Tuesday, August 04, 2015

Aldermaston Grand Prix circuit

There was sad news for those working in the British nuclear sector last week, when it was announced that there will be 500 job losses at AWE Aldermaston.

However, there may be hope on the horizon for the minions of Aldermaston, for the aerial photograph provided by the BBC clearly indicates that the former RAF Aldermaston airfield is the perfect location for a Grand Prix circuit.


The prospective layout sketched above suggests a mix of slow-speed 90-degree corners and long-straights, with a high braking and traction requirement. Particularly exciting is the long main straight, which resembles that at Macau, including a flat-out kink leading onto a long, wide stretch which eventually funnels into the heavy-braking area for a tight hairpin. Rather like Turn 1 at the Cleveland airport circuit in the USA, this would, no doubt, become a key overtaking spot.

One imagines wisps of tyre-smoke mixing with the gaseous tritium discharges, as the drivers battle it out, wheel-to-wheel. Happily, with the lower noise emissions of contemporary Formula 1, there seems little chance of triggering an unexpected criticality in one of the facilities, but in such an event the odd blue flash would simply add to the razzmatazz of the event.

The nearby town of Tadley might seem an unlikely host for a round of the World Championship, but in some respects it is not dissimilar to parts of Azerbaijan, which will feature on the Formula 1 calendar for the first time in 2016

Ferrari, cheating, and pop-off valves

The September 2015 issue of Motorsport Magazine contains an interesting interview with erstwhile McLaren and Ferrari engineer, Gordon Kimball. Together with some revealing anecdotes about Senna and Berger, Kimball also concedes the following:

"In 1988 I was engineering Gerhard Berger in the F187/88C. That was the year McLaren dominated with Honda and Bernie did all he could to help us. It was the era of turbos and pop-off valves and we had a low-pressure passage that went past the pop-off valve and would pull it open, so we could run more boost. We kept pushing that further and further, waiting to get caught, but we never were. I guess Bernie wanted somebody to try to beat McLaren, so he helped us."

FISA Pop-off valve (drawing by Bent Sorenson, reproduced from 'The Anatomy and Development of the Formula One Racing Car from 1975', Sal Incandels, p200)
Now, the first point to make here is that it is actually fairly well-known that engine manufacturers were flouting the pop-off valve regulations in the late 1980s. The pop-off valve was first introduced in 1987, when it was intended to restrict turbo boost pressure to 4.0 bar. The valve was supplied by the governing body, FISA, and attached to the plenum chamber, upstream of the inlet runners to each cylinder. A new design pop-off valve was then introduced for 1988, which was intended to restrict boost pressure to 2.5 bar.

Ian Bamsey noted the following in his monumental 1988 work, The 1000bhp Grand Prix cars, "In 1987 some engines were coaxed to run at more than 4.0 bar. With a carefully located single pop off valve merely an irritating leak in a heavily boosted system as much as 4.4 bar could be felt in the manifold. The key was in the location of the valve. It was possible to position it over a venturi in the charge plumbing system. Air gained speed through the venturi losing pressure. Either side of the venturi the flow was correct and the pressure was higher," (p29).

In fact, there appears to have been at least two distinct methods of flouting the 4.0 bar limit. If one attached the pop-off valve over a venturi, then one could keep the valve closed (contra Kimball's explanation) even if the effective boost pressure was greater than 4.0 bar. A second method simply involved inducting compressed air into the plenum chamber at a greater mass-flow rate than the open pop-off valve could vent it:

 "Turbo boost was theoretically restricted to four bar via popoff valves, but there was a way around this on self-contained V6s like the Honda. They required just one pop-off valve (as opposed to those like the Porsche and Ford which effectively ran as two separate three-cylinder units and so needed two pop-off valves) by overboosting, forcing the pop-off to open and then controlling it against boost. It meant 900bhp in races, 1050bhp in qualifying," (Mark Hughes, Motorsport Magazine, January 2007, page 92).

Indeed, the general suggestion at the time is that it was Honda, rather than Ferrari, which first identified these loophole(s). Bamsey makes this point in his superb 1990 work, McLaren Honda Turbo - A Technical Appraisal: "By mid-season [1987]...Ferrari is believed to have achieved levels of 4.1/4.2 bar through careful location of the pop off valve, a technique Honda is alleged to have pioneered," (p92).

