Preliminary design and off-design performance analysis of an Organic Rankine Cycle radial-inflow turbine based on mathematic method and CFD method

Accepted Manuscript Research Paper Preliminary design and off-design performance analysis of an Organic Rankine Cycle radial-inflow turbine based on mathematic method and CFD method Ya Zheng, Dongshuai Hu, Yue Cao, Yiping Dai PII: DOI: Reference:

S1359-4311(16)32254-2 http://dx.doi.org/10.1016/j.applthermaleng.2016.10.036 ATE 9238

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

14 February 2016 25 July 2016 8 October 2016

Please cite this article as: Y. Zheng, D. Hu, Y. Cao, Y. Dai, Preliminary design and off-design performance analysis of an Organic Rankine Cycle radial-inflow turbine based on mathematic method and CFD method, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.10.036

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Preliminary design and off-design performance analysis of an Organic Rankine Cycle radial-inflow turbine based on mathematic method and CFD method

Ya Zhenga, Dongshuai Hub, Yue Caoa, Yiping Daia* a

Institute of Turbomachinery, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China b

China Datang Northwest Electric Power Test and Research Institute. China Datang Corporation, Xi’an 710075, China

Abstract: As a critical component of Organic Rankine Cycle (ORC) system, the turbine selection has an enormous influence on the system performance. Challenges in the numerical modeling of radial-inflow turbines using high-density working fluids still need to be addressed in order to improve the turbine design and better optimize ORCs. This paper carries out the full design process of the R134a radial-inflow ORC turbine. The 1D design of the candidate radial-inflow turbine is presented in details. Furthermore, commercially-available software ANSYS-CFX is used to perform preliminary steady-state 3D CFD simulations of the candidate R134a radial-inflow turbine. Also a turbine model based on 1D analysis is performed for a number of operating conditions including off-design conditions. The performance prediction codes of an ORC radial-inflow turbine based on mathematic method and CFD method

1

can be used to provide basic data for future detailed design, and predict off-design performance in the initial design phase. Keywords: Preliminary design; Off-design performance; ORC; Radial-inflow turbine; CFD * Corresponding author: Yiping Dai* Institute of Turbomachinery, Xi'an Jiaotong University, No.28 Xianning West Road, Xi'an 710049, PR China E-mail address: [email protected] (YP. Dai) Tel: +86 029 82668704 Fax: +86 029 82668704 Nomenclature b

blade height (mm) zero pressure ideal gas specific heat capacity (kJ/kg·K)

C0

spouting velocity (m/s)

F

area (m2)

h

enthalpy (kJ/kg)

K

loss coefficient

L

loss (kJ/kg) mass flow rate (kg/s)

M

absolute Mach number

2

n

incidence angle (deg)

N

rotational speed (rpm)

P

pressure (kPa)

Pc

absolute pressure at the critical point (kPa)

r

radius (mm)

R

ideal gas constant (J/mol· K)

Re

Reynolds number

T

temperature (K)

Tc

absolute temperature at the critical point (K)

u

circular velocity (m/s)

U/C0

velocity ratio

w

relative velocity (m/s)

W

power (kW)

y+

non-dimensional grid spacing at the wall

Zs

stator number of blades

Zr

rotor number of blades

Greek symbols α

absolute fluid velocity angle (deg)

β

relative fluid velocity angle (deg)

η

efficiency (%)

3

μ

dynamic viscosity (kg/m·s) pressure ratio

ρ

density( kg/m3)

ω

acentric factor

Subscripts 1,2,3,4

state point in the turbine

cr

critical

de

design

e

exit energy

f

friction

hub

hub

i

incidence

in

inlet

is

isentropic

m

mean

min

minimum

opt

optimum

out

outlet

p

passage

r

radial component

4

rotor

rotor

s

isentropic

S

static

stator

stator

turbine

turbine

tip

tip

T

total

T-S

total-to-static

T-T

total-to-total

u

tangential component

y

tip clearance

z

axial component

Superscript st

stagnant

1 Introduction

With the accelerated consumption of fossil fuels, Organic Rankine Cycles (ORCs) have drawn lots of attention for many years [1]. ORC systems have been regarded as one of the most promising technologies to convert low-grade heat energy into mechanical energy. The utilization of low-grade heat sources, such as renewable energy and waste thermal energy from industrial or generating processes, appears to 5

