SSCAR - Steady State Cycle AnalyseR
SSCAR - Steady State Cycle AnalyseRMechanical Engineering Technical Report 2017/8Ingo Jahn (i.jahn@uq.edu.au)School of Mechanical and Mining EngineeringThe University of Queensland.With Contributions from: Samuel Roubin, Joshua KeepMay 23, 2017AbstractThis report describes the Steady-State Cycle AnalyseR (SCCAR), a solution enginethat enables the steady state evaluation of thermodynamical cycles. SCCAR can be usedto parametrically define thermodynamic cycles using a library of predefined building blocks,such as compressors, turbines, heat exchangers, and other user defined components. Steadystate performance of a cycle is evaluated such that energy, mass flow rate and thermodynamicproperties around the cycle are balanced.To allow accurate off-design analysis the component library in SCCAR includes components that incorporate accurate physics or map based performance characteristics. Usingthese characteristics allows the accurate analysis of changes in the operating point andoverall efficiency as external parameters are altered.This reports summarises the underlying theory and modelling approach for the tool andalso describes the theory that is implemented for the different building blocks. This isfollowed by a example section illustrating the usage of the code by analysing a number ofvalidations cases.1
Contents1 Introduction1.1 Compatibility . . . . . .1.2 Citing this tool . . . . .1.3 Distribution . . . . . . .1.4 Installation . . . . . . .1.5 Modifying the code . . .1.6 Structure of this report.44555562 Main solver2.1 Defining a problem2.2 Running the Code2.3 Results . . . . . . .2.4 Solution process .777810.3 Building Blocks3.1 GDATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2 MASS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3 POINT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.4 COMPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.5 HX - Source / Sink heat exchanger . . . . . . . . . . . . . . . . . . . . . . . . . .3.6 RECUP - Block for co and counter flow heat exchangers . . . . . . . . . . . . . .3.7 RECUP HALF - Block for co and counter flow heat exchangers connected to fixedconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.8 COMP MASSF - Compressor maintaining target mass flow . . . . . . . . . . . .3.9 COMP - Compressor operating from a compressor map . . . . . . . . . . . . . .3.10 TURB ER - Turbine maintaining target expansion ratio . . . . . . . . . . . . . .3.11 TURB - Turbine operating from a turbine map . . . . . . . . . . . . . . . . . . .3.12 MERGE - Flow merge 2 streams 1 stream . . . . . . . . . . . . . . . . . . . .3.13 PIPE - Pipe section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.14 New Custom Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.15 Parameter Settings - Generic . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.15.1 Heat exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121212131617184 Debugging Hints4.1 Incorrect number of equations and unknowns . . . . . . . . . . . . . . . . . . . .4.2 Crashing of CoolProp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.3 Solution diverges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .323232325 Examples and Validation5.1 Recuperated sCO2 Brayton cycle - fixed mass flow and expansion ratio . . . . . .5.2 Recuperated sCO2 Brayton cycle - compressor and turbine maps . . . . . . . . .5.3 Recuperated sCO2 Brayton recompression cycle . . . . . . . . . . . . . . . . . . .343537396 References41218192023242728293030
7 Appendix7.1 Example sCO2 Compressor map7.2 Example sCO2 Turbine map . . .7.3 Non-linear Solver . . . . . . . . .7.3.1 scipy.optimize.fsolve . . .3.4242424343
1IntroductionOne of the most important tools during the preliminary design stages is an efficient way tosimulate the overall system performance. For example during the design of a gas turbine, usinga tool that accurately models the thermodynamic cycle can be used to evaluate different designchoices (e.g. 2 spool or 3 spool design) and different operating points (e.g. pressures ratiosor combustor temperatures). Using such tools provides an efficient way to compare differentdesign concepts, to perform preliminary design optimisations, and to define trade-off costs forsubsequent detailed design. Furthermore, it is desirable to have a tool that can accuratelycapture changes in operation as the operation moves from the nominal design point to off-designconditions. To meet these requirements the tool needs to be easily adaptable (meaning that it iseasy to prototype different systems), the models must correctly capture physical constraints, andthe tool must be able to accurately capture how component performance changes as conditionschange.To address these requirements the Steady-State Cycle