NCENTRIX
Machine Learning Software for Compressor Performance Analysis
Technical Manual
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Release No. 
Date 
Revision Description 
Rev. 0 
15/05/2019 
Technical Manual Template and Checklist 
Rev.1 
04/01/2020 
Revised template and logo 
Rev.2 
17/02/2020 
Updated rotor schematization and calculation section 












TABLE OF CONTENT
DISCLAIMER
NOTATIONS
ABBREVIATIONS
SOFTWARE DOWNLOAD REPOSITORY
INTRODUCTION
PART A – GENERAL PROCEDURES
1 PERFORMANCE CALCULATION PROCEDURES
1.1 Performance Modeling Approach
1.2 Performance Model for DVEC
1.3 Performance Calculation at Design Point
1.4 Procedure for MultiStage Performance Stacking
1.5 Performance Curve for Design Condition
2 EQUATION OF STAGE PACKAGES
2.1 ISO20765 Part I  Equation of State
2.2 ISO20765 Part II  Equation of State
2.3 EOSCG Equation of State
2.4 SRK Equation of State
3 POLYTROPIC HEAD CALCULATION METHODS
4 TEMPERATURE CALCULATION METHODS
4.1 Root Search Method
4.2 Subdivision Method (T2SDIV)
5 DATA DRIVEN MODEL FOR NEW MACHINE DESIGN
5.1 Methodology Overview
5.2 Neural Network Topology
5.3 Data Scaling
5.4 PreBuilt Stages Database
5.5 Model Scalability
PART B – NEW MACHINE DESIGN
1 DETAILED STAGE DESIGN
1.1 Impeller Exit Parameters
1.2 Diffuser Ratio
2 VERIFICATION OF DESIGN LIMITS
2.1 Rotor Schematization
2.2 Shaft Stiffness and Stability Screening
2.3 Impeller Yield Strength Utilization
2.4 Gas Velocities at Inlet and Outlet Flanges
3 VERIFICATION CHECK LIST
PART C – MODELING OF EXISTING MACHINES
1 METHODOLOGY OVERVIEW
2 ORIGINAL MAP CHARACTERIZATION (DESIGN CASE)
2.1 User Information to be Supplied
3 STANDARD METHODS
3.2 Linear Method
3.2 NLQUAD/R and NLCUBIC/A Methods
3.3 Prediction Range Extension
4 DATASET EXTENSION
5 VERSATILE ARTIFICIAL NEURAL NETWORK
5.1 Methodology Overview
5.2 Configuration Parameters
5.3 Prediction Task Procedure
5.4 Output Information
6 PERFORMANCE DEGRADATION SIMULATION
REFERENCES
APPENDIX – A STATUS CODES
APPENDIX – B PARAMETERS
Variable 
Description 
Unit 
KT 
Isentropic Temperature Exponent 

KV 
Isentropic Volume Exponent 

ENTH 
Enthalpy 
kJ/kg 
ENTR 
Entropy 
kJ/(kg K) 
RHO 
Density 
m3/kg 
CP 
Isobaric Calorific Capacity 
kJ/(kg K) 
CV 
Isochoric Calorific Capacity 
kJ/(kg K) 
MW 
Molecular Weight 
kg/kmol 
R 
Gas Constant = 8314.472 
kJ/kg.K 
Q1 
Actual Inlet Volume Flow 
Am3/h 
Q1C 
Actual Inlet Volume Flow at Choke 
Am3/h 
Q1S 
Actual Inlet Volume Flow at Surge 
Am3/h 
Z 
Compressibility Factor 

P 
Absolute Pressure 
MPaa 
T 
Temperature 
K 
W 
Speed of Sound 
m/s 
RPM 
Shaft Speed 
rpm 
DRPM 
Design Speed 
rpm 
RPMC 
Corrected Shaft Speed 
rpm/ 
GFLOW 
Mass Flow 
kg/h 
CRF 
Corrected Mass Flow 
(kg/h) 
HPOL 
Polytropic Head 
kJ/kg 


NIMP 
Total number of stages (and impellers) in a process section 

BETA2 
Impeller Backward Lean Angle (Metal Exit Angle) 
Degree 
ALPHA2 
Impeller Exit Flow Angle 
Degree 
ZBLADE 
Number of Impeller Blades 

KSI 
Nondimensional Absolute Velocity at Impeller Exit 

RHO01_RHO2 
Impeller Total (Stagnation) to Static Density Ratio 

SIGM 
Slip Factor at Impeller Exit 

FI1 
Actual Inlet Flow Coefficient (universal definition) 

FI2 
Actual Flow Coefficient at Impeller Exit 

FI1* 
Design Inlet Flow Coefficient 

FI1S 
Inlet Flow Coefficient at Surge 

FI1C 
Inlet Flow Coefficient at Choke 

SRR 
Ratio FI1S / FI1* 

CKR 
Ratio FI1C / FI1* 

MU 
Peripheral Mach Number 

MU* 
Design Peripheral Mach Number 

ETAP 
Polytropic Efficiency 

TAU 
Head Coefficient 

C2 
Impeller Absolute Exit Velocity 
m/s 
U2 
Impeller Peripheral Tip Speed 
m/s 
D0 
Impeller Bore Diameter 
mm 
D2 
Tip Impeller Diameter 
mm 
D2* 
Tip Impeller Diameter Before Trim (MASTER) 
mm 
D4 
Diffuser Diameter 
mm 
DR 
Diffusion Ratio 

MDIAM 
Ratio D2*/D2 

b2 
Impeller Exit Width 
mm 
b3 
Diffuser inlet Width 
mm 
LS 
Stage Axial Length 
mm 
T 
Blade Thickness 
mm 


DVEC 
Efficiency Conditioning Factor (Last Stage  Discharge Scroll) 