be an appropriate solution to maintain sustainable development [2]. The working fluid and the turbine are two key parameters for the optimization of the ORC performance [3]. Almost research mainly focus on the organic fluid selection [4-9] and the preliminary one-dimensional turbine design [10, 11]. The feature of these heat sources is that their thermodynamic parameters may be unstable and uncontrollable [12-14]. Taking industrial waste heat for example, both its mass flow rate and temperature vary with the plant production process and production quantity [15]. Therefore, it is meaningful to investigate the off-design performance of the turbine as the critical component of ORC system. Generally, the turbine of ORC will undergo an unstable process when ORC systems operate deviating from the design point [16]. Therefore, the purpose of the design phases (preliminary and detailed) should not only include an aerodynamic design that will correctly and completely achieve a design that delivers the desired outputs, but also predict the turbine off-design performance well. As underlined by Aungier [17], the preliminary design of a radial inflow turbine costs about 50% of the engineering time because of superabundant empirical parameters applied in the process of turbine preliminary design. In fact, there is no notable difference between the design principles of ORC turbine and steam turbine. The special thermodynamics properties of organic fluids includes: high molecular weight, high gas constant and low sound velocity which have great effects on the ORC turbine’s design and performance.

6

Furthermore, the ORC turbine has a high expansion ratio and the fluid specific volume changes a lot what will easily cause high Mach number transonic flow. Therefore, one of the purposes in the design phase is to control the Mach number at the stator outlet and rotor outlet in order to avoid excessive leaving velocity loss by optimizing turbine structure and selecting the suitable organic fluids. Pasquale et al. [18] also highlighted the need to use more advanced 3D viscous computational simulations to further investigate the proposed turbine configuration. Computational Fluid Dynamics (CFD) will provide detailed flow analysis which is required to improve the aerodynamic performance of the machine [19]. P. Colonna et. al [20] indicated that the analysis and design of turbomachinery is usually performed by means of fluid dynamic computations employing ideal gas laws which can lead to inaccurate predictions for ORC turbines. In the meantime, they investigated the influence of three different equations of state (EoS), a simple polytropic ideal gas law, the

Peng–Robinson–Stryjek–Vera

cubic

equation of state (EoS)

and

the

state-of-the-art Span–Wagner EoS, on the aerodynamic performance of a two-dimensional ORC

stator blade.

The two

more

sophisticated

models

(Peng–Robinson–Stryjek–Vera and Span–Wagner) were shown to produce similar results. Recent studies have looked at the whole process including thermodynamic cycle, 1D design and numerical simulations of the expander. Sauret and Gu [21] provided a complete ORC analysis including the thermodynamic cycle, the

7

preliminary meanline design and finally pioneering three-dimensional CFD simulations of a radial-inflow turbine in sensible geothermal brine and cycle conditions. Nonetheless, it should be noted that so far, very few studies [22, 23] including the whole process for high mass flow conditions have been presented in the literature. Table 1 gives a summary of the recent published numerical simulations of expanders working with organic fluids. It has been found that the off-design performance of the ORC turbine can be predicted accurately and conveniently by CFD simulation through the achievements of the previous literatures presented in Table 1. However, it still has some shortages. Firstly, the CFD simulations still cost too much time and computer resource on the preliminary design phases of a turbine working with high-density fluid. Secondly, the CFD simulation results are affected by the real gas properties. Sauret and Gu [21] also pointed that the CFD simulations on a fully-optimized 3D geometry with a more accurate modeling of the real gas properties will provide more reliable results due to the sensitivity of real gas properties to the temperature variations. If the mathematical model method based on 1D analysis can be applied in the prediction of turbine’s off-design performance, the shortage of CFD method can be solved well. The main purpose of this paper is to propose a complete design process of ORC radial inflow turbine and discuss its performance under off-design conditions. In this

8

paper, a complete ORC analysis including the thermodynamic cycle, the preliminary meanline design and finally pioneering three-dimensional CFD simulations of a 640 kW-R134a radial-inflow turbine in high mass flow conditions has been finished. Firstly, the meanline design has been finished by the software of ANSYS-Vista RTD and the turbine’s geometry dimension has been obtained. After that, using two different methods to analyze turbine’s performance: mathematical method based on the designed model and CFD method based on the software of CFX. Specially, the radial-inflow turbine model has been established to predict the turbine’s off-design performance, and has been validated against the CFD and preliminary design results. The paper contributes to provide a preliminary design method of radial inflow turbine for future detailed design, and two methods to analyze turbine’s off-design performance in the initial design phase which is the basis of predicting ORC’s off-design performance.

