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Research Papers: Power Engineering

# A New Model for the Analysis and Simulation of Steam Turbines at Partial and Full Load

[+] Author and Article Information
Mario Álvarez Fernández1

Department of Mechanical Maintenance, Santa María de Garoña Nuclear Power Plant, 09212 Burgos, Spainmario.alvarez@nuclenor.es

Cristina Alonso-Tristán

Escuela Politécnica Superior, University of Burgos, Avda. Cantabria, 09006 Burgos, Spaincatristan@ubu.es

There is one extraction from the steam supplied to the HP turbine, but placed in the discharge, so the mass flow through all the control volumes to be considered will be constant.

If the calculation is described, for example, for an expansion from the saturated liquid condition, a valid polytropic equation will not be obtained.

Kinetic energy has been neglected when calculating the power. The potential energy was neglected in Eq. 7.

In Fig. 7, the isentropic exponent is approximately constant because the steam conditions at the inlet remain constant (typical of power plants). The isentropic exponent could be calculated by using the procedure applied in Sec. 2 using the average value of inlet pressure plotted in Fig. 6. The value obtained can be used as a constant for a particular steam turbine (in this case, the value obtained by simulating an expansion from 65.74 bars to 0.45 bar will be $γ=1.1149$).

The “bean-valve” is used in order to damp the pressure from the “sensor line” to the mechanical pressure regulator, which controls the turbine during the loading.

Without the subscript, the surface surrounding and delimiting the control volume.

1

Corresponding author.

J. Eng. Gas Turbines Power 133(11), 113002 (May 18, 2011) (10 pages) doi:10.1115/1.4003643 History: Received November 06, 2010; Revised January 23, 2011; Published May 18, 2011; Online May 18, 2011

## Abstract

A model is described that studies the behavior of a steam turbine on the basis of the law of conservation of energy even under wet-steam conditions at particular points in time. Initially, the hypothesis that steam expansion follows a polytropic function will be demonstrated, and a procedure for the calculation of the polytropic exponent will be introduced. Then, the real thermal power given by the steam turbine will be calculated when the steam at the discharge section is wet steam. This calculation has not been analytically developed until now. Two factors will likewise be introduced: a flow factor (used in order to simulate the discharge pressure) and a loss factor (used in order to simulate the discharge enthalpy). With these factors, the steam at the outlet section of a steam turbine will be fully simulated. Furthermore, the loss factor can be used to evaluate the efficiency of the steam turbine. All the equations are validated at both partial and full loads and will be implemented in a real case study: the High Pressure Turbine of the Santa María de Garoña Nuclear Power Plant, which operates at all times under wet-steam conditions, making it particularly relevant for this study.

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## Figures

Figure 1

Expansion of steam at constant entropy (s=5.779 kJ/kg °C) compared with isentropic expansion considering the same isentropic exponent for superheated and wet steam

Figure 2

Error as a function of the pressure between the specific volume calculated during an expansion at constant entropy (s=5.779 kJ/kg °C) and the specific volume calculated assuming the same isentropic exponent for superheated and wet steam

Figure 3

Error as a function of the pressure between the specific volume calculated during an expansion at constant entropy (s=5.779 kJ/kg °C) and the specific volume calculated using different isentropic exponents for superheated and wet steam

Figure 4

Expansion of steam at constant entropy (s=5.779 kJ/kg °C) compared with isentropic expansion considering different isentropic exponents for superheated and wet steam

Figure 5

Control volume applied to a steam turbine

Figure 6

Relationship between the inlet/outlet pressure (P1 and P2) and the mass flow (ṁ) in the course of rising load at the Garoña Nuclear Power Plant (July 12, 2008)

Figure 7

Relationship between the polytropic (k) and isentropic (γ) exponents and the mass flow (ṁ)

Figure 8

Relationship between the efficiency (η) and the mass flow (ṁ)

Figure 9

Relationship between the power (Ẇ) and the mass flow (ṁ)

Figure 10

Relationship between the overall loss coefficient (Kt) and the mass flow (ṁ)

Figure 11

Relationship between the flow factor (Kqs) and the mass flow (ṁ)

Figure 12

Comparison between the values of discharge pressure (P2) calculated and real

Figure 13

Comparison between the experimental outlet pressure measured on April 25, 2009, P2 (real), and the calculated one, P2 (calc), using the flow factor as a function of the mass flow (ṁ)

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