The first reason is the economical benefit. The higher the efficiency of the cycle is, the less fuel must be burned to obtain the same power generation. Additionally, the smaller the amount of fuel burned, the fewer emission. Therefore, the increase in efficiency also positively affects the environmental situation. Also, by lowering the temperature of the discharged gases, it is possible to install additional equipment to clean exhaust gases further reducing pollution.

So how does all of this come together? Figure 1 demonstrates a Supercritical CO2 power cycle with heating by flue gases modeled in AxCYCLE. This installation is designed to utilize waste heat after some kind of technological process. The thermal potential of the exhaust gases is quite high (temperature 800° C). Therefore, at the exit from the technological installation, a Supercritical CO2 cycle was added to generate electrical energy. It should be noted: if the thermal potential of waste gases is much lower, HRSG can be used. More information on HRSG here: http://blog.softinway.com/en/introduction-to-heat-recovery-steam-generated-hrsg-technology/

Any cycle of a power turbine installation should consist of at least 4 elements : 2 elements for changing the pressure of the working fluid (turbine and compressor) and 2 elements for changing the temperature of the body (heater and cooler). The cycle demonstrated in Figure 1 has an additional regenerator, which makes it possible to use a part of the heat of the stream after the turbine (which should be removed in the cooler) to heat the stream after the compressor. Thus, part of the heat is returned to the cycle. This increases the efficiency of the cycle, but it requires the introduction of an additional heat exchanger.

The heat exchangers used in the sCO2 cycle are of three basic types: heaters, recuperators, and coolers. Typical closed Brayton cycles using sCO2 as the working fluid require a high degree of heat recuperation.

Having examined this scheme and examined the process in detail, we can draw the following conclusions about the advantages of this cycle which is demonstrated in Figure 2:

- If the fluid at the inlet to the compressor is in a supercritical state and close to the critical point, then the pressure ratio is so small that we can use a compressor almost like a pump
- The installation comes out quite compact due to the high working pressure.
- Vastly reduced water consumption due to dry cooling (suitable for arid environments).

But in addition to the obvious advantages of this installation, there are also negative aspects:

- Even though the installation itself is compact, heat exchangers occupy a large portion of the size due to a large amount of heat transfer.
- Heat exchangers in a cycle without phase transition have a low heat transfer coefficient in comparison to cycles with phase transition as with a heat exchanger in a Carnot cycle. This results in a large metal consumption of heat exchangers and their high cost.

Thus, when designing the optimal supercritical CO2 cycle, two factors must be taken into account that affect the efficiency of the installation oppositely:

- An increase in the heat transferred in the regenerator leads to an increase in the efficiency of the cycle. Consequently, during operation, installation costs will be lower with the same power output.
- On the other hand, the more the regenerator transfers heat, the higher its dimensions and cost are. This leads to an additional capital investment in the installation.

Therefore, the designer must find a balance between these two factors to achieve the highest economic efficiency of the installation. For this balance, it is necessary to combine the calculation of the cycle with a preliminary design of heat exchangers in a single iterative process.

AxSTREAM NET is excellent for the design of heat exchangers of this cycle. It has many features for building hydraulic networks, including heat exchangers including:

- A wide range of built-in models for calculating heat transfer coefficients and hydraulic resistances, including CO2-specific ones. If you need to use your empirical data or use other formulas for calculation in AxSTREAM NET, you can write this in the form of scripts in C # or Python, or use tabular data.
- A built-in model for calculating radiant heat transfer.
- It is possible to change the properties of materials depending on temperature.
- It is possible to conduct off-design calculations of heat exchangers in conjunction with the entire pipeline network, including in a transient setting.
- It is possible to automatically combine AxSTREAM NET calculations with the calculations of the cycle and other elements of the system (for example, turbines and compressors) through AxSTREAM ION. This allows you to automate the process of optimizing the system and its components at different stages of design.

Let’s take a look at the design of heat exchangers in AxSTREAM NET using the example of a heater.

To start, let’s look at the design of the heater, demonstrated in Figure 3.

We can see that the design consists of an array of staggered microtubules, inside of which CO2 moves. These tubes are located inside a rectangular channel through which combustion products move. The heating gas and CO2 flows have a common countercurrent flow, although each tube is perpendicular to the gas flow.

A significant advantage of AxSTREAM NET is the ability to create schemes with different levels of details.

For example, at the initial stages of design, you just need to estimate the design of the future heat exchanger. At this stage, it is possible to create a simplified diagram of the heat exchanger. A simplified diagram of the heater is shown in Figure 4.

When constructing such a simplified scheme, the calculation of the heat exchanger will be based on the average flow parameters. But for this option, it is possible to make a slight modification in the design of the heat exchanger and its optimization. The total length of the snake-water pipes is modeled; the heat transfer coefficient is determined (the average for the entire length of the heat exchanger), radiation heat transfer can also be considered. It is easy to change the pipe lengths, their number across and along with the flow, pipe pitch, etc.

When the preliminary design of the heat exchanger is selected, it is possible to carry out its accurate calculation. An example of such a Heater simulation is shown in Figure 5. In the detailed method, the heat exchanger is “broken down into elements”, this way we can get accurate data, which takes place at a particular length of the apparatus. Here we can observe in detail all the characteristics of interest. For example, we can check the temperature of the pipe walls. In Figure 5, the change in this temperature is indicated by a colored outline.

When designing sCO2 cycles, we should take into account the fact that the dimensions of the heat exchangers will be significant. Therefore, it is important to optimize the parameters of the cycle and the design of its elements for maximizing the efficiency of the cycle at economically feasible sizes of the heat exchangers.

The use of the AxSTREAM NET tool is convenient for designing heat exchangers as it allows designers to create heat exchanger circuits with various levels of detail. Moreover, the calculation accuracy is very high: in comparison with CFD calculations, the difference is less than 5%!

Read more about AxSTREAM NET here: http://www.softinway.com/en/software-applications/cooling-flows-secondary-systems

Join our webinar on Off-Design Simulation of Supercritical CO2 Power Plants and Components by following this link: http://www.softinway.com/en/education/webinars/off-design-simulation-of-supercritical-co2-power-plants-and-components/

]]>Turbomachinery design is critical in industries like aerospace, oil and gas, defense, and clean technology. Dr. Leonid Moroz’s company, SoftInWay Inc., also helps some of the world’s largest manufacturers of turbines, turbochargers, pumps, and fans. But Moroz is happy to explain that his company’s innovations also impact the car you drive, the vacuum cleaner you use, the air conditioning in which you work, and the electricity needed to power your mobile phone.

A lover of music and athletics as a child, Moroz knew early on that engineering held promise as a lifelong career. So he started his career as a Group Leader at TurboAtom. TurboAtom, while a state-owned entity, is one of the world’s top thermal, nuclear, and hydropower plant turbine construction companies. It’s a company that operates at the level of companies like General Electric and Siemens.

Moroz designed both gas and steam turbines during his eight years at TurboAtom. While he was there, he also earned his Ph.D. in Turbomachinery from the Kharkiv Polytechnic Institute in Ukraine.

When he founded global aerospace engineering leader SoftInWay, Inc. in 1999, he intended to assist turbomachinery manufacturers needing his expertise. What evolved from that intent has revolutionized engineering design and allowed improved efficiencies for multiple system types: Its flagship software, AxSTREAM.

AxSTREAM helps engineers develop efficient turbomachinery flow path design, redesign, analysis, and optimization. Under Moroz’ direction, AxSTREAM itself has also evolved into a design platform supporting rapid development of a new generation of liquid rocket engines.

