turbomachinery design tools for teaching design concepts for axial flow fans - compressors and...

Proceedings of ASME Turbo Expo 2006 Power for Land, Sea, and Air

May 8-11, 2006, Barcelona, Spain

GT2006-90105

A TURBOMACHINERY DESIGN TOOL FOR TEACHING DESIGN CONCEPTS FOR AXIAL-FLOW FANS, COMPRESSORS, AND TURBINES

Mark G. Turner University of Cincinnati

[email protected]

Ali Merchant MIT

[email protected]

Dario Bruna University of Genoa, Italy

[email protected]

Proceedings of GT2006 ASME Turbo Expo 2006: Power for Land, Sea and Air

May 8-11, 2006, Barcelona, Spain

GT2006-90105

ABSTRACT

A new turbomachinery design system, T-AXI, is described and demonstrated. It is intended primarily for use by educators and students, although it is sophisticated enough for actual designs. The codes, example cases and a user’s manual are available through the authors’ web sites. The design system can be used to design multistage compressors and turbines from a small number of physical design parameters. Students can understand the connection between these physical parameters such as Mach number and flow angles to the cross sectional area and angular momentum. There is also a clear connection between the angular momentum, work and blade loadings.

Loss models are built-in and results are compared against tested geometries. The code also has a built-in blade geometry generator and the geometry can be output for running the MISES blade-to-blade solver on each section or visualizing the blades.

A single stage compressor from the US Air Force Stage Matching Investigation rig, the 10 stage NASA/GE EEE high pressure compressor and the NASA/GE EEE 5 stage low pressure turbine have been used to validate T-AXI as a design tool.

INTRODUCTION There are very few non-proprietary turbomachinery

design tools available for teaching fan, compressor or turbine design. Mattingly [1,2] provides the codes COMPR and TURBN as part of a CD in ref. [1]. The algorithms for these codes are described in [2], and this method of design has been extended in this paper. One of the issues with this software is that bleed and blockage cannot be analyzed, and only one value of solidity can be specified for the entire machine. Blade gaps are also hard-coded. In addition, the loss in a blade row must be specified in order to get an answer, and is not calculated.

A recent effort at Lund University [3,4] is a turbine analysis code available from within MATLAB. One needs to know MATLAB to run it, and this software is not available for a compressor.

Because of these limitations, a new turbomachinery design system, T-AXI, was created from some tools that had been used by Merchant to create high pressure ratio aspirated fan designs [5,6]. This new design system can create a new multistage compressor or turbine from a table of design parameters. In addition, the performance of an existing compressor or turbine can be approximated. A built-in loss model is applied that has most loss sources accounted for. A geometry generator is also available so that an initial geometry can be created to jump-start a mixed inverse blade-to-blade design tool, estimate weights, or create a 3D blade that can be visualized or analyzed in 3D.

This paper is intended to describe and demonstrate this new turbomachinery design system, T-AXI, for gas turbine educators as well as undergraduates and graduate students studying gas turbines. Executable versions of the codes making up this new design system are available from the authors’ web sites along with the examples shown in this paper and a user’s manual. Although this design system is aimed for educational use in the context of this paper, it is sophisticated enough for creating actual designs.

NOMENCLATURE

a Speed of sound c chord h Static enthalpy or blade height m& Mass flow q Meridional velocity magnitude

1 Copyright © 2006 by ASME

mailto:[email protected]



r Radius s Entropy A Area

pC Specific heat at constant pressure

DR Diffusion ratio H Total enthalpy M Mach number P Pressure

gasR Gas constant

S Blade spacing, bladesNrS /2π= T Temperature U Rotor wheel speed V Absolute velocity W Rotor relative velocity Y Turbine loss coefficient Z Zweifel oefficient

Greek α Absolute flow angle β Relative flow angle

δ Blockage source *δ Boundary layer displacement thickness

γ Ratio of specific heats λ Blockage coefficient θ Tangential direction ρ Density σ Solidity ω Rotor angular velocity ω Compressor loss coefficient

Subscripts h hub t tip x axial Q Heat Transfer S Secondary flow T Total W Work θ Tangential direction 1 Leading edge 2 Trailing edge

ANALYSIS Figure 1 is a schematic of the T-AXI Turbomachinery

Design System. It is made up of the T-AXI solver described in detail later in this section, as well as the compressor and turbine design modules and the turbine set-up module. The T-AXI solver works with non-dimensional input. The “walls” file defines the hub and casing geometry, and the “stack” file includes the details needed for each blade row including the leading and trailing edge geometry, the angular momentum at

the blade row trailing edge, the rotation speed, blockage, and number of airfoils.

T-AXI is an axisymmetric solver. Most axisymmetric solvers use a streamline curvature method as described by Smith [7] and Novak [8]. The method employed in the T-AXI solver is more like the MISES algorithm [9,10]. Loss models are applied at each spanwise section depending on whether it is a compressor or turbine. To increase the robustness of the calculation, the loss is smeared out just downstream of the trailing edge. This has the effect of spanwise mixing described by Adkins and Smith [11] with an extremely simple approach.

The input “walls” and “stack” files can be created by hand for a general calculation. Detailed knowledge of the code non-dimensionalization and formatting are needed to do this. Alternatively, the compressor design code T-C_DES, the turbine design code T-T_DES, or the turbine set-up code T-2-T-AXI, can be used to automate the calculations based on design parameters. Straight leading and trailing edges are used without contouring as well as a free-vortex assumption. A fourth approach to creating the input files for T-AXI is to extract the axisymmetric geometry, trailing edge angular momentum and rotation rates from a 3D simulation. This approach has been used for the SMI example case, but is too specific to make available for general use.

The input to T-C_DES is an “init” file, a “stage” file, and an optional “igv” file. If the “igv” file does not exist, it is assumed that there is no igv in the design. These files provide tabular input to the code that is similar to COMPR developed by Mattingly [1]. The clearance ratio is the clearance divided by radius. This is the tip radius for a rotor and hub radius for a stator. For a preliminary compressor layout, this one clearance to radius number was felt to be more “constant” than a clearance to height or clearance to chord ratio. The input to T-T_DES is an “init,” “stage,” and an optional “ogv” file that are similar to the T-C_DES input, but tailored for a turbine. The input to the turbine set up code is an “init” file, a geometry file (“cgeo”) with leading edge and trailing edge coordinates at the hub and casing, and a file that describes the number of blades and angular momentum for each blade row (“cvth”). Files that can be edited have been used as code input. These could also be accessed by an optimizer so that the T-AXI system could be part of an overall compressor or turbine optimization system.

