E stimations of the resolution necessary for a pure LES on the example of ship flow

16.4 E stimations of the resolution necessary for a pure LES on the example of ship flow

In the CFD community one can observe tendency to use pure LES without paying any attention to resolution problems. Very often LES is running on typical RANS grids. In fact, such computations can give correct results if the flow structures to be captured are large enough and exist for a long time. In some cases modeling of such structures does not require detailed resolution of boundary layers and a thorough treatment of separation regions. As an example one can mention flows around bluff bodies with predefined separa- tion lines like ship superstructures. Application of underresolved LES for well streamlined hulls should be considered with a great care. First of all, one should not forget that the basic LES subgrid models are derived under the assumption that at least the inertial turbulent subrange is resolved. Sec- ond, underresolution of wall region leads to a very inaccurate modeling of the boundary layer, prediction of the separation and overall ship resistance. It is clearly illustrated in the Table 16.1. The ship resistance obtained from underresolved LES using the wall function of (Werner, Wengle [31]) is less than half of the measured one and that obtained from RANS. Obviously, the application of modern turbulence LES models, more advanced than RANS models, does not improve but even makes the results much worse with the same space resolution. The change from RANS to LES should definitely be followed by the increase of the resolution which results in a drastic increase of the computational costs. These facts underline necessity of further devel- opment towards hybrid methodology. Although in (Alin et al. [32]) it has been shown that the accuracy of the resistance prediction using pure LES at

a very moderate resolution with y C functions, the most universal way for the present, to our opinion, is applica-

tion of hybrid methods. The impossibility of pure LES is illustrated below for flow around the KVLCC2 tanker.

The precise determination of the necessary LES resolution is quite difficult. Estimations presented below are based on the idea that about 80% of the turbulent kinetic energy should be directly resolved and the rest is modeled in a properly resolved LES simulation. Implementation of this idea implies

used to draw the typical spectra of the full developed turbulence E.k/. The wave number k separating the resolved and modeled turbulence is found from the condition

k E.k/d k

R 1 (16.8)

0 E.k/d k

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. The scales L and

max

3 ="/ 1=4 and Eq. (16.4), where the kinetic energy k and the dissipation rate " are taken from RANS simula-

is then used as the scale parameter for grid generation. Both lengths vary in space which makes the grid generation procedure very complicated. To roughly estimate the size of

max

in the ship boundary layer and ii) the point in the propeller disk where the

vorticity ! E is maximal (region of the concentrated vortex structure). The lat-

ter is dictated by the wish to resolve the most intensive vortex flow structures which have the strongest influence on the propeller operation. Since LES ap- plication is required in the ship stern area only this part of the computational volume has been meshed. It covers the boundary layer of the stern region starting from the end of the parallel midship section. The thickness of the meshed region has been constant and equal to the maximum boundary layer thickness at the stern ı BL . The grid for a pure LES is generated using the

min is determined in the near wall region. The cell sizes in x and z directions along the wall

min

sizes remain constant for all cells row in y direction which is normal to the ship surface (see Fig. 16.5). The cells have at least two equal sizes which is desirable from the point of view of LES accuracy. The choice of the size in y direction is dictated by proper resolution of the boundary layer. Close to the

D min.y w min / . Since y w is chosen as the ordinate where y C

D 1 the first nodes lay deeply in the viscous sublayer. The size in y direction at the upper border of the boundary layer

ı is the Kolmogorov scale at y Dı BL .A

Results of the estimations are as follows: the required grid size ranges from

6 , and from

Re 6 they should be considered as very rough estimations. Together with simi-

lar estimations for the nonlinear k-" model these results show that the LES

grid should have the order of tens of millions of nodes. Nowadays, the com- putations with hundred millions and even with a few billions of nodes are becoming available in the research community. However, a numerical study of engineering problems implies usually many computations which have to be performed within a reasonable time with moderate computational resources. In this sense, the results of the present subsection clearly demonstrate that the pure LES is impossible for ship applications so far. To verify that the resolution estimation procedure we used gives meaningful results, it has been applied for turbulent boundary layer (TBL) benchmark. We found from me- thodical calculations that the pure LES with 1M cells is quite accurate for prediction of the velocity distribution, TBL thickness, TBL displacement thickness and the wall shear stress. The estimation procedure presented above predicted the necessary resolution around 0.5M. Therefore, the esti- mations presented for a ship model are rather lower bound for the resolution required for a pure LES.

KRISO Exp. 3 15% 85%

2 RANS k"v 3 f 16% 84%

k-! SST SAS 3 18% 82% Underresolved LES 3 81% 19% Hybrid RANS LES 3 17% 83%

Table 16.1: Results of the resistance prediction using different methods. C R is the resistance coefficient, C P is the pressure resistance and C F is the friction resistance

Part III

CFD applications to human

thermodynamics