**5.2.3 Effects of dimensionless translator ignition position**

Ignition timing is one of the major parameters that control the engine's operating conditions, such as frequency and compression ratio. Since the dimensionless ignition timing is changing with different dimensionless stroke length, the ignition timing is defined by the compression ratio the engine has already achieved when the spark plug ignites in the calculation, and it means that the lower the ignition compression ratio is the bigger the ignition advance is.

According to some literatures [3][5], it's held that an earlier combustion in diesel free-piston engines would lead to more waste of energy to reverse the translator, thus the efficiency and frequency would drop. However, according to the results of spark ignited FPLA obtained in this paper, with different effective stroke length to bore ratio the best ignition advance differs with each other, since an early ignition is associated with negative work in the compression stroke and a late ignition is associated with low peak in-cylinder pressure, as is shown in Fig.16.

As is described in Figs.17~18, with smaller effective stroke length to bore ratio (closer to 0.5), a bigger ignition advance would lead to higher dimensionless compression ratio, higher dimensionless effective efficiency, higher dimensionless frequency and higher dimensionless effective power output. The reason is that with small dimensionless effective

Dimensionless Parametric Analysis of Spark Ignited Free-Piston Linear Alternator 293

stroke length, the dimensionless frequency of FPLA is high and most of the energy is released after TDC. Thus, the in-cylinder peak pressure is higher with a bigger ignition advance, which will help improve the performance of the engine. With a high effective stroke length to bore ratio (closer to 1.1), the frequency of the engine decreases a lot since the translator has to travel a longer stroke and a bigger proportion of energy will be released before TDC, which is associated with negative work in the compression stroke. According to the results derived, when the dimensionless effective stroke length is longer than 1.0, the

The dimensionless effective power output is determined by dimensionless effective efficiency and dimensionless frequency, as has been discussed before. As is shown in Fig.18, the biggest dimensionless power output is achieved when effective stroke length to bore ratio is 0.9 and ignition compression ratio is 4. Since the dimensionless frequency has little deviation with different ignition compression ratios, the dimensionless effective power

In order to analysis the effects of different ignition timings, the combustion duration was assumed to be invariant. However, the combustion duration is strongly depend on the working conditions of the engine, thus CFD tools were taken to analysis the effects of

Fig. 18. Effects of dimensionless translator ignition position to dimensionless frequency and

The modeling of the heat release in free-piston engine is one of the factors with the highest degree of uncertainty in the simulation model [11]. The piston motion of free-piston engines

dimensionless effective power output

**5.2.4 Effect of dimensionless combustion duration** 

ignition compression ratio of 5 would leads to the best engine performance.

output has similar trends with the dimensionless effective efficiency.

different ignition timings to verify the dimensionless results later.

Fig. 16. Effects of dimensionless translator ignition position to dimensionless peak pressure and dimensionless frictional power

Fig. 17. Effects of dimensionless translator ignition position to dimensionless compression ratio and dimensionless effective efficiency

Fig. 16. Effects of dimensionless translator ignition position to dimensionless peak pressure

Fig. 17. Effects of dimensionless translator ignition position to dimensionless compression

and dimensionless frictional power

ratio and dimensionless effective efficiency

stroke length, the dimensionless frequency of FPLA is high and most of the energy is released after TDC. Thus, the in-cylinder peak pressure is higher with a bigger ignition advance, which will help improve the performance of the engine. With a high effective stroke length to bore ratio (closer to 1.1), the frequency of the engine decreases a lot since the translator has to travel a longer stroke and a bigger proportion of energy will be released before TDC, which is associated with negative work in the compression stroke. According to the results derived, when the dimensionless effective stroke length is longer than 1.0, the ignition compression ratio of 5 would leads to the best engine performance.

The dimensionless effective power output is determined by dimensionless effective efficiency and dimensionless frequency, as has been discussed before. As is shown in Fig.18, the biggest dimensionless power output is achieved when effective stroke length to bore ratio is 0.9 and ignition compression ratio is 4. Since the dimensionless frequency has little deviation with different ignition compression ratios, the dimensionless effective power output has similar trends with the dimensionless effective efficiency.

In order to analysis the effects of different ignition timings, the combustion duration was assumed to be invariant. However, the combustion duration is strongly depend on the working conditions of the engine, thus CFD tools were taken to analysis the effects of different ignition timings to verify the dimensionless results later.

