Tuesday, December 23, 2014
The purpose of the insulation was to increase the temperature of the exhaust gases entering the turbine. Similarly, increasing the exhaust gas temperature was a purported beneficial side-effect of the log-type exhaust on the Mercedes.
A couple of general points about the physics of turbines might provide some useful context here. First, the work done by the exhaust gases on the turbine comes from the total enthalpy (aka stagnation enthalpy) of the exhaust gas flow.
This is perhaps a subtle concept. The total energy E in the fluid-flow through any type of turbine consists of:
E = kinetic energy + potential (gravitational) energy + internal energy
However, to understand the change of fluid-energy between the inlet and outlet of a turbine, it is necessary to introduce the enthalpy h, the sum of the internal energy e and the so-called flow-work pv:
h = e + pv ,
where p is the pressure, and v is the specific volume, (the volume occupied by a unit mass of fluid).
One way of looking at the flow-work is that it is part of the energy expended by the fluid maintaining the flow; the fluid performs work upon itself, (in addition to the external work it performs exerting a torque on the turbine), and this work can be divided into that performed by the pressure gradient and the work done in compression/expansion.
For a system which is flowing, it possesses energy of motion (kinetic energy) in addition to enthalpy. The so-called total enthalpy hT is simply the sum of the enthalpy and kinetic energy:
hT= e + pv + 1/2 ρ v2 ,
where ρ is the mass density and v is the fluid-flow velocity.
This quantity is also called the stagnation enthalpy because if you brought a fluid parcel to a stagnation point, at zero velocity, without allowing any heat transfer to take place to adjacent fluid or solid walls, the kinetic energy component of the total energy in that parcel would be transformed into enthalpy.
In the case of a Formula 1 turbine, there is no difference in the potential energy of the exhaust gas at the inlet and outlet, so this term can be omitted from the expression for the change in energy. What remains entails that the rate at which a turbine develops power is determined by subtracting the enthalpy-flow rate at the outlet from the enthalpy-flow-rate at the inlet. The greater the decrease in total enthalpy, the greater the power generated by the turbine.
However, (and here is the crux of the matter), for a given pressure difference between the turbine inlet and outlet, the reduction in total enthalpy increases with increasing temperature at the inlet. In other words, this is another expression of the fact that the thermal efficiency of a turbine is greater at higher temperatures (a fact which also dominates the design of nuclear reactors).
So, all other things being equal, increasing exhaust gas temperature with insulation or a log-type exhaust geometry will increase the loss of total enthalpy between the inlet and outlet of the turbine, increasing the power generated by the turbine.
However, there is another side to this coin: the required pressure drop between the turbine inlet and outlet for a desired enthalpy-reduction, decreases as the inlet temperature increases. Hence, if there is a required turbine power-level, it can be achieved with a lower pressure drop if the exhaust gases are hotter. This could be important, because the lower the pressure at the inlet side of the turbine, the lower the back-pressure which otherwise potentially inhibits the power generated by the internal combustion engine upstream. So increasing exhaust gas temperatures might be about getting the same turbine power with less detrimental back-pressure on the engine.