The shadowgraph is the simplest form of optical system suitable for observing a flow exhibiting variations of the fluid density. In principle, the system does not need any optical component except a light source and a recording plane onto which to project the shadow of the varying density field (Figure 1). A shadow effect is generated because a light ray is refractively deflected so that the position on the recording plane where the undeflected ray would arrive now remains dark. At the same time the position where the deflected ray arrives appears brighter than the undisturbed environment. A visible pattern of variations of the illumination (contrast) is thereby produced in the recording plane. From an analysis of the optics of the shadow effect [see, e.g., Merzkirch (1981,1987)], it follows that the visible signal depends on the second derivative of the refractive index of the fluid. Therefore, the shadowgraph as an optical diagnostic technique is sensitive to changes of the second derivative of the fluid density.
It is evident that the shadowgraph is not a method suitable for quantitative measurement of the fluid density. Owing to its simplicity, however, the shadowgraph is a convenient method of obtaining a quick survey of a flow in which the density changes in the described way. This applies particularly to compressible gas flows with shock waves that can be considered as alterations of the gas density with an extremely intense change in curvature of the density profile, i.e., a change of the respective second derivative. The observation of shock waves in gases by means of shadowgraphy goes back to the 19th century when these flow phenomena were discovered by means of this optical technique.
Due to the very simple optical setup, the shadow effect resulting from inhomogeneous density fields can be observed also outside a laboratory, with the sun serving as the light source, e.g., the sun light may project onto a solid wall shadow patterns that are caused by fuel vapor rising in the air. For laboratory experiments one often uses an optical system with a beam of parallel light transmitted through the flow (Figure 2). The camera that records a down-scaled picture is focused onto a plane at distance l from the test field. This plane corresponds to the position of the recording plane in Figure 1. The intensity of the shadow effect, or the sensitivity of the shadowgraph, increases with the distance l. On the other hand, the flow picture is the more out of focus the greater l, so that a compromise between optical sensitivity and image quality has to be found. The optical sensitivity of the shadowgraph is, in principle, an order of magnitude lower than that of schlieren or interferometric techniques (see Photographic Techniques).
Figure 2. Setup for shadowgraph with a beam of parallel light transmitted through the test section of a flow facility.
Figure 3 is a shadowgraph showing a complicated pattern of shock waves and vortices in air. The flow field is caused by the interaction of an unsteady shock wave with the triangular obstacle in a shock tube.
Figure 3. Shadowgraph of shock wave diffraction around a triangular obstacle taken in an air shock tube (Courtesy German-French Research Institute, St. Louis, ISL).
Merzkirch, W. (1981) Density sensitive flow visualization, in: Fluid Dynamics, Ed. R. J. Emrich, Methods of Experimental Physics, Vol. 18, Academic Press, New York.
Merzkirch, W. (1987) Flow Visualization, 2nd edn., Academic Press, New York.