The Economics of Power Generation

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Implementation feasibility of power plant design relies heavily on the economic benefits. More often than not, newer technology cannot be implemented due to high cost of electric generation which would not be acceptable in the market since energy is a price sensitive commodity. Sometimes while deciding on a design to choose, we are given a choice between a high initial equipment cost and efficiency versus a lower capital cost with lower efficiency. The designer must be able to choose which design would fit best with their needs and goals.

While running a power generation plant, there are three types of cost that need to be taken into consideration: capital cost, operational cost and financing cost. With point one and two to being of higher priority.

Capital cost generally covers the cost of land, construction, equipment and so on. In other words, capital cost includes all costs in the initial phase of building the plant itself. Capital costs varies from time to time, and from one location to another. Largely, it is a function of labor costs, material costs and regulatory cost –which all is dependent on investment time and the availability of resources as well as the administrative regulation that governs the area. For example, building a power plant in an engineering hot spot like Texas would be much easier then it would be in a residential area such as near a neighborhood in California due to environmental laws as well as construction regulations. Consequently, the time needed to build a plant of the same size in both cases could be significantly different, thus making a noticeable gap in the capital cost. In common practices, capital costs are not necessarily paid in advance as cash, rather sometimes in debt and equity. This fact brings us to financing cost, which would be the cost of paying off the capital expenditure for a period of time.

In practice power plants take into consideration three main things while calculating for operating cost: fuel, labor and maintenance. With that being said, there are many other aspects to consider that could vary based on each individual designs. Operational cost usually varies with the capacity of the plant or with plant operations. In most cases, fuel cost dominates the marginal cost of a conservative power plant, say fossil-fuel, whereas newer technology such as biomass or geothermal, the cost of fuel is generally “free” though higher capital cost. The trade-off between operating and capital cost investment should be taken into consideration while designing a power plant.

For more information and to calculate your power plant costs, check out AxCYCLE Economics!

Reference:

  1. https://www.e-education.psu.edu/eme801/node/530

Mesh Generation Characteristics for an Accurate Turbomachinery Design

This post will examine the meshing requirements for an accurate analysis of flow characteristics in terms of turbomachinery applications, based on Marco Stelldinger et al study [1]. Computational Fluid Dynamics (CFD) are widely used for the analysis and the design of turbomachinery blade rows.  A well-established method is the application of semi-unstructured meshes, which uses a combination of structured meshes in the radial direction and unstructured meshes in the axial as well as the tangential direction. Stelldinger’s paper presents a library for turbomachinery meshing, which enables the generation of semi-unstructured meshes for turbomachinery blade passages, including cavities, fillets and varying clearance sizes. The focus lies on the generation of a mesh that represents the real geometry as accurately as possible, while the mesh quality is preserved.

The above was achieved by using two different approaches. The first approach divides the blade passage into four parts. Inside of these parts, a structured grid is generated by solving a system of elliptic partial differential equations. The second approach is based on the domain being split into fourteen blocks. It has benefits concerning computational time towards the first one, because of a faster generation procedure as well as a faster performance of the inverse mapping.

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Figure 1 Mesh View

Another key aspect in mesh generation is the improvement of the mesh quality applying suitable methods. Since mesh smoothing algorithms have been shown to be effective in improving the mesh quality, two smoothing algorithms, a constrained Laplace smoothing and an optimization-based smoothing were presented. Both algorithms showed benefits concerning the achieved mesh quality compared to the standard Laplace smoothing, while the computational time is longer. For the investigated turbomachinery meshes the constrained Laplace smoothing is exposed as the most feasible choice, because of a suitable combination of mesh quality and computational time.

Several methods for the modelling of fillets between blade and the casing were also presented. The methods provide meshes with different qualities, that results into different convergence rates and residuals. Furthermore, the axisymmetric surfaces are dependent on the axial position that enables the modelling of clearances with a variable size. CFD simulations for a variable stator vane with a constant clearance size between blade and inner casing as well as with a variable clearance size were performed. The results show a different flow behavior near the clearance. This emphasizes the requirement of an accurate representation of the real geometry for CFD simulations of turbomachinery flows.

