# Mesh Twisting Technique for Swirl Induced Laminar Flow Used to Determine a Desired Blade Shape
## 1 Introduction  
Swirling flow can by found in many applications: heat exchangers, combustion chambers of jet engines, mixing tanks and more. Swirl increases the friction coefficient and consequently the heat transfer coefficient is increased [1]. Swirling flow in pipes can be produced by active methods (rotating cylinders [2] or rotating propellers [3]) or passive methods (like tangential inlet (e.g., [4, 5]), radial/axial swirl blades at the inlet (e.g., [6, 7]) or guided swirlers further downstream (more on passive swirl methods in [8, 9]). Active methods generate sustained swirl (but require in turn external work) whereas passive methods experience swirl decay downstream unless they cover the entire length of the pipe. Swirl can also be generated by sudden expansion of the pipe (e.g., [10]) and in annular pipes (e.g., [11] and references therein). The most common guided swirlers are twisted tape (generally covering the full length of the pipe e.g., [4, 12, 13], which then leads to greater pressure drop), either fixed [14] or free to move with the flow, [15] propeller-type or other types of fixed vanes [16]. Most approaches on swirled flow have been aimed at turbulent flow, which is dominant in most heat exchangers, and the literature on laminar swirl flow is sparse. However, laminar swirl flow does also appear in heat exchangers and can be of great interest in the design of microfluidic heat exchangers where laminar flow only occurs. In addition, an ideal velocity profile for laminar swirl flow has been found in [17], where a specific tangential/angular velocity distribution is shown to givethe lowest decay of swirl along the flow direction in a circular pipe. Therefore, it is easier to determine if the swirl flow induced is optimal in laminar flow than in turbulent flow, where at present no such ideal flow profile has been determined. It should be noted that fixed blade swirlers need to have irregular geometry (i.e., they neither follow planes in \(xyz\) nor \(r\theta z\) coordinate systems) in order to induce swirl flow. Therefore, meshing an irregular geometry for the purpose of numerical simulations can be a challenge. Particularly, when using the finite volume method, it is important that individual cell shapes in the mesh are aligned with flow direction, corresponding to a structured mesh. Traditionally (including structured, unstructured and combined structured/unstructured grids [18]), cells are manually forced to conform to internal walls (blades), often causing increased skewness, loss of orthogonality of the cell walls and more seriously, a rastering of the boundary cells closest to the blades. This rastering will alter the boundary of the computational domain and induce errors in the velocity field of the flow. A mesh twisting/morphing method introduced in this paper is simple and minimizes the rasterizing effect and therefore accurately represents the domain's size and shape in spite of the cell shape changes during the morphing process. In this paper, the focus is on exploring a new efficient way of meshing devices that are meant to create a swirling flow. It is well known that a continuous twisted tape creates a too high pressure loss. Hence, short length swirlers are studied; and the shorter, the better. Although a rational approach is described in a previous paper [19], only a few profiles have been studied. Thus, new blade profiles have to be explored. To avoid geometrical meshing limits, it is important to find a \"simple\" and reliable way to mesh complex shapes that allows the control of the cell dimensions and distribution. The technique presented here consists in twisting an initial straight mesh instead of manually conforming a mesh to already designed blades. With this meshing technique, fixed curved blades are numerically generated from straight blades by this mesh twisting and the mesh automatically conforms to the blades. This efficient mesh generation approach is much less expensive than the conventional technique of generating a CAD and then discretizing the computational domain.