Flexible, Fast and High Fidelity Approach to Gas Turbine Unit Part-Load and Off-Design Performance Predictions

Gas turbine (GT) engines are the primary engines of modern aviation. They are also widely used as power propulsion engines for power stations. The specificity of these engines implies they frequently work at off-design/part load modes that occur with:

  1. Different modes of aircrafts:
    1. Ground idle mode
    2. Take off
    3. Maximum continuous mode
    4. Cruising mode
  2. Different ambient conditions
  3. Grid demands (for power generation engines and gas pumping (compressor) stations)

 

Due to the off-design/part load operating conditions, the parameters of the engines might change significantly, which influences not only the engine efficiency, but also the reliable work of the turbine (high temperature at turbine inlet) and compressor (surge zone) at joint operational points. This is why accurate predictions of the gas generator parameters are crucial at every off-design mode.

To define the joint operational point, the compressor and turbine maps which are created for specified ambient conditions can be used. For example, pressure equal 101.3kPa, temperature – 288.15K. Maps method is widely used, relatively simple and allows you to find the needed engine parameters in the shortest time. However, when cooling is present, engine operation at low power modes (ground idle) impede the accurate determination of joint operational conditions based on maps. The significant drawback to the maps based approach is that it does not give the full picture of the physical processes in turbomachine flow paths which is critical for off-design calculations.

Compressor and Turbine Maps
Compressor and Turbine Maps [1]
Utilization of the digital twin concept allows significant increase of the off-design performance calculation accuracy. Use of the digital equivalent of object was introduced in 2003 [2]. Despite this, less 1% of machines that are in use today are modeled with digital twin technology [3]. Utilization of digital twin leads to a significant decrease in time and cost for developing and optimization of an object.

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The Pros and Cons of Wind Energy

Who knew passing wind would be so exhilarating?

Last month we discussed a few basic aspects of wind as a source of clean energy. We showed what wind was, how it forms and where it goes.  Then after going on a tangent about the history of turbines, we showed where on the Earth we could recover the highest amount of wind energy and how this potential changes with altitude. Today’s post offer the pros and cons of wind energy while touching upon several topics discussed in the previous post before diving into the optimal where and when.

Getting into the “What”

With an established worldwide potential of more than 400 TW (20 times more than what the entire human population needs) and a clean, renewable source wind is definitely attractive to the current and future generations. In terms of harvesting it, over 99% percent of wind farms in the USA are located in rural areas with 71% of them in low-income counties. Indeed, the more land is available (and the fewer buildings), the higher the possibility and interest to transform this kinetic energy into mechanical work and then most likely electricity.

Where one would see sporadic turbines on the side of the highway, these stand-alone equipment have begun to turn into actual modules (farms) that can work as an overall unit instead of individual ones. This strategy of creating a network of turbines follows the philosophy of “the Whole is Greater than the Sum of its Parts”. What this translates into is that by having 20 (arbitrary number) wind turbines working together to determine the best orientation, pitch, etc. of their blades in such a way that it least negatively impacts the downstream units we can produce more energy than if each of them were live-optimized individually (some interesting A.I. work is going into this). This means that the overall system is more efficient at converting energy and therefore it is more cost effective to provide bulk power to the electrical grid. This is similar to the concept in the post on solar energy comparing PV panels and CSP. Read the full post here. 

In terms of power production per wind turbine, the utility-scale ones range from about 100 kW to several MW for the land-based units (Offshore wind turbines are typically larger and produce more power – getting ahead of myself here but check out the figure below for wind potential in Western Europe that clearly showcases coast vs. non-coast data). On the low-power end of the spectrum, we find some below 100 kW for some non-utility applications like powering homes, telecommunications dishes, water pumping, etc. Solar power (PV) is generally regarded as the first choice for homeowners looking to become energy producers themselves, but wind turbines make an excellent alternative in some situations. It would take a wind turbine of about 10 kilowatts and $40,000 to $70,000 to become a net electricity producer. Investments like this typically break even after 10 to 20 years.

Wind potential in Western Europe
Figure 8 Wind potential in Western Europe – https://globalwindatlas.info/

Onto the “Where”

One of the elements of wind formation we covered in the last post here was a different in pressure (and therefore temperature). This simplification works rather well at the macro-scale, but as we zoom in closer to the surface we can see that wind flow speeds and patterns vary quite significantly based on more than just the general location of Earth. On top of the altitude we already discussed, factors like vegetation, presence of high-rise buildings or bodies of water come into play.