The next question, however, concerns what happened in 1988, when the more stringent 2.5 bar limit was imposed, and a new design of pop-off valve was supplied to the teams. This valve (perhaps by deliberate design), was somewhat tardy in closing once it has been opened:

"The new pop off opened in a different manner and once opened pressure tumbled to 2.0 bar and still the valve didn't close properly...on overrun the effect of a shut throttle and a still spinning compressor (the turbine not instantly stopping, of course) could cause pressure in the plenum to overshoot 2.5 bar. In blowing the pop off open, that adversely affected the next acceleration...The answer to the problem was in the form of the so called XE2 [specification engine]...run by all four Honda cars in the San Marino Grand Prix.

"The XE2 changed the throttle position, removing the separate butterfly for each inlet tract and instead putting a butterfly in each bank's charge plumbing just ahead of the plenum inlet and thus ahead of the pop off," (ibid 1990, p91-92).

No questions of dubious legality there. However, Bamsey also explains that an XE3 version of the engine was developed by Honda, purportedly for exclusive use in the high-altitude conditions of Mexico City: "The Mexican air is thin - the pressure is around a quarter bar - so the turbine has to work harder. Back pressure [in the exhaust manifold] becomes a potential problem, affecting volumetric efficiency and hence torque. Power is a function of torque and engine speed: Honda sought higher revs to compensate. Thus the XE3 employed an 82mm bore size [compared to 79mm on the XE2] and it was apparently tuned for a higher peak power speed. It was a complete success and on occasion was tried for qualifying elsewhere thereafter (in particular, at Monza)," (ibid. 1990, p92).

What's interesting here is that the XE3 seems to have caused some scrutineering difficulties at Mexico. Road and Track magazine reported that there was "a claim that Honda had built vortex generators into its system - which would allow it to use more than 2.5 bar - and FISA scrutineers spent an unusual amount of time examining the McLarens in Mexico," (Road and Track, volume 40, p85).

Generating a vortex would offer an alternative means of keeping the pop-off valve closed. Even with a constant diameter pipe, the pressure could be lowered by transforming some of the pressure energy into the rotational energy of a vortex. One would presumably need an expanding section downstream to burst the vortex in a controlled manner, but it does offer a method of reducing the pressure without using a venturi. It's intriguing to read that an engine ostensibly developed for high-altitude conditions was used in qualifying for the rest of the season...

So perhaps it would be wrong to cast Ferrari here in their stereotypical role as regulatory bandits. Although Kimball does also suggest that their fuel-tanks carried somewhat more than the mandatory 150 litres of fuel when they won the Italian Grand Prix that year!

Tuesday, May 05, 2015

A history of porpoising



Skirted ground-effect Formula 1 cars of the late 1970s and early 1980s were occasionally afflicted by a type of instability referred to as 'porpoising'. Many cars suffered, but the phenomenon is nicely described by Peter Wright in relation to the development of the Lotus T80:

"The car was so sensitive that, above a certain critical speed, it became aerodynamically unstable in pitch. One test day at Silverstone, Mario Andretti coined the term 'porpoising' to describe the phenomenon when he observed daylight under the front wheels while at speed on the straight.

"Since 1977 I had been working with David Williams, Head of the Flight Instrumentation Department at the Cranfield College of Aeronautics. He had designed and built a digital data system for use on the T78 when it had become apparent that it would be absolutely essential to gather data from the chassis in order to progress with the development of ground effect. When the T80 porpoising started, I discussed the phenomenon with him, and he offered to model it and validate the results with the data we had. He established that it was an aero-elasticity problem, akin to flutter in an aircraft wing. The changing aerodynamic loads, as the car bounced and pitched, excited the pitch and heave modes of the sprung mass on its springs and tires." (Formula 1 Technology, p36 and p308.)

However, pace Wright, the same phenomenon had already been identified and named at least as early as the 1940s, albeit in the field of seaplane hydrodynamics; specifically, during the take-off and landing of such craft. A Wartime Report issued by NACA in June 1943, begins:

"Porpoising is a self-sustaining oscillatory motion in the vertical longitudinal plane...Observations of porpoising show that there are two principal oscillatory motions (1) a vertical oscillation of the center of gravity and (2) an angular oscillation about the center of gravity. These two motions are seen to have the same period but to differ in phase." (Some systematic model experiments on the porpoising characteristics of flying-boat hulls, Kenneth S.M. Davidson and F.W.S. Locke Jr, p7).

