Unleashing radiation in a wind-tunnel

There are currently two primary methods of wind-tunnel flow visualisation: Particle Image Velocimetry (PIV) and Laser Doppler Anemometry (LDA). Both techniques seed the airflow with tracer particles, and use lasers and optical detectors and cameras to provoke and record a pattern of scattered light. This poses a problem, in that the wheels, wings, and diffusers of interest to the aerodynamicist, are normally opaque to the passage of optical radiation. Hence, PIV and LDA experiments typically require the construction of transparent wings and aerodynamic appendages.

There is, however, a possible solution to this problem: Why not use radioactive isotopes to obtain quantitative flow data from wind-tunnel testing? One could inject a harmless radioactive tracer into the flow, such as one of those used in the medical imaging industry; technetium-99m-labelled DTPA (diethylene triamine pentaacetic acid) would be an obvious candidate here. One could then use gamma (ray) cameras to image the flow in a similar way that optical cameras are currently used in PIV and LDA.

There would, of course, be the need for some additional precautions. However, an isotope such as technetium-99 is considered sufficiently harmless to be injected into medical patients, and has a half-life of only 6 hours, so a wind-tunnel would not need to be decontaminated by the Nuclear Decommissioning Authority!

In fact, taking a closer look reveals that there are already significant areas of shared technology between wind-tunnel flow visualisation and lung scintigraphy, the use of gamma cameras to record 2-dimensional images formed by the emission of gamma rays from inhaled radioisotopes:

“99mTc labelled aerosols, 0.5-3 [microns] in size, are used routinely in lung ventilation studies. Radiolabelled aerosols are produced by nebulizing 99mTc-DTPA (or other appropriate 99mTc-products) in commerically available nebulizers,” (p276, Fundamentals of Nuclear Pharmacy, 2010, Saha).

When such aerosols are inhaled for lung scintigraphy, droplet sizes must be small enough to permit diffusion deep into the lungs; specifically, diameters smaller than 2 microns are preferred. In the case of wind-tunnel flow visualisation, the tracer particles must follow the flow. Given that the ratio of the tracer particle density to the flow density is typically of the order 10³ in gas flows, it is necessary to use tracer particles of diameter between 0.5 and 5 [microns], (p288, Springer Handbook of Experimental Fluid Mechanics, Tropea, Yarin and Foss, 2007). The method by which such tracer particles are injected into the airflow suggest close reciprocities with lung scintigraphy:


"By far the most common method of seeding gas flows is through liquid atomization. Of the many atomizer types available the common nebulizer used in inhalation devices is the most suitable...The droplet size depends primarily on the atomizing airflow rate and on the liquid used. Typical mean particle sizes range from 0.2 [microns] using DEHS...to 4-5 [microns] with water...For many applications, the common inhalation or medication nebulizer offers an economical solution and can be obtained through medical suppliers," (ibid., p293).

Thus, the medical and wind-tunnel industries already use the same nebulizing technology, and comparable droplet diameters. In particular, technetium-labelled DTPA has a comparable density, in solution, to the DEHS (di-ethyl-hexyl-sebacat) widely used for seeding airflows in PIV experiments.

One potential limiting factor, however, may be the current resolution of gamma-ray cameras. A gamma camera consists of a scintillation crystal, which converts gamma rays into optical-wavelength light, detected by photomultiplier tubes behind the crystal. However, despite a recent breakthrough which demonstrates that gamma rays can be focused, there is currently no equivalent of an optical lens. Instead, a collimator, consisting of an array of tiny pin-holes, is used. The collimator absorbs some of the radiation, limiting the sensitivity of a gamma camera, and also places a limit on the spatial resolution. Typical current resolution is 7-12mm at a distance of 10cm, (p96, Nuclear Medicine Instrumentation, Prekeges, 2009).

Despite such problems, the possibilities for development abound.

How Red Bull create streamwise vorticity

Red Bull arrived in Singapore this year with interesting little mini-arches in their front-wing, where the inner end of each main plane meets the 50cm-wide neutral central section. Craig Scarborough suggested at the time that "this shape is to create a vortex along the Y250 axis." As Craig explains elsewhere, "flow structures along this axis [250mm from the centreline] drive airflow under the floor towards the diffuser and around the sidepod undercuts."