The output of the T-AXI solver is a tabular listing of the profiles of aerodynamic quantities at each leading and trailing edge. Profiles of loss, loading, and geometry are tabulated for each blade row. Average loss, total pressure and temperature ratio, and efficiency are calculated for each blade row as well as the entire component. Given a maximum thickness to chord ratio at the hub and casing, a blade shape is created for 5 spanwise sections. This can be viewed as a 3D solid with a Blade Viewer, or the volume and mass of a blade can be calculated. The 5 sections are also output as files consistent with a MISES calculation [9,10]. A blade-to-blade solution can therefore be obtained for this geometry including a coupled boundary layer solution. MISES has been used by industry to


T-AXI

bladedata-xxx.dat

cgeo.xxx

cvth.xxx

blade3d.brx

stack.xxxwalls.xxx

Blade Viewer

Blade Volume

Mises files Mises

T-C_DES

init.xxx

igv.xxx

stage.xxx

tcdes-results.xxx

T-2-T-AXICompressor design code

Turbine Set-up code

3D mesh+

SolutionCompressor or Turbine 3D RANS

Blade Design

Feedback To T-AXI

init.xxx

T-T_DES

init.xxx

ogv.xxx

stage.xxx

ttdes-results.xxx

Turbine design code

T-AXI

bladedata-xxx.datbladedata-xxx.dat

cgeo.xxxcgeo.xxx

cvth.xxxcvth.xxx

blade3d.brxblade3d.brx

stack.xxxstack.xxxwalls.xxxwalls.xxx

Blade Viewer

Blade Volume

Mises filesMises files Mises

T-C_DES

init.xxxinit.xxx

igv.xxxigv.xxx

stage.xxxstage.xxx

tcdes-results.xxxtcdes-results.xxx

T-2-T-AXICompressor design code

Turbine Set-up code

3D mesh+

Solution

3D mesh+

SolutionCompressor or Turbine 3D RANS

Blade Design

Feedback To T-AXI

init.xxxinit.xxx

T-T_DES

init.xxxinit.xxx

ogv.xxxogv.xxx

stage.xxxstage.xxx

ttdes-results.xxxttdes-results.xxx

Turbine design code

Figure 1. Schematic for T-AXI Turbomachinery Design System.

optimize airfoils as shown in references [12,13]. A mixed-inverse option is also available so that an improved pressure distribution can be specified, and a new blade shape determined. The ability of the design system to create a starting geometry can then be used to generate more optimum blade sections. The output of MISES can also be used to update the loss and turning in the “stack” file to be fed back into T-AXI. MISES is currently freely available for educational use, and can be obtained from Mark Drela through the ACDL website at http://raphael.mit.edu. For commercial use it must be obtained through the MIT Technology Licensing Office.

T-C_DES Compressor Flow Path Creator The compressor design code T-C_DES is similar to

COMPR described by Mattingly [1,2]. The analysis presented in reference [2] is similar except that a blockage term has been added that is often used by compressor designers to define the build up of wakes and endwall boundary layers as well as other non-uniform flow circumferentially. In addition, the input allows for bleed, a unique solidity for each blade row, and the flowpath for each stage is smoothed at the end of the design. The following equations can be applied from the given input.

T =Tt

1+ [(γ −1) /2]M 2 (1)

P =Pt

1+ [(γ −1) /2]M 2{ }γ /(γ −1) (2)

ρ =P

RgasT (3)

a = γRgasT (4)

MaV = (5)

αcosVVx = (6)

αθ sinVV = (7)

λρ xVmA&

= (8)


where λ is the blockage. In reality this blockage is a term that represents the area reduction due to endwall boundary layers, wakes, and other circumferential non-uniformities. For the T-AXI solver with the coupled boundary layer turned on, some of this blockage affect will be calculated.

The cross sectional area is then: A = π rt

2 − rh2( ) (9)

A hub, tip or midspan radius is given. From this and the area, the flowpath radii can be defined. It should be realized that the design aspect of turbomachinery is to determine how the flowpath area varies. This is the real output of this design code, and is the critical quantity in an optimum compressor design.

The loss coefficient is specified as an input. The total pressures in the following equation are relative total pressure if applied for a rotor.

11

12

PPPP

t

tt

−−

=ω (10)

The average loss coefficient is also calculated in the T-AXI solver. The input loss coefficient can be updated, or viewed as a parameter that is used along with the other parameters to create the flowpath area of the compressor. If the loss is not updated, the other specified parameters such as the Mach number and angles will not be set precisely, but will vary depending on the actual loss calculated.

Euler’s Turbomachinery equation is used to define the total enthalpy rise due to stage work as

∫Ω=Δ )( θrVdHW (11)

Equation (11) can be applied across the rotor ( )11221212 )( θθ VrVrTTCHH TTp −Ω=−=− (12)

The free vortex assumption is applied where constrV =θ (13)

across the span of the blade row. The velocity triangle relations are:

⎟⎟⎠

⎞⎜⎜⎝

⎛= −

xVVθα 1tan ;

αcosxV

V = ; UWVrrr

+=

UVW −= θθ ; xx VW = ; ⎟⎟⎠

⎞⎜⎜⎝

⎛= −

xWWθβ 1tan

βcosxW

W = (14)

T-T_DES Turbine Flow Path Creator The turbine design code T-T_DES is similar to T-C_DES

described above and TURBN described by Mattingly [1,2]. There are several advantages over the TURBN code: an average meanline radius can be specified for each blade row;

and the blade row gap parameters can be specified after each nozzle and rotor. These additional input parameters allow for a very general turbine design capability.

Euler’s Turbomachinery equation is used for the turbine to define the change in tangential velocity across the rotor just as it was for the compressor. The equations used are similar, except that the turbine loss coefficients are normalized by the trailing edge dynamic pressure.

22

12

PPPP

Yt

tt

−−

= (15)

In addition, the Zweifel coefficient [14] is used to set the number of blades in a blade row.

22

21 costantan2 ααα −⎟⎟⎠

⎞⎜⎜⎝

⎛=

xcSZ (16)

for a nozzle, and relative flow angles are used in Equation (16) for a rotor. The blade spacing bladesNrS /2π= .

