The effect of mesh resolution on the flow field in a simplified engine geometry

A short review and some results of grid dependency studies for the compression and expansion stroke of a motored engine with a flat piston can be found in [29]. The simulations of a generic four-stroke, two-valve engine geometry were carried out using a Smagorinsky SGS

6.2. The effect of mesh resolution on the flow field in a simplified engine geometry model. Coarse and relatively fine computational grids with 220.000 and 440.000 control volumes, respectively, were used. The smallest cell size of the finer grid was Δ=2mm. It has been shown that smaller scales are resolved with the finer grid, leading to higher levels of resolved turbulence intensity.

The present paragraph focuses on evaluation of the effect of the grid resolution on LES results in a complex configuration. For this propose a numerical simulation, using a motored engine-like geometry shown in figure 6.1, was carried out for three different grid resolutions.

The geometry and computational grids were created using ICEM CFD Hexa. The selected configuration is based on the vertical valve IC-engine geometry considered in paragraph 3.4. The main parameters of the engine under consideration are collected in table 6.1. The choice of this simplified configuration was first of all motivated by the limitations imposed through the meshing software and KIVA-3V. The generation of a high resolution computational grid for a complex reciprocating configuration is an intricate task as discussed in chapter 4. Therefore, the relatively simple geometry with a flat piston and a flat cylinder head with a single intake / exhaust duct without valve has been selected. Including the valve into the considered geometry leads to a significant complication in view of mesh generation.

Figure 6.1: Single-port, non valve, engine-like geometry.

Table 6.1: Parameters of the simplified IC-engine with a single port.

Bore [mm]

Stroke [mm]

Clearance height

[mm]

Engine speed [rpm]

82.55 92.075 5.70 1600

Table 6.2: Specification of computed variants.

Variant Grid resolution (cylinder), cells

Grid size Δ, [mm]

Time for 1 cycle (0° - 360°), P4-3.0GHz

Case A 33×33×33 2.50 1.5 h.

Case B 66×66×66 1.25 28 h.

Case C 99×99×99 0.83 240 h.

The wall-flow interaction was treated with a no-slip velocity boundary condition and atmospheric pressure was set at the open boundary of the port. A description of the different meshes is given in table 6.2. The grid size for the finest mesh is Δ=0.83mm (case C) with the amount of cells of about 1.2 millions. The maximal cell size on the coarsest grid is equal to

mm 2.5

Δ= (case A). Hence, the grid refinement factors relative to case A are 2 and 3, respectively. The total amount of engine cycles has been limited to 5, taking into account the considerable computational time required for the finest grid.

a) b) c)

Figure 6.2: The effect of grid resolution on LES predictions in the engine-like geometry at BDC,

°

=180

CA ; top: isocontours of velocity averaged over 5 cycles; middle: rms of velocity;

bottom: velocity cycle-to-cycle variations at z=0.05m; a) case A; b) case B; c) case C.

6.2. The effect of mesh resolution on the flow field in a simplified engine geometry Figure 6.2 collects the averaged velocity flow fields (top) in the cross section of the cylinder, the standard deviation of velocity (middle) and the cycle-to-cycle velocity fluctuations (bottom) at z=0.05m obtained on the coarse (a), medium (b) and fine (c) grids, i.e. cases A, B and C, respectively. Inspection of the obtained results reveals that both flow structure and velocity magnitude are different especially comparing cases A and B. The maximal velocity in the cylinder predicted by LES in case C is 32% respectively 23% higher compared to cases A and B. Consideration of the standard deviation of velocity (figure 6.2, middle) shows that refining the computational mesh by a factor of 3 leads to an increase of intensity of fluctuations by a factor of 2.3. It can be seen from figure 6.2 (middle and bottom) that the information about instantaneous quantities including information about the cycle-to-cycle variations is nearly completely lost using the coarse grid (case A). Examination of the turbulent kinetic energy, shown in figure 6.3, let to conclude, that the amount of resolved turbulent kinetic energy in case C is 6 times more compared to case A. However, the peak values of turbulent kinetic energy in cases B and C are considerably closer to each other: Refinement of the grid by a factor of 1.5 results in a variation of turbulent kinetic energy in the order of 15%.

a) b) c)

Figure 6.3: Isocontours of the turbulent kinetic energy in the cross section of the cylinder at BDC, CA=180° for coarse (a), medium (b) and fine (c) grids, averaged over 5 samples.

Since the geometry does not include a valve, either intake or exhaust strokes can be realized in the considered configuration. LES results for the so-called “exhaust stroke” at

°

=270

CA for the mean velocity flow fields in the cross section of the cylinder (top), rms of velocity (middle) and velocity profiles (bottom) are depicted in figure 6.4. The velocity fields are predicted with similar velocity magnitudes for all examined cases as it can be seen from figure 6.4 (top). Nevertheless, figure 6.4 (middle and bottom) indicates big differences in the captured velocity fluctuations as well as in the turbulent kinetic energy shown in figure 6.5. Large eddy simulation does not predict cycle-to-cycle variations in case A, however they can be resolved in cases B and C. Comparison of figures 6.2 - 6.4 reveals that the intensity of cyclic fluctuations at

°

=180

CA (BDC) is approximately 2 times more compared to their values during exhaust stroke at CA=270°. Figure 6.6 shows that all cases give similar results for the mean velocity profiles during exhaust stroke (b) while differences between profiles are visible at BDC (a).

a) b) c)

Figure 6.4: The effect of grid resolution on LES prediction in the simplified engine geometry during exhaust stroke at CA=270°; top: isocontours of velocity averaged over 5 cycles;

middle: rms of velocity; bottom: velocity cycle-to-cycle variations at z=0.05m; a) case A;

b) case B; c) case C.

6.2. The effect of mesh resolution on the flow field in a simplified engine geometry a) b) c)

Figure 6.5: Turbulent kinetic energy in the cross section during exhaust stroke at CA=270° for coarse (a), medium (b) and fine (c) grids, averaged over 5 samples.

a) b)

Figure 6.6: The mean velocity profiles at z=0.05m averaged over 5 samples; a) BDC,

°

=180

CA ; b) Exhaust stroke, CA=270°.

From the above results it can be concluded that the distinctions between cases A and B are considerable. At the same time LES predicts rather similar flow fields for cases В and С even in spite of a clear lack of sufficient statistical samples. Also the intensity of fluctuations is comparable for both cases B and C. Increasing the number of cells by a factor of 2 (cases A and B) leads to an increase of computation time by a factor of 18 using the QSOU advection scheme in the KIVA-3V program. Further increase of the number of cells up to 99 in each direction, i.e.

3 times more compared to case A, results in an increase of computation time by a factor of 160 (case А) and 8.5 (case B), respectively. For the realistic configurations, such as the “BMBF” IC-engine, the calculations will be even considerably more time expensive. One of the most critical parts in real configurations is the valve zone. In order to include all geometrical features and to provide the valve motion, the mesh in this area has often the highest resolution compared to the rest of the geometry. The flow passing through the valve slit region has the highest magnitude of

velocity over the whole computational domain. This results in a limitation of the computational time step based on the CFL condition. Hence, the computational costs for LES calculation in that case may be too high on a very fine grid and a compromise in grid resolution is required. The mesh resolution in case B is taken as a guideline for the realistic engine configuration presented in chapter 5.