Aerodynamics

Spin, and the low pressure it leaves behind

Picture air leaving the swirler: a ring of angled vanes around the fuel nozzle. Each parcel now moves forward and around. Rotating fluid needs a force pointing inward to keep it on its circular path (the same reason you feel pushed outward on a merry-go-round), and in a fluid that force can only come from pressure. So the pressure must be higher at the outside and lower at the centre:

$\frac{\partial p}{\partial r} = \frac{\rho\, \cair{W}^2}{r}$

where $W$ is the tangential (swirl) velocity. Strong swirl carves out a low-pressure core on the axis.

Now follow that core downstream. As the swirling jet spreads out into the wider liner, it slows its spin (angular momentum is conserved while the radius grows), so the pressure deficit on the axis weakens. That means the pressure on the axis rises along the flow direction. Downstream is at higher pressure than upstream, and the fluid on the axis, which has little forward momentum to begin with, gets pushed back upstream.

That is vortex breakdownVortex breakdownThe abrupt reversal of flow on the axis of a strongly swirling jet as its swirl decays and axial pressure rises., and the bubble of reversed flow it creates is the central recirculation zone (CRZ)Central recirculation zoneA bubble of reversed flow on the combustor axis, created by vortex breakdown, that returns hot products to ignite fresh mixture..

The CRZ is the combustor's pilot light. Hot, radical-rich products circulate back toward the nozzle and meet the fresh fuel–air mixture along a shear layer, igniting it continuously. Everywhere along that boundary the flame is being relit, thousands of times a second.

Measuring swirl

The strength of the swirl is captured by the swirl numberSwirl number SₙRatio of the axial flux of angular momentum to that of axial momentum. Above ~0.6 the flow on the axis reverses.: the ratio of the axial flux of angular momentum to the axial flux of axial momentum (times a radius):

$S_n = \frac{G_\phi}{G_x R} = \frac{\int_0^R \rho\, U W\, r^2\, dr}{R\int_0^R \rho\, U^2\, r\, dr}$

For a flat-vaned annular swirler with hub-to-tip radius ratio $h$ and vane angle $\theta$, this integrates to a handy result:

$S_n = \frac{2}{3}\,\frac{1-h^3}{1-h^2}\,\tan\theta$

And in the widget you can see the thresholds that matter:

• $S_n \lesssim 0.4$: weak swirl. The flow spins but never reverses, and there is nothing to hold the flame.
• $S_n \approx 0.6$ and above: strong swirl. Vortex breakdown creates a robust CRZ; this is where production swirlers live, typically $S_n \approx 0.6$–$1.0$.
• $S_n \gg 1$: the bubble grows and creeps upstream onto the nozzle, where hot products can overheat and coke the injector tip, and the pressure loss climbs.

Jets in crossflow: the liner's surgical tools

The swirler handles the dome, but much of the air enters through rows of holes in the liner, as jets fired sideways into the hot flow. Each row has a job:

• Primary jets feed and shape the primary zone. Opposed jets from the outer and inner walls collide on the axis and help close the recirculation from downstream.
• Intermediate jets supply the oxygen to burn out CO, H₂ and soot, while keeping the gas hot enough for the burnout to finish.
• Dilution jets, the largest holes, must drive cold air all the way into the hot core and quench it to the turbine's temperature.

A jet fired into a crossflow bends over like smoke from a chimney in a wind. How far it penetrates depends overwhelmingly on the jet-to-mainstream momentum-flux ratioMomentum-flux ratio JρⱼVⱼ² / ρₘVₘ² — the jet-to-crossflow momentum ratio that sets how deep a liner jet penetrates.:

$J = \frac{\rho_j V_j^2}{\rho_m V_m^2}, \qquad \frac{y}{d} \approx 0.89\, J^{0.47}\left(\frac{x}{d}\right)^{0.36}$

Notice what controls $J$. The jet velocity comes from the pressure drop across the liner, so penetration is bought with pressure loss. The jet air is also cold and dense relative to the 2000 K mainstream, which helps a lot: $\rho_j/\rho_m$ can be 2–3.

Pressure loss: the price of mixing

Every vane and every hole takes a toll. The overall combustor pressure loss:

$\frac{\Delta P}{P_t} = \frac{P_{t,\text{in}} - P_{t,\text{out}}}{P_{t,\text{in}}}$

is typically held to 3–6%. Within it, the liner pressure drop is what drives the jets and the swirler; the rest is lost in the diffuser and annuli. More liner drop means faster jets, better penetration, more turbulence and shorter, more stable flames. It also means a less efficient engine. That window of 3–6% is where the mixing benefit and the cycle penalty balance for most engines.

The report card: pattern factor

Everything in this lesson (swirl, jets, pressure drop, even the diffuser's uniformity) is graded in one place: the temperature distribution at the combustor exit, as the first turbine vanes see it.

$\text{PF} = \frac{T_\text{max} - \bar T_\text{exit}}{\bar T_\text{exit} - T_\text{inlet}}$

The pattern factorPattern factor(T_max − T_mean)/(T_mean − T_inlet) at the combustor exit: how much hotter the worst hot streak is than average. compares the single hottest spot with the average temperature rise. Turbine cooling must be designed for the hottest spot, so a high PF is paid for directly, in turbine life or turbine cooling air.

Typical modern values are around 0.15–0.25. Notice how a single partly blocked injector creates a hot streak far out of proportion to its size: that is why fuel-injector uniformity and deposits (Lesson 6) matter so much.

We now have a flame and a flow to hold it. Next question: how do we know the combustor is working, and at what point does it stop?