4.2 Overview of existing heat transfer models
4.4.3 Ringing combustion
As shown in the previous chapter, ringing combustion increases the heat transfer.
It is verified now whether the models are able to predict the heat transfer during ringing combustion. This is only possible if they capture the increased heat transfer caused by the pressure oscillations. Tsurushima et al. [75] found that the existing heat transfer models need to be modified to accurately predict the total heat loss under both normal and ringing conditions. They suggested multiplying the modelled convection coefficient with a value that is proportional to the ringing intensity. Therefore, they added a term that is proportional to the pressure rise rate, to Eichelberg’s [76] heat transfer correlation according to Eq. 4.12:
hT surushima= hEichelberg·(1+ 1 c3·d p
dt) (4.12)
With hEichelbergthe convection coefficient calculated with Eichelberg’s correlation and c3 a scaling coefficient. They found that the pressure rise rate has a nearly linear relation with the amplitude of the pressure waves caused by ringing combustion. This modification allowed them to predict the total heat loss under ringing conditions.
The models of Annand, Woschni and Tsurushima et al.’s modification are evaluated under ringing conditions. The models of Annand and Woschni are calibrated by adjusting the scaling coefficient a in such a way that the modelled value of the peak heat flux equals the measured value for the base operating point, where no ringing occurs. Note that this is a different calibration method for Woschni’s model than previously, where the model coefficients c1and c2 were calibrated separately. It was chosen to retain the original model coefficients c2 for the pressure difference term in the characteristic velocity. This was done to investigate whether the pressure difference is able to account for the additional heat transfer during ringing combustion. The model of Annand is used as the base model for Tsurushima et al.’s modification, as it is better able to predict the heat flux during normal combustion compared to Eichelberg’s model. The model coefficients a and b are left unchanged and the scaling coefficient c3 is calibrated to match the measured peak heat flux for severe ringing conditions.
Ringing conditions were obtained by increasing the fuel mass rate until the ringing intensity exceeded the threshold value for severe ringing of 1 MW/m2. All other engine settings were constant. The measured and modelled heat flux traces are shown in Fig. 4.12 for the base point (full line) and for severe ringing conditions (dotted line).
300 320 340 360 380 400 420
Figure 4.12: The measured and modelled heat flux during normal (full line) and ringing combustion (dotted line)
Annand’s model is able to accurately predict the heat flux during the compression and combustion when no ringing occurs. Under ringing conditions on the other hand, it underpredicts the heat flux during the combustion. Annand’s model does not predict the additional heat transfer caused by the ringing combustion.
The difference between the measured and modelled maximum heat flux appears when ringing occurs and gets larger with an increasing ringing intensity. This was expected, since the mean piston speed does not represent the velocity of the in-cylinder flow during ringing operation. Also, the mixture’s gas properties do not change significantly when ringing occurs, as they are mainly driven by the bulk gas temperature. The model of Woschni is not able to model the instantaneous heat flux under normal operating conditions. The heat flux is underpredicted during the compression, because the model overpredicts the effect of the combustion on the heat transfer. Under ringing conditions, the model overestimates the peak heat flux for light ringing. When the ringing intensity is increased further, the peak heat flux is underpredicted. This demonstrates that the pressure difference caused by the combustion is also not sufficient to capture the additional heat transfer caused by the ringing combustion. With Tsurushima et al.’s modification, Annand’s model overestimates the peak heat flux for no and light ringing conditions. This indicates that the increase in peak heat flux is not proportional to the increase in the pressure rise rate due to the ringing combustion. It can be seen that the
shape of the modelled heat flux trace does not correspond to the shape of the measured heat flux trace during ringing combustion. The fast rise rate, sharp peak and oscillations in the modelled heat flux trace are not present in the measured heat flux trace. Furthermore, the instantaneous heat flux is overestimated before the combustion and underestimated after the combustion. This is because the ringing combustion only enhances the heat transfer during the combustion, when the pressure oscillations are present. Hence, multiplying the convection coefficient with the pressure rise rate does not yield accurate results.
Two modifications to the heat transfer model of Annand are proposed that take into account the additional heat transfer during ringing combustion. In both cases a time-dependent term is added to the characteristic velocity that is proportional to the intensity of the ringing combustion.
Modification 1
A first suggested modification is to model the characteristic velocity as a step function multiplied with a time-dependent exponential decay function. The amplitude is proportional to the maximum of the pressure rise rate squared and the step coincides with the moment this maximum occurs in the cycle. This should represent the sudden increase in the flow motion due to the pressure oscillations and its diminishing effect with time when the amplitude of the pressure waves decreases. The resulting characteristic velocity is shown in Eq. 4.13.
