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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1.1 Mathematical Models and the Object Design Problem

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The methodology of a turbine optimal design as a complex multi-level engineering system should support the operation with diverse mathematical models, providing for each design problem communication between the neighboring subsystems levels.

One approach to turbine design with using of block-hierarchical representation consists in the transition from the original mathematical models for the subsystems and numerical methods of optimization to “all-purpose” mathematical model and general method of parameters optimization.

We will specify as original the mathematical model (OMM), which is a closed system of equations that describe the phenomena occurring in the designed object.

Regardless of the mathematical apparatus (algebraic, ordinary differential, integral, partial differential equations, etc.), OMM can be represented symbolically as follows:

Formula 1.1
(1.1)

where  X ⃗={x ⃗,u ⃗ };L(B ⃗,X ⃗) – the operator defining the model’s system of equations.

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Aerospace Industry and Propulsion Advancements – A Teaser for the Farnborough International Airshow

Due to technological advancements in the aerospace industry, air transportation has become the primary means of travelling. This begs the question of “what are the key factors that could push the industry to the next level and allow for higher performance, low cost and low carbon emission flights?”

Airplane - Aerospace

For a low carbon aviation to be achieved, a lot of effort is currently put on the aircraft-propulsion integration. Low-pressure-ratio fans are one of the concepts that is being studied in this regard. The lower the pressure across the propulsive element the more the exhaust velocities will decrease and therefore the higher the propulsive efficiency will be. However, a constant level of thrust would require an increase of the fan area, which could lead to an increase of the total weight of the configuration and ultimately cancel the efficiency benefits of the concept.
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Organic Rankine Cycles: Low Temperature, High Efficiency

Nowadays the scientific community is strongly concerned about problems of efficiency increase and emissions reduction in power generation, ship, and vehicle drives such as internal combustion engines (ICE). A system utilizing waste heat recovery (WHR) is an effective solution for the aforementioned problems.

ORC (meaning organic Rankine cycle, not the scary monsters from Lord of the Rings) is one WHR solution which delivers additional power from the turbine/engine exhaust gas/steam energy.  ORC systems operate on hydrocarbon-based fluids which effectively avoid the typical disadvantages associated with water-based steam turbine systems while bringing the advantage of better performance at part load and in non-continuous operation. ORC systems, capable of utilizing low temperature heat sources of 100-200°C, can be designed in compact and modular packages which require very little maintenance.

The design criteria of an ORC system and its components includes finding the maximum possible heat recovery from the available high and low temperature waste heat flows of a turbine or ICE to produce the maximum amount of additional power while decreasing the load on the turbine’s cooling system, under certain restrictions like geometry and cost.

The first step is to design the thermodynamic cycle configuration. Figure 1 is a flow diagram of a dual loop supercritical organic Rankine cycle (SORC) with separate turbines and given design parameters of the components, generated with AxCYCLE™ software, developed by SoftInWay. The cycle consists of 6 heat exchangers, 2 turbines (HPT and LPT), 2 pumps (HPP and LPP) and the condenser. Both turbines operate with the same backpressure – 1.3 bars. The flows of the working fluid (R245fa in this case) are mixed at the condenser inlet and split at its outlet. The temperature – entropy diagram for the presented cycle is shown on Figure 2. The process 1-2-3-4-5-1 corresponds to the high pressure loop operation and the process 10-20-30-40-10 is for the low pressure loop operation. All these can be easily manipulated and obtained with user-friendly interface of AxCYCLE™.

Flow Diagram - ORC CYCLE
Figure 1. The flow diagram of the SORC with separate turbines
The T-S Diagram for the SORC with separate turbines
Figure 2. The T-S Diagram for the SORC with separate turbines

In terms of component design, ORC turbines can be of axial, radial inflow and radial outflow configurations. The type of turbine you should select depends on the application. To delve further into the topic, check out  SoftInWay’s webinar on “Radial Inflow versus Outflow Turbines – Comparison, Advantages and Applicability” here – http://learn.softinway.com/Webinar/Watch/102
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