The schlieren apparatus

Anyone wanting to study supersonic flow will want is to be able to “see” how air behaves in some relevant application. The schlieren apparatus has been developed for this purpose and utilises the fact that light passing through air will be refracted at any place where there is a density gradient and if there is uniform density there will be no refraction. This effect can be seen in a bath that has been filled with water when light shines on the bath. I used to have access to a schlieren apparatus and a supersonic tunnel and I always used a candle flame as a way of producing regions of fluctuating density in order to get the equipment set up properly. The candle flame does not produce large density differences but the density gradients show up very well. Supersonic flow is characterised by its shock waves and compression waves in which there are very large density gradients and by its expansion waves where the density changes but much more gradually.

 

It is 30 years since I used this apparatus and no doubt there have been many refinements in those years. I will give the principle of operation of the one that I used because there are fundamental consequences of the way in which it operates.

The schlieren equipment is not portable like say a camera. It is obviously capable of “seeing” the shock waves made by a bullet that passes through its main beam but its main application is its use with a supersonic tunnel. The tunnel must have optically flat windows of optical quality glass and somehow the models have to be mounted between the two windows. That, in itself, is a technical problem and, in the tunnel that I used the windows had matching slots cut through them and the models were made with lugs to go into these slots. Mounting models was not a job for the ham-fisted.

 

I will describe the schlieren equipment by starting at the lamp and ending at the video camera. The lamp should be a point source of light but we make do with a quartz halogen bulb or the like. The light from the bulb is focussed by a lens at a point where there are two knife-edges that come together to form a slit through which some of the light passes. In figure 14-2 I have drawn the arrangement of the fitting used to give this adjustable slit. There is a ring mounted on a base that will go on a adjustable stand of some sort. A plate with a bevelled edge to give a very sharp, well-defined edge is fixed in this ring with its edge vertical. The fitting has a similar moving plate mounted in the ring so that can be adjusted with a screw and a thumb-nut to give a narrow slit to let light through. Usually the light source and the slit are made into one unit so that it can be moved without upsetting the adjustment of the two components.

 

Now the light source and the slit must be moved so that the slit is at the focus of a concave mirror that is silvered on its concave surface and adjustable for direction and azimuth. This produces a beam of light with parallel rays that can be directed to pass through the schlieren windows as shown in figure 14-1

 

As this beam passes through the air that is flowing at supersonic speed over the model, density gradients divert rays of light that pass through them. Now the beam, with its deflected rays, falls on the second mirror that focuses the beam on to a second fitting shown in fig 14-3 with one moveable plate. See the arrangement in figure 14-1. This plate is carefully adjusted so that it intercepts only those rays that have been diverted towards it and prevents them from going on to the video camera for display on the VDU. This produces black lines on the screen. However some of the light that has been diverted in the opposite direction goes on to appear on the screen and create regions of brighter light than the background level. Furthermore the fact that the slit is vertical makes the detection of areas of changing densities biased in one direction. I have copied a schlieren picture from Prandtl as figure 14-4 and it is evident that the apparatus has correctly found the waves that cross and are compression waves and expansion waves but has failed to recognise the upper and lower edges of the jet to be of the same character.

 

So the schlieren equipment produces lighter and darker area on the screen and often for the same type of wave. This means that interpreting schlieren pictures can only be done properly in the context of the application and that the interpretation improves with experience.

 

Then there is the problem of definition. Because the schlieren equipment is most frequently used with wind tunnels and the flow is normally two-dimensional I do not think that anyone would expect the various waves to be exactly two-dimensional so the rays passing through the flow will become blurred. When one thinks of the fact the shock waves are very thin it becomes evident that we shall never get very accurate photographs.

 

We have all seen schlieren pictures of bullets in flight. Ignoring the problems of high-speed photography we must now be looking at three-dimensional flow. This means that the shock waves are cone shaped and we are looking through those cones. If the rays of the schlieren equipment are horizontal we shall be looking at the upper and lower tangents to the cones and inevitably there will be shading inside the cones. See figure 14-5.

 

The definition of the photos is further dependent on the width of the slit and the narrower the slit the better the definition. This means that when the best definition is obtained the light level is very low. This can be overcome with digital cameras etc. but ultimately the accuracy of the knife-edges will set yet more limits.

 

Experimentalists have been ingenious and skilful at showing flow patterns as distinct from wave patterns in the low velocity flow of air and water round and through various objects. They have used smoke, dye, solid particles and any method that they can think of. I do not think that any comparable methods have been produced for the supersonic flow of gases. The schlieren equipment shows us the density gradients but not the flow lines and we must count ourselves fortunate to have it to help us.

 

In the wider context of science that means that we are heavily dependent on a difficult technique for all our visual material and we must expect to have to make a greater input from mental modelling and mathematical modelling than we needed to for, say, open channels. In doing so we have to take notice of the fact that we may be being misled by the effects of having the air moving round the body and not the body moving through the still air. [1]