An oil system should provide:

– continuous supply of the required amount of oil in all modes of operation of the turbine unit, which guarantees:

- – prevention of wear on friction surfaces;
- – reduction of friction power losses;
- – removal of heat released during friction and transmitted from the hot parts of the turbine

– maintaining the required temperature of the oil in the system; and

– cleaning the oil from contamination.

At the same time, the necessary qualities of the lubricating oil system are reliability, safety of operation, ease of maintenance.

The pressure and the temperature of the oil should be constantly monitored during operation of the turbine unit. Specifically, the lube oil temperature after the bearings requires special attention. Overheating of the bearing leads to wear of the working parts and changes in the properties of the lubricant itself. The quality of the lube oil is controlled by physicochemical characteristics such as density and viscosity. The system leaks must be stopped quickly and oil replenished on time. These factors will significantly extend the service life of the steam turbine.

Nowadays, computer simulation is a very powerful and useful tool. It helps you predict the processes occurring in the bearing chambers, and determine the flow of the working fluid when the operating modes change, all without installing expensive experimental equipment.

We suggest using the 1D-Analysis AxSTREAM NET tool to simulate the lubrication system. This software product allows you to quite simply, clearly and quickly build the desired model. It provides a flexible method to represent fluid path as a set of 1D elements, which easily can be connected to each other to form a thermal-fluid network. The program calculates fluid flow parameters for inlet and outlet of each element. There are many different components that allow you to simulate stationary and non-stationary modes. Also there is a convenient library of fluids. It is also possible for a user to add fluids of their choice.

The example of modeling in AxSTREAM NET is the system of oil supply for the K-500-240 turbine. This turbine is quite massive with bearing loads of up to 450 kN. The schematic diagram of the oil supply K-500-240-2 is shown in Figure 1.

(1 – main tank; 2 & 3 – pumps; 4 – oil cooler; 5 – damp tank; 6 – journal bearings; 7 – thrust bearing).

The main elements of the scheme are:

– the main lube oil tank;

– the oil cooler;

– the centrifugal oil pump;

– the damping tank;

– the emergency tanks;

– 12 journal bearings with diameters of 300, 420 and 520 mm; and

– 1 hydrodynamic thrust segmented bearing with a diameter of 520 mm.

This scheme provides the oil lubrication system for the turbine, generator, hydrostatic lifting of the turbine rotors and the emergency oil supply system. The hydrostatic lift system of the rotors is autonomous and operates at high pressure. The emergency oil supply system is integrated into the bearing oil supply system.

Let’s consider the key elements of the scheme. The oil is sent from the main tank to the oil coolers, where it is cooled to the temperature of 45 degrees.Then lubricating oil is supplied to a damping tank installed at a height of 24 m. It ensures uninterrupted flow and stable pressure in front of the bearings 0.1 MPa. The lube oil flows by gravity from the damper tank to the lubrication manifold and further to the bearings. Then it drains into the common lubrication system manifold, and from there, back to the main tank. The lube oil purity is provided by filters installed in the main lube oil tank. The lube supplying is provided by a centrifugal oil pump. This scheme uses oil brand T-22. The limiting factors are the maximum oil heating temperature and the minimum thickness of the lubricating layer for bearings operating on petroleum oil. The oil heating is not more than 15 degrees in the bearing for the conditions of this scheme. The thickness of the oil film is not less than 0.015 mm.

Figure 2 shows the model of the oil supply system was made by using the AxSTREAM NET software.

The software allows setting the performance of the oil pump by using a special function “Tabular”. This will provide an opportunity to automatically take the effect of changes into account in oil consumption on the head and the efficiency of the pump.

The model calculates the flow and pressure in any part and in every modeling components of the lube oil system. We can calculate the necessary mass flow rates, track the increase of oil temperature, changes in pressure, thermophysical properties of the oil, a lube oil film thickness, as long as we know the design characteristics of the bearings. We can choose the required geometrical dimensions of the bearings if we know the load and the necessary expenses of lubricating oil.

The results of calculations in AxSTREAM NET coincide with the experimental data.

The simulation tool allows users to predict and analyze the behavior of the system in different situations; highlight vulnerabilities; and draw the necessary conclusions and recommendations. Learn more about AxSTREAM NET here.

]]>The major types of axial flow fans are: propeller, tube axial, and vane axial.

- – Propellers usually run at low speeds and handle large volumes of gas at low pressure. Often used as exhaust fans these have an efficiency of around 50% or less.
- – Tube-axial fans turn faster than propeller fans, enabling operation under high-pressures 2500 – 4000 Pa with an efficiency of up to 65%.
- – Vane-axial fans have guide vanes that improve the efficiency and operate at pressures up to 5000 Pa. Efficiency is up to 85%.

The aerodynamic design of an axial fan depends on its applications. For example, axial fans for industrial cooling applications operate at low speeds and require simple profile shapes. When it comes to aircraft applications however, the fan must operate at very high speeds, and the aerodynamic design requirements become significantly different from more traditional fan designs.

