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ScienceDirectEnergy Procedia 00 (2017) 000–000

www.elsevier.com/locate/procedia

IV International Seminar on ORC Power Systems, ORC201713-15 September 2017, Milano, Italy

Comparison of steady and unsteady RANS CFD simulation of a supersonic ORC turbineBenoit Oberta*, Paola Cinnellab

aEnertime, 1 rue du moulin des bruyères, Courbevoie 92400, FrancebArts et Métiers ParisTech, 151 Boulevard de l'Hôpital, Paris 75013, France

Abstract

This article presents computational fluid dynamics (CFD) simulations of a supersonic flow inside the first stage of an Organic Rankine Cycle (ORC) turbine. The expander considered in this work is the first stage of a three-stage axial turbine that uses hexamethyldisiloxane (MM) as the working fluid. The thermodynamic properties of the working fluid are modelled by a Helmoltz free energy-based equation of state during both the design and simulation steps to accurately account for the non-ideal nature of the fluid under the considered conditions. The high expansion ratio of the turbine leads to a supersonic flow in the stator and rotor blade passages. The design of the stator blade shape is carried out by means of the generalized method of characteristics (MOC). The CFD code used in this work is the commercial ANSYS CFX solver and the simulations are based on the two-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations supplemented by a k-ω turbulence model. Results provided by steady mixing plane simulations are compared to those of unsteady sliding mesh simulations in order to understand the implications of stator/rotor flow interaction on blade loading, torque, entropy generation and flow structure.

© 2017 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems.

Keywords: Turbine ; ORC ; CFD ; Superconic; Unsteady

*

Corresponding author. Tel: +33(0)1 80 88 59 82 E-mail address: benoit.obert@enertime.com

1876-6102 © 2017 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems.

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Introduction

Organic Rankine Cycles (ORC) are systems that convert low temperature and low power heat sources into electrical power. The ORC’s principle of operation is similar to the traditional steam Rankine cycle but it differs in the working fluid used. In an ORC, water is replaced by an organic fluid such as a refrigerant, an alkane or a siloxane. The variety of working fluid options allows for the adaptation of ORC systems to a wide range of heat sources. The use of an organic fluid commonly leads to a dry expansion. Together with the heat exchangers and the pump, the expander is a critical component of the ORC, and its design is essential to the overall system’s performance and availability. For ORC plants of power ranging from several hundred kWe to a few MWe, one of the most commonly used expanders is the multi-stage axial turbine. In this work, we study the flow inside the first stage of a three-stage axial ORC turbine using hexamethyldisiloxane (MM) as the working fluid. In the considered configuration, this first stage is the most loaded of the three as it extracts over 50% of the total turbine work. Its expansion ratio of more than 7 leads to a supersonic flow at the outlet of the nozzle row. The flow conditions and geometry of the first stage are presented in the second section of this paper. The design Mach number at the outlet of the stator blade row of above 1.8 is reached using a converging-diverging supersonic nozzle. The design method of the nozzle blades and rotor impulse blades is detailed in the third section. The performance of this supersonic turbine stage operating with a non-conventional fluid is assessed by means of computational fluid dynamics (CFD). Steady state CFD is commonly used in the design and optimization of ORC turbine blades [9,10,11]. In this paper, we use the commercial CFD software ANSYS CFX coupled with thermo-physical look-up tables to simulate the expansion of the fluid inside the turbine. The details of the simulation setup and models, the mesh, and the thermo-physical model are provided in the fourth section of this paper.To account for the transient nature of flow inside turbomachinery, unsteady 2D Reynolds Average Navier-Stokes (RANS) simulations are carried out. The effect of rotor/stator unsteady interaction on the flow structure, the blade loading, and the blade forces are investigated in the fifth section. The final section of the paper compares the results of the unsteady simulations to the results of the steady mixing plane simulations.

Nomenclature

Latin GreekCp total pressure loss coefficient ηtt total to total isentropic efficiencyh static specific enthalpy Ф quantities used for convergence criteriaH total specific enthalpy τ periodp static pressure P total pressure Subscripts specific entropy in turbine stage inlett time is isentropic

out turbine stage outlet

1. Turbine Parameters

The ORC expander considered in this work is a 2.5 MW, three-stage axial turbine using MM as the working fluid. Its nominal speed is 3000 rpm and the overall expansion ratio is 85.3. Table 1. presents the main geometrical characteristics and flow conditions of the first stage of this expander. The rotor blades of this turbine will be shrouded.