T-AXI Solver The T-AXI inviscid solver is based on the multiple

interacting streamtube Euler equation formulation that is the foundation of several design codes developed by Drela and Giles [9] and Youngren and Drela [10]. In T-AXI, the axisymmetric equations are discretized in a strong conservative form on a meridional streamline grid. In contrast to typical streamline curvature codes, T-AXI has no inherent limitation at high subsonic Mach numbers, and can be used in subsonic as well as supersonic flow regimes.

The streamwise momentum equation has the form:

0)()(

])([

=Δ−Δ

+−++

WHdspd

drVrVdrVqdqdp

ρ

ρρ θθθ

(17)

Here, p is the pressure, ρ is the density, and q is the

meridional velocity given by 22rx VV + . The differentials d()

are applied at each grid point along each streamtube, including the blade rows. sΔ is the prescribed entropy change in the streamtube that is a result of losses from various sources. The entropy s is defined as

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡⎟⎠⎞⎜

⎝⎛⎟⎠⎞⎜

⎝⎛≡

−1ln γγ

inlet

inleth

hp

ps (18)

Here, h is the static enthalpy and p is static pressure. The total enthalpy rise due to stage work is defined using Equation (11), the Euler’s Turbomachinery Equation. The angular momentum, θrV , is prescribed as an input along with the

rotational speed, Ω , of the blade row. Therefore, the enthalpy change due to a compressor or turbine rotor is explicitly available. The energy equation is also not explicitly solved, but


the enthalpy at every point along a streamtube is calculated using

QW HHqhH Δ+Δ++= 2

21

(19)

The last term in the above equation accounts for any total enthalpy change due to heat addition or removal to the streamtube, and is also explicitly specified. The definition of the enthalpy can be combined with the streamwise momentum equation to produce the entropy-advection equation with imposed source terms due to heat addition and adiabatic loss

0)()( =Δ+Δ+− QHdspdpds ρ (20)

This equation can be used in all or parts of the flow field to replace the momentum conservation equation with the benefit of reducing spurious entropy generation due to numerical errors.

Finally, conservation of mass is imposed internally due to the streamline grid, and in addition mass can be discretely added or removed from each cell of a streamtube

0)( =Δ+ fmdmd && (21)

where fm&Δ is the prescribed bleed or injection flow.

Conservation of mass also takes into account circumferential area change referred to as blockage in the context of this paper. The meridional speed is calculated from the definition of mass flow at a point in the streamtube

λρAmq&

= (22)

A is the flow area of the streamtube and λ is the blockage defined as a reduction in flow area

rπδλ

21−= (23)

Here, δ could be a result of metal blockage due to the blades, boundary layers, or tip clearance flows, and other sources arising from non-uniformities in the flow.

The discrete equations described above are arranged in a form where the unknowns are the change in density and streamline positions, and the non-linear system is solved using a global Newton method [9]. A particular advantage of this approach is that the streamline positions are simultaneously calculated as part of the solution and no explicit iteration is required to update the streamline positions as in traditional streamline curvature codes making T-AXI computationally inexpensive and extremely robust.

Endwall boundary layer development is calculated using the two-equation integral boundary formulation [9]. These equations are coupled with the inviscid equations described above and solved simultaneously. The endwall boundary layer

captures the effect of meridional velocity changes across a blade row and due to variations in the flowpath. While this formulation does not model many of the effects seen in turbomachines [15], it was found to add an adequate amount of blockage and loss to the endwalls to capture most of the endwall effects. In particular, it was found that for a multistage compressor, the endwall boundary layer evolution captures the trend seen on repeating blade row machines.

Loss Models Loss is introduced into the streamtubes using the entropy

source term described above. Different loss models are used for compressors and turbines determined by the operating mode. The T-AXI code is modular enough to support implementation of custom loss models or databases, and not restricted to the models described below. An important distinction on using these models in T-AXI when compared to a meanline code is that relatively accurate flow information in terms of Mach numbers, velocities, angles, etc. are available to use as inputs to the loss models.

Compressor a) Diffusion Loss: The loss due to boundary layers on the

blade is estimated using a correlation for momentum thickness using the blade diffusion ratio as the driving parameter. The blade diffusion ratio defined as the ratio of the peak velocity to the trailing edge velocity is estimated using an assumption of a roof-top profile with the roof-top extending to 40% of blade chord.

)/,,,,,,,( 212121 ctWWrrfDR σββ= (24) The inputs are the radii, relative flow angles, and relative velocities at the inlet and exit, and the solidity and thickness to chord ratio. The momentum thickness is estimated using the correlation by Fottner [15] modified to account for low Reynolds numbers effects.

b) Shock Loss: The shock loss is estimated by assuming that the loss is entirely generated by a normal shock at the inlet relative Mach number. While this is a simple assumption, it is shown to be adequate for many compressors [16]. The relative Mach number input to the loss model is limited to 1.5, with the assumption that appropriate blade design will limit the Mach number to values that do not cause excessive flow separation.

c) Clearance Loss: Hub and tip clearance losses are estimated based on the model described by Denton [17]. The model calculates the mass flow through the clearance gap driven by the pressure difference across the blade. This is estimated from the velocity components available in the axisymmetric calculation. A discharge coefficient value of 0.8 is used. This same model is also used for shrouded stators even though the physics are different.

d) Endwall Loss: The end wall loss is directly estimated from the integral boundary layer calculation on the hub and casing walls. The displacement and momentum thickness are readily available and used to calculate the entropy rise that is added to the overall loss.


Turbine a) Profile Loss: Most profile loss calculation methods for

turbines are based on fitting experimental data and involve a look-up table approach. This was found to be much too complex an approach for T-AXI with little sound physical basis. The approach that has worked well for compressors loss in T-AXI is to assume a pressure distribution from which to estimate the profile loss. For sake of simplicity, the profile loss is estimated based on the idealized surface velocity distribution described by Denton [17]. The loss coefficient is given by

)tan(tan62 12 ββ −⎟⎠

⎞⎜⎝

⎛ Δ+

Δ=

WW

WWCY D (25)

Absolute velocities and angles are used for stationary blade rows. The flow angles and velocity are available locally, and

WΔ is estimated from the local angular momentum change. The dissipation coefficient DC is assumed to be 0.002 for

turbulent flow and 6/1Re0056.0 θ for laminar flow. In addition to the base profile loss, a small additional loss is added based on the diffusion that occurs near the trailing edge on highly loaded turbines. The diffusion factor defined by Lieblein [18] is used to estimate this additional loss, and it is only applied when the diffusion factor is positive.