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Figure 2: AxCFD mesh view

The AxCFD module of the AxSTREAM platform allows the user to employ an automatic turbomachinery-specific, structured hexagonal meshing by customization in the setup period. Different types of mesh generation are available and can be refined in each direction. Take some time to use AxSTREAM and enjoy the design process!

A Look into Combined Cycle Power Plants – Problems, Advantages and Applications.

urs Combined Cycle Power Plants are among the most common type of power generation cycle. Demand of CCP application has risen across board due to the rising energy demand (and consumption) as well as growing environmental awareness. Combined cycle is a matured energy that has been proven to generate much lower CO2 (and other environmental footprints) compared to a traditional fossil fuel steam or gas turbine power generation cycle Consequently, this application is often looked as a “better” substitute compared to other a fossil fuel technologies. That being said, CCP is still a temporary alternative to substitute SPP since although CCP generally is more environmentally friendly, CCP process still requires the combustion of fossil fuel (though at a significantly lower degree compared to SPP) for initial heat/energy source.

The application takes two kinds of thermodynamic cycle in assembly to work together from the same heat source. Fluid Air and fuel enters a gas turbine cycle (Joule or Brayton) to generate electricity, waste heat/energy from working fluid will then be extracted then go through a Heat Recovery Steam Generator and towards steam turbine cycle (Rankine) to generate extra electricity. The main advantage of this cycle combination is the improvement of overall net efficiency (around 50-60% higher compared to each cycle alone), thus, lower fuel expenses. With that being said, net efficiency of a CCP is often inflated especially on systems which use a low-temperature waste heat.

There are two configurations of a combined cycle power plant – single-shaft and multi-shaft. The first configuration has one gas turbine and one steam turbine coupled to one generator and one heat recovery steam generator. A multi-shaft has one large steam turbine, condenser and heat sink for up to three gas turbines — each gas turbine and each steam turbine also has its own generator. Each configuration comes with its own advantages and disadvantages, for example single shaft design has a slightly smaller initial cost and smaller footprint whereas multi-shaft is found to be more economical in the long run due to the number of gas turbine to operate in conjunctions. Though overall it’s hard to say which configuration is best to be applied, judgement should be based on needs and consideration of the designer since each wins and losses in different categories.
Design the optimal combined cycle for your application using AxCYCLE!

Reference:
http://arthur.shumwaysmith.com/life/content/the_problems_with_combined_heat_and_power_chp_critique_part_3

Achieving Successful 3-Dimensional Hand Tracking Using Quasi-Random Sequences

With the advent of emerging technologies in the space of human-computer interaction (HCI), a prevalent challenge has been finding methods that can accurately represent these motions in real time.  Applications using RGB-D cameras to track movements for consumer-based systems has already been employed by Microsoft in the space of tracking silhouette movements in video games as well as app navigation in the Microsoft Kinect system.  However, tracking methods must evolve in order to successfully represent the complexity of human hand motion.  The two main categories of 3D hand articulation tracking methods consist of appearance-based and model-based tracking.  Appearance-based tracking methods are efficient in the limited space of comparing the present model to a number of already defined hand configurations.  Model-based tracking methods allow the computational configuration to explore a continuous space in which the hand motions are optimized at a high dimensional space in near real time.

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Figure 1 – 256 Points from a Pseudorandom Number Source (Left) Compared to a Quasi-Random Low-Discrepancy Source (Right)

If the computer tracks the human wrist with six degrees of freedom and the other joints accordingly, the ensuing dimensional analysis occurs at a high dimensional space.  A saddle joint (2 DOF) at the base of the each finger plus the additional hinge joints (1 DOF each) at the middle of the finger describes each finger with four degrees of freedom.  In turn, the problem of tracking the articulation of a single hand is performed in a dimensional space of 27.  This highly dimensional problem formulation requires an optimization technique specific to the problem that can provide a uniform coverage of the sampled space.  Quasi-random sequences are known to exhibit a more uniform coverage of a high dimensional compared to random samples taken from a uniform distribution.  The Sobol sequence, developed by Russian mathematician Ilya Sobol, describes a quasi-random low-discrepancy sequence that more evenly distributes a number of points in a higher dimensional space.  Figure 1 represents the distribution discrepancy between a pseudorandom number generation and a quasi-random low-discrepancy Sobol sequence generation.

