5.5 Optimal Profiling Examples

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The created profiling algorithms have allowed to design a series of profiles of turbine cascades.

As a starting (1O) was taken the standard profile P2 with a high aerodynamic quality. Wherein were accepted such flow conditions that ensure the smallest possible profile P2 (1O) losses: t = t/b=0.722, βb= 76°26′,β1 = 29°30′.

Retaining the basic, necessary for the machine profiling raw data:

with the help of the developed algorithms were obtained new profiles: 1MMC (for the geometric quality criteria – the minimum of maximum curvature) and 1MPL (the minimum of profile loss).

From technological considerations subsequently profile 1MMC contour was approximated by the radii (Fig. 5.4, 5.5, Table 5.2). Fig. 5.6–5.8 shows the distribution of the velocity and the parameter B (the Buri boundary layer separation criterion) along the contours of the original and newly created profiles.

The calculated profile loss ζpr values correspondingly are 3.35, 3.16 and 3.00%. Attention is drawn to the different law of the parameter B variation along the profiles contours. Apparently, the possibility of the boundary layer separation, or the intensity of its thickening (which leads to increased losses) must be judged not only by the maximum value of the parameter B, which (usually) achieved at cascade’s oblique cut, but also the character of its change within the channel prior bevel, particularly on the convex side of the profile.

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Oil Systems for Turbine Lubrication

The oil system is an integral element of the turbine unit, which largely determines its reliability and trouble-free operation. The main purpose of the turbine lubricating oil system is to provide fluid friction in the bearings of turbines, generators, feed pumps, and gearboxes.

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.

Figure 1 Principle Scheme of K-500-240 Steam Turbine
Figure 1. Principle Scheme of K-500-240 Steam Turbine.


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

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An Overview of Axial Fans

Axial fans have become indispensable in everyday applications starting from ceiling fans to industrial applications and aerospace fans.  The fan has become a part of every application where ventilation and cooling is required, like in a condenser, radiator, electronics etc., and they are available in the wide range of sizes from few millimeters to several meters. Fans generate pressure to move air/gases against the resistance caused by ducts, dampers, or other components in a fan system. Axial-flow fans are better suited for low-resistance, high-flow applications and can have widely varied operating characteristics depending on blade width and shape, number of blades, and tip speed.

Fan Types

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%.
Types of Fans
Figure 1 Different Types of Axial Fans
Aerodynamic Design of an Axial Fan

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. Read More

5.4 Minimum Profile Loss Optimization

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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 ζfr and edge loss coefficient ζe.

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.

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Redesigning Anakin Skywalker’s Podracer

Ever since circa 100 BBY, Podracing in its modern version has drawn crowds from far far away to watch pilots compete in races like the Boonta Eve Classic which made Anakin Skywalker famous and won him his freedom. By beating Sebulba, the Dug, and the other Podracers, Anakin became the first human to be successful at this very dangerous sport. The Force helped him in his victory by sharpening his reflexes, but his repulsorcraft was also superior due to its size and the modifications made to its twin Radon-Ulzer 620C engines, especially the fuel atomizer and distribution system with its multiple igniters which makes them run similarly to afterburners seen on some military planes on Earth.

Figure 1 Pilots and their Repulsorcrafts at the Start of the Boonta Even Classic Race on Tatooine
Figure 1 Pilots and their Repulsorcrafts at the Start of the Boonta Eve Classic Race on Tatooine

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. Read More

5.3 Optimization of Geometric Quality Criteria

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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 [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

Complex Modeling of a Waste Heat Boiler


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.

HRSG Flows Direction
Picture 1 – HRSG Flows Direction
Different Approaches

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5.2 Profiles Cascades Shaping Methods

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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.

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 [25]; 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.

Figure 5.1 The design parameters of the profile cascade.
Figure 5.1 The Design Parameters of the Profile Cascade

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Aircraft Fuel Pump Design and Optimization

Introduction to Aircraft Fuel Pumps

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]

Fuel Pump Impeller
Fig.1 Various Fuel Pump Impellers
Designing an Aircraft Fuel Pump with AxSTREAM®

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5.1. The Cascade’s Basic Geometry Parameters Optimization

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Chapter 5 Introduction: Optimal Cascades Profiling

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