Demystifying S1-S2 Optimization in Turbomachinery

  1. Historically turbomachinery development began with empirical rules postulated by early pioneers. With the need for jet engine for aircraft propulsion, dimensionless analysis became popular, followed by the 1 D mean line design and 2D meridional methods. Today 2D meridional methods with 3D blade to blade CFD/FEA methods are a necessity as efficiency and reliability requirements are further pushed.

 

  1. One key aspect of 2D meridional design is S1-S2 optimization, which is a time consuming, laborious task and hence subject to human errors. S1-S2 optimization is a task of reviewing, adjusting and optimizing the flow path in the Tangential (S1 or blade-to-blade or pitchwise) and the Meridional (S2 or span wise) planes. The main purpose is to:
  • Fit the flow path to specific meridional dimensional constraints
  • Adjust blade-to-blade parameters while taking into account structural constraints.

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The Optimization Challenge in the Development of Turbomachinery

Optimization (or parametric studies) of a twin spool bypass turbofan engine with mixed exhaust and a cooled turbine can be considered one of the most complex problem formulations. For engine selection, determining the thrust specific fuel consumption and specific thrust is necessary against variables such as design limitations (Inlet temp, etc.), design choices (fan pressure ration, etc.) and operating conditions (speed & altitude). The task involves cycle level studies following machine, module, stage and component level optimization. This calls for an integrated environment (IE) and it is desirable to have such an IE operating on a “single” platform.

Historically IE was developed for the design of axial turbines (mainly steam). Later, it was expanded for gas turbines (especially blade cooling calculations) and axial compressors via plug-in modules. The new challenge designers face today is developing mixed flow machinery. An effective system for modern turbomachinery design needs to do the following:

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Rerates, Upgrades, and Modifications to Steam Turbine

Steam Turbine DesignSteam turbines are designed to have long, useful lives of 20 to 50 years. Often, many parts of steam turbine are custom designed for each particular application, however, standardized components are also used. It is therefore inherently possible to effectively redesign a steam turbine several times during its useful life while keeping the basic structure (foot print, bearing span , casing etc) of these turbines unchanged! Indeed this is also true for many turbomachines. These redesigns are usually referred to as rerates and upgrades, depending on the reasons for doing them. The need for changes to hardware in an existing turbine may be required for (a) efficiency upgrades, (b) reliability upgrade (including life extension), (c) rerating due to a change in process (Process HMDB, use in combined cycle etc), and (d) modification for a use different from that of its original design. Typical changes include hardware components such as buckets/blades, control system,  thrust bearing , journal bearing , brush and laby seals, nozzle/diaphragm , casing modification,  exhaust end condensing bucket valves, tip seals and coatings.

Performance and Efficiency Upgrade The basic power and/or speed requirements of a steam turbine may change after commissioning for various reasons. The most common reason is an increase (or decrease) in the power required by the driven machine due to a plant expansion or de-bottlenecking. Other reasons include a search for increased efficiency, a change in the plant steam balance, or a change in steam pressure or temperature. Because steam turbines are periodically refurbished, an opportunity exists to update the design for the current operating environment. Turbine OEM’s , services companies and end users often face a challenge of undertaking engineering work within the very tight  time frame available for maintenance.  The AxSTREAM® software suite provides users with an automated capability of rerate, upgrade and modifications for performance and efficiency objectives. A summary of such features highlighting the capabilities is presented below:

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Thermo-Physical Properties of Fluids for Simulation of Turbomachinery

Computer simulation and use of CAE/CAD are well-established tools used to understand the critical aspects of energetics (various losses), kinematics (velocities, mach no. etc.) and thermodynamics (pressures, temperatures, enthalpy etc) in thermodynamic cycles and turbomachinery. Computational models are now enabling the design and manufacture of machines that are more economical, have higher efficiency and are more reliable. Accuracy of complex processes that are simulated depends on thermos-physical properties of the working fluid used as input data. The importance of such properties was recognized when it became evident that a steam turbine cycle can have efficiency variance by a few percentage points depending on the chosen set of fluid properties.