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Figure 2 – High Dimensional Design Space with Given Constraints from Preliminary Design Module in AxSTREAM™

Clearly described in the figure, it is possible to visualize how the quasi-random distribution would employ a better system for tracking hand articulations on 27-dimensional space with much fewer missteps. This particular technology will continue to evolve as the steps of the process are improved. The quasi-random sampling presents a candidate solution in the parametric space of hand configurations, and objectively creates iterations for each frame in which these points are captured. Although the commercial application of this technology still seems rather futuristic, the ability to interact with a computer system by using a number of hand gestures has seen massive improvement in the past years. This technology could potentially represent the next big advancement for upcoming interactive computer systems. Aside from the applications displayed in this article, SoftInWay has been using this technology in order to optimize the highly dimensional system seen in the preliminary design of turbomachines. The solution generator in AxSTREAM® uses a quasi-random search algorithm to successfully distribute a high dimensional system characterized by geometry limits, performance bounds, and different flow conditions. To learn more about the preliminary design module for applications in any turbomachinery platform follow the link – http://www.softinway.com/software-functions/preliminary-design/

Reference:

http://www.cv-foundation.org/openaccess/content_cvpr_2014/papers/Oikonomidis_Evolutionary_Quasi-random_Search_2014_CVPR_paper.pdf 

Enhanced Design Capabilities Using CFD

The use of computational fluid dynamics (CFD) in turbomachinery design is getting more and more popular given the increased computational resources. For the design process, however, there is no need for extensive CFD capabilities as the effort is put on minimizing engineering time while obtaining a design which is about 90% optimized. Here we are presenting two cases where CFD is used to derive significant information for pump design.

First, the influence of the blade shape on the parameters of the single blade hydrodynamic pump was studied by Knížat et al [1]. The investigation of the pump properties was carried out experimentally with a support of CFD methods. The accuracy of applied steady-state calculations was satisfactory for the process of design of a single blade pump, because of the good agreement between measured and calculated power curves.

For the CFD the Menter SST (shear stress transport) model of turbulence was chosen. This model effectively combines robustness and accuracy of the k-ω model in regions close to the wall with the model k-ε working better in a free stream away from the wall. These improvements make the SST model more accurate and reliable compared with the standard k-ω model. The CFD calculations served for the estimation of pump power curves. The specific energy, torque and hydraulic efficiency were evaluated for each flow rate.

This studied showed that the position of the best efficiency point is sensitive on the blade shape. Thus, it is necessary to form the blade more carefully than in a case of a classical multi-blade pump. It also follows from the calculations that the pump flow is non-symmetrical and it may cause increased dynamical load of the shaft.

In a second study conducted by Yang et al, a double volute centrifugal pump with relative low efficiency and high vibration was redesigned to improve the efficiency and reduce the unsteady radial forces with the aid of unsteady CFD analysis. The concept of entropy generation rate was proposed to evaluate the magnitude and distribution of the loss generation inside the pump. It was found that the wall frictions, wakes downstream the blade TE, flow separation near hub on pressure surface side, and mixing loss in volute are the four main sources leading to significant entropy generation in baseline pump. In the redesigned model, the entropy generation near the hub on pressure surface side was diminished and the loss in the volute was also reduced, while the loss generated by wall friction was increased with the blade number increasing. In general, the entropy generation rate was a useful technique to identify the loss sources and it is really helpful for the redesign and optimization of pumps. The local Euler head distribution (LEHD) obtained in viscous flow was proposed to evaluate the flow on constant span stream surfaces from the hub to shroud. It was found that Kutta condition was not necessarily satisfied at blade leading edge in viscous flow. A two-step-form LEHD was recommended to suppress flow separation and secondary flow near the hub on pressure side of the blade in a centrifugal impeller. The impeller was redesigned with two-step-form LEHD, and the splitter blades were added to improve hydraulic performance and to reduce unsteady radial forces.

The use of CFD integrated in a streamline engineering platform like AxSTREAM would be a valuable tool for every engineer. Try AxSTREAM and AxCFD to conduct your own research and lead to significant outcomes related to turbomachinery design, analysis and optimization!

