Summerfield criterion

Vulcain-2 engine on an Ariane 5

Stall in a nozzle

The Summerfield criterion makes a statement about the maximum permissible expansion of a nozzle.

Basics

If you want to bring a flow to supersonic speed without jerks, you have to expand it via a Laval nozzle (shown on the Vulcain-2 engine shown here ). Starting from a narrowest cross-section, the so-called critical cross-section, in which the flow velocity Ma = 1, the cross-section of the nozzle is now expanded using the condition . Here, the change in cross-section is the change in speed and Ma is the Mach number . This only works at the expense of the falling temperature. ${\displaystyle {\frac {dA}{A}}=(Ma^{2}-1){\frac {dw}{w}}}$ ${\displaystyle {\frac {dA}{A}}}$ ${\displaystyle {\frac {dw}{w}}}$

The Summerfield Criterion

According to the Summerfield criterion, flow separation occurs at a nozzle at a pressure ratio of

${\displaystyle {p_{\mathrm {e} } \over p_{\mathrm {a} }}}$ ≈ 0.25 to 0.4.

Here are the pressure at the nozzle outlet (exit) and the ambient pressure (ambient) of the nozzle. ${\displaystyle p_{\mathrm {e} }}$ ${\displaystyle p_{\mathrm {a} }}$

The phenomenon can be explained clearly in such a way that the pressure drops further and further as the fluid accelerates in the nozzle . If the pressure falls below the given value of the Summerfield criterion, the higher ambient pressure "pushes" the nozzle jet in so far that it detaches from the nozzle wall. This usually occurs immediately at the start, since the ambient pressure is highest there.

example

Let's say we are at sea level and the ambient pressure is 1 bar. According to the Summerfield criterion, we can calculate a minimum pressure at the nozzle cross-section of 0.25 bar from the pressure ratio of 0.25. From the isentropic relationships , the Mach number at the outlet cross-section and the entire outlet state can now be calculated for a given combustion chamber pressure. ${\displaystyle p_{\mathrm {a} }}$ ${\displaystyle p_{\mathrm {0} }}$

Consequences

If the flow separates above the nozzle, this happens at unpredictable points due to minimal pressure fluctuations. The separation takes place asymmetrically in each case, however, and thus moments arise as a result of pulse currents of different strengths over the nozzle outlet. These moments can damage the engine and in the worst case lead to the loss of the carrier system.