Turbomachinery Compressor Design

Turbomachinery Compressor Design(1-D meanline design code of the T-AXI suite)Version 1.2USER MANUALMay 2007Mark G. TurnerDepartment of Aerospace Engineering & Engineering MechanicsUniversity of Cincinnati, OH, USAmark.turner@uc.eduAli MerchantGas Turbine LaboratoryMassachusetts Institute of Technology, MA, USAmerchant@mit.eduDario BrunaDepartment of Fluid-Machinery, Energy Systems and TransportationUniversity of Genoa, Italydario.bruna@unige.itCopyright owned by:Mark G. Turner, Ali Merchant, Dario Bruna

IntroductionThe T-C_DES (Turbomachinery Compressor DESign) code is a meanline axial flowcompressor design tool, the first step of T-AXI, an axisymmetric method for a completeturbomachinery geometry design. This manual describes the thermodynamic theory of the code andthe I/O files.Nomenclaturea Speed of sound H Total enthalpyc chord M Mach numberh Static enthalpy or blade height P Pressurem& Mass flowRgasGas constantq Meridional velocity magnitude S Blade spacing, S = 2πr/ Nbladesr Radius T Temperatures Entropy U Rotor wheel speedA Area V Absolute velocityCpSpecific heat at constant pressure W Rotor relative velocityDF Diffusion factorDR Diffusion ratioGreekα Absolute flow angle θ Tangential directionβ Relative flow angle ρ Densityδ Blockage source σ Solidity*δ Boundary layer displacement thickness Ω Rotor angular velocityγ Ratio of specific heats ω Compressor loss coefficientλ Blockage coefficientSubscriptsh Hub S Secondary flowLE Leading Edge T Totalm Mean or pitch TE Trailing Edget Tip W Workx Axial direction θ Tangential directionQ Heat Transfer

Stage Equations – Rotor & Stator + IGVThis section of the manual deals about the theory and the equations included in the code andused for the turbomachinery design. The basic configuration for an axial-flow compressor oftencomprises the IGV (inlet guide vane) and a series of stages, combination of a rotating row (rotor)and a stationary row (stator). The last stage usually has a guide vane (or stator) that turns the fluidinto the axial direction.IGVROTORSTATORThe first blade row: it develops the swirl or tangential velocity forwhich the first rotating row is designed. Guide vanes also serve thepurpose of preventing the injection of foreign objects into thecompressor and of breaking up large turbulent eddies in theatmosphere. The flow is accelerated through the IGV, resulting in adecrease in static pressure. If the first rotating row is designed for noinlet swirl, the inlet guide vane will normally be omitted. The IGV isa fixed vane and it is here treated as a generic stator row.The rotor, with its rotational motion, imparts energy to the workingmedium: it elevates the total pressure, the temperature and the kineticenergy of the fluid converting the major part of the mechanicalenergy into potential energy.The stator row removes the swirl developed by the rotor to convertkinetic energy to static pressure (by flow diffusion) and to establishthe proper swirl velocity for the flow to enter in the next rotor.The inlet and the outlet sections of each stage are labeled in this way:0. Inlet IGV1. Inlet Rotor = Outlet IGV2. Outlet Rotor = Inlet Stator3. Outlet Stator = Inlet Rotor for Multistage compressorAs already mentioned, the rotor is the rotational element by which it is possible to transferenergy to the fluid. Usually its flow is viewed and analyzed in the relative system (also rotatingframe), fixed to the rotor geometry. The absolute system (also stationary frame) is the reference,fixed to the ground, used to study the stator rows. The relationship between the relative velocityvector W rand the absolute velocity vector V ris:rV = U r+ Wrwhere U ris the rotor wheel speed,rU = Ω× rΩ is the rotor angular velocity and r is the meanline radius in the selected section. In the T-AXIsuite the rotation direction of Ω is defined positive if it is clockwise when the observer, behind theblade row, is looking forward.The next figure (Fig.1) shows the velocity triangles for a complete axial compressor stage,including the IGV row at the inlet and the second rotor row at the outlet section.