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Applications of Centrifugal Pumps

Centrifugal Pumps are the most popular and commonly used type of pump for the transfer of any type of fluid. The volumetric flow rate range of centrifugal pumps can vary from several tens of ml/hour to  one hundred thousand m3/hour , while the pressure can be normal pressure to nearly 20MPa; and the liquid temperature can be as low as -200℃ or as high as 800℃. The fluid being transferred can be water (clean or sewage), oil, acid or alkali, suspension or liquid metal, etc. Therefore, centrifugal pumps are used across numerous industries:

  1. In the oil and gas or chemical industries, converting crude oil to products requires a complex process. Pumps play an important role in transferring these liquids, providing the required pressure and flow rate for chemical reactions. Sometimes, pumps are used to adjust temperature in certain parts of the system.
  2. In agriculture, centrifugal pumps are used in the majority of irrigation machinery. Agriculture pumps make up half of the total amount of centrifugal pumps being used today.
  3. In mining and metallurgy industries, centrifugal pumps are the most widely used equipment, for draining, and cooling of water supplies, etc.
  4. For power generation, the nuclear power plants need large amounts of primary, and secondary system pumps, while the thermal power plants also need boiler feed pumps, condensate pumps, loop pumps and as well as ash pumps.
  5. In military applications, the adjusting of airplane wings and rudders, turning of turret on ships and tanks, the up and down of submarines, all rely on pumps for hydraulic fluids.
  6. In shipbuilding, there are more than 100 different types of pumps in one typical ocean ship.
  7. Other applications include municipal water supplies and drainage; water supplies of locomotives; lubricating and cooling of machining equipment; bleach and dye transfer of textile industry; and milk and beverage pumping and sugar refining in the food industry.

 

Centrifugal pumps can be classified based on the number of impellers in the pump:

A single-stage pump, with only one impeller, is commonly used for high flow and low to moderate total dynamic head, as in Figure 1.

Single Stage Centrifugal Pump
Figure 1. Single Stage Centrifugal Pump

A multi-stage pump has two or more impellers working in a series to achieve higher total dynamic head.
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Torsional Transient Analysis of a Single Piston Engine

In reciprocating engines, the reciprocating motion of pistons is transformed into a rotating motion of the crankshaft, which is responsible for the drive of a whole engine system. Instantaneous torque excitation due to gas forces after firing on the shaft system have to be investigated to ensure proper functioning. A typical torque function over the crankshaft angle can be seen in Figure 1.

Tangential forces acting on the crankpin
Figure 1 Example of tangential forces acting on the crankpin (Mendes, A., S.; Zampieri, D.E.; Siqueira Meirelles, P.: Analysis of torsional vibration in internal combustion engines: Modelling and experimental validation) and implementation in AxSTREAM RotorDynamics™ (orange curve)

Such a 720°-periodic function can be created in AxSTREAM RotorDynamics™, which provides a transient approach to determine the response torque in the shaft after a respective torque excitation. In this example, a rotor speed of 3000 rpm is considered. With this information, the total time for two crankshaft-revolutions (720°) reads:
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The What, Where and How of Wind Power

Choosing how to start something is often the most challenging part since the rest is usually about moving with the flow (turbomachinery pun intended). So, now that we got that out of the way let’s talk about our next topic after we do a quick flashback on the previous episodes of this Clean Energy series.

In the first post in this series, we discussed clean energy as a whole. After describing what it is and what it is not, we pointed out some of the energy sources we would analyze in subsequent articles.

The second post in this series took us on an extraterrestrial journey for two reasons: we looked at solar energy and we also went on a tangent about the rovers operating on planet Mars. I got so many “Likes” on these little droids that I figured I would keep going with them (that or I found a cool article that I’ll be sharing here) for this current post on one of the fastest-growing energy sources in the world: Wind Energy. What’s the link between Mars equipment and wind? See this recent discovery – https://www.space.com/41023-mars-wind-power-landers-experiment.html

Side note: ever wondered what would happen if the sun just blinked out? Check it out here – https://what-if.xkcd.com/49/

The wind we are looking at in today’s post is somewhere in between bovine flatulence and hurricanes in terms of intensity. Wind as we know it is created by air (or any fluid) moving from a zone of high pressure to one of low pressure. This high-to-low concentration migration might sound tricky, but it is easy to understand if you think of cars on a highway. It is more likely that cars stuck in a slow lane on the highway would move on to a lane with less traffic rather than the other way around.

