1. Overview
The tuyere (inlet nozzle) of a centrifugal compressor stage converts static pressure into kinetic energy, accelerating and directing gas flow onto the impeller blades. Proper nozzle design is critical to stage efficiency, operating range, and surge margin.
Inlet Nozzle
Flow Acceleration
Converts P_static to velocity head before impeller eye
Tuyere Geometry
Converging Passage
Area ratio A_inlet/A_eye governs acceleration
Design Goal
Uniform Flow
Even velocity distribution at impeller eye inlet
Standard
API 617 Ch. 2
Performance test and mechanical requirements
Nozzle Components
| Component | Function | Design Parameter | Typical Range |
|---|---|---|---|
| Inlet Cone | Smooth flow transition | Contraction ratio | 1.5:1 to 3.0:1 |
| Inlet Guide Vanes | Pre-swirl for turndown | Vane angle | -20 to +30 deg |
| Eye Seal | Minimize recirculation | Clearance gap | 0.010-0.030 in |
| Inlet Volute | Radial-to-axial turn | Turning radius | 1.5-3.0 x D_eye |
Why nozzle design matters: Inlet flow distortion accounts for 2-5% stage efficiency loss. Poor nozzle geometry causes non-uniform impeller loading, increased vibration, and reduced surge margin.
2. Nozzle Theory
The tuyere nozzle accelerates gas from the inlet plenum velocity to the impeller eye velocity. The flow is governed by conservation of mass, momentum, and energy through a converging passage.
Continuity and Velocity
Continuity Equation:
rho_1 × A_1 × C_1 = rho_eye × A_eye × C_m
Where:
rho = gas density (lb/ft3)
A = flow area (ft2)
C_1 = inlet velocity (ft/s)
C_m = meridional velocity at impeller eye (ft/s)
Nozzle Velocity (isentropic):
C_eye = sqrt(2 × gc × Cp × T_0 × [1 - (P_eye/P_0)^((k-1)/k)])
Where:
gc = 32.174 lbm·ft / (lbf·s2)
Cp = specific heat at constant pressure (Btu/lb·R)
T_0 = total (stagnation) temperature (R)
P_eye = static pressure at eye (psia)
P_0 = total pressure at inlet (psia)
Mach Number at Eye:
M_eye = C_eye / a_eye
a_eye = sqrt(k × gc × R_gas × T_eye)
Keep M_eye < 0.90 to avoid choking.
Flow Coefficient
Flow Coefficient (phi):
phi = C_m / U_tip
Where:
C_m = meridional (axial) velocity at impeller eye (ft/s)
U_tip = impeller tip speed at eye diameter (ft/s)
U_tip = pi × D_eye × N / 60
Typical values: phi = 0.20 to 0.35
Design guidelines:
phi < 0.20: Low flow, risk of stall/surge
phi = 0.25-0.30: Optimal efficiency range
phi > 0.35: High flow, approaching choke
Nozzle Discharge Coefficient
| Nozzle Type | Cd Range | Contraction Ratio | Application |
|---|---|---|---|
| Well-rounded bell | 0.97-0.99 | 2.0-3.0 | High-performance stages |
| Conical inlet | 0.94-0.97 | 1.5-2.5 | Standard industrial |
| Sharp-edged entry | 0.60-0.65 | 1.0 | Not recommended |
| Elliptical profile | 0.98-0.995 | 2.0-3.5 | Aerospace-derived designs |
3. Velocity Triangles
Velocity triangles at the impeller eye define the relationship between absolute velocity (C), relative velocity (W), and blade speed (U). Proper matching of the nozzle exit angle to the blade inlet angle minimizes incidence losses.
Velocity Triangle at Impeller Eye (no pre-swirl):
Absolute velocity: C = C_m (purely axial, no tangential component)
Blade speed: U = pi × D_eye × N / 60
Relative velocity: W = sqrt(C_m^2 + U^2)
Relative flow angle:
beta_1 = arctan(C_m / U) = arctan(phi)
With Pre-Swirl (IGV angle alpha):
C_theta = C_m × tan(alpha) (tangential component)
C = sqrt(C_m^2 + C_theta^2)
Relative tangential: W_theta = U - C_theta
W = sqrt(C_m^2 + W_theta^2)
beta_1 = arctan(C_m / W_theta)
Incidence Angle:
i = beta_blade - beta_1
Target: i = 0 to +3 deg (slight positive incidence)
High incidence (>8 deg) causes blade stall and efficiency loss.