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Table 1. First stage characteristics

First stage characteristics Value Unit First stage characteristics Value Unit

Inlet total pressure 14.52 bar Number of rotor blades 142

Inlet total temperature 233.4 °C Rotor inlet relative Mach number 0.8

Outlet static pressure 1.95 bar Rotor outlet relative Mach number 1.2

Specific speed 0.204 Rotor inlet blade angle 62 °

Specific diameter 6.28 Rotor outlet blade angle 64 °

Nozzle outlet design Mach number 1.84 Rotor inlet mean diameter 391 mm

Nozzle outlet blade angle 76 ° Rotor blade height 20.4 mm

Number of nozzle blades 47 Nozzle blade height 20.4 mm

2. Blade design methodology

The first step of the turbine design is the calculation of the supersonic nozzle shape. To this end, the design of the Laval nozzle part of the stator blade is carried out through the method of characteristics (MOC) extended to account for dense gas effects similarly to what is presented in [2,5]. The impact of dense gas effects on the design of supersonic nozzles has been shown in [1,8]. The physical properties of MM are obtained using the reference equation of state (EOS) [3], available in the thermo-physical properties library REFPROP [4]. Simple geometrical shapes to design the leading edge, trailing edge and subsonic part of the nozzle are then assembled to form the stator blade. The second step is the design of the impulse rotor blade shape. Using a similar method to that presented in [5], the rotor blade pressure side is a circular arc as well as part of the suction side. The leading and trailing edges are two elliptical arcs that are connected to the suction side circular arc by cubic splines. To determine the nozzle and rotor blade number we use the Zweifel empirical coefficient [6]. The results of the design process are presented in Fig. 1. (a).

Fig. 1. (a) Blade Geometry; (b) Partial view of the computational mesh

3. CFD simulation setup

Unsteady RANS 2-D numerical simulations are carried out using the commercial CFD code ANSYS CFX 17.2. The number of rotor blades was changed from 142 to 141 to reduce the size of the computational domain by taking advantage of the periodicity of the turbine geometry. The computational domain contains one stator blade and three rotor blades. The mesh consists of 150,000 elements in the stator domain and 200,000 elements in the rotor domain. These number of elements have been selected after a grid independence sturdy. The height the first element near the blade surface is set to obtain y+ values of roughly one. For RANS turbulence closure, we use the k-ω Shear Stress Transport two-equation model. The total inlet temperature and pressure, as well as the static outlet pressure are

a b

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imposed at the domain boundaries. The blade surfaces are set as adiabatic no-slip walls and the stator/rotor interface as a simple sliding mesh which is rendered possible by the fact that the rotor pitch (for three blades) is equal to the stator pitch. In the results presented in this paper, each blade passage period is discretized by using 60 equally spaced time steps. Calculations with double and triple the number of steps per period were carried out and gave identical results. Computations are considered converged when the two-norm of the squared difference over a period of time τ between some quantities of interest separated by τ is less than 0.1%. This means that convergence is attained when simulation time t 0 satisfies the condition presented in equation (1).

∫t0

t0+τ

(Φ (t+τ )−Φ ( t ) )2dt

∫t 0

t0+τ

Φ (t )2dt

¿10−3

(1)

Where Ф represents the quantities used for the convergence criteria, i.e. mass flow rate at inlet and outlet and torque on rotor blade. The integrations over time are carried out by a simple trapezoidal numerical method. The fluid thermo-physical properties are interpolated from 300 by 300 look-up tables that were generated using the Helmholtz free energy equation of state presented in [3]. These tables cover the superheated vapor region of the turbine expansion.

4. Transient Results

The flow structure is very similar to that of the highly supersonic radial inflow ORC turbine presented in [7]. Fig. 2. (a), Fig 2. (b) and Fig. 2. (c) respectively present the pressure gradient, entropy, and absolute Mach number fields. Roman numerals are used to locate on the figure the phenomena discussed in this part.