- – To generate an efficient axial fan, the flowpath should be properly sized (i.e. tip diameter, blade height etc.) along with the optimal inlet/outlet blade angle selection and the corresponding blade profile that should have minimal profile and secondary losses.
- – As an aerodynamic engineer, it is important to understand the flow along the blade height for which the designer can control the inlet swirls and blade loading by altering the blade angle distributions from hub to tip.

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The design cycle time for fans can be considerably reduced using well established turbomachinery design software tools such as AxSTREAM®. Using such programs not only reduces the design cost, but also gives the best performance for the specified application, as the user can evaluate the entire design space in which the fan has to operate.

The design cycle time for fans can be considerably reduced using well established turbomachinery design software tools such as AxSTREAM®. Using such programs not only reduces the design cost, but also gives the best performance for the specified application, as the user can evaluate the entire design space in which the fan has to operate. The AxSTREAM® platform also provides opportunities for designers to analyze the design using the 1D/2D solver where the designer can control different flow distributions from hub to tip using different types of blade twists.

After that, the designed fan can be analyzed for the flow physics and behavior using 3D CFD (Computational Fluid Dynamics). AxCFD within the AxSTREAM® platform helps users to quickly perform a 3D CFD analysis for the design and off-design conditions with automated mesh generation and post-processing. The results of 3D CFD is presented in the figure below.

Working in fan development? We’ve love to help! For more information, contact us at Info@Softinway.com

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A more rigorous formulation of creating an optimal cascade profile problem that provides design parameters of the flow at the exit and meet the requirements of strength and workability, is the problem of profiling, which objective function is the profile (or even better – integral) losses.

As mentioned above, the profile loss ratio can be presented as the sum of the friction loss coefficients of the profile ζ_{fr} and edge loss coefficient ζ_{e}.

Given that the ratio of the edge losses associated with the finite thickness of trailing edges, the value of which is predetermined and is practically independent of the profile configuration, the objective function can be assumed as [8].

In terms of flow profile, you must set a limit, excluding the boundary layer separation. Unseparated flow conditions according to Buri criterion can be written as [22]:

The constants B and m can be taken equal to: B = 0.013…0.020, m = 6.

The task is set of determining the coefficients of the polynomials (5.7) for a description of the convex and concave profile with given geometric, strength and processability parameters so as to reach the minimum of the functional (5.15) and satisfy the constraints (5.16).

Formulated the optimal profiling problem is essentially non-linear with inequality constraints and mathematically formulated as follows:

where

vector of varied parameters objective function, whose role in the problem plays an equation for the coefficient of friction (5.12); g(Y^{→}) – constraint, which on the basis of Buri separation criterion (5.14), is defined as follows:

i = 0, 1, …, 2n (2n – the number of points on the profile contour).

Applying to the problem solution method the penalty functions method [3], we reduce the problem of finding the extremum in the presence of constraints to the problem without restriction. Form the generalized functional I^{*}

For the unconstrained minimization of the functional (5.20) Nelder and Mead algorithm was used [3].

An algorithm for constructing an optimal profile of the minimum profile loss is as follows:

1. As the initial data for profiling on the basis of thermal calculation and the conditions of durability and adaptability the quantities are introduced:

*a* – throat inter-blade channel; *b* – chord; *t* – cascade step; *f* – profile square; r_{1} and r_{2} input and output edges radii; ω_{2} – trailing edge wedge angle.

2. An initial approximation for the leading edge wedge angle ω_{1}, the stagger angle of the profile β_{s}, geometric (constructive) entry β_{1g} and exit β_{2g} angles, unguided turning angle δ, derivatives of higher orders

3. Determines the coordinates of the points C_{1}, C_{2}, D, K_{1}, K_{2}, and their first derivatives.

4. Sought the coefficients of polynomials describing the concave and convex portion of the profile according to the procedure set out in section 5.1.

5. The profile area determined and, using one of the one-dimensional search methods, varying angle ω_{2}, a minimum of residual F=|f(ω_{2})- f| is found.The process of profiling is carried out from step 2.

6. Calculate the profile velocity distribution, as well as the coefficient of friction ζ_{fr} by (5.15) and the G_{i} value by (5.19).

7. We call the routine of optimization for finding the minimum of the functional (5.20), each time making the profile area fit before the calculation of the objective function. A minimum of the functional (5.20) corresponds to the optimum value of the vector of variable parameters

8. The optimal profile construction is made, satisfying the strength, geometrical and technological constraints, and provides a minimum profile loss while maintaining the unseparated flow. By the designer’s wish optimization may also be performed using the parameter t/b,and the trailing edge wedge angle ω_{2}.

Let’s take a deeper look at what repulsorcrafts are and how we can help Anakin redesign his to gain an even better advantage against the competition, provided that Watto has the correct equipment in his junk yard.

They can be propelled by several different means – gas turbine, ion motor or rocket motor (sorry, no 2a fission engines from X-Wings allowed) – which are linked together via plasma energy binders. The gas turbine air-breathing configuration is what is most common among these vehicles as we can see by looking at the engines of Teemto Pagalies (Figure 2) and Ben Quadinaros (Figure 3) among others. The former uses a turbojet configuration (like Anakin Skywalker) while the latter features a turbofan approach.