V= cm+(β ·d p
dθmax)2· e−0.1·θ (4.13) With the scaling coefficient β set to 0.035 and θ the crank angle starting at the step. The time constant for the exponential decay was set at -0.1, which represents the time constant for the decay of the pressure waves’ amplitude, as can be seen in Fig. 4.13.
In the modified model, the same model coefficients are used as in the previous model evaluation of Annand’s model. The relative difference between the measured and the modelled peak heat flux is listed in Table 4.7 for the different operating conditions (Mod. 1). This difference is within the experimental uncertainty for all operating conditions. The modified model is able to capture the trend of the increasing heat transfer when ringing occurs. In Fig. 4.14, the measured (full line) and modelled (dotted line) instantaneous heat flux traces are shown under normal and ringing conditions. The modified model is able to predict
300 320 340 360 380 400 420 440
Figure 4.13: The decay of the pressure fluctuations
300 320 340 360 380 400 420
0
Figure 4.14: The measured (full line) and modelled (dotted line) heat flux according to modification 1
the instantaneous heat flux under both normal and ringing conditions. However, as the ringing intensity increases, the model advances the location of the peak heat flux. This trend is also visible for the base Annand model and can be attributed to a phase-shift between the instantaneous heat flux and the in-cylinder pressure.
Table 4.7: Measured and modelled maximum heat flux for ringing combustion in the CFR engine
Fuel rate [mg/cycle] Meas. [W/cm2] Mod. 1 Mod. 2
8.5 98.5 +1.5% +0%
9.1 106.3 +3.2% +3.8%
9.4 112.3 +3.9% +4.5%
9.8 120.8 +3.1% +3.3%
10.1 134.7 -0.1% +1.9%
10.4 150.0 -0.9% +0%
10.7 167.1 -0.4% +0%
Modification 2
A second modification to Annand’s model is proposed, where the characteristic velocity is represented by the square root of the turbulent kinetic energy. A simplified k-ε model is used and the additional heat transfer caused by the ringing combustion is included into the production term. The initial value of the turbulent kinetic energy is constant and the change in turbulent kinetic energy is calculated with Eq. 4.14 as proposed by Bargende.
dkt
dt = c3· kt· 1 Vc
·dVc
dt −c4·k3/2t
Lc +Pringing (4.14)
With kt the turbulent kinetic energy, c3 and c4 scaling coefficients calibrated to match the heat flux during normal combustion, Lcthe instantaneous combustion chamber height and Pringing the production of turbulence caused by ringing according to Eq. 4.15.
Pringing= (c5·d p
dθmax)3 (4.15)
With c5a scaling coefficient calibrated to match the peak heat flux during severe ringing. Pringing is zero throughout the cycle and has the value calculated with
Eq. 4.15 when the maximum in the pressure rate rise occurs. This results in the characteristic velocity shown in Fig. 4.15 for normal and ringing combustion. It can be seen that Pringinghas almost no effect on the characteristic velocity when no ringing occurs, but increases the characteristic velocity substantially when ringing does occur. During severe ringing the maximum of the characteristic velocity is increased by 51% compared to normal combustion. The relative difference between the measured and the modelled peak heat flux is listed in Table 4.7 for the different operating conditions (Mod. 2). This difference is within the experimental uncertainty for all operating conditions. The modified model is able to capture the trend of the increasing heat transfer when ringing occurs. Although this modification is more complex than modification 1, they both perform in the same way.
300 320 340 360 380 400 420
0 1 2 3 4 5 6 7
Crank angle [°ca]
Characteristic velocity [m/s]
no ringing ringing
Figure 4.15: The modified characteristic velocity under normal (blue) and ringing (red) combustion.
In Fig. 4.16, the measured (full line) and modelled (dotted line) instantaneous heat flux traces are shown under normal and ringing combustion. The modified model is able to predict the instantaneous heat flux under both normal and ringing conditions. It shows the same phase-shift between the measured and modelled heat flux as the other models based on Annand’s correlation.
300 320 340 360 380 400 420 0
30 60 90 120 150 180
Crank angle [°ca]
Heat flux [W/cm2 ]
8.5mg 9.4mg 10.1mg 10.4mg 10.7mg
Figure 4.16: The measured (full line) and modelled (dotted line) heat flux according to modification 2
4.5 PPC operation
The heat transfer models are now evaluated for PPC operation. The heat flux measured in the bowl zone of the Scania engine is used for the model evaluation, since the CFR engine is not capable of PPC operation. Although the heat flux measured in the bowl and the squish zone are different for PPC operation, the results of the model evaluation are similar and the same conclusions can be drawn.
