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The aerodynamic properties of a BMW car model, representing a 40%-scaled model of a relevant car configuration, are studied computationally by means of the Unsteady RANS (Reynolds-Averaged Navier-Stokes) and Hybrid RANS/LES (Large-Eddy Simulation) approaches. The reference database (geometry, operating parameters and surface pressure distribution) are adopted from an experimental investigation carried out in the wind tunnel of the BMW Group in Munich (Schrefl, 2008). The present computational study focuses on validation of some recently developed turbulence models for unsteady flow computations in conjunction with the universal wall treatment combining integration up to the wall and high Reynolds number wall functions in such complex flow situations. The turbulence model adopted in both Unsteady RANS and PANS (Partially-Averaged Navier Stokes) frameworks is the four-equation ζ − f formulation of Hanjalic et al. (2004) based on the Elliptic Relaxation Concept (Durbin, 1991).

This paper presents calculations of engine flows by using the Partially-Averaged Navier Stokes (PANS) method (Girimaji [1]; [2]). The PANS is a scale-resolving turbulence computational approach designed to resolve large scale fluctuations and model the remainder with appropriate closures. Depending upon the prescribed cut-off length (filter width) the method adjusts seamlessly from the Reynolds-Averaged Navier-Stokes (RANS) to the Direct Numerical Solution (DNS) of the Navier-Stokes equations. The PANS method was successfully used for many applications but mainly on static geometries, e.g. Basara et al. [3]; [4]. This is due to the calculation of the cut-off control parameter which requires that the resolved kinetic energy is known and this is usually obtained by suitably averaging of the resolved field. Such averaging process is expensive and impractical for engines as it would require averaging per cycles.

Reynolds-averaged Navier-Stokes (RANS) computations of heat transfer involving wall bounded flows at elevated Prandtl numbers typically suffer from a lack of accuracy and/or increased mesh dependency. This can be often attributed to an improper near-wall turbulence modeling and the deficiency of the wall heat transfer models (based on the so called P-functions) that do not properly account for the variation of the turbulent Prandtl number in the wall proximity (y+< 5). As the conductive sub-layer gets significantly thinner than the viscous velocity sub-layer (for Pr >1), treatment of the thermal buffer layer gains importance as well. Various hybrid strategies utilize blending functions dependent on the molecular Prandtl number, which do not necessarily provide a smooth transition from the viscous/conductive sub-layer to the logarithmic region.

The present work deals with a computational study of a ‘DrivAer’ car model, the rear-end shape of which corresponds to the Notchback configuration (Heft et al. [1] and Heft [2]). The study investigates the effects of the underbody geometry and wheel rotation on the aerodynamic performance. The configurations with detailed and smooth underbody as well as with stationary and rotating wheels are considered. The computational model applied relies on a VLES (Very Large Eddy Simulation) formulation, Chang et al. [3]. The residual turbulence related to the VLES framework is presently modelled by a RANS-based (Reynolds-Averaged Navier-Stokes), four-equation (D(k,ɛ,ζ, f)/Dt) near-wall eddy-viscosity model, Hanjalic et al. [4].

Aerodynamic properties of a BMW car model taking over a truck model are studied computationally by applying the scale-resolving PANS (Partially-averaged Navier-Stokes) approach. Both vehicles represent down-scaled (1:2.5), geometrically-similar models of realistic vehicle configurations for which on-road measurements have been performed by Schrefl (2008). The operating conditions of the modelled ‘on-road’ overtaking maneuver are determined by applying the dynamic similarity concept in terms of Reynolds number consistency. The simulated vehicle configuration constitutes of a non-moving truck model and a car model moving against the air flow, the velocity of which corresponds to the car velocity.

This paper presents calculations of external car aerodynamics by using the finite volume (FV) immersed-boundary method. The FV numerical codes primarily employ Reynolds-Averaged Navier-Stokes (RANS) models. In recent years, and due to possibility to run very large computational meshes, these models are usually used in conjunction with the advanced near-wall models. Moreover, it has been often demonstrated that the accuracy of RANS near-wall models relies on the mesh quality near the wall so by the rule, larger number of wall body-fitted cell-layers are employed. An immersed boundary (IB) method becomes an attractive alternative to the ‘standard’ FV approaches especially when applied to low quality CAD data. In general, the IB method is less investigated and validated for the car aerodynamics, particularly in conjunction with advanced near-wall turbulence models and an adaptive mesh refinement (AMR).

The aim of this paper is to present the adjoint equations for shape optimization derived from steady incompressible Navier-Stokes (N-S) equations and an objective functional. These adjoint Navier-Stokes equations have a similar form as the N-S equations, while the source terms and the boundary conditions depend on the chosen objective. Additionally, the gradient of the targeted objective with respect to the design variables is calculated. Based on this, a modification of the geometry is computed to arrive at an improved objective value. In order to find out, whether a more sophisticated approach is needed, the adjoint equations are derived by using two different approaches. The first approach is based on the frozen turbulence assumption and the second approach, which is advanced in this paper, is derived from the near wall k − ζ − f turbulence model.

This paper presents calculations of external car aerodynamics by using the Partial-Averaged Navier-Stokes (PANS) variable resolution model in conjunction with the finite volume (FV) immersed-boundary method. The work presented here is the continuation of the study reported in Basara et al. [1]. In that work, it was shown that the same accuracy of predicted aerodynamic forces can be achieved by using Reynolds-Averaged Navier-Stokes (RANS) k-ζ-f model on both types of meshes, the standard body-fitted (BF), and on the immersed boundary (IB) mesh. Due to all well-known shortcomings of the steady state approach, in this work we deal with the Partially Averaged Navier-Stokes (PANS), which belongs to the hybrid RANS-LES (scale resolving / high fidelity) methods. This approach was developed to resolve a part of the turbulence spectrum adjusting seamlessly from RANS to DNS (Direct Numerical Simulation).

This paper presents calculations of external car aerodynamics by using the Partial-Averaged Navier-Stokes (PANS) variable resolution model in conjunction with the Finite Volume (FV) immersed-boundary method. The work presented here is the continuation of the study reported in Basara et al. [1, 2]. In that work, it was shown that the same accuracy of predicted aerodynamic forces could be achieved for both types of computational meshes, the standard body-fitted mesh and the immersed boundary (IB) Cartesian mesh, by using the Reynolds-Averaged Navier-Stokes (RANS) k-ζ-f model as well as by using the Partially-Averaged Navier-Stokes (PANS) method. Based on the accuracy achieved, Basara et al. [2] concluded that further work could focus on evaluating the turbulence modelling on the immersed boundary meshes only.