**3. Dimensionless analysis**

278 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

*dp* 1 *dQ dV p dt V dt V dt*

In the combustion model, since the engine is crankless, a time-based Wiebe functions (as opposed to a conventional crank angle-based approach) is used to express the mass fraction

<sup>0</sup> 1 exp

*t t t a*

*<sup>Q</sup> <sup>t</sup> tt tt Q Qa b <sup>a</sup> t tt t t*

 *ht cyl w <sup>Q</sup> hA T T*

<sup>5</sup> 130 1.4 10 *<sup>p</sup> h V TU*

Since most heat transfer models, like the ones proposed by Woschni and Hohenberg, are made for Diesel engines. This means that they take radiative heat transfer effect into account, which is hardly present in premixed combustion. Hence, in the numerical

So the total energy that is used to increase the in-cylinder pressure in equation (18) can be

*Q Q c ht dQ dt t t*

Exhaust blown down is modeled to be a polytrophic expansion process while the exhaust

*dp n dQ dV* <sup>1</sup> *<sup>p</sup> <sup>n</sup> dt V dt V dt*

For two-stroke spark ignition engines with under piston or crankcase scavenging, the scavenging efficiency is about 0.7~0.9 [20], , a scavenging efficiency of 0.8 is introduced to evaluate the effects of incomplete scavenging effect. The moment the scavenging ports are open, the pressure and temperature are assumed to be the same with the scavenging

0.8 0.8 \_ 0.06 0.4

1

*c*

0 0 <sup>1</sup> <sup>1</sup> exp

*cc c*

*t*

*b*

(18)

(19)

(20)

1

*b b*

(21)

(22)

(23)

(24)

The in-cylinder heat transfer effect is modeled according to Hohenberg [19]:

*t*

simulations a factor of 0.5 is introduced to reduce the heat transfer coefficient [9].

port is opening and the scavenging ports are still covered by the piston [11].

conditions and the incoming gases mix entirely with the burned gases.

and the heat rate released during combustion is:

*<sup>c</sup> in in*

burned in combustion process [4]:

expressed in the following equation:
