# Intercooled Cycle > Use when you must analyze a gas turbine cycle with intercooling: split the total pressure ratio into two compression stages with an intercooler between them, compute the intercooler exit temperature from the stage pressure ratio and effectiveness, determine the optimum intercooler pressure ratio minimizing total compressor work, and quantify net specific work and thermal efficiency against the simple non-intercooled cycle. Produces the intercooled cycle efficiency, the simple cycle baseline efficiency, the optimum intercooler pressure ratio, the specific work gain, and the station temperatures that gate an engine cycle comparison. Trigger: intercooled cycle, two-stage compression, intercooler effectiveness, intercooler pressure ratio, compression work split, cycle work gain. - Skill: `ashfordeou/intercooled-cycle` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/intercooled-cycle` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/intercooled-cycle/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - License: Apache-2.0 - Author: ashfordeOU (https://skillmd.com/u/ashfordeou) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/ashfordeou/intercooled-cycle --- # Intercooled Cycle (propulsion/gas-turbine-cycle/intercooled-cycle) Use when the task is intercooled gas turbine cycle analysis: splitting the total pressure ratio into two compression stages around an intercooler, computing the intercooler exit temperature from its effectiveness, taking the equal-split optimum pi_1 = pi_2 = sqrt(pi_total), and comparing net specific work and thermal efficiency against the simple single-stage cycle. This leaf implements the air-standard two-stage analysis in pure Python, stdlib only. It pairs with propulsion/gas-turbine-cycle/ gas-turbine-cycle for the simple cycle baseline and with propulsion/gas-turbine-cycle/regenerative-cycle, the heat-recovery variant that recovers the efficiency penalty this cycle accepts. It does not cover the single-stage baseline analysis, heat recovery, exhaust augmentation, or non-ideal component behavior; those belong to the sibling leaves above. ## Domain quick reference - Cycle layout: stage 1 compresses from T_1 to the intercooler at pressure ratio pi_1, the intercooler cools the discharge toward T_1, stage 2 compresses from the intercooler exit to the combustor at pi_2, with pi_1 * pi_2 = pi_total. - Optimum pressure split: pi_1 = pi_2 = sqrt(pi_total) minimizes the total compressor work for a fixed total ratio when intercooling returns the air to the ambient temperature (equal stage split). - Stage discharge temperature: T_exit = T_in * (1 + (pi_stage**((GAMMA-1)/ GAMMA) - 1) / eta_c), the real discharge with the stage isentropic efficiency applied once (stage_exit_temperature). - Intercooler exit: T_ic_exit = T_2a - eps_ic * (T_2a - T_1); eps_ic = 0 leaves the discharge uncooled, eps_ic = 1 returns the ambient temperature (intercooler_exit_temperature). - Compressor work: per stage w_c = cp * (T_exit - T_in), equal to cp * T_in * (pi_stage**((GAMMA-1)/GAMMA) - 1) / eta_c; the total is the sum over the two stages (compressor_work_total). - Turbine work: w_t = cp * eta_t * T_3 * (1 - pi_total**(-(GAMMA-1)/ GAMMA)) expands through the FULL total ratio (turbine_work). - Cycle: q_in = cp * (T_3 - T_2b), w_net = w_t - w_c_total, eta_th = w_net / q_in (intercooled_cycle). - Comparison baseline: the simple cycle with one compression stage at pi_total (simple_cycle); gain = (w_net_i - w_net_s)/w_net_s * 100 percent and eta_delta = (eta_th_i - eta_th_s) * 100 percentage points (cycle_comparison). - Trade: intercooling lowers the compressor work and raises the net specific work, but at fixed T_3 it also raises q_in through the lower T_2b, so the thermal efficiency falls slightly when no heat recovery is present. Units are SI: K, J/kg for specific work, dimensionless ratios and efficiencies. - FAR-33 frames the aircraft engine certification context (reference only, standards-map.yaml); the relations above are standard air-standard methodology, summary-only. ## Workflow 1. Fix the operating point: inlet temperature T_1, turbine inlet temperature T_3, total pressure ratio pi_total, intercooler effectiveness eps_ic, and efficiencies eta_c and eta_t. 2. Take the optimum split with optimum_intercooler_pressure_ratio: pi_1 = pi_2 = sqrt(pi_total). 3. Run compressor_work_total(T_1, pi_total, eps_ic, eta_c) to get the station temperatures T_2a, T_ic_exit, T_2b and the stage works w_c1, w_c2, w_c_total. 4. Get the expansion side with turbine_work(T_3, pi_total, eta_t). 5. Assemble the intercooled cycle with intercooled_cycle(T_1, T_3, pi_total, eps_ic, eta_c, eta_t) for w_net, q_in and eta_th. 6. Run the baseline with simple_cycle(T_1, T_3, pi_total, eta_c, eta_t) and compare with cycle_comparison to get the specific work gain in percent and the efficiency change in percentage points. 