Still a relatively small company, SoftInWay supports over 400 companies worldwide and works closely with universities, research laboratories, and government organizations. The company takes its educational responsibilities seriously, continually offering webinars, training sessions, educational blogs, and online workshops on topics like When To Upgrade Your Pump, The Pros and Cons of Wind Energy, and Radial Outflow Turbine Design.

Moroz loves to talk about his work, his company, its innovations, and his team. He’s proud to have had the same group of engineers for 30 years, so SoftInWay feels more like a family than a workplace. As the company has become a leading global R&D engineering company, it has expanded to encompass locations in Boston, Massachusetts; Zug, Switzerland; Ukraine; and India.

Yes, Moroz’ specialty is indeed a bit technical for people who aren’t in turbomachinery engineering design. But Moroz and his team clearly enjoy what they’re doing because it benefits society and makes life easier and more comfortable in myriad ways.

Next time you switch on that ShopVac or Hoover, be sure to thank Dr. Leonid Moroz.

**Monica:** We often take for granted how engineering plays a huge role in our daily lives. How much of the world depends on the kind of technology and engineering capabilities you produce?

** Dr. Moroz:** Quite substantially. For example, society produces a lot of waste and heat. If you have options, it utilizes waste and heat to produce power, or it is thrown away. We’ve helped companies to utilize this energy and to produce power to heat or cool our houses, to prepare food, and to help our businesses survive.

Another example again would be launchers design. Launchers are important for turbomachinery. A significant part of space development depends on turbomachinery inside those launchers.

It’s important to understand two directions where people can utilize turbomachinery with power consumption and power generation. Power generation is when you produce power, so we need to be more efficient, but the second part, when we get this power, we need to cool our houses, we need to cool our cars, and so on, and again, it’s turbomachinery.

You can be sure that you utilize turbomachinery to develop an air conditioning system that is efficient and is quite substantially in large buildings.

Power consumption for air conditioning is like 30 or 40 percent of the overall power consumption. Can you imagine if you were to decrease this by 10 to 20 percent? It would be a considerable saving…Read the full interview here

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In the age of green energy and increased efforts to minimize our carbon footprint, the design of a turbocharger plays an important role in reducing engine fuel consumption and emissions while increasing the performance. When developing an engine with a turbocharger, the general approach is to select a turbocharger design from a product list. The primary issue with this approach is that it does not cover 100% of the requirements of engine characteristics, i.e. it has non-optimal construction for the engine being developed. The operational characteristics of an engine directly depends on the interactions between the system components. This non-optimal construction will always lead to a decrease in the engine’s performance. In addition, the iteration process of turbocharger selection is time and resource consuming.

That is why the most optimal way to develop an engine with turbocharging is to design a turbocharger from scratch; wherein the operational points of compressor needed to satisfy the engine’s optimal operation are known, i.e. compressor map (Figure 1). But how do we quickly get a compressor map? Even at the preliminary design level, the design of turbocharger flow path requires dozens of hours for high-level engineers. And what about less experienced engineers?

Incorporating a digital engineering approach with a turbomachinery design platform such as AxSTREAM® allows designers to find the compressor design with all the required constraints which correspond to the specified compressor map needed. The design process is presented in Figure 2.

The main stages of a compressor design process are as follows:

– Specify required map;

– Automatic design of compressor flow path generated in Preliminary Design;

– Generate the map using AxSTREAM’s 1D/2D Streamline Solver, if design is valid;

– The final design is selected based on minimal deviation between designed compressor map and specified one.

Utilizing AxSTREAM’s Preliminary Design module in combination with well proven compressor component loss models allows a designer to quickly get close to the final design. To complete the compressor design procedure, the stress calculation and 3D calculations can be performed in AxSTRESS and AxCFD modules respectively to fine tune the design.

As a result, a compressor design with generated map is produced. Figure 3 shows the example of the found compressor design and map in comparison to the specified map. The blue lines correspond to the required map while red line show the compressor as automatically designed in Preliminary Design governed by AxSTREAM ION.

It can be seen in Figure 3, utilizing the automatic design system in AxSTREAM® allows for the preliminary design of a turbocharger compressor based on the required map with speed and accuracy.

Interested in learning about how you can utilize AxSTREAM® to automatically design a compressor for your turbocharger? Contact us at Info@Softinway.com to schedule a demo!

]]>In the months ahead, you can expect to learn more about:

- – What is rotor dynamics? And where is it put to use?
- – Why should we care about rotor dynamics?
- – What industrial standards govern rotor dynamics?
- – Basic definitions and the fundamental concepts of rotating equipment vibrations.
- – The purposes and objectives of rotor dynamics analysis
- – Rotor dynamics analysis procedure
- – Rotor-Bearing system modeling
- – Lateral rotor dynamics
- – Torsional rotor dynamics

This series will endeavor to get readers’ feet wet in the world of rotor dynamics, which is still considered a niche discipline of rotating equipment and turbomachinery engineering. Despite being such a niche subdiscipline of mechanical engineering though, it’s crucial for the safe operation of turbomachinery and high-speed rotating equipment. As we’ll learn, failure to take rotor dynamics into account can have disastrous results. So stay tuned for further editions in this series; we hope you learn something new, whether you’re brand new to rotor dynamics or a seasoned veteran in the field!

In the next blog, we’ll cover the basic definition of what rotor dynamics is, as well as where rotor dynamics is considered. You can read an excerpt of the next post below:

*Rotor dynamics is a branch of applied mechanics in mechanical engineering and is concerned with the behavior of all rotating equipment; considering phenomena like vibration, resonances, stability, and balancing. It accounts for many effects: from bearings, seals, supports, loads and other components that can act on the rotating system. Unaddressed, such phenomena can significantly shorten the life of or even destroy a machine. So where can rotor dynamics be found?*

*Well, unsurprisingly, the answer lies in the name, rotor. Anywhere that a rotating machine is used such as a turbine, compressor, pump, electric motor, turbocharger, or even a reciprocating machine, rotor dynamics analyses are (and should be!) performed. In terms of industry, this discipline is common throughout the power generation, oil and gas, automotive, and aviation industries to name a few, as well as marine transportation.*

In the meantime, if you are looking to learn more about rotor dynamics analysis and SoftInWay’s consulting and software solutions for rotor dynamics, you can reach us at info@softinway.com

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Like any stationary refrigeration unit, a unit used for cooled transportation includes an** intermediate heat exchanger,** a **pump**, an **evaporator**, a **compressor**, a **condenser, **and a** throttle. **The most common refrigeration scheme uses three heat fluids in the industrial refrigeration cycle. There is* Water*, which is used for heat removal from *Refrigerant- R134A* and *Propylene glycol 55%**. *These other fluids are used as intermediate fluids between the refrigerator chamber and refrigerant loop. The working principle of all fridge systems are based on the phase transition process that occurs during the refrigerator cycle shown in Figure 1. The propylene glycol is pumped into the evaporator from the heat exchanger, in which it cools and transfers heat to the refrigerant. In the evaporator, the refrigerant boils and gasifies during the heat transfer process and takes heat from the refrigerator. The gaseous refrigerant enters the condenser due to the compressor working, where its phase transition occurs to the liquid state and cycle repeats.

Keeping cold product at the proper temperature during transportation is of vital importance to many industries. The better the cooling system operates, the longer products can be saved safely without losing quality. It is also important to keep the refrigeration unit as small as functionally possible. The use of advanced methods for estimating the parameters of refrigeration equipment allows us to more accurately designing installations which keeps products at the proper temperature. The proper design of industrial refrigeration has several stages:

**– Thermal scheme cycle modeling.**In this stage, pressure levels, flow rate, and heat capacity are considered and evaluated.**– Preliminary calculation of scheme elements.**This stage assumes HEX preliminary design calculation using the averaged parameters such as heat transfer coefficients averaged over all heat exchangers, temperatures, pressures, etc.**– Refined thermal and hydraulic calculation of complete scheme.**In this stage, the accurate discretized calculations of all HEX and heat gains in the transport networks are -compared to the newly obtained results. Geometric parameters are also clarified, if necessary.**– Off-design analysis of developed schemes (including transient operation)**. This stage the transient analysis parameters are estimated for the extensive hydraulic networks with an intermediate coolant.

