Modeling grooved rolls with moving 2D porous media

Abstract

Rolls are widely used in paper machines to heat, press and support paper webs and fabrics in order to facilitate rapid drying and transport of the paper web through the machine. In modern high speed paper machines, however, the interaction of boundary layer flows on the rolls, fabrics and the paper web often results in an undesirable pressure development at nip regions, ultimately causing an uncontrolled motion of the paper web. This runnability issue can be mitigated by using a so-called suction roll construction, which forces the required pressure profile over the paper web. Its operational costs are high, however. One result of the study is that the topology and the material of the roll surfaces, in particular the introduction of grooves on the smooth roll surfaces, can have a tremendous impact on the overall runnability potential of the paper web.

The complexity of solving the governing Navier-Stokes equations and the sheer variability of paper machine constructions makes a comprehensive analytical study of the roll-grooving effect difficult. To the authors' knowledge, analytical solutions for nip pressures only exist for two-dimensional geometries and for smooth roll's. Moreover, numerical 3D simulations of grooved rolls in large paper machine sections are not feasible with today's computational or modeling resources.

In this article, we propose a computational 2D model for a grooved roll. The model reproduces three-dimensional wall friction effects and minor losses in 2D by treating a grooved roll surface as a moving porous medium. The nip pressures are calculated and compared for:

a grooved roll interacting with a rigid impermeable horizontal wall at a tangent point (symmetric 3D)

a grooved roll interacting with a rigid impermeable horizontal wall at a tangent point where the groove geometry is described in 2D with moving porous media.

The roll models describe the roll as infinitely wide, thus capturing friction effects between the roll and the surrounding air. The simulations are conducted with the RANS-method of computational fluid dynamics (CFD) on a commercial solver.

The results show that the proposed computational 2D model for a grooved roll yields similar pressure profiles at nip regions as the more computationally expensive full-scale 3D models. The significance of this observation is that the 2D model now facilitates the study of grooved rolls in large sections of paper machines.