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One means of the flow control in the axial turbine stage is the use of blades with non-radial setting. In this case, there is a non-zero the blade surface lean angle.

Vortex equation for the case of flow in a rotating crown can be written as:

Turning to the new independent variable ψ – the stream function, we write (4.16) in final form:

Equation (4.17) for given geometrical parameters of the surface S’_{2} forms a closed system of ordinary differential equations in cross-section z = const together with the continuity equation:

Consider a three sections stage calculation which located on the entrance and exit edges of the guide vane and on the trailing edge of the impeller. Derivative:

is defined in terms of the flow of the working fluid in the free space (right side of the design section):

In the absence of lean (tgδ = 0 ) the equation (4.17) coincides with the previously obtained. Upheld algorithm for the stage calculation by sections and supplements it by specifying the lean angles of the guide and rotor blades output edges. Agreed δ(r) = const.

The above numerical study results, confirmed experimentally, show, that leakages significantly affect the axial turbine stage crowns optimal twist laws. With a decrease in the length of the rotor blade (increase of D_{m}/ι ratio) this effect is amplified.

In this regard, the problem arises of determining the guide vanes and rotor optimal twist laws for a given stage geometry, inlet parameters, the rotor angular velocity, flow rate and heat drop. We restrict ourselves to the task of practically important case of the blades angles specification in the form (4.4). At the same time, while setting the flow and heat drop together, thermal calculation is performed by adjusting one of the angles α_{1m} or β_{2m} Described below optimization technique based on repeated conduct this kind of thermal calculations for the purpose of calculating the internal stage efficiency depending on one of α_{1m}, β_{2m} angles, and the exponents m_{1}, m_{2} in the
expression (4.4).

Assume that the control variables are β_{2m}, m_{1} and m_{2}, whereby the back pressure at a predetermined flow rate must be specified by changing the angle α_{1} at the mean radius. The problem of the thermal stage calculation is written as

and its numerical solution is based on finding the roots of transcendental equations

After the solution of (4.7), which is conducted with the specification form of the stream lines, leakage values, velocity and flow rate coefficients, internal stage efficiency calculated as a function of three variables β_{2m}, m_{1} and m_{2}.

Reverse Engineering, or back engineering, is a term used for the process of examining an object to see how it works in order to duplicate or enhance the object when you don’t have the original drawings/models or manufacturing information about an object.

There are two major reasons reverse engineering is used:

create replacement parts to maintain the function of older machines;

improve the function of existing machines while meeting all existing constraints.

Reverse engineering is extremely important in turbomachinery for replacement parts in turbines or compressors which have been operating for many years. Documentation, reports and drawings for a significant amount of these machines is not available due to a variety of reasons, therefore keeping these important machines running is a challenge. One of the options to deal with this issue is to buy the modern analogue of the machine, which is not always feasible due to economic constraints or that there is no replacement available. Reverse engineering of the worn out parts might be the best option in the majority of cases.

In any case, the process to recovery original geometry of the object is the first and major step for all reverse engineering projects, whether you want just replacing/replicate parts or proceed with an upgrade to the machine.

Basic Steps to Any Reverse Engineering Project

Any reverse engineering process consist of the following phases:

Data collection: The object needs to be taken apart and studied. Starting in ancient times, items were disassembles and careful hand measurements were taken to replicate items. Today, we employ advanced laser scanning tool and 3D modeling techniques to record the required information in addition to any existing documentation, drawings or reports which exists.

Data processing: Once you have the data, it needs to be converted to useful information. Computers are essential for this stage as it can involve the processing of billions of coordinates of data converting this information into 2D drawings or 3D models by utilizing CAD systems.

Data modeling: This step was not available in beginning of reverse engineering. People just tried to replicate and manufacture a similar object based on the available data. Nowadays, engineers can utilize digital modelling, which represents all details of the geometrical and operational conditions of the object through a range of operation regimes. Typically, performance analysis and structural evaluation are done at this stage, by utilizing thermo/aerodynamic analytical tool, including 3D CFD and FEA approaches.

Improvement/redesign of the object: If required, this is the step where innovations can be created to improve the effectiveness of the object based on the collected data about the object’s geometry and operation.

Manufacturing: After the part is been modeled and meets the design requirements, the object can be manufactured to replace a worn out part, or to provide increased functionality.