2 Organic Rankine Cycle

A thermodynamic model for a binary power cycle was developed based on the basic components of an ORC system: evaporator, turbine, generator, condenser and fluid pump. Fig. 1 illustrates the diagram of Organic Rankine Cycle applied in a certain petrochemical facility of China. Simulations for realistic condensing ORC cycles for petrochemical applications were carried out and analyzed. The heat source studied in this paper is the waste heat of diesel oil (a stable temperature and flow rate 9

of 418 K and 30.56 kg/s) which is generated from the process of diesel refining. The turbine and pump efficiencies were assumed to be 82% and 72%, respectively. Promising cycles were identified by varying the evaporator pressure in order to optimize the net cycle power. In this study, the refrigerant R134a is selected as the working fluid for the turbine based on the study of Sauret and Rowlands [24]. This study evaluated 5 different fluids based on the QGECE (Queensland Geothermal Energy Center of Excellence) thermodynamic modeling and published results from others [7, 25-28]. It showed the highest performing cycle based on R134a produced 33% more net power than the lowest performing cycle based on n-Pentane. The choice of R134a is based not only on its theoretical thermodynamic performance, but a balance of several different desired criteria such as relatively low critical pressure and temperature and low flammability, low toxicity and relative inert behavior. Striking an acceptable balance among the impact on the environment – low GWP (Global Warming Potential) and low ODP (Ozone Depletion Potential); cost and thermodynamic performance is a significant challenge for ORC system designers [4]. The condensing temperature was set at 310 K (10 K above ambient, assumed to be 300 K) and the condensing pressure of R134a is set as 950 kPa to ensure the full condensation of R134a. In addition, both the pinch temperature difference in heat exchangers and the superheat degree in the evaporator are set as 5 K. The overall performance of ORC cycle for petrochemical applications is summarized in Table 2

10

through the thermodynamic calculation using Matlab software and the real fluid properties are referred to the NISTREFPROP 9.0[29]. Assumptions applied in the model are given as below, 1. The system is assumed in steady state. 2. The leakage of working fluids is ignored. 3. The pressure drop and energy loss in pipelines and heat exchangers are ignored. The radial-inflow turbine is selected as the expander due to its compact structure, high efficiency and smooth off-design performance [30]. The design point of this 640kW-R134a radial-inflow turbine was preliminarily obtained base on the cycle calculation and the thermodynamic data required for the turbine design are summarized in Table 3.

3 Preliminary design and meanline analysis

The preliminary design of a radial inflow turbine costs about 50% of the engineering time because of superabundant empirical parameters applied in the process of turbine preliminary design [17]. The thermodynamic properties and flow features are determined at key stations are illustrated in Fig.2. In the section of preliminary design, α2, β2, r4/r3, β4, U/C0 and N were chosen as decision variables to control the main dimension of the turbine. b2/r2, r4,tip/r4 and r4,hub/r4 were limited to ensure the reasonability of the design. Boundaries of parameters are shown in Table 4.

11

3.1 Methodology

The preliminary design procedure addresses the basic stage components defining the inlet volute, nozzle row, rotor and exhaust diffuser, providing an aerodynamic design that completely achieves a design with required outputs. Nowadays, there are several preliminary design methodologies like software RITAL and RADTURB [31]. In this study, the preliminary design of the turbines was performed using the commercial software ANSYS-Vista RTD developed by PCA Engineers and integrated in ANSYS BladeModeler software. The general procedure implemented was to determine overall dimensions of the machine for the stator, rotor and diffuser along with blade and flow angles and isentropic efficiency by fixing the mass flow rate, inlet and outlet pressures as calculated by the cycle analysis (Table 3) and by assuming flow and loading coefficients. The required aerodynamics inputs are inlet stagnation temperature and pressure (360K and 2500kPa), mass flow rate (40.34kg/s), total-to-total expansion ratio (2.58), rotational speed (8000r/min) and blade speed ratio (0.711), stage efficiencies (activate correlation), fluid properties, inlet relative angle (-40.675ᵒ) and exit absolute angles(0ᵒ). For geometrical inputs, the number of vanes (nozzle:16 impeller:19), impeller diameters and axial length (refer to [26]) are given. The whole design process of the radial inflow turbine is illustrated in Fig. 3.