To see how we can redesign Ani’s Podracer to improve its performance let’s take a look at its current stats.

We also need to understand under which conditions the engine will operate. Due to the lack of weather stations on Tatooine several assumptions were made:

- – Normal (Earth-like) gravity despite its 3 moons – estimated from the lack of labored efforts from non-Tatooine residents to move around and the fact that they don’t take leaps when walking
- – 1 atmosphere pressure with standard (Earth) composition – neither residents nor most travelers at the cantina require breathing masks
- – Climate – it is widely known that Tatooine has a very dry and very hot climate with temperatures reaching up to 160F most likely achieved by the presence of its two suns (The very low humidity is what makes moisture farms like the Skywalker’s a wealth that requires protection.)

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It is therefore reasonable to consider dry air at 1 atm and 160F as our ambient conditions design point since gas turbines show better performances with colder intake.

Based on this, we can model the thermodynamic cycle of the engine while assuming kerosene as the fuel since no data is available regarding specs for Tradium nor injectrine (used for the power boost).

The thrust required was calculated to ensure the vehicle could reach its current top speed based on common, similar commercial aviation engines weight while initially using rough estimations regarding the compressor and turbine efficiencies.

Preliminary design of both turbomachines in AxSTREAM® enabled for a more accurate engine calculation – the compressor efficiency was overestimated while the turbine one was underestimated slightly. As a result, the mass flow rate of the system was updated from 30.1 to 32.1 kg/s to ensure the target thrust is reached.

The second iteration of the preliminary design was performed to actually determine accurate size and performance for each of the turbomachinery components while keeping a few crucial things in mind:

- Looking for highest efficiency while strongly keeping weight of engine under consideration – a lighter engine means more useable power, better maneuverability and tighter corners which is especially useful in the Arch Canyon and its stone wickets or around the Canyon Dune Turn to escape gunfire from the Tusken Raiders.
- Achieved by reducing axial length by selecting fewer stages
- And limiting the radial dimensions (smaller tip diameter on the compressor with appropriate sizing match on the turbine side)

- Performing turbine design with a constant streamwise tip diameter to preserve current configuration with fuel tank inside the compressor rotor (Figure 4) therefore minimizing redesign operations
- Ensuring that mechanical integrity of the blades is preserved based on materials available on Earth, therefore eliminating Steelton used to link the engines to the cockpit
- Maintaining stable operation throughout different regimes (full throttle in Hutt Flats for the finish vs. dodging rocky obstacles in Bindy Bend) including stall prevention through equivalent diffusion factor monitoring

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As a result, the preliminary geometries are presented in the figures below.

The compressor features 5 stages instead of the original 8 stages with an efficiency of 81%, a reduction of radial dimensions by 70% and of axial length by 80% – Note, selecting a 6-stage configuration would have resulted in a higher efficiency (82.9%) but less substantial weight reductions (+2.5% diameter and +25% length vs. selected 5-stage design). By analyzing the blueprint of the current fuel tank located inside the core of the compressor, its volume is 0.018 m^{3} which suggests than Tradium is about 50 times denser than kerosene jet fuel given the fuel consumption calculated at the thermodynamic cycle level when considering full throttle for the 15min42s record race time. The redesigned compressor can allow up to 0.035 m^{3} of fuel in the same location so this configuration and geometry are considered suitable for this purpose.

The new turbine comprises 2 axial stages instead of the 3 in the current design with an efficiency of 90%, a reduction in tip diameter of 19% and an axial length cut of 23%.

To help put these size reductions into perspective the figure below has been created so readers can easily compare the original vs. redesigned geometries at the same scale.

Although the fuel efficiency advantages of using a turbofan configuration instead of a turbojet one, like in the present case, are interesting to commercial aviation, racing sports typically do not make it their priority, especially in competitions where being a small, maneuverable target brings significant benefits. For this reason we kept our focus on the turbojet approach. However, if you are interested in seeing what we can do for turbofans, I invite you to contact us for some technical material on, for example, automation of bypass ratio optimization using the AxSTREAM ION software. Speaking of automated design, check out this cool video on a rocket turbopump design – http://www.softinway.com/en/automatic-preliminary-design-process-of-turbopump-for-liquid-rocket-engine/

To conclude, Ani’s Podracer has some margin for improvement. We have seen that the size of the compressor and turbine can be reduced which allows for a substantial weight reduction of the propulsion system. This in turn makes it practical to focus on improving the shields to protect against debris and collisions, improving the engine cooling to use the injectrine boost more often, etc.

Future studies could look into the applicability of the axial-radial configuration of compressor used by Sebulba in his engine or even diagonal compressors which feature interesting advantages in cases where pressure rise and space are major constraints.

And who knows, maybe next year we will take a look at Luke Skywalker’s X-34 Landspeeder mini-gas turbines.