So how does such a shape create streamwise vorticity? Well, the answer lies in a subfield of fluid mechanics called 'secondary flows', (with thanks to Professor Gary Coleman of Southampton University, for pointing me in the direction of this field). Such flows typically involve a primary flow - with the streamlines oriented in a particular direction, and a vorticity field perpendicular to the primary flow - in which there is also some type of differential convection to the primary flow. ('Convection' here simply means the transport of fluid by bulk motion, sometimes referred to as advection if there is any confusion with thermal convection). This differential convection tilts and stretches the vorticity lines, increasing the magnitude of the vorticity, and re-directing it in a streamwise orientation. The streamlines corresponding to this vorticity constitute the secondary motion, superimposed upon the primary streamlines.

This type of secondary flow is exactly what Red Bull are using to create separated streamwise vortices from the boundary layer on their front-wing. But before proceeding further, let's establish some notation. In what follows, we shall denote the streamwise direction as x, the direction normal to the wing as y, and the spanwise direction as z. We also have three components for the velocity vector field, which will be denoted as U, V and W, respectively. There is also a vorticity vector field, whose components will be denoted as ω_x, ω_y, and ω_z.

On the underside of the front-wing is a boundary layer, and like all boundary layers, there is a velocity gradient ∂U/∂y in a direction normal to the wing, given that the velocity is zero at the solid surface. This entails that the boundary layer possesses vorticity in a spanwise direction ω_z. The vortex lines in this boundary layer are perpendicular to the streamwise direction of flow. The trick is then to convert some of this spanwise vorticity into streamwise vorticity ω_x. It transpires that the way to do this is to create a lateral pressure gradient ∂p/∂z.

Now, the front-wing operates in ground effect, so the pressure in an elevated mini-arch will be less than it is underneath the adjacent portion of the main plane, creating just such a pressure gradient. The crucial point is that this lateral pressure gradient corresponds to the creation of a spanwise-gradient in the streamwise velocity ∂U/∂z > 0. To see why this is crucial, however, we need to look at the Vorticity Transport Equation (VTE) for ω_x, the streamwise component of vorticity. The effect in question can be seen by studying incompressible, inviscid, laminar flow, so we can simplify the VTE by omitting the turbulent and viscous terms to obtain:

Dω_x/Dt = ω_x(∂U/∂x) + ω_y(∂U/∂y) + ω_z(∂U/∂z)

The left-hand side here, Dω_x/Dt, is the material derivative of the x-component of vorticity; it denotes the change of ω_x in material fluid elements convected downstream by the flow. Now, we started with ω_z > 0 in the boundary layer, and by virtue of creating a lateral pressure gradient, we also have ∂U/∂z > 0. This means that the third term on the right-hand side in the equation above is positive, which (assuming the other pair of terms are non-negative) entails that Dω_x/Dt > 0.

Thus, the creation of the spanwise-gradient in the streamwise velocity ∂U/∂z, skews the initially spanwise vortex lines ω_z until they possess a significant component ω_x in a streamwise direction. The lateral pressure gradient has created streamwise vorticity.

As Peter Bradshaw writes, "if the lateral deflection that produces longitudinal vorticity extends for only a small spanwise direction, then the longitudinal vorticity becomes concentrated into a vortex," (Turbulent secondary flows, Ann. Rev. Fluid Mechanics 1987, p64). Which is exactly what Red Bull, and for that matter, many other Formula 1 teams, do when they incorporate mini-arches into their front-wings.

As a final aside, note that there is an interesting duality at the heart of fluid mechanics, namely that between a description which uses the velocity and pressure fields, and a description which uses the vorticity field instead. The vorticity has been described as "the sinews and muscles of fluid mechanics," (Kuchemann 1965, Report on the IUTAM Symposium on concentrated vortex motions in fluids, Fluid Mech. 21). P.A. Davidson points out that in the case of incompressible flow, because pressure waves can travel infinitely fast, the velocity vector field is a non-local field; the vorticity field, in contrast, is local. "While linear momentum can be instantaneously redistributed throughout space by the pressure field, vorticity can only spread through a fluid in an incremental fashion, either by diffusion or else by material transport (advection). Without doubt, it is the vorticity field, and not [the velocity field], which is the more fundamental," (Turbulence, 2004, p39).

