The determination of the volume function variation of Panu-Stanescu rotary engine.

Chioreanu, Nicolae ; Catas, Adriana ; Blaga, Vasile 等

1. INTRODUCTION

The Panu-Stanescu rotary engine is a heat rotary piston engine, Romanian letters-patent of engineers Mihai Panu and Gheorghe Stanescu. As we seen in figure 1, (Chioreanu & Blaga, 2002 and Panu & Stanescu, 2000), the engine consists on a cylindrical carcass (1) with two different values and antipodal ovalizations. The rotary piston (rotor) (2) is mounted inside the carcass and includes six box-fires for each chamber. On the external surface of the piston there are six radial channels disposed at sixty degree, in which six obturation bars ([P.sub.i], i = [bar.1,6]) glides. During the running, the bars are in permanent contact with the surface of the carcass due to centrifugal forces. For other geometrical details see also (Chioreanu & Chioreanu, 2006; O'Neill, 1991 and Nice, 2004).

2. THE GEOMETRY OF THE INNER SURFACE OF THE CARCASS

Denote by ([p.sub.1], [phi]) the polar coordinates of the point M situated at the external extremity of the bar [P.sub.1] when this passes through the first ovalization and let ([p.sub.2], [phi]) be the polar coordinates of the point M when the bar passes through the second ovalization. From the triangles [DELTA] [OO.sub.1] [P.sub.1] and [DELTA] [OO.sub.1] M we get the relations

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

[FIGURE 1 OMITTED]

The equation yields the polar line of the first ovalization

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)

Similarly, from the triangles [DELTA] [OO.sub.2] [P.sub.4] and [DELTA] [OO.sub.2] M we get the polar line of the second ovalization

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)

3. THE VOLUME FUNCTION VARIATION

Between carcass, piston and the bars six chambers with variable volume are formed. When the bar [P.sub.1] passes through the first ovalization, inside the chamber [P.sub.1] - [P.sub.6] the admission-compression processes take place while when the bar passes through the second ovalization the expansion-evacuation processes take place.

The volume of a chamber formed between the piston and carcass has a cyclical variation as a function of [phi] angle given by the formula

V ([phi]) = [l.sub.p] A ([phi]) + [V.sub.ca] (3)

where [l.sub.p] is the breadth of the piston, A([phi]) is the plan area of one chamber and [V.sub.ca] is the volume of the combustion chamber.

The [phi] position of the piston determines the following expressions of the A([phi]) area:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The volume function variation V ([phi]) depends continuously on [phi] and it has the branches [V.sub.i] ([phi]) = [l.sub.p] [A.sub.i] ([phi]) + [V.sub.ca], i = 1,7 with the angle [phi] in the suitable intervals. The maximal volume at the admission compression is obtained for [phi] = [pi] / 3 and the maximal volume at expansion evacuation is obtained for [phi] = 4 [pi] / 3.

Denote by [epsilon] = [V.sub.max] / [V.sub.min] the ratio of compression and by [delta] = [V.sub.d max] / [V.sub.min] the ratio of expansion, where [V.sub.d max] is given by the formula

[V.sub.d max] = [l.sub.p] [A.sub.5] (4 [pi] / 3) + [V.sub.ca] (4)

The volume of combustion chamber [V.sub.ca] = [V.sub.min] is given by the relation

[V.sub.ca] = 1 / [epsilon] - 1 [l.sub.p] [A.sub.2] ([pi] / 3). (5)

By means of (4) and (5) we get

[delta] = 1 + ([epsilon] - 1) [A.sub.5] (4 [pi] / 3) / [A.sub.2] ([pi] / 3) (6)

At a single rotation of the piston, six working cycles take place. Figure 2 shows the variation of the volume of a rotary engine with the following specific parameters: the ratio of compression [epsilon] = 8.5, the values of ovalizations [e.sub.1] = 9.25 mm, [e.sub.2] = 14.72 mm , the radius of the piston R = 130 mm, the breadth of the piston [l.sub.p] = 125 mm.

[FIGURE 2 OMITTED]

4. ENGINE POWER

For a chamber with variable volume, the working cycle is performed at one rotation of the piston([phi] = 2 [pi]). Let [omega] [rad / s] be the angular speed and n[rot / min] be the number of rotations of the motor shaft. The time [[tau].sub.c] [S] necessary to perform a working cycle is given in the following relation [[tau].sub.c] = 2[pi] / [omega] = 60 / n [s]. We also denote by [z.sub.c] = 6 the number of the chambers with variable volume, by [i.sub.r] the number of the rotors and by [p.sub.e] [N / [m.sup.2]] the averaged effective pressure at a one cycle. The effective power [P.sub.e] of the engine is one obtains by the following relation

[P.sub.e] = [z.sub.c] x [i.sub.r] x [p.sub.e] x [V.sub.s] / [[tau].sub.c] = [z.sub.c] x [i.sub.r] / 60 x n x [p.sub.e] x [V.sub.s] [W] (7)

where [V.sub.s] is the cylinder of one chamber.

5. CONCLUSION

If it is compared a Panu-Stanescu rotary engine ([z.sub.c] = 6, [i.sub.r] = 1) with an internal combustion four-cycle engine ([upsilon] = 4), having the same cylinder capacity, which at a certain number of rotations develops the same power

i / 30 x v x n x [p.sub.e] x V = [z.sub.c] x [i.sub.r] / 60 x n x [p.sub.e] x [V.sub.s] [??] i = 12 x [i.sub.r] (8)

From the implication (8) we conclude: a Panu-Stanescu rotary engine is equivalent to an internal combustion four-cycle engine having twelve cylinders.

6. REFERENCES

Chioreanu N. & Blaga V. (2002). Panu Stanescu rotary engine, Proceedings of the International Conference AMMA, vol.II, 227-230.

Chioreanu, N. & Chioreanu, S. (2006). Heat engine for nonconventional motor vehicles, Ed. Univ. of Oradea.

Nice, K. (2004). How Rotary Engines Work, 2002. Accessed October 18, 2004.

O'Neill, P.V. (1991). Advanced Engineering Mathematics, Wadsworth Eds.

Panu, M. & Stanescu, Ghe. (2000). Heat engine with rotary pistons, X-th National Conference on Heat Engineering, Sibiu, May, 25-27.