PTOL 
Absolute Tolerance on Discharge Pressure Calculation 
MPaa 


YS_{UTILIZATION} 
Material Yield Strength Utilization 
% 
SIGMA_{OST} 
Impeller Stress @ Over Speed Test (OST) Speed 
N/mm2 
RP_{02} 
Material Yield Strength Performed 
N/mm2 
Table 1 – Notations
Subscripts
S: Suction; D: Discharge.
Ref.: Reference Case
‘01’: static quantity; ‘1’: total (stagnation) quantity.
Abbreviations
OST: Over Speed Test
RPM: Round per Minute
ANN: Artificial Neural Network
YS: Yield Strength
Software Download Repository
INTRODUCTION
NCENTRIX is turbomachinery software for the prediction of centrifugal compressor performance; outputs such as efficiency, power, and speed can be analyzed and the performance maps also generated. It is convenient software for rotating and process engineers during preliminary design and concept/feasibility study phase.
When it comes to existing machines (field operations/maintenance), NCENTRIX can be employed in order to build a mathematical representation of the performance maps of an original machine or a compression train; based on this representation NCENTRIX can for example, predict the performance output and the new operating envelope in response to a variation of operating conditions and/or gas composition from the design specification. In the field of predictive maintenance, NCENTRIX as a predictive tool combined with field data monitoring enables plant End Users and Operators to assess the health of their machinery and investigate faults signature.
NCENTRIX has fundamentally two registers of applications:
(1) SELECTION AND SIZING which applies to new machine design, and
(2) FIELD PERFORMANCE PREDICTION applicable to existing machines.
The purpose of this document is to describe the technical concepts and methodologies of the software.
PART  A
GENERAL PROCEDURES
1 PERFORMANCE CALCULATION PROCEDURES
NCENTRIX calculates the performance of singleshaft multistage compressors for train with single casing or multiple casings arrangement.
The process by which NCENTRIX calculates the performance is described as follows. NCENTRIX first models the performance characteristics (by means of the non dimensional coefficients) of a compression stage as the fundamental element. A compression stage consists of a single impeller, its diffuser and the return channel (Figure 1). A special case is the first stage that is directly connected to the inlet plenum and the last stage, where a discharge scroll replaces the return channel.
All compression stages within the control volume delimited by an inlet flange, or an injection stream, and an outlet flange, or an extraction stream, form a process section. NCENTRIX calculates the overall performance envelope of a process section based upon the performance models of the individual stages. For the purpose of merging all the stages into one combined performance map, a stagestacking method shall be used.
One or more process sections that are assigned to the same physical shaft (between bearing design) form a casing which contains them (Figure 2). A single shaft casing can comprise one process section (single section, straightthrough arrangement), two (example: back to back arrangements) or more process sections (example: multiple injection/extractions). More generally, for a train that comprises two or more process sections (Figure 3), the procedure applied to determine the performance of a single process section is repeated and extended to the complete train.
Figure 1 – Illustration of a compression stage (impeller + diffuser + return channel) (C2)
Figure 2 – Typical multistage compressor casing crosssection (API 617 7^{th} edition)
Figure 3 – Shaft line arrangement with multiple casings
NOTE
Only single section in straightthrough arrangement can presently be configured in NCENTRIX. Back to back arrangements, injection/extraction configurations shall be added in a later revision.
1.1 Performance Modeling Approach
The performance analysis method used here does not rely on calculating the individual losses in order to predict performance. In general, such an analysis requires extensive information about the stage geometry. Since non dimensional characteristic curves aggregate the losses of the stage, i.e. the impeller (skin friction, entrance diffusion, recirculation, incidence loss, clearance loss, disk friction loss) and diffuser (skin friction and diffusion losses), a datadriven methodology is used instead which models key nondimensional parameters at the design point in order to determine the stage performance map. A shortcoming of such methodology is that it is dependent upon the availability of data (manufacturer data or CFD simulations). Yet, it can be assumed that compressor stages that are aerodynamically well designed for a given duty tend to have fundamentally similar shapes of their performance maps [REF 5].
Figure 4  Modular Approach for Performance Prediction of Stacked Stages
In order to work at the individual stage level, we will divide the process section flow path into four distinct blocks as follows:
For the sake of simplicity, the scope of the analysis is restricted to the ‘rotor condition’ (i.e. C2 and C3); this is for instance a special case of ‘flange to flange condition’ with inlet and outlet loss coefficients set to zero. Accounting for inlet and outlet losses can be done later as an extension to the present work.
With regard to C3, it is proposed to treat the last stage similarly to any other intermediate C2 stage provided a special conditioning of the efficiency is done (factor DVEC).
In view of the assumptions and simplifications above, determining process section performance reduces essentially to the modeling of the stage performance of C2 stage and setting up a model for efficiency conditioning of a C3 stage. The following transfer functions are introduced:
è For new machines (stage by stage performance characterization):
ETAP, TAU = FUNCTION (MU, FI1, GEOMETRY, STAGE GROUP)
SRR, CKR = FUNCTION (MU, FI1, STAGE GROUP)
DVEC = FUNCTION (MU, FI1, STAGE GROUP)
è For existing machines (flange to flange characterization):
ETAP, TAU, SRR, CKR = FUNCTION (MU, FI1, GEOMETRY)
The stage non dimensional coefficients MU and FI1 are calculated using the formulas as follows:
where
If applicable, a correction based on trim diameter ratio shall be done as follows:
The stage head coefficient TAU formula is:
The stage polytropic efficiency ETAP formula is:
NOTE
Reynolds and windage effects are not modeled in NCENTRIX. Impact on accuracy is deemed limited. If needed and on case by case basis, adjustment can be applied to ETAP and TAU (GUI parameters mask).
1.2 Performance Model for DVEC
The last stage efficiency (outlet scroll) of a process section is corrected by a factor DVEC defined as
Where is the polytropic efficiency of the stage treated as C2 type of stage and is the efficiency of the C3 stage.
The correlation model for DVEC is then defined as
1.3 Performance Calculation at Design Point
In this section, we give a procedure to calculate the performance of compressor at design condition.
 Assume initial reference values for ETAP and TAU
 Estimate HPOL via thermodynamic routine REVH3PT
 Calculate initial guess RPM0 based on formula:
where
 Set current RPM=RPM0 and calculate for each stage i = 1 to NIMP