For this example shown in Figure 1, we estimated the refrigerator values in 0D thermodynamics software AxCYCLE. HEX’s design was created by average parameters. Inputting this information, the following values of HEXs were obtained:

- – Due to technical and economic considerations, the shell layout with
*12 passages*and the tube heat exchangers with*3 tubes*were chosen; - – Refrigerant flows go in shell side for both evaporator and condenser;
- – Tubes are ribbed from the outside;
- – Condenser total length is
*6 m;* - – Evaporator total length is
*4 m;* - – The condenser contains parts that act as Refrigerant desuperheater and parts that act as a condenser
*.*

Accurate discretized calculation of industrial refrigerator was provided by thermal-fluid network software AxSTREAM NET as shown in Figure 2. In the application, there are different modeling levels. The accurate approach provided by using the interval method of scheme simulating that allows users to automatically determine the condensation and evaporation process in the facilities and provides accurate heat transfer modeling that is critical for a successful design.

Detailed simulation of the refrigerator is necessary for obtaining the process of phase transition in a condenser. As you can see in Figure 3, the beginning of the phase transition is marked by a sharp change in the heat transfer coefficient, a critical data point easily shown in the first two sections in AxSTREAM NET. This is where the condensation process starts. Tracking this critical processes helps to avoid errors in the design of any refrigeration units. This is especially true for units that transport cooled items over long distance.

It should be noted that the thermal-fluid network software such as AxSTREAM NET provides accurate values not only in the estimation of hydraulic resistance in the network, but also in the thermal processes simulating. This approach gives the assessment of refrigerant and propylene glycol for proper pump and compressor selections. Characteristics of the pump and compressor are chosen automatically depending on the main parameters of hydraulic analysis such as flow rates and pressure distribution. This approach provides an accurate calculations of off-design regimes.

Analysis of refrigerator performance shows that heat transfer coefficients strongly depend on wall temperature during refrigerant condensation and evaporation. So these processes need to be estimated with special care. Nowadays, using an averaged-based calculation simulation does not give adequate calculation precision. As shown in Figure 4, the averaged calculation model provides multiple inaccuracies compared to the discretized scheme calculated with AxSTREAM NET.

When the updated calculations from AxSTREAM NET are considered for the redesign of heat exchangers, more accurate geometric parameters are obtained:

- – Condenser pipe length is
*5 m*(compared to*0.6 m*previously, a 24.1% difference); - – Evaporator is
*5 m*(vs.*1.4**m**,*a 2.8% difference); - – Air-Propylene Glycol HEX is
*5 m*(vs.*7 m**,*a 3.7 % difference)

As shown in our analysis, the use of AxSTREAM NET provides an accurate estimation of HEX surfaces heat loads, which makes it possible to design heat exchangers with the smaller surface margin. The AxSTREAM NET scheme created can then be used for off-design modeling of this (and others) refrigerator systems including for transient operation. This model may be used to analyze the reliability of the system under varying conditions, such as: determining the amount of power the refrigerator requires when chambers are loaded; preventing condensate discharge into compressor while reducing the evaporator capacity; and to change cooling water parameters, etc.

]]>The selection of radial or axial for turbomachinery is typically performed based on the operating conditions (adiabatic head H and inlet volumetric flow Q). Non-dimensional turbomachinery parameters of specific speed Ns and specific diameter Ds can be selected from NsDs charts to estimate size, speed, and type of turbomachinery. Turbomachinery types for a sCO_{2} recompression cycle with scales ranging from 100 kW to over 300 MW have been studied and concluded that systems below 10 MW will likely feature only radial turbines and compressors with a single-stage or low stage counts. Such recompression cycle can be simulated in AxCYCLE tool which is shown in Figure 1. As size increases, the most efficient configuration for the turbine and recompressor transitions from radial to axial at approximately 30 MW and 100 MW, respectively. Suitable types of turbomachinery and its components for different power range can be reviewed in Figure 2. A radial configuration for the main compressor was expected at all scales due to its lower volume flow and wider range to facilitate variation in gas properties due to operation near the critical point.

Both open (with fully visible blades) and shrouded impellers can be designed for centrifugal compressors. A closed impeller improves efficiency by eliminating blade tip leakage while its performance is unaffected by axial thermal growth mismatches between the rotor and stator assemblies. Also, covered impellers are generally less prone to high-cycle fatigue failures than open impellers. Therefore, closed impellers are considered favorable for most sCO_{2} cycles as the high pressure and high-density fluid would require very tight clearances to keep leakages as low as possible. The high fluid density in sCO_{2} impellers will also affect the natural frequencies of blade-dominant modes and generates relatively high aerodynamic loading amplitudes. Thus, impeller designs should consider the dynamic stresses resulting from wake excitation from upstream and downstream stator components such as inlet guide vanes, diffuser vanes, and struts that apply periodic excitation to the blades.

From an aerodynamic performance side, there are some unique design considerations that must be understood. First, a good design should be optimized to maximize design point efficiency since the compressor power has a first-order effect on cycle efficiency. Second, the inlet conditions to the main compressor section are usually near the critical point of the working fluid to reduce the compression work and maximize the cycle output. To operate near the critical point a stage should be designed to manage a wide variation in inlet properties associated with small changes in temperature.

Through all phases of design, it is critical to use accurate fluid properties models to capture the real gas variations in the gas. The NIST REFPROP software produces accurate properties for pure CO_{2} near the critical point and can be coupled directly to many compressor design software like AxSTREAM®. Figure 3 is a sCO2 centrifugal compressor designed in AxSTREAM®.

The inducer should be designed to minimize either the tip relative velocity or the inlet relative Mach number. Too large an inducer will reduce the inlet blade angle beyond optimum which limits the efficiency. Too small an inducer will cause static pressure and suppressed temperature, so that static properties may move closer to the saturation line, therefore potentially leading to unwanted phase change.

Some test data showed steady operation at a variety of points across the entire saturation region with no apparent harmful effects. These results suggest that even if two-phase operation occurs, the densities for liquid and vapor phases at high pressure are similar enough to avoid harmful operation. However, until additional experimental exploration and practical operating data are available, it is good practice to maintain some margin from the saturation line during the design process.

High-temperature components in sCO_{2} cycles operate at temperatures similar to ultra-supercritical steam turbines, and much of the work on alloys for steam applications is applicable to sCO2 cycles. For sCO_{2} turbines operating at high temperatures approaching or exceeding 700 °C, designs are creep-limited and nickel-based alloys are required to achieve sufficient creep strength. Different materials suitable for sCO_{2} are compared in Figure 4. In addition to creep properties, another critical consideration for turbine materials is corrosion performance in an sCO2 environment. There is a continued need for materials testing to determine sensitivity to CO_{2} purity, corrosion performance for various CO_{2} mixtures, and testing in a high flow velocity environment to confirm real-world corrosion behavior.