Pressure varies with things like irregularities on the Earth surface, AKA altitude (“in case loss of cabin pressure occurs, oxygen masks will drop […]”), but also with temperature. This means that two people at the same altitude but in areas of different temperatures would experience different pressures. For example, think of standing at the North Pole vs. standing on a Caribbean beach vs. standing on a paddleboard in the Great Lakes. This example of standing at different places demonstrates the uneven heating of the Earth from the sun due to its shape (not flat), its rotation and its tilt, as we introduced in the previous post. But which location is under the most pressure? Colder temperature equals higher pressure.  Let me explain with another analogy, (even though this example has nothing to do with pressure, it will help the information stick).  When people get stressed, we say they are under pressure.  We can imagine somebody above the Arctic Circle is more stressed (cold, where to find food, shelter, etc.) than somebody enjoying a Mai Tai on the beach at an all-inclusive resort in Aruba. So here is your mnemonics; colder equals higher pressure.

Wind creation example
Figure 1 Wind creation example – http://www.ei.lehigh.edu/learners/energy/wind1.html 

Now that we have seen what wind was and the theory behind how it forms, we can start thinking about how to utilize this energy. Today we will talk about the aerodynamic aspect of wind turbines while in a future post we will be focusing on the assessment of such technology as wind power; pros, cons, where, what, etc.
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1.2 Optimization of Complex Technical Devices

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1.2.1 Design Hierarchy

Block-hierarchical representation of the design process, implemented with the creation of complex technical devices, leads to a problem of such complexity that can be effectively resolved by means of modern computing, and the results of the decision – understood and analyzed by experts. Typically, the design hierarchy of tasks is formed along functional lines for turbine can have the form shown in Fig. 1.1.

Hierarchy of Turbine Design Problems
Figure 1.1 Hierarchy of turbine design problems
Nearby Hierarchy Levels of Optimization Problems
Figure 1.2 Nearby hierarchy levels of optimization problems.

The uniformity of mathematical models of the subsystems of the same level and local optimality criteria make it possible to organize the process of multi-level design, providing maximum global quality criterion of the whole system, in our case – the turbine. This process is based on the idea of so-called multilevel optimization approximation scheme that involves aggregation of mathematical models of the subsystems in the hierarchy when moving upward and disaggregation based on optimization results when moving downwards.

The problem of optimization the subsystem parameters described by OMM has the form (1.5). It can be solved by the methods of nonlinear programming and optimal control, depending on the form of the equations and the optimality criterion of the OMM.
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Anti-Icing Systems for Land Based Gas Turbines

It is very important to have Anti-Icing Systems for ground-based gas turbines located in humid climates (where air relative humidity can be more than 80% and dense fog can cause air temperatures to drop below 5 0C). Such climatic conditions lead to ice formation. This ice can plug the inlet filtration system causing a significant drop in pressure in the inlet system, which in turn leads to performance loss. In extreme cases, there is even a possibility that the ice pieces get ingested into the compressor (first blade stage) which may cause foreign object damage. Ice may also cause the disruption of compressor work because of excessive vibration, or surging by decreasing the inlet flow. The major factors that lead to the ice formation in gas turbines are ambient temperature, humidity and droplet size. So, under the climatic conditions which are prone to ice formation, an anti-icing system is employed which heats the inlet air before entering the compressor. Let us discuss some important aspects of Anti-Icing Systems.

The objective of an Anti-Icing System is to prevent or limit the ice formation in the gas turbine inlet path.

Gas turbine image

Gas Turbine Anti-Icing Systems (GT-AIS) can be categorized in two groups.

  1. Inlet heating systems
  2. Component heating systems


Inlet heating systems operate by transferring heat from a heat source (exhaust gases can be used) to the cold ambient air at the entrance of the gas turbine. If the temperature of inlet air raises sufficiently by this heat transfer, icing cannot form in the gas turbine intake.

AxCYCLE™ is a tool, which provides the flexibility and convenience to study various parameters and understand the performance of thermodynamic cycles.