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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 [25]. 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 [x_{c2},x_{c1}] for the convex and for [x_{k2},x_{k1}] 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 C_{2}, and K_{2} 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 [x_{c2},x_{c1}] on the convex portion of the profile and [x_{k2},x_{k1}] – on the concave part of the profile using one of the one-dimensional search methods.

Formulated the problem of minimizing the functional (5.12) can be solved by the methods of nonlinear programming. In this case, a very successful was a flexible polyhedron climbing algorithm.

An algorithm for an optimal profile constructing using the geometric quality criterion is as follows:

It was also developed somewhat different algorithm for constructing an optimal profile of the geometric quality criteria. The main stages of the algorithm are as follows:

The process of the profile convex portion constructing continue from step 1 until the throat is not held with the desired accuracy.

The calculation of the velocity distribution around a plane cascade profile and loss coefficients made by sequentially the following tasks: calculation of potential ideal incompressible fluid flow around a flat cascade; approximate calculation of the compressibility of the working fluid; the boundary layer calculation and loss factor determination.

Methods for potential flow of an incompressible ideal fluid calculation in the plane cascade can be divided into methods based on conformal mapping of the flow domain and methods of solving tasks given to integral equations [8, 22].

Considering the profile loss ratio ζ_{pr} as the sum of the friction ζ_{fr} and edge losses ζ_{e} coefficients using proposed in [8] approximate formula for

determining the value of the expression ζ_{pr} can be written as:

wherein δ**_{ss}, δ**_{ps} – the momentum thickness on the convex (suction side) and the concave (pressure side) portions of profile.

The calculation of the boundary layer can be produced by known methods of boundary layer theory [22]. There is reason to believe the boundary layer in real turbomachinery cascades fully turbulent. At least the treatment the boundary layer as turbulence do not gives low loss coefficient values in the cascades. Before values of Mach numbers M < 0.5, calculation of the boundary layer on a single cascade profile can produce satisfactory accuracy as an incompressible fluid [22]. As a possible formulas for the momentum thickness calculation can take the expression obtained in the solution of the turbulent boundary layer by L.G. Loytsyanskiy method

where Re – Reynolds number; w_{2} – – cascade output velocity; w(S) – the profile contour velocity distribution function.

The integral in (5.14) is determined by a numerical method. Determined with the help of (5.14) the δ**_{ss}, δ**_{ps} values, and substituting them into (5.12), we will

find the profile loss ratio.

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 boiling process takes place in both the steel economizer tubes and in the shell side of the evaporator while the HRSG is operating. As a result, the two-phase flow is formed. Boiling leads to the intensification of heat exchange processes, changes in the flow structure and produces bubbles, which must be accurately taken into account during the simulation. Thermal-fluid network software AxSTREAM NET was used to determine the hydraulic resistance of heat exchangers and the recovery boiler as a whole, as well as simulating the processes of phase transition. In addition, the software allows taking into account convective and radiant heat exchange. These complex methods allow users to determine all the necessary parameters of gas and water and accurately simulate the heat transfer coefficients.

It should be noted that AxSTREAM NET could be used for the detailed modeling of each HRSG component and for non-interval modeling depending on the task required. What are the differences between these two approaches? Let’s figure out!

We have used both of these approaches in the modeling of HRSG. The interval method was used to simulate a cast-iron economizer. In this case, the number of pipes was divided into 7 bundles of 95 tubes each, and the length of the pipes was split in half. The non-interval method was used for simulations of a steel economizer of boiling type. In this case, the heat exchanger was modeled by two elements – a pipe element for modeling the resistance of the tube bundle – it specified the total number of heat exchanger tubes and the element for modeling pipe flow resistance in the shell side. It should be noted that the interval method allows the user individually to perform simulation of various schemes depending on the task, as well as to obtain more accurate results in the modeled installation.

Nowadays, it is necessary to apply an integrated approach to solve any engineering problems which evaluate the work of the entire cycle, where installations are used, and to conduct an accurate analysis of their interaction. Thus, we consider the analysis of the influence and interaction of the turbine installation parameters and HRSG in various operating modes, which depend on environmental parameters.

To analyze the impact of environmental parameters on HRSG values, we additionally used software systems developed by SoftInWay. This provides a modern approach to cycle analysis implementation and calculation at the same time all components of the scheme. Thus, the 0D software for thermodynamics cycle analysis and calculation (AxCYCLE) and integration and optimization software (AxSTREAM ION) were used for automatically matching gas turbine cycle calculations from different regimes in AxCYCLE with the flow rate calculations, temperatures and heat transfer coefficients in AxSTREAM NET .

It is no secret that usually GT’s typically do not work on the design modes (T_{air}=15 C;P=0.1031 MPa;Humidity=60%-ISO-2314) when compared to a steam turbine. Outside air parameters are constantly changing. As a result, the main characteristics of the GT-cycle is changed such as electric power, efficiency, gas parameters at the turbine outlet.

Obviously, the efficiency of a gas turbine cycle grows with a drop in outside air temperature, which affects the entire thermodynamic cycle. As a result, the amount of generated steam decreases with increasing ambient temperature, and generated steam temperature increases. Moreover, the gas flow rate from the GT and HRSG resistance increases with reducing ambient temperature.