Reverse Engineering in Today’s World

It very common to find the situations where reverse engineering is necessary for parts replacement, particularly with turbomachinery – steam or gas turbines, compressors and pumps. Many of these machines have been in operation for many years and experienced damaging effects of use over that time – like water droplets and solid particles erosion, corrosion, foreign objects, and unexpected operating conditions. Besides these expected needed repairs, some other reasons for reverse engineering might arise from a components part failure, as well as part alterations needed due to previous overhauls and re-rates.

All the conditions mentioned above require not only recovering the original geometry but also an understanding of the unit’s history, material properties and current operating conditions.

This article focuses on reverse engineering objects which have experienced significant change in their geometry due to the challenges of long term operation and their shape could not be directly recovered by traditional methods – like direct measurement or laser scanning. Pictures below are examples of such objects – steam turbines blading with significant damage of the airfoils with different causes such as mechanical, water/solid particle erosion, and deposit.

In the situations shown above, recovering the original geometry may be impossible if an engineer only has the undamaged portion of original part to work with. Which means that relying on undamaged portion of an original part it may be impossible to recover the needed portion due to significant level of damage.

Looking at the eroded turbine blading in Figure 1, recovering these airfoils with sufficient accuracy based on only a scan of the original part, would be very difficult, if not impossible, considering that 1/3 to ½ of the needed profile is wiped out by erosion.

In order to recover the full airfoil shape for turbines / compressors / or pumps blading, the information about flow conditions – angles, velocities, pressure, temperature – is required to recreate the airfoils profiles and a complete 3D blade.

In many cases with significant blading damage, the information obtained from aero/thermodynamic analysis is the only source of the information available for a designer and the only possible way to recover turbomachinery blading. In fact, in such a situation, the new variant of the airfoils is developed based on aero/thermodynamic information and by considering the remaining portion of the part, which would be the most accurate representation of the original variant. A structural evaluation should also be performed for any recovered part to ensure blading structural reliability in addition to the aero/thermodynamic study.

All of these engineering steps require employment of dedicated engineering design and analysis tools, which can perform:

– Accurate modelling of the turbo machinery flow path,

– 1D/2D aero/thermodynamic analysis and in some cases 3D CFD,

– Profiling and 3D staking of the blading,

– Structural evaluation, including 3D FEA tools.

SoftInWay’s team offers a comprehensive set of turbomachinery design and analysis tools within the integrated AxSTREAM® platform, which covers many steps, required for reverse engineering activities.

In Figure 6 below, a process diagram shows how AxSTREAM® products are used for reverse engineering.

After data collection, most of the geometry recovering steps are processed by AxSTREAM® modules:

– AxSLICE™ to process original geometry data, available from the scanned cloud of points.

– AxSTREAM® solver to perform 1D/2D aero/thermodynamic

– AxSTREAM® profiler to recover profile shape and 3D airfoil stacking.

– AxSTRESS™ for structural evaluation and 3D design.

– AxCFD™ for detailed aerodynamic analysis and performance evaluation.

Geometry recovered in this way is now ready to be used to develop detailed 3D CAD models and 2D drawings for further technological and/or manufacturing processing.

As an example of such capabilities, Figure 7 demonstrates the reverse engineering process for the 1000 mm last stage of 200 MW steam turbine with significantly damaged blades due to water erosion.

It is possible to recognize and extract the profile angles with a specialized tool – AxSLICE™, obtain slices on the desired number of sections and insert the extracted geometric data to an AxSTREAM® project.

The AxSTREAM® platform can provide seamless reverse engineering process for all components of complex turbomachinery.

Meet an Expert!

Dr. Boris Frolov is the Director of Engineering at SoftInWay, Inc. and manages all of the turbomachinery consulting activities. He has over 35 years of experience in steam/gas turbines design, analysis and testing.

Earning his PhD in turbine stages optimization with controlled reaction, he is an expert in steam turbines aerodynamics and long buckets aeromechanics. Dr. Frolov has over 50 publications and 7 registered patents and he shares this vast knowledge as a lecturer in steam turbines, gas dynamics and thermodynamics for students studying power engineering sciences. Prior to joining SoftInWay, he was the engineering manager at GE Steam Turbines.