Fig. 18. Effects of dimensionless translator ignition position to dimensionless frequency and dimensionless effective power output

#### **5.2.4 Effect of dimensionless combustion duration**

The modeling of the heat release in free-piston engine is one of the factors with the highest degree of uncertainty in the simulation model [11]. The piston motion of free-piston engines

Dimensionless Parametric Analysis of Spark Ignited Free-Piston Linear Alternator 295

Fig. 20. Effects of dimensionless combustion duration to dimensionless frequency and

The free-piston engine investigated in this paper is a spark-ignited engine and the input energy is varied by changing the opening proportion of the throttle. For FPLA, a much narrow range of operating speeds is expected to be utilized, which is due to the electrical generating scheme employed by the device [23]. Therefore, the opening proportion of the throttle is confined to low speed range. According to the load of FPLA, efficient generation

The effects of different dimensionless input energy while other parameters remain the same with the base case are shown in Figs.21~22. As expected, with more input energy, the dimensionless frequency, dimensionless compression ratio and dimensionless effective power output of the engine are increasing since more energy is released in the combustion process. The amount of energy input to the engine is strictly determined by the load of FPLA. If we keep increasing the amount of input energy, the current load coefficient is not suitable for the current load coefficient and the speed of the translator will keep increasing since extra energy cannot be extracted, and at last the piston will crush with the cylinder head, which is strictly forbidden. However, if we decrease the amount of input energy, the translator will stop since the amount of energy is not enough to sustain the stable operation of the engine. Therefore, the operation range of the engine is confined by the load of the linear alternator, and the amount of the input energy has to be adjusted with the load coefficient to obtain a

In order to verify the results of dimensionless translator ignition position of spark ignited free-piston engines, multi-dimensional CFD tools were used to calculate the combustion

dimensionless effective power output

**5.2.5 Effects of dimensionless input energy** 

higher efficiency or higher power output.

**5.3 CFD calculated results** 

will be achieved by operation at a fixed oscillating rate.

differs significantly from that of conventional engines and very little research exists on how this influences the combustion process. In the dimensionless calculation, the heat release rate is defined by the combustion duration and shorter combustion duration will lead to a faster heat release rate. Based on the base case, four cases of combustion duration were chosen to instigate its effects to the engine's performances.

Fig. 19. Effects of dimensionless combustion duration to dimensionless compression ratio and dimensionless effective efficiency

Seen in Fig.19, a shorter combustion duration which means a faster heat release rate would lead to a higher compression ratio and higher effective efficiency when the dimensionless effective stroke length is less than 0.68 and 0.75. However, as the dimensionless effective stroke length increases, the dimensionless frequency will decrease and more energy will be released before TDC. For shorter combustion duration a lot more percentage of energy is released before TDC, which is associated with more negative work in the compression stroke. Thus, shorter combustion duration would lead to a lower dimensionless compression ratio and lower dimensionless effective efficiency with a longer dimensionless effective stroke length and fixed ignition compression ratio.

As is shown in Fig.20, shorter combustion duration leads to a higher frequency with smaller dimensionless effective stroke length and as dimensionless effective stroke length grows, shorter combustion duration leads to faster decreasing of dimensionless frequency as more energy is released before TDC to stop the translator. The dimensionless effective power output is determined by the dimensionless frequency and dimensionless effective efficiency and it has a similar trend with dimensionless efficiency.

Therefore, with a longer effective stroke length to bore ratio it is recommended to postpone the ignition timing to achieve a good performance of the free-piston engine.

differs significantly from that of conventional engines and very little research exists on how this influences the combustion process. In the dimensionless calculation, the heat release rate is defined by the combustion duration and shorter combustion duration will lead to a faster heat release rate. Based on the base case, four cases of combustion duration were

Fig. 19. Effects of dimensionless combustion duration to dimensionless compression ratio

Seen in Fig.19, a shorter combustion duration which means a faster heat release rate would lead to a higher compression ratio and higher effective efficiency when the dimensionless effective stroke length is less than 0.68 and 0.75. However, as the dimensionless effective stroke length increases, the dimensionless frequency will decrease and more energy will be released before TDC. For shorter combustion duration a lot more percentage of energy is released before TDC, which is associated with more negative work in the compression stroke. Thus, shorter combustion duration would lead to a lower dimensionless compression ratio and lower dimensionless effective efficiency with a longer dimensionless

As is shown in Fig.20, shorter combustion duration leads to a higher frequency with smaller dimensionless effective stroke length and as dimensionless effective stroke length grows, shorter combustion duration leads to faster decreasing of dimensionless frequency as more energy is released before TDC to stop the translator. The dimensionless effective power output is determined by the dimensionless frequency and dimensionless effective efficiency

Therefore, with a longer effective stroke length to bore ratio it is recommended to postpone

the ignition timing to achieve a good performance of the free-piston engine.

chosen to instigate its effects to the engine's performances.

and dimensionless effective efficiency

effective stroke length and fixed ignition compression ratio.

and it has a similar trend with dimensionless efficiency.

Fig. 20. Effects of dimensionless combustion duration to dimensionless frequency and dimensionless effective power output

### **5.2.5 Effects of dimensionless input energy**

The free-piston engine investigated in this paper is a spark-ignited engine and the input energy is varied by changing the opening proportion of the throttle. For FPLA, a much narrow range of operating speeds is expected to be utilized, which is due to the electrical generating scheme employed by the device [23]. Therefore, the opening proportion of the throttle is confined to low speed range. According to the load of FPLA, efficient generation will be achieved by operation at a fixed oscillating rate.