The sCO_{2} turbine may be of the radial inflow or axial design. In most sCO_{2} cycles, the turbine inlet temperature is well above the critical temperature, and the gas behavior approximates that of an ideal gas. Because of this, the turbine design can be achieved using existing design practices and tools like AxSTREAM® from steam and gas turbines for other applications. Generally, turbines are designed with the objective of maximizing efficiency in the fewest number of stages. Their blade/impeller attachments are similar to other turbomachinery applications with several key differences. One critical difference is that a sCO_{2} turbine has a higher power density than other types (the one exception being rocket engines turbopumps), so the pressure (static) loading on turbine blades cannot be ignored as it is with low-density applications. For axial turbines, in order to avoid large bending and tensile stress on blades, an impulse type can be chosen since a reaction type will have higher stress. However, if the bending and tensile stresses allow it, flow paths for the reaction type are proven to be more efficient than the impulse type but do ultimately lead to more stages and therefore increase the plant footprint. Also, nozzles and rotors should be designed to have longer chord and larger LE and TE radius to reduce these blade stresses. The flow meanline aero-structural optimization algorithm is integrated in AxSTREAM®. Its goal is to find the maximum efficiency value while satisfying the structural limitations (the value of chords for which actual stresses will be lower than allowable). With the optimization process in AxSTREAM® for blades which makes them suitable for sCO2 turbine, the value chords will be increased significantly to satisfy the structural requirements as shown in Figure 5. In addition, integral shrouds are typically used and improve blade dynamics, damping, and aerodynamic performance.

Wide operating range requirements and potential for condensation in the compressors and high-temperature pressure containment and compact thermal management in the turbines have been discussed above. Furthermore, the combined high-pressure, high-temperature, and high-density operating environment also bring multiple design challenges like high bearing surface speeds and loads, dense gas effects on rotordynamics and blade loading, low-leakage shaft end sealing and etc. These challenges require significant engineering to overcome before sCO_{2} turbomachinery can begin to displace steam turbines or gas turbines, which have been developed and refined for over 100 years. Despite these challenges, a number of sCO_{2} turbomachinery designs and prototypes have been successfully developed in the past decade. With existing technologies and tools, in addition to data from prototype testing, development and eventual commercialization of sCO_{2} turbomachines for a variety of applications are expected to succeed in the coming years.

- Musgrove, Grant & Allison, Timothy & Ames, Robin & Anderson, Mark & Bennett, Jeff & Brese, Rober & Brun, Klaus & Bueno, Pablo & Carlson, Matt & Chordia, Lalit & Clementoni, Eric & Dennis, Rich & Ertes, Bugra & Fleming, Darryn & Fourspring, Patrick & Friedman, Peter & Held, Timothy & Lawson, Seth & Moisseytsev, Anton & Wright, Steven. (2017). Fundamentals and Applications of Supercritical Carbon Dioxide (SCO2) Based Power Cycles 1st Edition.
- Allison, Tim; Wilkes, Jason; Brun, Klaus; Moore, Jeffrey (2017). Turbomachinery Overview for Supercritical CO2 Power Cycles. Turbomachinery Laboratory, Texas A&M Engineering Experiment Station.
- Moroz L, Frolov B, Burlaka M, Guriev O. Turbomachinery Flowpath Design and Performance Analysis for Supercritical CO2. ASME. Turbo Expo.

In recent years, there have been many innovations in implementing newer materials as well as improvements in hydraulics. Improving pump designs is an ongoing process with designers looking for increasing performance by a few percentage points. The goal of the present pump manufacturers is to offer higher efficiency and reliability, but replacing an older pumps with newer pumps can mean higher costs. The focus for replacing the internals of the pumps with improved design has gained prominence since many of the components, like the casing and rotor, of the existing pumps can be reused. So instead of replacing the entire pump, it can be upgraded or retrofitted. When it comes to an upgrade, the first thing that should be considered is the return on investment which includes the initial investment, operating costs, and the reduction in energy consumption due to the improved pump performance.

Also, sometimes the simplest of upgrades can improve pump efficiency from 5-10% or even more. Such upgrades can yield significant savings on maintenance and repairing cost of the pumps and the benefits of these upgrades can be observed with less downtime than more complex upgrades. A few examples of these simple upgrades are custom coatings for internal and external components, shafts, seals and bearing modifications.

Before considering the upgrade of an existing pump, one should analyze the existing pump performance to make an informed decision on how much needs to be invested and what will be the payback period. Sometimes, small modifications can eliminate the necessity of an entire pump upgrade.

Eventually running pumps will have to be replaced by newer pumps over a period of time because of the natural wear and tear of use. Figure 2 shows impeller degradation due to different operational causes. But it needs to be ensured that one can get maximum benefit from the maintenance or upgrade of a running machine.

Things to remember while considering an upgrade:

**Significant Performance Enhancement**: If you are upgrading for significant performance enhancement, then it may be beneficial to upgrade existing pump even though the running pump performed satisfactorily. In another circumstances when efficiency of the running pump becomes a major issue then replacement of pump is completely justifiable.**Maximum Capital Gain**: Here, it is required to consider several factors like running pump performance, physical condition, capital for new pumps, payback period etc. Another important consideration is to think about cost effectiveness of continued maintenance of the existing equipment or replacement.**Numerical Simulations to Identify the Need to Upgrade:**While considering an upgrade, it is always better to simulate the running pump using commercially available turbomachinery design platform such as AxSTREAM® and identify the cause of performance degradation. Then, performance enhancement can be achieved by redesigning the identified components. The redesign will help in making an informed decision on the performance improvement. Based on this, further analysis can be done to check on the overall return on investment considering an update versus a complete replacement. Different components of a pump (impeller, diffuser, volute, bearings, shaft etc.) can be numerically simulated and redesigned using different schemes of the pump design to get maximum efficiency for specific applications. For example, different layouts like diagonal flow pumps, radial flow pumps, axial pumps, single or multistage pumps (Figure 3) can be considered based on the application and requirements by using AxSTREAM® in which different hydrodynamic schemes, bearings, rotor-dynamics, 3D-flow analysis can be easily carried out within a very short duration of time and which can give good returns on investment.

Interested in learning about how AxSTREAM® can help you? Follow the below link to learn more or contact us at Info@SoftInWay.com !

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The simplest scheme of a Combined Cycle Gas Turbine (CCGT) is presented in Figure 1.

In Figure 1, the exhaust flue gases temperature on the outlet of the turbine is equal to 551.709 ℃. This is a too high a temperature to release the gasses into the environment. The excess heat is able to be disposed of while receiving additional electric power which is approximately equivalent to 30% of the capacity of a gas turbine.

To reach the maximum economical and eco-friendly criteria possible for the installation, many pieces of equipment are used including: a waste heat boiler (HRSG); turbines with a selection for a deaerator (Turbine With Extraction, Deaerator); feed and condensate pumps (PUMP2, PUMP); a condenser (Condenser); and a generator (Generator 2). Exhaust gases entering into the HRSG transfer heat to water which is supplied by the condensate pump from the steam turbine condenser to the deaerator and further by the feed pump to the HRSG. Here boiling of water and overheating of the steam occurs. Moving further, the steam enters the turbine where it performs useful work.

Thanks to the use of such devices, the thermal efficiency of the installation increases, and as a result, this positively affects the economic component of enterprises using them.

For our example in Figure 1, the gas turbine has a capacity of 300 MW, the establishment of HRSG allows you to increase the efficiency of the installation.

In addition to the economic benefits, the ecological benefits should also be noted, since the flue gases at the exit from the gas turbine contain unburned fuel components such as nitrogen oxides NOx, CO, and others. To neutralize NOx, a SCR (Selective Catalytic Reduction) catalyst is used, which neutralizes and converts nitrogen oxides to nitrogen (N2) and water (H2O) by using NH3 injection [Figure 2].

For example, the exhaust gases of energy gas turbines have a fairly high temperature, and have a volume concentration of O2 in them is at 13-16%, which means this gas can be used as a low-activity oxidizer of the combustion process. Burning a certain amount of fuel is recommended to increase power and stabilize the parameters of the generated steam in the boiler.

