Real Cycle Effects (propulsion/gas-turbine-cycle/real-cycle-effects)
Use when the task is a non-ideal gas turbine (Brayton) cycle: the
compressor and turbine isentropic efficiencies, the combustor
total-pressure loss, the real thermal efficiency, and the actual
specific fuel consumption. This leaf is the lossy follow-on to the
ideal gas-turbine-cycle leaf: the ideal relations are recovered at
eta_c = eta_t = 1 with no pressure loss.
Domain quick reference
Units are SI throughout: temperatures in kelvin, pressure ratio
dimensionless, gamma = 1.4 and cp = 1005 J/(kg K) air-standard
values, LHV in J/kg.
- Compressor with isentropic efficiency eta_c:
T2s = T1 * PR**((gamma-1)/gamma), and the actual exit temperature
T2 = T1 * (1 + (PR**((gamma-1)/gamma) - 1)/eta_c). Example:
T1 = 288.15 K, PR = 20, gamma = 1.4, eta_c = 0.85 give T2s about
678 K and T2 about 747 K. The compressor work per kg is
w_c = cp * (T2 - T1).
- Turbine with isentropic efficiency eta_t:
T4s = T3 / PR**((gamma-1)/gamma), and the actual exit temperature
T4 = T3 - eta_t * (T3 - T4s). Example: T3 = 1500 K, eta_t = 0.88
give T4s about 637 K and T4 about 741 K. The turbine work per kg
is w_t = cp * (T3 - T4).
- Real thermal efficiency with the actual temperatures:
eta_th = (T3 - T4 - T2 + T1)/(T3 - T2) = (w_t - w_c)/q_in; cp
cancels. The example gives eta_th about 0.40 against the ideal
cycle value 1 - PR**((1-gamma)/gamma) of about 0.575.
- Specific fuel consumption: SFC = 3600/(eta_th * LHV) with LHV in
J/kg, the cycle-basis value in kg/(kNs) at the reference effective
velocity V_ref = 3.6 m/s (the 3600 factor is the hourly scaling of
the classic SFC = 3600/(eta * LHV) form). For a real engine scale
with the effective jet velocity: SFC_T = 1000 * V_eff/(eta_th * LHV)
in kg/(kNs) with V_eff in m/s (typical 500 to 700 m/s for a
turbojet); the example gives SFC about 2.1e-4 kg/(kNs) on the
cycle basis and SFC_T about 3.5e-2 kg/(kNs) at V_eff = 600 m/s.
- Combustor total-pressure loss: PR_eff = PR * (1 - loss_frac) with
loss_frac the fractional loss (typical 0.02 to 0.06). The
compressor still sees the full PR; the turbine sees PR_eff, so
T4s (and T4) rise and the real efficiency falls. Example: a 5%
loss at PR 20 cuts eta_th from about 0.399 to about 0.388, roughly
one percentage point; the penalty grows at higher pressure ratio.
- Sensitivity verdicts: d(eta_th)/d(eta_c) > 0 and
d(eta_th)/d(eta_t) > 0 - improving either component efficiency
always raises the real cycle efficiency, and the gains flatten as
the cycle approaches the ideal limit; d(eta_th)/d(loss) < 0 - any
combustor pressure loss lowers efficiency. At PR 20 the turbine
efficiency is the stronger lever in the example.
Workflow
- Fix the inlet temperature T1, the turbine inlet temperature T3,
the pressure ratio, gamma, the compressor efficiency eta_c, and
the turbine efficiency eta_t; add the combustor loss fraction if
the burner pressure loss matters.
- Compute the actual compressor exit temperature with
compressor_exit_temperature(t1, pressure_ratio, gamma, eta_c).
- Compute the actual turbine exit temperature with
turbine_exit_temperature(t3, pressure_ratio, gamma, eta_t).
- Compute the real thermal efficiency with
real_thermal_efficiency(t1, t2, t3, t4) using the ACTUAL
temperatures.
- Compute the actual SFC with sfc_from_efficiency(eta_th, lhv) and,
when the effective jet velocity is known, the thrust SFC with
sfc_thrust(eta_th, lhv, v_eff).
- Apply the combustor loss with pressure_loss_penalty(pr, loss) or
cycle_efficiency_with_losses(...) and compare against the lossless
case to size the penalty.
- Run efficiency_sensitivity() to report which component efficiency
dominates at the design point.