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Torsional Analysis of a Four-Stroke Engine

Reciprocating machines fall into many categories. Despite different applications and designs, e.g. pumps or internal combustion engines with a varying number of pistons, a simple approach to determine torsional modes of regardless which crankshaft assembly can be investigated. The resulting natural frequencies are required by ISO 3046 for rotor dynamic analysis.

Internal Combustion Engine with piston and flywheel geometry
Figure 1 Internal Combustion Engine with piston and flywheel geometry, (https://www.quora.com/What-is-a-starter-flywheel)

Below, a common way to express a crankshaft assembly with massless shaft and mass-inertia elements is presented, whereas the reciprocating and revolving mass around the crack can be expressed as follows:
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Steam Turbine Seal Leakage Calculation in Design

Steam turbine seals are parts inserted between moving and stationary components, to reduce and prevent steam leakage and air leaking into the low pressure areas. The leakage can happen through vane, gland, and shaft, etc. To reduce leakage from those parts while guaranteeing smooth operation of a steam turbine, engineers have to design these seals, taking into account not only efficiency, but also mechanical strength, vibration and cost.

As an example, steam turbine flow path seals improve overall efficiency installing various types of shrouds, diaphragms, and end seals which prevent idle leaks of working steam in the cylinders. In steam turbines, labyrinth seals are widely used. Some labyrinth seals are also used with honeycomb inserts. It is believed that the use of such seals makes it possible to achieve a certain gain due to smaller leaks of working fluid and more reliable operation of the system under the conditions in which the rotor’s rotating parts may rub against the stator elements. However, we can only consider it as a successful design if the structures are compliant with the manufacturing capabilities and have good vibration stability. [1] Furthermore, seal leakage can significantly affect efficiencies. Better seals increase efficiencies but add extra cost to both manufacturing and maintenance, so the design needs to be done with the turbine flow path design. Although modeling the seals in 3D CFD is theoretically possible, the calculation resources and time are extremely demanding.

This important task can be completed very easily with AxSTREAM NETTM. AxSTREAM NETTM provides a flexible method to represent fluid path and solid structure as a set of 1D elements, which can be connected to each other to form a thermal-fluid network. For each fluid path section, the program calculates fluid flow parameters for inlet and outlet cross-sections, like velocity, density, temperature, mass flow rate, etc. Therefore, the leakage from the whole system can be modeled in this network, as shown in Figure 1.

Steam Turbine Seal Leakage Calculation with AxSTREAM NET
Figure 1. Steam Turbine Seal Leakage Calculation with AxSTREAM NET™

AxSTREAM NET™ is capable of doing:

  1. Choice of seal design at the stage of the steam/gas turbine preliminary design.
  2. Calculation of balances of pressures and mass flow rate to correctly account for the efficiency of the steam/gas turbine.
  3. Calculation of seals fluid flow parameters on the startup mode to estimate the thermal expansion of rotor and casing element.
  4. Calculation of thermal boundary conditions for thermo stresses estimation.

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Steam Turbine Aerodynamic Improvements for Significant Efficiency Gains

The steam turbine is one of the most important power generating equipment items in use. Around half of the electricity generated worldwide comes from steam turbines. Steam turbines can be fueled by coal, nuclear energy, petroleum or natural gas, alternatively by biomass, solar energy or geothermal energy. Thus a large amount of fuel can be saved and CO2 emissions significantly reduced by optimizing key components of these widely used machines.

An important goal in steam turbine technology is to improve efficiency. The continuous flow of steam conditions is one of the commonly accepted efficiency contributor for steam power plants. The chart below shows expected improvement in thermal efficiency for USC double-reheat fossil-fuel power units compared to common supercritical-pressure ones, according to Hitachi.

Expected Improvement in Thermal efficiency for USC power units
Figure 1: Expected improvement in thermal efficiency for USC power units.

Besides steam condition elevation, other areas help the development and refinement of innovative aerodynamic flow path design approaches and the improvement of design procedures for nozzle and blades design and analysis. Continuous growth of steam conditions since the mid-1990s and some advanced steam path design for large steam turbines have brought about 5% of efficiency gain. This effect is almost the same as the transition from subcritical-pressure steam conditions to the supercritical-pressure ones with elevated steam temperatures illustrated in the figure above. Here are some practical examples of steam turbines high efficiency, achieved during the last decade by advanced aerodynamic design (source: Leizerovich, A. Sh. Steam turbines for modern fossil-fuel power plants, ©2008 by The Fairmont Press).
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