An aerodynamicist with an especially strong visual imagination, perhaps someone who had been stimulated to develop such mental capabilities to compensate for dyslexia, might be able to develop a better understanding of the fluid flow around a Formula 1 car by thinking in terms of vorticity, or by developing the ability to mentally switch back and forth between the vorticity and velocity representations. Such an individual might even reject tools such as CAD and CFD, preferring instead to work on a drawing board...

Linking Red Bull's fuel loads to McLaren's rear-wing

One of the oddities of the 2011 Formula 1 season has been the contrast between the alacrity with which McLaren responded to the failure of their experimental 'bagpipe' exhaust system in pre-season testing, and their belated, late-season introduction of a Red-Bull style rear-wing, featuring a more powerful DRS effect.

Whilst a new and highly effective exhaust-blown diffuser was available on the McLaren from the first race, the new rear-wing combination, with smaller flap and larger main plane, only began to make sporadic appearances in practice from the middle of the season, and the system was only definitively installed for the Japanese Grand Prix at Suzuka.

Now, it's well-understood that a major aerodynamic component cannot be changed independently of the other primary aerodynamic components on a car, so McLaren presumably needed to make changes to the airflow feeding the rear-wing, or deal with the consequent change to the centre-of-pressure, before they could introduce the smaller flap design. Nevertheless, given the clear benefits of a powerful DRS system, as demonstrated by Red Bull from day one, McLaren do seem to have been a little tardy in this respect.

There is, however, a possible exculpatory explanation. Mark Hughes has recently drawn attention to the fact that during Friday practice this year, Red Bull have apparently used a second stint fuel load in the long run phase of these sessions, whilst McLaren have used a first stint fuel load. Conversely, Red Bull have tended to fuel more heavily on the short-run practice laps. This fuel-load combination has disguised Red Bull's real qualifying pace, relative to McLaren, but exaggerated their prospective race pace.

Perhaps, then, in the early stages of the season, McLaren came away from the races believing that their potential qualifying performance was stronger than their potential race performance, relative to Red Bull, and they therefore needed to continue optimising their car for race performance. This, in turn, meant retaining a larger rear-wing flap with a less powerful DRS stall.

Airbox spillage and fluidics

A couple of weeks ago, the FIA issued a Technical Directive to the Formula One teams, announcing that off-throttle blowing of the exhausts will be severely curtailed in 2012 by engine mapping restrictions.

In combination with stringent requirements on the position and angle of the exhaust exits, this is intended to minimise the exploitation of exhaust flow for aerodynamic purposes. It will, however, have a secondary consequence. As Gary Anderson recently explained, off-throttle exhaust flow also serves to reduce spillage from the airbox:

"In the past when the driver closed the throttle to slow for a corner, the airbox spillage became a lot worse. If the airflow attachment on the sides of the engine cover was not good, the performance of the rear wing would be compromised – not something the driver wants under braking or on corner entry.

"Step forward the blown diffuser. Hot or cold blowing allows the engine to work like an air pump, moving this airflow through and out of the exhausts. This reduces the potential turbulent airflow creating negative performance on the rear wing.

If off-throttle blowing of the exhausts is genuinely to be prohibited next year by means of engine mapping restrictions, this will presumably re-create the problem of airflow spilling out of the airbox when the driver lifts off the throttle on turn-in to a corner.

So here's an idea: Why not introduce a fluidic switch which, under certain circumstances, re-routes the airbox airflow through the chassis to the lower leading edge of the sidepods? This could have the joint benefit of boosting the velocity of the underbody flow, and improving airflow to the rear wing, just at the time when the driver most needs it, when the car is in pitch under braking and turn-in.

Exhaust-blown diffusers in 2012?

The 2012 Formula One regulations are intended to prohibit the use of exhaust-blown diffusers: stringent requirements have been placed on the location of the exhaust exit, and a recent announcement from the FIA suggests that engine mapping restrictions will be imposed to eliminate off-throttle pumping of the exhaust jet.

