Numerical Study of Turbulent Secondary Flows in Curved Ducts

Abstract

The pressure driven, fully-developed turbulent flow of an incompressible viscous fluid in curved ducts of square cross-section is studied numerically by making use of a finite volume method. A nonlinear K -I model is used to represent the turbulence. The results for both straight and curved ducts are presented. For the case of fully-developed turbulent flow in straight ducts, the secondary flow is characterized by an eight-vortex structure for which the computed flowfield is shown to be in good agreement with available experimental data. The introduction of moderate curvature is shown to cause a substantial increase in the strength of the secondary flow and to change the secondary flow pattern to either a double-vortex or a four-vortex configuration.

Laminar secondary flows in curved rectangular ducts

“…It should be noted that in the finite-volume scheme, the formulation assures the conservation of mass (Patankar 1980). The algorithms used in the present study is a modification of that proposed by Patanakar (1980) to increase its rate of convergence by extracting information of the pressure field from a given velocity field (Hur 1988).…”

“…Since the normal velocity on the boundary is known (in this case based on the 'no-slip' condition) the pressure at the centroid can be obtained from the conservation of mass. Descriptions of the numerical implementation of the boundary conditions for finite-volume schemes can be found in, for example, Roache (1972), Patankar (1980), Hur (1988).…”

“…At the centroid of each cell the variables such as the pressure and the axial velocity are defined, whereas the velocities u and v are defined a t the horizontal and vertical cell walls, respectively. The details of the difference equation and the algorithms may be found inHur (1988).…”

Prandtl’s Secondary Flows of the Second Kind. Problems of Description, Prediction, and Simulation

“…This class of models is called nonlinear (or anisotropic) models of turbulent viscosity [95]. The nonlinear realizations of the and models proposed in [123] were applied for calculating flows in rectangular straight channels [124] and curvilinear channels [125]. It was shown that, as distinct from their linear counterparts, the nonlinear models are capable to more successfully predict turbulent secondary f lows and their effect on the primary flow.…”

Assessment of linear and non-linear two-equation turbulence models for aerothermal turbomachinery flows

“…Reynolds stresses are assumed to only depend on mean velocity gradients and turbulent scales k and ε [28,29] . A non-linear l k − model was developed by Speziale [30] and validated in curved ducts [31] . The non-linear l k − model differs from its linear version by the addition of two terms in the expression of ij τ .…”