 Determine absolute pressure and temperature at suction and discharge and for each stage (i)
 Calculate density, compressibility and sound speed for each stage using EOS package.
 Determine the flow coefficients FI1 and tip Mach number MU.
 Obtain design ETAP(i) and TAU(i) at each stage using TF1transfer function (block C2).
 Use TF2 to determine DVEC (block C3) and correct last stage efficiency as follows:
ETAP(NIMP) = DVEC * ETAP(NIMP)
 Apply correction due inlet scroll and outlet plenum losses if required (blocks C1 and C4)
 Solve for speed DRPM using tolerance criteria PTOL
ABS(P_{D}(NIMP)  P_{D}_SPECIFIED) < PTOL
 Compute using EOS package thermodynamic outputs for each stage at design condition:
OUTPUTS = {HPOL, ETAP, BHP, P_{S}, P_{D}, T_{S}, T_{D}, W_{S}, RHO_{S}, RHO_{D}}
NOTES
1 Presently, inlet and outlet losses are not taken into account in the performance calculation (i.e. loss coefficients set to zero). Impact of such losses will be incorporated in a later revision.
2 – We only have modeled stages of vane less type; tests have not been done yet with vaned diffusers.
1.4 Procedure for MultiStage Performance Stacking (MSPS)
At current operating speed:
 Set the flow position GFLOW so that it satisfies FI1/FI1* = 1
 Set switches SWC=0, DIR=1, INCR=1
 Increment to higher flow F1=F1 * INCR. with INCR= INCR +0.01*DIR
While SWC=0 and DIR=1, loop through all stages:
If FI1/FI1* < SRR, reduce INCR.
Repeat until FI1/FI1* > SRR (in which case set SWC=1)
While SWC=1 and DIR=1, loop through all stages:
If FI1/FI1* > CKR. Stop and note FI1/FI1* (CHOKE) of impeller = 1
Set DIR=1 and SWC=0.
 Set the flow position GFLOW that satisfies FI1/FI1* = 1
 Set switches SWC=0, DIR=1
 Increment to lower flows F1=F1 * INCR. with INCR= INCR +0.01*DIR
While DIR=1, loop through all stages:
If FI1/FI1* < SRR. Stop and note FI1/FI1* (SURGE) of impeller = 1
1.5 Performance Curve for Design Condition
 Determine surge limit ratio (SRR) and choke limit ratio (CKR) for each stage using transfer function TF3.
 Determine surge limit ratio (SRR) and choke limit ratio (CKR) for overall section using stage stacking procedure MSPS.
 Set the speed at DRPM (constant MU) and vary flow rate GFLOW from surge to choke using regular increments already preset.
 Using transfer function TF1 obtain ETAP(i) and TAU(i) at each stage and for each flow.
 Compute using EOS package thermodynamic outputs at each stage and for each flow:
OUTPUTS = {HPOL, ETAP, BHP, P_{S}, P_{D}, T_{S}, T_{D}, W_{S}, RHO_{S}, RHO_{D}}
 Compute HPOL, ETAP and BHP for overall section
Similar procedure can be generalized to generate performance curves for speeds other than design speed.
2 EQUATION OF STATE PACKAGES
In order to accurately predict gas mixtures thermodynamic properties for reallife compression applications, an equation of state is needed. There is a prominent risk of doing improper estimate of the compressor performance under assumption of ideal gas behavior. In particular, for multistage machines the aerodynamic mismatching effect makes the requirement of accuracy even more relevant. Thus an equation of state is required and it has to be as accurate as possible.
EOS Package 1 
ISO 20765 Part I (AGA892DC) 
EOS Package 2 
ISO 20765 Part II (GERG2008) 
EOS Package 3 
EOSCG 
Table 2 – EOS packages in NCENTRIX
NCENTRIX uses equations of state based on the Helmholtz free energy whose implementation is described in ISO20765 standard [REF 1]. ISO20765 methods use a standardized 21component gas system in which all of the major and minor components of natural gas are included. Trace component present but not identified as one of the 21 specified components may be reassigned (see ISO20765 for details).
The next paragraphs provide a brief outline of each equation of state available.
2.1 ISO 20765 Part I  AGA892DC (Natural Gas and Similar Mixtures)
The AGA892DC equation was published in 1992 by the American Gas Association, having been designed specifically as a procedure for the high accuracy calculation of compression factor. In this respect, it is already the subject of ISO122132.
In order for the AGA8 equation to become useful for the calculation of all thermodynamic properties, the equation itself, published initially in a form explicit only for volumetric properties, was mathematically reformulated. This reformulation has been the subject of the ISO 20765part I standard which specifies a method of calculation for the volumetric and caloric properties of natural gases based on the Helmholtz free energy.
2.2 ISO 20765 Part II – GERG2008 (Natural Gas and Similar Mixtures)
The GERG2008 equation of state was developed by the University of Bochum in Germany as a new widerange equation of state for the volumetric and caloric properties of natural gases and other mixtures. It is now the subject of the ISO 20765 Part II.
The ranges of temperature, pressure, and composition to which the GERG2008 equation of state applies are much wider than the AGA8 equation and cover an extended range of application. In addition, the GERG2008 is applicable across the complete phase regions of the fluid, i.e. the liquid phase, the densefluid phase, the vaporliquid phase boundary, and to properties for twophase states.
Figure 5 – Phase diagram for natural gas (typical)
Figure 6 – 21component available for gas composition
2.3 EOSCG (CO2 and Combustion Gas like Mixtures)
This equation of state is a new Helmholtz energy mixture model for humid gases and CCS mixtures (also referred to as Equation of State for Combustion Gases and Combustion Gas like Mixtures, EOSCG) developed by the University of Bochum in Germany [REF 3].
Using the mathematical approach in the GERG2008 with some minor adjustments, the EOSCG improves the description for binary and multicomponent mixtures of six components as follows:
▪ Carbon dioxide
▪ Water
▪ Nitrogen
▪ Oxygen
▪ Argon
▪ Carbon monoxide
Applications include Compressed Air Energy Storage (CAES) and Compression, Transport and Injection of Separated Carbon Dioxide (CCS).
CAUTION
Compressor calculations deal with gas phase. Phase equilibrium calculations and stability test are outside the scope of NCENTRIX. It is User’s responsibility to verify (using for example a process simulator) that the fluid conditions at the inlet and along the compression path remain in the gaseous phase.
2.4 SOAVEREDLICHKWONG (SRK) EOS
The SRK equation of state is implanted in NCENTRIX however it is not used to perform compressor calculation per se; instead it is part of the ISO 20765 routines (density solver) in obtaining an initial approximation of the density roots. More specifically, SRK equation of state is used to narrow down the root search interval of the NCENTRIX density solver for ISO20765 part II.
For reference, SRK equation of state formulation, i.e. alpha function, mixing rules and binary interaction coefficients are those from the API Technical Data Book 6^{th} edition [REF 2].
3 POLYTROPIC HEAD CALCULATION METHODS
Among the most widely used methods for polytropic head calculation, the Shultz method is an industry standard and is available in NCENTRIX. Refer to ASME PTC10 for implementation.
As an alternative to the Shultz method, the 3point method proposed by Huntington in 1985 [REF 4] is more accurate. It is also deemed not necessary to implement more sophistication and we consider the 3point method adequate for accurate calculation. The procedure for this method is briefly outlined herein.
Let (P_{1}, T_{1}) and (P_{2},T_{2}) be the end points of a polytropic compression path. The compressibility term is expressed as follows:
where R is gas constant (=8.314472 kJ/kg.K). Once the polytropic efficiency is calculated, the polytropic head can be derived. The calculation of the coefficients a,b and c is based on intermediate point (P_{3},T_{3}).
As first estimate T_{3} is assumed ~ (T_{1}*T_{2})^{0.5}. This enables to make a first calculation of Z_{3}. The estimation of T_{3} is then improved via recursive method. The details for this are described in [REF.4].
4 TEMPERATURE CALCULATION METHODS
For the case where the outlet pressure P_{D} and polytropic efficiency ETAP are known and we want to calculate the polytropic head EPOL and outlet temperature T_{D}; NCENTRIX has two alternative methods for this calculation, described as follows:
5.5 Root Search Method
 Calculate the Isentropic Outlet Temperature T_{DISEN}
 Define a Root Search Interval as follows:
MIN. INTERVAL = T_{S}
MAX INTERVAL = T_{DISEN} + ΔT (LARGE ENOUGH)
 Use Root Search Method to find the temperature T_{2} that satisfies
ETAP(T_{D}) is determined using 3point method.
5.6 Subdivision Method ( T2SDIV)
Base method procedure:
 Assume the equivalent isentropic coefficients CP_{EQ}, KV_{EQ}, KT_{EQ} and the compressibility Z_{EQ} equal to the values at inlet, CP_{S}, KV_{S}, KT_{S} and Z_{S}, respectively.
 Calculate outlet temperature and polytropic head based on formulas for real gas compression:
 Determine the new values for CP_{EQ}, KV_{EQ}, KT_{EQ} and the compressibility Z_{EQ.}
 Iterate the procedure until convergence of T_{D}
_{ }
_{ }
In order to further improve accuracy, the compression path is subdivided into SDIV subdivisions; the base is applied assuming constant efficiency:
 Define P_{RATIO} = P_{D}/P_{S}
 Set P_{RATIO_NEW} = P_{RATIO}^{(1/SDIV)}
 Calculate outlet pressure of a singular interval as P_{D_INTERM} (i) = P_{D_INTERM} (i1) * P_{RATIO_NEW}
_{ }
 Apply base method to each interval i (=1 to SDIV) to calculate T_{D_INTERM} (i) and HPOL_{ INTERM} (i)
 When i= SDIV, P_{D INTERM }(i)=_{ }P_{D}; T_{D_INTERM}(i) =_{ }T_{D} and
5 data driven model fOR new machine design (ANN)
5.1. Methodology Overview
The proposed approach to characterize the performance of an individual compressor stage relies on a artificial neural network model (ANN), so called “black box”, between selected thermodynamic variables; the only geometrical parameter that is considered in the model relates to the diameter D2 of the impeller.
Four transfer functions F1, F2, F3 and F4 are proposed as basis for this characterization.
Each function connects a selected nondimensional dependent variable (Head Coefficient, polytropic efficiency, ratio surge flow to design and ratio choke flow to design) to a corresponding set of independent variables (ratio actual flow to design, ratio actual mach number to design, design flow coefficient, design mach number and geometry, i.e. tip diameter). The transfer functions are formulated as follows:
5.2. Neural Network Topology
To each transfer function is assigned a dedicated neural network. Common neural network architecture is adopted and is applied to each output; for efficiency and head coefficient, the diameter information is added using additional neurons in the input/intermediate layer.
The neural network proposed is composed of an input layer, an intermediate layer and an output layer. The hidden layer includes 6 neurons. This architecture has proven to be fit for purpose following a number of trials on other variants. These trials ranged from basic to complex topology (additional intermediate layers and/or increased number of neurons) and also revealed inadequacy of using complex configuration (prone overfitting). The table hereunder summarizes the neural network topology for each transfer function.
Variable 
ETAP 
TAU 
FI_{1c}/FI_{1} 
FI_{1s}/FI_{1} 
Dependency 
D_{2}, D_{2}*, FI_{1}/ FI_{1}*, Mu/Mu*, FI_{1}*, Mu* 
FI_{1}/ FI_{1}*, Mu/Mu*, FI_{1}*, Mu* 

