Test Case F : Engine Valve

Test case calculated with FLUENT version 5.1 supplied by Fluent.

9.7.1. Introduction

The fluid flow inside an automobile engine cylinder is important for combustion efficiency and engine performance. Understanding this flow is crucial in the design of the cylinder, the valve, and the inlet port. This example has been included to show the effects of boundary condition uncertainty, discreti-sation and convergence level in a realistic three-dimensional industrial geometry where important re-circulation phenomena occur. The geometry and problem set-up for this case refers to the experimen-tal study of a generic model engine valve (Chen et al, [1995]) in which a mixture of liquid phase tur-pentine and tetraline was used to represent the working fluid.

9.7.2. Geometry and boundary conditions

The geometry consists of the cylinder connected to the inlet port by means of the valve passage, as shown in Figure 1. The port axis is offset from the cylinder axis by 4.00 mm in the x direction and 21.87 mm in the y direction, and it is elevated from the horizontal plane at an angle of 40 degrees. The cylinder diameter is 93.65 mm, the inlet port diameter is 46 mm, and the valve diameter is 43 mm. For more details about the geometry of the problem refer to Figure 1 of Chen et al. [1995]. For the inlet, the turbulence length scale was taken to be the diameter of the port (46 mm). In the absence of ex-perimental measurements, the turbulence intensity was initially assumed to be 10%. This value was later reduced to 1% so that the effect of boundary condition uncertainty could be illustrated. The inlet velocity was calculated from the known mass flow rate (of 1.379 kg/s) and is 0.928 m/s. A zero gauge pressure boundary condition was used at the outlet. The wall boundaries have been given a no-slip condition.

9.7.3. Grid

A tetrahedral grid with 176461 cells, was used. The concentration of cells is higher in the vicinity of the valve, due to the complexity of the flow in this region. The maximum skewness of the cells is 0.875.

Skewness is defined as (Optimal-Cell-Size – Cell Size)/(Optimal-Cell-Size) where optimal-cell-size is the size of an equilateral cell with the same circumradius. According to this definition of skewness, a

value of 0 indicates an equilateral cell (best) and a value of 1 indicates a completely degenerate cell (worst).

9.7.4. Features of the simulation

The fluid used in the experimental work was a mixture of turpentine and tetraline. Constant values were used for the fluid properties:

• Density ρ = 894 kg/m³

• Viscosity µ = 0.00152875 kg/(m·s)

The Reynolds number based on the diameter of the inlet port is Re = 24 970. The RNG k−ε turbulence model with standard wall functions was employed in the calculation. The first order discretisation scheme was used for momentum and turbulence equations. The calculation was then repeated with second order discretisation to illustrate sensitivity to the discretisation method. All the variables were initialised with a zero value prior to calculation. Results have been produced at two levels of conver-gence to illustrate its impact on accuracy.

9.7.5. Results

For each of the best practice issues, figures have been produced in which FLUENT predictions can be compared with experimental data. The plots show the velocity component in z direction at two different values of the z co-ordinate. Plots are also shown for turbulent viscosity (although no experimental data is available for this quantity). Where ‘best practice’ is applied the predicted velocities are seen to be in good agreement with the measurements from Chen et al. [1995].

Figure 1: Grid of the computational domain.

• Discretisation Method

Calculations were performed using both first and second order discretisation. The predicted velocity profiles obtained in both cases are compared with experimental measurement in figures 2 and 3. It can be seen that the second order scheme yields results that are in slightly closer agreement with the experimental data points. However, for this application it would appear that the accuracy of the first order results might be sufficient for most engineering purposes.

Z YX

Grid

Flow Through an Engine Inlet Valve

FLUENT 5.1 (3d, segregated, rngke)Jul 26, 1999

Z-Velocity at z=+10 mm

Figure 2: Discretisation – Z Component of Velocity at z= +10 mm

Z-Velocity at z=-5 mm

Figure 3: Discretisation – Z Component of Velocity at z = -5mm

• Convergence

The iterative calculation was monitored and stopped when the ‘maximum residual’ value had fallen to 1.0E-2 and overall mass imbalance was 1.4%. [‘residual’ is defined in this case as the error associated with the discretised equation, summed over all computational cells and normalised by the sum of the centre coefficients of the equation. The term ‘maximum’ refers to the ‘residual’ for the transport equa-tion showing the largest ‘residual’ value.] The situaequa-tion described above represents the ‘not converged’

result shown in figures 4 and 5.

Further iterations were then performed to obtain the ‘fully converged’ result shown in figures 4 and 5.

Full convergence was deemed to have occurred when there was no further noticeable change in the monitored variables, ‘maximum residual’ value was at 1.0E-5 and overall mass imbalance had fallen to 0.002%.

Figures 4 and 5 clearly show the error that can result if the user relies on an insufficiently converged solution.

Figure 4: Convergence – Z Component of Velocity at z = -5 mm

• Boundary Condition Uncertainty

As already noted, no experimental data on inlet turbulence intensity was available. To examine the ef-fect of this uncertainty two cases with different values of turbulence intensity were compared. The comparison has been carried out by using the code’s default value of 10% in the first case and 1% in the second case. The velocity plots in Figures 6 and 7 show the results.

For this application the assumption about inlet turbulence intensity is seen to have negligible effect on the predicted velocity field down stream of the narrow valve opening. However, other transported quantities are affected. This can be seen in figure 8 where predicted turbulent viscosity is compared for the two cases.

Z Y

X

Z Velocity at z=-5mm, x=0mm Flow through an Engine Inlet Valve

FLUENT 5.1 (3d, segregated, rngke) Jul 22, 1999

Position (m) (m/s)

Velocity Z

0.080 0.060

0.040 0.020

0.000 -0.020

-0.040 1.50

1.00

0.50

0.00

-0.50

-1.00

-1.50 measurements

fully converged not converged

Figure 5: Convergence - Z Component of Velocity at z = +10mm

9.7.6. Conclusions

This example has illustrated the effects of discretisation, level of convergence and boundary condition uncertainty on the quality of CFD prediction.

It has been shown that the use of a second order scheme can yield more accurate results than those obtained using first order methods. However, in this particular application, the difference is very small and might not warrant the additional computational expense.

The study of convergence error has clearly illustrated the need to ensure a properly converged solu-tion and shows that unconverged solusolu-tions can be very misleading.

The effect of boundary condition uncertainty has also been demonstrated. For this application it has been shown that uncertainty about inlet turbulence levels does not have any significant impact on the quality of velocity predictions within the system. However, other transported quantities have been shown to be more sensitive.

9.7.7. References

Chen, A., Lee, K.C., Yianneskis, M., and Ganti, G. (1995), “Velocity Characteristics of Steady Flow Through a Straight Generic Inlet Port”, International Journal for Numerical Methods in Fluids, 21:571-590.

Z Y

X

Z Velocity at z=+10mm, x=0mm Flow through an Engine Inlet Valve

FLUENT 5.1 (3d, segregated, rngke) Jul 22, 1999

Position (m) (m/s)

Velocity Z

0.020 0.015 0.010 0.005 0.000 -0.005 -0.010 -0.015 -0.020 -0.025 0.00

-0.20

-0.40

-0.60

-0.80

-1.00

-1.20

-1.40

-1.60 measurements

fully converged not converged

Figure 6: Boundary Conditions - Z Component of Velocity at z = -5mm

Figure 7: Boundary Conditions - Z Component of Velocity at z = +10mm Z

Turbulent Viscosity at Z = -5mm

Figure 8: Boundary Conditions – Turbulent Viscosity at z = -5mm