Datos do laboratorio

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Several studies in the literature by various authors, thermodynamically and mathematical analysing the effects of the design parameters on the performance of an axis between the compressor, turbine and generator components using maps as Okelah [5], have performed this study performance of a fixed geometry turbo shaft engine co-using component maps; Al Hamdan and Ebaid [6] have performed the modelling and simulation of a gas turbine engine ideal single axis. Aklilu et al [7] developed a mathematical model to simulate a part-load operation of a single shaft gas compressor turbine with variable geometry, while Zhang and Cai [8] have made the study of the performance of generalized components. For commercial reasons, the manufacturer of microturbine not yield maps published turbines and compressors in the open literature, hence the usefulness of universal formulas of performance.

With the availability of these formulas, the microgasturbine suitability for the intended use can be checked, to then predict their behaviour at different loads. The methodology used for the model is based on the laws of the thermodynamics cycles of heat engines, and relies on correlations developed by authors such as Malinowski and Lewandowska [3].

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Turbine Characteristic Curves – Analyti

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cal Model

This article uses an analytical model as proposed in Refs. [8, 9, 3], to calculate the performances of the main components of a microgasturbine [10]. It is an useful tool because the turbine manufactures didn’t provide an extensive data that permits to model and predict the turbine behavior at part-load and outside standard conditions. Its main equations, that calculate the pressure relations and efficiencies of the compressor and turbine, are dimensionless, parametrized to design parameters, and are functions of the relative turbine rotational speed, and the relative mass flow, as presented in the equations (1 - 3).

Where is the relative turbine Rotational Speed defined as: [pic 1]

(1)[pic 2]

(2)[pic 3]

(3)[pic 4]

Where and are the relatives mass flow difined as[pic 5][pic 6]

To model the compressor the dimensionless equations used to predict the pressure relation and efficiency, are the equation (4) and (5), and it uses also, uses analogues equations to calculate the turbine performance.

(4)[pic 7]

(5)[pic 8]

Where C1, C2, C3, C4 and t4, are parameters, as were described in Refs. [8, 9, 3], are functions of the relative rotational speed, relatives mass flow, and of experimental data. In the parameters mentioned above, there are to others parameters, namely p and m, that permits to fit the equations to the set of data with manufacturer’s standard data and experimental data from one turbine operating at part-load and outside the standard conditions. The design point parameters used to parametrize the characteristics curves, as inlet and outlet temperatures, isentropic efficiencies, etc [9].

Pressure drop calculation: The model calculates the pressure drop along the cycle using equation (6):

(6)[pic 9]

Where is the pressure at the inlet to that element, and is that of the outlet of this element, and k [pic 10][pic 11]

Is the relative pressure loose that can be calculated using equation (7):

(7)[pic 12]

The measure of the overall system pressure loss is the coefficient:

(8)[pic 13]

Where The following values of k, were used: kin0=0,01; kout0=0,01; kcc0=0,02; krl0=0,02; krh0=0,02.

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Microgasturbine Modelling

Microgasturbine used has a heat exchanger regenerator inside of it, as can be seen at the schematic model of the gas turbine in Figure 1. It also shows, a control volume (vc) involving the turbine. Following the schematic diagram, the combustion air is fist filtered and used to cool the electric generator before it enters the compressor (1). In this component, it is pressurised and pass into the regenerator and is preheated by the heat recovery from the exhausted gases passing through this heat exchanger. (2) After this, the preheated air (2r) is mixed with fuel (3) in the combustion chamber and is burned out. The hot exhaust gas converts its energy in a expansion process through the turbine (4) that drives the compressor and the electric generator then enters the recuperator (4r) and finally goes out the waste heat.

The modelling procedure based in some basic assumptions, consisted in to obtain a set of equations, generated by the application of an energy and entropy balance to each component of the equipment, the use of the isentropic efficiencies equations, and with equations to calculate the pressure relation at compressor and turbine, and the pressure drop along the cycle. The modelling procedure will be shown in the next paragraph, presented in a summarized way, that is, only to one component, the turbine. Input data used in calculations for the model corresponding table 1.

[pic 14]

Figure 1. Schematic model of microgasturbine.

Basic assumptions:

- The turbine operates at a constant controlled exit Temperature

- The air and combustion gases are ideal gases.

- The specific heat is variable and is used as in [18].[pic 15]

Table 1. Input data nominal conditions used in calculations

Description

Value

Unit

Microgasturbine electric power

30

kW

Natural gas pressure

360 – 380

kPa