b) Trailing Edge Loss: Mixing loss due to thick trailing edges commonly found on turbines is estimated using a stream thrust calculation using the flow conditions at the trailing edge of a blade row. A fixed value of base pressure drag coefficient

15.0−=PbC is used in the momentum balance. c) Trailing Edge Shock Loss: A small amount of shock

loss is added when the relative flow exiting the turbine is supersonic. This accounts for weak shocks that may occur near the turbine trailing edge. The compressor shock loss model is used, but the Mach number in the loss model is limited to 1.2.

d) Clearance Loss: The clearance model described above for compressors is also used for turbines.

e) Endwall Loss: The endwall loss is calculated from the endwall boundary layer parameters as described above for compressors.

f) Secondary Flow Loss: The secondary flow loss is estimated using the equation given by Dunham:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

cgCf

hcY L

inlet

exitS

*

)()cos()cos( δ

ββ

(26)

SY is the total pressure loss normalized by the downstream

dynamic head, hc / is the chord to span ratio, )( LCf is Ainley’s parameter that depends on the lift or circulation of the blade row, and )/( * cg δ is a function that depends on the incoming boundary layer thickness. A fixed value of g=0.034 is currently used in T-AXI. The relative flow angles are used for rotating blade rows and absolute for stationary blade rows. A detailed description of this model can be found in [19].

Spanwise Mixing or Averaging The T-AXI code also includes a simple spanwise mixing

model to capture the mixing of losses that occurs in multistage compressors. The physical mechanisms of the mixing process are described by Adkins and Smith [11]. This is also required for numerical reasons to prevent accumulation of loss in the streamtubes nearest to endwalls. The option used in T-AXIS is spanwise averaging of the losses, where entropy is mass averaged over all the streamtubes. This makes T-AXI a quasi-meanline code, but the distinction is that the loss is calculated based on the local spanwise conditions in a blade row.

Modes of operation T-AXI is essentially a design code with “rubber” blade

geometry. The design angular momentum downstream, θrV , of a blade row is prescribed and held fixed. With the T-C_DES or T-T_DES code, a free vortex assumption is used and a constant value of θrV is calculated behind each blade row. In other design scenarios, the angular momentum can be obtained as a spanwise profile from a 3D CFD calculation or a quasi-3D blade-to-blade calculation, where the objective is to design a blade shape to meet the required conditions in T-AXI.

A constant spanwise angular momentum, θrV , in T-AXI is a free vortex design. Other variations of angular momentum can also be imposed creating a forced vortex design. At a minimum, the hub and tip angular momentum values must be prescribed.

Blade Design The axisymmetric design solution provided by T-AXI is

rich enough to begin and rapidly explore blade designs that can produce the desired performance. T-AXI is therefore equipped with a blade generator that uses the flow solution as input to generate blade sections as well as a complete 3D stacking of the blade. Blade sections and flow conditions on streamtubes can be exported with blade shapes in the MISES [9,10] design code format. The initial blade shapes provided by T-AXI can then be used to perform redesign in MISES.

RESULTS In order to demonstrate the capability of the T-AXI design

system, the approach has been applied on a single stage compressor, a ten stage high pressure compressor (HPC), and a 5 stage low pressure turbine (LPT). The single stage compressor was designed for the Stage Matching Investigation (SMI) rig for the US Air Force [20-22]. The 10 stage HPC and the five stage LPT were developed by GE Aircraft Engines as part of the NASA Energy Efficient Engine (EEE) Program. Many of the design and test reports can be downloaded from the web as pdf files. The web site is http://ntrs.nasa.gov. In the search dialogue box, just put the Contract Report number and one can access the pdf files for references [23-26].


Single Stage Compressor The SMI rig as described by Chriss [20] has been analyzed

with T-AXI and designed with T-C_DES. Figures 2 and 3 show the rig cross section and the measured stage characteristic respectfully. Table 1 lists the parameters that define this stage design. The 3D solution for the close wake generator configuration was used to create the walls and stack file for the T-AXI calculation. The inputs for the one stage design in T-C_DES are in Tables 2 and 3. These design parameters were set based on the measured flow rate and wheel speed as well as comparing to the geometry of the actual hardware. The overall results are in Table 4. The T-AXI results assume a good design execution. The comparison between the two T-AXI runs is very similar. It is not known why the measured efficiency was so much lower than the T-AXI calculation.

Figure 4 shows the initial T-AXI grid for the one stage design as well as the T-AXI screens during the different runs. The initial screen shows the input angular momentum. With Euler’s Turbomachinery equation, the enthalpy rise is calculated.

The boundary layers are turned on once the solution is converged with the loss model.

Figure 2. Stage Matching Investigation rig cross-section (from Chriss [20].

Figure 3. SMI measured overall stage characteristic for the “clean” inlet and 40 wake generator configurations (from Chriss [20]).

Table 1. SMI Aerodynamic Design Parameters (from Chriss [20]).

Parameter Rotor Stator Number of airfoils 33 49 Aspect Ratio - average 0.961 0.892 Inlet Hub/Tip Ratio 0.75 0.816 Flow/Annulus Area, lbm/sec/ft^2 40 Flow/Frontal Area, lbm/sec/ft^2 17.502 Flow Rate, lbm/sec 34.46 Tip Speed, Correcte (ft/sec) 1120 Mrel, LE Hub 0.963 0.82 Mrel, LE Tip 1.191 0.69 PR, Rotor 1.88 PR, Stage 1.84 D factor, Hub 0.545 0.502 D factor, Tip 0.53 0.491 LE Tip Diameter, in. 19 19 LE Hub Diameter, in. 14.25 15.502

Table 2. Stage data for one stage design (stage.smi-des).

Parameter Stage 1 Stage rotor inlet angle [deg] 0 Stage rotor inlet Mach no. 0.5635 Total Temperature Rise [K] 61.38 Rotor loss coef. 0.076 Stator loss coef. 0.04 Rotor Solidity 1.892 Stator Solidity 1.838 Stage Exit Blockage 1 Stage bleed [%] 0 Rotor Aspect Ratio 0.69 Stator Aspect Ratio 0.84 Rotor Axial Velocity Ratio 0.863 Rotor Row Space Coef. 0.07 Stator Row Space Coef. 0.05

Table 3, Initial data for one stage design (init.smi-des).

