turbocharger-design

name	turbocharger-design
description	Turbocharger design — compressor/turbine matching, surge margin, efficiency islands, boost pressure, wastegate, intercooler, twin-scroll, electric turbo, SAE sizing.
metadata	{"priority":7,"promptSignals":{"phrases":["turbocharger","turbo design","compressor map","turbine map","boost pressure","surge margin","wastegate"],"minScore":3}}

Turbocharger Design — Complete Skill

Basic Turbocharger Thermodynamics

Compressor (isentropic): T₂s = T₁ × PR_c^((γ-1)/γ) η_c = (T₂s - T₁)/(T₂ - T₁) (isentropic efficiency, typically 0.70–0.80) W_c = ṁ_a × c_p × (T₂ - T₁) = ṁ_a × c_p × T₁ × (PR_c^((γ-1)/γ) - 1) / η_c

Turbine (isentropic): T₄s = T₃ × (P₄/P₃)^((γ-1)/γ) (γ = 1.33 for exhaust gas) η_t = (T₃ - T₄)/(T₃ - T₄s) (typically 0.70–0.78) W_t = ṁ_g × c_p,g × η_t × T₃ × [1 - (P₄/P₃)^((γ-1)/γ)]

Power balance (energy matching): W_t × η_mech = W_c ṁ_g × c_p,g × η_t × (T₃ - T₄s) × η_mech = ṁ_a × c_p × (T₂ - T₁)/η_c

Compressor Map

Compressor map: pressure ratio vs. corrected mass flow Axes: x = ṁ_corr = ṁ√(T₁/T_ref) / (P₁/P_ref); y = PR = P₂/P₁ Speed lines: constant N_corr = N/√(T₁/T_ref)

Surge line: left boundary; below this flow rate → backflow → instability Choke line: right boundary; Mach = 1 at impeller throat → flow blockage

Surge margin: SM = (ṁ_operating - ṁ_surge) / ṁ_operating × 100% at same PR Minimum SM: 10–15% steady-state; 5% transient

Efficiency islands: contour lines of η_c on map; design at peak island for best efficiency

Turbine Map

T-map: mass flow parameter vs. pressure ratio; efficiency contours ṁ_t × √T₃ / P₃ vs. PR_t = P₃/P₄

VGT (Variable Geometry Turbine): adjustable nozzle vanes → changes effective turbine area → increases low-speed torque, reduces lag, controls boost without wastegate at low speeds

Compressor Impeller Sizing

Tip speed: U₂ = √(c_p × T₁ × (PR_c^((γ-1)/γ) - 1) / (ψ × η_c)) ψ = work coefficient (0.6–0.85 typical)

Tip diameter: D₂ = 2U₂/ω

Flow coefficient: φ = C_r2/U₂ (radial velocity ratio, 0.2–0.4 typically)

Specific speed: N_s = n √(Q) / H^(3/4) (dimensionless form; optimum ≈ 0.5–1.0 for centrifugal)

Wastegate

Bypasses exhaust around turbine to limit boost pressure Opens when P_boost > setpoint (typically 1.5–3.0 bar absolute for SI) Electronic wastegate: variable duty cycle → precise boost control

Sizing: wastegate diameter 20–50 mm (depends on engine size) Wastegate flow coefficient C_d ≈ 0.6–0.75

Intercooler (Charge Air Cooler)

Purpose: reduce compressed-air temperature → increase density → more airflow → more power T_out = T_in - ε × (T_in - T_coolant) ε = heat exchanger effectiveness (0.70–0.90 for air-to-air; 0.80–0.95 air-to-water)

Density increase: ρ ∝ 1/T → cooling from 180°C to 60°C increases density by ~26%

Pressure drop: must minimize; ΔP ≤ 0.05–0.1 bar target

Turbo Lag

Defined: time from throttle input to 90% boost pressure (typically 0.5–3 s)

Reduction methods:

• Smaller turbine: faster spool-up but higher backpressure at high power
• Twin-scroll: better exhaust pulse use → faster spool
• Ball bearing CHRA: reduced rotating inertia → 25–40% faster response
• Electric motor-assisted (e-turbo): instant torque from motor; BMW 48V e-turbo
• Two-stage: small high-speed turbo for low range; large for high range

Two-Stage Turbocharging

Stage 1 (LP): large turbo; PR = 1.5–2.0; moderate temperature Stage 2 (HP): small turbo; PR = 1.5–2.0; operates downstream Overall PR = PR_1 × PR_2 = 3–4 bar Intercooler between stages required Used in: large diesel trucks, marine, high-efficiency diesel cars

Bearing and Cooling

CHRA (Center Housing Rotating Assembly): journal bearings (plain) or ball bearings Oil supply: 2–3 bar, 5–15 L/min; temperature ≤ 130°C Water cooling: prevents coking of oil after hot shutdown Max turbine inlet temperature: 950°C (standard) to 1050°C (Inconel turbine wheel)

Matching Procedure

1. Determine engine ṁ_air at rated power (from volumetric efficiency × V_d × n)
2. Select target boost pressure PR_c; calculate ṁ_corr
3. Plot operating point on compressor map → check surge margin and efficiency
4. Match turbine: calculate required ṁ_g × √T₃/P₃ and PR_t from engine exhaust conditions
5. Check power balance: W_t ≥ W_c
6. Verify boost over full speed range (from low-rpm torque to rated power)

Output

Provide: PR_c, PR_t, ṁ_corr [kg/s × √K / kPa], compressor η [%], turbine η [%], T₂ [°C], boost pressure [bar], surge margin [%], intercooler ΔT [°C], wastegate opening fraction at rated power.