Craig Scarborough has produced a fantastic analysis of the exact restrictions to be placed on the location and orientation of the exhaust exit. In short, these move the exhaust exit to at least 500mm in front of the rear axle line, and 250mm above the reference plane underneath the car. The exhaust exit must also be angled upwards by at least 10 degrees. Hence, it will no longer be possible to blow the exhaust directly between the outer edge of the diffuser and inner face of the rotating rear wheel. Moreover, it will be illegal to place any sprung bodywork in a cone-shaped region, aligned with the exhaust exit, diverging at 3 degrees, and terminating at the rear axle line.

So will this be sufficient to eliminate exhaust-blown diffusers? Well, the first thing to note is that whilst it will be impossible to point the exhaust exit down at the diffuser, this won't necessarily prevent the exhaust jet itself from playing in that direction. When an exhaust jet exits into a cross-stream, the jet almost behaves like a deformable solid, as emphasised by F.L.Parra and K.Kontis in their 2006 paper, Aerodynamic effectiveness of the flow of exhaust gases in a generic formula one car configuration, from which the illustration here is taken.

If the exhaust exit is placed flush in the rearward face of sidepods sweeping downwards at a fairly steep angle, then the freestream airflow could deflect the exhaust jet towards the diffuser. The degree to which the jet is deflected is determined by the ratio between the velocity of the jet and the velocity of the cross-stream flow. The smaller the ratio, the more the jet is deflected.

Hence, there is something of a trade-off necessary here. To allow the exhaust jet to be deflected down towards the diffuser requires a lower exhaust jet velocity, yet for the exhaust jet to be effective in that region, requires higher jet velocities. There may be a compromise solution available here, an optimum exhaust velocity, which permits the jet to be directed towards the outer edge of the diffuser with sufficient velocity to have an effect, but that's something which only CFD and wind-tunnel experimentation will be able to determine...

Turbulence in Singapore

The fourth Grand Prix of Singapore will take place this weekend, and whilst the city-state forms an impressive backdrop for a race, overtaking has been notoriously difficult in previous years here. As difficult, in fact, as it is at Valencia, another street-circuit situated at sea level.

Which is intriguing, because the atmospheric density is greater at sea level, and this has certain aerodynamic ramifications. Assuming the pressure at Singapore is 101 kPa (the standard sea level pressure), a temperature of 20 degrees Celsius corresponds to an air density of 1.196 kg/m³.

Singapore, however, is also notoriously humid, and because water vapour is lighter than dry air, humid air is less dense than dry air. Assuming a relative humidity of 80%, and a temperature of 20 degrees, the air density at Singapore is about 1.190 kg/m³. (The tables here are taken from Soil mechanics for unsaturated soils, Fredlund and Rahardjo, p23-24).

In contrast, at a circuit such as Spa Francorchamps, which lies at an altitude of about 400m, the standard atmospheric pressure is about 95 kPa, and at a temperature of 20 degrees the air density is only 1.124 kg/m³.

Now, greater air density increases downforce and drag, but it also changes the Reynolds number:

Re = (airspeed x length x air density)/viscosity of air

The viscosity of air increases as a function of temperature, (as tabulated on the left here), but is largely independent of pressure. Hence, the increased air density entails that the Reynolds number of the airflow at Singapore (and Valencia) will be slightly greater than it is at venues such as Spa.

How much greater? Well, by a factor of 1.190/1.124 = 1.058. In other words, the Reynolds number at Singapore is about 5% greater than it is at Spa.

Now, the Reynolds number specifies the ratio of the inertial forces to the viscous forces, and this is important for quantifying the effect of turbulence. The greater the Reynolds number, the more turbulent the flow. In particular, as a rule-of-thumb, viscous dissipation of turbulent energy only kicks-in when the Reynolds number of the turbulent eddies approaches unity. Thus, if the air density at Singapore is 5% greater than that at Spa, the viscous dissipation of turbulence doesn't kick-in until the turbulent eddies reach a size about 5% smaller than at Spa.

