3.1 Analytical Solutions

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Indexes and Other Signs
Abbreviations

An important objective in the design of a multi-stage axial turbine is to determine the optimal number of stages in the module and the distribution of heat drop between stages.

Typically, a given quantity is the module’s heat drop, and should vary the number of stages and the rotational speed (diameter). It should be understood that the circumferential velocity reduction, and hence the diameters of the stages, reduces the disc friction losses, increase height of the blades (and therefore reduce the proportion of end losses), decrease the flow path leakage. At the
same time it leads to an increase in the optimal number of stages, which causes an increase in losses due to discs friction and an additional amount of the turbine rotor elongation. Immediately aggravated questions of reliability and durability (the critical number of revolutions), materials consumption, increase cost of turbine production and power plant construction.

A special place in the problem of the number of stages optimization is the correct assessment of the flow path shape influence, keeping its meridional disclosure in assessing losses in stages. As you know, the issue is most relevant for the powerful steam turbines LPC. It is therefore advisable for the problem of determining the optimal number of stages to be able to fix the form of the flow path for the LPC and at the same time to determine its optimal shape in the HPC and IPC.

It should also be noted that the choice of the degree of reaction at the stages mean radius (the amount of heat drop also associated with it) must be carried out with a view to ensuring a positive value thereof at the root. Formulated in this section methods and algorithms:

  • – May serve as a basis for further improvement of the mathematical model and complexity of the problem with the accumulation of experience, methods and computer programs used in the algorithm to optimize the flow of the axial turbine;
  • – Allow the analysis of the influence of various factors on the optimal characteristics of the module, which gives reason for their widespread use in teaching purposes, the calculations for the understanding of the processes taking place in stages, to evaluate the impact of the various losses components on a stage operation;
  • – Allow to perform heat drop distribution between stages and to determine the optimal number of stages in a module within the modernization of the turbine, i.e. at fixed rotational speeds (diameters) and a given flow path shape or at the specified law or the axial velocity component change along the cylinder under consideration.

A possible variant of the form setting of n stages group of the flow path can be carried out by taking the known axial and circumferential velocity components in all cross-sections, which the numbering will be carried out as shown in Fig. 3.1.

The sections numbering in the turbine flow part section,

The axial velocity components we refer to the axial velocity at the entrance to the stages group: Read More

Role of AxSTREAM® in Radial Turbine Design

Radial turbines are quite popular for turbochargers and micro-gas turbines. They can also be found in compact power sources like in auxiliary power units of aircrafts. In short, they are suitable in power generation applications where expansion ratios are high and mass flow rates are relatively small. In a radial turbine, the flow enters radially and exits either axially or radially depending on whether it is an inflow or outflow type radial turbine. The most commonly used type of radial turbine is a radial-inflow turbine, in which the working fluid flows from a larger radius to a smaller radius. A centripetal turbine is very similar in appearance to the centrifugal compressor, but the flow direction is reverse. Figure 1 shows the radial-inflow turbine on the left and radial-outflow turbine on the right.

Radial-inflow turbine on the left; Radial-outflow turbine on the right
Figure 1: Radial-inflow turbine on the left; Radial-outflow turbine on the right

Nowadays, the popularity of radial-outflow turbines, in which the flow moves in the opposite direction (from the center to the periphery), is growing. With recent advancement in waste heat recovery applications, there has been a renewed interest in this type of turbines. These radial-outflow turbines are most commonly used in applications based on organic Rankine cycles (ORC).

The radial-outflow turbine design was first invented by the Ljungström brothers in 1912, however it was rarely used for a number of reasons. One of which was related to the decrease of turbine-specific work due to the increase of the peripheral velocity from inlet to outlet while expanding the vapor. Another reason was the usage of steam as a working fluid. It is known from thermodynamics that the expansion of steam is characterized by high enthalpy drops, high volumetric flows and high volumetric ratios. Thus, a significant number of stages are needed to convert the enthalpy drop of the fluid into mechanical energy.

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Modern Approaches and Significance of Multiphase Flow Modeling

Introduction

Corresponding with the development of industrial technology in the middle of the nineteenth century, people  dealt with multiphase flows but the decision to describe them in a rigorous mathematical form was first made only 70 years ago. As the years progressed, development of computers and computation technologies led to the revolution in mathematical modeling of mixing and multiphase flows. There are a few periods, which could describe the development of this computation:

«Empirical Period» (1950-1975)

There were a lot of experiments which were done during this period. All models were obtained from experimental or industrial facilities which is why using them was difficult for different cases.

