centrifugal-compressor-design

name	centrifugal-compressor-design
description	Centrifugal compressor design — Euler work, impeller geometry, velocity triangles, slip factor, vaneless/vaned diffuser, stage pressure ratio, polytropic efficiency, surge and choke, API 617.
metadata	{"priority":7,"promptSignals":{"phrases":["centrifugal compressor","centrifugal compressor design","impeller design","slip factor","compressor diffuser","API 617 compressor"],"minScore":3}}

Centrifugal Compressor Design — Complete Skill

Euler Work and Stage Performance

Euler work input per stage: W_stage = U₂ C_θ2 - U₁ C_θ1 [J/kg] U = blade tip speed [m/s]; C_θ = tangential component of absolute velocity [m/s] Subscripts: 1 = impeller inlet; 2 = impeller exit

With zero inlet swirl (C_θ1 = 0; axial inlet): W_stage = U₂ C_θ2 [J/kg]

Slip factor σ_s (Wiesner): Reduces actual C_θ2 below ideal: C_θ2_actual = σ_s × U₂ σ_s ≈ 1 - √(sin β₂) / N_b^0.7 [β₂ = backward blade angle; N_b = number of blades; Wiesner] Typical: σ_s = 0.85–0.95

Actual specific work: W_act = σ_s × U₂² [J/kg; for radial or backward-swept impeller with axial inlet]

Impeller Geometry

Blade backsweep angle β₂: β₂ = 0°: radial blades (straight); W_act = U₂² β₂ = 30°: backward-swept; C_θ2 = U₂ - C_r2/tan(β₂); lower pressure rise per stage → flatter curve; better stability β₂ = -30°: forward-swept; high head; steep curve; surges easily; rarely used

Design recommendations: β₂ = 20–55° backward (most modern industrial compressors) Higher backsweep → lower stage loading → wider stable range but lower pressure ratio

Impeller tip speed U₂: U₂ = π D₂ N / 60 [m/s; N = RPM; D₂ = tip diameter [m]] Practical limit: U₂ ≤ 350 m/s (cast Al); U₂ ≤ 500 m/s (forged Ti) Material yield check: σ_centrifugal = ρ × (U₂/2)² × C_stress ≤ σ_y / SF

Stage loading coefficient ψ: ψ = W / U₂² = σ_s × (1 - C_r2 tan β₂ / U₂) ≈ σ_s [for radial; 0.5–0.9 typical]

Flow coefficient φ: φ = C_r2 / U₂ [typical 0.2–0.35; related to impeller width and flow rate]

Velocity Triangles

At impeller exit (rotor station 2): C_r2 = Q / (π D₂ b₂) [m/s; radial (meridional) velocity; b₂ = impeller width at exit] C_θ2 = σ_s × U₂ [tangential; from slip factor] C₂ = √(C_r2² + C_θ2²) [absolute velocity] W_θ2 = C_θ2 - U₂ = (σ_s - 1)U₂ [relative tangential; negative for backward-swept] β₂ = atan(C_r2 / (U₂ - C_θ2)) [relative flow angle at exit]

Stage Pressure Ratio

Isentropic stage pressure ratio: π_s = (1 + η_s × W / c_p T₀₁)^(γ/(γ-1)) η_s = stage isentropic efficiency (0.78–0.88 for single stage) c_p = 1005 J/(kg·K) for air; γ = 1.4; T₀₁ = inlet stagnation temperature [K]

Polytropic efficiency η_p: π_s = (T₀₂/T₀₁)^(γ η_p / (γ-1)) [for polytropic process] η_p relates to η_s via: η_s = (π^((γ-1)/γ) - 1) / (T₀₂/T₀₁ - 1)

Diffuser Design

Vaneless Diffuser

Angular momentum conservation: r × C_θ = const → C_θ decreases as r increases Radial velocity: C_r × r × b = const (continuity)

Diffuser length for velocity reduction: V₂/V₃ = target (typically 0.5–0.6 for kinetic to static conversion) Vaneless: simple; no choke at high flow; wide range; lower recovery than vaned

Vaned Diffuser

Throat blockage: A_throat = Q_design / C_sound × (1 + (γ-1)/2 × M²)^(γ+1)/(2(γ-1)) [choked throat area] Throat must not choke at design flow; add margin ≥ 5%

Diffusion coefficient: D = 1 - V₃/V₂ + ΔC_θ/(2σ V₂) [similar to axial; D < 0.45 to avoid separation] Better pressure recovery than vaneless; narrower flow range

Surge and Choke

Surge: flow reversal at low flow; unstable; violent Choke (stonewall): maximum flow at unit mass flow rate; right side of map

Surge margin: SM = [(Q_design - Q_surge) / Q_design] × 100% [%] API 617 requirement: SM ≥ 10% from design point to surge line

Surge line: connects surge points at each speed → operating line must stay to right Anti-surge valve (ASV): recirculate gas when flow drops toward surge

Stonewall condition: M = 1 at impeller eye or diffuser throat → choke; flow cannot increase further Tip Mach M₂ = U₂ / a₂ → high M₂ → moves choke limit to lower flows

Multistage Configuration

Series staging: Total pressure ratio: π_total = Π π_stage [product of all stage ratios] Intercooling: reduce temperature between stages → maintain gas density → higher pressure per stage Intercooled at P_intermediate = √(P_inlet × P_outlet) [equal work split]

Number of stages: n_stages = log(π_total) / log(π_stage)

API 617 Requirements

Rotor dynamics: First critical speed: N_c1 > 1.25 × maximum operating speed (rigid rotor preferred) Or: N_c1 < 0.6 × N_min (operates supercritically with adequate damping)

Vibration limits: Unfiltered bearing vibration < 25.4 μm p-p (standard) At trip: 50.8 μm p-p or 2× normal (whichever less)

Performance test: ASME PTC-10 Type 1 (gas of same molecular weight as process) or Type 2 (substitute gas) Acceptance: head within ±4%; efficiency within -3%; shaft power within +4%

Material: Impeller: AISI 4140/4340 forged steel; Ti-6Al-4V for high-speed Casing: ASTM A216 Gr. WCB (carbon steel); alloy steel for sour gas (API 617 App A)

Output

Provide: impeller tip speed U₂ [m/s], slip factor σ_s, specific work W [J/kg], stage loading ψ, flow coefficient φ, stage pressure ratio π_s, polytropic efficiency η_p [%], diffuser type (vaneless/vaned), surge margin SM [%], number of stages, total pressure ratio, critical speed vs. operating speed (API 617 check), vibration limits [μm p-p], intercooling (if applicable), material selection, and applicable standard (API 617, ASME PTC-10).