Thus, we were able to perform complex optimization tasks for flow analysis calculation and parameter interactions in sophisticated systems (such as combined gas-steam cycles) via AxSTREAM ION, and provide an opportunity to use different modeling approaches which reduces the time of scheme analysis (very important for every engineer 🙂 ). If you need more information about complex modeling, please feel free to contact the SoftInWay team at __info@softinway.com.__

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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

stacking [25].

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 [25]. 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.

Initial data for the profile construction. Analysis of the thermal calculation results (entry β_{1} and exit β_{1} angles, values of flow velocities W_{1} and W_{2}) and the requirements of durability and processability lead to the following initial profiling data (Fig. 5.1): β_{1g} 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 [25]; a – inter-blade chanel throat; ω_{1} – entry wedge angle; r_{1} – the radius of the leading edge rounding; r_{2} – the radius of the trailing edge rounding; ω_{2} – exit wedge angle; β_{s} – profile stagger angle; β_{2g} – constructive exit angle; δ – unguided turning angle.

Of the last six parameters three (r_{1}, r_{2}, ω_{1}) are determined by calculation, the remaining three (β_{s}, β_{2g}, δ) can also be determined in the first approximation by the empirical formula [25]. In further at constructor’s option last three parameters or part of them, may be maintained constant during the profiling, or changed, as variable parameters. As a first approximation for the profile stagger angle β_{s} the next relationship can be recommended:

Profile is built in a Cartesian coordinate system. Coordinates of the circle center of input and output edges, as is easily seen, is given by (Fig. 5.1):

The coupling coordinates of the edges circles with convex and concave sides of the profile C_{1}, C_{2}, K_{1}, K_{2} and their derivatives at these points are defined as follows:

In the formulas (5.4), (5.5) the angles are in radians. The K_{ω} value is often taken as equal to 1. It can influence the position of the center of gravity of the profile. In the process of profile building angle ^{ω}1 specified from the conservation of a given area.

Preserving the value of the throat a, for point D we have:

In the construction of the profile convex and concave parts must first achieve coupling of describing their curves with circumferential edges, while the profile’s convex part with the circumference of the throat at the point D. This means that these curves must satisfy the boundary conditions which are defined by formulas (5.2), (5.6) to the convex and (5.3) for the concave portions of the profile.

As for the convex part the number of these conditions is six, and for the concave – four, in order to have an opportunity to widely vary the outline profile to produce a minimum loss, the convex portion of the profile should be described by a polynomial of higher than 5-th, and the concave portion – than 3-d degree.

Let the order of the polynomial is n. In this case, the question of choosing the correct n-5 boundary conditions for the convex portion of the profile and n-3 boundary conditions for the concave part. As such one can take, for example, the high-order derivatives (second and higher) in the points C_{2} and K_{2}. Not stopping until the solution of this problem, assume that the boundary conditions are somehow chosen.

Due to the fact that the number of points at which the boundary conditions are given, may be different for the convex portion and the concave profile (as mentioned above), for generality, we consider the task of determining the coefficients of the polynomial in the case of setting the boundary conditions in any number of points.

This problem is formulated as follows:

It is easy to see the elements of the matrix C, and the right-hand part column B may be determined by the following formulas:

Now, if the index m in (5.8) will run from 1 to k, we arrive at a system of linear algebraic equations of order n + 1 relatively of unknowns a_{0}, a_{1}, a_{2}…,a_{n}, the elements of the coefficient matrix and the right sides of the column which are determined by formulas (5.9). Solving this system of linear equations, we will determine the coefficients of the polynomial (5.7) separately for convex and concave profile parts.

The area is calculated using the difference between the integrals of the curves describing the convex and concave portion of the profile. Be aligned with a given area can be varying wedge angle of the leading edge ω_{1}, repeating at the same time building a profile with the formulas (5.2), (5.3).

The developed method of turbine profiles design allows the construction of an oblique cut with straight section. Such profiles can be used for supersonic expiration and work well in conditions other than nominal.

A more simple and clear way to build the base curve is a Bezier curve (which is especially convenient for interactive construction of complex curves), but to automate profiling with its help some special measures should be taken. There no doubt also the fact that that the minimum of maximum curvature is a prerequisite for high aerodynamic qualities of turbine profiles cascades. In many cases, probably this criterion prevails over the condition of the absence of curvature jumps, as evidenced by still competitive CKTI profiles [33], designed from arcs and line segments.

Based on these considerations, we will build a profile consisting of two circles describing the input and output edges and three Bezier curves, one of which forms the pressure side, and the other two – convex part, respectively, from the trailing edge to the throat and from the throat to the leading edge.

Bezier curve that passes through two given end points and having at these points specified derivatives, will be called the base curve (BC).

The simplest base curve satisfying the above requirements, a Bezier curve, based on the polygon consisting of two segments passing through the given points with a given slope (Fig. 5.2). It is not difficult to assume that the use of the support polygon of the two segments gives BC, having a very large maximum curvature. In addition, when the angle between segments tends to be zero, the maximum curvature increases indefinitely.

