# Schlieren

### The Sclieren phenomena

In general deflection of lightbeams passing through an inhomogeneus media is called the Shlieren phenomena. The phenomena can be the effect of surface roughness of transparent solids and/or changing properties in fluids and gases. What is similar in these effects is that the lightbeams deflect causing image distorsion in an optical system. As an example, on Figure 1 a thermal boundary layer is shown above the hot roof of a car. Lightbeams passing through this boundary layer will deflect distorting the image of the bars behind the car.
The phenomena is fairly complex, however in some special cases it can be well described. Based on these special cases the Schlieren phenomena can be used for visualization and measurement purposes as well.
Figure 1 – Thermal boundary layer on the roof of a car [1]

### Physical background

Let’s consider a gasous media with a distribution in its properties including the refractive index of the gas. The change of the refractive index field can be described with the  gradient as it is a scalar filed: grad(n). If the lightbeams are passing through a media in which the gradient of the refractive index is constant (see Figure 2) than the lightbeams will change their lineal propagation into a circular path with a radii of R.

Figure 2 – Deflaction of lightbeams in a gasous media with continously changing refractive index

The radii of the new path is the following:

### Angle of deflaction

The angle of deflaction is defined as the angle between the original lineal path and the tangent line of the new curved path (see Figure 3):

Figure 3 – The Angle of deflaction

### Phisical properties affecting the refractive index

The refractive index depends on the wavelength and on the properties of the gas it is passing through. The latter ones are: temperature, pressure, material properties, composition (in case of gas mixture)

For a given material the refractive index is dependent on the density. Considering the equation of state for that gas (the equation of state gives a relation betveen density, temperature and pressure) it is obvious that the refractive index is a function of pressure and temperature:

The so called Gladstone-Dale equation gives the relation between the refractive index and density:

Applying the ideal gas law for two states :

, and:  .

For an isobaric process

On Figure 4 the refractive index is shown as the function of temperature at ambient pressure. At high temperature ranges the curve becomes flat. In case of a measurement of temperature based on a refractive index measurement one should count with decreasing sensitivity at high temperatures.

Figure 4 – Refractive index as the function of temperature for Air at ambient pressure

### Schlieren equipments with parallel lightbeams

The scematic of a Schlieren equipment operating with parallel lightbeams is shown on Figure 5.

Figure 5 – Schematic of a Schlieren equipment
 R Splot O1,O2 Schlieren objectives S Subject B Blend, knife S’ Plane of projection

The light source is placed on the left side. The light beams are collected with a lens system in the plane of the slot (R). With this set up the light source acts as a „slot light source”. After leaving the slot light enters the Shlieren objectives – and the subject in between them –, and is collected in the plane of the knife (B). The image of the subject is formed in the plane of projection after going through an additional lens system.

The lightbeams leaving the same point from the plane of the slot are parallel between the Shlieren objectives as to be seen on Figure 6:

Figure 6 – parallel lightbeams between the Schlieren objectives

The maximal angle between two lightbeams:
, for low angles :

In the schematic of Figure 5 and 6 the longer side of the slot (R) and knife (B) are perpendicular to the page. Moving the knife up to the optical axis (dashed line on Figure 5) the knife would cover the half of the lightbeams.
If we now apply a subject with only one small hole on it, the lighbeams will cross this hole in a cone with an agle of  . The image of this point is similar to the shape of the slot (R) in the plane of the knife (B) and it is a point in the plane of projection (S'). When there is no Shlieren effect the knife will cover the half of the lightbeams setting the brightness of this point. If we cover more or less of the lightbeams the point will be darker or lighter respectively.
The Shlieren effect is visualized in a similar way. When the lightbeams are deflected in the subject the image of the slot in the B plane will move up~ or downwards and the fixed knife will cover less or more of the lightbeams respectively and hence the corresponding point of the image in the plane of projection will be lighter or darker.
Deflactions parallel with the longer side of the knife have no effect in the Shlieren imaging.

### Shlieren eguipment at the Departmen of Energy Engineering

The schematic of our Schlieren equipment is visible on Figure 7. The light source is a mercury-vapor lamp. The diameter of the Shlieren objectives is 80 mm. The angle of the slot and knife, and the distance of the knife from the optical axis is adjustable.

Figure 7 – Schematic of the Shlieren equipment at Laboratory (Schlieren – Aufnahmegerät 80)
 1 Light source 2 Condensor 3 Slot 4,6 Schlieren Objectives 5 Subject 7 Blend 8 Photo objective 9 Objective for projection 10 Plane of projection 11 Mirror 12 Objective 13 Place to check knife position

### Colored Schlieren images

It is possible to place a slide with colored stripes instead of the knife (Figure 5 - B, Figure 7 – 7):
Figure 8 – Colored slide to be used With the Schlieren equipment

Using the colored slide the different light deflactins will be visualized with different colors. Knowing the order and the width of colored stripes the value of deflaction can be calculated.

### Examples:

Figure 9 – Flow visulaization around a rocket model, Supersonic flow [2]

### References

1. Gary S. Settles: Schlieren and Shadowgraph Imaging in the Great Outdoors , Proceedings of PSFVIP-2, Honolulu, USA, May 16-19, 1999