**Design Component of a HRSG System**

A successful HRSG is comprised of the following components.

**Duct (Duct-burner):**Provides transfer of flue gases through the HRSG path (installation of an auxiliary burner is possible here)**Superheater***:*Used for the overheating of steam inside it.**Evaporator:**Can be either a drum or direct-flow type.**– Drum type**The drum has three major functions. Firstly, a drum is needed to supply saturated water to the evaporator circuit. Secondly, a separation device installed inside it separates water from water vapor and prevents transfer water droplets to the superheater and then to the steam turbine. And thirdly, continuous blowing takes place from the boiler drum. As a result, the process of removing part of the boiler water from the upper water level takes place. Due to this, the salt balance of the boiler water is maintained. Therefore, the requirements for the quality of the feed water at the inlet to the boiler drum may be decreased. It should also be noted that this type of boiler can have up to three circuits (pressures). HRSG with two or more pressures may have an intermediate superheater. [Figure 3]*:***– Direct-flow type:**A direct-flow boiler does not include a drum in its design. Water passes through evaporation tubes once, gradually turning into steam. The region where vaporization finishes is called transitional. After the evaporation tubes, the steam-water mixture (steam) enters the superheater. Once-through, boilers very often have an intermediate superheater. Such boilers operate at both subcritical and supercritical pressures.

**Economizer:**is designed for heating water.

** There are three general configurations for HRSG.**

**Single-circuit (1-pressure)**configurations are generally used at small and medium capacities, with an exhaust gas temperature equal to 450 – 550 ℃. The simplest circuit of a single-circuit CCGT unit was considered above in Figure 1.**HRSG two-loop circuits (two pressure)**are the most common [Figure 3], but regulating of them are much more difficult to achieve. There is a pinch economizer, evaporator, superheater for each circuit. There is the smallest temperature difference between heating gases and water. Usually, the smallest temperature difference is at the outlet of the evaporator. The temperature difference is quite significant at the exit from the HRSG block, and if you need to dispose of it, another block is added. In order to organize the same pinch in the next block, the mass flow rate through it must be different. The efficiency of a CCGT with two circuits increases by increasing the temperature and the high-pressure steam. The limit value of this temperature is determined by the temperature of the flue gases. These circuits are used when deeper cooling is needed than with single-circuit HRSG can provide.-
**HRSG three-loop circuits (three pressure)**is able to increase plant efficiency further. These configurations are used for powerful energy gas turbines with high exhaust gas parameters where temperatures exceed 580 ℃.

**Conclusion: **

HRSG use allows for up to a 30% increase in the power from a gas turbine. Additionally, HRSG can be equipped with different devices which eliminate harmful substances in flue gases. But including these environmental safeguards creates additional hydraulic resistance at the outlet of the GT. This can significantly reduce its efficiency.

The decision to add HRSG can be made only after a careful analysis. To do this critical calculation, use proven software products, such as AxCYCLE , which greatly simplify this complicated task. For more information, contact us at Info@SoftInWay.com

**References:**

- http://www.ccj-online.com/take-control-of-your-catalyst-management/ (Figure 2)
- Stepanov DV Boiler installations of industrial enterprises / Stepanov DV, Korzhenko ES, Bodnar LA – Vinnitsa, 2011, VNTU
- https://en.wikipedia.org/wiki/Heat_recovery_steam_generator (Figure 3)

Key Symbols

Indexes and Other Signs

Abbreviations

For demonstration of opportunities of the developed complex of the methods, algorithms and mathematical models for solving the problems of optimal design of the turbine units taking into account their mode of operation [38, 40–42] the results of optimization research of turbine expander flow path and of gas turbine unit GTU GT-750-6M low pressure turbine flow path are presented below.

In gas pipelines, natural gas is transported under the pressure 35–75 atmospheres. Before serving the natural gas to the consumer its pressure must be lowered to the level of pressures local supply systems. At the moment gas distribution stations widely are using technologies of utilization of natural gas let-down pressure before serving the consumer. To extract energy from compressed gas the special rendering turbine expander units (RTEU) are used in which the potential overpressure energy is converted into mechanical work of a rotor rotation of a turbine, which serves as generator drive.

Seasonal unevenness of natural gas consumption, usually caused by environmental temperature, leads to a deeply no projected RTEU operation modes and adversely affect their performance and service life. For example, the gas flow through the flow path of the RTEU during the year may vary in ranges from 0.25–0.35 to 1.05–1.25 from the rated value. The foregoing attests to the relevance and necessity of taking into account the factor variability of operation loads during the selection of the basic geometric parameters of the RTEU FP.

This section provides results of optimization of 4-stage flow path of existing design of RTEU taking into account real operation modes of it, using the developed algorithm [40].

Operating conditions of the considered RTEU are characterized by significant monthly uneven mass flow rate of the working fluid through the flow path of the unit with fixed heat drop and rotor speeds:

The mass flow rate of natural gas, depending on the operating mode, changed in the range from 4.94 to 20.66 kg/s (the mass flow rate at the design mode is G_{nom} = 16.66 kg/s).

At present several ways to regulate the mass flow through the RTEU FP are known. The changing of the walk-through sections of nozzle cascade (NC), thanks to the use of rotary nozzle blades, is the most effective.

It is known that the implementation of the rotary nozzle blades can significantly extend the range of workloads of the turbine installation and improve performance indicators of FP. However, to get the maximum effect from the rotation of the nozzle blades, there is a need to further address the challenge of defining optimal angles α_{1e} for each stage, depending on the

operating mode of the RTEU FP.

In accordance with the terms of the design, mass flow regulation of the working fluid through the flow path of the RTRU has been carried out by turning of the nozzle blades (changing the outlet angles α_{1e}) of all stages. Optimization was carried out taking into account the 12 operational modes of turbine expander (one month duration of each mode). The mass flows of natural gas through the FP for the specified modes are shown in the Table 7.4.

Two levels of recursive optimization algorithm (section 1.2.1) – “Cylinder” (Layer 1 and Layer 2) and “Stage” were involved in the optimization process. At the level of “Cylinder” recursive optimization algorithm is called on not only for “Stage” level but for Layer 1 and Layer 2. As can be seen from Fig. 7.5, at the top level “Cylinder” (Layer 1) the vector of varied parameters of created FMM has been generated from 16 parameters, one of which is operational mode (the mass flow at the cylinder inlet – G_{0}) and the remaining 15 are design parameters.

They included effective outlet flow angles from nozzle and blades (α_{1e}, β_{1e}), and average diameters and heights of the blade wheel cascades (D_{2} and l_{2}). Mean diameters and heights of nozzle wheel cascades (D_{1} and l_{1}) for each stage were determined based on values similar to the parameters of the blade wheel cascades taking into account recommendations about overlap size for each RTEU stage.

At the below laying level “Stage” for each stage except the first the vector of varied parameters of FMM was formed of 9 parameters (D_{2},l_{2}, α_{1} β_{2}, u/C_{0},z_{1,2}, b_{1,2}).

The sequence of the general optimization task solution looks as follows. Previously, using the DOE theory (paragraph 1.3) the FMMs of the level “Stage” were created in the form of full quadratic polynomials (1.2). The FMM of the “Cylinder” level (Layer 1) was build next.

According to a design of experiment matrix from top level “Cylinder” to level”Stage” parametric restrictions in the form of values D_{2},l_{2}, α_{1e} β_{2e}, u/C_{0} arrive. Concrete level of these parameters is defined by a current point of the plan of numerical experiment of level “Cylinder” (Layer 1). At level “Stage” taking into account the arrived parametric restrictions local optimization tasks by definition of optimal values of blades numbers (z_{1,2}) and chords values (b_{1,2}) of nozzle and blade wheel cascades of each stage are solved.

