Tuesday, December 23, 2014

Formula 1 turbines and enthalpy

A couple of interesting developments occurred around the exhaust systems on both the Ferrari and Mercedes-engined Formula 1 cars in 2014: the Ferrari-engined vehicles acquired insulation around the exhaust-pipes, and the Mercedes-equipped cars appeared with a so-called log-type exhaust.

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.

Another way of looking at it is that the energy released into the fluid from a combustion process may have been released at a constant pressure as the fluid performed work expanding against its environment. The internal energy e doesn't take that into account, but the enthalpy h = e + pv does. As the diagram above from Daniel Schroeder's Thermal Physics suggests, the enthalpy counts not only the current internal energy of a system, but the internal energy which would be expended creating the volume which the system occupies.

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.

As the exhaust gases pass through the turbine, they lose both kinetic energy and static pressure, but gain some internal energy due to friction. As a consequence, the entropy of the exhaust gas increases, and the enthalpy reduction is not quite as large as it would otherwise be (see diagram above from Fluid Mechanics, J.F.Douglas, J.M.Gasiorek and J.A.Swaffield).

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.


Unknown said...

Hello Professor McCabe !!

This is Peter again from Canada !!
I was thinking of asking you stuff along these lines. Apparently turbulence results in shear stress based losses that is converted to internal energy which apparently is of no use any more to an F1 car?

Can internal energy be recovered ? How does one attempt to measure it ?

Merry X-mas and Happy New Year !!

Your "presents" below:



Just found these a month ago. The first one is the most comprehensive paper ever that I've seen on Formula 1 car aerodynamics.

All of them are free (for the time
being). Just register your email
with them and you can read
these 20 or so amazing papers
for free and download the pdf files.

I will let you read the aero paper before I proceed to ask more questions.

I hope you are hard at work
on the aero analysis for Mark
Hughes next "F1 Retro" book.
His writing seems to get more
technical with time, presumably
your influence on him.

Nonetheless a CFD analysis
on the March 881 Newey car
from 1988 would be super.
The pictures of that car's
diffuser is mind blowing.
Far more complex than the diffuser
of the Tyrell 019 two years later
or even the 1992 McLaren MP4-7A
diffuser. You will notice
no corners or 90 degree angle
bends on the megaphone style
arches. I have just read in a book I bought on fluid mechanics
rectangular style diffuser channels general have a slightly
lower stall threshold compared
to conical or annular diffusers
with no such creases where the boundary layer thickens.

Anyways is there any way to post pictures to you (email or facebook)? I have some plots of
underbody pressure plots and want
your opinion on some things about them. I don't think I can post pictures into this comments section.


Gordon McCabe said...

Hi Peter.

That's a super find on the Honda site!

I think it's fair to say F1 has yet to find a use for turbulence. There are academic proposals, however, for harvesting such energy:


Unknown said...

I have a question. I have been reading this very old paper by some guy Dr. Otto G. Feil who most likely worked with the research group at Stanford University in the 1960's. I have talked to Gino Sovran on the phone
twice about the research there and more specifically race car diffusers. Putting aside the application to race cars, the pioneering research in the 1960's was based on two dimension water flow tables and vanes. Several publications focused on explaining how vanes worked. Stephen Kline was the head of that group. The initial research summed up the effect as chopping up a big diffuser into several parallel stall free passages/channels. Little diffusers designed for optimum
effectiveness and minimal losses.
It was found the length of the vanes did not need to span the entire length of the diffuser and in fact it could decrease the performance and reduce the potential pressure recovery.

(As an aside I as quite pleased to find this out as several diffusers on the pre-1994 neutered
diffusers had strakes that did not span the whole diffuser and often ended with this huge "lip"
that had not vanes/strakes on it at all).

But anyways this paper by
Feil attempted to prove (or did prove) that these vanes could be
adjusted using the concept of source point translation (for two
dimensional flow). The vane
angles could be increased
to "translate" this two dimensional source point downstream in the "throat"/
inlet pipe leading to the
diffuser. The whole paper
then goes on to evaluate the
effectiveness of this method.

My question is, what does
this source point translation
mean ? It is a purely
abstract concept? How does it work ?

Feil stated moving this source
point downstream would
cause a larger streamline
divergence through the vaned portion of the diffuser
resulting in less or no
stalled flow and a flow regime
much closer to the ideal
potential flow solution.

Here is a black and white video
of these experiments in the 1950's
on vaned water table diffusers.


This video is quite amazing.

Gordon McCabe said...

Cheers, I'll have a look if I get a chance in the near future.