2.1 Equations of State

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Abbreviations

The equation of state can be written in different forms depending on the independent variables taken. Numerical algorithms should allow to calculate and optimize the axial turbine stages, both with an ideal and a real working fluid. It uses a single method of calculating the parameters of the state of the working fluid, in which as the independent variables are taken enthalpy i and pressure P:

For a perfect gas equation of state with P and i variables are very simple:

For the water steam approximation formula proposed in [7] is used, which established a procedure to calculate parameters of superheated and wet fluid. It is easy to verify that the knowledge of the value of the velocity coefficient Read More

1.5 The Practice of Numerical Methods Usage for Local Leveled Optimization Problems Solution

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To solve demanded by practice of axial turbines design multi-criteria problems, multi-parameter and multi-mode optimization of the multistage flow path further development and improvement of appropriate numerical methods and approaches required.

It should be noted some features of numerical solution of problems related to the optimization of design objects based on their modes of operation, multi-modal objective functions, as well as issues related to the multi-objective optimization problems.

Some aspects of the above problems solutions are given below.

1.5.1 Solution of the Multi-Criteria Optimization Problems

Set out in section 1.4 are the basic optimization techniques. However, depending on the formulation of the optimization problem, as well as the selected design object there are some features of numerical implementation of these methods and their applications.

It is known that the actual design object is usually characterized by a number of quality indicators and improvement in one of them leads to a deterioration in values of other quality criteria (Pareto principle). In such cases it is necessary to consider the optimization problem from many criteria.

The authors offer a well-established practice in solving multi-objective optimization problems – “convolution” of partial objective function weighted by u depending on the importance of a particular quality criteria in a comprehensive quality criteria based on the following:

Formula 1.37

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1.4 Optimization Methods

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Abbreviations

1.4.1 General Information About the Extremal Problems

To solve problems with the single criterion of optimality rigorous mathematical methods are developed.

Direct methods of the calculus of variations – one of the branches of the theory of extreme problems for functional – reduce the problem of finding the functional extremum to the optimization of functions.

There are analytical and numerical methods for finding optimal solutions. As a rule, the real problems are solved numerically, and only in some cases it is possible to obtain an analytical solution.

Functions optimization using differentiation

Finding the extremum of the function of one or more variables possible by means of differential calculus methods. It’s said that the   point gives to function f (x) local maximum, if there is a number Ɛ>0 at which from the inequality | x-x̂| < Ɛ the inequality f (x) ≤ f (x̂) comes after.

The function is called one-extremal (unimodal) if it has a single extremum and multi-extremal (multimodal), if it has more than one extremum. The point at which the function has a maximum or minimum value of all local extrema, called a point of the global extremum.

A necessary condition for an extremum of a differentiable function of one variable gives the famous Fermat’s theorem: let f  (x) – function of one variable, differentiable at the point x̂. If x̂ – local extreme  point, then f’ (x̂) = 0.

The points at which this relationship is satisfied, called stationary. The stationary points are not necessarily the point of extreme. Sufficient conditions for the maximum and minimum functions of one variable – respectively f” (x̂) <0,  f” (x̂) > 0.

Before proceeding to the necessary and sufficient conditions for extrema of functions of several variables, we introduce some definitions. The gradient of function f  (x) is a vector

Formula Chapter 4

The real symmetric matrix H is called positive (negative) defined if XT = Hx>0(<0) for every set of real numbers x1 , x2, …. xn, not all of which are zero. Read More

Computational Fluid Dynamics for Centrifugal Pumps

Pumps are important for many common systems which deal with water, such as heating circulating flows, consumer or industrial water supply, fountains, and fire protection systems.

Pumps are classified into two major categories: Rotodynamic pumps and positive displacement pumps (piston pumps). Rotodynamic pumps can be further classified as axial pumps, centrifugal (radial) pumps, or mixed pumps.

Centrifugal pumps are the devices which impart energy to the fluid (liquid) by means of rotating impeller vanes, and the fluid exits radially from the pump impeller. Such pumps are simple, efficient, reliable, relatively inexpensive, and easily meet the pumping system requirements for filtration. This is a great pump choice for moving liquids from one place to another using pressure.

