# Simulation accuracy of the unsteady flow past slender cylinders: Evaluation and improvement of under hood simulation accuracy

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The aim of the present study is to improve the accuracy of the predicted ow topology in the engine bays of cars when using both simple turbulence models based on the concept of Reynolds averaged Navier-Stokes (RANS) and more advanced models such as Detached Eddy Simulations (DES) and Large Eddy Simulations (LES). The focus has been to investigate the simple RANS models capability of predicting separation and the in uence of unsteady wake movements (i.e vortex shedding) on the size of the created regions with recirculating ows and how much the accuracy can be improved by switching to the more advanced modelling approaches. In order to simplify the analysis of the studied models, they were tested on simple blu bodies of cylindrical shape with dierent cross sections. The investigated geometries included polygonal shapes with 2, 4, 7, 8 and 16 sides and a circular cross section. The geometries were tested at dierent orientations and at a Reynolds number of Red = 1 104, which is equivalent to that found for similar geometries in engine bays. The square cross section was also tested at a Reynolds number of Red = 2:2 104. Both of these Reynolds numbers are below the critical number, which means that the boundary layers prior to separation is laminar. The behaviour of the dierent models have been compared to both experimental results, the LES results obtained in the present study and those from other numerical studies. The investigated RANS models included k Realizable, k ! SST, Reynolds Stress Model, k v02 2f and Spalart-Allmaras. An investigation of the development of the vortices and the transport of momentum into the base region predicted by eddy viscosity models, represented by k ! SST, was performed for the square cross section. It was found that the initial creation of the vortices is fundamentally dierent than that found in experiments and by scale resolving methods. The actual creation of the vorticies takes place in the free shear layers after the separation points where small disturbances are amplied, turned into vortices and then enlarged by roll-up. For the eddy viscosity models, which are unable to resolve the roll-up process, the creation of the vortices are instead provided by separation at the trailing corner of the geometry. The modelled development of the vortex and the accumulation of mass and momentum into the vortices seems to be connected to their shape during the initial part of their existence, during which the vortices stick to the back side of the cylinder. The behaviour was found to be the result of a low pressure zone in the inner most part of the viscous sub-layer, which creates a force toward the surface of the cylinder. Further out in the buer layer and the log-layer the force changes sign and is directed donwstream, partially due to the turbulent diusion term. As a result an overestimation of the turbulence kinetic energy promotes the release of the vortices. The current ow contains many of the known weaknesses of the eddy viscosity approach, like a number of regions with stagnation ow and curved streamlines, which gives an overestimation of turbulent kinetic energy. The consequence is that the recirculation region lengths is underestimated by the eddy viscosity models due to increased transport of momentum into the wake. It is believed that this behaviour also in uences the Strouhal number by increasing the vortex shedding frequency. It was found that the eddy viscosity models are able to predict the vortex shedding process with an acceptable level of accuracy for polygonal shapes. However, the circular cross section constituted a bigger challenge. The recirculation region length was underestimated by approximately 30%. The separation was predicted to occur later than experiments performed by Bearman [2] and correlates with the expected separation behaviour at increased levels of turbulence. In order to get results of adequate accuracy for the separation point and recirculation region length, scale resolving approaches were needed.

**Nyckelord: **Engine bay, Vortex shedding, Flow topology, Separation, Reattachment, Blu body, Computational Fluid Dynamics, Cylinder