Numerical Procedure for the Laminar Developed Flow in a Helical Square Duct

Abstract

The incompressible fully developed laminar flow in a helically duct of square cross section is studied expressing the governing equations in terms of an orthogonal coordinate system. Numerical results are obtained with the described continuity, vorticity, and pressure (CVP) numerical method using a colocation grid for all variables. Since there are not approximations, the interaction effects of curvature, torsion and axial pressure gradient on the velocity components and the friction factor are presented. The results show that the torsion deforms substantially the symmetry of the two centrifugal vortices of the secondary flow, which for large values of torsion combined with small curvature tend to one vortex covering the whole cross section. The friction factor decreases for torsion in the range 0 to 0.1 and increases as the torsion increases further, a behavior which is more profound as the Dean number increases. Our results are stable for the calculated Dean numbers.

Numerical Study of Turbulent Flow and Convective Heat Transfer Characteristics in Helical Rectangular Ducts

“…However, helical coiled channels with rectangular cross section are often used in cooling system for gas turbine, rocket engine, or scramjet applications [11][12][13]. Some studies about laminar flow in helical rectangular ducts have been reported [14][15][16][17][18][19][20][21]. But literatures of turbulent flow and heat transfer in helical rectangular ducts for the turbulent flow are very few.…”

Improved CVP scheme for laminar incompressible flows

“…All the implementations of the CVP method that have been published up to now concern the Q3D formulation and the solution procedure has been described in detail in [3,4,6]. All the implementations of the CVP method that have been published up to now concern the Q3D formulation and the solution procedure has been described in detail in [3,4,6].…”

“…It was pioneered by Hatzikonstantinou et al [3] and it has been applied successfully to quasi-3D (Q3D) internal hydrodynamic [4,5] and thermal [6,7] flow problems. It was pioneered by Hatzikonstantinou et al [3] and it has been applied successfully to quasi-3D (Q3D) internal hydrodynamic [4,5] and thermal [6,7] flow problems.…”

“…The original CVP method was also implemented in the demanding problem of flow in a helical duct [4]. It is stated by Sakalis et al that there were some convergence difficulties when considering the full cross-section of the duct instead of using the half cross-section with symmetry boundary conditions.…”

“…Similar problems have been encountered in the works of Bolinder [8] who used the SIMPLE method and of Winters [9] who employed a finite elements scheme. In the CVP method an obvious cause of these asymmetric perturbations is the technique used to treat the numerical violation of the variational equations of continuity and vorticity [4]. In the CVP method an obvious cause of these asymmetric perturbations is the technique used to treat the numerical violation of the variational equations of continuity and vorticity [4].…”