Types of Rotodynamic Pumps
Figure 1. Types of Rotodynamic Pumps

Centrifugal Pump Design

A centrifugal pump is a very common component in turbomachines, but as with any component, it still needs continual improvement in the design methodology, from conceptual level to the final product development including testing at different levels. The challenge is to design a pump with improved efficiency while minimizing the possibility of cavitation.

Need of Numerical Simulation

Years ago, engineers performed prototype testing at each level of design to check the performance (which was very costly and time consuming). Now with advancements in the computation technology and resources, it is comparatively easier to design high efficiency pumps within a short duration of time. These simulations can be done with a computer, so, the number of physical prototypes required is greatly reduced. The main advantage of numerical simulation is that it allows engineers to virtually test the CAD model early in the design process, and provides flexibility for engineers to iterate the design until getting the required performance.

Computational Fluid Dynamics for Centrifugal Pumps

Computational fluid dynamics (CFD) replaces the huge number of testing requirement. This not only shortens the design cycle time but also significantly reduces development cost.

In a CFD model, the region of interest, a pump impeller flow-path for example, is subdivided into a large number of cells which form the grid or mesh. The PDEs (partial differential equations) can be rewritten as algebraic equations that relate the velocity, pressure, temperature, etc. in a cell to those in all of the cell’s immediate neighbors. The resulting set of equations can then be solved iteratively, yielding a complete description of the flow throughout the domain.

To accomplish CFD simulations, there are several software programs available, but user must select a very well validated software that can provide and easy user interface, automatic mesh generation and flexibility to modify the geometry to perform optimization without needing to move to some other software platform.

In the current trend, automatic mesh generation tools like AxCFD™ are employed in the AxSTREAM® software platforms which reduces the turbomachines meshing complications and generate good quality mesh in considerably short timeframe which can capture the accurate flow features needed. Figure 2 shows the discretized impeller and pressure contour after CFD analysis.

Discretized Impeller and Pressure Contour After CFD Analysis
Figure 2. Discretized Impeller and Pressure Contour After CFD Analysis

AxCFD™, in AxSTREAM® platform, provides user an opportunity to perform CFD analysis by applying standard methods of full three-dimensional CFD, axisymmetric CFD (meridional), and blade-to-blade analysis. User can even perform optimization of the blade profiles and other geometrical parameters within the AxSTREAM® platform and perform CFD simulation without altering any CFD settings.

An Introduction to Accurate HVAC System Modeling

HVAC (Heat, Ventilation and Air Conditioning) is all about comfort, and comfort is a subjective feeling associated with many parameters like air quality, air temperature, surrounding surface temperature, air flow and relative humidity. For example, while it is easy to understand how the temperature of the air in your living impacts how good you feel, the surfaces with which you are in contact also strongly affect your comfort. For example, last night I got out of bed to clean up after my dog who thought it would be a good idea to swallow (and give back) her chew toy. If I was wearing my slippers, it would have been much easier to go back to sleep between the warm bed sheets without the discomfort of waiting my cold feet warm up to normal temperature.

Speaking of sleep discomfort, many stem from HVAC imbalances.  If you wake up in the middle of the night quite thirsty, then you should probably check how dry your bedroom is. The recommended range is 40-60% relative humidity. A higher humidity puts you at risk for mold while lower humidity can lead to respiratory infections, asthma, etc.

Now that we know how HVAC contributes to our comfort, let’s look at the HVAC unit as a system and see its role, functioning and simulation at a high level. The following examples provided are for a house, but similar concepts apply to residential buildings, offices, and so on.

Controlling Temperature

The easiest parameter to control is the air temperature. It can be set by a thermostat and regulated according to a heating or cooling flow distributed from the HVAC unit to the different rooms through ducting. Without the introduction of thermally-different-than-ambient air, the house will heat or cool itself based on a combination of outside conditions and how well the building is insulated. Therefore, to keep a constant temperature a certain amount of energy must be used to provide heating (or cooling) at the same rate the house is losing (or gaining) heat.  This is a match of the house load and heating/cooling capacity. Figure 1 provides a graph of the energy needed.

