Numerical study of an axial gas-turbine stage.

Vilag, Valeriu ; Popescu, Jeni ; Petcu, Romulus 等

1. INTRODUCTION

Gas turbines engines are very largely used in power generating systems such as aircraft, energy and industry. Their main advantages are related to small dimensions to power ratio when speaking about aviation and relatively small fuel consumption and high reliability when speaking about ground applications (Carlanescu, 1997).

The advance in computer technology made possible the virtual tests in form of Computational Fluid Dynamics simulations for many thermodynamic and flow applications. These simulations have advantages related to lower costs and shorter time to market in comparison to classical analytical and experimental methods. This relatively new tool allows us to validate geometries from gas-turbines and to predict the performances for new or improved products. It offers a better perspective on parameter variation helping us to better understand the phenomena by conducting numerical experiments.

2. BLADE GEOMETRY DESIGN

2.1 Symetrical profile

The following parameters are used for the base profile: [[bar.y].sub.Gmax]: maximum thickness (% chord)

[[bar.R].sub.ba]: radius of curvature of the leading edge (% maximum thickness)

[[bar.R].sun.bf]: radius of trailing edge (%maximum thickness)

[omega]: half of the angle between the tangents at the trailing edge (degrees)

For simplifying formulas some additional notations are required, resulting the following formula for thikness distribution along the symmetrical profile (Ainley 1951):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

The graphical expression of that is displayed in Fig.1

2.2 Actual profile

This base profile must be curved and aligned considering the desired working regime. The working regime is translated into necessary angles at the inlet and the outlet of the row blade and they are function of the radius and the type of row blade: stator or rotor. The profile camber is curved along a parabola tangent to these necessary angles (Novak 1967), as shown in Fig. 2:

[[alpha].sub.1]--inlet flow angle

[[alpha].sub.2]--outlet flow angle

[[beta].sub.1]--inlet blade angle

[[beta].sub.2]--outlet blade angle

In order to obtain the curved profile we need to find the arc length, to be able to position the resulted thickness of the base profile.

The parabola is now written parametrically:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

and the arc length is given by:

[bar.s](t) = [a.sub.0][t[square root of 1 + [t.sup.2]] + ln(t + [square root of 1 - [t.sup.2])] (3)

If we apply one more rotation we obtain the profile in one section, aligned with the gas-engine axis.

3 CFD CASE

3.1 Geometry and mesh description

The profiles with respect to the radius of the axial-turbine, for the stator and the rotor blade rows, were given by analytical methods in form of sets of points (Sellers 1975). Using this series of points and the radiuses of the flow canal into CAD software the following geometry was obtained. Due to the fact that we are studying the first turbine stage, the stator blades are cylindrical. In order to obtain a predominant axial velocity at the outlet of the rotor row blade, the rotor blades are twisted. The inner and outer diameters of the flow canal are constant and are taken from the preliminary design calculus.

[FIGURE 1 OMITTED]

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The necessary CFD mesh for such a complex geometry would be too large to be use on desktop computers or even on dedicated calculus machines, so we need mesh reduction. The reduction of the mesh is done by using the assumption that the stator blades are identical and the rotor blades are identical and also that they respectively behave identical. This results in that we can use only a smaller part of the geometry but with some constrains:

--the angle of the used sector must contain integer number of sections corresponding to one blade; this is valid both for stator and rotor

--the ratio between the angle used for the stator and the angle used for the rotor must be close to unity.

The first constrain is obvious, and the second contains relation to mass flow through the interface between the stator and the rotor.

In our case study we used 3 stator blades giving an angle equal to [a.sub.s] = 3x 360[degrees]/20 = 54[degrees] and 7 rotor blades giving an angle equal to r = 7x 360[degrees] = 53.61[degrees]. The ratio between them is [a.sub.s]/[a.sub.r] = 1.0071 that is close enough to unity, Fig. 4.

3.2 Working conditions

Thermodynamic and mechanic imposed conditions are the user input for the CFD code concluded into inlet and outlet conditions and rotational speed for the rotor.

It was imposed on the stator inlet the total pressure at the value of 9.12 bars and the total temperature equal to 1300 K, and on the outlet of the rotor the mass flow per machine equal to 8.1 kg/s. All imposed values are taken from the thermodynamic cycle (Pimsner 1988) proposed for the gas-turbine to be equipped with this axial turbine, MTI--1500. Each sector is limited by two periodic boundaries, by two walls, the hub and the shroud, and by the inlet and the outlet surfaces.

The working fluid is assumed to be air ideal gas that is close to reality at these relatively reduced pressures.

The rotational speed of the rotor has been varied between 14000 and 28000 rpm with a step equal to 2000 rpm. At every rotational speed, the regime was considered stationary.

3.3 Results

The major advantages of CFD is that it can give parameters variation in space, and time if appropriate, in form of contours plot. This means that one can easily identify problems related to flow continuity, backflow or other types of losses. We present in the following figures contour plots of static pressure and static temperature, Fig. 5, at half span of the axial-turbine. The pictures are taken at the nominal working regime, at 22000 rpm.

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One other important result is the efficiency variation with respect to the rotational speed of the rotor. We present the variation of four types of efficiency in Fig. 6.

The most important parameter in this stage of development is the useful power of this axial turbine stage. We present in Fig. 7 the variation of the power with the rotational speed of the rotor row blade.

We can observe that according to CFD results the maximum power is obtained at 22000 rpm which is the nominal proposed working point. The value of the power is around 2050kW which is higher than expected, 1/3 4500kW = 1500kW. This is mainly due to the higher temperature imposed at the inlet of the stator row blade.

4. CONCLUSIONS

The overall scope of the research is to have a good algorithm using analytical and numerical methods for designing axial turbines. The main conclusion is that we have obtained a good correlation between the analytical way to draw turbine profiles and CFD numerical simulations. The maximum efficiency and the maximum power are obtained at the same rotational speed which was imposed for the analytical method.

Another conclusion is that by combining the two methods we can improve the efficiency, into an iterative cycle, by modifying parameters of the analytical method and verifying the corresponding changes using CFD simulations. The efforts of doing that are considerable lower comparing to experiments for which the production stage takes time and costs a lot more money. The experiments are not excluded, but their time should arrive into a further development stage, after the best geometry had been obtained through the proposed combined method.

Future work consists in CFD simulations of the entire axial turbine for the MTI 1500 industrial turbo-engine.

5. REFERENCES

Carlanescu C. (1997), Turbomotoare de Aviatie. Aplicatii Industriale (Aviation gas turbines. Industrial Applications), Editura Didactica Si Pedagogica, Bucuresti

Ainley D.G. (1951), A Method of Performance Estimation for Axial-Flow Turbines, Reports and Memoranda No.2974, A.R.C. Technical Report, Decembre

Novak R.A. (1967), Streamline Curvature Computing Procedures for Fluid-Flow Problems, Transaction of the ASME Journal of Engineering for Power, A Series

Sellers J.F. (1975), DYNGEN--A Program for Calculating Steady-State and Transient Performance of Turbojet and Turbofan Engines, Lewis Research Center, NASA TN D-7901

Pimsner V. (1988), Masini cu Palete (Bladed machines), Editura Tehnica, Bucuresti