tag:blogger.com,1999:blog-7598615455712402973.post4060331462771840200..comments2024-03-25T11:14:45.840-04:00Comments on Polymath: Altitude compensation to allow the use of American engines on the Antares rocket. Robert Clarkhttp://www.blogger.com/profile/16114043697010364282noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-7598615455712402973.post-83433409284070442812014-11-18T18:22:41.412-05:002014-11-18T18:22:41.412-05:00Rocket motor nozzles work at all because of pressu...Rocket motor nozzles work at all because of pressure drop chamber to ambient. Thrust in vacuum (stream momentum plus an exit plane pressure term) minus the back pressure term Pamb*Aexit IS the thrust at any altitude (including sea level ) AS LONG AS an overexpanded nozzle is not separated. <br /><br />For an overexpanded nozzle, the backpressure term Pamb*Ae is larger than the exit-plane pressure term (Pe*Ae). <br /><br />Up to a point, this backpressure correction term works. That point is where flow separates from the nozzle walls. There are empirical equations that roughly predict when separation occurs. Once flow separation occurs, there are no models that correctly compute thrust in that separated-flow nozzle. <br /><br />You can size an expansion bell to operate overexpanded but unseparated at sea level, which for a given design puts perfect expansion up at some altitude. Above that altitude the exit plane pressure > ambient, and the net exit plane pressure term (Pe - Pamb)*Ae) term adds to (instead of subtracting from) vacuum thrust. <br /><br />Overall delivered impulse-wise, you do better if you size first stage engine bells for perfect expansion (Pe = Pamb) at sea level, and get a positive addition from the net static pressure term (Pe - Pamb)*Ae all the way up. <br /><br />Aerospike nozzles allow you to avoid overexpanded flow separation, because the plume flow cross section adjusts to "perfect expansion" by shrinking or swelling in size. The penalty is lower thrust efficiency, because there is less solid material in contact with the expanding plume. <br /><br />GW<br /><br />Gary Johnsonhttps://www.blogger.com/profile/06723964751681093047noreply@blogger.com