The British were also heavily involved in the early study of porpoising, an Aeronautical Research Council report in 1954 defining the phenomenon as follows:

"Porpoising, basically, consists of a combination of oscillations in pitch and heave. It includes both stable and unstable oscillations, a stable oscillation being one which damps out. (A review of porpoising instability of seaplanes, A.G.Smith and H.G.White, p5).

All of which is an important reminder that ground-effect was of crucial importance to hydroplanes long before Formula 1 happened upon the phenomenon.

Saturday, April 04, 2015

Optimal control theory and Ferrari's turbo-electric hybrid

The Department of Engineering Science at the University of Oxford, published an interesting paper in 2014 which appears to shed some light on the deployment of energy-recovery systems in contemporary Formula One.

Entitled Optimal control of Formula One car energy recovery systems, (a free version can be downloaded here), the paper considers the most efficient use of the kinetic motor-generator unit (ERS-K), and the thermal motor-generator unit (ERS-H), to minimise lap-time, given the various regulatory constraints. (Recall that the primary constraints are: 100kg fuel capacity, 100kg/hr maximum fuel flow, 4MJ Energy Store capacity, 2MJ per lap maximum energy flow from ERS-K to the Energy Store, and 4MJ per lap maximum energy flow from the Energy Store to the ERS-K). The paper outlines a mathematical approach to this Optimal Control problem, and concludes with results obtained for the Barcelona track.

In the course of the paper, a number of specific figures are quoted for engine power. For example, the power of the internal combustion (IC) engine under the maximum fuel-flow rate, with the turbo wastegate closed, is quoted as 440kW (590bhp); it is claimed that by having the turbo wastegate open, the power of the IC engine can be boosted by 20kW (~27bhp), but in the process the ERS-H has to use 60kW of power from the Energy Store to power the compressor; and with the wastegate closed, the 20kW reduction in IC power is compensated by the 40kW generated by the ERS-H. (Opening the wastegate boosts IC power because the back-pressure in the exhaust system is reduced).

Running with the wastegate closed is therefore considered to be the most efficient solution for racing conditions. However, the paper also considers qualifying conditions, where the Energy Store can be depleted over the course of a lap without any detrimental consequences:

"In its qualifying configuration the engine is run with the waste gate open for sustained periods of time when maximum engine power is needed. During these periods of time the energy store will be supplying both the MGU-K and the MGU-H, with the latter used to drive the engine boost compressor...In contrast to the racing lap, the waste gate is typically open when the engine is being fully fuelled. On the entry to turns 1, 4, 7 and 10 the waste gate is being closed a little before simultaneously cutting the fuel and the MGU-K."


Professor of Control Engineering David Limebeer delivered a presentation of the work at a Matlab conference the same year (video here). Another version of the work, Faster, Higher and Greener, featuring Spa rather than Barcelona, was published in the April 2015 edition of the IEEE Control Systems Magazine. In his Matlab presentation, Professor Limebeer also credits Peter Fussey, Mehdi Masouleh, Matteo Massaro, Giacomo Perantoni, Mark Pullin, and Ingrid Salisbury.

After reading their work, I e-mailed Professor Limebeer, and asked if he'd considered collaborating with a Formula One team. I received a slightly odd response. After a further internet search, I found out why. In the November 2014 issue of Vehicle Electronics, David reports "We have done this work with one of the Formula One teams, but we can’t tell you which one."

Which is totally understandable. University departments have to protect the confidentiality of their work with Formula One teams. Unfortunately, however, the University of Oxford, Department of Engineering Science Newsletter 2013-2014, proudly reveals:

The Ferrari F1 Connection. 
Mr Stefano Domenicali, Scuderia Ferrari Team Principal, visited the Department in May 2013 to deliver the annual Maurice Lubbock Memorial Lecture. During this lecture he announced the evolving research partnership between the University and Ferrari.

DPhil Engineering Science students Chris Lim, Giacomo Perantoni and Ingrid Salisbury are working with Ferrari on novel ways to improve Formula One performance. Chris Lim said: “I’m very excited that I’ll be the first student working with Ferrari in the Department’s Southwell Laboratory, under the supervision of Professor Peter Ireland, the Department’s Professor of Turbomachinery. It’s a privilege to work with a prestigious manufacturer such as Ferrari in an industry like Formula One where the application of thermo-fluids has such a large impact”.

