N-CENTRIX

Machine Learning Software for Compressor Performance Analysis

Technical Manual

 

 

 

 

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Revision Sheet

 

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 Multi-Stage 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   EOS-CG 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 Pre-Built 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 NL-QUAD/R and NL-CUBIC/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

 

 

 

 

 

 

 

 

 

Disclaimer

N-CENTRIX SOFTWARE IS PROVIDED “AS IS” WITHOUT ANY EXPRESS OR IMPLIED WARRANTY OF ANY KIND INCLUDING WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE. IN NO EVENT SHALL THE DEVELOPER BE LIABLE FOR ANY DAMAGES WHATSOEVER (INCLUDING, WITHOUT LIMITATION, DAMAGES FOR LOSS OF PROFITS, BUSINESS INTERRUPTION, LOSS OF INFORMATION) ARISING OUT OF THE USE OF OR INABILITY TO USE THE SOFTWARE, EVEN IF THE DEVELOPER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

Notations

 

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

MPa-a

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

Non-dimensional 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

MPa-a

 

YSUTILIZATION

Material Yield Strength Utilization

%

SIGMAOST

Impeller Stress @ Over Speed Test (OST) Speed

N/mm2

RP02

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

www.n-centrix.com

 

 

 


INTRODUCTION

 

N-CENTRIX is turbo-machinery 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), N-CENTRIX 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 N-CENTRIX 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, N-CENTRIX 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.

N-CENTRIX 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

N-CENTRIX calculates the performance of single-shaft multi-stage compressors for train with single casing or multiple casings arrangement.

 

The process by which N-CENTRIX calculates the performance is described as follows. N-CENTRIX 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. N-CENTRIX 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 stage-stacking 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, straight-through 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 multi-stage compressor casing cross-section (API 617 7th edition)

Figure 3 – Shaft line arrangement with multiple casings

NOTE

Only single section in straight-through arrangement can presently be configured in N-CENTRIX. 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, re-circulation, incidence loss, clearance loss, disk friction loss) and diffuser (skin friction and diffusion losses), a data-driven methodology is used instead which models key non-dimensional 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 N-CENTRIX. 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(PD(NIMP) - PD_SPECIFIED) < PTOL

 

-                      Compute using EOS package thermodynamic outputs for each stage at design condition:

 

                                    OUTPUTS = {HPOL, ETAP, BHP, PS, PD, TS, TD, WS, RHOS, RHOD}

 

 

 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 Multi-Stage 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, PS, PD, TS, TD, WS, RHOS, RHOD}

 

-          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 real-life 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 multi-stage 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 (AGA8-92DC)

EOS Package 2

ISO 20765 Part II (GERG2008)

EOS Package 3

EOS-CG

Table 2 – EOS packages in N-CENTRIX

N-CENTRIX uses equations of state based on the Helmholtz free energy whose implementation is described in ISO-20765 standard [REF 1].  ISO-20765 methods use a standardized 21-component 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 ISO-20765 for details).

 

The next paragraphs provide a brief outline of each equation of state available.

 

2.1   ISO 20765 Part I - AGA8-92DC (Natural Gas and Similar Mixtures)

The AGA8-92DC 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 ISO12213-2.

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 20765-part 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 GERG-2008 equation of state was developed by the University of Bochum in Germany as a new wide-range 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 GERG-2008 equation of state applies are much wider than the AGA-8 equation and cover an extended range of application.  In addition, the GERG-2008 is applicable across the complete phase regions of the fluid, i.e. the liquid phase, the dense-fluid phase, the vapor-liquid phase boundary, and to properties for two-phase states.

 

Figure 5 – Phase diagram for natural gas (typical)

Figure 6 – 21-component available for gas composition

2.3   EOS-CG (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, EOS-CG) developed by the University of Bochum in Germany [REF 3].

Using the mathematical approach in the GERG-2008 with some minor adjustments, the EOS-CG improves the description for binary and multi-component 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 N-CENTRIX.  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   SOAVE-REDLICH-KWONG (SRK) EOS

The SRK equation of state is implanted in N-CENTRIX 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 N-CENTRIX 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 6th 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 N-CENTRIX. Refer to ASME PTC10 for implementation. 

 

As an alternative to the Shultz method, the 3-point 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 3-point method adequate for accurate calculation. The procedure for this method is briefly outlined herein.

 

Let (P1, T1) and (P2,T2) 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 (P3,T3).

 

 

 

 

As first estimate T3 is assumed ~ (T1*T2)0.5. This enables to make a first calculation of Z3. The estimation of T3 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 PD and polytropic efficiency ETAP are known and we want to calculate the polytropic head EPOL and outlet temperature TD; N-CENTRIX has two alternative methods for this calculation, described as follows:

 

5.5   Root Search Method

 

- Calculate the Isentropic Outlet Temperature TDISEN

 

- Define a Root Search Interval as follows:

 

MIN. INTERVAL = TS

 

MAX INTERVAL = TDISEN + ΔT (LARGE ENOUGH)

 

- Use Root Search Method to find the temperature T2 that satisfies

 

 

ETAP(TD) is determined using 3-point method.