 

[1] Impeller design of a single blade hydrodynamic pump, Knížat,B. and Csuka,Z. and Hyriak,M., AIP Conference Proceedings, Volume 1768, 016

[2] Computational fluid dynamics- based pump redesign to improve efficiency and decrease unsteady radial forces. Yan, P., Chu, N., Wu, D., Cao, L., Yang, S., & Wu, P. (2017).  Journal of Fluids Engineering, Transactions of the ASME, 139(1)

Can 1D Tools be Used to Design an HVAC System?

The heating, ventilation, and air-conditioning (HVAC) system is arguably the most complex system that is installed in a house and it is responsible for a substantial amount of the total house energy used. A right-sized HVAC system will provide the desired comfort and will run efficiently. Right-sizing of a HVAC system is the selection of equipment and the designing of the air distribution system to meet the accurate predicted heating and cooling loads of the house. Rightsizing the HVAC system begins with an accurate understanding of the heating and cooling loads on a space, however, a full HVAC design involves more than just the load estimate calculation as this is only the first step of the iterative HVAC design procedure. Heating and cooling loads are dependent on the building location, sighting, and the construction of the house, whereas the equipment selection and the air distribution design are dependent upon the loads and each other.

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Figure 1: A 3D model representing the HVAC          ducting in a building.
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Figure 2: Ducts layout for HVAC

The initial design iteration starts with tools such as AxCYCLE™, the thermodynamic design, analysis and optimization tool offered by SoftInWay Inc., based on which the initial specification for the equipment selection is obtained. Furthermore, it is more important to study the distribution of the air into the building to further refine the design iterations. Figure 1 shows the ducting layout in a typical building. The ducting design is a major activity not only from the point of pressure loss but also to ensure the air flows into the room effectively.

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Figure 3: Design and Analysis of the                            HVAC ducts in AxSTREAM® NET.

Figure 2 shows the ducting layout with the air discharge ports. The branching of the duct and the location of the discharge ports affect the cooling in the room which needs to be analyzed in detail. However, to begin the initial design process, it is more appropriate to use a 1D tool such as AxSTREAM® NET which can be used to model the flow through the duct and estimate the pressure loss and cooling effectiveness based on whether the thermodynamic cycle can be further fine-tuned iteratively before any detailed 2D/3D analysis is performed.

To learn more about how AxSTREAM® NET can be used for HVAC design and analysis, please write to info@softinway.com.

Mixed Flow Pumps

As with any turbomachinery, pump design requires a lot of effort on finding the right blade profile for the specified application. As there is no right or wrong in the process, engineers have to make some general assumptions as a starting point. Generally, we can say that the focus of this task is to minimize losses. It is obvious that the selected blade shape will affect several important hydrodynamic parameters of the pump and especially the position of optimal flow rate and the shape of the overall pump performance curves. In addition to axial and radial pump design in recent years, we also have seen the development of mixed-flow pumps. A mixed flow pump is a centrifugal pump with a mixed flow impeller (also called diagonal impeller), and their application range covers the transition gap between radial flow pumps and axial flow pumps.

Let’s consider a dimensionless coefficient called “specific speed” in order to be able to compare different pumps with various configurations and features. The “specific speed” is obtained as the theoretical rotational speed at which a geometrically-similar impeller would run if it were of such a size as to produce 1 m of head at a 1l/s flow rate. In formulas:
formulawhere ns is the specific speed, n the rotational speed, Q is the volume flow rate, H is total head and g is gravity acceleration.

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Fig1: Picture courtesy of KSB Pumps

The specific speed for mixed flow pumps might go from ns=30  to ns=80  for low-speed mixed flow pumps and can increase between ns of 80 and 160  for higher speed mixed flow pumps, as shown in Fig 1 to the left.

As you can see, Mixed-flow pumps have specifics speeds right in-between radial and axial configurations. For mixed flow pumps we can mainly see two casing configurations. In case of low peed pumps, the most appropriate configuration is the volute casing, which shows big similarities with centrifugal pump designs. However, for higher specific speeds raising above the ns =~130/140  value, we see configurations combining the  mixed flow impeller with a diffuser + tubular casing. This solution is chosen to avoid the unreasonably large volute outlet cross sections that would be required to maintain the flow due to the very low tangential component of the absolute velocity at the impeller outlet.