Pictured from left to right are: Chris Lim (postgraduate), Ingrid Salisbury (postgraduate), Mr Stefano Domenicali, Giacomo Perantoni (postgraduate) and Professor David Limebeer (supervisor to Giacomo Perantoni and Ingrid Salisbury). 

In light of this, then, the figures quoted in these papers can be interpreted as pertaining to Ferrari's turbo-electric hybrid. The first paper was submitted for publication in late 2013, and the assumptions used there are the same as those used in the 2015 paper, so it appears that Ferrari development data from no later than 2013 was used throughout.

Monday, March 09, 2015

Adrian Newey and the bar-headed goose

The April edition of Motorsport Magazine contains a fabulous F1 season preview from Mark Hughes, which includes the news that Adrian Newey has recently been taking a break in the Himalayas.

Now, whilst it's likely that the principal purpose of this expedition was to enlighten the Dalai Lama on the importance of using large-eddy simulation to understand the interaction of brake-duct winglets with the spat vortex, it's also possible that Adrian was drawn by the legendary bi-annual migration of the bar-headed goose.

 

These birds are amongst the highest-flying in the world, and travel across the Himalayas in a single day. William Bryant Logan claims in Air: Restless Shaper of the World (2012), that "the bar-headed goose has been recorded at altitudes of over thirty-three thousand feet. This is the altitude where your pilot remarks that the outside temperature is 40 degrees below zero, where the great fast-flowing rivers of the jet streams set weather systems spinning. The air here contains only one-fifth of the oxygen near sea-level, where the goose winters in lowland India wetlands and marshes. Yet in the space of a few hours the bird can fly from the wetlands to the top of the high peaks and then out onto the world's largest high plateau. There are lower passes through the mountains, but the goose does not take them. It may even preferentially go higher."

However, it seems that some of the claims made for the bar-headed goose lack empirical support. Research led by Bangor University tracked the bar-headed geese with GPS as they migrated over the Himalayas, and reached the following conclusion in 2011:

"Data reveal that they do not normally fly higher than 6,300 m elevation, flying through the Himalayan passes rather than over the peaks of the mountains...It has also been long believed that bar-headed geese use jet stream tail winds to facilitate their flight across the Himalaya. Surprisingly, latest research has shown that despite the prevalence of predictable tail winds that blow up the Himalayas (in the same direction of travel as the geese), bar-headed geese spurn the winds, waiting for them to die down overnight, when they then undertake the greatest rates of climbing flight ever recorded for a bird, and sustain these climbs rates for hours on end."


A more recent iteration of the research, The roller-coaster flight strategy of bar-headed geese conserves energy during Himalayan migration, (Science, 2015), suggests that the geese "opt repeatedly to shed hard-won altitude only subsequently to regain height later in the same flight. An example of this tactic can be seen in a 15.2-hour section of a 17-hour flight in which, after an initial climb to 3200 m, the goose followed an undulating profile involving a total ascent of 6340 m with a total descent of 4950 m for a net altitude gain of only 1390 m. Revealingly, calculations show that steadily ascending in a straight line would have increased the journey cost by around 8%. As even horizontal flapping flight is relatively expensive, the increase in energy consumption due to occasional climbs is not as important as the effect of reducing the general costs of flying by seeking higher-density air at lower altitudes.

"When traversing mountainous areas, a terrain tracking strategy or flying in the cool of the night can reduce the cost of flight in bar-headed geese through exposure to higher air density. Ground-hugging flight may also confer additional advantages including maximizing the potential of any available updrafts of air, reduced exposure to crosswinds and headwinds, greater safety through improved ground visibility, and increased landing opportunities. The atmospheric challenges encountered at the very highest altitudes, coupled with the need for near-maximal physical performance in such conditions, likely explains why bar-headed geese rarely fly close to their altitude ceiling, typically remaining below 6000 m."

Tuesday, March 03, 2015

Driver core-skin temperature gradients and blackouts

Whilst it is highly beneficial to reduce the surface-to-bulk temperature gradient of a racing-tyre, the same cannot be said for the cognitive organisms controlling the slip-angles and slip-ratios of those tyres.