Input Layer 
6 
4 

Hidden Layer 
6 
6 

Output Layer 
1 
1 

Learning Method 
Quick Propagation or Equivalent 
Table 3: Neural Network Topology vs. Transfer Functions

Figure 7 Neural Network Proposed Topology (example: F1 and F2)
A neural network predictor is not suitable for extrapolating data outside the training data set. Also when the prediction involves input data approaching the bounds of the training data set, the neural network saturates especially with conventional activation functions (e.g. logistic sigmoid). This saturation occurs because the activation function gradient tends toward zero when input is approaching the limits of the training data set; for the limit case, a zero gradient means that the neural network has stopped learning.
Figure 8 Neural Network Activation Function (Tanh) in Hidden Layer
In practice, the saturation effect could create some concern, near the choking line for example; in this region the efficiency drops significantly and the curve profile (efficiency vs. flow coefficient) changes abruptly, taking an even steeper slope at higher Mach numbers.
5.3 Data Scaling
A normalization scaling of the data is done in order fit them into a span smaller than the activation function full span ([0.7, 0.7] vs. full span [1, +1] for Tanh activation function). The scaling combined with the choice of a Tanh activation function of variable slope in the intermediate layer and a linear activation function in the output layer offer acceptable results. The process and formula for the scaling and back transform procedure is outlined as follows:
Figure 9 Scaling and Back Transform Flow Chart
Var_{INPUT.NET}= 0.7 +1.4 * (Var_{INPUT} – Var_{MIN}) / (Var_{MAX}Var_{MIN})
Var_{OUTPUT }= Var_{MIN }+ (Var_{OUTPUT.NET }+ 0.7) * (Var_{MAX}Var_{MIN }) / 1.4
Where the overline symbol denotes unscaled (or back transformed) variable and the underline symbol denotes a scaled variable. The subscripts _{MIN} and _{MAX} represent respectively the minimum and maximum values of the considered variable across the training data set. Subscript _{.NET }denotes Network (Input, Output).
Training Example
The neural network has been trained on manufacturer data for general purpose 2D stage; design flow coefficients range from ~0.02 to ~0.06 (vaneless type).
The following table summarizes for each transfer function the outcome of the training process. Since the number of sample is relatively high (>1000), the obtained accuracy is in favour that the transfer functions F_{1}, F_{2}, F_{3} and F_{4} were adequately chosen to build the model.
Variable 
ETAP 
TAU 
FI_{1}c/FI_{1} 
FI_{1}s/FI_{1} 
Residual Mean Squared Error (RMSE) 
0.03 
0.017 
0.0081 
0.0083 
Determination Coefficient 
>0.976 
>0.995 
>0.999 
>0.9988 
Correlation Coefficient 
>0.988 
>0.997 
>0.999 
>0.9994 
Table 4: Neural Network RMSE, Determination and Correlation Coefficients
5.4. PreBuilt Stage Database
2D general purpose, 3D pipeline and 3D high Mach number have been included in NCENTRIX as prebuilt stages after characterizing them using the neural network technique.
The individual characterization is stored in the files *.NCM in a format readable to the ANN. The NCM stage group is selectable via the drop down list assigned to each stage.
Figure 10 –Mechanical Stage Configuration Mask
User is responsible to check the design coefficients (FI*, MU) against the selected stage allowed application range; outside the boundary of applicability, the performance cannot be calculated properly and may lead to erroneous or wrong results.
Figure 11 –Available prebuilt stages and their applications ranges
CAUTION
It is NOT recommended to operate the network outside of the training range. As a minimum requirement, each variable injected into the network shall be within the training data set [min, max] interval of that variable. This can be checked by clicking on “STAGE LIMITS” in the parameters mask; ensure for each stage that the inputs D2, FI1*, MU*, FI1/FI1* and MU/MU* are within their min/max respective limits.
Figure 12 –Stage limits verification
In addition, the mechanical properties of the prebuilt stages have been approximated and included in a file ROTOR_DEF (weight, dimension and inertia). This information is used for design verification of new machines.
5.5. Model Scalability
In general, the neural network technique is scalable to any database provided there is enough sample data that allows building a representative model. The database can contain information gathered from master model testing or Computational Fluid Dynamics (CFD) simulations, or a combination of both. Once the individual stages are modeled and stored in NCM files, NCENTRIX routines will take care of the stacking of all stages in order to deliver a performance run for multistage compressors.
PART – B
DESIGN VERIFICATION OF NEW MACHINES
1 DETAILED STAGE DESIGN
In the following section, we will present the procedure and formulas used to approximate detailed stage design parameters for NEW MACHINE DESIGN; these parameters are used for shaft schematization and verification of design limits.
1.1 Impeller Exit Parameters
The flow coefficient at impeller exit is given by
The slip factor is calculated according to Wiesner formula:
Note that the formula by Wiesner may not be accurate for all cases; it is here proposed as baseline for a preliminary approximation. The blade metal exit angle BETA_{2}, impeller blade thickness T and the number of blades ZBLADE also vary from one manufacturer stage design to the next. When stages are individually modeled in NCENTRIX, it is advised to calibrate BETA_{2}, T and ZBLADE based on manufacturer data for the stage group (impeller family) under consideration. One can approximate BETA_{2} by simple interpolation over flow coefficient FI1
Blade thickness T can be approximated using a linear relationship as follows
Once FI2 is determined, the following quantities are calculated:
Squared nondimensional absolute speed:
Absolute exit velocity:
Exit flow angle:
Impeller totaltostatic density ratio:
Where the impeller efficiency is obtained from stage efficiency using correction formula:
ETAP_COR is taken as a constant = 0.1
Finally, the impeller exit width can be estimated as follows
1.2 Diffuser Ratio
The diffuser ratio (DR) is given by
As a rule of thumb, DR is typically comprised between ~1.4 (2D stags) and 1.65 (3D stage). Nevertheless, the final value shall be set in accordance to manufacturer data for the stage group that is modeled.
Detailed stage parameters are summarized in the Thermodesign sheet; an example is illustrated below:
Figure 13 – Stage detailed parameters (Thermodesign sheet output)
2 VERIFICATION OF DESIGN LIMITS
Once a candidate thermal design is defined, it is needed to assess it is within mechanical limits.
NCENTRIX provides verification options for prebuilt stages (NEW MACHINE DESIGN) so that a very rough check can be done encompassing the aspects described in the next paragraphs.
2.1 Rotor Schematization
The tool will build a schematization of the rotor which includes estimating rotor dimensions, weights and inertia. These quantities are estimated using regression or equivalent methods based on manufacturer data. For example, the stage axial span (LS) is estimated for each stage group as a function of the design flow coefficient FI1*, design Mach number MU* and diameter D_{2}. Tabulated data are available for export to specialized software (rotordynamics tools, e.g. Dyrobes®).