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Fig2: Picture courtesy of Sulzer Pumps

Mixed-flow pumps with tubular casing are often installed in a vertical arrangement, and can be found in multistage configuration for high flow applications, such as irrigation, urban water supply, thermal power plants etc.

In a nutshell, the advantage of mixed-flow pumps over the “competition” is to be a “jack of all trades”. They combine higher massflow of axial configurations with higher pressure achievable by centrifugal machines.

 

Foundations of Rotordynamics – Part 1

In order to succeed as an engineer focused on rotor dynamics in rotating equipment, it is important to be fully aware of its foundation. The foundations of rotor dynamics consists of two parts, lateral analysis and torsional analysis. For part one of this blog, I will be focusing on lateral analysis and then exploring torsional analysis in part two next week.

Lateral analysis, also referred as critical speed analysis, is the study of when rotational speed meets or exceeds the shaft natural frequency. This is important since not knowing the critical speed can lead to instability, unbalance or even cause unknown forces to alter the functionality of rotating machinery. Since a rotating machinery consists of many components (rotor, bearing, motor, seals, etc), lateral analysis is made up of three categories: undamped critical speed analysis, steady state synchronous analysis (also known as damped unbalance response analysis) and stability analysis.

Influenced by the rotor’s mass and stiffness properties, undamped critical speed analysis is used for the estimation of critical speeds, mode shape characteristics and eigenvalues. Generally, this analysis excludes any damping in the system as well as any unbalance forces. For the estimation of undamped critical speed, an undamped critical speed map is a common tool that can be used. This map generally represents the first four undamped, forward-whirling modes as a total bearing/support stiffness. Calculated using bearing principles stiffness, mode shapes are helpful because they provide an approximate indication of the relative displacements that the shaft undergoes when the rotor operates in the vicinity of the associated critical speeds.

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Figure 1: Example of critical speed calculation on front bearing using AxSTREAM RotorDynamics

Next, unbalance response analysis takes into consideration all damping effects. There are three requirements needed to satisfy unbalance performance: separation between critical speeds and operational speeds, operational speed should not be exceeded, and no rubbing should occurs when the rotor’s balance stage degrades to the probe vibration limit. Performing this analysis confirms whether or not these requirements have been achieved. It is a good idea to keep your API requirements handy when evaluating this analysis for reference.

Latestly, stability analysis calculates damped eigenvalues, and also takes into consideration oil whirl and shaft whip to avoid self-exited instabilities. It is known, that if the damping exponent of an eigenvalue is negative, then stable rotor vibrations occur, and if positive, the oppsite effect will occur. Understanding these categories relating back to lateral analysis as a whole, will allow the respective engineer, to design and analyze a stable and reliable rotating machinery.

Check in for next week’s blog post – Foundations of Rotor Dynamics: Part 2  and check out AxSTREAM RotorDynamics or SoftInWay’s upcoming webinar on rotordynamics!

Introduction to your Supercritical CO2 Power Cycle

Supercritical carbon dioxide cycles have slowly become more popular in the engineering market for electricity generation from various sources. SCO2 is found to be an ideal working fluid for generating power cycles due to its high efficiency –more than supercritical or superheated steam, which results in lower cost of electricity.

Supercritical carbon dioxide is a fluid state where carbon dioxide is operated above its critical point which causes the compound to behave as both a gas and a liquid simultaneously with the unique ability to flow as a gas though at the same time dissolve materials like a liquid. SCO2 changes density over small difference in temperature or pressure, though stay in the same phase; allowing large amount of energy to be extracted at higher temperatures.
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This cycle works in a similar manner to other power generation cycles, and is potentially applicable to wide variety of power generation applications. Hypothetically speaking, any cycle that is running with steam as the working fluid should be able to be upgraded to SCO2 application. In an example for applications using fossil fuel as a main heat source, cycle could be designed as an indirectly-heated non-condensing closed-loop Brayton cycle or directly fired SCO2. In the first event, CO2 is heated non-directly through a heat exchanger. After that, the hot CO2 flow expands in the turbine where the mechanical energy is extracted and any remaining heat is extracted in the recuperator to preheat the CO2 going back to the inlet loop, resulting to high efficiency systems. Where for second arrangement, fossil fuel is directly combusted with oxygen, resulting to steam/CO2 mixture to drive the turbine and generate electricity. The remaining heat in the fluid mixture will be recuperated to preheat the CO2 that is used as the combustion diluent.