«Awakening Period» (1975-1985)

Because of sophisticated, expensive and not universal experiments, the researchers’ attention was directed to the physical processes in multiphase flows.

«Modeling Period» (1985-Present)

Today, the models for multi-flow calculation using the equations of continuity together with equations of energy conservation are obtained, which allow describing phase’s interaction for different flow regimes. (A.V. Babenko, L. B. Korelshtein – Hydraulic calculation two phase gas liquid course: modern approach // Calculations and modeling journal. – 2016. – TPА 2 (83) 2016. – P.38-42.)

Technology Development

Since the time of industrial development, installation designs have undergone great changes. For example, there are shell and tube evaporators for freeze systems where the heat transfer coefficient has increased 10 times over during the last 50 years. These results are a consequence of different innovation decisions. Developments led to research into mini-channels systems, which is the one of the methods to increase intensification of phase transition. Research has shown that heat exchange systems with micro and nano dimensions have a much greater effect than the macrosystems with channels dimensions ≤3-200 mm.

In order to organize fundamental research, it is very important to understand hydro, gas dynamics and heat changes in two-phase systems with the phase transition. At present, the number of researchers using advanced CFD-programs has increased. Our team is one of the lead developers of these program complexes.

Mathematical modeling of compressible multiphase fluid flows is interesting with a lot of scientific directions, and has big potential for practical use in many different engineering fields. Today it is no secret that environmental issues are some of the most commonly discussed questions in the world. People are trying to reduce the emissions of combustion products. One of the methods to decrease emissions is the organization of an environmentally acceptable process of fuel burning with reduced yields of nitrogen and sulfur. The last blog (http://blog.softinway.com/en/modern-approach-to-liquid-rocket-engine-development-for-microsatellite-launchers/) discussed numerical methods, which can calculate these tasks with minimal time and cost in CFD applications.

Waste Heat Boiler
Picture 1 – Waste heat boiler http://tesiaes.ru/?p=6291

For more effective use of energy resources and low-potential heat utilization, the choice of the Organic Rankine Cycle (ORC) is justified. Due to the fact that heat is used and converted to mechanical work, it is important to use a fluid with a boiling temperature lower than the boiling temperature of water at atmospheric pressure (with working flow-boiling temperature about 100⁰C). The usage of freons and hydrocarbons in these systems makes a solution impossible without taking into account the changes of working fluid phases. Read More

2.5 Thermal Cycles Modelling

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Abbreviations

Imagine the process of analyzing the thermal cycle in the example of gas turbine unit (GTU) (Fig. 2.18) in the following sequence:

  1. the structure diagram presentation as a set of standard elements and connections between them;
  2. entering the input data on the elements;
  3. generation of computer code in the internal programming language based on the chosen problem statement;
  4. processing;
  5. post-processing and analysis of results.

 

Figure 2.18 Thermal schemes graphical interactive editor window.
Figure 2.18 Thermal schemes graphical interactive editor window.

This sequence of actions combines a high degree of automation of routine operations (input-output and storage of data, programming, presentation of the results of calculations, and so on) with the possibility of human intervention in the process of calculations at any stage (editing of data, changing the program code in the domestic language, writing additional custom code for non-standard calculations performing, etc.).

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2.4 Flow Path Elements Macro Modelling

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Macromodels are dependencies of the “black box” type with a reduced number of internal relations. This is most convenient to create such dependence in the form of power polynomials. Obtaining formal macromodels (FMM) as a power polynomial based on the analysis of the results of numerical experiments conducted with the help of the original mathematical models (OMM).

Therefore, the problem of formal macro modelling includes two subtasks:

1. The FMM structure determining.
2. The numerical values of the FMM parameters (polynomial coefficients) finding.

As is known, the accuracy of the polynomial and the region of its adequacy greatly depend on its structure and order. At the same time, obtaining polynomials of high degrees requires analysis of many variants of the investigated flow path elements, which leads to significant computer resources cost and complicates the process of calculating the coefficients of the polynomial.

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2.3 Geometric and Strength Model

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Key Symbols
Indexes and Other Signs
Abbreviations

2.3.1 Statistical Evaluation of Geometric Characteristics of the Cascade Profiles

For accurate estimates of the size of the blades, which takes into account not only their aerodynamic properties and conditions of safe operation, it is required to calculate the set of dependent geometric characteristics of the profiles (DGCP) as a function of a number of parameters that determine the shape of the profile. When the shape of the profiles is not yet known, to assess DGCP should use statistical relations. From the literature are known attempts to solve a similar problem [25, 26] on the basis of the regression analysis.

