3 Turbulent Flows in Internal Combustion Engines: Description, Modelling &
3.2 Numerical Models and Issues
3.2.4 A Hybrid Approach: Detached Eddy Simulation (DES)
DES appeared among the CFD environment in the late nineties, with the main objective to conciliate the advantages of LES in “detached” flow regions and the RANS formulation in the
“attached” regions, i.e. for the eddies located in the boundary layer. Some important computational cost savings were expected, compared to the prohibitive application of pure LES to complete vehicles simulations or complex wall-bounded flows. DES belongs to the category of seamless hybrid turbulence models, such as the Limited-Numerical-Scales (LNS) from Batten et al. [12] or the Two-Scale Method from Willems [139], in opposition to the zonal methods (for more details please refer to [8, 35]). Both categories are differentiating from each other by the transition between RANS and LES formulations and the treatment of the so-called grey area existing in this particular region.
From the time of emergence of hybrid approaches, the main issue was to define the parameters controlling the transition between the two different models used. In 2001, Strelets [129]
developed a so-called SST-DES formulation based on the idea to switch from the Shear-Stress Transport (SST) RANS model, from Menter [89], to a LES model in regions where the turbulent length, Lt, predicted by the RANS model is larger than the local grid spacing.
The equation of the turbulent kinetic energy
( )
k from the SST model reads:( ) ( ) ( )
∂ + ∂
∂ + ∂
−
∂ = + ∂
∂
∂
i t k i
k i
i x
k k x
P k x u t
k ρ β ρ ω µ σ µ
ρ ~ *
( 3.51 )
The DES modification from Strelets is occurring in the destruction term as follows:
ω β
ε = *k β*kω⋅FDES ( 3.52 )
with
=max ∆,1
DES t
DES C
F L ( 3.53 )
where Lt is the turbulence length scale predicted by the RANS model, Lt = k/
(
β*ω)
, ∆ is the local grid spacing, β* and CDES are two constants.The model used in this paper is the one implemented in CFX 10 from Ansys, which is offering an improved formulation of the zonal treatment of DES [96]. The former models (Spalart and Strelets) were lacking a mechanism for preventing the limiter to become active in the attached portion of the boundary layer, a phenomenon that could lead to grid-induced flow separation [96]. In order to avoid or reduce this counter-effect, the present model is using the blending factors employed by the zonal formulation of the SST model to shift between the k-ω model in the wall vicinity to k-ε away from it. This differentiation between the boundary layer and the free flow field can also be used here as blending functions for the DES limiter.
( )
−
= ∆
− max 1 SST ,1
DES t CFX
DES F
C
F L ( 3.54 )
with
2
, 1
0 F or F
FSST = ( 3.55 )
In the equation above, FSST=0 recovers the Strelets model; F1 and F2 are the two blending functions of the SST model given in Eq. (3.34) and (3.40). By forcing the solver to work with one function or the other allows the control of the sensitivity of the model in shifting between RANS and LES.
Production term
Dissipation term
Diffusion term
Figure 3.4: Blending functions for the SST model as a function of the non-dimension wall distance y/δ
(left: F1, right: F2) (reprinted from [96])
Figure 3.4 is showing the evolution of the two different blending functions used by the SST model and allows comparing the difference of sensitivity between both functions for the shift between k−ω and k−ε.
Considering that the DES SST model is based on both the k −ω and k−ε models, the constant CDES from Eq. (3.54) needs to be calibrated for each of them separately. Then, a blending is used to generate the overall model constant as follows:
(
SST)
k DES SST
k DES
DES C F C F
C = −ω ⋅ + −ε ⋅ 1− . ( 3.56 )
According to the work of Strelets [129], for the hybrid model employed later in this study, these two constants are taking the following values:
78 .
=0
−ω k
CDES andCDESk−ε =0.67. ( 3.57 )
With regard to the numerical treatment of the DES model in CFX, the same numerical schemes as the one suggested by Strelets [129] are used, that is to say a second-order upwind-biased scheme for the RANS region and a second-order central difference scheme for the LES region.
This is necessary to avoid excessive numerical diffusion in the LES regions resulting from an upwind biased scheme.
Most of the references available in the literature are referring to applications related to external aerodynamics or bluff-body flows. This is mainly due to the original motivation of industrials and researchers to develop an alternative to LES for aeronautical cases, especially to perform full aircraft calculations at flight Reynolds numbers. Some complementary and quite exhaustive surveys are given in [102, 114, 126]. As general conclusion from the various analyses of massively separated flow fields, it was stated that DES is presenting some very positive features. Indeed, it has been observed that DES naturally provides unsteady information of the turbulent flow, since small-scale turbulence is generated by the shear-layer instabilities present in this type of flows.
But it has been shown that the good performance of a DES simulation is strongly connected to the grid quality and refinement in critical regions. This is the only way to ensure, in the RANS region, the mixing length to be much smaller than the grid size, while in the LES region, where the resolved eddies dominate the momentum and energy transport, the opposite must occur.
On the other hand, only few reports are concerned with internal flows and those are mainly dealing with simulations of academic channel flows. For real industrial applications of wall-bounded flows, where turbulent separation in a complex 3-d geometry occurs, modelling errors in the RANS region may become significant.
This could be the case in engine applications and more particularly in the intake port, where flows separation in the flow splitter or in the port elbow may occur. In the work from Sohm [121], the potential of DES to predict engine cyclic variations has been investigated. Despite the lack of validation data, encouraging results have been obtained, showing the capability of this hybrid model to account for the turbulence development and resulting fluctuations of the velocity field within the cylinder. Nevertheless, for this study, some hypotheses and compromises had to be made in order to be able to compute several engine cycles. Among those “restrictions”, the author had to use rather coarse grids (up to 3 million elements at the Bottom Dead Centre), especially in the engine port, upstream of the valves. The low treatment of the engine in-flow probably affected the computations based on a steady configuration (without moving boundaries). The assumption that the flow characteristics in the cylinder are essentially driven by the shear layer induced turbulence in the wake of the valves was utilized to justify the use of RANS modelling in the intake port region. This led to the conclusion that the discrepancy observed in different sections of the cylinder was likely to be related to some manufacturing tolerances. This work also pointed out the difficulty to represent and quantitatively compare instantaneous results of fluctuating quantities.
The present study will be based on the same SST-DES model implemented in ANSYS-CFX. The focus will be put on the accurate resolution of the intake flow condition, with high mesh-densities for a precise resolution of both the core of the flow and the boundary layers. Some new post-processing methods will also be proposed in order to better visualize and quantify the turbulent structures developing in Direct Injection Spark-Ignition engines.