There are many benefits that come with SCO2 power conversion technology when compared to other power cycles such as higher efficiency (which correspondent to higher productivity with the same thermal input), environmentally friendly/low greenhouse gas emission, and lower capital cost from reduced size compared to a conventional steam cycle.

Want to optimize your SCO2 cycle? Check out our simulation technology AxCYCLE

References:

http://energy.sandia.gov/energy/renewable-energy/supercritical-co2/
http://breakingenergy.com/2014/11/24/supercritical-carbon-dioxide-power-cycles-starting-to-hit-the-market/
https://www.netl.doe.gov/research/coal/energy-systems/turbines/supercritical-co2-power-cycles
http://www.swri.org/4org/d18/sco2/papers2014/systemConcepts/06-Moroz.pdf

Design Challenges of Boiler Feed Pump Turbines in Thermal Power Stations

 The design of a boiler feed pump turbine features some unique characteristics that presents certain challenges in terms of efficiency management, varying operating ranges, and many other features.  In order better understand the accepted designs of Boiler Feed Pump Turbines (BFPTs), it is important to know how the operation of steam turbines used to drive boiler feed pumps can fundamentally improve fossil and nuclear plants.  Much like the design of mechanical drive turbines, feed pump turbines also feature the same thermodynamic objectives as the main turbine and all of the engineering difficulties with optimal blade design, rotor and bearing harmonic conditions, ideal flow path definitions, and so on.  However, some distinctions can make a BFPT design particularly distinct from a regular mechanical drive turbine.  Figure 1 shows a basic heat balance diagram for a plant using a boiler feed pump turbine arrangement.

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Figure 1 – Simple Process Diagram for Plant with Boiler Feed Pump Turbine in AxCYCLE®

Inherent in its name, the BFPT must be fully compatible with the boiler feed pump. In other words, the necessary power and speed of the BFPT are determined by the requirements of the pump. In a fully integrated and dynamic system such as this, a large portion of the design requires developing a proper heat balance that will optimize the plant performance. In general, the boiler feed pump turbine uses both steam from the boiler and the main turbine to drive the mechanical shaft connected to the boiler feed pump. This arrangement has proven highly successful in efficiently applying the steam’s thermal energy throughout the plant. In certain arrangements, the BFPT can instead accept steam from cold reheat lines, main unit crossover piping lines, and different extractions from the main turbine. Regardless of the source, one distinction specifically unique to the BFPT is that it must accept steam from two separate sources.

In reference to schematic in Figure 1, the BFPT accepts steam at different pressures from both the boiler and the main turbine.  The low-pressure steam extracted from the main turbine, generally between the high-pressure (HP) turbine and intermediate pressure (IP) turbine sections, will range from 75 psig to 250 psig.  On the other hand, high-pressure steam directed from the boiler can reach pressures as high as 2400 psig, even 3500 psig in supercritical plants.  The ability to utilize two vastly separate steam sources is made possible with the use of two separate inlet designs for the BFPT.  The inlet designs for both the high pressure and the lower pressure sections of the BFPT consist of a series of valves driven by an actuator.  The percentage in which each of these valve sections are open controls the different operating conditions of the plant.  Three main operating points are considered for the feed pump turbine based on solely the lower pressure steam conditions coming from the main turbine.  The conditions with these valves wide open (VWO), 40% of the main unit load (MUL), and the run out point (65% of MUL) all define the operating ranges of this section of the turbine.  The range associated with each of these points allow the engineer to size the correct areas of the LP nozzles.

High-pressure steam from the boiler can be used to start the BFPT without using an auxiliary steam source.  These start up requirements determine the nozzle sizing for the HP steam inlet section.  As seen above, in order to achieve an optimal and efficient design for a BFPT, a number of different intermediate design points must be considered due to the expansive operating range that this particular turbine experiences.  The analysis of different off-design curves becomes crucial in the design of boiler feed pump turbines and is a must for any engineers looking to improve their axial turbine design for boiler feed pump turbines.  To learn more about the full design of process of SoftInWay’s AxSTREAM®, please click here.