Pitfalls
- Passing eta_c or eta_t above 1: non-physical (the exit would be
colder than isentropic); the module raises ValueError.
- Using the ideal (isentropic) temperatures in the real efficiency:
T2 and T4 must be the actual lossy station temperatures, and cp
cancels only when both work terms use the same cp.
- Mixing units: temperatures in kelvin, never Celsius; LHV in J/kg,
not kJ/kg or MJ/kg, or the SFC shifts by factors of 1000.
- Quoting the efficiency as a percent in the SFC formula: eta_th is
a fraction (0.4), not 40.
- Forgetting the combustor loss: the turbine sees PR_eff, not the
full pressure ratio, and the loss compounds at high PR.
- Reading the cycle-basis SFC as a thrust SFC: the 3600/(eta*LHV)
value carries the reference effective velocity; the thrust value
needs V_eff, or the answer is off by an order of magnitude.
- Treating the sensitivity verdicts as exact: the derivative signs
are robust, the magnitudes move with the design point.
- Treating any of this as a certification requirement: FAR-33 sets
the certification context for aircraft engines; the component
efficiencies and loss fractions are assessment inputs, and the
relations above are common cycle assessment practice.
Behavior contract (gate 3)
The real-cycle relations are exercised by the gate 3 contract test:
scripts/test_real_cycle_effects.py against
scripts/real_cycle_effects.py (stdlib unittest, offline). Run:
python3 scripts/test_real_cycle_effects.py
Compliance
- Standards referenced, not reproduced: FAR-33 is US government work
(public domain); the component efficiency and pressure-loss
relations are common cycle assessment methodology, summary-only
per standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.
1---2name: real-cycle-effects3description: Use when you must compute the real-cycle gas turbine performance with component losses: the compressor exit temperature and the turbine exit temperature from the pressure ratio and the component-efficiency (isentropic-efficiency) of each machine, the real-cycle thermal efficiency of the non-ideal Brayton cycle, the actual-SFC from the efficiency and the fuel lower heating value, and the efficiency penalty from the combustor pressure-loss. Produces the actual station temperatures, the real-cycle efficiency, the actual-SFC, and the pressure-loss penalty in SI units that gate the engine cycle assessment. Trigger: real cycle, component efficiency, isentropic efficiency, pressure loss, combustor loss, actual SFC, off-ideal Brayton.4license: Apache-2.05---67# Real Cycle Effects (propulsion/gas-turbine-cycle/real-cycle-effects)89Use when the task is a non-ideal gas turbine (Brayton) cycle: the10compressor and turbine isentropic efficiencies, the combustor11total-pressure loss, the real thermal efficiency, and the actual12specific fuel consumption. This leaf is the lossy follow-on to the13ideal gas-turbine-cycle leaf: the ideal relations are recovered at14eta_c = eta_t = 1 with no pressure loss.1516## Domain quick reference1718Units are SI throughout: temperatures in kelvin, pressure ratio19dimensionless, gamma = 1.4 and cp = 1005 J/(kg K) air-standard20values, LHV in J/kg.2122- Compressor with isentropic efficiency eta_c:23 T2s = T1 * PR**((gamma-1)/gamma), and the actual exit temperature24 T2 = T1 * (1 + (PR**((gamma-1)/gamma) - 1)/eta_c). Example:25 T1 = 288.15 K, PR = 20, gamma = 1.4, eta_c = 0.85 give T2s about26 678 K and T2 about 747 K. The compressor work per kg is27 w_c = cp * (T2 - T1).28- Turbine with isentropic efficiency eta_t:29 T4s = T3 / PR**((gamma-1)/gamma), and the actual exit temperature30 T4 = T3 - eta_t * (T3 - T4s). Example: T3 = 1500 K, eta_t = 0.8831 give T4s about 637 K and T4 about 741 K. The turbine work per kg32 is w_t = cp * (T3 - T4).33- Real thermal efficiency with the actual temperatures:34 eta_th = (T3 - T4 - T2 + T1)/(T3 - T2) = (w_t - w_c)/q_in; cp35 cancels. The example gives eta_th about 0.40 against the ideal36 cycle value 1 - PR**((1-gamma)/gamma) of about 0.575.37- Specific fuel consumption: SFC = 3600/(eta_th * LHV) with LHV in38 J/kg, the cycle-basis value in kg/(kN*s) at