Velocity Components Summary
| Component | Symbol | Without IGV | With IGV | Units |
|---|---|---|---|---|
| Meridional velocity | C_m | Q / A_eye | Q / A_eye | ft/s |
| Tangential velocity | C_theta | 0 | C_m × tan(alpha) | ft/s |
| Absolute velocity | C | C_m | sqrt(C_m^2 + C_theta^2) | ft/s |
| Blade speed | U | pi D N / 60 | pi D N / 60 | ft/s |
| Relative tangential | W_theta | U | U - C_theta | ft/s |
| Relative velocity | W | sqrt(C_m^2+U^2) | sqrt(C_m^2+W_theta^2) | ft/s |
Design rule: Match the nozzle exit flow angle to within 2-3 degrees of the impeller blade inlet angle. Larger mismatch creates shock losses at the leading edge and reduces stage efficiency by 1-3 points per degree of incidence beyond 5 degrees.
4. Inlet Guide Vanes
Inlet guide vanes (IGVs) are adjustable vanes upstream of the impeller eye that impart pre-swirl to the gas. They are the primary flow control mechanism for centrifugal compressors, providing turndown without recycling.
IGV Operating Modes
| IGV Angle | Pre-Swirl | Effect on Head | Effect on Flow | Application |
|---|---|---|---|---|
| 0 deg (open) | None | Maximum | Design flow | Normal operation |
| +10 to +20 deg | Positive (with U) | Reduced | Reduced | Turndown to 70-80% |
| +20 to +30 deg | Strong positive | Significantly reduced | 50-70% design | Deep turndown |
| -10 to -20 deg | Negative (against U) | Increased | Increased | Overload / boost |
Effect of IGV on Euler Head:
Euler Head: H_euler = U_2 × C_theta2 - U_1 × C_theta1
Without IGV: C_theta1 = 0 (no pre-swirl)
H_euler = U_2 × C_theta2
With positive IGV: C_theta1 > 0
H_euler = U_2 × C_theta2 - U_1 × C_theta1 (reduced head)
With negative IGV: C_theta1 < 0
H_euler = U_2 × C_theta2 + U_1 × |C_theta1| (increased head)
Power Reduction with Positive IGV:
Power_ratio = 1 - (U_1 × C_theta1) / (U_2 × C_theta2)
At 20 deg IGV: Power reduction ~ 15-25%
At 30 deg IGV: Power reduction ~ 25-40%
Efficiency Impact:
IGV efficiency penalty ~ 0.5-1.5% per 10 deg of vane closure.
IGV Design Parameters
| Parameter | Typical Value | Effect |
|---|---|---|
| Number of vanes | 11-19 (prime number preferred) | Avoids resonance with impeller blades |
| Vane chord | 0.3-0.5 x eye diameter | Longer chord = better flow turning |
| Aspect ratio | 1.5-3.0 | Higher = more uniform exit flow |
| Profile | NACA 65-series or circular arc | Low-drag, predictable turning |
| Solidity (c/s) | 0.8-1.2 | Higher = better turning but more loss |
| Maximum angle | 30-40 deg | Beyond 30 deg, flow separation occurs |
Practical limit: IGVs are effective up to approximately 30 degrees of closure. Beyond this angle, flow separation on the vane surfaces causes excessive pressure drop and flow distortion that negates the benefit of pre-swirl control.
5. Loss Modeling
Nozzle and inlet losses reduce the total pressure available to the impeller, directly impacting stage head and efficiency. Losses are expressed as loss coefficients referenced to the dynamic head at the impeller eye.
Nozzle Loss Coefficient:
zeta_nozzle = Delta_P_loss / (0.5 × rho × C_eye^2)
Where:
Delta_P_loss = total pressure loss across nozzle (psi)
rho = gas density at eye (lb/ft3)
C_eye = velocity at impeller eye (ft/s)
Total Inlet Loss:
zeta_total = zeta_inlet_duct + zeta_IGV + zeta_nozzle + zeta_eye_seal
Typical values:
zeta_inlet_duct = 0.01-0.03
zeta_IGV (open) = 0.01-0.02
zeta_IGV (30 deg) = 0.05-0.10
zeta_nozzle = 0.03-0.08
zeta_eye_seal = 0.005-0.015
Efficiency Impact:
Delta_eta = zeta_total × phi^2 / (2 × psi)
Where psi = head coefficient (H / U^2), typically 0.4-0.6.