The DGCP include: f – area; Ie and In minimum and maximum moments of inertia;Iu – moment of inertia about an axis passing through the center of gravity of the cross section parallel to the axis of rotation u; φ the angle between the central axis of the minimum moment of inertia and the axis u; Χgcgc the coordinates of the center of gravity;βi – stagger angle;lss – the distance from the outermost points of the edges and suction side to the axis Ε; linlout – the distance from the outermost points of the edges to the axis Ν; We, Wss, Win, Wout, – moments of profile resistance.

The listed DGCP values most essentially dependent on the following independent parameters (IGCP) β1g – geometric entry angle; β2eff – effective exit angle; – chord; t/b  – relative pitch; r1, r2 – edges radii; ω1, ω2 – wedges angles.

Formal macromodelling techniques usage tends to reduce the IGCP number, taking into account only meaningful and independent parameters. In this case, you can exclude from consideration the magnitude of  r1, r2, ω2 taking them equal r1 =0.03b; r2=0.01b ; ω2=0.014Kωω1/(0.2 +ω1) , Kω = 1…3 , depending on the type of profile [26].

We obtained basic statistical DGCP relationships using profiles class, designed on the basis of geometric quality criteria – a minimum of maximum curvature of high order power polynomials [15] involving the formal macromodelling technique. Approximation relations or formal macromodel (FMM) are obtained in the form of a complete quadratic polynomial of the form (1.2):

Formula for chapter 2.3

The response function y(q ⃗’) values (DGCP) corresponding to the points of a formal macromodelling method, calculated by the mathematical model of cascades profiling using geometric quality criteria.

Analysis of profiles used in turbine building reveals, that two of remaining four IGCP β1g and t/b highly correlated.

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Modern Approach to Liquid Rocket Engine Development for Microsatellite Launchers

Microsatellites have been carried to space as secondary payloads aboard larger launchers for many years. However, this secondary payload method does not offer the specificity required for modern day demands of increasingly sophisticated small satellites which have unique orbital and launch-time requirements. Furthermore, to remain competitive the launch cost must be as low as $7000/kg. The question of paramount importance today is how to design both the liquid rocket engine turbopump and the entire engine to reduce the duration and cost of development.

The system design approach applied to rocket engine design is one of the potential ways for development duration reduction. The development of the design system which reduces the duration of development along with performance optimization is described herein.

The engineering system for preliminary engine design needs to integrate a variety of tools for design/simulation of each specific component or subsystem of the turbopump including thermodynamic simulation of the engine in a single iterative process.

The process flowchart, developed by SoftInWay, Inc., integrates all design and analysis processes and is presented in the picture below.

Execution Process Flow Chart
Execution Process Flow Chart

The preliminary layout of the turbopump was automatically generated in CAD tool (Block 11). The developed sketch was utilized in the algorithm for mass/inertia parameters determination, secondary flow system dimensions generations, and for the visualization of the turbopump configuration. The layout was automatically refined at every iteration. Read More

2.2 Aerodynamic Models

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Key Symbols
Indexes and Other Signs
Abbreviations

2.2.1 Axisymmetric Flow in the Axial Turbine Stage

Assume that in the flow path of the turbine:

  • The flow is steady relatively to the impeller, rotating at a constant angular velocity ω about the z-axis or stationary guide vanes.
  • The fluid is compressible, non-viscous and not thermally conductive, and the effect of viscous forces is taken into account in the form of heat recovery in the energy and the process equations, i.e., friction losses are accounted energetically.
  • If the working fluid is real (wet steam) it is considered the equilibrium process of expansion.
  • the flow is axisymmetric, i.e., its parameters are independent of the circumferential coordinate.

Under these assumptions the system of equations describing the steady axisymmetric compressible flow motion, includes:

1. The equation of motion in the relative coordinate system in the Crocco form

2.6

2. Continuity equation

3. The equation of the process or system of equations describing the process

4. The equations of state

5. The equation of the flow surface

where n ⃗’ – normal to the S2 surface (Fig. 2.1).

6. The equation of blade force orthogonality to the flow surface

Projections of the vortex in the relative motion rot W ⃗’ = ∇ * W ⃗’ to be determined by the formulas:

Figure 2.1 The surfaces of the three-dimensional flow relative

Taking into account (2.12), projection of the equation of motion (2.6) on the axes of cylindrical coordinate system can be written as follows: Read More

Hydrodynamic Journal Bearings Optimization Considering Rotor Dynamics Restrictions

This is an excerpt from a technical paper, presented at the ASME Turbo Expo 2018 Conference in Oslo, Norway and written by Leonid Moroz, Leonid Romanenko, Roman Kochurov, and Evgen Kashtanov. Follow the link at the end of the post to read the full study! 

