1. CommonMeanline (CML) Analysis

2. Common Meanline (CML) Program Physics-based predictive approach
CML code synthesizes compressor as 1D model
superimposes loss corrections and deviation rules
CML code based on combination of empirical and limited physics-based models
Tip-leakage vortex
Hub boundary layer
Casing boundary layer
Airfoil
boundary
layers
+ shocks,
horseshoe
vortices, ...
Capture for 1D
Meanline
In this analysis, losses are broken into "2-D" losses and endwall losses. These loss mechanisms are then modeled as zero-order models for each blade row throughout a complete machine. The "2-D" losses are assumed to be a function of blade loading, Mach number, Reynolds number, surface roughness, thickness ratio, and leading edge radius. The endwall losses are assumed to be a function of rotor tip clearance, flow path cavities and additional aerodynamic endwall losses. These loss models are based on a combination of empirical and legacy rules as well as physics-based models. The aim of the current effort is to decrease the amount of empiricism in the CML, by replacing it with either first principles models or models derived from CFD (e.g. NASTAR) calculations.
Develop new models based on first-principles constructs and from CFD predictions

4. CommonMeanline Review Outline
Loss modeling approach:
Superposition of effects
where or
The loss coefficient can be defined in a number of ways. A conventional form (Cumpsty, Dixon, Lieblein) in terms of  and an alternative form (Lieblein) used in CML code in terms of the momentum thickness ratio (/b). This latter form has been developed by Lieblein from 2D incompressible theory and is cited in NASA SP-36 p Lieblein developed the following loss coefficient expression.
Basis of the latter model:
Lieblein observed that a simplified pressure loss coefficient could be used, in that it more closely approximated the wake thickness effect (more fundamental expression of basic loss across blade section). Lieblein observed that a term in the general expression was primarily a function of the shape factor H and was only a secondary issue to consideration of the blade loss of unseparated blade. The revised express introduced is shown abov. Lieblein observed that Term 1 is a better form to track loss, than one with both Term 1 and Term 2 (too flat) as D factor is increased.

5. Mach Number Effects Shock losses due to supersonic inflow
Shock losses due to normal / passage loss (Prince)
Choke losses
There are two ways in which Mach number effects contribute to the total loss of a blade row: (1) shock induced total pressure losses and (2) shock induced boundary layer losses. Shock losses occur whenever finite strength shocks occur within the blade row. When the relative inflow in supersonic, an oblique shock wave is generated off the leading edge. Total pressure losses across the shock are proportional to the inlet normal Mach number (M1rel sin ). Shock losses also arise when the inlet Mach number is sufficiently high such that, when the flow locally accelerates to a supersonic state, it chokes at the maximum thickness location and a normal shock forms across the blade row. In this case, the resultant total pressure losses are proportional to the upstream local Mach number. On the other hand, any shock wave that interacts with the blade boundary layer tends to locally separate the boundary layer (SBLI-shock boundary layer interaction) and produce additional viscous losses. In isolated airfoils, this combination of normal shock losses and wall boundary layer separation losses leads to the onset of "drag rise" from the baseline or profile loss. One should note that these effects are increased with increased positive incidence. Little evidence is found to indicate a similar dependence with negative incidence.
Choke Losses: The loss model shown above is found in OMEG. It represents two corrections to the blade loss. The first term is a Mach number correction corresponding to the drag rise seen in the above figure. The second term is an empirical model of incidence effects developed by S. Baghdadi. We do refer to the incidence term later in the validation charts,

6. Profile Losses  s M1 
CML profile loss: blended average of Lieblein (2D) and Monserrat data (3D)
Current model missing: AR effect, sidewall blockage, correct negative incidence
Deviation only from modification of Carter’s rule
The base or 2-D loss is the rotor or stator loss arising from a profile section away from the case endwalls. The mechanisms contributing to this loss arise from pressure drag (also called form or profile drag) and viscous forces. The pressure drag has two sources; (1) a blade thickness effect, and (2) an incidence effect (drag due to lift). In isolated airfoils, this net drag is called the parasitic drag.
In general, this loss is not significant, but when the incidence on the blade is increased, a pronounced increase in base loss occurs when the blade approaches its stall point. The stall point is arbitrarily defined as the point at which the profile loss twice the minimum loss value. The reference incidence is defined either as the incidence at minimum loss of the midpoint of the loss "bucket" (between positive and negative incidence induced stall).
The CML base or 2D profile loss is calculated from a modified form of the equation used in the E82G (AXPDY) version of meanline code. The equation is an empirical fit for the base or 2-dimensional profile loss coefficient and is given above. Empirical knob factors, for the stator (k3, k5, k7) and for the rotor (k3, k5, k7), were introduced in the CML code to adjust, either manually or in optimizer, the code agreement along speedline. The above correlation represents an average of the endwall and midspan distributions.

7. Baseline Calibrations Identify Empirical Model Limits Hobbs-Weingold cascade loss bucket problem at negative incidence seen
Subsonic cascade analysis from choke to stall
Calibration performed of CML with RANS, data
Two models identified with nonphysical behavior
In the 1980's, a series of controlled diffusion or supercritical airfoils were developed for multistage compressor application. They were designed to avoid suction surface boundary layer separation for a range of inlet conditions necessary for stable compressor operation. Cascade experiments (Hobbs & Weingold) and CFD RANS analyses (Davis, et al.) were performed to verify the performance of these designs. In the current situation a single design, called airfoil D, was selected to verify the stator loss models over a range of inlet incidence conditions.
Analyses were performed for the subsonic test condition (M1 = ). The incidence range considered ran from degrees (choke) to +7.0 degrees (stall). Results of the CML code analyses, compared to experiment and Navier-Stokes CFD analyses are shown above. The left figure shows the loss bucket predicted by the CML code against the experimental data and the Davis VICAS Navier-Stokes (RANS) predictions, indicating good agreement with the RANS prediction at positive incidence. The agreement with data for both analyses is reasonable, with both codes indicating a larger range before the onset of stall.
A more detailed examination of the CML is shown on the right figure above. The individual loss components that have been calculated and applied to the base loss are shown. The negative incidence behavior is clearly driven by the choke losses. A closer examination of the RANS results is shows the flow is not choked, but has large losses due to pressure side flow separation. Please remember that this term represents two effects; a Mach number driven drag rise effect and an incidence effect, with the latter term apparently driving the negative incidence loss bucket range.