AnalyseR (SCCAR) solver has beendeveloped. It provides the ability to quickly construct open and closed loop cycles from a libraryof standard components. In addition by using component models that can include performancemaps, it is possible to analyse how a given system, meaning a system of a given size and a givenset of components responds to changes in the external conditions.By using different components from the components library SCCAR can be operated in twomodes.Nominal Here systems components are modelled with a single performance parameter (e.g.efficiency or pressure ratio or outlet temperature). This allows a quick analysis of differentsystem configurations. The outcome from such a study is the theoretical performance atthe nominal design point and parameters such as heat fluxes and power outputs can beused for sizing of the components.Off-design Here system components are modelled with physics based analytical (or numerical)models that take account for component dimensions, component performance, and externalconditions. For example a turbine, which previously had a fixed expansion ratio and isentropic efficiency, now uses a model that calculates these parameters based on inlet pressure,inlet temperature, mass flow rate, and rotational speed. This ensures the performance ofthe cycle at off-design conditions are accurately modelled.The advantages of using SCCAR for system analysis are: Cycle is defined using multiple blocks, allowing fast system prototyping. A library of most common system components with associated performance maps. Usage of physics based models or maps to analyse component performance. Using these,rather than design point parameters allows accurate off-design performance predictions. Open-source. With the code written in python, this allows the easy modificiation, creation,and integration of component models.This report describes the theory on which SCARR is based, provides detailed descriptions onthe already mplemented components, and provides a summary of examples that can be used asa starting point for further analysis.1.1CompatibilityCycle.py is written in python. The following packages are required:4
python 2.7 - any standard distribution numpy scipy version 0.18.0 or above CoolProp available from http://www.coolprop.org/ matplotlib version 2.0.0 or above1.2Citing this toolWhen using the tool in simulations that lead to published works, it is requested that the followingworks are cited: Jahn, I. (2017), SSCAR - Steady State Cycle AnalyseR, Mechanical Engineering TechnicalReport 2017/8, The University of Queensland, Australia1.3DistributionCycle.py is distributed as part of the code collection maintained by the Turbomachinery andPower Conversion Group at the University of Queensland. This collection is free software: youcan redistribute it and/or modify it under the terms of the GNU General Public License aspublished by the Free Software Foundation, either version 3 of the License, or any later version.This program collection is distributed in the hope that it will be useful, but WITHOUT ANYWARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FORA PARTICULAR PURPOSE. See the GNU General Public License for more details http://www.gnu.org/licenses/.Please contact the authors for access to the code repository.1.4InstallationThe code is designed to be run from the command line. The job.py file defining the currentsimulation can be stored in a local directory. The main code file Cycle.py and any code usedfor the building blocks (e.g. turb funct.py, comp funct.py, HX solver.py, .) stored in the /src directory should be added to a folder that is on your python search path. The installation folder can be added to the search path by adding the following lines to the .bashrc file (orequivalent on non-Linux platforms).export CYC {HOME}/path/to/loc/direxport PYTHONPATH {PYTHONPATH}:{CYC}export PATH {PATH}: {CYC}After editing run: source ./bashrcIf installing the complete geotherm repository, the above references should point to the/geotherm/geobin directory.1.5Modifying the codeThe working version of Cycle.py and other supporting programs are installed in the /srcdirectory of the repository. If you perform modifications or improvements to the code please5
submit an updated version together with a short description of the changes to the authors. Oncereviewed, the changes may be included in future versions of the code.1.6Structure of this reportThis report is divided into the following sections:1. Introduction (current part) (page 4)2. Description of main solver setup and solution process (page 7)3. Theory description of implemented building blocks (page 12)4. Debugging Hints - What to do if I can’t get a solution.5. Examples - illustration of code for a range of simple validations cases (page 34)6. References7. Appendix6