If the premises here are correct, and the reasoning is valid, then the cars will have a slightly longer turbulent wake at Singapore (and Valencia), than they have at venues such as Spa. That would help to explain why it's so difficult to overtake at Singapore (and Valencia).

Nevertheless, circuit design is still by far the most important factor. Zandvoort, after all, was situated amongst the sand dunes bordering the North Sea, yet the racing there was amongst the best you could care to see.

The Miles-Phillips Mechanism

Two distinct mechanisms have been proposed to explain the means by which the wind is capable of generating waves and perturbations on the surface of lakes and oceans: Kelvin-Helmholtz instability (KHI), and the Miles-Phillips Mechanism.

Now, KHI reputedly requires a minimum wind speed of 6 m s^-1 to make waves grow against the competing effects of gravity and surface tension. Thus, whilst KHI is relevant to the generation of large wavelength perturbations, it is the Miles-Phillips Mechanism which is relevant to low wind speeds, and short-wavelength perturbations. In particular, the Miles-Phillips Mechanism involves a resonant interaction between the surface of the water and turbulent fluctuations in the air.

So, in the interests of science, I wandered down acorn-strewn paths to my local lake, to see if I could identify the Miles-Phillips Mechanism in action. What I observed over the course of several days, were a complex sequence of meta-stable and transient patterns. All the photos here were taken at the same time of day, around 2pm.

The first couple of pictures are from Friday 16th September. There was a light breeze blowing from left-to-right here, and this appeared to maintain a band of short wavelength perturbations in the middle of the lake. There is a clearly-defined transition, however, towards the margins of the lake, where the ripples were of a visibly longer wavelength. The shorter modes completely disrupt the reflective properties of the lake, but you can still see distorted images of the surrounding trees in the areas with the longer wavelength disturbances.

This is in sharp contrast with the pattern exhibited on two days previously, when a stable pattern of short-wavelength perturbations covered most of the lake. Note the absence of any reflective images at all.

On Sunday 18th September, the breeze was light, but rapidly fluctuating, and bands of short-wavelength perturbations would arise, and then dissipate, over a timescale of just a few minutes. In the first photo here, virtually the entire surface is smooth and reflective...

But within little more than five minutes, a band of short-wavelength ripples had covered the middle of the lake.

Such patterns would rise and fall, and drift back and forth across the lake as the local wind shifted and fluctuated. The wind variation was imperceptible from the viewpoint of the observer, and the patterns became as inexplicable and mesmerising as a mere screen-saver.

The cost of motorsport books

Here's a rather stark illustration of US/UK pricing differentials.

The Autocourse 60 Years of Grand Prix Motor Racing is available on Amazon.co.uk for a whopping £44.96. Exactly the same book is also available on Amazon.com for the rather more affordable sum of $41.97, which equals £26.58 at current exchange rates.

There is, it seems, a somewhat different pricing strategy in different markets...

Formula 1 aerodynamics in the 1970s

For most of the 1970s, there seems to have been a fundamental schism in the front-end aerodynamic concept of Formula 1 cars. Some of the cars, such as the McLarens, Lotuses and Ferraris, continued to run with front wings, but another group appeared to abandon that concept for most of the decade, running instead a front spoiler/airdam/splitter. This latter group included luminaries such as March, Brabham and Tyrrell, with Jackie Stewart winning the 1971 and 1973 World Championships in Tyrrell designs sporting just such a front-end.

So what was the idea? Well, part of the motivation was presumably to reduce the lift, drag and turbulence created by the front wheels. The front spoilers were much wider than front wings, and partially shrouded the front wheels, diverting airflow down the sides of the car.

So that was part of the idea. The other possible motive is perhaps more interesting, because it involves ground-effect. A spoiler/airdam provides a vertical barrier which (i) maximises the high pressure stagnation point at the front of the car, and (ii) accelerates the airflow through the restricted gap between the spoiler/airdam and the ground surface. A horizontal splitter projecting from the bottom of the spoiler/airdam then takes advantage of the high pressure of the stagnation point to generate some extra downforce.