Number of Stages 1 Mass Flow Rate [kg/s] 15.631 Rotor Angular Velocity [rpm] 13,508.92 Inlet Total Pressure [Pa] 101,353 Inlet Total Temperature [K] 288.167 Alpha 3 - Last Stage [deg] -2.5 Mach 3 - Last Stage 0.458 Ratio of Specific Heats 1.4 Gas Constant [kJ/kg*K] 0.28704 Clearance Ratio 0.00158 Tip Radius [m] 0.2413


Table 4. Performance Data for SMI example.

SMI Overall

Goal SMI "clean" measurement

T-AXI calculation with SMI flowpath

T-AXI calculation for

free-vortex design

Temperature Ratio 1.213 1.213 Pressure Ratio 1.84 1.8 1.865 1.863 Efficiency 87 91.53 91.37

Figure 4. T-AXI screens during the solution of the one stage design. Graphics are used to check input and some guidance on solution convergence. Angular momentum is the primary input downstream of each blade row. It is uniform for this free-vortex design.

Figure 5 is a 3D representation of the stage design using

the blade viewer. The max thickness to chord used is the same as for rotor 1 and stator 1 of the EEE described in the next subsection. Figure 6 shows the T-AXI screen after the loss is converged and the initial grid for the true SMI flowpath. From these plots, it can be seen that the profiles of angular

b.) Initial screen

c.) Screen after convergence without boundary layers

d.) Screen after convergence with boundary layers

Angular momentum

Boundary layer parameters

Total enthalpy

a.) Initial T-AXI grid showing blade edge stations.

entropy

momentum and the real leading and trailing edge shapes are applied from the 3D solution.

Figure 7 shows how the T-C_DES design compares to the actual flowpath of the SMI stage.

NASA/GE EEE 10 Stage Compressor The NASA/GE EEE high pressure compressor was

designed during the late 1970’s using the best methods available to industry at the time. A six stage build and two ten stage builds were used to refine the design [23,24]. Figure 8 is a cross section of the EEE HPC. This 10 stage design was scaled up in size to become the high pressure compressor for the GE90.

T-C_DES was used to create geometry similar to the actual EEE flowpath. Reference [23] contains output from the GE axisymmetric code, CAFD, which was used to construct the actual EEE flowpath and blade row angular momentum distributions. Table 5 was initially constructed from the meanline data shown in Figures 10-14, and 17 in ref [23]. The throughflow information was used to get the axial velocity ratios. The individual stage total temperature rise values were adjusted to match the overall temperature ratio from the actual EEE T-AXI calculation. The losses were modified to get an overall pressure ratio from T-C_DES of 25. The rotor inlet Mach number values were tweaked to get the stage rotor leading edge hub locations to match up with the actual design. The blockage was set based on the report that stated an inlet

Figure 5. 3D representation of the one stage design. The Blade Viewer program can output all the blades of a design.


value of 0.97 and an exit value of 0.90 with an approximately linear distribution. This blockage is a very important parameter for compressor design. It is used for sizing the area through the compressor, and the coupled boundary layer in T-AXI is used to approximate it. The aspect ratios and blade row gaps were set to get approximately the right axial extent of each blade row and stage. The stage tip radii are the values from the rotor leading edge of the actual flowpath. The bleed values were those specified in the report, and applied as a negative blockage in T-AXI. Finally the solidity values were set to get the same airfoil count as the actual EEE design.

Figure 6. T-AXI screens during the solution of the SMI case derived from the 3D simulation. This solution had contoured leading and trailing edges as well as profiles of angular momentum.

a.) T-AXI screen after loss is converged, but without boundary layers.

b.) Initial T-AXI grid showing blade edge stations.

Angular momentum

From T-C_DES

Actual 3D geometry

From T-C_DES

Actual 3D geometry

Figure 7. Comparison of the one stage flowpath generated with T-C_DES and the SMI geometry. Also shown are the leading edge and trailing edge stations.

Figure 8. GE EEE High Pressure Compressor. The initial data and IGV data are in Tables 6 and 7

respectively and come from the design intent. The clearance comes from the clearance goals for the front rotors. The ratio of specific heat is treated as a constant in T-AXI. The value used is the average of the value from the inlet TT and the expected exit TT.

Figure 9 shows the T-AXI screens for the 10 stage design. The distribution of angular momentum, total enthalpy, blockage and entropy are shown. The angular momentum plots give a quick picture to the user that the work and stator exit angles have been input correctly. For the EEE, as mentioned in the design report, the large reduction in temperature drop in stage 6 shown in Table 6 is to reduce the loading of that stage since the stator upstream is the last variable stator row. Although T-AXI cannot be used for off-design calculations, these design features can be built into the parameters to address stall margin at part power. The distribution of rotor inlet angle (the same as the upstream stator exit angle), also in Table 5, allows for a gradual build-up of inlet rotor swirl for improved efficiency and making sure the last stage stator or OGV is not too loaded.

Figure 10 shows the T-AXI screens for the actual EEE HPC geometry. The edge stations for stage 10 demonstrate the nonlinear edge stations for the actual design. Figure 11 compares the 10 stage design flowpath with the actual EEE flowpath demonstrating that the parameters available within T-C_DES are flexible enough to create a realistic flowpath.

The thickness distributions in Table 8 have been applied to the 10 stage design. They came from the actual EEE report [23]. Figure 12 demonstrates how the blade geometry capability within T-AXI can be used. Fig. 12 a) shows a 3D solid of the airfoil, b) shows the converged MISES grid for the mid-span section, c) shows the Mach number distribution, also for the mid-span section. Fig. 12 d) is a contour plot of the MISES Mach numbers and e) demonstrates how the “Pressure Editor” capability in MISES, EDP, was used to smooth out the suction side leading edge spike. A 3D representation of the 10 stage design as output by the Blade Viewer is shown in Figure 13.

The overall performance calculations are shown in Tables 9 and 10. The efficiency goal of the EEE was 85.7%. The two 10 stage builds did not reach 100% speed, or that efficiency goal. The T-AXI solution of the actual EEE flowpath with profiles of angular momentum calculates an efficiency of


Table 5. Stage data for 10 stage design (stage.e3c-des).