The received optimal values of these parameters are passed to the top level “Cylinder” (Layer 2) for calculation of the optimal angles α_{1e} along the FP depending on the mass flow of working fluid at the entrance to the turbine expander.

At the end of the optimization process under optimal values of “Cylinder”-level parameters, except values of chords and numbers of blades, inlet metal angles of nozzle and blade wheel cascades of each stage are specified. The values of the specified angles are defined taking into account a weight part of quality criterion of each operational mode.

As quality criterion for an estimation of the flow path efficiency at the level “Cylinder” the value equal to total work of the cylinder for a selected period of time one year (T)

defined according to the developed mathematical model (section 2.2.3), was used. Given the assumption that the duration of the modes is the same, this criterion was reduced to the sum of the “regime” cylinder capacity

where n is the number of modes). To assess the quality criterion at “Stage” level the internal relative efficiency of the corresponding stage was used.

Since this task was solved for the FP with standard type of the nozzles profiles H-2, changing the angle α_{1e} takes into account and corresponding changing of the inlet metal angle of the nozzle wheel cascade (α_{0g}). When calculating the losses, associated with incidence angles at the inlet of the cascade, the influence of the blade’s inlet flow angle on the losses in accordance with experimental data was taken into account.

Inlet metal angles of the blade wheel cascade for each stage were determined by averaging their values across 12 modes of operations taking into account weight proportion of quality criterion of each mode.

The values of the “basic” design parameters, obtained by solving the general optimization task, are listed in the Table 7.5.

The received distributions of angles α_{1} for each stage of the flow path as functions of mass flow change are presented in Fig. 7.6. Apparently from Fig. 7.6 optimal curves of angles differ greatly from the linear curve received at uniform simultaneous turn of nozzles.

Efficiency of an initial design of the flow path with synchronous turn of all nozzles and efficiency of the design received as result of optimal design with the optimal law of angles α_{1} change by operation modes are presented in Fig. 7.7. The efficiency of the received flow path essentially surpasses efficiency of initial flow path on all operation modes (Fig. 7.7). Significant improvements in efficiency has been observed in the low mass flow modes of operation (up to 5%), as well as to the modes of mass flow greater than 18 kg/s. Additional generation of electricity for operating cycle is equal to 914.793 MWh (3.64%).

It is obvious, that it is impossible to create the flow path equally well working in a range of loadings from 30 to 125% of the nominal. So the efficiency of any flow path on modes with low mass flows remains at low enough level due to the great values of incidence angles, negative degrees of reaction, a substantial redistribution of disposable heat drop, offset u/C_{0} of the stages aside from optimal values.

The gain of optimal variant, in comparison with initial variant of design, on modes with low mass flows is provided by selection of optimal angles α_{1} for all nozzle cascades along the flow path. As can be seen from Fig. 7.6 for optimal variant of RTEU FP, when small mass flow rate, value of the 1st stage angle α_{1e} significantly lower compared to the values of the same angles of subsequent stages, that increases its heat drop and value of output velocity from the nozzle cascade (velocity c_{1} close to the speed of sound M_{c1} = 0.997).

Despite some deterioration in the effectiveness of 1st stage, this solution allowed unload the subsequent stages and significantly improve their work conditions (positive degree of reaction on the mean radius of the second and third stages has been achieved) and get a positive final outcome.

On operation modes with the mass flow close to or surpassing on-design, increase of efficiency of the flow path became possible due to selection of an optimal combination of “base” design parameters (D_{1,2},l_{1,2}, β_{1g}, β_{2e}, z_{1,2}, b_{1,2}) for each stage. This helped to reduce the losses associated with the inlet of the

working fluid on the cascades and exit velocity losses, as well as to improve the efficiency of the nozzle and blade wheel cascades. Also on the considered operation modes there is a redistribution of heat drops between the stages: reducing load of 1st and 4th stages and increasing load of 2nd and 3rd.

In the current section the example of applying developed methods and algorithms for the solution of the problem of optimization of gas turbine flow path taking into account the modes of operations is given. As the object of study the gas turbine installation GТ-750-6M was chosen [40]. This GTU is used at the compressor station as a driver of gas-compressor unit. Selection of the specified unit is linked to the fact that such installations are quite widespread in the gas transportation system of Ukraine and more than 80% of them exhausted its resource.

In addition, the authors had at their disposal all the necessary project documentation and the results of the field tests of the manufacturer that was the necessary condition for optimization and the validation of the computational research results.

Optimization of FP of the low-pressure turbine installation GT-750M was carried out taking into account the actual operating loads and the inclusion in consideration of the thermal scheme (TS) of installation.

A direct one-dimensional flow model through the axial turbines FP (section 2.2.3) and the procedure of thermal schemes calculation of GTU (section 2.5) were involved in this case. A screenshot of a window of the specialized CAD system with active project of GT-750M installation is presented at Fig. 7.8. One-dimensional mathematical model of the turbine stages group is used in the process of solving common optimization tasks and to build the universal characteristics of the gas turbines, and the model of thermodynamic processes in thermal schemes of GTU – for thermodynamic calculation of the unit’s thermal cycle (TC) for real operating modes.

Thermal cycle scheme consists of the following main elements: compressor (C); combustion chamber (CC); high pressure turbine (HPT), located on the same shaft with compressor; free power turbine low pressure (LPT); regenerator (R); external consumer of net power – natural gas blower (B). As can be seen from Fig. 7.8, GT-750-6М is a split-shaft gas turbine unit with waste-heat recovery.

Such a scheme, thanks to good surging characteristics, is more flexible, reliable and cost-effective in terms of variable operating mode and can be equally well applied for driving propeller, for ground transportation, for blast furnace production etc. When operating on the gas pipeline such a gas turbine unit can provide any mode of operation of the gas pipeline without throttling at

the suction and without pressure lowering of the blower.

For operation modeling of the compressor and turbine, while calculating on the various modes the universal characteristics were used. Moreover, the characteristic of the compressor was built according to the manufacturer’s data but turbines characteristics were obtained using specialized CAD system.

Fields on the characteristics of high and low pressure turbines covering ranges of operating modes of FP, obtained by calculating the GТ-750-6M unit thermal scheme for one calendar year of real modes of operation.

Calculations have showed that area of the work of the HPT FP is close to the on-design regime, but LPT works in more wide range of operating modes.

The problem of flow path geometrical parameter multi-mode optimization with consideration of the thermal scheme of the unit is difficult and extremely labor-intensive. At present, in the available literature, recommendations and examples of the solution of optimization problems in similar papers are practically not existent. Considering the above, for the purpose of the

development of approaches to finding solutions to specified problems, preliminary research directed at the consideration of the influence of the efficiency of high and low pressure flow paths of GT-750-6M on its integral characteristics (fuel consumption, GTU efficiency, cycle initial parameters, etc.) have been carried out.

The increase of the efficiency of gas turbines flow paths is one of the preferable methods of increasing GTU efficiency and useful power. However, as studies have shown, in some cases the increase of the efficiency of gas turbine separately used in the thermal scheme within modernization does not produce the expected effect. It is connected with features of the configuration of turbines within GTU, and also with the interaction of turbines with other elements of the thermal scheme. The influence of gas turbines flow paths efficiency on GTU performance parameters using a GT-750-6M unit (Fig. 7.8) is considered as an example.