A front airdam/spoiler is partially, then, a ground-effect device, which perhaps explains why cars such as the Brabhams and Tyrrells were still able to win Grands Prix against those utilising conventional front-wing arrangements. The photo here shows a Tyrrell running quite a degree of rake, which would serve to accentuate the ground-effect of the front spoiler.

So, perhaps surprisingly, ground-effect in Formula 1 actually predates the underbody venturi tunnels and skirts used on the Lotus 78/79. And in fact, Gordon Murray began experimenting with ground-effect on the Brabham BT44 back in 1974, arriving at "an inch-deep underbody vee, something like a front airdam, but halfway down the car." (Vacuum Clean-Up, Adam Cooper, Motorsport, May 1998, pp64-69).

The introduction of underbody venturi and skirts presumably spelt the death-knell for front spoilers, as the emphasis then shifted to feeding the underbody with as much airflow as possible. Still, it would be interesting to hear from those involved, what the initial impetus was for adopting those spoilers, and how effective they really were.

Suspension camber in Grand Prix racing

Formula One's latest cause celebre revolves around Red Bull's decision to race at Spa with a greater degree of negative front-wheel camber than recommended by Pirelli.

Negative camber simply means that both wheels are inclined inwards at the top. The benefit of this is that the outer wheel generates greater lateral force on the entry to a corner (so-called camber thrust, similar to the way a motorbike rider generates lateral force by keeling the bike over), but the disadvantage is that the inner shoulders of both front tyres will suffer greater stress when the car runs in a straightline, and at Spa this caused both Red Bull drivers to suffer tyre blisters.

It's interesting to recall, however, that in the pre-war era of Grand Prix racing, the cars were actually set-up with visible levels of positive front-end camber. In other words, the front-wheels were inclined outwards at the top.

So why was this? Well, there seem to be at least two distinct reasons. The first was relevant prior to the mid-1930s, when cars employed what now look like rather primitive beam axle front suspension systems. Under the extra load generated by braking, the front axle would sag, and pull the front wheels inward at the top, as illustrated in this diagram taken from Matt Joseph's excellent 'Collector Car Restoration Bible: Practical Techniques for Professional Results'. Thus, a degree of positive static camber was necessary to offset this effect.

The eventual transition to independent, double-wishbone, ball-joint suspension, meant that wheel camber was no longer affected by the loads generated under straightline braking (or acceleration). However, even after the adoption of more modern suspension in the mid-1930s, the Mercedes and Auto Union Grand Prix cars continued to run with appreciable levels of positive camber. The primary reason for this appears to involve a concept called the scrub radius.

Now, when the front wheels of a car are steered, the wheels pivot around some axis. Originally, this steering axis was implemented with a physical rod called a king-pin, which was attached to each end of the beam axle. With independent, double-wishbone suspension, this king-pin is replaced by the line drawn between the upper and lower ball-joints at the outer end of the wishbones. This axis is also the line along which the weight of the car is projected down to the ground. The distance between the point where this line intersects the ground and the contact patch of the tyre, is called the scrub radius.

As Joseph explains (p261), a non-zero scrub radius causes several problems: it puts large forces into the king-pins; it acts like a lever, thereby putting large shocks into the steering; and it makes it harder to steer a car. Positive camber was the common solution devised for minimising the scrub radius. If the wheels are inclined outwards at the top, then the contact patches will be placed directly under, or at least closer to, the point where the steering axis intersects the road surface.

There's just one more complication to consider. Under the chassis roll generated by cornering, a double-wishbone suspension system will experience a positive camber increment on the more heavily loaded outer wheel, and a negative camber change on the lightly-loaded inner wheel. By setting a car up with a degree of positive static camber, this will result in the outer wheel acquiring an even greater degree of positive camber during cornering, while the inner wheel reaches a more vertical inclination, as nicely demonstrated in the photo of the Mercedes above.

Spot the difference

This is Vittorio Brambilla, otherwise know as the Monza Gorilla, and best remembered for crashing immediately after winning the 1975 Austrian Grand Prix.

Not to be confused with...

Michela Vittoria Brambilla, Italian beauty queen, philosophy-graduate, businesswoman, and erstwhile Minister of Tourism in Silvio Berlusconi's government.