Stage Parameter 1 2 3 4 5 6 7 8 9 10

Stage rotor inlet angle [deg] 10.3 13.5 15.8 18 19.2 19.3 16.3 15 13.6 13.4 Stage rotor inlet Mach no. 0.59 0.51 0.475 0.46 0.443 0.418 0.402 0.383 0.35 0.313 Total Temperature Rise [K] 52.70 52.30 51.12 49.74 49.14 43.62 45.69 47.27 48.26 47.57 Rotor loss coef. 0.053 0.0684 0.0684 0.0689 0.069 0.069 0.069 0.069 0.069 0.07 Stator loss coef. 0.07 0.065 0.065 0.06 0.06 0.065 0.065 0.065 0.065 0.1 Rotor Solidity 1.666 1.486 1.447 1.38 1.274 1.257 1.31 1.317 1.326 1.391 Stator Solidity 1.353 1.277 1.308 1.281 1.374 1.474 1.379 1.276 1.346 1.453 Stage Exit Blockage 0.963 0.956 0.949 0.942 0.935 0.928 0.921 0.914 0.907 0.9 Stage bleed [%] 0 0 0 0 1.3 0 2.3 0 0 0 Rotor Aspect Ratio 2.354 2.517 2.33 2.145 2.061 2.028 1.62 1.417 1.338 1.361 Stator Aspect Ratio 3.024 2.98 2.53 2.21 2.005 1.638 1.355 1.16 1.142 1.106 Rotor Axial Velocity Ratio 0.863 0.876 0.909 0.917 0.932 0.947 0.971 0.967 0.98 0.99 Rotor Row Space Coef. 0.296 0.4 0.41 0.476 0.39 0.482 0.515 0.58 0.64 0.72 Stator Row Space Coef. 0.32 0.35 0.45 0.45 0.9 0.46 0.89 0.52 0.58 0.55 Stage Tip radius [m] 0.351 0.336 0.328 0.321 0.315 0.308 0.304 0.300 0.297 0.295

84.6% whereas the Build 2 adjusted peak efficiency was 84.8%. The 10 stage free vortex design solution has a calculated value of efficiency of 85.6%. These comparisons are excellent for these calculations.

Table 6. Initial data for 10 stage design (init.e3c-des).

Number of Stages 10 Mass Flow Rate [kg/s] 54.4 Rotor Angular Velocity [rpm] 12,299.49 Inlet Total Pressure [Pa] 101,325 Inlet Total Temperature [K] 288.15 Alpha 3 - Last Stage [deg] 0 Mach 3 - Last Stage 0.272 Ratio of Specific Heats 1.37836 Gas Constant [kJ/kg*K] 0.287 Clearance Ratio 0.0015

Table 7. IGV data for 10 stage design (igv.e3c-des).

Soldity 0.6776 Aspect ratio 5.133 Phi Loss Coef. 0.039 Inlet Angle 0 Inlet Mach 0.47 Lambda 0.97 IGV Row Space Coef. 0.4 IGV Tip Radius [m] 0.36211

Figure 9. T-AXI screens during the solution of the 10 stage design. Graphics are used to check input and help guide solution convergence. Angular momentum is the primary input downstream of each blade row. It is uniform for this free-vortex design.


b.) Initial screen c.) Screen after

convergence without boundary

d.) Screen after convergence with boundary layers

Angular momentum

Entropy

Blockage

Boundary layer parameters

Total enthalpy


Figure 10. T-AXI screens during the solution of the EEE full geometry. This solution had contoured leading and trailing edges as well as profiles of angular momentum as defined by the axisymmetric output in the EEE report.

Figure 11. Comparison of the 10 stage flowpath generated with T-C_DES and the EEE design. Also shown are the rotor 1 leading edge and stator 10 trailing edge.

Rotor 10 Stator 10


b.) Blow up of the Stage 10 grid showing details of the axisymmetric shape of the leading and trailing edge stations.

c.) T-AXI screen after loss is converged, but without boundary layers.

Angular momentum

From T-C_DES Actual 3D geometry

Table 8. Maximum Thickness to chord data at hub and casing for the GE EEE HPC applied to the 10 stage design.

Blade Row TM/C hub TM/C tip IGV 0.0850 0.0850 R1 0.0961 0.0250 S1 0.0599 0.1128 R2 0.0849 0.0260 S2 0.0462 0.0958 R3 0.1085 0.0261 S3 0.0626 0.0898 R4 0.0813 0.0335 S4 0.0666 0.0998 R5 0.0799 0.0340 S5 0.0703 0.0999 R6 0.0797 0.0359 S6 0.0730 0.1090 R7 0.0960 0.0390 S7 0.0671 0.0949 R8 0.0786 0.0380 S8 0.0799 0.1000 R9 0.0741 0.0390 S9 0.0799 0.1000 R10 0.0850 0.0435 S10 0.0601 0.0750

Table 9. Comparison of the EEE efficiency goals and measurements with the T-AXI calculation results.

NASA/GE EEE 5 Stage Low Pressure Turbine The NASA/GE EEE 5 stage low pressure turbine is used to demonstrate the turbine capability in T-AXI and the turbine design capability of T-T_DES. In the first case, the Turbine set up code T-2-T-AXI was used to create a “walls” and “stack” file from the flowpath geometry, the initial data in Table 11, and the blade row data in Table 12. The work split was presented in the NASA report [26], and adjusted to get the overall temperature rise of 133.33 K as indicated by the design point test reading 503. This work split and the nozzle exit angles were used to get the angular momentum for each blade row. This LPT case was also used by Reed and Turner [27] in the validation of an entropy-based meanline code. Figure 14 is a cross section of the 5 stage EEE LPT.

Figure 15 shows the initial grid, and Figure 16 shows the T-AXI screen after the loss is converged. The boundary layers are not applied for this turbine since the favorable pressure gradient makes its impact minimal.

EEE goal

EEE Build 1 Peak Adjusted Efficiency at 97.5% speed

EEE Build 2 Peak Adjusted Efficiency at 99% speed

T-AXI calculation

for EEE flowpath

T-AXI calculation for 10 stage Design with free-vortex

85.7 83.9 84.8 84.6 85.6


Table 10. Comparison of the EEE goals with the T-AXI calculation results.

EEE Goal

T-AXI calculation for EEE flowpath

T-AXI calculation for Design with free

vortex Temperature Ratio 2.686 2.686 Pressure Ratio 25 25.26 25.93

a.) Stator 7 geometry generated with T-AXI.

b.) MISES grid of the Stator 7 mid-span section,

c.) Stator 7 mid-span section analyzed with MISES.

e.) Stator 7 mid-span section modified with “Pressure Editor” capability in MISES.

d.) Stator 7 mid-span section Mach number contours from MISES solution.











Figure 12. Blade design features. The output of geometry and MISES files allows MISES to be run without changing files. With a small modification of the files, a coupled boundary layer can be run or a mixed-inverse can allow a blade row section to be redesigned.