Figure 14 – Rotor schematization in NCENTRIX
Rotor Geometry Modeling
Transfer functions available based on impeller type:
· ROTOR_DEF_D33
· ROTOR_DEF_T53
· ROTOR_DEF_T42
· ROTOR_DEF_GENERIC
Input Variable 
ID 
Output Variable 
ID 
D2 MASTER DIAM 
1 
INERTIA POLAR 
1 
FI DESIGN 
2 
INERTIA TRANSVERSE 
2 
MU DESIGN 
3 
IMPELLER MASS (KG) 
3 
D2 ACTUAL DIAM. 
4 
COG 
4 
// NOT USED // 
5 
IMPELLER SPAN (MM) 
5 
// NOT USED // 
6 
SPAN STAGE (MM) 
6 
// NOT USED // 
7 
DIAM_U 
7 
// NOT USED // 
8 
DIAM_TEN 
8 
// NOT USED // 
9 
PAS_COMP 
9 
ShaftEnd Geometry Modeling
Transfer function available: SHAFT_END
Input Variable 
ID 
Output Variable 
ID 
// NOT USED // 
1 
CONE SPANE (MM) 
1 
// NOT USED // 
2 
THRUST BEARING INT. DIAM. (MM) 
2 
// NOT USED // 
3 
THRUST BEARING SPAN (MM) 
3 
L/D BEARING RATIO 
4 
NUT_LENGTH (MM) (DE AND NDE) 
4 
D2 DIAMETER AVG 
5 
DRY GAS SEAL EXT. DIAM. (MM) 
5 
CASING TYPE (1=inline) 
6 
BALANCE DRUM NO. TEETH 
6 
CASING FRAME SIZE (DIGIT) 
7 
BALANCE DRUM TEETH STEP (MM) 
7 
NOZZLE SIZE (IN) 
8 
BALANCE DRUM #2 NO. TEETH 
8 
NOZZLE SIZE #2 (IN) 
9 
BALANCE DRUM #2 TEETH STEP (MM) 
9 
CASING RATING 
10 
DRY GAS SEAL LENGTH (MM) 
10 
CONE DIAM. MM 
11 
DRY GAS SEAL NOM. DIAM. (MM) 
11 
// NOT USED // 
12 
JOURNAL BEARING DIAMETER (MM) 
12 
// NOT USED // 
13 
JOURNAL BEARING LENGTH (MM) 
13 
// NOT USED // 
14 
THRUST BEARING EXT. DIAM. (MM) 
14 
// NOT USED // 
15 
BALANCE DRUM SPAN (MM) (SHAFT END) 
15 
// NOT USED // 
16 
BALANCE DRUM DIAM.(MM) (SHAFT END) 
16 
// NOT USED // 
17 
BALANCE DRUM #2 SPAN (MM) (INTERSTAGE) 
17 
// NOT USED // 
18 
BALANCE DRUM #2 DIAMETER (INTERSTAGE) 
18 
// NOT USED // 
19 
INLET PLENUM SPAN (MM) 
19 
// NOT USED // 
20 
INLET PLENUM #2 SPAN (MM) 
20 
// NOT USED // 
21 
CONE SPAN (MM) 
21 
// NOT USED // 
22 
CONE MASS (KG) 
22 
// NOT USED // 
23 
CONE DIAMETER (VIA FUNCTION) 
23 
// NOT USED // 
24 
THRUST BEARING DIAM. 1 TO 2 (MM) 
24 
// NOT USED // 
25 
THRUST BEARING SPAN 1 TO 2 (MM) 
25 
2.2 Shaft Stiffness and Stability Screening
1^{st} critical speed (NC1) is estimated based on rigid bearings and centered modal mass assumption [REF.7]. The shaft stiffness ratio L/D and Flex ratio MCS/NC1 is calculated, after which rotor stability flex ratio can be positioned on a KirkDonald diagram.
Figure 15 – Very rough rotor analysis and stability check
Estimation of 1^{st} critical speed under assumption of rigid bearings and centered modal mass
2.3 Impeller Yield Strength (YS) Utilization
Impeller stress at Over Speed Test (OST) speed is calculated. Then a corrosion risk assessment for Stress Sulfide Cracking (SSC) as per NACE MR0175 is performed.
The Yield Strength utilization is calculated based on selected material RP_{02} that is specified by user for both standard and NACE compatible materials (this can be done via editing the file: MATERIAL.CSV columns 2 and 3 respectively).
Figure 16 – Material corrosion check
Note: The relative humidity is calculated according to steam properties formulations of IAPWSIF97 [REF 7]. The gas service is considered wet when the relative humidity exceeds 80%, otherwise it is dry.
Figure 17 – Impeller stress analysis
The formulas used for the calculation of impeller peripheral stress are based on Ludtke [REF 6]. The calculation takes into account the impeller design (flow coefficient). A brief outline of the procedure is given as follows:
 Check NACE applicability and select material RP_{02}
 Calculate the impeller stress according to
C^{*} (m3/Gg) is a factor that takes into account material density (typically constant for steel) and that is linear function of the impeller design flow coefficient:
 Calculate the Yield Strength Utilization as per the formula
2.4 Gas Velocities at Inlet and Outlet Flanges:
ANSI/ASME flange rating is selected based on Maximum Allowable Working Pressure (MAWP). Flange size (inch.) is selected and velocities calculated based on flow area (editable via the file: NOZZLE.DAT)
Figure 18 – Inlet and outlet flange gas velocities calculation
3 VERIFICATION CHECK LIST
Finally, keeping in the mind the very rough character of this verification, we will summarize a set of acceptance criteria for a candidate thermal design as follows:
Criteria 
Acceptance 
Max. No. of impellers 
Less than 9 (preferably 8) stacked on single shaft 
Impeller YS utilization % 
Less or equal 100% 
Minimum operating speed 
As a minimum, shall be higher than NC1 (rigid bearings) 
Shaft Stiffness Ratio L/D 
Less than 10 
Rotor Stability (Flex Ratio) 
Within safe area as depicted in KirkDonald diagram 
Wet H2S service suitability 
If applicable: Material selected according to NACE MR0175 
Inlet flange gas velocity 
<35 m/s at certified point 
Outlet flange gas velocity 
<35 m/s at certified point 
Table 5 – verification check list
CHARACTERIZATION OF EXISTING MACHINES
1 METHODOLOGY OVERVIEW
For existing machine modeling, the transfer functions are simplified considering the fact that the machine has fixed design. Thus the diameter is kept out of the model as well as the design flow coefficient and Mach number which are no more required as direct input.
For convenience we keep a common structure between all transfer functions. This lead to the set of transfer functions F5, F6, F7 and F8 as follows:
The method for modeling these transfer functions is detailed in the next section.
2 ORIGINAL MAP CHARACTERIZATION (DESIGN CASE)
2.1 User Information to be Supplied
The user shall provide the map data of the compressor in tabulated format for the reference case. Ideally the condition basis of the reference case shall coincide with the design case that is to say it has to satisfy:
If this condition is not satisfied, it is necessary to know the amount of volumetric and Mach number shift of the reference case to the design condition so that it is accounted for in calculation (values to be reported in the GUI parameters mask).
In addition, information relative to the reference case condition basis and geometry shall be supplied as follows:
 Inlet Pressure, P_{Ref}
 Inlet Temperature, T_{Ref}
 Mass flowrate, GFLOW_{Ref}
 Gas Composition and Molecular Weight MW_{Ref}
 Reference Speed RPM_{Ref}.
 Average tip diameter of the impellers D2_{AVG}
The corresponding compressibility Z_{Ref }and speed of sound WS_{Ref} can be calculated via an equation of state. The design inlet flow coefficient and Mach number shall be determined as follows:
where
Two combinations of variables are accommodated for supplying the original map data:
Discharge Pressure and Temperature vs. Flow
For each curve at constant speed RPM_{N}, the polytropic head HPOL_{DATAPOINT} and polytropic efficiency ETAP_{DATAPOINT} are calculated for each data point based on discharge pressure and temperature by means of the Huntington method (which procedure is described in this document).
The average peripheral speed is calculated based on the following formula
This is used to calculate the head coefficient at each data point according to
Next, the actual inlet flow coefficient, the inlet flow coefficients at surge and choke are calculated using respectively, the data point actual flow and the flows at surge and at choke for the curve under consideration.
where
This allows the creation of a discrete data distribution of the transfer functions F5, F6, F7 and F8. Input and output are scaled and fitted into a square grid:
Polytropic Head and Polytropic Efficiency vs. Flow