The next (and decisive) step to improving the base curve is the addition of one more segment, intersecting the first two (Fig. 5.3).

We introduce relationship

The course of the base curve generated by polygon 1-3-4-2 much smoother. Furthermore, it is obvious that there must be optimum values of the parameters f and g. Indeed, at f and g, aspiring to unity, we have the case of two basic segments and a very large curvature in the central part of the curve, while f, and g, tending to zero, greatly increasing curvature at points 1 and 2.

A disadvantage of the third order base curve construction is the need to determine the optimal combination of parameters f, g, which greatly slowed the process of the profile design. Fortunately, the coefficients can be calculated only once and tabulated for different combinations of angles (Table 5.1). Since the optimum base curves do not depend on the polygon orientation or the size,

the calculations can be made for the polygon, whose base is the unit interval, which lies on the Ox axis. In addition, due to the obvious condition

it is enough to store the data for only one optimal ratio. If you have a table of dependencies, the basic curves of sufficient quality are built almost instantly.

Profile is constructed from two circles that form the input and output edges, one of BC, which describes the pressure side, and the two BCs, describing the suction side. In this way, initial profiling parameters are listed in Section 5.2.1 (Fig. 5.1).

This information is sufficient to build the support polygons of the profile sections. Formulas for determining the coordinates of the corresponding points and angles do not differ from those given in the previous section. An algorithm for constructing the profile is very simple, but it has a major disadvantage: in the point of the throat, where two base curves are joined, it is possible

discontinuity of curvature, which may lead to local deformation of profile velocity, and a sharp increase in the friction loss. There is a simple way to smooth BC docking at the throat. It lies in the selection of the unguided turning angle to match the curvature of parts at the throat point. Because of the high curvature sensitivity of the unguided turning angle, the variation turns minor.

Determination of δ_{opt} is carried out by solving the equation

by secant method.

Elimination of the curvature jump in the throat requires only a few profile evolutions and a decision is reached very quickly. Built in such a way will be called the basic profile (BP). After a slight modification the algorithm also allows to construct suitable profiles with elongated front part.

It should be borne in mind that the BP is not yet the final product, it is only a semi finished product intended for optimization of all the others, except for the initial, data. This optimization can be performed according to different criteria.

In the process of BP constructing assumed the specified parameters with the exception of the unguided turning angle, which was chosen in such a way as to eliminate the curvature jump at the throat. The remaining ten parameters can be varied to optimize a chosen cascade optimality criterion.

In general, the problem of optimal design of a flat cascade can be written as:

Vector of variable parameters X should in some way describe the shape of the profile. Criterion F(X) is a functional on X. Restrictions on the range of admissible values of the vector X associated with strength and technological requirements cascade imposed on, which are, in particular, the shape and thickness of the input and output edges. Because of the sufficient simplicity of accepted method for calculating the tensile and bending stress in the blade section, they can be defined directly in the process of the profile shape optimization. However, we will stick to a different approach, considering approximately known basic cascade dimensions (chord, relative pitch, etc.) on the basis of the calculation described in section 5.1.

Specifically, a vector of variable parameters includes the following characteristics which influence the configuration of the profile that is based on the procedure described in the previous section:

- – profile stagger angle;
- – relative pitch;
- – geometrical exit angle;
- – the radius of the leading edge;
- – wedge angle of the leading edge;
- – wedge angle of the trailing edge.

Restrictions on the range of the parameter is written in the simplest form:

The most important point in the cascade optimization is the correct criterion of quality selection, which generally represents the minimum total loss of kinetic energy in the cascade taking into account the relative time of its operation at different flow regimes in a given stage of the turbine. In connection with this problem distinguish multi-mode and single-mode optimization solution requires the calculation of cascade flow and constituting losses therein, respectively, at set of modes or in one of them.

As shown by previous studies, in some cases, an alternative criterion of aerodynamic quality can be geometric criterion of the profile smoothness. One could even argue that this observation even more relevant to a multi-mode optimization, than single-mode. The original method was developed in relation to the profiles submitted by power polynomials.

]]>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.^{ [1]}

AxSTREAM® helps create new designs, analyze existing designs and retrofit equipment. Users can optimize the flow path of fuel pumps from scratch using a small number of basic input parameters and a set of geometric constraints. Then users can get the specific design desired by editing and smoothing the flow path interactively, making sure the pump performance is as expected. Figure.2 shows some fuel pump designs with different flow path users can get from AxSTREAM®. Note that an inducer and a centrifugal impeller can be made as an integral part which also can be designed in AxSTREAM®, as shown in the right bottom of Figure 2.

The Fluid Designer (AxFDesigner) in AxSTREAM® allows users to create custom fluid files to be utilized for any pure fluid or a mixture of single species from the several reliable fluid properties databases (NIST RefPROP and Simulis Thermodynamic by ProSIM, etc.). This allows for very accurate treatment of fluid properties at each station along the hydraulic path and for all intended pump operating modes. A user can select the required common jet fuels (for example, Jet A) directly from Fluid library, as shown in Figure 3.

