Computational Fluid Dynamics for Centrifugal Compressors

In today’s world where “time is money,” each and every industry involving turbomachinery wants to deliver their high performance products in the quickest time possible. Computational fluid dynamics (CFD) replaces the huge number of testing requirements thus not only shortening the design cycle time, but also reducing development costs.

Today with advancements in computational resources, numerical methods, and the availability of commercial tools, CFD has become a major tool for the design phase of a project. With a large number of validations and bench markings available on the applicability of CFD for centrifugal compressors, it has become an indispensable tool for the aerodynamic designer to verify the design and understand the flow physics inside a compressor’s flow path. However, CFD is still computationally expensive and requires a high level of user-knowledge and experience to get meaningful results. CFD analysis can be performed with and without considering viscous effects of the flow. The inclusion of viscosity into the flow introduces additional complexities for choosing the most appropriate turbulence closure model. CFD however, has some limitations due to:

  • – Errors created during modeling where the true physics are not well-known and are very complex to model.
  • – Multiple approximation and model errors created during the calculation process (such as mesh resolution, steady flow assumption, turbulence closure, geometric approximation, unknown boundary profile etc.). These approximations impact the calculations of local values of vital parameters.

In CFD for example, if the 1D design is not accurate, (stage loading and blade diffusion factors etc.), then CFD cannot turn out a good design. It is critical to use a design tool such as AxSTREAM®  which can generate optimized designs with less time and effort starting from the specification.

The preliminary design modules of AxSTREAM® uses inverse design tasks to generate the initial flow path for the centrifugal compressor. By choosing the right combination of geometrical and design parameters from the start, AxSTREAM® reduces the number of design cycle iterations required in generating an accurate design.

This initial design obtained is further analyzed and optimized using throughflow solvers in AxSTREAM® which considers various operating conditions. The throughflow solvers in AxSTREAM®  predict the performance parameters at different sections and stations, and presents the blade loading, flow distribution along the flow path, etc.

The generation of 3D geometry for the impeller and diffuser is another complex activity which is greatly simplified by using the radial profiler and 3D blade design module in AxSTREAM®. The geometry generated in AxSTREAM® is fully parameterized with complete control for the user to modify as and when required. Figure 1 shows a parameterized impeller geometry generated using seven spanwise sections with contours of the curvature.

Parameterized Impeller Geometry
Figure 1. Parameterized Impeller Geometry

In CFD analysis of turbomachines, grid generation becomes a very challenging task due to the geometries of complicated, twisted blades. To achieve reliable CFD results, the grid must resolve the topology accurately to preserve this geometric information. The quality of the grid should be in an acceptable range especially the angle, aspect ratio, and skewness of the grid elements. Automatic mesh generation tools are employed to reduce the turbomachines meshing complications. The AxSTREAM® platform uses AxCFD™ to generate a high quality mesh in considerably short time which captures the accurate flow features.

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Volute Design in AxSTREAM®

Volutes are a tangential part, resembling the volute of a snail’s shell, which collects the fluids emerging from the periphery of a pump/compressor impeller. As such, they are utilized ubiquitously in turbomachinery applications. The words “volute”, “scroll”, “spiral collector”, “housing”, “casing”, “collector chamber”, and “collector” are used interchangeably across different industries. This elegant geometry is also found in nature – the snail is just one example.

Volute in AxSTREAM with Snail Example
Figure 1 – Volute in AxSTREAM® on the left; on the right – Snail – Natural Occurrence of Such Shape

There is a large number of different volute types and applications: centrifugal pumps, axial pumps, centrifugal compressors, axial-flow compressors, radial-inflow turbines, radial fans, and multi-stage blowers, to name a few. Within each group, there is a narrower division on volute types and every application has its own unique features as well as specific properties that can be shared among the group members. The purpose of this post is not to have a detailed discussion of every possible scenario, but rather to show a robust and proven method of volute geometry construction working as a part of aerodynamic design and analysis in a system such as AxSTREAM®.

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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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1.3 Building Subsystems FMM

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Key Symbols
Indexes and Other Signs
Abbreviations

1.3.1 FMM Basics

As noted, the FMM is an approximation of the original model, which means it can be obtained by statistical processing of the results of numerical experiment using OMM. The complexity of solving the equations of the original model forces minimize the number of sampling points, which is practically achieved by using methods of the theory of experiment design. Get the response function in the form (1.2) can, in particular, on the basis of three-level Box and Benken plans [1]. Special selection of sampling points on the boundary of the approximation:

Formula 1.11
Formula 1.11

and in its center possible in accordance with the least squares method to obtain the values of the coefficients according to (1.2), without resorting to the numerical solution of the normal equations. The number of sampling points is in the range from 13 at N = 3 to 385 at N = 16.

Similarly, relations (1.2) can also be obtained by using the three-level saturated plans by Rehtshafner [2]. In this case, the dimension of the observation vector will vary from 16 at N = 4 to 232 at N = 20. The feature of these plans is that it is the most economical plans that require a minimum number of calculations to generate a vector of observations, i.e. the number of calculations (experiments) equal to the number of the coefficients according to (1.2).
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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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Key Symbols
Indexes and Other Signs
Abbreviations

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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