There are a few things going on here that are preventing this from working. To start, it looks like your tiles are starting at level 9, and the default minimumLevel for the tile map service imagery provider is 0. So, you need to specify the minumum level. However, this will make cesium try to load every tile at level 9, which will make way too many requests. And it looks like you only have tiles for a specific area, so you can specify the bounding rectangle for the tiles you have. Here is an example:
url : ‘http://students.washington.edu/aritchie/quinault/’,
rectangle: Cesium.Rectangle.fromDegrees(-123.88542367690528, 47.46019710639955, -123.50940150003458, 47.64278544372370),
However, if you run this, you’ll see this error in the console: Image from origin ‘http://students.washington.edu’ has been blocked from loading by Cross-Origin Resource Sharing policy
This is because the server hosting the imagery doesn’t have CORS enabled. If you have any control over the server, you can see if they can enable CORS.