Figure 17 is a 3D representation of the LPT analyzed. The

required input of max thickness to chord ratio was set to 5%. The turbine design code, T-T_DES used the initial data in

Table 11 and the Stage data in Table 13 to create a 5 stage design that matched the flowpath of the EEE as shown in Figure 18 which is compared to the actual EEE flowpath. Notice how the flexibility of these parameters can be used to come very close to an existing design. Table 14 shows the overall result of the two T-AXI runs compared to the test data.

Table 11. Initial Data for 5 stage EEE LPT matching Reading 503 from Block II Configuration 5 (from Bridgeman [26]) (init.lpt-des).

Number of Stages 5 Mass Flow Rate [kg/s] 28.321 Rotor Angular Velocity [rpm] 3214.57 Inlet Total Pressure [Pa] 310,801.3 Inlet Total Temperature [K] 417.94 Nozzle 1 Leading Edge Mach Number 0.335 Inlet Duct Length/N1 Axial Width Ratio 1.441 Ratio of Specific Heats 1.39689 Gas Constant [KJ/(kg-K)] 0.287 Clearance Ratio 0.0009

Figure 13. 3D representation of the 10 stage design. The Blade Viewer program can output all the blades of a design.


Table 12. Number of blades and hub tangential velocity (specifies angular momentum) for each blade row.

Blade row

Number of blades

hub Vtheta (ft/sec)

N1 72 800 R1 120 -388.214 N2 102 820 R2 122 -404.072 N3 96 820 R3 122 -391.928 N4 114 780 R4 156 -247.716 N5 120 640 R5 110 -103.938

Figure 14. GE EEE LP Turbine Flowpath (from Bridgemann [26]) .

Figure 15. Initial grid for the 5 stage EEE LPT also showing the leading and trailing edge stations.

Figure 16. T-AXI screen during the solution of the 5 stage EEE LPT.


Figure 17. 3D representation of the 5 stage LPT analyzed. Blades were generated with 5% max thickness to chord ratio.

USE AS A TEACHING TOOL The T-AXI suite of codes is meant to be used as part of a

senior undergraduate or graduate level class, or as part of a research project. This paper has presented the overall theory of the codes and the validation using a single stage transonic compressor, a 10 stage high pressure compressor and a 5 stage low pressure turbine. Although not extensive, this validation provides a level of trust that the design system results can be used in a design process. The input files can be easily modified to quickly change a design. The tables can be read into a spreadsheet program such as Excel, modified and output. It becomes a very easy process to add stages to create a 14 stage HPC design, for example. The files output by Excel can then be read by the design codes T-C_DES or T-T_DES. As demonstrated, the input parameters are flexible enough to generate the flowpath for existing designs and therefore allow for an almost unrestricted design space.

The stage work input is easily specified through the temperature rise or drop. Using many of the parameters for the EEE cases for loss, aspect ratio, or blade row spacing builds on a successful design. A new design can be configured to meet a design condition, or an existing design can be reverse-engineered and validated to add to the database of cases. It is relatively easy to create a good design, and the codes could be tied to an optimizer to create an optimum design.

The ability to easily couple with a blade-to-blade solver such as MISES can be used for more advanced classes or advanced projects. This allows for a complete demonstration of the process so that calculated blade pressure profiles can be connected to the blade loading parameters. The ability to

generate a 3D model allows blade weights to be calculated, and it is very rewarding to visualize the design in 3D.

From the design system that has been described, a student can make the connection of key physical input parameters such as Mach number and angle with the cross sectional area and angular momentum. Because angular momentum is a primary quantity, its connection to the work is made obvious, and the ability of a blade-to-blade solver to be connected directly can present the connection of loading with a change in angular momentum. These concepts become second nature to those experienced in turbomachinery, but it is useful when explaining to students to have a design tool that makes these connections more obvious.

CONCLUSIONS AND CODE ACCESS The turbomachinery design system, T-AXI, has been

presented and described with real multistage compressor and turbine examples. Three test cases have been used to validate the method and loss models with good results. With a small amount of input, a design can be created that is similar to a real design. The design is then defined by a small number of parameters which can be used to explore the design space. This system is intended for use by educators and students to explain turbomachinery concepts and for use in a design class. The system is also sophisticated enough for actual design use.

Executable versions of the codes are available from the authors’ web sites in addition to the input from the examples presented and a user’s manual. The T-AXI web site URL’s are: http://gtsl.ase.uc.edu/T-AXI, http://web.mit.edu/merchant/www/taxi.html, and http://www.cfdg.unige.it/software.htm.

Table 13. Stage Parameters for 5 stage design using T-T_DES (stage.lpt-des); the temperature drop per stage came using work splits from Table IV of Bridgeman [26], and matching the overall temperature rise of Reading 503.

Stage Parameter 1 2 3 4 5 Nozzle Exit Ang. [deg] 61 64.1 64.8 62.3 55.3 Nozzle Exit Mach No. 0.5806 0.588 0.58 0.544 0.5 Stage TT Drop [K] 27.53 29.797 30.944 26.474 18.583Nozzle Zweifel Number 0.639 0.956 0.978 1.058 1.075 Rotor Zweifel Number 0.891 0.878 0.83 0.812 0.793 Nozzle Loss Coef. 0.08 0.05 0.05 0.05 0.05 Rotor Loss Coef. 0.12 0.1 0.1 0.1 0.05 Nozzle Aspect Ratio 1.8106 3.5 3.77 4.94 5.47 Rotor Aspect Ratio 4.088 4.57 5.38 7.76 6.05 Rotor Axial Vel. Ratio 0.85 0.989 1.029 1.051 1 Noz. Row Space Coef. 0.231 0.38 0.3 0.51 0.34 Rotor Row Space Coef. 0.575 0.47 0.472 0.63 0.567 Noz. Mean Radius [m] 0.2466 0.2729 0.2939 0.3141 0.3223Rotor Mean Radius [m] 0.2631 0.2845 0.3071 0.3203 0.3199


Table 14. Performance comparison between reading 503 and the T-AXI calculations.

Measurement Reading 503

T-AXI calculation

EEE flowpath

T-AXI calculation (T-T_DES design)

Pressure Ratio 4.409 4.351 4.326 Temperature Ratio 1.468 1.464 1.463 Efficiency 92.05 92.85 92.91

REFERENCES [1] Mattingly, Jack D., William H. Heiser, and David T. Pratt, Aircraft Engine Design Second Edition, AIAA Education Series, Reston, VA, 2002. Older versions of software in this book are available on the web at www.aircraftenginedesign.com.

