ONE AIRFLOW. SEVERAL COMPETING NEEDS.

Bleed Air, Cabin Cooling & Engine Performance

Allocate engine air to the cabin. Trace the heat removed, the pressure maintained and the propulsion consequence.

ONE CALCULATION · CONNECTED VIEWSA · AMBER B · TURQUOISE

Calculated state · choose a component below

Compressor work is paid on all incoming air. Extracted air leaves the combustor/turbine stream and enters the cabin supply path.

Event timeline

Drag a B event · A stays fixed

Preparing calculation…

Whole-run summary · live values appear above

CAUSE → RESPONSE → COMPARISON

Follow the response

B · solid turquoise A · dashed amber

Time plots share the playback cursor. Design sweeps and phase plots retain their own axes. A stopped run holds its final resolved state.

Compare A and B

Whole-run quantity	A · saved	B · live	B − A	Unit

A snapshot includes parameter values and event times. Export retains both configurations and their calculated traces.

THE PHYSICS BEHIND THE RESPONSE

Read the model

Back to the experiment ↑

Follow each balance, then connect it to the response above. Open Symbols & units for the notation. A dot denotes a time derivative unless a non-dimensional time is stated.

01 / Divide the compressor airflow

{\dot{m}}_{core} = {\dot{m}}_{bleed} + {\dot{m}}_{air,burner}

{\dot{m}}_{gas} = {\dot{m}}_{air,burner} + {\dot{m}}_{fuel}

Extracted air supplies the cabin system. The combustor receives the remaining air; fuel then adds mass to the turbine stream.

Symbols & units

$ṁ$: Mass-flow rate · kg/s
${\dot{m}}_{core}$: Compressor inlet air · 20 kg/s
${\dot{m}}_{bleed}$: Bleed air allocated by the flow control

02 / Pay the compressor power demand

η_{m} {\dot{m}}_{gas} c_{p} (T_{4} - T_{5}) = P_{compressor}

P_{compressor} = {\dot{m}}_{core} c_{p} (T_{3} - T_{2})

The turbine must drive compression of all incoming air, including the fraction later extracted. Each engine state here is a steady design point.

Symbols & units

$T_{2}, T_{3}$: Compressor inlet and outlet total temperatures · K
$T_{4}, T_{5}$: Turbine inlet and outlet total temperatures · K
$c_{p}, η_{m}$: Specific heat at constant pressure · J/(kg K); mechanical efficiency 0.99
$P_{compressor}$: Compressor shaft power · W

03 / Remove heat before cabin supply

{\dot{Q}}_{precooler} + P_{pack} = {\dot{m}}_{bleed} c_{p} (T_{3} - T_{supply})

Heat rejected by the precooler and work extracted by the expansion turbine account for the drop in supply-air enthalpy, including warm bypass mixing.

Symbols & units

${\dot{Q}}_{precooler}$: Heat rejected to the surroundings · W
$P_{pack}$: Expansion-turbine work rate · W
$T_{supply}$: Mixed supply-air temperature · K

04 / Keep the cabin mass balance

\frac{d m}{d t} = {\dot{m}}_{bleed} + {\dot{m}}_{vacuum} - {\dot{m}}_{out} - {\dot{m}}_{relief}

p_{cabin} V_{cabin} = m R T

Pressure follows the cabin’s stored mass and temperature. The vacuum valve admits ambient air; the outflow and relief paths remove cabin air.

Symbols & units

$m, T$: Stored cabin-air mass · kg; absolute temperature · K
$p_{cabin}$: Absolute cabin pressure · Pa
$V_{cabin}, R$: Cabin volume 60 m³; gas constant · J/(kg K)

05 / Store and transport cabin energy

\frac{d (m c_{v} T)}{d t} = {\dot{H}}_{in} - {\dot{H}}_{out} + {\dot{Q}}_{load} + {\dot{Q}}_{wall}

{\dot{H}}_{in} = {\dot{m}}_{bleed} c_{p} T_{supply} + {\dot{m}}_{vacuum} c_{p} T_{ambient}

{\dot{H}}_{out} = ({\dot{m}}_{out} + {\dot{m}}_{relief}) c_{p} T

Stored internal energy uses cᵥ; energy carried through an open flow boundary uses cₚ. All temperatures in these balances are absolute.

Symbols & units

$c_{v}, c_{p}$: Specific heats · J/(kg K)
${\dot{H}}_{in}, {\dot{H}}_{out}$: Incoming and outgoing enthalpy flow · W
${\dot{Q}}_{load}, {\dot{Q}}_{wall}$: Cabin heat load and signed wall-to-air heat flow · W

06 / Let the cabin wall exchange heat

{\dot{Q}}_{wall} = K_{aw} (T_{wall} - T)

C_{wall} \dot{T_{wall}} = - {\dot{Q}}_{wall} - K_{wa} (T_{wall} - T_{ambient})

The wall is a separate thermal store. Heat exchanged between wall and cabin cancels when their total energy balances are added.

Symbols & units

$C_{wall}$: Wall thermal capacity · 1 MJ/K
$K_{aw}, K_{wa}$: Air–wall and wall–ambient conductances · 800 and 80 W/K
$T_{wall}, T_{ambient}$: Wall and outside absolute temperatures · K

Equations describe this bounded teaching model. Assumptions and source references are retained below. Internal calculations use SI units; controls and plots show their own labelled units.

Model limits & sources

Generic steady engine design point: 20 kg/s compressor air, pressure ratio 12, constant gas properties, compressor/turbine efficiencies 0.88/0.91. No spool dynamics in this page. The exhaust area is re-sized at each design point; it is not a fixed-hardware off-design prediction. Cabin 60 m³, initial 2 km cabin altitude and 296 K, wall capacity 1 MJ/K, air/wall conductance 800 W/K, wall/ambient 80 W/K. Cabin pressure uses supply feedforward plus proportional outflow, leakage and 55 kPa differential relief; vacuum valve prevents underpressure. Pack has a prescribed heat-exchanger effectiveness, 80% expansion efficiency and warm bypass, not a full bootstrap air-cycle machine or humidity model.

NASA · Bleed-air reduction study ↗FAA · Aircraft systems ↗

Numerical checks test the stated equations. They do not establish aircraft certification or experimental accuracy. Schematic flow markers indicate direction; their speed is illustrative. No manufacturer geometry or performance data is reproduced. Version: coupled-labs-v1.1.

Bleed Air, Cabin Cooling & Engine Performance

Event timeline

Follow the response

Compare A and B

Read the model

01 / Divide the compressor airflow

02 / Pay the compressor power demand

03 / Remove heat before cabin supply

04 / Keep the cabin mass balance

05 / Store and transport cabin energy

06 / Let the cabin wall exchange heat

Continue the connection