page_title: Compressible flow
section_title: Prandtl-Meyer expansion fans
hierarchical_section_title: Compressible flow / Two-dimensional flow / Prandtl-Meyer fans / Prandtl-Meyer expansion fans
caption_attribution_description: English: basic PM expansion
context_page_description: Compressible flow is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number is less than 0.3. The study of compressible flow is relevant to high-speed aircraft, jet engines, rocket motors, high-speed entry into a planetary atmosphere, gas pipelines, commercial applications such as abrasive blasting, and many other fields.
context_section_description: To this point, the only flow phenomena that have been discussed are shock waves, which slow the flow and increase its entropy. It is possible to accelerate supersonic flow in what has been termed a Prandtl-Meyer expansion fan, after Ludwig Prandtl and Theodore Meyer. The mechanism for the expansion is shown in the figure below.
  As opposed to the flow encountering an inclined obstruction and forming an oblique shock, the flow expands around a convex corner and forms an expansion fan through a series of isentropic Mach waves. The expansion "fan" is composed of Mach waves that span from the initial Mach angle to the final Mach angle. Flow can expand around either a sharp or rounded corner equally, as the increase in Mach number is proportional to only the convex angle of the passage (δ). The expansion corner that produces the Prandtl-Meyer fan can be sharp (as illustrated in the figure) or rounded. If the total turning angle is the same, then the P-M flow solution is also the same.
  The Prandtl-Meyer expansion can be seen as the physical explanation of the operation of the Laval nozzle. The contour of the nozzle creates a smooth and continuous series of Prandtl-Meyer expansion waves.
caption: Prandtl-Meyer expansion fan diagram
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