The AxMAP module in AxSTREAM® is an effective tool to study the influence of operational parameters on pump performances. This module makes use of state-of-the art 1D/2D meanline/streamline solver taking into account real loss mechanisms. AxSTREAM® users commonly report faster compute times with good accuracy for this module.

Figure 4 shows a 3D view of a fuel pump designed from and based on 3/4 section view of Eaton fuel pump type 8810 (shown below) and its performance characteristics (taken from an open source).

Figure 5 shows the performance curve of the designed in AxSTREAM® fuel pump.

Once the preliminary and detailed design of the aircraft fuel pump has been completed, a user can easily use the AxSTREAM® embedded AxCFD to validate the performance and flow behavior utilizing 3D CFD technology.

Figure 6 shows the CFD analysis solution of the AxSTREAM® designed fuel pump in AxCFD. From the velocity contour, a pump designer can identify the vortex region in the stator and resolve this flow in a consequent design iteration. AxCFD allows users to evaluate a pump design early in the development process and make critical design decisions to better utilize development costs.

AxSTRESS is a structural, modal and harmonic analysis solver using a Finite Elements Method with a customizable, automatic turbomachinery-specific mesh generation, which is also a part of AxSTREAM® platform. Figure 7 shows the stress and displacement contour of the AxSTREAM® designed fuel pump obtained by AxSTRESS.

Learn more about how AxSTREAM® can help you and your team here or Contact Us for more information!

**Reference:**

Key Symbols

Indexes and Other Signs

Abbreviations

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.

The importance of solving the problem of the cascade’s basic characteristics definition can be seen from the following considerations. Let designed axial turbine stage blades at a predetermined height. Under certain parameters before and behind the stage is usually determined the number of blades and profile chords so that with an energy loss minimum satisfy strength and vibration requirements. The simplest solution is to select the “optimal” t/b ratio using known empirical relationships and determining the chords provide reliable operation. Upon closer examination the situation is not so simple: first, the optimum ratio t/b is determined by many factors (the relative thickness of the edge, the Reynolds number and the relative roughness of the surface, relative height and others); secondly, the permissible loss and the vibration characteristics depend on the influence of the previous cascade; third, the stage design can be carried out both from the set of standard profiles or suggest subsequent entirely new cascades profiling. Consideration of these circumstances makes the task of optimization of the basic cascade parameters quite challenging and promising in terms of using hidden in complicated situations reserves to increase efficiency and reduce consumption of materials in the created turbomachine design.

The calculation of the kinetic energy loss on the basis of empirical relationships has repeatedly been considered and, as experience shows, in the form set out in Chapter 2, is a reliable tool to assess the various components of the losses in the cascade. Calculation of the geometric characteristics of the profiles is carried out using a dependency suitable for working and nozzle profiles, including an elongated front portion. The stresses in the diaphragms, nozzle and rotor blades, as well as restrictions on the vibrational reliability calculated by the well-known and, as far as possible, the exact dependence.

When optimizing an isolated cascade the following problem statements species are considered.

I. Profile presentation method

- – I.1. Standard profile. The geometric characteristics are determined by the tabular data and restated for a specific profile stagger in the cascade, which provides the desired output stream angle at a known relative pitch.
- – I.2. “Macromodel”. The form of the profile is not known beforehand, but its defining geometrical characteristics can be estimated by empirical dependence of the type [26].
- – I.3. Profiling. In addition to the previous statement can be built demo profile, designed by a faster way. It is possible geometrical and strength characteristics evaluation on its configuration.

II. Variable parameters.

- – II.1. Optimization of chord when t/b = const.
- – II.2. Optimization of t/b when b = const.
- – II.3. The chord and the relative pitch optimization. In constructing the cascade of the standard profiles the profiles chord selection is in sequential enumeration of profiles of this type, but of different size [20, 33].

III. Boundary conditions.

- – III.1. Geometric, kinematic and gas-dynamic parameters in the first approximation are given from stage thermal calculation.
- – III.2. Cascade optimization process is conducted directly to the stage (multistage flow path) thermal calculation and optimization. In this case, the design of the cascade is embedded in an iterative process instead of the verifying energy losses in cascades, as is usually done.

Optimization is made by LP- search, and where this is not possible, brute force at defined ranges of variable parameters and the number of sampling points. The calculation is carried out in designer’s dialogue with a computer, which significantly reduces the time to find an acceptable solution.

]]>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.

After a long period of maintenance, there comes a phase when engineers face a challenging compromise between efficiency and investment. At this point, the decision must be made of whether to replace deteriorated blades, or to perform total retrofitting of the flow path, and receive efficiency and capacity benefits, for that renewed flow path. The most significant redesign and retrofitting variants are:

**Minimal**. Blades and nozzles replacement are performed, while casing and rotor are preserved.**Intermediate.**Retrofitting changes the number of stages, while keeping the existing meridional and axial dimensions. Casing is also preserved; rotor may be replaced or modified based on remaining life estimated on the rotor.**Maximal.**Complete redesign, with change of stage meridional dimensions, without fixing them in existing casing. The foundations and overall footprint is preserved to benefit the exiting foundations and civil structures.