Illustration of dependency of house load and heating capacity on outside temperature
Figure 1 Illustration of dependency of house load and heating capacity on outside temperature

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Turbojets – Basics and Off-design Simulation

The Brayton cycle is the fundamental constant pressure gas heating cycle used by all air-breathing jet engines. The Brayton cycle can be portrayed by a diagram of temperature vs. specific entropy, or T–S diagram, to visualize changes to temperature and specific entropy during a thermodynamic process or cycle. Figure 1 shows this ideal cycle as a black line.  However, in the real world, the compression and expansion processes are never isentropic, and there is always a certain pressure loss in the combustor.  The real Brayton cycle looks more like the blue line in Figure 1.

Ts_Real_Brayton_Cycle
Figure 1 T-S diagram for ideal and real Brayton cycle
(Source: https://commons.wikimedia.org/wiki/File:Ts_Real_Brayton_Cycle_2.png)

The four stages of this cycle are described as:

1-2: isentropic compression

2-3: constant pressure heating

3-4: isentropic expansion

4-0: constant pressure cooling (absent in open cycle gas turbines)

The most basic form of a jet engine is a turbojet engine. Figures 2a and 2b provide the basic design of a turbojet engine. It consists of a gas turbine that produces hot, high-pressure gas, but has zero net shaft power output. A nozzle converts the thermal energy of the hot, high-pressure gas at the outlet of the turbine into a high-kinetic-energy exhaust stream. The high momentum and high exit pressure of the exhaust stream result in a forward thrust on the engine. Read More

Design of a Competitive Axial Turbine for Downsized Turbocharged IC Engine

The following article was written by Lorenzo Baietta a student at Brunel University London and presented at the International CAE Conference Poster Competition in Vicenza, Italy. Lorenzo’s work placed 6th overall and 1st among articles written by a single author. We’re thrilled for Lorenzo and excited to continue supporting universities and young engineers all over the world. 

The continue research for engine efficiency improvements is one of the major challenges of the last decades, leading to the design of highly downsized boosted engines. Among other boosting strategies, turbocharging allows to recover part of the exhaust gas energy, improving the overall efficiency of the power unit. However, turbochargers lead to less responsive power units because of the widely known turbo-lag effect due to the inertia of the rotating parts in the system. With engine manufacturers testing different concepts to reduce this effect, for both commercial and motorsport applications, the work is about the development of a low inertia turbocharger axial turbine, evaluating pro and cons of several design solution. The idea is to initially evaluate the performance (mainly efficiency) difference between prismatic and twisted blades turbine for different size ranges. In fact, as one of the issue of axial turbines compared to radial ones is the production cost, the use of low aspect ratios blades, in such a way to minimize the difference between the use of 3D optimized turbines and prismatic turbines, should allow for more cost-effective solutions to be implemented.

After selecting a specific engine to develop the axial turbine, several CAE techniques were used to verify the idea and to obtain the best possible solution. The OEM turbocharger was 3D scanned, with a blue light technology stereoscopic optical system, to acquire accurate geometry data and calculate several properties. A 1D engine model, calibrated on the dyno, was used to calculate the aerothermal boundary conditions for the design of the turbine every 1000rpm from 1000 to 6000 to have all the required boundary conditions data to design/test the turbine at different engine operating points.

Several turbines were preliminary designed and optimized with AxSTREAM® and their performances were evaluated considering many parameters, mainly focusing on the reduction of the turbocharger spool-up time. The AxSTREAM® preliminary design module resulted crucial to compare the performance of over 1 million turbines allowing the comparison of the results with different loss models and a wide number on flow boundary conditions and geometrical constraints.

Turbine Design Methodology – Preliminary Design in AxSTREAM

The generated turbine preliminary CAD and the scanned OEM turbine mesh were used along with CAM programs at an external company to estimate the production cost of different solutions. A final turbine design was chosen, among the pre-designed ones, to be validated with generation of complete maps within the AxSTREAM® streamline solver which allowed an initial verification of the suitability of the turbine for the desired application. A further optimization of the results was obtained with increasing precision CFD simulations in the AxSTREAM® Profiling and CFD modules. 2D cascade simulations were used to optimize the stator and rotor airfoils in the Profiling module. Then, in AxCFD™, axisymmetric CFD simulations were run at several operating points to quickly investigate the suitability of the generated design for the whole power unit operating range. To conclude, full 3D CFD and FEA simulations were conducted to obtain more accurate values and complete the design process of the turbine and finally compare the data of the newly designed turbine and the OEM one.