Fig. 2. T = (11/15).τ (a) Pressure gradient field; (b) Entropy field; (c) Absolute Mach number field

V IV

III

II

I

a b

c

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The acceleration from sonic conditions at the nozzle throat to supersonic flow creates a series of weak oblique shocks (I). The flow in the nozzle row remains almost perfectly stationary until it reaches the trailing edge on the pressure side, where a fish tail shock is created (II). The latter impinges on the suction side of the adjacent blade and is reflected as an oblique shock (III). The interaction with the reflected shock leads to a thickening of the boundary layer and enhances entropy generation in this region Fig. 3. (b). A significant entropy rise is also observed at the rear part of the rotor blades (IV) and in the turbulent wakes of the stators. At the rotor blade row inlet, the relative Mach number remains greater than one, and a bow shock is generated upstream of the leading edge. The left branch of this

shock interacts with the shocks and wakes coming from the stator, while its right branch impinges on the next rotor blade suction side (V). In the aft part of the rotor passage, most of the entropy is advected from the stator wake, whose contribution to entropy generation dominates the one associated to shock losses. At the rear of the rotor, the circular arc design leads to the formation of a shock wave in the de Laval diverging part, which also contributes to entropy generation, along with the oblique shocks departing from the rotor trailing edge.

Fig. 3. t = 0 (a) Rotor blade loading; (b) Relative Mach number fieldFig. 4. t = (5/15).τ (a) Rotor blade loading; (b) Relative Mach number fieldFig. 5. t = (11/15).τ (a) Rotor blade loading; (b) Relative Mach number field

The torque applied by the flow turning greatly varies during a period. Fig 3, 4 and 5 present rotor blade loading and relative Mach number field in the rotating domain at three different points in time during a period. In particular, we focus on the blade marked with a red capital B. The abbreviation SS means suction side and PS pressure side. Up to roughly ¾ of the blade chord, the unsteady pressure distribution exhibits high-amplitude fluctuations with respect to the time-averaged pressure distribution, also reported in Fig. 3-5 for reference. As a consequence, blade loading on the aft part of the blades varies significantly, whereas the rear part is less affected by flow unsteadiness.

Fig. 6. presents the variation of the torque on the studied rotor blade (in red) and the variation of the average

torque on the three rotor blades of the domain (in blue). The torque on one blade varies by more than 40% and the

a

aa

a b c

B

b

B

b

B

b

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average torque on the three rotor blades of the domain varies by about 20%. However, we can expect that the real turbine’s first stage will be subject to more stable torque values because the actual number of rotor blades (142 rather than 141) is prime together with the number of nozzle blades (47).

Fig. 6. (a) Torque on rotor blade; (b) Nozzle Pressure loss coefficient; (c) Total to total efficiency

5. Comparison between unsteady and steady simulation

In this section, we discuss the differences between the steady mixing plane and unsteady simulations. The steady simulations were carried out using the same mesh, convergence criteria, numerical schemes, and boundary conditions as that of the unsteady simulations.

Fig. 7. Steady state relative Mach number fields

Table 2. presents the computed values in both cases. Time-averaging integrations are carried out using a trapezoidal numerical method and over one blade passage period. The nozzle pressure coefficient is defined in equation (2) and obtained by performing a mass-weighted average 8 mm downstream of the nozzle trailing edge. Torque on rotor blade is computed directly from ANSYS CFX post processing functions. Finally, we compute the stage’s total to total isentropic efficiency using equation (3). The unsteady total pressure loss, defined as:

C p=Pin−PPin−p (2)

is 2.2% higher than the one predicted using steady mixing plane simulations. Pin is the total pressure at the inlet of the nozzle. P and p are respectively the total and static pressure. Accordingly, the isentropic efficiency:

ηtt , is=H in−H out

H in−Hout , is (3)

is slightly overestimated by the steady model, compared to the unsteady result (about +0.15%). Hin and Hout are respectively the specific total enthalpy and the inlet and outlet of the turbine stage. Hout,is is the outlet isentropic total enthalpy computed using the inlet entropy and outlet total pressure. In terms of integral forces, the relative difference in calculated torque on the rotor blade between the steady and unsteady cases is less than 0.2%. In Table 2. Are also reported the entropy creation in the stator and the rotor.

Table 2. Steady/unsteady simulations comparison

Quantities Steady Simulation

Unsteady Simulation

Quantities Steady Simulation

Unsteady Simulation

Stator pressure coefficient

0.1000 0.1022 Stator Entropy Creation

(J/(kg.K))

3.258 3.174

Rotor blade torque (N.m/m)

2.6299 2.6255 Rotor Entropy Creation

(J/(kg.K))

3.215 3.492

Total to total isentropic efficiency

0.9193 0.9179

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In Fig. 8 we compare the time-averaged pressure distributions along the stator blades extracted from the preceding unsteady simulation and the results provided by steady calculations based on a mixing plane condition at the stator/rotor interface. Differences in blade loading are only noticeable near the trailing edge on the suction side, due to the fluctuations of the fish-tail shocks induced by the rotor/stator interaction.

