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Journal ArticleDOI

Performance and flow fields of a supersonic axial turbine at off-design conditions

22 Mar 2013-Vol. 227, Iss: 3, pp 285-294
TL;DR: In this article, a supersonic axial flow turbine is studied numerically to find the causes of efficiency decrement and explains the loss sources individually for the stator and the rotor.
Abstract: The increasing demand of energy efficiency and the utilisation of small-scale energy sources require efficient, small and versatile turbines. Supersonic turbines have a high power density and therefore small size and fewer stages than the subsonic ones. However, the performance of a supersonic turbine can decrease rapidly when operating at off-design conditions. This raises a need for the improvement of the turbine off-design performance. In this article, a supersonic axial flow turbine is studied numerically to find the causes of efficiency decrement. This article presents the most thorough study so far about the reasons that lead to the decreased off-design performance with supersonic axial flow turbines and explains the loss sources individually for the stator and the rotor. Three operating conditions are studied, and it is suggested that at the lower than design pressure ratios, the shock losses of the stator decrease while simultaneously the stator secondary losses increase. The high positive incidence at the lowest modelled pressure ratio, mass flow and rotational speed caused a significant decrease in the rotor and stage performance. This highlights the importance of incidence even in shock-driven supersonic turbine flows.

Summary (3 min read)

1 INTRODUCTION

  • Supersonic turbines are especially suitable for designs where the space is limited and high power is desired.
  • The increasing pressure ratio turned the rotor incidence more positive.
  • The main reason for the decreasing efficiency was concluded to be the increase of total pressure losses at the axial gap.
  • The fourth chapter presents the results that can be divided into two topics.
  • In the second part of Chapter 4, the performance and flow fields of a supersonic turbine stage are studied at three different operating conditions.

2 NUMERICAL METHODS

  • The Navier-Stokes solver Finflo is used in this study.
  • For the primary flow variables and conservative turbulent variables, the MUSCL type approach is used, and the DDADI-factorization [12] is used to integrate the discretized equations in time.
  • More detailed information about Finflo and different numerical methods can be found e.g. in a paper of Siikonen [14].
  • This can be considered to be the biggest drawback of the chosen modelling approach, but the relative differences between different operating conditions can be expected to be comparable.
  • These inlet and outlet boundary conditions are used both in the transonic cascade and supersonic turbine stage modelling.

3.1 Transonic Turbine Cascade

  • To demonstrate the reliability of the current study, a transonic turbine cascade is modelled with Finflo.
  • This modelling gives information about the code performance with shock waves.
  • The numerical model has two calculation blocks - one block covers one flow channel.
  • The total number of cells is 3014656 and the non-dimensional wall distance is less than unity in the blade surfaces.
  • The static pressure along the blade surface and the total pressure variations at measurement planes SS-37 and SS-02 are taken from the midspan.

3.2 Supersonic Turbine

  • The turbine under investigation is a low reaction supersonic axial turbine without twist in the rotor blades.
  • The main geometrical parameters of the turbine are presented in Table 1.
  • The inlet boundary is located 270% of the stator axial chord upstream from the stator leading edge.
  • The pressure ratio at medium conditions is slightly higher in the modelling than it was in the measurements (4.05), but it is still believed to give results that represent the real operating conditions.
  • It is believed that the results are comparable since the grid used at different operating conditions is the same in every case.

4.1 Cascade Modelling

  • The calculated isentropic Mach number along the turbine profile is compared with the measurements of Sonoda et al. [19] in Fig. Sonoda et al. [19] reported also nearly similar results since they found that the calculated Mach number was lower than the measured values at the front part of the blade surface.
  • The numerical model seems to be unable to fully predict the reflected shocks and compression waves at the suction surface which makes the curve flat compared to the drop in the measured value at x/cax=0.93.
  • Losses are well predicted between the suction surface and the wake, but the wake is wider than the measurements indicate.
  • The position of the trailing edge shock is reasonably well predicted.

4.2 Turbine Stage Performance at different operating conditions

  • The isentropic total-to-static efficiency is used to compare the performance of the turbine stage at different operating conditions and is defined as s41t 4t1t sts, TT TT . (4.2).
  • The performance of the stator and rotor is evaluated by calculating the stator and rotor isentropic efficiencies by Equations (4.3) and (4.4), respectively.
  • All thermodynamic and flow properties are mass flow averaged values, except the static pressures that are used to calculate the isentropic Mach number distributions.
  • The results show that the turbine performs with the highest efficiency at a slightly lower rotational speed (28500 rpm) than it was designed for (31500 rpm).
  • It is also interesting to notice that the stator operates well even under the low operating conditions.

