Calculation of the turbulent flow in plane diffusers

Abstract

PurposeTo provide an analysis of turbulent flow in plane diffusers for graduate and postgraduate students (researchers) which can help them to understand turbulent flows and turbulence modelling.Design/methodology/approachSteady, incompressible, turbulent flow in two‐dimensional plane diffusers, where Reynolds averaged Navier‐Stokes (RANS) equations were simplified using the theory of turbulent boundary layers in integral form adjusted for the internal flow. To close the RANS equations, the mixing length model proposed by Michel et al., which was previously used for the calculation of turbulent flow in a straight channel with a uniform cross section, is applied for the calculation of the turbulent flow in plane diffusers. Also, in this paper, the velocity profile is approximated in every cross‐section of the diffuser by a six‐order polynomial, whose coefficients depend upon the three form parameters. Using this transformation, the system of governing equations was reduced to the three ordinary differential equations which were solved numerically.FindingsA comparison between results obtained (velocity profiles) and experimental data obtained using HWA and LDA shows very good agreement. The method of integral equations of boundary layer is a relatively old method and tends to be forgotten since more advanced methods have been introduced. However, the results obtained using this method for the calculation of turbulent flow in a plane diffuser show a very good agreement with experimental data. Therefore, in engineering applications when simplicity and low‐cpu times are required, the integral method can still be applied successfully.Originality/valueThis paper offers practical help to an individual starting his/her research in the computational fluid dynamics (turbulence modelling).

Effect of flow arrangement on the removal of Bacillus spores from stainless steel equipment surfaces during a Cleaning In Place procedure

“…Sudden or gradual contraction or expansion pipes and bends with various curved edges are the most widely used geometries in industrial applications. It was shown that such hydraulic accidents strongly influence the flow arrangement inside production lines (Rizk et al, 1996;Vujičić and Crnojević, 2003). Due to the link between bacterial removal and the flow arrangement inside pipes, several studies were carried out in order to explain the residual contamination level upstream and downstream of these geometries after a CIP procedure (Jensen et al, 2005;Lelièvre et al, 2003).…”

Hygienic design: Effect of hydrodynamics on the cleanability of a food processing line

“…However, low values of local wall shear stress were observed (0.018 Pa for P 27 and 0.056 Pa for P 8 ) in comparison to the theoretical fully‐developed flow value for a pipe diameter of 2.30 × 10 −2 m (0.19 Pa), but the fluctuation shear rates were high enough, at both lower and higher sections (40% for P 8 , between 30 and 78% for probes P 26 , P 27 and P 28 ), to significantly contribute to the removal of spores after adhesion. The expansion angle close to 35.9° is high enough to induce streamlines separation from the wall, and, thus, recirculation zone theoretically characterized by mean wall friction forces close to zero and high‐fluctuation rate 17. This zone extends beyond the expansion, which explains the moderate contamination level (yellow zone) recorded at both top and bottom behind the expansion (zone 7).…”

“…According to Vujičić and Crnojević,17 the position of the separation point of the boundary layer near the wall depends on the angle of the diffuser and on the Reynolds number. The increase of the flow section due to the high‐opening angle of the expansion (35.9°), in addition to the highest Reynolds number tested (60,000 for 2.30 × 10 −2 m pipe dia.…”

“…These diameter changes are needed for the installation of various transducers (manometers and flowmeters). Vujičić and Crnojević17 showed that the flow arrangement after an axis‐symmetrical diffuser is widely influenced by the opening angle and the length of this geometry. In addition, it was shown that the stream cross‐section changes, resulting from this type of geometry, induce a flow disturbance throughout the downstream production line 18.…”

The Evaluation of k-ε and k-ω Turbulence Models in Modelling Flows and Performance of S-shaped Diffuser

“…Studies such as the flow in planar symmetrical diffusers and predicting the formation of symmetric [11] or asymmetric [12] separated flow regions depending on the divergence angle and Reynolds number has been applied using the Reynolds Averaged Navier-Stokes (RANS) approach. Gerolymos et al [13] adopted Reynolds stress model to analyse the flow field structure of a dual S-duct.…”