A 2014 paper in the Journal of Thermal Biology, Physiological strain of stock car drivers during competitive racing, revealed that not only does the core body temperature increase during a motor-race, (if we do indeed count a stock-car race as such), but the skin temperature can also rise to such a degree that the core-to-skin temperature delta decreases from ~2 degrees to ~1.3 degrees.


The authors suggest that a reduced core-to-skin temperature gradient increases the cardiovascular stress "by reducing central blood volume." Citing a 1972 study of military pilots, they also suggest that when such conditions are combined with G-forces, the grayout (sic) threshold is reduced.

Intriguingly, in the wake of the Fernando Alonso's alien abduction incident at Barcelona last week, they also assert that "A consequence of this combination may possibly result in a lower blackout tolerance."

Monday, March 02, 2015

McLaren front-wing vortices, circa 2003

Academic dissertations conducted in association with Formula 1 teams tend to be subject to multi-year embargoes. Hence, Jonathan Pegrum's 2006 work, Experimental Study of the Vortex System Generated by a Formula 1 Front Wing, is somewhat outdated, but might still be of some interest to budding aerodynamicists.

Currently an Aerodynamics Team Leader at McLaren, Pegrum's study concentrated on a front-wing configuration not dissimilar from that on an MP4-18/19 (2003-2004).

A constellation of four co-rotating vortices were created: (i) a main bottom edge vortex, generated by the pressure difference across the endplate due to the low pressure under the wing; (ii) a top edge vortex, generated by the pressure difference across the endplate due to the high pressure above the wing; (iii) a canard vortex, a leading edge vortex generated by the semi-delta wing ('canard') attached to the outer surface of the endplate; and (iv) a footplate vortex, generated by the pressure-difference across the footplate operating in ground-effect. 


Pegrum shows (in the absence of a wheel, below), that the strongest vortices are the bottom-edge and top-edge vortices, but all four mutually interact in the manner of unequal, co-rotating vortices, undergoing the early stages of a merger.

Now, whilst co-rotating vortices have a tendency to merge, counter-rotating vortices have a tendency to repel. Pegrum highlights the 1971 work of Harvey and Perry, Flowfield Produced by Trailing Vortices in the Vicinity of the Ground, which demonstrated that when a vortex spinning around an axis in the direction of the freestream passes close to a solid surface, it tends to pull a counter-rotating vortex off the boundary layer of the solid surface, (as illustrated below by Puel and de Saint Victor, Interaction of Wake Vortices with the Ground, 2000). 


The interaction between these counter-rotating vortices is such that the primary vortex is repelled away from the solid surface. This phenomenon, of course, is still very much of interest when it comes to the Y250 vortex and its cousins.

Thursday, February 19, 2015

Proof that Formula 1 was better in the past

If you're a long-time Formula 1 fan, then the chances are that you believe the sport was better in the past. However, the chances are that you will have also read arguments from younger journalists and fans, to the effect that Formula 1 in the modern era is better than it was in the past.

Fortunately, there is an objective means to resolve this dispute: churn.

In sport, churn provides a straightforward measure of the uncertainty of outcome. Churn is simply the average difference between the relative rankings of the competitors at two different measurement points. One can measure the churn at an individual race by comparing finishing positions to grid positions; one can measure the churn from one race to another within a season by comparing the finishing positions in each race; and one can measure the inter-seasonal churn by comparing the championship positions from one year to another.

The latter measure provides an objective means of tracking the level of seasonal uncertainty in Formula 1, and F1 Data Junkie Tony Hirst has recently compiled precisely these statistics, for both the drivers' championship and the constructors' championship, (see figures below). In each case, Hirst compiled the churn and the 'adjusted churn'. The latter is the better measure because it normalises the statistics using the maximum possible value of the churn in each year. The maximum can change as the number of competitors changes.

The results for the drivers' championship indicates that churn peaked in 1980. Given that the interest of many, if not most spectators, is dominated by the outcome of the drivers championship, this suggests that Formula 1 peaked circa 1980.


The results for the manufacturers' championship are slightly different, suggesting that uncertainty peaked in the late 1960s, (although the best-fit line peaks in the middle 1970s).

  
One could, of course, make the alternative proposal that the churn within individual races is more important to spectators' interest, but at the very least we now have an objective statistical measure which provides good reason for believing that Formula 1 was better in the 1970s and early 1980s.

