| name | axial-fan-design |
| description | Axial fan design — specific speed, blade element theory, solidity, tip clearance, pressure-flow characteristic, fan laws, noise, hub-to-tip ratio, AMCA 210, ISO 5136. |
| metadata | {"priority":7,"promptSignals":{"phrases":["axial fan design","axial flow fan","fan blade design","HVAC fan design","fan laws","fan pressure curve"],"minScore":3}} |
Axial Fan Design — Complete Skill
Specific Speed and Fan Selection
Specific speed (dimensionless):
Ω_s = ω Q^0.5 / (ΔP/ρ)^0.75 [ω in rad/s; Q in m³/s; ΔP in Pa; ρ in kg/m³]
Dimensional form (common):
N_s = N × Q^0.5 / ΔP^0.75 [N in RPM; Q in m³/s or cfm depending on convention]
Fan type selection by Ω_s:
| Ω_s (dimensionless) | Fan type |
|---|
| 0.2–1.0 | Centrifugal (backward curved) |
| 1.0–3.5 | Mixed-flow |
| 3.5–7.0 | Axial (low to medium pressure) |
| > 7.0 | Propeller fan (low pressure only) |
Axial fans: best for high flow, low-to-medium pressure; HVAC, cooling towers, tunnel ventilation
Euler Equation and Velocity Triangles
Euler work per unit mass:
W = U₂ C_θ2 - U₁ C_θ1 [J/kg; at constant radius for axial fan: U₁ = U₂ = U]
W = U × ΔC_θ = U × C_a × (tan β₁ - tan β₂) [C_a = axial velocity; β = relative flow angle]
Theoretical total pressure rise:
ΔP_t = ρ × W = ρ × U × ΔC_θ [Pa]
Actual pressure rise:
ΔP_actual = ΔP_t × η_stage [Pa; η_stage = 0.75–0.92 for well-designed axial fan]
Blade Element Theory
Blade element at radius r:
Section lift: dL = ½ ρ W²_rel c C_L dr [W_rel = relative velocity; c = chord; C_L = lift coefficient]
Section drag: dD = ½ ρ W²_rel c C_D dr
Axial force (pressure producing):
dF_a = dL cos β - dD sin β [contributes to pressure rise]
Torque force:
dF_τ = dL sin β + dD cos β [contributes to torque]
Blade loading L/D ratio:
For low-speed aerofoil: C_L/C_D = 50–100 at design point
C_L design ≈ 0.5–1.0 (avoid stall)
C_L_stall ≈ 1.2–1.5 (depends on profile; Clark Y, NACA 4412, NACA 65-series)
Hub-to-Tip Ratio
Hub-to-tip ratio η_h = r_hub / r_tip:
Low η_h (0.3–0.4): high volume flow; variable chord/twist required for uniform work
High η_h (0.6–0.7): more uniform conditions; less 3D effects; less flow per diameter
Typical axial fan:
η_h = 0.3–0.5 for cooling tower/HVAC
η_h = 0.6–0.75 for high-pressure axial (tunnel, aircraft engine)
Annulus area:
A = π(r_tip² - r_hub²) = π r_tip²(1 - η_h²)
Axial velocity:
C_a = Q / A [m/s; target C_a = 10–25 m/s for HVAC; up to 200 m/s for aircraft]
Solidity and Blade Spacing
Solidity σ = c/s = c × N_b / (2π r):
c = chord length; s = blade spacing at radius r; N_b = number of blades
Typical σ_mean = 0.6–1.2 for axial fans
Number of blades:
For propeller fans: N_b = 2–6
For HVAC axial: N_b = 4–12
For high-pressure: N_b = 12–24
Stagger angle γ:
γ = 90° - α_c [from chord line to rotation direction]
At hub (high U/C_a): low stagger; at tip (lower relative loading): higher stagger
Tip Clearance Effects
Leakage flow through gap:
Q_leak ≈ C_t × gap × U_tip [C_t = tip clearance coefficient ≈ 0.005–0.02]
Efficiency penalty: Δη ≈ 2.5 × (gap / h_blade) [per unit gap fraction]
Allowable tip clearance:
gap ≤ 0.5–1.0% of blade diameter (< 0.25–0.5 mm gap per meter diameter)
Tight clearance: better efficiency; risk of tip rubbing (need clearance > thermal expansion)
Fan Laws (Scaling)
For geometrically similar fans:
Q₂ = Q₁ × (N₂/N₁) × (D₂/D₁)³ [flow rate]
ΔP₂ = ΔP₁ × (N₂/N₁)² × (D₂/D₁)² × (ρ₂/ρ₁) [pressure rise]
P₂ = P₁ × (N₂/N₁)³ × (D₂/D₁)⁵ × (ρ₂/ρ₁) [shaft power]
Corrected speed and flow:
Q_c = Q × √(T_ref/T_actual) × (P_actual/P_ref)
N_c = N / √(T_actual/T_ref)
Fan Performance Curve
Characteristic (P vs. Q):
At shutoff (Q = 0): ΔP_max ≈ 1.2–1.5 × ΔP_design
At design: ΔP_design; Q_design
At runout (max Q): ΔP → 0; excessive power
Stall region:
Non-monotonic region on fan curve (saddle); operating here → instability → noise + surge
Design to operate right of stall on stable part of curve
System curve:
ΔP_system = R × Q² [R = system resistance; Q = operating flow rate]
Operating point: intersection of fan curve and system curve
Noise Estimation
Fan sound power level (AMCA 300):
L_w = K_w + 10 log(Q) + 20 log(ΔP_t) [dB; K_w = fan specific sound power level]
K_w = 25–38 dB for axial fans (from manufacturer data or AMCA handbook)
Blade passage frequency (BPF):
BPF = N × N_blades / 60 [Hz]
BPF harmonics: 2×BPF, 3×BPF create tonal peaks
Noise reduction:
Lower tip speed (U_tip < 50 m/s → quieter)
Increase N_blades (reduce blade loading per blade)
Skew/sweep blades (reduce tonal BPF amplitude by 3–8 dB)
Standards
| Standard | Scope |
|---|
| AMCA 210 | Laboratory test; fan performance rating |
| AMCA 300 | Sound rating; fan sound power |
| ISO 5136 | In-duct sound power measurement |
| ISO 13347 | Sound measurement for fans |
| ASHRAE 51 | Laboratory methods; equivalent to AMCA 210 |
Output
Provide: specific speed Ω_s (confirm axial type), hub-to-tip ratio, tip diameter D [m], rotational speed N [RPM], tip speed U_tip [m/s], axial velocity C_a [m/s], number of blades N_b, chord c [m] and solidity σ at r_mean, blade angles β₁ and β₂ [°] at hub/mean/tip, stage efficiency η_s [%], tip clearance [mm], fan curve operating point (Q [m³/s] and ΔP [Pa]), sound power level L_w [dB] and BPF [Hz], and applicable standard (AMCA 210/300).