Significant impact on the stage efficiency have leakage of the working fluid through the seal gaps and discharge openings. The dependence of the leakage (and associated losses) of the stage bounding surfaces parameters can dramatically affect the distribution of the optimal parameters along the radii and, hence, the spatial structure of the flow therein. The latter, in turn, is determined by the shape and twist law of guide vane and impeller.

Development of algorithms for the axial turbine stages crowns twist laws optimization demanded the establishment of appropriate in the terms of computer time methods for calculating the quantities of leaks and losses on them, allowing the joint implementation of the procedure for calculating the spatial parameters of the flow in the stage.

The leakage calculation is necessary to conduct together with a spatial calculation step, as the results of which the parameters in the calculation sections are determined, including the meridian boundaries of the flow path. The flow capacity depends on the clearance (or leakages) values, in connection with which main stream flow calculation is made with the mass flow amplification at fixed the initial parameters and counter-pressure on the mean radius, or clarifying counter-pressure at fixed initial parameters and mass flow. The need for multiple stage spatial parameters calculation (in the optimization problem the number of direct spatial calculations increases many times) demanded a less time-consuming, but well reflecting the true picture of the flow,
methods of spatial stage calculation in the gaps described above (Fig. 2.3).

When calculating stage in view of leakage the continuity equation is convenient to take as [8]:

where μ – the mass transfer coefficient, which allows to take into account changes in the amount of fluid passing through the crowns, and at the same time to solve a system of ordinary differential equations in sections in front of and behind the impeller like with a constant flow rate.

The leakage mass transfer coefficients [13] is defined as follows:

In the case of wet steam flow with loss of moisture, crown overall mass transfer coefficient is given by

where ψ_{m,i} flow coefficient, is usually determined in function of the degree of humidity and pressure ratio [8].

Hydrodynamic bearings operating at high speeds encounter instability problems of oil whirl and whip. Instability may ruin not only the bearings but the entire machine. It is well-known that hydrodynamics bearings play an important role in determining and controlling the vibrations of a rotating machinery, because of the springs and dampers, and bearings strongly influence the critical speed and imbalance response. Under certain conditions, the bearings can create rotor instability which results in significant self-excited vibrations.

The types of stability here are for a balanced journal and are mentioned below. If, as time increases, the trajectory of the journal center goes to a point of the clearance circle and remains there indefinitely, then the bearing is considered to exhibit “point stability,” Fig. 1(a). If, as time increases, the trajectory does not go to a point, as shown in Fig. 1(b) and (c), then the bearing, is considered to exhibit “point instability”. Two types of instability are shown in Figure 1. In Fig 1(b) the trajectory continues to increases without bound, ultimately reaching the limit of the clearance circle, therefore, this case is called “unbounded “. As time increases eases, if the trajectory closes on itself forming a limit cycle, as shown in Fig 1(c), then the trajectory can be said to be “orbitally stable”.

Satisfactory dynamic characteristics are essential to good bearing design. Hence it is very important for the designers to predict the journal center motion trajectories. AxSTREAM Bearing™ is used to calculate the hydrodynamic characteristics based on the mass-conserving mathematical model by applying the finite difference method with the successive over-relaxation (SOR) algorithm.

Mathematical models of gas and steam turbines stages, discussed above, allow to put the task of their geometry and gas-dynamic parameters optimization. This optimization problem is solved by the direct problem of stage calculation. The reason for this are the following considerations:

– it is most naturally in optimizing to vary the geometry of the blades;

– in the streamlines form refinement it is convenient to use well-established methods for the solution of the direct problem in the general axisymmetric formulation;

– only a direct problem statement allows to optimize the stage, taking into account the off-design operation;

– for the stages to be optimized, assumed to be given:

– the distribution of the flow at the stage entrance;

– the form of the meridian contours;

– the number of revolutions of the rotor;

– mass flow of the working fluid;

– averaged integral heat drop.

In general, you want to determine the distribution along the certain axial sections of angles α_{1} and β_{2} to ensure maximum peripheral efficiency of the stage:

Here the inlet geometric angle of the rotor we assume equal to the angle of the inlet flow. Selection of the optimal angle β_{1g} can be achieved solving an optimal profiling problem.