Loss Breakdown by Source
| Loss Source | zeta Range | % of Total | Mitigation |
|---|---|---|---|
| Inlet duct turning | 0.01-0.05 | 10-20% | Large bend radius, turning vanes |
| IGV profile drag | 0.01-0.10 | 15-35% | Low-drag airfoil profiles |
| IGV wake mixing | 0.005-0.03 | 5-15% | Fewer, thinner vanes |
| Contraction loss | 0.01-0.04 | 10-20% | Smooth contraction, no steps |
| Eye seal leakage | 0.005-0.02 | 5-10% | Tighter clearances, labyrinth seals |
| Incidence loss | 0.01-0.08 | 10-30% | Match beta_1 to blade angle |
Mach Number Effects
| M_eye Range | Flow Regime | Loss Multiplier | Notes |
|---|---|---|---|
| < 0.60 | Low subsonic | 1.0 | Incompressible methods adequate |
| 0.60 - 0.80 | Subsonic | 1.0-1.2 | Compressibility correction needed |
| 0.80 - 0.90 | High subsonic | 1.2-1.5 | Shock losses begin |
| 0.90 - 1.0 | Transonic | 1.5-3.0 | Significant shock losses; redesign |
Design target: Total inlet loss coefficient zeta_total should be below 0.10 at design point. Values above 0.15 indicate a poorly designed inlet system and may reduce stage efficiency by 2-4 percentage points.
6. Worked Examples
Example 1: Nozzle Velocity and Flow Coefficient
Given:
Volume flow Q = 8,000 ACFM at eye conditions
Eye diameter D_eye = 18 inches = 1.5 ft
Hub diameter D_hub = 7.2 inches = 0.6 ft
Impeller speed N = 10,000 RPM
Step 1: Eye flow area
A_eye = (pi/4) × (D_eye^2 - D_hub^2)
A_eye = (pi/4) × (1.5^2 - 0.6^2) = 1.484 ft2
Step 2: Meridional velocity
C_m = Q / (A_eye × 60) [convert CFM to CFS]
C_m = 8,000 / (1.484 × 60) = 89.8 ft/s
Step 3: Blade tip speed at eye
U_eye = pi × D_eye × N / 60
U_eye = pi × 1.5 × 10,000 / 60 = 785.4 ft/s
Step 4: Flow coefficient
phi = C_m / U_eye = 89.8 / 785.4 = 0.114
Note: phi = 0.114 is low, suggesting the stage is operating
at reduced flow. Typical design is phi = 0.25-0.30.
Step 5: Relative flow angle (no IGV)
beta_1 = arctan(C_m / U) = arctan(89.8 / 785.4) = 6.5 deg
Example 2: IGV Effect on Head
Given (from Example 1):
C_m = 89.8 ft/s, U_eye = 785.4 ft/s
U_tip = 1,200 ft/s (impeller OD tip speed)
C_theta2 = 900 ft/s (discharge tangential velocity)
Without IGV (alpha = 0):
C_theta1 = 0
H_euler = U_tip × C_theta2 = 1,200 × 900 = 1,080,000 ft2/s2
H = 1,080,000 / 32.174 = 33,570 ft·lbf/lb
With IGV at +20 deg:
C_theta1 = C_m × tan(20) = 89.8 × 0.364 = 32.7 ft/s
H_euler = (1,200 × 900) - (785.4 × 32.7) = 1,054,318 ft2/s2
H = 1,054,318 / 32.174 = 32,771 ft·lbf/lb
Head reduction = (33,570 - 32,771) / 33,570 = 2.4%
New relative flow angle:
W_theta = U - C_theta1 = 785.4 - 32.7 = 752.7 ft/s
beta_1 = arctan(89.8 / 752.7) = 6.8 deg
Example 3: Total Inlet Loss Estimation
Given:
C_eye = 200 ft/s, rho_eye = 3.5 lb/ft3
IGV at 15 deg closure
Individual losses:
zeta_duct = 0.02
zeta_IGV = 0.04 (closed 15 deg)
zeta_nozzle = 0.05
zeta_seal = 0.01
zeta_total = 0.02 + 0.04 + 0.05 + 0.01 = 0.12
Pressure loss:
Delta_P = zeta_total × 0.5 × rho × C_eye^2 / 144
Delta_P = 0.12 × 0.5 × 3.5 × 200^2 / 144
Delta_P = 58.3 psf = 0.41 psi
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