thermodynamic and fluid-dynamic analysis of

8/3/2019 Thermodynamic and Fluid-dynamic Analysis Of

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Thermodynamic and fluid-

dynamic analysis of

stages


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Classification of these methods depend on the type of

hypothesis formulated to analyze the machine flow rate. Onthe most general level we may distinguish between:

Monodimensional methods. This term indicates a group of

models deriving from application of the hypothesis of

monodimensional flow in the stage.

Non-viscous methods. This refers to numerical techniques

based on flow analysis in the individual components of the

stage in the approximation of non-viscous flow.

Viscous methods. These methods are based on flow

analysis conducted through numerical integration of the flowviscous equations.


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MonodimensionalMethods

Assumes that the fluid conditions are uniform over

certain flow cross-sections.

These cross-sections are taken before and after the

impeller as well as at inlet and exit of the entire machine. A specific operating condition is assumed, defined by the

following parameters ,assumed to be known:

P00= total inlet pressure

T00= total inlet temperaturem =mass flow rate

N=impeller speed of rotation


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Analysis of Impeller Inlet Section

The flow between stage inlet section and impeller inlet

section can usually be considered isentropic.

The conditions in section 1 can be evaluated by applying thecontinuity and momentum equations.

Determination of the quantities relevant to the streamline

passing in proximity to the blade tip is particularly important

since it is here that the highest relative Mach numbers are

found.

The meridian component of the absolute velocity Cm1 can

be determined by:

Where

r1= specific volume &CD

=blockage factor due to presence of theblades.


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The tangential component of the absolute velocity Cq1

depends on whether or not inlet guide vanes are utilized. In

the absence of vanes, we will have Cq1=0.

And also:


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Analysis of Impeller Discharge Section


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Monodimensional Analysis of Diffusers

Assume the inlet condition to diffuser is the exit from

impeller.

The most important diffuser performance parameter is

the pressure recovery coefficient Cp defined by theequation:

This parameter is utilized to quantify the amount kinetic

energy transferred to the fluid by the impeller, whichconverting into potential energy.

The diffusors most frequently utilized in centrifugal

stages can be classified under two headings: free vortex

and bladed.


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The approach most frequently used in analyzing free

vortex diffusors hypothesizes a succession of

monodimensional condition sections with r=constant lying

between impeller discharge section and diffusor dischargesection.

The fluid-dynamic balance equations relevant to this

representation, inclusive of the friction terms deriving from

the presence of side walls, can be integrated numericallystarting from known conditions in the discharge section.

This procedure can be used to evaluate the fluid-dynamic

state on discharge from the diffusor and the consequentperformance of the component.


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The best-known of these

correlations refers to

experiments conducted by

Runstadler on diffusors of

bidimensional geometry with

straight walls diverging on a

single plane. It shows that

the recovery coefficient

depends on a number ofgeometric and aerodynamic

parameters, such as the

length/width ratio L/w, throat

section, and divergence

angle 2.

With the bladed diffusor, the approach most commonly

employed for evaluating the performance of this component

consists of experimental correlations.


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Disadvantages of The monodimensional

methods

1. impossibility of obtaining an accurate representation of

the fluid-dynamic field at all machine points.

2. impossibility of diagramming the detailed geometry of

the components and its influence on the fluid-dynamic

characteristics.

3. need to introduce empirical data in the form of various

experimental correlations.

to overcome at least some of these limitations ,we need

for analysis methods capable of resolving, throughnumerical calculation procedures.

Because of the complexity and expense of using

viscous models, attention was initially focused on

models based on the hypothesis of non-viscous.


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Non-viscous Numerical Methods

The non-viscous methods can be divided into

four categories:

Bidimensional solutions relevant to streamline

surfaces lying in the hub-to-shroud direction

Bidimensional solutions relevant to streamline

surfaces lying in the blade-to-blade direction

Quasi-three-dimensional solutionsThree-dimensional solutions

In each of these categories the methods can be

classified to streamline curvature methods and

partial derivative methods.


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The streamline curvature methods are based on

the integration of ordinary differential equations

of the first order: these describe the momentum

balance along directions defined by the so-called quasi-normals to the streamlines.

The partial derivative methods are based on the

integration of differential equations with the

partial derivatives which describe the balance of

mass, that of quantity of motion and that of

energy at a point in the calculation domain.


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Bidimensional Solutions Relevant to Streamline

Surfaces in the Hub-to-shroud Direction.

These methods are based on representation of the

conditions existing on a hypothetical mean streamline

surface, extending in the hub-to-shroud direction within

the area lying between two adjacent blades.

A typical calculation code for this category, utilizing the

streamline curvature approach, is based on integration of

the momentum balance equations & mass balance

equations.

The codes based on the partial derivations approach

frequently utilize Wus formulation


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Bidimensional Solutions Relevant to

Streamlines in the Blade-to-blade Direction

These methods are based on the representation of conditionsin hypothetical streamlines consisting of surfaces between

two contiguous blades.

Many of these methods employ the streamline curvature

formulation. The most widely used approach utilizing finite differences

methods, frequently based on the formulation proposed by

Stanitz.

Have ability for evaluating the pressure and velocitydistribution, and consequently to predict the behavior of the

boundary layers in the real machine.

can be utilized as constituent elements of quasi-three-

dimensional or three-dimensional procedures.


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Quasi-three-dimensional and Three-

dimensional Solutions

A frequently used technique consists of producing quasi-

three-dimensional representations , obtained by

combining two bidimensional solutions relevant to

Streamline Surfaces in the Hub-to-shroud & Blade-to-

blade Direction .

Using of three-dimensional methods make an actual

representation. This model developed by Hirsch, Lacor,

and Warzee which utilizes a finite-element procedure.


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Viscous Methods The term viscous methods indicates a family of calculation

codes based on procedures of numerical integration of theviscous, compressible, and three-dimensional equations of

motion.

the system formed of the complete Navier-Stokes equations

in non-stationary form, the laws of fluid, and the equations

that specify the dependency of viscosity and thermal

conductivity on other variables.

In the case of laminar flow, a numerical simulation based on

this methods give accurate description & do not have another

information based on empirical data. It is possible to simulate a turbulent flow through integration of

the Navier-Stokes equations in non-stationary form.

thermodynamic and fluid-dynamic analysis of

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