The results of the model evaluation based on the measurements in the squish zone can be found in Appendix E.
4.5.1 Base point
The models are first evaluated for a base operating point. The engine settings for this point are listed in Table 4.8. It was demonstrated in the previous section that all the models need to be calibrated and that the model coefficients obtained from a motored calibration are not applicable for fired operation. Therefore, the models are calibrated again to match the maximum value of the measured heat flux for the base operating point. For Woschni’s model, the coefficients c1and
c2of the characteristic velocity are calibrated. Coefficient c1is calibrated during motored operation, similar as for HCCI operation, and coefficient c2is calibrated for PPC operation. The scaling coefficient is calibrated for the other models. The resulting model coefficients are listed in Table 4.9. Compared to HCCI operation, the scaling coefficients are reduced by 20 to 30%. The coefficient c2of Woschni’s model has been reduced by more than 95%, almost omitting it.
Table 4.8: Base operating point for PPC operation
Parameter Base point
Fuel PRF70
EGR rate [%] 40
Speed [rpm] 1200
Inlet pressure [bar] 1.2 Inlet temperature [○C] 25 Fuel mass rate [mg/cycle] 23
Table 4.9: Calibrated scaling coefficients for PPC operation of the Scania engine Model Model coefficient
Annand 0.326
Woschni c1=3.14 c2=0.05 · 10−3
Hohenberg 99
Chang 0.023
Hensel 0.092
Bargende 1.521
The difference between the modelled and the measured heat flux is shown in Fig. 4.17 for the base point, with the error bars representing the experimental uncertainty and the dashed vertical line indicating the start of the combustion.
Before and after the combustion, the same conclusions can be drawn as for motored operation. The heat flux during the expansion phase is overestimated by all the models. During the combustion, the models perform similar to each other.
They all overestimate the heat flux during the first part of the combustion, but underestimate it during the final part. This observation is even more pronounced for the heat flux measured in the squish zone. This is because of its higher maximum heat flux and its faster decline in heat flux after top dead center. The heat flux predicted by the model of Bargende lies closest to the measured heat
flux during the expansion phase. All the models perform very similar during the combustion. The similar performance of the models of Annand, Hohenberg and Woschni, can be attributed to the reduction of coefficient c2, which reduces the characteristic velocity to the mean piston speed for all these models.
250 300 350 400 450
−20
−10 0 10 20 30 40
Crank angle [°ca]
Absolute error [W/cm2 ]
Annand Woschni Hohenberg Bargende Chang Hensel
Figure 4.17: The absolute error of the calibrated, modelled heat flux during PPC operation of the Scania engine. The error bars denote the experimental uncertainty.
4.5.2 Predictive ability
The predictive quality of the models is investigated by varying the intake pressure, fuel mass rate and start of injection with respect to the base point. The model coefficients obtained from the base point calibration are kept. The measured and modelled values of the maximum heat flux as a function of the different engine settings is shown in Figs. 4.18, 4.19 and 4.20. The dashed black line indicates the experimentally observed trend obtained from the statistical analysis performed in the previous chapter. None of the models is able to predict the effect of the intake pressure, as they overpredict the maximum heat flux in both the low pressure and the high pressure case. The predictions are however within the experimental uncertainty for the heat flux measured in the squish zone. The models are able to capture the linear trend of the maximum heat flux as a function of fuel mas rate, although they all overpredict the maximum heat flux at the highest fuel mass rate.
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 60
90 120 150
Intake pressure [bar]
Maximum heat flux [W/cm2 ]
Measured Annand Woschni Hohenberg Bargende Chang Hensel
Figure 4.18: Model results for the effect of the intake pressure on the maximum heat flux for the Scania engine
16 18 20 22 24 26 28 30
60 90 120 150
Fuel mass rate [mg/cycle]
Maximum heat flux [W/cm2 ]
Measured Annand Woschni Hohenberg Bargende Chang Hensel
Figure 4.19: Model results for the effect of the fuel mass rate on the maximum heat flux for the Scania engine
10 15 20 25 30 35 40 60
90 120 150
Start of injection [°ca BTDC]
Maximum heat flux [W/cm2 ]
Measured Annand Woschni Hohenberg Bargende Chang Hensel
Figure 4.20: Model results for effect of the start of injection on the maximum heat flux for the Scania engine
The quadratic effect of the start of injection on the maximum heat flux is captured by the models, but not in the late and early injection cases. Hence, the models are able to capture the trends, but become inaccurate if the deviation from the base point is too large. The performance of all the models is very similar and their predictive capability is low.