2Main solver2.1Defining a problemTo illustrate the software we will explore two simple examples showing how cycles can be analysed.The first example shown in Fig. 1a is a standard closed loop Brayton cycle. For this cycle theoperating efficiencies of the compressor and turbine are defined and this cycle will be solved fora mass flow rate of 10 kg/s with a turbine pressure ratio of 2.2. The second cycle is a closed looprecuperated Brayton cycle (see Fig. 1b). Here, instead of enforcing a fixed isentropic efficiencyfor both the compressor and turbine, respective performance maps are used. The result of thismore complex modeling approach is that the efficiencies of the components and the pressure ratioacross the turbine are now functions of the cycle mass flow rate, which in turn is controlled bythe turbine speeds. Effectively if we want to increase the cycle mass flow rate, we can achievethis by increasing the turbine speed. However a consequence of the increased mass flow rate willbe changes to the turbine pressure ratio, which is a function of turbine mass flow rate. Thisin turn will influence other components in the cycle. Using maps to calculate the compressorand turbine performance allows a more realistic analysis of the cycle operation and performance.Thus the results obtained can be used to generate new insight towards the analysis of complexclosed loop cycles.For both the cycles in Fig. 1 supercritical CO2 has been selected as the working fluid andsource and sink temperatures have been fixed at 800 K and 305 K respectively.(a) Simple Brayton cycle(b) Recuperated Brayton cycleFigure 1: Schematic for two simple cycles.Input files for a selection of examples are available in section 5, and a ever increasing list ofexamples is available in the repository. Details about the MASS and POINT class used to definemass flow rates and the connecting nodes can be found in section 3.2 on page 12 and section 3.3on page 13. The different COMPONENTS that are available for cycle construction are defined insection 3 on page 12.2.2Running the CodeOnce the a job.py file has been created, which defines the components of the problem, the maincode is called to find the conditions (Pressure & Temperature & Mass Flow Rate) at all of theinterface points that result in a valid steady state operating point. The general run procedurefor the code is:1. Modify an existing job file to set simulation conditions (e.g. Job.py)Within this file the following is defined:gdata: This sets the simulation parameters.7
MASS: These are mass flow streams through the loop components. These are used toenforce continuity.POINTS: Nodes to which the component are connected. Multiple components can beconnected when the flow splits, however merges need to be modelled by specific components.COMPONENTS: Routines that describe the building blocks. These compute how theconditions (Pressure & Temperature) change across a building block as a function ofbuilding block specific parameters and cycle mass flow rate.2. Run using the command: Cycle.py --job Job.pyThe following options are available --help to show usage, --ts-diagram, to plot the results on atemperature-entropy diagram, --out-file outfile.txt, which writes the results to an outputfile, --noplot to suppress generation of graphs, and --verbosity 0 which can be used to seton-screen outputs (0 no output, 1 some outputs, 2 many outputs).2.3ResultsA successful run without any optional settings will return the following: on-screen output summarising the key performance parameters; plots showing pressure and temperature at all points; and components specific plots showing respective operating data.For the simple Brayton cycle from above the following on-screen output would be obtained: RESULTS :3 Mass f l o w r a t e: 1 0 . 9 8 ( kg / s )4 Pressures: [7687000.0 , 13838290.71398304 , 13838290.71398304 ,7687000.000000001]( Pa )5 Temperature: [ 305.322.79955619800.740.77698615]6 P r e s s u r e R a t i o (Pmax/Pmin ) : 1 . 8 0 0 2 1 9 9 4 4 6 77 Working F l u i d: CO28 Inventory: 1.18392256216( kg )9 message: The s o l u t i o n c o n v e r g e d .10 1211 CYCLE DATA14 Mass f l o w r a t e ( kg / s ) : 1 0 . 9 815 Turbine E f f i c i e n c i e s:16 TURBe t a : 7 5 . 7 5 (%)17 Compressor E f f i c i e n c i e s:18 COMPe t a : 6 7 . 0 0 (%)19 Q in(kW) : 7 6 0 5 . 6 220 Q out(kW) : 7 0 5 0 . 2 421 Q net( in ) (kW) : 5 5 5 . 3 822 W turb ( out ) (kW) : 7 1 0 . 1 023 W comp ( in ) (kW) : 1 5 4 . 7 2( out ) (kW) : 5 5 5 . 3 824 W net25 C y c l e e t a W net/ Q in :7 . 3 0 (%)26 Carnot e t a (1 T c /T h ): 6 1 . 8 8 (%)12138(K)