Monday, February 16, 2015

Lovelock and emergentism

In James Lovelock's 2006 work, The Revenge of Gaia, he concludes the chapter entitled What is Gaia? with a description of the regulator in James Watt's steam engine, and the following argument:

"Simple working regulators, the physiological systems in our bodies that regulate our temperature, blood pressure and chemical composition...are all outside the sharply-defined boundary of Cartesian cause-and-effect thinking. Whenever an engineer like Watt 'closes the loop' linking the parts of his regulator and sets the engine running, there is no linear way to explain its working. The logic becomes circular; more importantly, the whole thing has become more than the sum of its parts. From the collection of elements now in operation, a new property, self-regulation, emerges - a property shared by all living things, mechanisms like thermostats, automatic pilots, and the Earth itself.

"The philosopher Mary Midgley in her pellucid writing reminds us that the twentieth century was the time when Cartesian science triumphed...Life, the universe, consciousness, and even simpler things like riding a bicycle, are inexplicable in words. We are only just beginning to tackle these emergent phenomena, and in Gaia they are as difficult as the near magic of the quantum physics of entanglement."

Now Lovelock is an elegant and fascinating author, but here his thought is lazy, sloganistic and poorly-informed. There are multiple confusions here, and such confusions are endemic amongst a number of writers and journalists who take an interest in science, so let's try and clear them up.

Firstly, we encounter the slogan that a system can be 'more than the sum of its parts'. Unfortunately, the authors who make this statement never seem to conjoin the assertion with a definition of what they mean by the phrase 'sum of its parts'. Most scientists would say that the sum of the parts of a system comprises the parts of the system, their properties, and all the relationships and interactions between the parts. If you think that there is more to a whole system than its parts, their properties and the relationships between the parts, then that amounts to a modern form of vitalism and/or dualism, the notion that living things and/or conscious things depend upon non-physical elements. Calling it 'emergentism' is simply a way of trying to dress up a disreputable idea in different language, rather in the manner than creationism was re-marketed as 'intelligent design'.

Assertions that a system can be more than the sum of its parts are frequently combined with attacks on so-called 'reductionistic' science. Anti-reductionistic authors can often be found pointing out that whole systems possess properties which are not possessed by any of the parts of which that system is composed. However, if such authors think this is somehow anti-reductionistic, then they have profoundly mis-understood what reductionistic science does. Scientists understand that whole systems possess properties which are not possessed by any of the parts; that's precisely because the parts engage in various relationships and interactions. A primary objective of reductionistic science is to try and understand the properties of a whole system in terms of its parts, and the relationships between the parts: diamond and graphite, for example, are both composed of the same parts, (carbon atoms), but what gives diamond and graphite their different properties are the different arrangements of the carbon atoms. Explaining the different properties of carbon and diamond in terms of the different relationships between the parts of which they are composed is a triumph of so-called 'reductionistic' science.

The next confusion we find in Lovelock's argument is the notion that twentieth-century science was somehow linear, or Cartesian, and non-linear systems with feedback somehow lie outside the domain of this world-view. Given the huge body of twentieth-century science devoted to non-linear systems, this will come as something of surprise to many scientists. For example, in General Relativity, (that exemplar of twentieth-century science), the field equations are non-linear. Lovelock might even have heard the phrase 'matter tells space how to curve, and space tells matter how to move'; a feedback cycle, in other words! Yet General Relativity is also a prime exemplar of determinism: the state of the universe at one moment in time uniquely determines its state at all other moments in time. There is clearly no reason to accept the implication that cause-and-effect must be confined to linear chains; non-linear systems with feedback are causal systems just as much as linear systems.

It is amusing the note that Lovelock concludes his attack on so-called 'Cartesian' science with an allusion to quantum entanglement. Clearly, quantum entanglement is a product of quantum physics, that other exemplar of twentieth century physics. So, in one and same breath, twentieth century science is accused of being incapable of dealing with emergentism, yet also somehow yields the primary example of emergentism!

Authors such as Lovelock, Midgley, and their journalistic brethren, are culpable here of insufficient curiosity and insufficient understanding. The arguments they raise against twentieth-century science merely indicate that they have failed to fully understand twentieth-century science and physics.

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.