4.3 Stator Flow Fields at Different Operating Conditions

  • To be able to explain the reasons for the differences between the operating conditions from the previous chapter, it is necessary to look at the flow fields.
  • The amount of losses that originate from the trailing edge shocks is a function of outlet Mach number [4].
  • In Fig. 8, the isentropic Mach number distribution at the stator midspan is plotted over the stator axial length.
  • The shape of the distribution is similar also at the hub and shroud, and therefore only the midspan is presented here.
  • These losses are caused by the decreased loading at the stator suction surface due to more perpendicular trailing edge shock waves.

4.4 Rotor Flow Fields at Different Operating Conditions

  • In Figs. 9 (a) and (b), the contours of the relative Mach number are plotted at the rotor outlet for the design and medium conditions.
  • The areas of low Mach number are also noticeable at the suction and pressure surfaces from hub towards the midspan at the low operating conditions.
  • In a paper of He [21], it was also mentioned that the non-twist rotor blades lead to a negative incidence near the tip and a positive incidence near the hub.
  • The reason for large overturning is the high positive incidence at the rotor leading edge.
  • Yasa et al. [3] found that with a low rotational speed, the importance of the rotor incidence is higher than the stator exit losses.

5 CONCLUSIONS

  • This paper presents a throughout study about the reasons that lead to the decreased offdesign performance of a supersonic axial flow turbine.
  • The study showed similar trends in the flow behaviour and loss sources with the open literature giving verification for the results.
  • The performance of the rotor was found to be strongly affected by the incidence.
  • These loss sources can be used to explain the slightly better turbine performance at the medium off-design operating conditions which was attributed to the performance improvements in stator and rotor equally.

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Citations
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Cites methods from "Performance and flow fields of a su..."

  • ...Two main types of expanders are normally used in ORC systems: dynamic expanders [2-5] and volumetric expanders....

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Proceedings ArticleDOI
01 Jan 2019
TL;DR: In this article, the effects of the rotor blade sweep, velocity radial component at the rotor inlet and hub endwall contouring separately were investigated for a geometrically close turbine.
Abstract: The present paper continues the investigation started in Part I. The basic turbine stage remains the same as in Part I (an axial turbine stage with axisymmetric nozzles and mean diameter 103.5 mm). The numerical simulation method used in Part I was corrected by adding analytical correlation for disc friction losses. This approach was validated on the base of the experimental data for a geometrically close turbine. Variation of the radial velocity component at the rotor inlet was proposed as a new modification compared with Part I. The mathematical formulations of the rotor blade sweep and radial velocity component at the rotor inlet were proposed. The new modifications of the baseline were provided to establish the effects of the rotor blade sweep, velocity radial component at the rotor inlet and hub endwall contouring separately. The using of backward swept rotor blades together with the positive cinematic lean provided efficiency increasing up to 2.9% at the design conditions. It was also established that absence of a velocity radial component at the rotor inlet in the model with backward swept blades leads decreasing of the turbine performance. Axisymmetric hub contouring provided up to 1.9% efficiency growth at the part-load operation.

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References
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TL;DR: In this article, it is shown that these features can be obtained by constructing a matrix with a certain property U, i.e., property U is a property of the solution of the Riemann problem.

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TL;DR: In this paper, the Taylor series expansion technique was used to systematically investigate the proper behavior of the turbulent shear stress and the kinetic energy and its rate of dissipation near a solid wall.
Abstract: 2~5 However, the effects of the kinematic viscosity on the turbulence structure were ignored in many of these treatments. Consequently, the exact boundary conditions at the wall cannot be used when the turbulence Reynolds number is not high as, e.g., in flows with rapid expansions or near the transition/turbulence interface. The general goal of the present investigation was to develop a single transport model from the Navier-Stokes equation for accurate predictions of skin friction, heat transfer, and fluctuating kinetic energy distributions in transitional and turbulent flow regimes. As a first step toward this general goal, a new turbulence model valid down to the solid wall is formulated in this paper. Turbulence model equations which provide predictions of the flow within the viscous layer adjacent to the wall have been proposed by several investigators.3'4'6'7 Although the general approach of the present model is the same as that of Jones and Launder,3 the detailed proposals are substantially different. In the present study, the Taylor series expansion technique was used to systematically investigate the proper behavior of the turbulent shear stress and the kinetic energy and its rate of dissipation near a solid wall. The results were used in developing a new turbulence model which retains the proper physical behavior of the balance between the dissipation and the molecular diffusion of the turbulent kinetic energy at the solid wall. The model was applied to the problems of a fully developed turbulent channel flow and of a turbulent boundary-layer flow over a flat plate. Results on skin friction, the distribution of mean velocity, turbulent shear stress, and turbulent kinetic energy will be presented and compared with available experimental data and with the theory of Jones and Launder.

