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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.

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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_{c}_{2},x_{c}_{1}] for the convex and for [x_{k}_{2},x_{k}_{1}] 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_{c}_{2},x_{c}_{1}] on the convex portion of the profile and [x_{k}_{2},x_{k}_{1}] – 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
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 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.

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]}

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

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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.

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

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

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

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

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

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

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

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

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

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

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

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