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Fluid Mechanics & Aeroacoustics of Fans and Compressors

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Fluid Mechanics & Aeroacoustics of Fans and Compressors Fluid Mechanics & Aeroacoustics of Fans and Compressors Courtesy: Pollrich DLK Day 1: Axial Flow Compressors & Fans Short Course Offered at BCAM− July 2-4, 2013 Farzad Taghaddosi, Ph.D. Course Objective • Provide basic understanding of fluid flow in compressors and fans (axial & centrifugal) • Understand sources of noise and methods for acoustic analysis Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 2 Definition • Compressors & fans: – Use input mechanical energy to increase fluid total pressure – Fans (Δ푝 ~ 0.01 atm), compressors (Δ푝 ≥ 1 atm) – Configs: axial, radial/centrifugal, or mixed Flow Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 3 Choosing the Right Fan/Compressor • Performance variables: 푤푠푡푎푔푒, 휂, Δ푝 = 푓(푚 , , 푁, 퐷, 휇, 푎) • 휓, 휂, 푝02 = 푓(휙, 푅푒, 푀) Non-dimensional form: 푝01 푤푠 푚 – Where 휓 = 휙 = 푁2퐷2 푁퐷3 loading coefficient flow coefficient • Specific speed • Specific diameter 1/2 1/2 1/4 1/4 휙 푁(푚 ) 휓 퐷 푤푠 푁푠 = 3/4 = 3/4 퐷푠 = 1/2 = 1/2 휓 푤푠 휙 (푚 ) Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 4 Cordier Line/Diagram 푁 푚 퐷 푤푠 푁푠 ~ 퐷푠 ~ 푤푠 푚 −1.936 8.26 퐷푠 −0.916 2.5 퐷푠 3.23 Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 5 Sample 푁푠퐷푠 (Balje) Diagram Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 6 Axial-flow Compressors Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 7 Axial-flow Compressors • Applications: Industrial gas turbines, aircraft engines http://www.youtube.com/watch?v=CXSi4GXUojo Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 8 Axial-flow Compressors • Best for applications with high 푁푠 and low 퐷푠 – High mass flow w/ relatively small Δ푝 per stage – Therefore large number of stages are needed – Each stage: rotor followed by stator single stage compressor section of a turbofan engine Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 9 Terminology • Cylindrical coordinate system 푟 • Velocity components » 푐푥: axial 푥 » 푐푟: radial 휃 » 푐휃: tangential/circumferential 2 2 » 푐푚 = 푐푥 + 푐푟 : meridional • Relative frame of reference 푐푥 » 푈: blade tangential velocity = 푟휔 훼 훽 푐휃 » 푤: relative velocity 푐 » 푐 : absolute velocity = 푤 + 푈 푤 푤 푈 휃 • Flow angles 푥 » 훼: absolute » 훽: relative 휃 Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 10 Flow through Compressor Stage • Pressure increase through both 1 rotor and stator 푤휃1 푐휃1 • Moderate pressure rise (flow deceleration) due to adverse pressure gradient 2 푤휃2 푐휃2 • As a result, blades have small curvature/camber; are very thin • Need multiple stages to create 푝 3 푥 large pressure increase 푐 푥 Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 11 Stage Work (Loading) • Euler’s equation: 푤푠 = 푈2푐휃2 − 푈1푐휃1 푤 = 푈(푐 − 푐 ) at mean radius 푤휃1 푐휃1 푠 휃2 휃1 » All work done in rotor, none in stator • Loading coefficient 푤휃2 푐휃2 2 휓 = 푤푠/푈 = (푐휃2 − 푐휃1)/푈 = Δ푐휃/푈 » 휓 directly related to flow turning Δ푐휃 Δ푐 » Higher 휓 → reduced no. of stages 휃 » Reducing inlet swirl → higher 휓 » 휓푑푒푠푖푔푛 ~ 0.4 Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 12 Flow Coefficient • Definition: 휙 = 푐푥/푈 » Determines change in flow angles » Typically 푐푥 const. thru compressor 푤휃1 푐휃1 » Higher 휙 → reduced flow turning » 휙푑푒푠푖푔푛 ~ 0.4-0.8 » 휓 and 휙 are directly related: 푤 푐 휓 = (푐휃2 − 푐휃1)/푈 휃2 휃2 ⋮ 휓 = 휙 tan 훼2 − tan 훼1 = 휙(tan 훽1 − tan 훽2) Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 13 Stage Reaction rotor stator Δℎ푟표푡표푟 ℎ2 − ℎ1 Δ푝 푟표푡표푟 푅 = = ≈ , 0 ≤ 푅 ≤ 1 Δℎ푠푡푎푔푒 ℎ3 − ℎ1 Δ푝 푠푡푎푔푒 1 2 3 • Impacts asymmetry of velocity triangles hence blade shapes • Typical range: 푅푑푒푠푖푔푛 ≈ 0.5-0.8 • Relationship with 휓 and 휙: 휓 = 2 1 − 푅 − 휙 tan 훼1 » Higher reaction tends to reduce stage loading Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 14 Stage Thermodynamics • Work: 푤푠 = 푈2푐휃2 − 푈1푐휃1 = ℎ02 − ℎ01 → ℎ01 − 푈1푐휃1 = ℎ02 − 푈2푐휃2 퐼 ≡ ℎ − 푈푐 rothalpy 0 휃 2 2 푤 푈 2 퐼 ≡ ℎ + − → 퐼 ≡ ℎ0,푟푒푙 − 푈 /2 2 2 • Enthalpy change across rotor: » 퐼1 = 퐼2 or at mean radius (푈1 = 푈2): rotor 2 stator ℎ01,푟푒푙 = ℎ02,푟푒푙 ℎ0,푟푒푙 = ℎ + 푤 /2 • Enthalpy change across stator (푈 = 0): 1 2 3 2 ℎ02 = ℎ03 ℎ0 = ℎ + 푐 /2 Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 15 Stage Losses & Efficiency • Efficiency of the compressor is impacted by the losses in each stage (rotor+stator) • Losses are typically quantified using correlations obtained from experimental tests annulus/clearance Losses secondary profile 휙 Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 16 • Profile/annulus losses • Tip leakage losses – BL drag & wake mixing » Tip vortex mixing • Secondary flow losses – Corner stalls, 3D effects • Shock-induced losses Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 17 Stage Loss Metrics • Enthalpy loss coefficients: ℎ2 − ℎ2푠 ℎ3 − ℎ3푠 휁푅 = 2 휁푁 = 2 rotor 푤2 /2 stator 푐3 /2 • Stagnation pressure loss coefficients: 푝01,푟푒푙 − 푝02,푟푒푙 푝02 − 푝03 푌푅 = 푌푁 = 푝01,푟푒푙 − 푝1 푝02 − 푝2 • Loss coefficients are related: – At low Mach numbers: 푌 ≈ 휁 – But at higher Mach numbers: 푌 > 휁 Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 18 Stage Efficiency • Efficiency 훾 − 1 푌푅 1 − 푝1/푝01,푟푒푙 + 푌푁 1 − 푝2/푝02 휂푡푡 ≅ 1 − 훾 1 − 푇1/푇03 Or 2 2 휁푅푤2 푇3 푇2 +휁푁푐3 휂푡푡 ≅ 1 − 2 ℎ03−ℎ01 » For low-speed/incompressible machines: 푇03Δ푠푠푡푎푔푒 Δ푝0,푅 + Δ푝0,푁 휂푡푡 ≅ 1 − = 1 − ℎ03 − ℎ01 ℎ03 − ℎ01 Or 2 2 (푤1 푌푅 + 푐2 푌푁) 휂푡푡 ≅ 1 − 2(ℎ03 − ℎ01) Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 19 Measuring Losses: Cascade Flow Analysis • Sample Cascade Tunnel • Main objective: – Characterize losses – Measure exit flow angle • Based on simplified 2D, steady flow • Both design and off-design conditions are tested Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 20 Cascade Nomenclature c1 c1 c2 c2 b = axial chord c/s = solidity Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 21 Some Design Criteria • Diffusion factor 푤 −푤 Δ푐 푠 DF = 1 2 + 휃 ≈ 0.45 푤1 2푤1 푐 Losses deceleration turning » Helps determine space-chord ratio (푠/푐) » For given DF, higher turning requires reduced blade spacing to avoid separation » Typical values: 푠/푐 ≈ 0.8 − 1.2 • Inlet swirl angle: 훼1 ≈ 20° − 30° » Helps reduce relative inlet Mach number H » Reduces flow turning hence stage loading • Blade aspect ratio: 퐻 푐 ≈ 1 − 2 s • Blade spacing: 푠 푏 ≈ 0.5 Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 22 Multi-stage Compressors • Effective annulus area is reduced because of BL growth – Axial velocity is adversely impacted Impact reduced after ~ 4th stage – The effect is taken into account by introducing work-done factor (휆): 푤 = 휆푈(푐 − 푐 ) 푠 휃2 휃1 – American design practice: apply blockage factor to account for reduced annulus area Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 23 Radial Flow Variations • 2D flow assumption only • For 푟ℎ푢푏/푟푡푖푝 ≈ 0.4-0.8, valid when 푟ℎ푢푏/푟푡푖푝 is blade speed (푈) & flow large (≥ 0.8) – typically angles will significantly last stages blades vary from hub to tip » Blades require significant twist Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 24 Radial Flow Variations • Change in annulus shape means 푐푟 cannot be ignored, although still smaller than 푐푥 and 푐휃 • Pressure increase from hub to tip to counter centrifugal forces acting on the fluid will cause slight variation in the radial direction • Radial flow variation is taken into account by solving “radial equilibrium equation” Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 25 Flow Instability - Surge • It is caused by drop in delivery pressure due to reduction in 푚 • If 푝푒푥푖푡 does not drop fast enough, air will reverse direction and flow upstream due to resulting pressure gradient. This will cause sudden drop of compressor exit pressure, reversing air flow direction… • The cycle can then continue at high frequency • Surge characterized by vibration in “axial” direction, causes excessive blade vibration, and can lead to flame-out (flame extinction) http://www.youtube.com/watch?v=osAT6mwkr94 http://www.youtube.com/watch?v=9KhZwsYtNDE Fluid Mechanics & Aeroacoustics of Fans and Compressors Farzad Taghaddosi (July 2, 2013) − page 26 Flow Instability – Rotating Stall • An instability usually observed at low operating speed (푁) • Is caused by blade stall (due to increased loading, tip vortex or corner stall), leading to flow blockage and change in angle-of-attack of neighboring blades (increase on one side and decrease on another side) • This causes neighboring blade stall an recover creating stall patches that will travel around compressor annulus • Rotating stall can exist in normal operating conditions; both part-span and full-span stall has been observed • It causes vibration in circumferential direction Fluid
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