In this answer to Why do the shapes of these two exhaust plumes from an Atlas V 411 look different? the 'Summerfield criterion' is mentioned, saying:

Historically, the Summerfield criterion was used, where the minimum pressure in a nozzle must be greater than 0.35...0.4*atmospheric pressure.

What is the 'Summerfield criterion'? And can you explain how the exhaust pressure of 0.35 - 0.4 atm was arrived at?


The Ralf Stark paper linked from the answer which mentions the Summerfield and Schmucker criteria ends with a list of references; among them are a 1973 Schmucker paper (translated in 1984, here) and a widely cited 1954 Summerfield paper, “Flow Separation in Overexpanded Supersonic Exhaust Nozzles”, Jet propulsion, Vol. 24, No. 9, page 319-321, 1954. I cannot find the latter paper online with a brief search.

The Summerfield criterion in question is a rule of thumb, stating that flow separation in an overexpanded nozzle occurs at about 0.4 times ambient pressure. From the Schmucker paper:

Initial investigations on flow separation in nozzles were conducted by Buchner, Prandtl, Meyer, Flugel and Stanton and published by Stodola. After World War II the increased research work in the area of rocket engines led to numerous investigations of this problem. Forster and Cowles at the California Institute of Technology undertook the first publicized hot-gas tests with a small nitric acid/aniline motor. The result of this work was the separation condition that in an over-expansion to 40 percent of the surrounding pressure, the flow separates from the wall. This number is often called the "Summerfield Criterion" and is today considered to be a conservative design value.

According to the Schmucker paper, Summerfield's results are for a relatively low-pressure engine, where chamber pressure is 15-20 times ambient.

The exact value varies with the operating characteristics of the engine; there seems to be a half-century tradition of experimental papers giving different flow separation criteria for different sets of conditions and citing everyone else who's done the same. The appendix of the Stark paper contains a table listing a number of these.

(Note that Martin Summerfield has two criteria named after him! His earlier one, jointly formulated with his colleague Frank Malina (and so, often referred to as the Summerfield-Malina criterion) in 1946, states that (given certain assumptions) an optimal multistage rocket has equal payload mass ratios between stages.)


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