(a) Conditions at Points(b) Temperature - entropy diagramFigure 2: Results for simple Brayton cycle.27 28 POINT DATA31 p1 P ( avg ) (MPa) : 7 . 6 8 7 0T ( avg ) (K) : 3 0 5 . 0 0) : 1.3432 p2 P ( avg ) (MPa) : 1 3 . 8 3 8 3T ( avg ) (K) : 3 2 2 . 8 0K) : 1 . 3 633 p3 P ( avg ) (MPa) : 1 3 . 8 3 8 3T ( avg ) (K) : 8 0 0 . 0 0/K) : 2 . 7 834 p4 P ( avg ) (MPa) : 7 . 6 8 7 0T ( avg ) (K) : 7 4 0 . 7 8) : 2.8135 2930h ( kJ / kg ) : 3 0 4 . 7 5h ( kJ / kg ) : 3 1 8 . 8 4h ( kJ / kg ) : 1 0 1 1 . 5 1h ( kJ / kg ) : 9 4 6 . 8 4s ( kJ / kg /Ks ( kJ / kg /s ( kJ / kgs ( kJ / kg /K36 SIMULATION ASSESSMENT39 Energy Miss b a l a n c e (kW) : 0.0040 Energy Miss b a l a n c e ( f r a c t i o no f Q in ) : 0 . 0 0 (%)41 3738This will be accompanied by Fig. 2, which shows the pressure and temperature at the pointsp1 to p4. The correct convergence of the code can be assessed from the pressure and temperateplots shown in Fig. 2a. For a converged solution the respective lines for two components meetexactly at the interfacing point. If the points do not overlap exactly, this indicates that thesolution has not converged. A further indication of solution accuracy is available from the onscreen outputs under the SIMULATION ASSESSMENT heading. Here the energy miss-balance andmiss-balance fraction are calculated as: EErrorf rac Qnet Wnet E Qin(1)(2)For a converged solution both approach zero.In addition, by evoking the --ts-diagram option the cycle is also plotted on a TemperatureEntropy diagram as shown in Fig. 2b.9
(a) Conditions at Points(b) Temperature - entropy diagram(c) Compressor operating point(d) Turbine operating pointFigure 3: Results for recuperated Brayton cycle.The results from analysing the recuperated Brayton cycle using component maps are shownin Fig. 3. In addition to the pressure and temperature plots and the t-s diagram showing thecycle the output also includes the respective compressor and turbine maps. These highlight theposition of the operating point on the respective maps or performance curves. By altering settingsdefining the compressor and turbine operation, such as the respective speed, the performance ofthe overall cycle can be altered.2.4Solution processSolving thermodynamic systems such as the ones discussed above allow multiple approaches. Toensure SCARR is scalable and flexible with respect to different component models, an optimisation approach, which separates the component models and the part that solves the conservationequations for the system has been selected. Effectively the optimiser treats each component asa black box and the goal for the optimiser is to find a combination of output parameters (massflow rates, pressures and temperatures) that results in balanced conservation equations.Rather than solving the conservation equations directly the optimisation problem has beenposed as one where pressure, temperatures and mass flow rates at each point in the system arematched. Or to phrase it differently, if the outlet conditions from the upstream component(s)match with the inlet conditions of the downstream components at each point in the system avalid solution has been attained. This can be phrased as the following non-linear optimisation10
problem2min (A X Y ) ,X RwhereY F(X)(3)Here F contains the non-linear functions relating the downstream conditions for each componentto the respective upstream conditions, and A is a matrix defining the constraints.The resulting problem can be solved efficiently using any non-linear optimiser. Present optionsfor the code are described in the following section.11
3Building BlocksThis section describes all the building blocks that can be used to construct systems and theunderlying theory used for the solution process.3.1GDATAThe GDATA class stores general simulation specific data. The default settings of gdata should beadjusted in job.py to adjust for the current simulation.123456c l a s s GDATA:definit( self ) :s e l f . i t e r 0 # i n t e g e r t o s e t number o f i t e r a t i o n s f o r f s o l v es e l f . name ’ ’ # s e t name o f s i m u l a t i o n .s e l f . p r i n t f l a g 0 # a d j u s t how much d a t a w i l l be d i s p l a y e d t o t h e s c r e e ns e l f . optim ‘ r o o t : hyb r ’ # s e l e c t o p t i m i s e r t h a t w i l l be usedThe following settings are available.iter : Sets the number of iterations that will be completed using the non-linear solver. 0 simulation until convergence criteria is met.name : Set name of simulationprint flag : Define how much data will be printed to the screen.0 no outputs.1 (default) on screen summary of results.2 extensive outputs for debugging.optim : Select the
The rst example shown in Fig. 1a is a standard closed loop Brayton cycle. For this cycle the operating e ciencies of the compressor and turbine are de ned and this cycle will be solved for a mass ow rate of 10kg/s with a turbine pressure ratio of 2:2. The second cycle is a closed loop recuperated Brayton cycle (see Fig. 1b).
