10 o

1. Method of characteristics solution for wave reflection from wall, showing PowerPoint construction of flow field, for a total turn of 10 degrees i g d M=2 e h f a b c 10o • Notes: • Locations of a, b and c are given at the start of the problem (b is point where wall is at 5 degrees, c is point where turn completes). • Powerpoint only allows angles to be specified to nearest degree, but this is good enough here. Right click on wave or jet edge segments, select ‘Format...’ and then ‘Position’ to view angles. • Tables can be opened as XL worksheets so you can examine the relationships between the various angles and flow properties (right click, select ‘Open...’) • Flow properties at a, b and c are same as at d, e and f respectively.

2. Method of characteristics solution for wave reflection from a jet edge, showing PowerPoint construction of flow field d g i e M=2 h f o 10o p • Notes: • Powerpoint only allows angles to be specified to nearest degree, but this is good enough here. Right click on wave or jet edge segments, select ‘Format...’ and then ‘Position’ to view angles. • Waves don’t quite close at p due to fact that only 3 waves were used • Tables can be opened as XL worksheets so you can examine the relationships between the various angles and flow properties (right click, select ‘Open...’)

3. Method of characteristics solution for minimum length nozzle design example, showing PowerPoint construction of flow field and nozzle i h g o d Me=1.64 b Ae At e a c f • Notes: • PowerPoint only allows angles to be specified to nearest degree, but this is good enough here. Right click on wave or jet edge segments, select ‘Format...’ and then ‘Position’ to view angles. • Coarseness of wave mesh probably means nozzle shape not very accurate • Tables can be opened as XL worksheets so you can examine the relationships between the various angles and flow properties (right click, select ‘Open...’) • From drawing Ae/At=1.25. Area Mach number relation gives 1.28