7. Judge the trade: accept the efficiency slip only when the work gain or the downstream heat-recovery option justifies it. 8. Confirm the deterministic checks with the contract test scripts/test_intercooled_cycle.py. ## Worked example Air-standard intercooled cycle at T_1 = 288 K, T_3 = 1500 K, pi_total = 30, eps_ic = 0.8, eta_c = 0.85, eta_t = 0.9 (GAMMA 1.4, cp 1005 J/(kg K)). Module real outputs: - Optimum split: pi_1 = pi_2 = 5.4772 (sqrt of 30). - Stations: T_2a = 499.97 K; T_ic_exit = 330.39 K (cooled 169.6 K toward ambient); T_2b = 573.57 K. - Compressor: w_c1 = 213.03 kJ/kg; w_c2 = 244.39 kJ/kg; w_c_total = 457.42 kJ/kg. - Turbine: w_t = 843.34 kJ/kg (full pi_total expansion). - Cycle: w_net = 385.91 kJ/kg; q_in = 931.06 kJ/kg; eta_th = 0.4145. - Simple cycle baseline: w_net = 284.0 kJ/kg; eta_th = 0.4311. - Comparison: work_gain_pct = +35.9 percent; eta_delta_pp = -1.66 percentage points. Intercooling raises the specific work by about a third while the thermal efficiency slips by 1.66 points without heat recovery, the documented intercooling trade. ## Verification - Confirm the anchors: T_2a = 499.97 K, T_ic_exit = 330.39 K, T_2b = 573.57 K, w_c_total = 457.42 kJ/kg, w_net = 385.91 kJ/kg, q_in = 931.06 kJ/kg, eta_th = 0.4145, gain +35.9 percent, eta_delta -1.66 pp, each within 1 percent of the module output. - Confirm optimum_intercooler_pressure_ratio(36) == 6.0 and (30) == 5.4772; the exit temperature rises with pi_stage and falls with eta_c; eps_ic = 0 returns the hot inlet and eps_ic = 1 the coolant. - Confirm a higher-effectiveness intercooler reduces w_c_total at fixed pi_total, and that eta_th sits strictly between 0 and 1 here. - Confirm the eps_ic = 0 degeneration: the no-cooling two-stage total work approximates the single-stage work (the two differ by the stage-2 cascade term, which vanishes as eta_c -> 1). - Confirm every non-physical input raises ValueError: T_1 <= 0, T_3 <= T_1, pi_total <= 1, eta_c or eta_t outside (0, 1], eps_ic outside [0, 1], and coolant at or above the intercooler hot inlet. - Run the contract test offline: python3 scripts/test_intercooled_cycle.py (33 tests, deterministic). ## Related leaves - propulsion/gas-turbine-cycle/gas-turbine-cycle: the single-stage cycle analysis that supplies the comparison baseline. - propulsion/gas-turbine-cycle/regenerative-cycle: the heat-recovery variant that recovers the efficiency this cycle gives up. - propulsion/gas-turbine-cycle/propelling-nozzle: nozzle expansion downstream of the turbine. - propulsion/gas-turbine-cycle/afterburner-cycle: the augmentation variant for thrust beyond the turbine limit. - propulsion/gas-turbine-cycle/real-cycle-effects: loss accounting beyond the constant-efficiency assumption used here. ## Pitfalls - Quoting the pressure split as the work split: pi_1 = pi_2 = sqrt(pi_total) is the optimum only for the ideal case; with eps_ic = 0.8 the second stage still does more work (244.39 against 213.03 kJ/kg) because its inlet sits at 330.39 K, above ambient. - Reporting the work gain without the efficiency cost: at the worked point the net work rises +35.9 percent while eta_th falls 1.66 points, and the gain alone is what sells an intercooled design. - Dividing the efficiency in twice: stage_exit_temperature already applies eta_c to return the real discharge, so the stage work is cp * (T_exit - T_in) and not that value divided by eta_c again; the spec anchors pin the single application. - Reading the eps_ic = 0 case as a free win: without intercooling the two-stage chain charges the stage-2 inefficiency on the real stage-1 discharge, so its work (582.9 kJ/kg) slightly exceeds the single-stage value (559.3 kJ/kg); the two coincide only as eta_c tends to 1. This is a modeling artifact, not a physical gain. - Expanding the turbine at the stage ratio: the turbine sees the full pi_total (843.34 kJ/kg here), never the per-stage sqrt value, so mixing the two ratios understates the expansion work. - Mixing units: the module returns specific work in J/kg; the worked example tables divide by 1000 to quote kJ/kg. ## Behavior contract (gate 3) Run the deterministic contract test (stdlib unittest, offline): python3 scripts/test_intercooled_cycle.py The test covers the module constants, the optimum pressure ratio (36 -> 6.0, 30 -> 5.4772), stage and intercooler exit temperatures with their limits (eps_ic 0 and 1) and monotonicity, the worked-example anchors within 1 percent, the compressor total as the stage-work sum, the effectiveness work-reduction relation, the full cycle and simple-cycle baseline dicts with their identities (w_net = w_t - w_c_total, eta_th = w_net / q_in), the comparison signs and closed forms, the eps_ic = 0 degeneration identity, determinism, and ValueError rejection of every non-physical input class. ## Contract test Run from the leaf root: python3 scripts/test_intercooled_cycle.py. The logic module is scripts/intercooled_cycle_logic.py, pure stdlib with module constants GAMMA = 1.4 and CP = 1005.0. The test file is stdlib unittest, offline and deterministic, 33 methods, and asserts the module outputs against the prep-verified worked-example anchors plus the magnitude bounds of the spec (works within 1 percent, eta_th between 0 and 1). Exit code 0 means the leaf contract holds. ## Compliance - Standards referenced, not reproduced: FAR-33 (14 CFR Part 33) frames aircraft engine certification context; the intercooled cycle relations above are standard air-standard engineering methodology, summary-only per standards-map.yaml. - compliance: STANDARDS-REF, gated: false.