12

3.2 Preliminary design results.

The preliminary design data of R134a radial turbine are presented in Table 5. The turbine power and efficiency are the output results and the other parameters are input data for ANSYS Vista-RTD. The power is slightly higher than the expected value from the thermodynamic cycle. However, the total-to-total efficiency almost reached 82% while the total-to-static efficiency is 80%. This is in close agreement with the assumed turbine efficiency in the section of cycle analysis. In this study, the preliminary design of the turbines was performed using the commercial software Vista-RTD following the design procedure established by Moustapha et al. [32]. The general procedure implemented was to determine overall dimensions of the machine for the stator, rotor and diffuser along with blade and flow angles and isentropic efficiency by fixing the mass flow rate, inlet and outlet pressures as calculated by the cycle analysis. From the basic design specifications and the performance analysis, a refinement of the results was performed in order to optimize the geometry. The refinements included: rotational speed adjustments in order to get closer to the optimum 0.7 value of the U/C0 ratio [32], tip outlet rotor radius modification in order to reduce the swirl as much as possible at the outlet of the rotor; and, blade span (i.e. changes to throat area).

13

3.3 3D Geometry

The commercial software ANSYS-Vista RTD was used to define the 3D geometry of the turbine presented in Fig. 4. The initial geometrical data from preliminary design (Vista RTD) were exported to ANSYS-turbo system in which the 3D nozzle and rotor blades were created, including amongst the most important parameters, nozzle hub and shroud thickness (similar on hub and shroud), nozzle blade profile (adjust by Piecewise linear curves), rotor hub and shroud contours and rotor blade angle and thickness distributions for both hub and shroud separately (adjust by Piecewise linear curve) were applied in order to define an identical turbine. An annular diffuser at the exit of the rotor was built from 1D radius values and the 3D geometry was generated using ANSYS-geometry. The main 3D geometric parameters are presented in Table 6.

4 Mathematical method

The simulation model of the radial inflow turbine for ORC was completed in this section which can predict the turbine’s off-design performance accurately. In this section, all the mathematical models were developed by Matlab software. Real fluid properties are referred to the NISTREFPROP 9.0 [29]. The geometrical characteristics of a single stage radial inflow turbine are depicted in Fig. 4. The one-dimensional method applied in the turbine model is based on flow 14

conditions through the radial inflow turbine along the mean streamline. Therefore it’s also called meanline analysis method. In this model, expansion process is assumed isentropic in stator, vaneless space and rotor, and then the fluid flow process is corrected by loss models to make the results more reliable.

4.1 Expansion process

The organic fluid will flow to the turbine inlet after being heated in evaporator. In the turbine, the fluid flows through the stator, vaneless space and rotor in sequence and converts its heat energy into mechanical energy of the turbine. In stator vanes, the ideal expansion process in stator can be expressed by Eq. (1) [33].The relationship between geometric parameters and fluid dynamic parameters is shown by Eq. (2)-(5) [33, 34]. The influence of supersonic flow is taken into consideration in this section since it’s commonly happened in ORC, and the stator outlet angle α2 will be corrected if supersonic flow happens in stator. (1) If c1ccr (4) (5) 15

There is clearance between stator and rotor. The conservation of the tangential momentum is assumed in this vaneless space [35]. (6) (7) In rotor blades, the expansion process can be calculated by Eq. (8) and Eq. (9) [33]. (8) (9)