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Automotive Engine Lubrication System Modelling and Analysis

The lubrication system is one of the most important systems of an engine.

This system should ensure:

  1. Delivery of the required oil amount to the moving parts (e.g.-Bearings);
  2. Dissipation of the heat generated due to friction by circulation of lubricant throughout the system; and
  3. Cleaning of the oil from contamination and impurities introduced during engine operation.

 

To meet the above requirements, the lubricant circulation (lubricant reaching each component) should happen at appropriate pressure and mass flow rate throughout the system.  This is also required in order to avoid cavitation caused by adverse pressure, and excessive heat generation due to less mass flow rate, at any place or particularly at any component. However, sometimes lubricant does not circulate properly to each corner of the system or to the rotating components. In some cases, the rotation of the crankshaft can actually starve the bearings and increase the internal heat due to insufficient supply of lubrication.

To avoid such problems, simulation engineers must model the whole system at all operating modes. They can predict the best system by varying flow rates (volumetric or mass flow rates), system pressures, temperatures, heat flows, as well as by changing the system geometry itself. Such modelling can be performed easily and with sufficient accuracy in a 1D Thermal Fluid analysis tool, such as AxSTREAM NET™ developed by SoftInWay.

It is worthwhile to use a 1D-Analysis tool in this case, because it can be used at any stage of the system design process to explore more options for improving the final design and to reduce development cycle time. The simulation engineer can easily create a model of automotive engine lubrication system, using different elements (components) which are available in the element database of AxSTREAM NET™. The system configuration can also be easily changed at any stage in the design process without rebuilding the complex 3D models.

Let us try to understand how to build a 1D scheme for an automotive engine lubrication system in a 1D tool (AxSTREAM NET™). First, we need to identify the major elements (components) which are part of the automotive engine lubrication system as per their order or sequence in the scheme. A typical engine lubrication system involves components like Oil – sump, strainer, pump and filter, all of which are parts of the initial oil suction line. In addition, the main gallery involves components like flow passages within the connecting rods, crankshaft, and bearings. The typical connections among these elements are shown in Figure 1.

Figure 1 Main elements of a lubrication system
Figure 1 Main elements of a lubrication system

Now let’s see the arrangement of a few components with their specific purposes towards the construction of the whole model.

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Tidal Energy

If you’re looking for clean, free energy… a song comes to mind.

Tide after tide.
If you flow I will catch – I’ll be waiting.
Tide after tide.

With no particular link to Cyndi Lauper, waves just want to have fun so let’s allow them to do so while catching their drift as a potential energy source using tidal turbines.

Introduction:

Wave energy is a form of hydropower used to convert energy obtained from tides into mechanical and/or electrical power. Wave energy is produced when electricity generators are placed on the surface of the ocean. The energy provided is most often used in desalination plants, power plants and water pumps. Energy output is determined by wave height, wave speed, wavelength, and water density.

sea wave during storm
Figure 1 Ocean Waves

How are Tides Generated:

Tidal forces are periodic variations in gravitational attraction exerted by celestial bodies. It is these forces that are responsible for the currents in the world’s oceans. A local, strong attraction on a part of the ocean allied with moving celestial bodies and the rotation of the Earth leads this bulging part of water to meet the adjacent shallower waters of the shoreline which creates the tides.

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Turbine Blade Cooling – An Integrated Approach

It is a well-known fact in the turbomachinery community that the highest temperature achievable at the inlet of the turbine is a critical performance parameter for the turbine. For any given pressure ratio and adiabatic efficiency, the turbine specific work is proportional to the inlet stagnation temperature. Typically, a 1% increase in the turbine inlet temperature can cause a 2-3% increase in the engine output.

Increase in net power output of a gas turbine over a one percentage point rise in turbine inlet temperature
Figure 1 Increase in net power output of a gas turbine over a one percentage point rise in turbine inlet temperature

The major limitation for the maximum achievable value of the turbine inlet temperature comes from the material used for the turbine. The maximum material temperature has to be kept in check for multiple reasons, from the physical integrity to the structural reliability, and resulting temperature needs to be less than the turbine blade material’s maximum temperature.

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