*Increasing the efficiency of HPT*

As can be seen from Fig. 7.8, HPT is located on the same shaft as the axial compressor and provides its work. The mass flow rate, temperature and pressure of combustion products behind HPT must be in strict conformity with the values necessary for generation by LPT power, set by the external consumer (the natural gas blower) in the current operation mode. An increase of HPT

efficiency in the specified operating conditions of the turbine does not lead to the predicted improvement of the performance parameters of the turbine unit. For example, when saving the unit operation mode (useful power, the power turbine rotor speed and the air parameters), the increase of HPT efficiency leads to an increase of its power. The additional power of HPT is transmitted through the shaft to the axial compressor, which leads to the redistribution of the main parameters of the gas-turbine cycle, namely:

- – the increase of power for compressor drive causes an increase in compressor rotor speed, which causes an increase of the air flow rate and a slight increase of the compression ratio (compressor efficiency decreases because of the displacement of the compressor and HPT joint operation line takes place);
- – the new air flow rate and pressure at the compressor outlet are superfluous for this thermal cycle and cause a fall in combustion products at the combustion chamber outlet, which inevitably leads to a decrease in cycle thermodynamic efficiency.

The specified changes in the unit’s thermal scheme nullify the effect expected from HPT flow path optimization.

*Increasing the efficiency of LPT*

The calculations show that the increase of LPT efficiency has a favorable effect on the performance parameters of the GT-750-6M and allows getting increase the net power while maintaining fuel consumption or fuel economy while maintaining power, given to the external consumer. Considerable deviations of the gas-turbine cycle parameters from design are not observed in this case.

Thus, an increase in the efficiency of LPT flow path is the most rational variant of the GT-750-6M unit modernization. The specified modernization does not lead to an essential redistribution of the parameters of the gas-turbine cycle and therefore does not touch the expensive elements of the unit such as the compressor, combustor, regenerator and supercharger.

It is worth to note that these studies were carried out for the GT-750-6M unit but research results and conclusions are valid for all GTUs with a similar thermal scheme.

For the optimization of geometrical parameters of GT-750-6M LPT flow path, taking into account the actual modes of operation, three upper levels of developed recursive algorithm optimization, described in Chapter 1, were involved. The distribution of the tasks and interaction between the local design levels are depicted in Fig. 7.9.

The highest level in the hierarchy of the design process “Scheme” is intended to calculate the distributions of parameters of GTU cycle (pressure, temperature, capacity, and cost) between elements in the scheme, as well as to determine the integral indicators of the unit at the off-design operation modes. As can be seen from Fig. 7.9, from the level “Scheme” to the level “Cylinder” the sets of mode parameters come that uniquely identify modes of the FP operation (consumption of combustion products at the entrance to the FP – G_{0}, full gas

pressure at the inlet of FP – P^{*}_{0}, full gas temperature at the inlet to FP – T^{*}_{0}, full gas pressure at the outlet of the FP – P^{*}_{0}, turbine shaft speed – n).

the “Cylinder” level optimal values of basic geometrical parameters such as mean diameters of the nozzle and blade wheel cascades (D_{1}, D_{2}), the heights of the nozzles and the blades (l_{1}, l_{2}), inlet/outlet flow angles in both absolute and relative motions for nozzle and blades wheel cascades (α_{1}, α_{0g}, β_{2}, β_{1g}) were defined.

As a functional limitation at the level of “Cylinder” the flow rate of combustion products at the entrance to the LPT was chosen, that should match to the flow rate through the initial FP of the unit. For assessing the quality criterion in the process of optimization the value equal to the total work of the gas turbine (GT) for one year of operation was used.

At the next level “Stage” the optimal values of the numbers of the nozzle and rotor blades ( 1 2 z , z ) for their cascades were found, and optimized parameters on the “Cylinder” level were used as parametric constraints. Quality criterion is the internal efficiency of the stage.

A thermodynamic calculation of the GTU schemes procedure (section 2.5) is used as the mathematical model at the “Scheme” level. At the “Cylinder” and “Stage” levels a procedure for direct one-dimensional calculation of the axial turbines FP (section 2.2.3) is applied. When the optimal solution at the level of “Cylinder” was found, using direct one-dimensional model of FP, the universal characteristics of well-designed LPT are build. These characteristics are returning to the “Scheme” level for calculation of integral characteristics of the GTU.

Three iterations for refining the optimal solution were conducted during computation. The optimization task was solved taking into account 177 real operation modes of the GTU. Each mode corresponds to unit operation for 24 hours. Unit loading for the considered period varied in a range from 52 to 73% of the on-design mode, equal to 6 MW.

The calculations has shown that in the on-design operation mode of the GTU the gain of LPT useful capacity, without mass flow rate increase, was 1.5% (93.1 kW). Efficiency increase after optimization is caused by a decrease in the losses in nozzle and rotor cascades, exit energy losses, and a reduction of leakages in radial clearance. Therefore, in the on-design mode the velocity coefficient for nozzle and rotor cascades of an optimal flow path increased by 0.4 and 0.6% respectively, the absolute velocity downstream rotor (c_{2}) decreased by 22%, and the leakage in radial clearance decreased by 2.7%. There was an increase of heat drop for nozzle cascades and a decrease of heat drop for rotor cascades (reaction decreased from 0.478 to 0.368). When the optimal design of the turbine works within the thermal scheme of the studied unit, the reduced value of velocity c_{2} leads to a corresponding decrease of total pressure losses in the exhaust diffuser.

The optimum values of variable parameters, obtained through the optimization, are shown in the Table 7.6.

As the result of the optimization the efficiency increment depending on the operation mode of GTU is from 0.09 to 0.27%. The fuel economy (of natural gas) for GTU with optimal LPT flow path depending on operation modes is given in Fig. 7.10. The total fuel economy for the considered period of 177 days amounted to 50831 kg.

Before performing the work of such complexity, as the above examples of optimal design of multi-stage cylinders, the authors made a huge amount of the work related to the verification of the developed and implemented mathematical models as well as proposed methods of optimization.

It should be emphasized that the criteria of the calculation results is an experiment. Full-scale experimental investigation of powerful turbines is very expensive. However, at one of the thermal power plants the test of turbine 200 MW capacity was conducted in a wide range of operational modes.

Comparison of results of the calculation research of the HPC FP turbines with experimental data obtained as a result of field tests of the same turbine in a wide range of operating modes, have strongly affirmed that used in optimization designed and implemented mathematical models have high accuracy and adequately simulate physical processes of flow of the working fluid in axial

turbine flow path.

According to the results of the conducted studies one important conclusion can be formulated.

*The further improvement of the indicators level of the quality of existing and newly designed advanced multi-stage axial turbine installations is possible only using the most modern methods and software systems, capable of solving tasks of a multilevel object-oriented multi-criterion and multi-parameter optimization of the flow paths of axial turbines, taking into account their operational mode.*

Key Symbols

Indexes and Other Signs

Abbreviations

In this chapter, as an example of practical use of the developed theory of optimal design of axial turbines flow paths, the results of the studies, related to the optimization of parameters of flow path of the high pressure cylinders (HPC) of 220, 330 and 540 MW capacities turbines, operating at nominal mode, as well as examples of optimization turbo-expander and low pressure turbine of gas turbine unit, taking into account the mode of its operation, are presented. The entire complex of calculation research was conducted using mathematical models of flow path (FP) of axial turbines, described in Chapter 2.

In addition, in the studies variants of mathematical models of FP “with the specified profiles” [38] were also used, which allowed with more accuracy determine geometric characteristics of turbine cascades, in particular, the inlet geometric angles of working and nozzle cascades, that are changing with the changing of stagger angles of the profiles. The latter had a significant impact on the amount of additional losses related to the incidence angle of inlet flow of working fluid.

Practice of the optimal design of axial turbines cylinders has showed that when optimizing steam turbine cylinder with extraction of working fluid for regeneration and heat supplying at least two criteria – the efficiency of the cylinder flow path and its capacity must be taking into account [38, 40-42].