These are the velocity triangle relations:Fig. 1 – Velocity triangles diagram−⎛V ⎞= tan ⎜ θ⎟ ; V =⎝V x ⎠α1V xcosαW= V θ−UW = V ;θ;x x= tanβ−1⎛⎜⎝W θW x⎞⎟⎠W =W xcos βEuler’s Turbomachinery equation is used to define the total enthalpy rise due to stage work(transferred by the rotor row) as:Δ H = ∫ Ω d ( rV )WθThis equation can be applied across the rotor:H 2− H 1= C p(T T 2− T T1) =Ω( r 2V 2θ− r 1V 1θ )The following equations are some of all the formulas included in the code. Starting from thedata included in the input files, using these or rearranging these formulations, it is possible tocalculate the flow and the geometric quantities showed in the output files and needed for the design.T tT =; P =⎡ (γ −1) ⎤1+⎣⎢2 ⎦⎥ M 2 ⎧ ⎡ (γ −1) ⎤1+⎣⎢2 ⎦⎥ M ⎫⎨2 ⎬⎩⎭P tγγ −1

a = γR gasT ; V = Maρ =PR gasT ;A=m&ρVxλThe blockage coefficient λ is a term that represents the area reduction due to endwall boundarylayers, wakes, and other circumferential non-uniformities. For the T-AXI solver with the coupledboundary layer turned on, some of this blockage affect will be calculated.The cross sectional area is then:A = π r 2 2( t− r h )A hub, tip or midspan radius is given. From this and the area, the flowpath radii can be defined. Itshould be realized that the design aspect of turbomachinery is to determine how the flowpath areavaries. This is the real output of this design code, and is the critical quantity in an optimumcompressor design.The loss coefficient is specified as an input in T-C_DES. The total pressures in the followingequation are relative total pressure if applied for a rotor:ω = P T 2− P T1P T1− P 1The input loss coefficient can be updated, or viewed as a parameter that is used along with theother parameters to create the flowpath area of the compressor. The average loss coefficient is thencalculated in the T-AXI solver.In the following table 1 the calculated performance parameters for the turbomachine are listed.Compressor Pressure RatioCompressor Temperature RatioCompressor Adiabatic EfficiencyCompressor Polytropic EfficiencyPR Comp= P ToutP TinTR Comp= T ToutT Tinγ −1γη Comp _ ad= PR Comp−1TR Comp−1( )( )η Comp _ pol= γ −1 ln PR Compγ ln TR CompTable 1 – Compressor performance parametersIf the design includes the IGV then two different values for the Compressor Pressure Ratio arecalculated:

1. (No IGV) - PR Comp= P ToutP Tin2. (With IGV) - PR Comp= P ToutP TinP Tin = P T @Section 1, 1st StageP Tin = P T @Section 0, 1st StageThe definitions of the stage properties (included in the Tcdes-results file) are listed in Table 2.Stage Pressure Ratio PR = P T 3P T1Stage Adiabatic EfficiencyStage Polytropic Efficiencyγ −1η ad= PR γ−1T 3−1T T1η pol= γ −1γDegree of Reaction R = T 2 − T 1T 3− T 1( )ln PR⎛ln T ⎞3⎜ ⎟⎝ ⎠Rotor Diffusion Factor DF R=1− W 2W 1W 1θ−W 2θ2σW 1T T1Stator Diffusion Factor DF S=1− V 3V 2V 2θ−V 3θ2σV 2Stage Load Coefficient ψ = C p( T 2− T T1 )2U 2Stage Flow Coefficientφ = V 1xU 2Table 2 – Stage parameters

