diffuser-design

name	diffuser-design
description	Diffuser design — static pressure recovery coefficient Cp, conical/planar/annular diffusers, area ratio, divergence angle, stall limits (Sovran-Klomp), performance charts, separation, turbomachinery diffusers, AMCA standards.
metadata	{"priority":7,"promptSignals":{"phrases":["diffuser design","diffuser pressure recovery","conical diffuser","diffuser stall","pressure recovery coefficient","Cp diffuser"],"minScore":3}}

Diffuser Design — Complete Skill

Diffuser Fundamentals

Purpose: convert kinetic energy (velocity) to static pressure via area increase Ideal (inviscid): Bernoulli → Cp_ideal = 1 - (A₁/A₂)² = 1 - (1/AR)² [AR = area ratio = A₂/A₁] Actual: Cp_actual < Cp_ideal due to boundary layer separation, mixing losses

Pressure recovery coefficient Cp: Cp = (P₂ - P₁) / (½ρV₁²) [dimensionless; = (static pressure rise) / (inlet dynamic pressure)] Ideal Cp: Cp_ideal = 1 - 1/AR² [perfect recovery; no losses] Efficiency: η_diff = Cp / Cp_ideal [or: Cp / (1-1/AR²)]

Total pressure loss: ΔP₀ = P₀₁ - P₀₂ = ½ρV₁² × (1 - Cp - 1/AR²) [positive; represents losses] Loss coefficient: ξ = ΔP₀ / (½ρV₁²) = 1 - Cp - Cp_ideal... [combines separation + friction]

Performance Parameters

Area ratio: AR = A₂/A₁ = (D₂/D₁)² (conical); = W₂/W₁ (planar 2D)

Non-dimensional length: L/D₁ or L/R₁ (conical); N/W₁ (planar 2D) [N = length; W₁ = inlet width]

Semi-divergence angle (conical): α = arctan((D₂-D₁) / (2L)) = arctan((√AR - 1) × D₁ / (2L))

Blockage (boundary layer at inlet): B = δ*/W₁ [displacement thickness / inlet width; B = 0.02–0.10 typical; reduces effective AR] Effective AR = (W₁ - 2δ*) / W₁ × AR → use (1-B) × AR in performance

Stall Limits (Sovran-Klomp Design Chart)

Conical diffuser performance regimes: At given AR and L/D₁ → Cp from Sovran-Klomp charts (1967; standard reference)

Stall boundaries: Line a-a (first stall): oscillating stall at one wall; Cp begins to degrade Line b-b (two-wall separation): full separation; Cp drops significantly For best Cp at given L/D → operate near but below line a-a

Optimal 2D planar divergence angle: α_opt ≈ 7–11° (half-angle) for L/W₁ = 5–10; steeper for shorter diffusers Conical optimal: α_opt ≈ 5–7° (half-angle) for L/D₁ = 3–8

3C correlation (Kline, 1959): Stall initiates when: 2α > arctan(1.8 × (N/W₁)^(-0.45)) [planar; N = length; W₁ = inlet height]

Conical Diffuser Design

Given: inlet conditions (V₁, D₁), target AR, space constraint L:

1. Calculate ideal Cp_ideal = 1 - 1/AR²
2. Calculate half-angle α = arctan((D₂-D₁)/(2L))
3. Check stall: α < 7° → low stall risk; α > 12° → likely stall
4. From Sovran-Klomp chart: actual Cp at (AR, L/D₁)
5. Calculate actual pressure rise: ΔP = Cp × ½ρV₁²

Recommended ranges:

L/D₁	Optimal AR	α [°]	Cp/Cp_ideal
2	1.5	7.2	0.70
4	2.0	6.7	0.80
8	2.5	5.7	0.85
12	3.0	5.6	0.87

Short diffuser (length constrained): Add vaned diffuser (splitter vanes) → reduce effective angle per passage Vaned conical: α up to 20° with vanes (comparable Cp to 7° without vanes)

Annular Diffuser (Turbomachinery)

Application: centrifugal compressor, turbine exit Additional parameter: hub-to-tip ratio r_h/r_t

Effective area ratio (annular): AR_eff = A₂/A₁ = (r_t2² - r_h2²) / (r_t1² - r_h1²)

Vaneless diffuser (centrifugal compressor): Continuity: r × V_r = const → V_r decreases with r Angular momentum: r × C_θ = const → C_θ decreases with r Combined: radius ratio r₂/r₁ = 1.4–2.0 typical; Cp = 0.4–0.6 (lower due to swirl at inlet)

Vaned diffuser (wedge, channel): Vane inlet angle: match absolute flow angle from impeller exit β₂ - 3° to 5° (avoidance shock) Design: 15–30 vanes; passage AR = 2–4; divergence angle 5–8° per side Cp = 0.5–0.7 for well-designed vaned diffuser

2D Planar Diffuser (Turning Vanes)

Without turning vanes: Optimal α: 7–9° (half-angle); Cp = 0.6–0.75 at AR = 2, L/W₁ = 6 With turning vanes: effective angle per passage reduced; allows steeper walls

HVAC duct diffusers: Target: Cp ≥ 0.6 at AR = 1.5–2; L/H₁ = 3–5 Use turning vanes in elbows to reduce separation + pressure loss

Pressure Recovery Enhancement

Boundary layer control: Suction slots: remove BL; delay separation; Cp improvement +0.05–0.10 Vortex generators (VG): re-energize BL; tabs, triangular vanes h = 0.5δ; delay stall Riblets: reduce skin friction in attached BL; secondary effect

Splitter vanes: Divide passage → each passage sees smaller AR and shorter L/W → reduced stall risk Optimal vane location: at r/R = 0.6 for single splitter

Diffuser Total Pressure Loss Correlation

Sovran-Klomp empirical correlation (conical, 2D): ξ = 0.004 × (L/W₁) × (1 + 0.5 AR²) / AR [approximate; W₁ = inlet width or D₁] Plus separation losses if operating near stall

1D continuity + loss model: P₂ = P₁ + ½ρV₁² × (1 - 1/AR² - ξ)

Standards

Standard	Scope
AMCA 210	Laboratory methods for airflow testing
ISO 5801	Fan performance testing
ASME PTC-11	Fan testing
VDI 2044	Turbocompressor diffuser design (German)

Output

Provide: diffuser type (conical/planar/annular/vaneless/vaned), inlet velocity V₁ [m/s] and diameter D₁ (or width W₁) [mm], area ratio AR, diffuser length L [mm], half-angle α [°] vs. stall limit, ideal Cp_ideal and actual Cp (from Sovran-Klomp), pressure rise ΔP [Pa], total pressure loss ΔP₀ [Pa] and ξ, diffuser efficiency η_diff [%], stall margin (distance from line a-a), enhancement method if needed (vanes/VG/suction), and applicable standard (AMCA 210, ISO 5801).