat velocity profile in the (inviscid) core, whereas the flow in Boiron et al (2007) was pulsatile. Krishna, Gundiah & Arakeri (2017) performed dye flow visualization and Fluent simulations for flow in a 180 • curved square duct with a half-sine flow rate followed by a period of resting. They looked at the effect of different Reynolds and Womersley numbers on the flow features.…”