This is an excerpt from a technical paper, presented at the ASME Power & Energy Conference in Pittsburg, Pennsylvania USA and written by Oleksii Rudenko, Leonid Moroz, and Maksym Burlaka. Follow the link at the end of the post to read the full study!

Introduction

Supercritical CO2 operating in a closed-loop recompression Brayton cycle has the potential of equivalent or higher cycle efficiency versus supercritical or superheated steam cycles at similar temperatures [2]. The current applications of the supercritical CO2 Brayton cycle are intended for the electricity production only and the questions which are related to the building of CHP plants based on Supercritical CO2 technology were not considered yet.

CHP is the concurrent production of electricity or mechanical power and useful thermal energy (heating and/or cooling) from a single source of energy. CHP is a type of distributed generation, which, unlike central station generation, is located at located at or near the point of consumption. Instead of purchasing electricity from a local utility and then burning fuel in a furnace or boiler to produce thermal energy, consumers use CHP to improve efficiency and reduce greenhouse gas (GHG) emissions. For optimal efficiency, CHP systems typically are designed and sized to meet the users’ thermal base load demand. CHP is not a single technology but a suite of technologies that can use a variety of fuels to generate electricity or power at the point of use, allowing the heat that would normally be lost in the power generation process to be recovered to provide needed heating and/or cooling. This allows for much greater improvement in overall fuel efficiency, therefore resulting in lower costs and CO2 emissions. CHP’s potential for energy saving is vast.

It should be noted that CHP may not be widely recognized outside industrial, commercial, institutional, and utility circles, but it has quietly been providing highly efficient electricity and process heat to some of the most vital industries, largest employers, urban centers, and campuses. While the traditional method of separately producing useful heat and power has a typical combined efficiency of 45 %, CHP systems can operate at efficiency levels as high as 80 % (Figure 1) [1].

Taking into consideration the high efficiency of fuel energy utilization of CHP plants and the high potential of the supercritical CO2 technology, the latter should be also considered as the base of future CHP plants. The comparison with traditional Steam based CHP plants also should be performed.

The study of CHP plant concepts were performed with the use of the heat balance calculation tool AxCYCLE™ [3].

In the early stages of the flow path (FP) design of the turbine, when determined the diameter, the blade heights, heat drops and other main characteristics of the stages, required to study alternatives with a view to the design solution, in the best sense of a quality criterion.

Most effectively, this problem is solved within the created turbine flow path CAD systems, because manage: to achieve a rational division of the designer, defining the strategy and computer, quickly and accurately perform complex calculations and presents the results in human readable numeric or graphical form; to take into account many different factors influencing the efficiency,
reliability, manufacturability, cost and other indicators of the quality of the design being created; organize dialogue or fully automatic determination of optimal parameters, etc [29].

Most methods of the multi-stage turbine parameters optimization is designed to select the number of gas-dynamic and geometric parameters on the basis of the known prototype, the characteristics of which are taken as the initial approximation.

When using complex mathematical models, a large number of variables and constraints, the solution of such problems requires considerable computer time and for the purposes of CAD that require quick response of the system is often unacceptable.

It is desirable to have a method of design that combines simplicity, reliability and speed of obtaining results with an accuracy of the mathematical model, a large number of factors taken into account and optimized, the depth of finding the optimal variant. This inevitably certain assumptions, the most important of which are: the synthesis parameters of “good”, competitive structure without attracting accurate calculation models; in-depth analysis and refinement of the parameters are not taken into account at the first stage; optimization of the basic parameters by repeatedly performing the steps of the synthesis and analysis.

Design of the FP in such a formulation will be called preliminary (PD). PD does not claim to such a detailed optimization of parameters, as in the above-mentioned methods of optimal design. Its goal – to offer a workable, effective enough design, the characteristics of which, if necessary, can be selected as the initial approximation for more accurate calculations.

Major challenges in creating a PD method are:

– a rational approach to the problem of the preliminary design, the selection of the quality criteria and the constraints system;

– development of a method for the multi-stage flow path basic parameters selection;

– formation of requirements for a mathematical models complex describing different aspects of turbines and their efficient numerical implementation;

– selection of the appropriate algorithm for finding the optimal solution;

– a flexible software creation for a dialog based solution of the design problems in various statements and visual representation of the results.

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

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.

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.