Introduction

High-performance rotating machines usually operate at a high rotational speed and produce significant static and dynamic loads that act on the bearings. Fluid film journal bearings play a significant role in machine overall reliability and rotor-bearing system vibration and performance characteristics. The increase of bearings complexity along with their applications severity make it challenging for the engineers to develop a reliable design. Bearing modeling should be based on accurate physical effects simulation. To ensure bearing reliable operation, the design should be performed based not only on simulation results for the hydrodynamic bearing itself but also, taking into the account rotor dynamics results for the particular rotor-bearing system, because bearing characteristics significantly influence the rotor vibration response.

AxSTREAM Bearing

Numbers of scientists and engineers have been involved in a journal bearing optimal design generation. A brief review of works dedicated to various aspects of bearing optimization is presented in [1]. Based on the review it can be concluded, that the performance of isolated hydrodynamic bearing can be optimized by proper selection of the length, clearance, and lubricant viscosity. Another conclusion is that the genetic algorithms and particle swarm optimization can be successfully applied to optimize the bearing design. Journal bearings optimizations based on genetic algorithms are also considered in [2-5]. The studies show the effectiveness of the genetic algorithms. At the same time, the disadvantages of the approach are high complexity and a greater number of function evaluations in comparison with numerical methods, which require significantly higher computational efforts and time for the optimization. A numerical evolutionary strategy and an experimental optimization on a lab test rig were applied to get the optimal design of a tilting pad journal bearing for an integrally geared compressor in [6]. The final result of numerical and experimental optimizations was tested in the field and showed that the bearing pad temperature could be significantly decreased. Optimal journal bearing design selection procedure for a large turbocharger is described in [7]. In this study power loss, rotor dynamics instability, manufacturing, and economic restrictions are analyzed. To optimize the oil film thickness by satisfying the condition of maximizing the pressure in a three lobe bearing, the multi-objective genetic algorithm was used in [8]. In the reviewed studies the optimization has been performed for ‘isolated’ bearing and influence on rotor dynamics response was not considered.

For higher reliability and longer life of rotating mechanical equipment, the vibration of the rotor-bearing system and of the entire drivetrain should be as low as possible. A good practice
for safe rotor design typically involves the avoidance of any resonance situation at operating speeds with some margins. One common method of designing low vibration equipment is to have a separation margin between the critical natural frequencies and operating speed, as required by API standard [9]. The bearing design and parameters significantly influence rotor-bearing system critical speeds. Thus, to guarantee low rotor vibrations, the critical speeds separation margins should be ensured at rotor-bearing system design/optimization stage

Conjugated optimization for the entire rotor-bearing system is a challenging task due to various conflicting design requirements, which should be fulfilled. In [10] parameters of
rotor-bearing systems are optimized simultaneously. The design objective was the minimization of power loss in bearings with constraints on system stability, unbalance sensitivities, and
bearing temperatures. Two heuristic optimization algorithms, genetic and particle-swarm optimizations were employed in the automatic design process.

There are several objective functions that are considered by researchers to optimize bearing geometry, such as:

– Optimum load carrying capacity [5];
– Minimum oil film thickness and bearing clearance optimization [1, 6, 8];
– Power losses minimization [6, 7];
– Rotor dynamics restrictions;
– Manufacturing, reliability and economics restrictions [7]

The most common design variables which are considered in reviewed works are clearance, bearing length, diameter, oil viscosity, and oil supply pressure.

Finding the minimum power loss or optimal load carrying capacity together with the entire rotor-bearing system dynamics restrictions, require to employ optimization techniques, because accounting the effects from all considered parameters significantly enlarge the analysis process. Several numerical methods, such as FDM and FEM are usually employed to solve this complex problem and calculation process can sometimes be time-consuming and takes a large amount of computing capacity. To leverage this optimization tasks, efficient algorithms are needed.

In the current study, the optimization approach, which is based on DOE and best sequences method (BSM) [11, 12] and allows to generate journal bearings with improved characteristics was developed and applied to 13.5 MW induction motor application. The approach is based on coupled analysis of bearing and entire rotor-bearing system dynamics to satisfy API standard requirements.

Problem Formulation and Analysis Methods Description

The goal of the work is to increase reliability and efficiency for the 13.5 MW induction motor prototype (Fig. 1) by oil hydrodynamic journal bearings optimization.