Fig. 8. Stator blade loading

In the case of the rotor blades (Fig. 9), the most noticeable differences are observed near the leading edge, namely at the suction side. This is consistent with the presence of significant pressure fluctuations in this region, as mentioned in the above.

Fig. 9. Rotor blade loading

Conclusions

Unsteady 2D RANS simulations of an ORC turbine stage were carried out using ANSYS CFX. The CFD solver was supplemented by thermo-physical properties look-up tables in order to take into account dense gas effects. The analysis of the flow structure showed the presence of different types of shocks and their interaction with each other and with the blade surfaces. The characteristics of the flow are very similar to those of a highly supersonic radial ORC turbine operating with Toluene described in [7]. However, the fluctuations of the rotor blades loading and torque were much lower in the present case. In [7], fluctuations of up to 90% of the torque on the rotor blades are observed whereas in this paper these fluctuations are only of 40%. The much higher nozzle Mach number (M = 2.8 in [7] as opposed to M = 1.8 in this study) and the lower stator-rotor gap (around ¼ of the rotor chord in [7] as opposed to ½ in this study) might explain this difference. In both papers, the transient rotor stator interaction logically had little effect on the stator flow.

The results of the unsteady simulations were then compared to those of the steady mixing plane simulations. In the case of this turbine, it seems steady simulations are capable of accurately predicting the total to total efficiency and rotor blade forces. The relatively high stator-rotor gap might also explain the good accordance between steady

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and unsteady simulation results. It would be interesting to carry out the same study with a significantly reduced stator-rotor gap. Carrying out 3D RANS unsteady simulations of the turbine’s first stage would allow to account for end-wall effects and secondary flows.

References

[1] Wheeler AP, Ong, J. The role of dense gas dynamics on orc turbine performance. Proceedings of the ASME 2013 Turbo Expo: Turbine Technical Conference, San Antonio, Texas, USA; 2013[2] Bufi EA, Cinnella P, Merle X. Sensitivity of supersonic orc turbine injector designs to fluctuating operating conditions. Proceedings of the ASME 2015 Turbo Expo Turbine Technical Conference, Montreal, Canada; 2015. [3] Colonna P, Nannan NR, Guardone A, Lemmon EW. Multiparameter equations of state for selected siloxanes. Fluid Phase Equilib., vol. 244, pp. 193-211; 2006. [4] Lemmon EW, Huber ML, McLinden MO. NIST Reference Fluid Thermodynamic and Transport Properties REFPROP V9.1. NIST; 2013.[5] Bufi EA, Obert B, Cinnella P. Fast design methodology for supersonic rotor blades with dense gas effects. 3 rd International Seminar on ORC Power Systems, Brussels, Belgium; 2015.[6] Zweifel O. The spacing of turbomachine blading, especially with large angular deflection. Brown Bovery Review 32; 1945.[7] Rinaldi E, Pecnik R, Colonna P. Unsteady RANS simulation of the off-design operation of a high expansion ratio ORC turbine. 3rd

International Seminar on ORC Power Systems, Brussels, Belgium; 2015.[8] Guardone A, Spinelli A, Dossena V. Influence of molecular complexity on nozzle design for an organic vapor wind tunnel. Journal of Engineering for Gas Turbines and Power, 135(4):042307; 2013.[9] Harinck J, Pasquale D, Pecnik R, Buijtenen J, Colonna P. Performance improvement of a radial organic Rankine cycle turbine by means of automated computational fluid dynamic design. Proc IMechE Part A: J Power and Energy 227(6) 637–645; 2013.[10] Rodriguez-Fernandez P, Persico G. Automatic design of orc turbine profiles using evolutionary algorithms. 3rd International Seminar on ORC Power Systems, Brussels, Belgium; 2015.[11] Persico G. Evolutionary optimization of centrifugal nozzles for organic vapours. Proceedings to the NICFD 2016: 1 st International Seminar on Non-Ideal Compressible Fluid Dynamics for Propulsion & Power, Varenna, Italy; 2016.