4.2 Efficiency characteristic

Expansion process is assumed isentropic in every section of turbines, and then the fluid flow process is corrected by loss models to make the result more reliable. The turbine power Wturbine is expressed as (10) The efficiency

is the rate of the actual enthalpy drop and the isentropic

enthalpy drop as defined in Eq. (11). In additional, it is the total-to-static isentropic efficiency which is selected to represent the turbine performance in this paper. (11) Loss models play a significant role on the simulation of the turbine model. However there are few studies about the loss model of turbines using organic fluids. In this paper, many previous aerodynamic models are used to estimate flow losses. Six loss models are considered: stator loss, incidence loss, passage loss, friction loss, 16

leakage loss and exit energy loss. The stator loss Lstator occurs between the turbine inlet and the nozzle outlet as shown in Eq. (12) [36]. (12) When working fluid approaches to the rotor, the relative angle β3 may not equal to the optimum relative angle β3,opt. The incidence loss Li is calculated by Eq. (13) based on the value of incidence angle n, and the calculation of β3,opt following the method of Stanitz is shown in Eq. (15) [34] . (13) (14) (15) The passage loss Lp is calculated based on the average kinetic energy in rotor blades. The value of Kp as shown in Eq. (16) is supposed to be constant under design and off-design conditions [34]. (16) The friction loss Lf, occurring in the back face of the turbine disc, is caused by organic fluid leaks between the back plate and the rotor[37]. Tip Clearance Loss Ly is caused by radial and axial clearances[37], and the exit energy loss Le means the kinetic energy discharged from a radial inflow turbine. (17)

17

(18) (19)

4.3 Off-design performance

Expansion process and efficiency characteristics of a turbine are two key factors to estimate its off-design performance. The mass flow rate and efficiency can be obtained by giving the geometrical parameters of the turbine, the thermodynamic parameters of working fluids at turbine inlet, the required rotational speed and the turbine outlet pressure. When some of these parameters change, complicated iterations have to be conducted in the turbine model to update the turbine mass flow rate and efficiency. It is known that the current preliminary design tools can provide the different design plans of turbines with different values of decision variables. However they cannot predict the off-design performance of a certain turbine which is important in the practical application. The purpose of building this mathematical model of radial-inflow turbine is to fill this gap in the stage of preliminary design.

5 CFD simulation

In order to make comparisons between the mathematical method results and the CFD results, the viscous turbulent CFD simulation was carried out on the 3D turbine geometry at the nominal condition using commercially-available software 18

ANSYS-CFX.

5.1 Mesh

Ansys-TurboGrid was applied to generate O–H three-dimensional computational mesh for the simulation where the Automatic Topology and Meshing (ATM Optimized) option was used in stator and rotor flow passages. It can generate a high quality mesh avoiding negative volumes which are problematic for traditional mesh generations [38]. For the boundary layer refinement control, the first element method was used and the Reynolds number is 4×106 with Near Wall Element Size Specification to meet the y+ requirement for turbulence model, ranged from 6 to 147. The individual diffuser was imported into ANSYS-Mesh and Tetrahedrons Method was used to generate a fine mesh. After checking grid refinement and mesh quality, the total grid number is 1556,968 cells to satisfy the mesh independent criterion, 809,064 for the stator, 517,363 for the rotor and 230,541 for the diffuser. The grid independence analysis is shown in Table 7. The sensitivity analysis was carried out for proving the reliability of cells and the purpose of sensitivity analysis is to quantify the uncertainties in the results. Table 7 shows that the thermodynamics properties at state points have little difference under steady calculation with the increasing number of cells. The small variations of mass flow and temperatures can have a big impact on turbine power and efficiencies. Therefore, the results are still acceptable. With consideration of 19

computation resource, we chose the model with about 155×104 cells. The final mesh analysis of rotor and stator flow passages shows 30º for minimum face angle, 155ᵒ for maximum face angle with a positive minimum volume. Figs 5 and 6 illustrate the 3D views of rotor and stator blade flow passages, respectively. This initial mesh was found good enough to run pioneering simulations of the 3D candidate R134a radial-inflow turbine in high flow conditions and establish the complete methodology (thermodynamic cycle, meanline analysis and preliminary viscous CFD simulations).

