2 replies to this topic

[manolis]

In their recent US8220435 patent:



Mazda optimizes the Wankel rotary design by the selection of ,ore shallow (less-deep) rotors.

Quote from Mazda's patent:

The relationship of the dimension parameter L/b and the combustion stability can be explained as follows.

To increase the combustion speed, the rotary piston engine has two spark plugs, one on the trailing side and the other on the leading side, with a predetermined distance therebetween in the rotor rotation directions (in other words, the circumferential directions of the rotor; it should be noted that, in this specification, the "rotor rotation directions" include the direction in which the rotor rotates and the direction opposite to the rotation of the rotor) such that the spark plugs meet a working chamber in the compression interval through the expansion interval. The flames generated by ignition of the trailing side plug and the leading side plug (T-side flame and L-side flame) propagate in both rotor rotation directions and rotor breadth directions. Due to the structure of the rotary piston engine, the speed of propagation of the flames in the rotor rotation directions is relatively high while the speed of propagation of the flames in the rotor breadth directions is relatively low as compared with the propagation speed in the rotor rotation directions.

The T-side flame propagating toward the leading side seen in the direction of the revolution of the rotor and the L-side flame propagating toward the trailing side collide with each other near the midpoint between the two flames. After the collision, combustion of the T-side flame and the L-side flame both attenuate so that the flame propagation speed decreases in both rotor rotation directions and rotor breadth directions.

Now, consider decreasing the dimension parameter L/b on the premise that the rotary piston engine takes the above-described combustion form. Decreasing the dimension parameter L/b while the displacement is maintained constant corresponds to relatively decreasing the length L of one side of the rotor while relatively increasing the breadth b of the rotor. Namely, the rotor has smaller triangular faces but a greater breadth. Decreasing the length L leads to a shorter distance between the trailing side spark plug and the leading side spark plug so that the time between the generation of the T-side and L-side flames and the collision of the flames becomes shorter. Due to the increase in breadth b and the shortened time before the collision of the flames, the collision of the flames occurs before the T-side flame and L-side flame propagating in the rotor breadth directions reach the side housing. After the collision of the both flames, the flame propagation speed decreases, and as a result, the flames do not expand so much in the rotor breadth directions.

On the contrary, consider increasing the dimension parameter L/b. Increasing the dimension parameter L/b while the displacement is maintained constant corresponds to relatively increasing the length L of one side of the rotor while relatively decreasing the breadth b of the rotor. Namely, the rotor has larger triangular faces but a smaller breadth. Increasing the length L leads to a greater distance between the trailing side spark plug and the leading side spark plug so that the time before the collision of the flames becomes longer.

Due to the longer time before the collision of the flames and the decreased breadth b, the T-side flame and L-side flame propagating in the rotor breadth directions reach the side housing before the collision of the flames occurs. After the flames reach the side housing, the pressure in the vicinity of the side housing increases so that the flames are redirected to propagate in the rotor rotation directions. As a result, the propagation of the flames in the rotor rotation directions is enhanced. Thereafter, the T-side flame and L-side flame propagating in the rotor rotation directions collide with each other.

As the combustion stability is improved by increasing the dimension parameter L/b, improvement in the combustion pattern in the working chamber is also expected.

According to one aspect of the present invention, a rotary piston engine includes: a rotor which orbits around an output shaft axis, rotates around an eccentric shaft that is aligned in parallel to and offset from the output shaft axis, and has a generally triangular face as seen in the axial direction; a pair of side housings which are arranged at both axial sides of the rotor to be in contact with side seals of the rotor; a rotor housing which accommodates the rotor therein such that an inner surface of the rotor housing is in contact with apex seals of the rotor, the rotor, the pair of side housings and the rotor housing defining three working chambers; an intake port formed in at least one of the side housings to be capable of communicating to one of the working chambers to induct air into the working chamber; and an exhaust port formed in at least one of the side housings to be capable of communicating to one of the working chambers to exhaust combusted exhaust gas from the working chamber.
…

As described above, increasing the dimension parameter L/b while the displacement is maintained constant corresponds to increasing the length L while decreasing the breadth b, hence corresponding to a more elongated shape of the working chamber. Therefore, the surface/volume ratio (S/V ratio) of the working chamber over the compression interval and the combustion interval decreases. This leads to an improvement in thermal efficiency so that the fuel efficiency is further improved.