8. PW6000 CML Simulation of On/Off Design Identify loss and modeling problems over operating speedlines
CML used to match engine data and
analyze speedline characteristics
5-stage HPC conceptualized using 1D
model
Analysis performed at 100%, 90% flow
using baseline code
The PW6000 HPC is a high-speed highly-loaded 5-stage machine providing the same compression as current 11-stage machines, see above. CML analyses have been performed at PW and UTRC for the 100% and 90% flow cases. Shown below is a compressor map for the PW6000 HPC.
A schematic view of the CML model for the HPC is shown abov. The reference locations through the machine are the planes 1 to 20. The CML has been applied to the baseline or design intent configuration.

9. PW6000 CML output results: 100% flow
by the rear stages and at stall by the front stages. The results of these calculations for the 100% flow speedline are shown above from choke flow to stall. In each figure, the axial coordinate refers to the axial stations (1-20), while the vertical coordinate is the normalized weight flow rate, referenced to the Op-line value (Wac/Wac-design), with the bottom going towards stall and the top towards choke. The display provides a quick overview of the machine performance, deviation, losses, etc.
The magnitude or intensity of the variables shown should be considered relative to the color bar used for each variable. The colorbar has been selected to enhance the view of the entire compressor. Some quick observations can be made from these displays:
· The rear end of the machine, stations , has large negative incidence, large choke losses and therefore large total loss as the machine approaches choke flow.
· The front end of the machine, stations 4 - 9, have large positive incidence, more so as the machine approaches stall. The corresponding losses are small, but do increase approaching stall.
· The relative Mach number of the front stage rotors, stations 5, 7, and 9, is supersonic.
· The total loss of the compressor is dominated at choke
Choke
Stall
Vertical coordinate is WAC/WAC_design; horizontal axis is station number

10. PW6000 CML output results: 100% flow Rescaled view of output parameters from choke to stall
The present document is a summary of the normalized variables from the CML code which are displayed in the form of color bar charts using the Matlab tool GetLossDistr.m. The following color bar charts are generated by abovementioned Matlab script, for each speedline.
Loss as a fraction of design point loss : w(iStation, jWAC)/ wDesign
Blade incidence angle: DINC
Other parameters that could be displayed are:
Total loss coefficient (max value of 0.2): OMEGABAR
Base loss as fraction of total loss: wBASE(iStation,jWAC)/ w(iStation, jWAC)
Choke loss as fraction of total loss : w(CRIT+CHOKE)(iStation, jWAC)/ w(iStation, jWAC)
Clearance loss as fraction of total loss: wCLEARANCE(iStation, jWAC)/ w(iStation, jWAC)
Shock loss as a fraction of total loss: wSHOCK(iStation, jWAC)/ w(iStation, jWAC)
Reynolds number loss as fraction of total loss: wREY(iStation, jWAC)/ w(iStation, jWAC)
Thickness loss as fraction of total loss: wTHICK(iStation, jWAC)/ w(iStation, jWAC)
The notation iStation and jWAC are used to identify the station index and the index of mass flow rate along a speedline. The horizontal axis is the index of the station used in the CML input file. The vertical axis is the ratio of the mass flow rate to the mass flow rate at the design point. Hence, the design point value is identically equal to unity. The use of this normalized mass flow rate permits comparison between quantities on different speedlines.

11. PW6000 CML output results: 100% flow Rescaled view of output parameters from choke to stall
The present document is a summary of the normalized variables from the CML code which are displayed in the form of color bar charts using the MATLAB tool GetLossDistr.m.
The following color bar charts are generated by the abovementioned MATLAB script, for each speedline.
Blade incidence angle: DINC
Relative Mach number: MREL
Note the PW6000 results show on the previous figure and this figure that station 17 has large negative incidence, resulting in high losses.

12. 2-Dimensional Blade Model Improvement Identified Implementation and validation in progress
Current Approach
New Approaches
Option 1
Loss
Lieblein correlation
Deviation
Carter’s rule correlation
Blockage
None
Generic loading (“stick”)
+ Boundary layer analysis
= Result
loss  
deviation   *
blockage   * Ps 
incidence
loss
D factor
X/b
The current profile loss modeling approach applies a modified form of Lieblein’s correlation. The blade incidence is accounted for using Carter’s deviation rule. Using this approach, several features of the flow field are not accounted for, e.g.
- AR is not accounted for in loading
- airfoil boundary layer blockage is not specified or modeled
- negative incidence deviation is not accounted for
- ….
The new proposed approach is to improve the loading model, making it a 1 1/2D model. Using a specified or generic velocity distribution, loss is calculated using a rapid Thwaite’s integral boundary layer procedure.

13. Profile loss model Development of physics-based models Current model
model may need to be calibrated for airfoil family, etc.
Current model
D-factor calculated based on 10% thickness, Re
T.E. momentum thickness (loss) computed based on D-factor
loss then adjusted for other thicknesses, Re, ...
geometry of blading and associated loading is not systematically accounted for
different correlation for rotor and stator