volute-design

name	volute-design
description	Pump/fan volute design — spiral volute geometry, constant velocity vs. constant angular momentum methods, diffuser design, radial force, throat area, scroll design, double volute.
metadata	{"priority":7,"promptSignals":{"phrases":["volute design","pump volute","spiral volute","fan volute","volute throat","scroll casing","radial thrust pump"],"minScore":3}}

Volute Design — Complete Skill

Volute Function

Converts kinetic energy at impeller exit to pressure Collects flow from impeller circumference → guides to discharge nozzle Spiral geometry maintains design velocity → minimizes losses

Design Methods

Method 1 — Constant Mean Velocity (Hydraulic Institute / Stepanoff)

Maintain constant average radial velocity in volute cross-section: V_v = C_u2 × r₂ / r_v = constant [for uniform angular momentum]

Actually: set V_mean = constant = V_3 (throat velocity) V_3 = Q / A_throat

Cross-section area at angle θ (0 to 2π): A(θ) = A_throat × θ/(2π)

This ensures flow collected from each arc length adds linearly to total area

Method 2 — Constant Angular Momentum (Free Vortex Volute)

Based on angular momentum conservation after impeller: C_u × r = C_u2 × r₂ = constant

Volute width b(θ) × r_v(θ) = constant × θ/(2π) For rectangular cross-section at angle θ: A(θ) = Q_total × θ/(2π × V_3)

Resulting cross-section usually trapezoidal or circular

Throat Area

At θ = 2π (full wrap): A_throat = Q / V_3

Design throat velocity: V_3 = (0.5 to 1.0) × C_m2 (meridional velocity at impeller exit)

Or from continuity: V_3 = Q / (π r₂ × 2b₂ × ψ_blockage)

Typical V_3 / U₂ = 0.15–0.30 (where U₂ = impeller tip speed)

Throat coefficient c_3 (Kaplan's method): V_3 = c_3 × √(2 × H_design / η) where c_3 ≈ 0.15–0.25

Volute Cross-Section Profiles

Circular Cross-Section

Minimum wetted perimeter → lowest friction loss r_c(θ) = r₂ + R_c(θ) = r₂ + √(A(θ)/π) Used in high-efficiency pumps

Trapezoidal Cross-Section

Trapezoidal: base b, top B, height h A = (B + b)/2 × h; easy to cast More common in industrial pumps

Rectangular Cross-Section

Simple geometry; used in fans and blowers b = constant width; H(θ) = A(θ)/b

Volute Spiral Geometry

Outer radius at angle θ: For constant velocity: r_outer(θ) = r₂ + A(θ)/b_v [for rectangular section width b_v]

For circular section: r_outer(θ) = r₂ + √(A(θ)/π)

Base circle: r_base = r₂ + clearance (1–3 mm typical gap at cutwater)

Cutwater (tongue/tongue radius): Located at θ = 0; determines flow split Cutwater angle: 0–20° from radial; sharper reduces mixing loss; rounder reduces noise Gap at cutwater: g/r₂ = 0.03–0.08 (larger → less noise, more recirculation)

Diffuser Cone (Conical Diffuser after Throat)

Area ratio AR: AR = A_outlet / A_throat = (D_outlet/D_throat)²

Diffuser half-angle θ_d: θ_d = 5–7° (maximum; beyond this → stall) L_diffuser = (D_outlet - D_throat) / (2 tan θ_d)

Pressure recovery coefficient C_p: C_p = 1 - 1/AR² [ideal, no loss] Actual: C_p = η_diff × (1 - 1/AR²) where η_diff = 0.70–0.85

Radial Thrust Force

At off-design conditions, non-uniform pressure around volute → net radial force

Pump with single volute: F_radial = K_r × ρ g H × D₂ × b₂ [N] K_r = thrust coefficient (max ≈ 0.36 at shutoff; = 0 at BEP)

Double Volute: two 180° offset throats; radial forces partially cancel F_radial_double ≈ 0.1–0.15 × F_single (significant reduction near BEP) Required when: power > 50 kW or frequent off-BEP operation

Diffuser (vaned): more uniform pressure → near-zero radial thrust at BEP; poor at off-design Used for multistage high-efficiency pumps

Discharge Nozzle

Transition from volute to outlet flange Typically concentric reducer 10°–15° half-angle Final velocity: V_outlet = Q / A_flange ≤ 3–5 m/s (reduce water hammer risk)

Double Volute Design

Start at θ = 0 with half the total throat area; second channel starts at θ = π Both channels spiral to individual throats; merge at discharge Cutwater at 0° and 180°; both cutwater angles identical for symmetry

Fan/Blower Volute Differences

Blower volute: air density low → large cross-section relative to impeller Backward-curved fan: volute designed for C_m2/U₂ = 0.10–0.25 Spiral: r_outer(θ) = r₂ × exp(b × θ) where b = growth constant b = ln(r_outer,360 / r₂) / (2π)

Fan cutwater clearance: larger than pump (3–5% D₂) to reduce BPF noise

Output

Provide: throat area A_throat [m²], throat velocity V_3 [m/s], cross-section dimensions at θ = 90°, 180°, 270° [mm], cutwater gap g [mm], diffuser angle θ_d [°] and length L_d [mm], radial thrust estimate F_r [N] at shutoff, single vs. double volute recommendation, volute drawing coordinates r_outer(θ) at 30° increments.