Today the thermo-physical properties data is represented in the form of a set of combined theoretical and empirical predictive algorithms that rest on evaluated data. These techniques have been tested and incorporated into interactive computer programs that generate a large variety of properties based upon the specified composition and the appropriate state variables. Equations of state, correlations, or empirical models are used to calculate thermos-physical properties of fluids or mixtures. Examples of this include Helmholtz energy based equations, cubic equation of state, BWR pressure explicit equations, corresponding states models, transport models, vapor pressure correlations, spline interpolations, estimation models or calculation methods for vapor-liquid equilibrium or solubility, and surface tension correlations. Further fitting techniques, and group contribution methods are incorporated. The following broad level properties are often used in simulation tools:

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Turbomachinery Software for Education

Turbomachinery design has significantly evolved over the last two decades, as supporting education and training methods and techniques remains a challenge. Diversity of technologies covered in the varying courses and extensive use of software by industry designers makes the task of delivering the course curriculum that meets expectations of industry and students difficult. Many educational institutes and business use generic CAE tools for the purpose of learning turbomachinery through student projects. While generic tools have proven their value in research and design, the comprehensiveness of these tools to tackle real life turbomachinery situations is far from desired. The inexperience of fresh graduates from universities and colleges in their inability to perceive a 4D machinAxSTREAM EDUe (3D plus time), traditionally taught using a 2D blackboard, is evident. A student is not only required to have a very good understanding of underlying fundamentals, but is also required to address multitude of design, analysis and optimization problems within the limited time available for education. Coupling of theoretical and computer aided design knowledge to augment the capability of students to contribute to the industrial endeavor is necessary. Such a solution provides students with implicit understanding of the level of detail required by final designs, such as mean line design to the specification of a blade profile varying from hub to tip of a blade, and further complexities of iteration due to an aerodynamically correct blade profile being unsuitable because of stress levels or excitation frequencies and much more. AxSTREAM® EDU introduces multiple dimensions of design required by turbomachinery very early in the instruction process which, by using,  the students are able to develop insights that traditionally are difficult to attain in the same time frame. The use of AxSTREAM® EDU as a design software has been proven to multiply the skills of the students, enabling broad 3-D design considerations and visualization seldom possible otherwise.

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Expander Configurations and Torsional Analysis

Lateral rotor-dynamic behavior is often discussed as one the critical aspects in determining the reliability and operability of rotating equipment. However, as multiple equipment are coupled together to form trains for centrifugal pumps, fans/blowers, compressors, steam or gas turbines and motors or generators, torsional behavior requires a thorough analysis. As per industry standards, torsional response is sought only for train units comprising of three or more coupled machines (excluding any gears).Blog 6

The configurations of the expanders used in the oil and gas industry makes it not only ideal but mandatory to perform train torsional analysis.  Expander trains are commonly used in CCU and FCU units and in the production of nitric acid. Serving the purpose of energy recovery, various arrangement for power recovery train are illustrated to the left:

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Performance Simulation and Optimization of CCPP with Turbine Inlet Air Cooling

It is well established that the performance of combustion air turbines (gas turbines) is sensitive to ambient air temperature. As the ambient air temperature increases beyond standard design point  (ISASLS), the power output and exhaust gas flow rate reduces while the heat rate and exhaust gas temperature increases. While the trends are similar for heavy duty and aeroderivative gas turbines, due to the inherent nature of design the results are steeper for aeroderivatives.  Various types of turbine inlet cooling technologies such as evaporative cooling, refrigerated inlet cooling and thermal energy storage systems have been practiced with varying degree of success, each having its potential advantages and limitations.  Simplicity and cost advantage gained in evaporative cooling is offset by limitation of cooling along web bulb depression line (and is a function of site relative humidity). Refrigerated inlet cooling (direct and indirect) offer advantage of higher cooling and lesser sensitivity to site conditions, and result in greater power output with an impact on relative cost and complexity. Selection of optimum technology of turbine air inlet cooling is hence a tradeoff between competing factors.

Combined Cycle
Combined Cycle Power Plant

The complexity of combined cycles, without any turbine inlet air cooling, poses significant challenge in design of steam system and HRSG due to competing factors such as pinch point, heat and mass flows optimization etc. Knowledge of fluid viz properties of standard air (psychrometrics), standard gas for Joule Brayton cycle, steam for bottoming Rankine cycle and refrigerant for cooling system( for refrigerated inlet air cooling) as applied to complete cycle makes the process complete as well as complex. AxCYCLE™ is one such unique tool to simulate such combined cycle processes with multi fluid-multi phase flows including refrigeration. The standard HVAC features can easily be used for inlet air cooling refrigeration and integrated into the CCPP. Once a digital representation of the complex process is replicated and successfully ‘converged’ at design point, the challenge of optimization emerges. To facilitate optimization various tools namely AxCYCLE™ Map, Quest, Plan and Case are embedded integrally. As a first cut, users based on their experience apply AxCYCLE™ Map and vary one or two parameters to see the effect of operational parameters on cycle performance. AxCYCLE™ Quest opens the gates by allowing users to vary unlimited parameters, according to quasi-random Sobol sequences. mutli-Parameter optimization tasks are possible using AxCYCLE™ Plan – it uses design of experiments concepts. Once optimized the AxCYCLE™ Case tools allows off design simulation tasks. Exhibit below represents complexity of a combined cycle plant represented conveniently:

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