The effects of different dimensionless input energy while other parameters remain the same with the base case are shown in Figs.21~22. As expected, with more input energy, the dimensionless frequency, dimensionless compression ratio and dimensionless effective power output of the engine are increasing since more energy is released in the combustion process.

The amount of energy input to the engine is strictly determined by the load of FPLA. If we keep increasing the amount of input energy, the current load coefficient is not suitable for the current load coefficient and the speed of the translator will keep increasing since extra energy cannot be extracted, and at last the piston will crush with the cylinder head, which is strictly forbidden. However, if we decrease the amount of input energy, the translator will stop since the amount of energy is not enough to sustain the stable operation of the engine. Therefore, the operation range of the engine is confined by the load of the linear alternator, and the amount of the input energy has to be adjusted with the load coefficient to obtain a higher efficiency or higher power output.

### **5.3 CFD calculated results**

In order to verify the results of dimensionless translator ignition position of spark ignited free-piston engines, multi-dimensional CFD tools were used to calculate the combustion

Dimensionless Parametric Analysis of Spark Ignited Free-Piston Linear Alternator 297

Fig. 23. In-cylinder pressure with different translator ignition position while *Leff*\*=0.6765

Fig. 24. In-cylinder pressure with different translator ignition position while *Leff*\*=1.0294

process of the FPLA with four different ignition timings and two kinds of effective stroke length to bore ratio..

Fig. 21. Effects of dimensionless input energy to dimensionless compression ratio and dimensionless effective efficiency

Fig. 22. Effects of dimensionless input energy to dimensionless frequency and dimensionless effective power output

process of the FPLA with four different ignition timings and two kinds of effective stroke

Fig. 21. Effects of dimensionless input energy to dimensionless compression ratio and

Fig. 22. Effects of dimensionless input energy to dimensionless frequency and dimensionless

length to bore ratio..

dimensionless effective efficiency

effective power output

Fig. 23. In-cylinder pressure with different translator ignition position while *Leff*\*=0.6765

Fig. 24. In-cylinder pressure with different translator ignition position while *Leff*\*=1.0294

Dimensionless Parametric Analysis of Spark Ignited Free-Piston Linear Alternator 299

The in-cylinder pressure curves with different ignition compression ratio while *Leff*\*=1.0294 are shown in Fig.24. The sequence of the peak pressure achieved with different ignition

The combustion duration calculated via CFD is about 4.4~5.6ms with different ignition timings and effective stroke length, which has some deviation with the value in numerical simulating program which is defined based on the heat release rate of FPLA prototype. The deviations can be eliminated by using an iterative procedure between the numerical simulating program and CFD calculation when calculating a specific free-piston engine.

A detailed dimensionless modeling and dimensionless parametric study of spark ignited FPLA was presented to build up a guideline for the design of FPLA prototype with desired operating performances. The parameters of the numerical simulation program were amended by comparing the simulated in-cylinder pressure with experimentally derived data. At last CFD calculation of the combustion process was carried out to verify the effects of translator ignition position with two kinds of typical effective stroke length to bore ratios.

1. For FPLA, a much narrow range of low operating speeds is expected to be utilized, which is due to the electrical generating scheme employed by the device. Therefore, a bigger stroke to bore ratio is favorable to decrease the to and fro frequency of the translator. 2. According to the load of FPLA, efficient power generation will be achieved by operating at a fixed oscillating rate. With smaller effective stroke length to bore ratio, bigger load coefficient is advantageous to achieve a higher effective efficiency while smaller load coefficient would lead to higher effective efficiency with bigger effective stroke length to bore ratio. Smaller load coefficient would lead to higher effective power output. 3. It has been found that an optimum ignition advance is available for the free-piston engine to achieve its best performance since earlier ignition is associated with more negative work in the compression stroke and a later ignition is associated with low peak

4. The efficiency of the engine is mainly associated with the proportion of the energy released before TDC which is associated with negative work to stop the translator. With a longer effective stroke length to bore ratio it is recommended to postpone the ignition

5. According to the CFD calculated results with typical effective stroke length to bore ratio

[1] Hannson J, Leksell M, Carlesson F. Minimizing power pulsation in a free piston energy

[2] Mikalsen R, Roskilly AP. The control of a free-piston engine generator. Part 2: Engine

[3] Goertz M, Peng LX. Free piston engine its application and optimization. SAE paper 2000-

converter. Proceedings of the 11th European Conference on Power Electronics and

dynamics and piston motion control. Appl Energy (2009), doi: 10.1016/

, which supports the dimensionless results.

compression ratio is <sup>4563</sup> *ign ign ign ign pppp*

**6. Conclusion** 

in-cylinder pressures.

j.apenergy.2009.06.035

01-0996, 2000

**7. References** 

According to the dimensionless results, it can be concluded that:

timing to achieve a good performance of the engine.

Applications (EPE05), Dresden, Germany, 2005

and ignition timings, the dimensionless results were reasonable.