Rotor of 13.5 MW Induction Motor
Figure 1: Rotor of 13.5 MW Induction Motor

The motor operating parameters and rotor characteristics are presented below:

– Rated speed rpm: 1750
– Minimum operating speed rpm: 1750
– Maximum operating speed rpm: 1750
– Mass of the rotor kg: 6509
– Length of the rotor mm: 3500

Initially, for the motor application, plain cylindrical journal bearings were chosen to support the rotor. The scheme of the DE (drive end) and NDE (non-drive end) baseline bearings designs
is presented in Fig. 2. For baseline designs, bearing loads were 35 kN for DE and 28 kN for NDE bearing.

Plain Cylindrical Bearing
Figure 2: Plain Cylindrical Bearing

The methodology for the bearing characteristics simulation is based on the mass-conserving mathematical model, proposed by Elrod & Adams [13], which is by now well-established as the
accurate tool for simulation in hydrodynamic lubrication including cavitation.

Read full paper here 

Design of Waste Heat Recovery Systems Based on Supercritical ORC for Powerful Gas and Diesel Engines

This is an excerpt from a technical paper, presented at the ASME ORC 2015 Conference in Brussels, Belgium and  written by Oleksii Rudenko, Leonid Moroz, Maksym Burlaka, and Clement Joly.  Follow the link at the end of the post to read the full study! 

1. Introduction

Internal combustion piston engines are among the largest consumers of liquid and gaseous fossil fuels all over the world. Despite the introduction of new technologies and constant improving of engines performances they still are relatively wasteful. Indeed, the efficiency of modern engines rarely exceeds 40-45% (Seher et al. (2012), Guopeng et al. (2013)) and the remainder of the fuel energy usually dissipates into the environment in the form of waste heat. The heat balance diagram of typical engine is given in Figure 1. As is evident from Figure 1, besides the mechanical work energy the heat balance includes a heat of exhaust gas, a heat of charge air, a Jacket Water (JW) heat, a heat of lubricating oil and a radiation heat. The energy from all the heat sources except the last one (radiation), due to its ultra-low waste heat recovery potential, can be used as heat sources for WHRS (Paanu et al. (2012)) and are considered here.

Heat Balance Diagram
Figure 1: Typical heat balance diagram for CAT engine (Caterpillar (2011))

Waste heat utilization is a very current task because it allows to reduce the harmful influence of ICPE operation on the environment as well as to obtain additional energy and to reduce the load on the engine’s cooling system. Different WHRS can produce heat energy, mechanical energy or electricity and combinations of the converted energy forms exist as well. In general, the type of WHRS to be used is determined by the engine type, fuel cost, available energy customers and other factors. In the presented paper, only WHRS for mechanical power and electricity production were considered because these kinds of energy are preferable for this type of applications and they can be easily converted into other forms of energy.

For vehicle engines the WHRS based on Organic Rankine Cycle (ORC) are the most commercially developed (Paanu et al. (2012)). Because of strict restrictions on weight and dimensions, the
mentioned systems typically operate on the base of a simple or recuperated ORC and utilize only high temperature waste heat from the exhaust gases and the exhaust gas recirculation. They usually produce mechanical power or electricity. More complex cycles and a larger number of heat sources are used for waste heat recovery from powerful internal combustion engines where additional weight and dimensions are not crucial factors. Waste heat from stationary, marine and another more powerful ICPE can be recovered using a typical steam bottoming cycle. Steam WHRS allow utilizing almost all a high temperature waste heat and partially utilizing a low temperature heat. The high efficiency steam WHRS are presented in (MAN Diesel & Turbo (2012), Petrov (2006)), they provide up to 14.5% of power boost for the engine.

Addition of the internal heat recuperation to a WHR cycle:

  1. Appropriate working fluid selection;
  2. Increment of initial parameters of bottoming cycle up to supercritical values;
  3. Maximize waste heat utilization due to the usage of low temperature heat sources;
  4. Bottoming cycle complexification or usage of several bottoming cycles with different fluids
    (Maogang (2011)).



This paper focuses on the development of new WHRS as an alternative to high efficiency steam bottoming cycles by accounting for the latest progress in the field of waste heat recovery. The
application range of the proposed system extends to powerful and super powerful ICPEs.

The goal of the presented work is the development of a new, high efficiency WHRS for powerful and super powerful ICPEs based on ORC principles. To solve the assigned task, a thorough study of the currently existing works was performed and the best ideas were combined. The principles of the maximum waste heat utilization, maximum possible initial cycle parameters, recuperation usage and single working fluid were assumed as a basis for the new WHRS design.

Read the full paper here