When used for the formation of the profile contour of polynomials of degree n (n > 5 for the convex part of the profile, and n > 3 for the concave part) the question arises about the correct choice of the missing n–5 (or n–3) boundary conditions which must be selected on the basis of the requirements of aerodynamic profile perfection.
One of the requirements of building the turbine profiles with good aerodynamic qualities is a gradually changing curvature along the outline of the profile . Unfortunately, the question concerning the nature of the change of curvature along the profile’s surface, is currently not fully understood. Curvature along the profile’s surface, is currently not fully understood.
As a geometric criterion for smooth change of curvature in the lowest range of change in the absence of kinks on the profile, you can take the value of the maximum curvature on the profile contour in the range [xc2,xc1] for the convex and for [xk2,xk1] the concave parts, by selecting the minimum of all possible values at the profile designs with the accepted parameters and restrictions. The requirement for the absence of curvature jumps in the description of the profile contour by power polynomials automatically fulfilled as all the derivatives of the polynomial are continuous functions. Agree to consider determined based on the geometric quality criterion, the missing boundary conditions in the form of derivatives of high orders in points C2, and K2 components of a vector Y ⃗ . For the concave part of the profile vector of
varied parameters Y ⃗ is as follows:
wherein k – the curvature of the profile, and the maximum is searched for in the range [xc2,xc1] on the convex portion of the profile and [xk2,xk1] – on the concave part of the profile using one of the one-dimensional search methods. Read More
Waste heat boilers are a sophisticated piece of equipment important for recovering heat and in turn protecting the environment. Waste heat boilers are needed during the operation of facilities in the energy sector such as gas turbine plants and diesel engines, as well as in metallurgy and other industries where excessive heat of high temperature up to 1,000 degrees form during the technological processes. Waste heat boilers are used to recover excess heat energy, as well as to increase the overall efficiency of the cycle. Another feature of waste-heat boilers used at these installations is to protect the environment – by disposing of harmful emissions.
This article discusses the accurate modeling of these sophisticated waste heat boilers. We will consider the simulation of a Heat Recovery Steam Generator (HRSG), which is used in a combined steam-gas cycle for utilizing the outgoing heat from a gas turbine plant and generating superheated steam, using the programs thermal-fluid network approach and complexes of optimization.
The HRSG has four main heat exchangers: cast-iron economizer, boiling type steel economizer, evaporator with separator, and superheater.
On the one side of the HRSG, feed water is supplied from the cycle, and on another side, hot gas is supplied from the gas turbine in the process of operation. The water is preheated and goes to the steel economizer where the boiling process begins in the tubes. After the process in the economizers, the water goes to the shell side of the evaporator, where its active boiling occurs. In the separator, the steam-water mixture is divided into saturated steam and overflow. Saturated steam is sent to the superheater, where superheated steam is formed and goes to the steam turbine cylinder. Overflow water returns to the steam formation. An induced-draft fan is used for gas circulation and removal in the HRSG. The HRSG model also has a spray attemperator for steam cooling. The operation principle of desuperheater is the following: feed water is taken from the economizer and goes to the superheater section, passes to superheated steam flow through nozzles, finely divided water droplets mix, heat up and evaporate and as a result, the steam is cooled.
The resulting thermal calculations of optimal geometry and gas-dynamic parameters of the working fluid at the inlet and outlet of the blade row let you go to the next stage of optimization of the turbine flow path – the blade design. The solution of the latter problem, in turn, can be divided into two stages: the creation of planar profiles cascades and their reciprocal linkage also known as
The optimal profiling problem formulated as follows: to design optimal from the standpoint of minimum aerodynamic losses profiles cascade with desired geometrical characteristics, provides necessary outlet flow parameters and satisfying the requirements of strength and processability.
To optimize the cascade’s profile shape profiling algorithm is needed, satisfying contradictory requirements of performance, reliability, clarity and high profiles quality.
Earlier, considerable effort has been expended to develop such algorithms . Analyzing the results of these studies, the following conclusions may be done. First, great importance is the right choice of a class of basic curves, of which profiles build (which may be straight line segments and arcs, lemniscate, power polynomial, Bezier curves, etc.), which primarily determines the reliability and visibility of solutions. The quality of the obtained profiles associated with the favorable course of the curvature along the contours, the choice of which is carried out using the criteria of “dominant curvature”, minimum of maximum curvature, and other techniques.
First, consider the method of profiles constructing with power polynomials [15, 34]. The presentation will be carried out in relation to the rotor blade.