E.SSENTIAL TESTING EQU! YJMEYTS REQUIRED FOR QUALITY ASSURANCE DC Power Supply I' Power Source (0 V to -100 V DC) Precision nigital Multimeter CRO (500 MHz Digital phosphor oscilloscope ar Digital st orag'e osci ilascope) Digital hrfillion Meg- Ohm meter Breakdown Tester Rheostat PCM Channel Analyser or Primary Digital MuItiplexer Analyser Digital Transmission Analyser or SDHlPDH /ATM Analyser
Fiche-professeur n 4 : Comprendre un dialogue du film 17 Fiche-élève n 5 : Analyser les lieux du film 18 Fiche-professeur n 5 : Analyser les lieux du film 19 III. ANALYSE D‘UNE SÉQUENCE 20 Fiche-élève n 6 : Analyser une séquence du film 20 Fiche-professeur n 6 : Analyser une séquence du film 21 IV. ANNEXES 22
bf1systems Mini Analyser User Guide bf1systems TPMS Mini Analyser User Guide - V3_08.docx 3.08 Page 6 of 33 RD096 071112 2 Permit List Upload Before the Mini Analyser can be used it is a requirement that a permit list be loaded into the unit.
The STI-CIS Analyser (Figure 3) comes equipped with its own microphone and LED display and has buttons to activate dB(A) and CIS1 measurements. There is provision for a PC interface (RS-232) for use with the STI-CIS Noise Effect Correction Software Tool. Introduction STI-CIS Analyser Description Figure 3. STI-CIS DSP2 Analyser Equipment Description
testo 320 Flue Gas Analyser Advanced Set Part No. 0563 3220 78 testo 320 Flue gas analyser with O2 & CO sensor and Bluetooth, International mains unit, Basic flue gas probe (180 mm, Ø 6 mm), Differential Pressure Set, Differential Temperature Set and hard carry case testo 320 Flue Gas Analyser Advanced Set with Printer Part No. 0563 3220 79
Steady State - Normal Operation SAE J1455, Sec 4.11.1 Steady State - Reverse Polarity -24V SAE J1455, Sec 4.11.1 Steady State - Jump Start 24V SAE J1455, Sec 4.11.1 Steady State - Cold Cranking 0 -6 V SAE J1455, Sec 4.11.1 Steady State - Series Charging 48V SAE J1455, Sec 4.11.1 Transients: Load Dump SAE J1455, Sec 4.11.2
steady state response, that is (6.1) The transient response is present in the short period of time immediately after the system is turned on. If the system is asymptotically stable, the transient response disappears, which theoretically can be recorded as "! (6.2) However, if the system is unstable, the transient response will increase veryFile Size: 306KBPage Count: 29Explore furtherSteady State vs. Transient State in System Design and .resources.pcb.cadence.comTransient and Steady State Response in a Control System .www.electrical4u.comConcept of Transient State and Steady State - Electrical .electricalbaba.comChapter 5 Transient Analysis - CAUcau.ac.krTransient Response First and Second Order System .electricalacademia.comRecommended to you b
ASTM C 1702 external mixing Sample 1 Sample 2 Not tested Cement, g 9.81 3.38 Water, g 4.90 1.69 Sand reference, g 37.37 12.61 Test duration, h 168 168 3. Results and Discussion 3.1 Signal to noise Figure 1 shows the heat flow measured from the sample cell charged with sand that displayed the highest overall heat flow. This was taken as a measure of noise for the purpose of this study. Figure 1 .