The procedure is identical as with temperature and pressure; Huntington method is no more required.
3 STANDARD METHODS
3.1 Linear Method
The linear method is generally the most robust in regard to situations where the quality of the original map data is not very good (datasets with irregular, scarce and/or noisy data).
A limitation of the method is that it cannot be used outside of the boundary of the data grid. In order to accommodate the iterative solver (for example when solving for speed with the discharge pressure imposed), the data points are constrained using the rules indicated below, before they are passed to the model:
In practice, under these rules, predictions follow the fan laws outside the data grid boundaries; the iterative solver can carry on with the iterations until convergence.
3.2 NLQUAD/R and NLCUBIC/A Methods
NLQUAD/R and NLCUBIC/A methods can improve the accuracy of the characterization provided the quality of the data set is good enough. The speed search interval shall also be narrowed down by means of the parameters LRPM and URPM in the Parameters mask.
We recommend the following guidelines for user supplied information:
 Supply a minimum of 11 points regularly spaced along each speed curve;
 Supply a minimum of 4 speed curves for each map, at regular intervals of speed;
 Prefer head and efficiency curves vs. flow;
 If available, obtain from manufacturer the original map in tabulated / numeric format.
NLCUBIC/A method has a tuning parameter NCP.
è Observe 2 ≤ NCP < No. of samples. Recommended NCP value = 30.
For NLQUAD/R method, the tuning parameters are NQ and NW.
è Observe 5 ≤ NQ ≤ No. of samples, or 40 whichever is lower. Recommended NQ value = 13.
è Observe 1 ≤ NW ≤ No. of samples, or 40 whichever is lower. Recommended NW value =19.
3.3 Prediction Range Extension
The prediction range limits are defined by a ratio Mu/Mu* not to exceed the lower and upper bounds of the input dataset [Mu/Mu*min; Mu/Mu*max]. User may override the limits by applying a range extension factor (%). The extension feature is enabled by double clicking on the warning label in the performance characterization mask; a warning message will be prompted. Note that outside of the normal range, predicted values will be obtained by extrapolation which is NOT recommended; extension of the normal range, if ever applied, shall NOT exceed 5 % in any case.
Figure 19 – MU/MU* range extension
4 DATASET EXTENSION
NCENTRIX intends to add innovation on top of past works affected by others (see patent ref. WO2013005129A2 by M. Di Febo). So when additional information is available from the manufacturer in terms of original performance maps for ALTERNATIVE CASES on top of the design case, advantage can be taken thereof as the data can then be used to train the model onto a wider window. Depending on the particular process design (alternative cases with inlet pressure, inlet temperature, speed and/or gas compositions slightly different or faroff design) this would mean that the MU/MU* range of the training dataset could be more or less extended, subsequently the prediction range too.
NCENTRIX can accommodate this operation (DATASET EXTENSION); the procedure is as follows:
In the performance characterization mask / data grid area, the user shall use the column <CONDITION BASIS> and assign a condition basis to its corresponding set of data. In other words, each input data raw (flow, polytropic head or outlet pressure, polytropic efficiency or outlet temperature, and speed) will be mapped to the process section tree view in terms of condition basis irrespective of its kind (design condition or alternative case(s))
In general, we recommend to use one or two alternative cases and select those that offers the larger span in terms of the MU/MU* variations.
Figure 20 – Condition Basis Assignment Column (GUI performance characterization mask)
5 VERSATILE ARTIFICIAL NEURAL NETWORK
5.1 Methodology Overview
As an alternative to the standard methods offered (LINEAR, NLQUAD/R, and NLCUBIC/A), an artificial neural network is integrated into NCENTRIX for the analysis of multivariate systems. In this case, the set of transfer functions F5, F6, F7 and F8 is adapted by adding to the input vector a slot for an optional thermodynamic variable DVAR (preselected in the software); the reason for implementing a neural network is to widen the portfolio of options available to the user for tackling problems exhibiting more complicated data structures, such as those arising from a dataset extension approach (see previous section).
For convenience, we keep a common structure to the transfer functions. This lead to the new set of transfer functions F9, F10, F11 and F12 as follows:
We call the artificial neural network system versatile (VANN) in that it is equipped with a wide range of features (highly configurable topology, 13 learning methods, available noise and regularization techniques) which can be reconfigured at wish to suit a particular problem; for example, the following tuning of the parameters can be done:
 Set the number of layers and number of units per layer;
 Select an activation function per layer;
 Set the scaling parameters;
 Select between various weight updating methods (including first and second order methods);
 Introduce noise and/or use basic regularization scheme.
In most cases however, and based on a dozen numbers of trials, we recommend a baseline configuration as follows:
 Learning method (updating): Resilient BackPropagation
 Number of hidden layer: 1
 Number of units in hidden layer: 4 when run in multiple outputs mode (4 units in the output layer).
 Activation functions: TANH in the hidden layer and LINEAR in the output.
 Input and Output Scaling: [0.8, 0.8]
5.2 Configuration Parameters
The parameters are entered via the GUI mask as depicted below.
Figure 21 –Neural Network Parameters GUI Mask
When more advanced configuration can be made via the file “SETTLEMENT.CFG” as follows:
method,15 : Default Updating Method
multiout,1 : Default Output Mode (Multiple <1> or Single <0>)
nlr,3 : Total No. of Layers
fs1,0.8 : Scaling Factors (Min. Bound)
fs2,0.8 : Scaling Factors (Max. Bound)
afx1,2 : Activation Function, Layer 1 (ATAN <1>, LINEAR <4>)
afx2,2 : Activation Function, Layer 2 or Output (ATAN <1>, LINEAR <4>)
afx3,2 : Activation Function, Layer 3 or Output (ATAN <1>, LINEAR <4>)
afx4,4 : Activation Function, Output (ATAN <1>, LINEAR <4>)
ns_width,0.00 : Noise Width
ns_scale,0.99 : Noise Scale Factor
bsize,10 : MiniBatch Size
mnt,0.5 : Momentum
lrate,1 : Learning Rate
refresh,1000 : Screen Refresh Rate
errmsr,0 : Error Measurement Method (<0> for MSE)
winit,0.1 : Initial Width
lambda,0.0 : Weight Decay Simple Pruning
vselect,0 : Single Output Mode Select (<0> Loop, <N> Train Selected Output N)
rhoratio,1 : Not Used <0>
vsound,0 : Select DVAR (<0> Sound Speed, <1> Isentropic Coefficient KT)
sd,10 : Grid No. Subdivision (Linear or Spline Densification Option)
autolp,0 : Not Used <0>
edgl1,4 : Default Size (No. Units ) First Hidden Layer w/ Option: SMALL.
edgl2,8 : Default Size (No. Units ) First Hidden Layer w/ Option: NORMAL.
edgl3,10 : Default Size (No. Units ) Second Hidden Layer w/ Option: LARGE.
 Available updating methods and their assigned code:
0 > Standard BackPropagation updating
1 > Manhattan updating
2 > Langevin updating
3 > Quickprop
4 > Conjugate Gradient  PolakRibiere
5 > Conjugate Gradient  HestenesStiefel
6 > Conjugate Gradient  FletcherReeves