Using the convolution of quality criteria in accordance with (1.37) allows efficiently solve the multi-criterion optimization problems corresponding the Pareto front.

As an example of the effectiveness of the use of convolution (1.37) the results of the optimization of HPC FP of a powerful steam turbine by two criteria – power and cylinder efficiency for different values of the weight coefficients μ_{i} are presented in Table 7.1 and Fig. 7.1.

Numbers on the curve corresponds to the numbers of optimization problem in the Table 7.1.

The number of optimization parameters – 33:

- – level 1 (cylinder) – optimized for 19 parameters:
- – Root diameter and height of the nozzle blades of the first stage of the cylinder.
- – Meridional disclosing of the channels of the nozzle and working cascades.
- – Effective exit angles of the nozzle and working cascades of all turbine stages.

- 2-nd level (stage) – optimized for 14 parameters:
- – The number of the blades in the nozzle cascades for all turbine stages.
- – The number of the blades in the working cascades for all turbine stages.

Quality criteria applied when optimizing – the criterion vector that includes the normalized values of internal relative efficiency of the cylinder η_{oi} and its power (N) with equal weight coefficients.

The results of the optimization of the HPC FP of the 220 Mw capacity turbine [39] are listed in Table 7.2 and in Fig. 7.2, where η_{d} – Moliere diagram efficiency of FP η’ – the ratio of efficiency of the stages to Moliere diagram efficiency of the initial variant of the cylinder η_{oi} – internal efficiency of FP; Δη_{d} – gain of the internal efficiency of the optimal FP; *N* – power; Δ*N* – the power gain of the optimal variant of the HPC FP.

Improvement of the quality indicators of the optimized FP obtained through:

- – rational distribution of the cylinder heat drop, having in its disposal, between the stages;
- – some decreasing of the axial speed components and ensuring closer to axial outlet working fluid from the stages, resulting in reducing the exit velocity losses;
- – reducing the incidence angles, that provides the improving efficiency of the nozzle and working cascades;
- – increasing the mean diameter of the stages, that led to obtaining the optimal values of the ratio of the velocities
*u*/C_{0} - – reducing the specific weight of the losses near the hub and the shroud boundaries by increasing the height of the blades;
- – the optimal value of the nozzle and working cascades relative pitch, which also led to an increase of their effectiveness.

The final variant is obtained by optimization taking into account the technological restrictions on the production of the flow path parts. This explains the slight decreasing of efficiency and cylinder capacity compared to the best option without restrictions.

The optimal variant of HPC FP of the 220 MW capacity turbine for nuclear power plant is obtained, which characterized by high perfection levels of aerodynamic indices, providing a boost of power on 5.4 MW, of internal efficiency on 2.71% and Moliere diagram efficiency on 2.27% as compared to the initial version of FP.

The number of optimization parameters – 55:

- – level 1 (cylinder)-optimized for 44 parameters:
- – Root diameter and height of the nozzle blades of the first stage of the cylinder.
- – Meridional disclosing of the channels of the nozzle and working cascades.
- – Effective exit angles of the nozzle and working cascades of all turbine stages.

- – 2-nd level (stage)-optimized for 11 parameters:
- – The number of the blades in the working cascades for all turbine stages.

Quality criteria applied when optimizing – the criterion vector that includes the normalized values of Moliere diagram efficiency of the cylinder (η_{d}) and its power (*N*) with equal weight coefficients.

The results of the optimization of the HPC FP of the turbine 330 MW capacity turbine are listed in Table 7.3 and in Fig. 7.3, where η_{d} – Moliere diagram efficiency of FP; η’ – the ratio of efficiency of the stages to Moliere diagram efficiency of the initial variant of the cylinder; η_{oi} – internal efficiency of FP;Δη_{oi} – gain of the internal efficiency of the optimal FP; *N* – power; Δ*N* – the power gain of the optimal variant of the HPC FP.

Improvement of the quality indicators of the optimized FP obtained through:

- – more rational distribution of the cylinder heat drop, having in its disposal, between the stages;
- – application of the optimal configuration of meridional shape of FP with a slightly reduced heights blades;
- – increasing value of the effective nozzle exit angles, providing the reduction of the incidence angles on the working cascades;
- – improving the efficiency of working cascades through the optimal choice of stagger angles and numbers of the blades, resulting in a significant reduction of losses from the incidence angle;
- – reducing the degree of reaction level of the stages and, as a consequence, reducing the losses from root and radial leakages.

Practical application of the developed optimization theory provided the solution of the task: the optimum variant HPC PF of the 330 MW capacity turbine was obtained, which characterized by high perfection levels of aerodynamic indices, providing a boost of power on 6.2 MW, of the relative internal efficiency on 5.76% and Moliere diagram efficiency on 3.94% in comparison with the initial version of FP.

Features of the initial variant of the HPC FP:

- – FP of the 9 stages HPC has high enough quality integral indicators, which have been achieved thanks to the very high level of aerodynamic perfection of the flow path of the cylinder:
- – numbers of the nozzle and working cascades blades are close to the optimal values;
- – the inlet flow incidence angles at the nozzle and work cascades are close enough to the possible minimum values given used profiles and blades production technology;
- – the root degrees of reaction provide fairly low levels of hub leakages;
- – the use of highly effective radial seals has significantly reduced radial leakages.

However, in the construction of FP reserves of possible efficiency gains were identified associated with not quite rationally distribution of disposable heat drop between the cylinder stages and somewhat inflated level of root leakages in first stage.

The number of optimization parameters of HPC FP of the turbine 540 MW capacity – 55:

- – level 1 (cylinder) – optimized for 37 parameters:
- – Root diameter and height of the nozzle blades of the first stage of the cylinder.
- – Meridional disclosing of the channels of the nozzle and working cascades.
- – Effective exit angles of the nozzle and working cascades of all turbine stages.

Due to the fact that in the initial variant of the HPC FP number of the nozzle and working cascades blades near by the optimal values, the second level of optimization (stage) was not used in this task.

Quality criteria applied when optimizing – the criterion vector that includes the normalized values of Moliere diagram efficiency of the cylinder (η_{d}) and its power (*N*) with equal weight coefficients. The results of the optimization of the HPC FP of the turbine 540 MW capacity are listed in Fig. 7.4, where (*N*) – power and η’ – the ratio of efficiency of the stages to Moliere diagram efficiency of the initial variant of the cylinder.

Improvement of the quality indicators of the optimized FP obtained through:

- – a more rational distribution of the disposal cylinder heat drop, between the stages, thereby improving the integral indicators of the cylinder quality;
- – some decrease of axial velocity component and ensuring closer to axial outlet of working fluid from the stages, that reduced the exit velocity losses, improving inlet conditions for nozzles cascades (which led to an improvement in their effectiveness);
- – close to optimal values of velocities ratio (u/C
_{0}), obtained by increasing the mean diameter of the stages; - – reduction in the share of the losses near the hub and the shroud boundaries associated with increasing the heights of the blades;
- – using in 6–9 stages of the blades a highly effective 1MMC profile (Chapter 5), which provided a good matching flow inlet angles and the geometric inlet angles of the working cascades, that resulted in increasing their efficiency;
- – obtaining the optimal twist laws of the β
_{2e}angles at the outlet of the working wheels of 6–9 stages that contributed to the rational distribution of the gas-dynamic parameters along the radius of these stages.

So, the practical application of the developed optimization theory secured the solution of the requested task: the optimum variant of HPC FP of the 540 MW capacity turbine was obtained, which characterized by high perfection levels of aerodynamic indices, providing a boost of power on 1.4 MW, of inner efficiency on 1.52% and Moliere diagram efficiency on 1.63% in comparison with the initial version of FP.

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