5.2 Numerical model

The ANSYS-CFX is selected to perform the steady-state 3D viscous flow simulations. Many published literatures have proved the reliability of this commercial software as turbomachinery code. For robustness consideration and the experience obtained from the previous CFD work, the discretization of the Reynolds-averaged Navier-Stokes (RANS) equations is realized using a first order Upwind advection scheme, and the

turbulent model with scalable wall function was selected as

recommended by [39, 40] which is simple, stable, computation resource saving and widely used in aeronautical flows and turbomachinery. In additional, the flow simulations are solved by the general equations (Energy, Momentum, Mass) provided by ANSYS-CFX. The properties of the refrigerant R134a in the radial-inflow turbine is described by 20

the equation of state (EoS) of Peng-Robinson which is same to the equation of Sauret and Gu [21]. Peng-Robinson EoS provided by ANSYS-CFX is not also simplicity but also accuracy of this model to perform preliminary real gas computational simulations. And the EoS also has reasonable accuracy especially near the critical point [41]. The equations are given as: (20-a) (20-b) (20-c) (20-d) (20-e) (20-f) where

0.326 is the acentric factor of refrigerant R134a,

374.26 K and

4059 kPa are respectively the critical temperature and pressure of R134a,

, the

molar volume and R is the universal gas constant. To complete the description of the real gas properties, the CFD solver calculates the enthalpy and the entropy using relationships which are detailed in [42]. These relationships depend on the zero pressure ideal gas specific heat capacity derivatives of the Peng–Robinson EoS.

and the

is obtained by a fourth-order polynomial

whose coefficients are defined by Poling et al. [43].

21

5.3 Boundary conditions

An extension of the domain was placed in front of the stator blades at a distance equivalent to approximately 25% of the axial stator chord. The boundary conditions are list below: 1. The nominal rotational speed for this case is defined from the preliminary design and set to 8000 rpm (Table 5). 2. The total pressure (2500 kPa) and total temperature (360 K) obtained from the meanline design analysis were set at the inlet of the domain (Table 3). 3. The static pressure (950 kPa) was specified at the exit of the diffuser (Table 3). In addition, single flow passage for both stator and rotor is simulated and Rotational Periodicity is applied. There are two interfaces placed between the outlet of the stator flow passage and the inlet of the rotor flow passage and the outlet of rotor flow passage and the inlet of the diffuser where both are modeled as a Stage Frame Change/Mixing and Automatic Pitch Change. The flow in the impeller is simulated in the rotating coordinate system to represent the rotating effect.

6 Results and discussion

6.1 Comparisons among the 3D CFD, preliminary analysis and turbine model at the nominal condition

The Meridian view of static pressure and temperature through stator and rotor flow 22

passages are presented in Fig. 7. The static pressure distribution is shown in Fig.7 (a) where it reduces from

= 2500 kPa to

= 949.6 kPa at the stator entrance and

rotor exit, respectively. As shown in Fig.7 (b), the highest static temperature of 360K occurs at the stator inlet, decreasing throughout stator and rotor flow passages and reaches its minimum value of

= 319 K at the rotor outlet. In additional, Studying

Mach number distribution from Fig. 7 (c) shows that the Mach number at the rotor flow passage inlet and outlet is 0.73 and 0.30 respectively whereas the turbine was designed to work in the transonic region. The related experiments of radial-inflow turbine working with high-density fluids are lacking, therefore the validation of the present 3D viscous simulation was made against the meanline analyses. Table 8 compares the results from the preliminary 1D design, turbine model and the numerical 3D turbulent simulations. It is observed that the results from these three codes are in relatively good agreement with each other especially in terms of temperatures, pressures, enthalpy and Mach number. However, the slight difference (nearly 0.1%) on the total enthalpy at the outlet of rotor and the difference (nearly 1.39%) on the mass flow between the viscous simulation and the preliminary analysis leads to approximately 4% difference in terms of Eq. (10) explaining the difference of power. The CFD results are in fairly good agreement with the other 1D analyses except for efficiencies for which a maximum difference of approximately 5.4% is obtained. The

23

overestimation of the efficiency has already been highlighted in a less extent by Sauret [31] on the simulations of an ideal gas high pressure ratio radial-inflow turbine. The present result can be attributed to the use of real gases which are extremely sensitive to small temperature variations. The isentropic efficiencies defined below in Eq. (21) are function of the enthalpy drop:



(21)



(22)

Thus, any small variations of temperatures can have a big impact on efficiencies. Several studies [41, 44] have shown that the Peng–Robinson EoS was comparing fairly well against the high accuracy models implemented in REFPOP [45] and especially near the critical point. Thus, it is not assured that a more accurate EoS will dramatically improve the CFD efficiencies. It is remarkable that the radial-inflow turbine model shows great accuracy to the preliminary analysis except the Mach number at the outlet of rotor. Indeed, CFD can be regarded as a convenient tool to predict the turbine performance, but it is still too complicated and wastes too much time. The comparison results at the nominal condition prove that the radial-inflow turbine model can predict the turbine performance accurately with acceptable error.