However, the Surface to Volume ratio (S/V) of the working chamber increases when the breadth b of the rotor decreases.
And this is pure / simple Geometry / Mathematics.

On the other hand, Mazda deals with the Wankel rotary for some fifty years.

Am I wrong?

Thanks
Manolis Pattakos

[gm914]

It made me wonder today, while watching the three Mazda6 diesel entries at the Rolex 24 Hours of Daytona all fail with cylinder issues (and not even past the six hour mark, mind you) why Mazda is bothering with diesels and cylinders in the first place. I mean, they were competing in the GX class, so obviously this is where Mazda R&D is heading. But why?
They should be working full-time on Rotary Hybrids. Engine size, relative power, and weight must have more appeal and place in their future line-ups than a big old V6 diesel.

Edited by gm914, 27 January 2013 - 23:45.

[manolis]

Mazda is right.
By decreasing the breadth of the rotor, the surface to volume ratio decreases.

Suppose the breadth (i.e. the width normal to the drawing plane) of the rotor is b, the length of the curve of the one side of the “triangular” rotor is L1, the length of the curve of the epitrochoidal (casing) between the two apexes of the rotor at the ends of the combustion chamber is L2 and the surface between the L1 curve and the L2 curve is Su.
Suppose, for simplicity, that there are no combustion bowls on the rotor.



The surface of the combustion chamber is S=b*(L1+L2)+2*Su
The volume of the combustion chamber is V=b*Su

So the surface to volume ratio is R=S/V=(L1+L2)/Su + 2/b

In case the breadth b of the rotor is multiplied by a factor x (x=1.02 means an increase of the breadth by 2%), the surface Su and the lengths L1 and L2 must change accordingly in order the volume of the combustion chamber to remain unchanged.

The surface Su must be multiplied by the factor 1/x, so that:
V=Su*b=Su’*b’=((1/x)*Su)*(x*b).
In case x=1.02, i.e. the breadth is increased by 2%, the 1/x is 1/1.02=0.9804 or 98%, i.e. by increasing the breadth by 2%, the surface of the flat side of the combustion chamber must be decreased by 2% so that the combustion chamber volume remains the same.

Multiplying all the dimensions of the engine section by k (i.e. keeping the similarity on the normal to the power shaft plane, which means the ratio of any dimensions in the section plane is unchanged), the surface Su is multiplied by k^2.
On this reasoning, in order to multiply the Su by 1/x (as above) all the linear dimensions of the section must be multiplied by the sqrt(1/x)=(1/x)^0.5 (square root of y).

For instance, in order to decrease the flat surface Su by 2% (i.e.(1/x)=0.98), all the linear dimensions of the engine section must be multiplied by (1/x)^0.5=0.98^0.5=0.9899, which is about 0.99 or 99% (i.e. all the linear dimensions of the section view need to decrease by 1%).

So, in order to keep the capacity of the combustion chamber the same, an increase of the breadth by 2% causes a decrease of the L1 and L2 by 1%.

So, the surface to volume ratio becomes:

R’=S’/V’=(L1’+L2’)/Su’ + 2/b’= ((1/x)^0.5) * (L1+L2) / (Su/x) + 2/(x*b)= =x^0.5*(L1+L2)/Su + 2/(x*b)
(for x=1.02, x^0.5=1.01)

With b=8cm and L1=22cm and L2=23cm :

R= (45cm/8cc) + 2/8cm=5.88
(with V=654cc and b=8cm and a compression ratio of 10.2:1, the Su is: Su=(654/10.2)/8=8 at the TDC)

R’=(1.01*(45/8))+2/(8*1.02)=5.93

R1/R=1.01, i.e. by increasing the breadth of the rotor by 2%, the surface to volume ratio increases by nearly 1%.

Note: the surface to volume ratio can similarly be calculated at various angles of the power shaft (i.e. not exactly at the TDC).

Note: the surface to volume ratio as described by the equation
R=S/V=(L1+L2)/Su + 2/b
is the sum of two members.
When the first member is increased by 1.01 and the second member is decreased by 1.02, the sum of the two increases because in the case of the Wankel Rotary the first member (L1+L2)/Su is several times bigger than the second member.

Note: By decreasing the breadth b of the rotor, the surface to volume ratio R decreases. But there is a limit below which any further decrease of the breadth b of the rotor causes an increase of the surface to volume ratio; but this limit is far below the current dimensions of the Wankel rotary engine (a plot of the R versus the x is explanatory).

Thanks
Manolis Pattakos