the reference effective39 velocity V_ref = 3.6 m/s (the 3600 factor is the hourly scaling of40 the classic SFC = 3600/(eta * LHV) form). For a real engine scale41 with the effective jet velocity: SFC_T = 1000 * V_eff/(eta_th * LHV)42 in kg/(kN*s) with V_eff in m/s (typical 500 to 700 m/s for a43 turbojet); the example gives SFC about 2.1e-4 kg/(kN*s) on the44 cycle basis and SFC_T about 3.5e-2 kg/(kN*s) at V_eff = 600 m/s.45- Combustor total-pressure loss: PR_eff = PR * (1 - loss_frac) with46 loss_frac the fractional loss (typical 0.02 to 0.06). The47 compressor still sees the full PR; the turbine sees PR_eff, so48 T4s (and T4) rise and the real efficiency falls. Example: a 5%49 loss at PR 20 cuts eta_th from about 0.399 to about 0.388, roughly50 one percentage point; the penalty grows at higher pressure ratio.51- Sensitivity verdicts: d(eta_th)/d(eta_c) > 0 and52 d(eta_th)/d(eta_t) > 0 - improving either component efficiency53 always raises the real cycle efficiency, and the gains flatten as54 the cycle approaches the ideal limit; d(eta_th)/d(loss) < 0 - any55 combustor pressure loss lowers efficiency. At PR 20 the turbine56 efficiency is the stronger lever in the example.5758## Workflow59601. Fix the inlet temperature T1, the turbine inlet temperature T3,61 the pressure ratio, gamma, the compressor efficiency eta_c, and62 the turbine efficiency eta_t; add the combustor loss fraction if63 the burner pressure loss matters.642. Compute the actual compressor exit temperature with65 compressor_exit_temperature(t1, pressure_ratio, gamma, eta_c).663. Compute the actual turbine exit temperature with67 turbine_exit_temperature(t3, pressure_ratio, gamma, eta_t).684. Compute the real thermal efficiency with69 real_thermal_efficiency(t1, t2, t3, t4) using the ACTUAL70 temperatures.715. Compute the actual SFC with sfc_from_efficiency(eta_th, lhv) and,72 when the effective jet velocity is known, the thrust SFC with73 sfc_thrust(eta_th, lhv, v_eff).746. Apply the combustor loss with pressure_loss_penalty(pr, loss) or75 cycle_efficiency_with_losses(...) and compare against the lossless76 case to size the penalty.777. Run efficiency_sensitivity() to report which component efficiency78 dominates at the design point.7980## Pitfalls8182- Passing eta_c or eta_t above 1: non-physical (the exit would be83 colder than isentropic); the module raises ValueError.84- Using the ideal (isentropic) temperatures in the real efficiency:85 T2 and T4 must be the actual lossy station temperatures, and cp86 cancels only when both work terms use the same cp.87- Mixing units: temperatures in kelvin, never Celsius; LHV in J/kg,88 not kJ/kg or MJ/kg, or the SFC shifts by factors of 1000.89- Quoting the efficiency as a percent in the SFC formula: eta_th is90 a fraction (0.4), not 40.91- Forgetting the combustor loss: the turbine sees PR_eff, not the92 full pressure ratio, and the loss compounds at high PR.93- Reading the cycle-basis SFC as a thrust SFC: the 3600/(eta*LHV)94 value carries the reference effective velocity; the thrust value95 needs V_eff, or the answer is off by an order of magnitude.96- Treating the sensitivity verdicts as exact: the derivative signs97 are robust, the magnitudes move with the design point.98- Treating any of this as a certification requirement: FAR-33 sets99 the certification context for aircraft engines; the component100 efficiencies and loss fractions are assessment inputs, and the101 relations above are common cycle assessment practice.102103## Behavior contract (gate 3)104105The real-cycle relations are exercised by the gate 3 contract test:106scripts/test_real_cycle_effects.py against107scripts/real_cycle_effects.py (stdlib unittest, offline). Run:108python3 scripts/test_real_cycle_effects.py109110## Compliance111112- Standards referenced, not reproduced: FAR-33 is US government work113 (public domain); the component efficiency and pressure-loss114 relations are common cycle assessment methodology, summary-only115 per standards-map.yaml.116- compliance: STANDARDS-REF, gated: false.
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