 

 

5.6   Subdivision Method ( T2SDIV)

Base method procedure:

 

- Assume the equivalent isentropic coefficients CPEQ, KVEQ, KTEQ and the compressibility ZEQ equal to the values at inlet, CPS, KVS, KTS and ZS, respectively.

 

- Calculate outlet temperature and polytropic head based on formulas for real gas compression:

 

 

 

 

 

- Determine the new values for CPEQ, KVEQ, KTEQ and the compressibility ZEQ.

 

- Iterate the procedure until convergence of TD

 

 

In order to further improve accuracy, the compression path is subdivided into SDIV subdivisions; the base is applied assuming constant efficiency:

 

- Define PRATIO = PD/PS

 

- Set PRATIO_NEW =    PRATIO(1/SDIV)

 

- Calculate outlet pressure of a singular interval as PD_INTERM (i) = PD_INTERM (i-1) * PRATIO_NEW

 

- Apply base method to each interval i (=1 to SDIV) to calculate TD_INTERM (i) and HPOL INTERM (i)

 

- When i= SDIV,   PD INTERM (i)= PD; TD_INTERM(i) =  TD 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 non-dimensional 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 over-fitting). The table hereunder summarizes the neural network topology for each transfer function.

 

Variable

ETAP

TAU

FI1c/FI1

FI1s/FI1

Dependency

D2, D2*, FI1/ FI1*,  Mu/Mu*, FI1*, Mu*

FI1/ FI1*,  Mu/Mu*, FI1*, 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

                                                VarINPUT.NET= -0.7 +1.4 * (VarINPUT – VarMIN) / (VarMAX-VarMIN)  

                                               

VarOUTPUT = VarMIN  +  (VarOUTPUT.NET +  0.7) * (VarMAX-VarMIN )  / 1.4

 

Where the over-line symbol denotes un-scaled (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 (vane-less 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 F1, F2, F3 and F4 were adequately chosen to build the model.

Variable

ETAP

TAU

FI1c/FI1

FI1s/FI1

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.    Pre-Built Stage Database

2D general purpose, 3D pipeline and 3D high Mach number have been included in N-CENTRIX as pre-built 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 pre-built 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 pre-built 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, N-CENTRIX routines will take care of the stacking of all stages in order to deliver a performance run for multi-stage 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 BETA2, 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 N-CENTRIX, it is advised to calibrate BETA2, T and ZBLADE based on manufacturer data for the stage group (impeller family) under consideration. One can approximate BETA2 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 non-dimensional absolute speed:

 

 

Absolute exit velocity:

 

Exit flow angle:

 

 

Impeller total-to-static 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.

N-CENTRIX provides verification options for pre-built 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 D2. Tabulated data are available for export to specialized software (rotor-dynamics tools, e.g. Dyrobes®).

Figure 14 – Rotor schematization in N-CENTRIX

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

Shaft-End 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

1st 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 Kirk-Donald diagram.

 

Figure 15 – Very rough rotor analysis and stability check

 

Estimation of 1st 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 RP02 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 IAPWS-IF97 [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 RP02

- 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 Kirk-Donald 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


PART – C

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, PRef

-       Inlet Temperature,  TRef

-       Mass flowrate,  GFLOWRef

-       Gas Composition and Molecular Weight  MWRef

-       Reference Speed RPMRef.

-       Average tip diameter of the impellers D2AVG

 

The corresponding compressibility ZRef and speed of sound WSRef 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 RPMN, the polytropic head HPOLDATAPOINT and polytropic efficiency ETAPDATAPOINT  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   NL-QUAD/R and NL-CUBIC/A Methods

NL-QUAD/R and NL-CUBIC/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.

 

NL-CUBIC/A method has a tuning parameter NCP.

è Observe 2 ≤ NCP < No. of samples.  Recommended NCP value = 30.

 

For NL-QUAD/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

 

N-CENTRIX 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 far-off design) this would mean that the MU/MU* range of the training dataset could be more or less extended, subsequently the prediction range too.

 

N-CENTRIX 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, NL-QUAD/R, and NL-CUBIC/A), an artificial neural network is integrated into N-CENTRIX 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 (pre-selected 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 re-configured 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 Back-Propagation

-          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           : Mini-Batch 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 Back-Propagation updating

             1 -> Manhattan updating

             2 -> Langevin updating

             3 -> Quickprop

             4 -> Conjugate Gradient - Polak-Ribiere

             5 -> Conjugate Gradient - Hestenes-Stiefel

             6 -> Conjugate Gradient - Fletcher-Reeves

             7 -> Conjugate Gradient - Shanno

             10 -> Scaled Conjugate Gradient - Polak-Ribiere

             11 -> Scaled Conjugate Gradient - Hestenes-Stiefel

             12 -> Scaled Conjugate Gradient - Fletcher-Reeves

             13 -> Scaled Conjugate Gradient - Shanno

             15 -> Resilient Back-Propagation

 

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 (back-transform).

 

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 over-fitting.

 

 

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 ETAPDGD, TAUDGD, 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

 

References

 

[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 Turbo-machinery 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

 

APPENDIX-A

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.

APPENDIX-B

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:

§  3-Point (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 *( FLOWCONTROL LINE – FLOWSURGE)   / FLOWCONTROL 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

 

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