Block Diagram – I/OV θ1= a r − b r mr mrV θ1= a r + b r mr mrThe input to T-C_DES is an “init” file, a “stage” file, and an optional “igv” file. If the “igv” filedoes not exist, it is assumed that there is no igv in the design. These files contain all the informationneeded for the design: geometrical, fluid and turbomachinery working data. Moreover in the “init”file it is also included the clearance ratio (the clearance divided by radius), an input quantity for thenext axisymmetric code of T-AXI. The radius is the tip radius for a rotor and hub radius for astator. For a preliminary compressor layout, the one clearance to radius number was felt to be more“constant” than a clearance to height or clearance to chord ratio.The output of T-C_DES is a “tcdes-results” file, a “cgeo” file, a “crvth” file, a “stack” file anda “walls” file. Some of these files are the input for the T-AXI code and they are detailed describedin this section.Figure 2 shows the T-C_DES input/output block diagram. The file extension, here “xxx”, has tobe the same for all the input files in order to run the code. Then it will return the output files namedwith the same extension.Fig. 2 – T-C_DES input/output block diagram- Init.xxx – This file contains the general informations for the single or multistage compressordesign. The next table shows all the options and the data included.Units1- SI: International System2- EN: English SystemRadius Option1- Constant HUB2- Constant PITCH3- Constant TIP4- ArbitraryDesign Option1- Free Vortex2- Forced Vortex3- Exponential4- First Power5- CustomableinFLAG4inFLAG5inFLAG6N° Stages Maximum stage number: 20

Mass Flow RateSI: [kg/s] – EN: [lbm/s]Inlet Total PressureSI: [Pa] – EN: [psi]Inlet Total TemperatureSI: [K] – EN: [R]Alpha 3 (Absolute angle) – Last Stage[deg]Mach 3 – Last Stage [-]Ratio of Specific Heats [-]Gas ConstantSI: [kJ/(kg K)]- EN: [ft 2 /(s 2 R)]Ratio of Clearance [-]Radius if constant hub, mean or tip radii design SI: [m] – EN: [in]option usedTable 3 – Init.xxx file data- Stage.xxx – In this file the geometrical information and thermo-fluid dynamic data for eachstage are included. The data are organized in columns whose numbercorresponds to the stage number of the multistage compressor. The Table 4 isan example of all the information included for each stage.Alpha 1 (Absolute angle)[deg]Mach 1 [-]Total Tempearature RiseSI: [K] – EN:Rotor Loss Coefficient [-]Stator Loss Coefficient [-]Rotor Solidity [-]Stator Solidity [-]Stage Lambda [-]Stage Bleed [-]Rotor Aspect Ratio [-]Stator Aspect Ratio [-]Rotor Axial Velocity Ratio [-]Rotor Row Space Coefficient [-]Stator Row Space Coefficient [-]Stage Tip RadiusSI: [m] – EN: [in]This data has to be specified if the 4 th radiusoption in the “init” file is usedTable 4 – Stage.xxx file data- Igv.xxx – If this file is included in the same directory with the “init” and “stage” files thedesign starts automatically with IGV as first blade row (Table 5).IGV Solidity [-]IGV Aspect Ratio [-]IGV Loss Coefficient [-]Alpha 0 (Absolute angle)Mach 0 [-]IGV Lambda [-][deg]IGV Row Space Coefficient [-]IGV Tip RadiusSI: [m] –EN:[in]Table 5 – Igv.xxx file data

- Tcdes-results.xxx – This file is a result summary for all the compressor. Many usefulinformations about the fluid, row and stage properties are included andsummarized in the present way. These quantities are analyzed forevery stage of the turbomachine in the sections:0. Inlet IGV1. Inlet Rotor = Outlet IGV2. Outlet Rotor = Inlet Stator3. Outlet Stator = Inlet Rotor for Multistage compressorThe thermo-fluid dynamic properties summarized in Table 6 arecalculated at the different span-wise sections (hub, mean or tip),according to the only free-vortex design option. If a different angularmomentum distribution (forced, exponential, first power and custom)is selected just the stack file, input for the 2-D floe solver, is updated.This file reflects always the free-vortex option values.TT Total Temperature SI: [K] – EN: [R]Ts Static Temperature SI: [K] – EN: [R]PT Total Pressure SI: [kPa] – EN: [psi]Ps Static Pressure SI: [kPa] – EN: [psi]Mach Mach Number [-]Vel Velocity SI: [m/s] – EN: [ft/s]Ax V Axial Velocity SI: [m/s] – EN: [ft/s]TangV Tangential Velocity SI: [m/s] – EN: [ft/s]α / β Fluid Angle SI: [m/s] – EN: [ft/s]Radius Streamline Radius SI: [m] – EN: [in]Table 6 – Thermo-fluid dynamic properties output in the “tcdes-results” fileThe other quantities included in the files for each stage are:- Section Area & Height- Rotor Tip Relative Mach Number- Rotor – Stator Chord & Blades Number- Stage Pressure Ratio- Stage Adiabatic & Polytropic Efficieny- Degree of Reaction- Rotor – Stator Diffusion Factor- Stage Load & Flow CoefficientFor the complete machine:- Compressor Pressure Ratio (With & Without IGV)- Compressor Temperature Ratio- Compressor Adiabatic & Polytropic Efficiency- cgeo.xxx – This file presents the annulus channel geometry of the compressor: the hub andtip coordinates of the leading and trailing edge of each row are included. Withthis file it is possible to check the medirional view of the machine. For eachstage there are four lines: two are the leading and trailing edge of the rotor, the