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Journal ArticleDOI
S. C. Kacker1, U. Okapuu1
TL;DR: In this paper, a mean line loss system is described, capable of predicting the design point efficiencies of current axial turbines of gas turbine engines, which is a development of the Ainley/Mathieson technique of 1951.
Abstract: A mean line loss system is described, capable of predicting the design point efficiencies of current axial turbines of gas turbine engines. This loss system is a development of the Ainley/Mathieson technique of 1951. The prediction method is tested against the ''Smith's Chart'' and against the known efficiencies of 33 turbines of recent design. It is shown to be able to predict the efficiencies of a wide range of axial turbines of conventional stage loadings to within 1 1/2 percent. 13 refs.

298 citations


"Performance and flow fields of a su..." refers background in this paper

  • ...The amount of losses that originate from the trailing edge shocks is a function of outlet Mach number.(4) The average stator outlet Mach number for design and medium operating conditions is 1....

    [...]

Journal ArticleDOI
TL;DR: In this paper, three linear cascades of highly loaded, low aspect ratio turbine blades have been tested in order to investigate the mechanisms by which blade lean (dihedral) influences loss generation.
Abstract: Three linear cascades of highly loaded, low aspect ratio turbine blades have been tested in order to investigate the mechanisms by which blade lean (dihedral) influences loss generation. The blades in all three cascades have the same section but they are stacked perpendicular to the endwall in the first cascade, on a straight line inclined at 20° from perpendicular in the second and on a circular arc inclined at 30° from perpendicular at each end in the third cascade.Lean has a marked effect upon blade loading, on the distribution of loss generation and on the state of boundary layers on the blade suction surfaces and the endwalls, but its effect upon overall loss coefficient was found to be minimal. It was found, however, that compound lean reduced the downstream mixing losses, and reasons for this are proposed. Compound lean also has the beneficial effect of substantially reducing spanwise variations of mean exit flow angle. In a turbine this would be likely to reduce losses in the downstream bladerow as well as making matching easier and improving off-design performance.Copyright © 1990 by ASME

86 citations


"Performance and flow fields of a su..." refers background or methods in this paper

  • ...The share of losses is calculated based on the assumption that blade row losses are proportional to R U3dA as presented by Harrison.20 Free-stream velocities are derived from the inlet stagnation pressure and local static pressure following Harrison.20 This causes error in the evaluation of the free-stream velocity due to relatively high Mach numbers, but the relative values are expected to be comparable....

    [...]

  • ...Free-stream velocities are derived from the inlet stagnation pressure and local static pressure following Harrison.(20) This causes error in the evaluation of the free-stream velocity due to relatively high Mach numbers, but the relative values are expected to be comparable....

    [...]

  • ...The share of losses is calculated based on the assumption that blade row losses are proportional to R U(3)dA as presented by Harrison.(20) Free-stream velocities are derived from the inlet stagnation pressure and local static pressure following Harrison....

    [...]

Frequently Asked Questions (2)
Q1. What are the contributions mentioned in the paper "Performance and flow fields of a supersonic axial turbine at off-design conditions" ?

In this paper, a supersonic axial flow turbine is studied numerically to find the causes of efficiency decrement. This paper presents the most throughout study so far about the reasons that lead to the decreased off-design performance with supersonic axial flow turbines and explains the loss sources individually for the stator and the rotor. Three operating conditions are studied, and it is suggested that at the lower than design pressure ratios, the shock losses of the stator decrease while simultaneously the stator secondary losses increase. 

It could be beneficial in the future to study experimentally the performance of a supersonic turbine at the off-design conditions and also to conduct more numerical modelling in order to verify the presented observations. One possible area for future research could be the use of variable stator geometry in supersonic axial flow turbines that could solve the presented stator trailing edge shock wave and rotor incidence problems. In general, higher stage efficiencies can be achieved at design conditions by redesigning the turbine rotor with twist.