[2] Mattingly, Jack D., Elements of Gas Turbine Propulsion, McGraw-Hill, AIAA Education Series, Reston, VA, 2005.

[3] Genrup, Magnus, Ivan Carlsson, Ulf Engdar, and Mohsen Assadi, “A Reduced-Order Through-Flow Program for Choked and Cooled Axial Turbines,” ASME Paper GT2005-68716.

[4] Carlsson, Ivan, “A Reduced-Order Through-Flow Program for Choked and Cooled Axial Turbines,” MS Thesis for the Department of Heat and Power Engineering Lund University, Lund, Sweden, February, 2005.

[5] Merchant, A., Kerrebrock, J. L., Adamczyk, J.J., and Braunscheidel, E., “Experimental Investigation of a High Pressure Ratio Aspirated Fan Stage,” Journal of Turbomachinery, Vol. 127, No. 1, pp. 43-51, January 2005.

10

15

20

25

30

35

40

45

-5 0 5 10 15 20 25 30 35 40 45

Axial distance (cm)

Rad

ius

(cm

)

Hub EEETip EEEHub T-T_DESTip T-T_DES

Figure 18. Comparison of the flowpath generated with T-T_DES using the stage input parameters compared with the actual EEE 5 stage flowpath.

[6] Merchant, A., Epstein, A. H., and Kerrebrock, J. L., “Compressors with Aspirated Flow Control and Counter-Rotation,” AIAA-2004-2514, 2nd AIAA Flow Control Conference, Portland, Oregon, June 28-1, 2004.

[7] Smith, L. H. Jr., “The Radial-Equilibrium Equation of Turbomachinery,” J. of Engineering for Power, pp 1-11, Jan. 1966.

[8] Novak, R. A., “Streamline Curvature Computing Procedures for Fluid-Flow Problems,” J. of Engineering for Power, pp 1-13, Jan. 1966.

[9] Drela, M. and M.B. Giles, “Viscous-Inviscid Analysis of Transonic and Low Reynolds Number Airfoils,” AIAA Journal, 25(10):1347–1355, Oct 1987.

[10] Youngren, H.H. and M. Drela, “Viscous/Inviscid Method for Preliminary Design of Transonic Cascades,” AIAA-91-2364, 1991.

[11] Adkins, G. G., Jr., and L.H. Smith, Jr., “Spanwise Mixing in Axial-Flow Turbomachines,” J. of Engineering for Power, Jan. 1982, Vol. 104, pp.97-110, also ASME paper 81-GT-57.

[12] Koller, Ulf, Reinhard Monig, Bernhard Kusters, and Heinz-Adolf Schreiber, “Development of Advanced Compressor Airfoils for Heavy-Duty Gas Turbines--- Part I: Design and Optimization,” Journal of Turbomachinery Vol. 122, Issue 3, pp. 397-405, 2000. (Also ASME 99-GT-95).

[13] Küsters, B., Heinz-Adolf Schreiber, Ulf Köller, and Reinhard Mönig, “Development of Advanced Compressor Airfoils for Heavy-Duty Gas Turbines— Part II: Experimental and Theoretical Analysis,” Journal of Turbomachinery -- July 2000 -- Volume 122, Issue 3, pp. 406-414. (Also ASME 99-GT-96).

[14] Zweifel, O., “The Spacing of Turbomachine Blading, Especially with Large Angular Deflection,” Brown Boveri Review 32, 1945.

[15] Hirsch, C.H. and J. D. Denton Editors, “Axial Compressor Performance Predictions,” in “Throughflow Calculations in Axial Turbomachines,” 1981. AGARD-AR-175.

[16] Koch, C.C. and L.H. Jr. Smith, “Loss Sources and Magnitudes in Axial Flow Compressors,” Journal of Engineering for Power, pages 411–424, July 1976.

[17] Denton, J.D., “Loss Mechanisms in Turbomachines,” J. of Turbomachinery, Vol 115, pg 621-656, October 1993.

[18] Leiblein, S., F.C. Schwenk, and F.L. Broderick. “Diffusion Factor for Estimating Losses and Limiting Blade Loadings in Axial Flow Compressor Blade Elements,” Tech. Report RME53D01, NACA, 1953.

[19] Ucer, A.S., Stow, P., and Hirsch, Ch., (Editors), “Thermodynamics and Fluid Mechanics of Turbomachinery,” Volume II, NATO ASI Series, 1985.

[20] Chriss, Randall M., William W. Copenhaver and Steven E. Gorrell, “The Effects of Blade-Row Spacing on the Flow Capacity of a Transonic Rotor,” ASME paper 99-GT-209., June, 1999.

[21] Turner, Mark G., Steven E. Gorrell, and David Car, “Radial Migration of Shed Vortices in a Transonic Rotor Following A Wake Generator: A Comparison Between Time Accurate and Average Passage Approach,” ASME Paper No. GT2005-68776, Reno, June 2005.


[22] Gorrell, S. E., Car, D., Puterbaugh, S. L., Estevadeordal, J., and Okiishi, T. H., “An Investigation of Wake-Shock Interactions in a Transonic Compressor with DPIV and Time-Accurate CFD,” ASME paper GT2005-69107, Reno, NV, 2005.

[23] Holloway, P.R., G.L. Knight, C.C. Koch, and S.J. Shaffer, “Energy Efficient Engine High Pressure Compressor Detail Design Report,” NASA CR-165558, 1982.

[24] Cline, S.J., W. Fessler, H.S. Liu, R.C. Lovell, and S.J. Shaffer, “High Pressure Compressor Component Performance Report,” NASA CR-168245, 1983.

[25] Cherry, D.G., C.H. Gay, and D.T. Lenahan, “Low Pressure Turbine Test Hardware Detailed Design Report,” NASA CR-167956, 1982.

[26] Bridgeman, M.J., D.G. Cherry, and J. Pedersen, “NASA/GE Energy Efficient Engine Low Pressure Turbine Scaled Test Vehicle Performance Report,” NASA CR-168290, 1983.

[27] Reed, John A., and Mark G. Turner, “An Entropy Loss Approach For A Meanline Bladerow Model With Coupling To Test Data and 3D CFD Results,” ASME Paper No. GT2005-68608, Reno, June 2005.


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