7 > Conjugate Gradient  Shanno
10 > Scaled Conjugate Gradient  PolakRibiere
11 > Scaled Conjugate Gradient  HestenesStiefel
12 > Scaled Conjugate Gradient  FletcherReeves
13 > Scaled Conjugate Gradient  Shanno
15 > Resilient BackPropagation
5.3 Prediction Task Procedure
 The network is initialized with parameters stored in file (done in the modeling step)
 The input vector is scaled
 The neural network parameters are set up
 The input vector is fed forward into the network
 The calculation results are stored in the output vector
 The output vector is scaled (backtransform).
5.4 Output Information
The program writes the network parameters, RMSE error and coefficient of determination in file.
STANDARD: network will write unformatted in a file “Fort.X” (X=process section)
OPTION: network writes formatted in a file “Fort.X” (X=process section)
Note that unformatted writing is machine dependant which may affect the portability of the “Fort.X “file
Figure 22 –Network Error (RMSE) monitoring window
CAUTION
If VANN method is applied, network shall be configured with a number of layers and units as small as possible to prevent overfitting.
6 SIMULATION OF PERFORMANCE DEGRADATION
Hereunder we present a description of the procedure in order to simulate performance degradation, we introduce coefficients of degradation applied to the clean case (#CLN) with respect to the following fault parameters:
Performance for the degraded case (#DGD) is subsequently calculated based on ETAP_{DGD}, TAU_{DGD}, FI*_{DGD} at imposed discharge pressure; the results are compared against the data obtained from field monitoring with respect to the machine health status SPEED, POWER AND TEMPERATURE; we can write the relative deviations:
The coefficients of degradation shall be adjusted such as to minimize each of the deviations (VAR=0)
With the constraints
Figure 23 –Performance Degradation Mask
[1]. Technical Standard, ISO20765 Parts I (AGA8) and II, Edition 2015
[2]. Technical Standard, API Technical Data Book, 6th Edition (1997)
[3]. PhD Thesis “A New Helmholtz Energy Model for Humid Gases and CCS Mixtures”, G. Gernert (2013)
[4]. ASME Proceedings, “Evaluation of Polytropic Calculation Methods for Turbomachinery Performance”, R. Huntington (1985)
[5]. ASME Proceedings, “A Method to Estimate the Performance Map of a Centrifugal Compressor Stage”, M. Casey and C. Robinson (2013)
[6]. Book, “Process Centrifugal Compressors”, K. Lüdtke (2015)
[7]. ASME Proceedings, “The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam”, W. Wagner et al. (2000)
[8]. Dyrobes publications, “Introduction To Rotor Dynamics, Critical Speed and Unbalance Response Analysis”, E.J. Gunter (2004)
[9]. Technical Standard, API617, 7th Edition
APPENDIXA
STATUS CODES
STATUS CODE 
EXPLANATION 
INF1 
Specified flow TOO LOW (SURGE). Flow is automatically adjusted to control line flow using recycle control. 
inf3 
Inlet pressure TOO LOW (VACUUM). User should inspect the result to ensure the specified duty has been matched. 
inf4 
No plotting at the flagged speed. Not enough operating margin on curve, OR Speed TOO HIGH (exceeds the upper bound of allowed Mu/Mu* range). 
INF5 
No plotting at the flagged speed. Speed TOO LOW (exceeds the lower bound of allowed Mu/Mu* range). 
err1 
Specified duty cannot be matched with iterated variable set on FLOW. No flow can satisfy the imposed duty. OPERATING POINT FAILURE. 
ERR2 
Not enough operating margin on speed curve for the actual case. OPERATING POINT FAILURE. 
ERR3 
Specified flow TOO HIGH (CHOKE). Flow is automatically adjusted to chocking line. OPERATING POINT FAILURE. 
err4 
Specified duty cannot be matched with the fixed speed motor speed. 
APPENDIXB
PARAMETERS
PARAMETER 
EXPLANATION 
FI*, MU IMPOSED 
When checked, design will be calculated based on user specified/imposed values for FI* and MU* entered via the mechanical stage configuration. 
ETAP CORRECTION 
ETAP Correction Factor. ETAP = ETAP * Correction Factor / 100. Default value = 100% (no adjustment) 
TAU CORRECTION 
TAU Correction Factor. TAU= TAU * Correction Factor / 100. Default value = 100% (no adjustment) 
FI_RATIO 
Volumetric shift by means of ratio FI1/FI1*(Design condition) Default value = 1.00 (no adjustment) 
MU_RATIO 
Mach number shift by means of ratio MU/MU1*(Design condition) Default value = 1.00 (no adjustment) 
TAU (PRESELECT) (*) 
TAU assumed value for 'PRESELECT' program. Default value = 0.55 
ETA (PRESELECT) (*) 
ETAP [%] assumed value for 'PRESELECT' program. Default value = 80% 
T2SDIV METHOD 
When checked, selects T2SDIV temperature method in lieu of Root Search Method (Default) 
POLY. METHOD 
Select among 3 options, the polytropic calculation method: § 3Point (Default) § Shultz § Average Suction and Discharge 
POINT PERFORMANCE ONLY 
When checked, configures the performance calculation output as follows: Performance point calculation only for alternative cases. Performance point calculation and single speed curve for design (Default). 
ADD % LABELS TO CURVES 
When checked, displays a label on each speed curve of the performance map, indicating the speed in % in addition to RPM’s. 
PLOT USING LINES 
Plot the performance curves using LINES instead of SPLINES (Default). 
csf 
Change the intervals distribution of the control points used to generate the performance curves. Adequate for steep curvature near the choke region. Default value = 1.00 (regular intervals). 
corv 
When checked, the operating range (available turndown) of the performance curves is verified. Default value unchecked. 
ECS 
When checked, convergence stabilization measure is used. The program will set minimum (floor) values for TAU and ETAP while the solver performs the iteration process. Default value is unchecked. 
PTOL 
Absolute tolerance on discharge pressure [kPa]. Stop criteria for iterations set on discharge pressure. Default value=0.5 kPa. 
INIT_RPM 
Initial guess for speed [RPM]. If left blank, the software will attempt to calculate INIT_RPM automatically. 
LRPM 
Sets lower bound of speed search interval defined by LRPM * INIT_RPM Default value = 0.6 
URPM 
Sets upper bound of speed search interval defined by URPM * INIT_RPM Default value = 1.15 
FTOL 
Relative tolerance on flow [%]. Stop criteria for iterations set on flow. Default value=0.01% 
SDIV 
Defines the number of subdivisions for T2SDIV and H2SDIV methods. Default value =1 (lower accuracy / faster). T2SDIV = option method, returns P2, T2 that satisfies inputs HPOL, EPOL. H2SDIV= default method, returns HPOL,T2 that satisfies inputs P2,EPOL 
LFSS (*) 
Flow initial increment step for the MSPS method. Default value = 0.05 (moderate precision / normal execution speed). 
SSM 
Speed safety margin [%]. Default value=0%. Effects U2 and RPM values by a factor (1+SSM/100) 
CLM 
Control line to surge limit line margin [%]. Default value=12% CLM = 100 *( FLOW_{CONTROL LINE} – FLOW_{SURGE}) / FLOW_{CONTROL LINE} 
FLOW F2F (*) 
When checked, inlet flow reference is taken at the flange in the datasheets and performance maps. Otherwise the total flow passing through the stages (inclusive of leakages) will be considered (NETFLOW, default). The power is always calculated based on NETFLOW. 
MECHANICAL LOSSES 
Specifies the mechanical losses (bearings, seals) at 10000 RPM. The program linearly extrapolates different speeds. 
(*) Not available for “field performance prediction” analysis (existing machines).
Figure 24 –Parameters Mask