5.2.1 Turbine Profiles Building Using Power Polynomials
Initial data for the profile construction. Analysis of the thermal calculation results (entry β1 and exit β1 angles, values of flow velocities W1 and W2) and the requirements of durability and processability lead to the following initial profiling data (Fig. 5.1): β1g constructive entry angle; f – cross-sectional area; b – chord; t – cascade pitch. Optimal relative pitch of the cascade can be determined beforehand on the recommendations discussed in ; a – inter-blade chanel throat; ω1 – entry wedge angle; r1 – the radius of the leading edge rounding; r2 – the radius of the trailing edge rounding; ω2 – exit wedge angle; βs – profile stagger angle; β2g – constructive exit angle; δ – unguided turning angle.
Aircraft fuel pumps are one of the most important elements of a fuel system. The operating characteristics and reliability of it are critical for the performance and safety of the aircraft.
Usually, the inlet pressure of the aircraft fuel pump is very low, for example, the aircraft fuel pump of a commercial aircraft needs to operate at altitudes up to 45,000 feet, where the standard atmospheric pressure is about 2.14 psi (about 0.146 atm). What’s more, because fuel is the only consumable fluid carried by the aircraft, it needs to provide all of the cooling necessary for the proper function of the airframe and engine systems. As a result, the temperature of the fuel in the pump increases significantly. The vapor pressure of common fuel used in aircraft gas turbine engines, like Jet A, Jet B, JP-4 etc., gets higher as the temperature increases. Cavitation may occur when the local static pressure in the fluid drops below the vapor pressure of the fuel.
It is very important to avoid the cavitation problem when designing the aircraft fuel pump, because it will cause serious wear, tear, damage of the impeller and performance penalty, which reduces the pumps’ lifetime dramatically. In order to prevent cavitation and have a better suction performance, aircraft fuel pumps use inducers either alone or in conjunction with radial or mixed-flow impeller depending upon the flow and pressure requirements. Figure 1 shows an assortment of fuel pump impellers including radial, mixed flow and inducer types. 
There are two different approaches to determining the optimal parameters of planar cascades of profiles for the designed axial turbine flow path.
The first one which is suitable for the early stages of design, does not takes into account the real profile shape, i.e. based on the involvement of empirical data on loss ratio, geometrical and strength characteristics depending on the most important dimensionless criteria (the relative height and pitch, geometric entry and exit angles, Mach and Reynolds numbers, relative roughness, etc.). The advantages of this approach are shown in the calculation of the optimal parameters of stages or groups of stages, as allow fairly quickly and accurately assess the mutual communication by various factors – aerodynamics, strength, technological and other, affecting the appearance of created design – and make an informed decision.
The second approach involves a rigorous solution of the profile contour optimal shape determining problem on the basis of a viscous compressible fluid flow modeling with varying impermeability boundary conditions of the profile walls. In practice, the task is divided into a number of sub-problems (building the profile of a certain class curve segments, the calculation of cascade fluid flow, the calculation of the boundary layer and the energy loss) solved repeatedly in accordance with the used optimization algorithm, designed to search for the profile configuration that provides an extremum of selected quality criteria (e.g., loss factor) with constraints related to strength, and other technological factors. Read More
[:en]One of the challenges of maintaining infrastructure is deciding how best to keep the operational costs in check while delivering the highest amount of service. This is especially true for aging equipment. One option is to replace the equipment with a newer version entirely, continue to maintain the existing machine, or a third option, retrofit the current machine with updated features.
Retrofitting is a term used in the manufacturing industry to describe how new or updated parts are fitted to old or outdated assemblies to improve function, efficiency or additional features unavailable in the earlier versions.
Retrofitting, like any investment of capital requires careful thought. SoftInWay’s Manage ring Director, Abdul Nassar has put together a simple list of questions to ask yourself before committing to a retrofit project. Answering these seven questions before you start can save you considerable time and effort. Read More
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 Dm/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 α1m or β2m 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 α1m, β2m angles, and the exponents m1, m2 in the
Assume that the control variables are β2m, m1 and m2, whereby the back pressure at a predetermined flow rate must be specified by changing the angle α1 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 β2m, m1 and m2.
[:en]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 :
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  is defined as follows:
In the case of wet steam flow with loss of moisture, crown overall mass transfer coefficient is given by
where ψm,i flow coefficient, is usually determined in function of the degree of humidity and pressure ratio .