other two the leading and trailing edge of the stator. The first and the last lines ofthe file are refferred to the inlet and outlet sections. The first parameter is thestage index. For a design with the IGV row (two lines in the file) the IGV indexis 0.Stage IndexHub coordinateAxis directionSI: [m] – EN: [in]Hub coordinateRadius directionSI: [m] – EN: [in]Tip coordinateAxis directionSI: [m] – EN: [in]Tip coordinateRadius directionSI: [m] – EN: [in]Table 7 – Cgeo.xxx file data- cvrth.xxx – The number of blades and the R*V θ product are the quantities included in thisfile. The first parameter is the blade row index; if the IGV is present in thedesign (first line of the file) the first rotor data will be included in the secondline.Blade Row Index Number of Blades (R HUB *V θ ) ROW INLETTable 8 – Cvrth.xxx file dataThese last two files are the input needed to run the T-AXI solver.- stack.xxx – This file includes the overall information for each blade row and for the fullcompressor axis-symmetric calculation. For each blade row the data included(Tab.9) are: LE and TE geometry coordinates (radius, axis), loss, bleed andangolar momentum. The geometric coordinates are non-dimensionalized by theRotor 1 leading edge radius at the tip (reference length). The angularmomentum is non-dimensionalized by the reference length and the referencevelocity (sonic velocity at the inlet). If the design vortex is not the free-vortexthe stack file includes the geometry, loss, bleed and angolar momentum for 12different spanwise sections (included the hub and the tip), not just for the huband tip.For the custom angular momentum design option the starting, but customableR*V θ , is the free-vortex value, included for 12 different spanwise sections.Number ofBladesRotationalSpeedHubClearanceTipClearanceRadial_LE@HubRadial_TE@HubAxial_LE@HubAxial_TE@HubLoss Bleed R HUB *V θRadial_LE@TipRadial_TE@TipAxial_LE@TipAxial_TE@TipLoss Bleed R TIP *V θTable 9 – Stack.xxx file data

Table 10 shows the data needed for the full compressor calculation.γTT_inlet[deg R]Type Flag0 - Comp/1 - TurbMachReBoundaryLayerSwitchViscousFlagTable 10 – Stack.xxx file data- walls.xxx – The dimensionless coordinates of the meridional section of the compressor arehere listed.

ReferencesM. G. Turner, A. Merchant, D. Bruna, “A Turbomachinery Design Tool for Teaching DesignConcepts for Axial-Flow Fans, Compressor and Turbines”, ASME Turbo ExpoGT2006-90105, May 8-11, 2006, Barcelona, Spain.D. Bruna, M. G. Turner, A. Merchant, C. Cravero, “An Educational Software Suite forTeaching Design Strategies for Multistage Axial-Flow Compressors”, ASMETurbo Expo GT2007-27160, May 14-17, 2007, Montreal, Canada.J. D. Mattingly, “Elements of Gas Turbine Propulsion”, 2005, AIAA Education SeriesB. Lakshminarayana, “Fluid Dynamics and Heat Transfer of Turbomachinery”, 1996, WileyR. H. Aungier, “Axial-Flow Compressors – A strategy for Aerodynamic Design and Analysis”,2003, ASME-PressM. Schobeiri, “Turbomachinery Flow Physics and Dynamic Performance”, 2005, Springer-Verlag Berlin Heidelberg