Normally, power plant owners hire consultants or EPC’s to perform a feasibility study in order to identify possible improvements and economic viability of retrofitting machines. The consultants perform steam path audits and invite the original equipment manufacturer (OEM’s) or third parties to offer solutions. The OEM’s generally are not very keen on redesigning the existing machinery, and would offer a best compromise from their existing product lines. Third parties would reverse engineer the blades and try to restore the machine back to the original state. However, there is a third option, which is not usually explored. The EPC’s or even power plant owners themselves can do the engineering activities and provide the owners the most appropriate solutions based on which decision can be made.

There is a great opportunity for the engineering team from utilities to take on this task and help determine the best course of action for their budgets. The first step is to perform a quick study by analyzing the existing power plant and seeing if the current plant is in-line with the existing state-of-the-art power plants. The plants considered for retrofitting are typically older with 20+ years of operation. The technologies used at that time and presently have changed. The engineering team can start by performing a feasibility study to help take the right decision. Performing an existing design analysis and redesigning the existing machines can be done using the AxSTREAM® platform (even for engineering who have minimal expertise on turbomachinery).

Thanks to its advanced preliminary design module, AxSTREAM® offers versatile opportunities in retrofitting. The inverse task solver of AxSTREAM®, finds the most efficient flow path, for a number of restrictions given as a range of acceptable values. These restrictions can be in terms of specific diameter for hub, mean, or tip, in terms of number of stages, axial length, blades height or even in terms of stator and rotor angles ranges. Later during detailed design, the obtained design can be further analyzed and optimized which can be done by experts or OEM’s. Completing these preliminary studies and designs can save considerable amounts of time and money.

Not necessarily. Retrofits using third parties often offers more flexibility, while OEM’s with readily available new state-of-the-art equipment prefer to place aging equipment as it is more suitable for them from a commercial standpoint. However, with the remaining life civil structure, casing and rotor of the existing equipment, it may be wiser to retain those components and not replace the equipment with new machine. By retrofitting the existing machine, the flowpath can be upgraded to meet the state-of-the-art performance and stay competitive in terms of both performance, and reliability.

The main factor, determining the lifetime of steam turbines, is the strength and reliability of their high temperature design components. They can fail due to excessive deformations, or burst in, as a result of long-term influence of pressure or centrifugal force. Cracking can also occur, under pure creep, or creep-fatigue conditions. As the initially assessed lifetime of a turbine nears its end, a possibility of its further extension needs to be determined individually. This is done, based on inspection of the state of the turbine’s major design elements. Such an inspection allows estimating the actual wear of their metal, and assessing their residual lifetime, by means of non-destructive examination. New calculations can be performed then, taking into consideration, the actual history of the turbine’s operating conditions. This includes actual duration of operation, at the diverse levels of steam temperatures and loads, as well as, the number and characteristics of start-ups, load discharges, and other types of the transients.

This information can be found in the power plant’s archives, in the form of stored computer data and recorder tapes. The more detailed the data, the more definite and trustworthy the assessments will be. Once these calculations are performed, the remaining life can be estimated and decisions about replacing vs retrofitting can be made.

Yes. In the last few years, significant developments have been made in blading technology, sealing, materials, etc. These have resulted in highly efficient steam turbines. The principle reason for carrying out retrofitting or uprating, is not just because of aging, but also to improve plant performance. It increases efficiencies and reliability, while reducing emissions. Due to this, the plant remains competitive in the market. Moreover, it makes perfect sense, and is even more economical, to extend life of the equipment, rather than retiring the plant.

Today, in addition to addressing the aging fleet issue, utilities are also looking for the competitive technological edge, that additional capacity and better performance through retrofitting will provide. Other factors that enter into the economic model, are the desire for sustained performance, with minimal degradation over period of at least ten years, and the desire to extend time between major overhauls, to at least ten years.

Power plants can have many different retrofit needs. Many power plants perform these retrofits to address common issues. The first option is to convert the steam turbines, for usage in a combined cycle. Another option is to get a turbine rerating, to increase capacity, or to get cycle upgrades, with change of extraction and induction conditions or parameters. Also, replacement of blading, seals etc. can be a good way to increase turbine performance. Retrofitting can be performed to obtain the highest performance, with, or without, change to inlet and outlet conditions.

Whichever retrofit you consider, an evaluation of material life for each different components, like casing, rotor etc., needs to be done before the decision is made.

Abdul Nassar is the Managing Director at SoftInWay, with over 23 years’ of industrial, academic and research experience. He has substantial expertise in designing and retrofitting turbomachinery and currently oversees many projects related to development of turbines, compressors, and pumps. In addition, he has delivered a number of courses on steam and gas turbine design throughout Europe and Asia. The author of more than 22 technical publications, Mr. Nassar is currently leading multiple projects for SoftInWay in India.

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