6.2 Validation

In order to further verify the reliability of the designed 1D turbine model, the 24

comparison with the numerical investigation data of a R143a-radial inflow turbine derived from [21] is carried out and the results are presented in Table 9. In addition, the validation of the turbine model at off-design conditions is also finished as shown in Fig. 8. The most sensitive parameter of turbine output power is selected as the comparing factor. The results of 1D model have good agreement with the literature results. The maximum deviation for turbine output power is 3.27% within the test range. The results also show that the turbine model can predict accurate off-design performance. At below, this model will be used to study the off-design performance characteristics of the ORC turbine.

6.3 Results at off-design conditions

The radial-inflow turbine model has also been performed at off-design conditions for various rotational speeds, inlet total temperatures and pressure ratios. The evolution of the total-to-static efficiency with the total inlet temperature and rotational speed are presented in Figs. 9 and 10 respectively. It can be seen in Fig. 9 that at the nominal rotational speed, the turbine can effectively handle temperature variations with a maximum efficiency difference of 1.53% over the range of tested temperature. The maximum efficiency is reached at = 370 K, slightly higher than the nominal temperature 360 K. At the condition of 80% rpm, the total-to-static efficiency continually decreases with the inlet temperature. Rather, at the highest rotational speed of 120% rpm, the efficiency increases with the 25

temperature. As one can note in Fig. 10, at low temperature, the maximum efficiency is reached at a low rotational speed. After that point, the total-static efficiency rapidly drops with an increase of the rotational speed. At the nominal temperature (360 K), the turbine can better handle the variation of rotational speed. In that case, the maximum efficiency is reached at 95% of the nominal rotational speed (7600 rpm), slightly below the nominal rotational speed of 8000 rpm. At higher temperature, the efficiency keeps increasing with the rotational speed. Figs. 11 and 12 present the variation of power with the inlet temperature and the rotational speed respectively. For all rotational speeds, the power increases with the inlet turbine temperature as shown in Fig. 11. However, this increase is more pronounced at the highest rotational speed. It is also observed in Fig. 12 that, as the temperature increases, the maximum power tends to move towards higher rotational speeds. Furthermore, the power increases with the temperature for a constant rotational speed. A variation of the pressure ratio was also performed and the results at three different inlet temperatures for the nominal rotational speed are presented in Fig. 13. The efficiency gradually decreases with an increase of the pressure ratio at the nominal condition. Similar trends are observed at the highest temperature with a faster drop compared to the nominal temperature. The efficiency fluctuation ratios are

26

6.56%, 7.77% and 9.93% respectively from low temperature to high temperature. It can illustrate that the turbine can better handle the variation of pressure ratio at the nominal condition. The evolution of the efficiency with the pressure ratio was also plotted at three different rotational speeds as shown in Fig. 14 at the nominal inlet temperature. At low rotational speed, the efficiency continually decreases with the total-to-static pressure ratio while at the nominal rotational speed, but the rate of decent is higher at low rotational speed. At the highest rotational speed, the maximum efficiency is reached at

= 2.3 and then decreases. The lowest rotational speed provides the

lowest efficiency. The highest efficiency is obtained at the nominal rotational speed. Based on the characteristics analysis of the turbine’s off-design performance, we can note that the effects of rotational speed, inlet temperature and pressure ratio are less pronounced at the nominal conditions. Therefore, the nominal point is the most capable of handling a variation of rotational speed, temperature or pressure ratio while maintaining a relatively high efficiency over the range of variation. The nominal point is then compared to the best efficiency point as presented in Table 10. We can also note that the best efficiency are obtained at the nominal inlet temperature and nominal rotational speed. However, the best efficiency is obtained at a lower pressure ratio due to a lower mass flow rate, In return, the power is lower. At the nominal point, the best efficiency is achieved by varying the pressure ratio. A

27

coupled optimization of the thermodynamic cycle and 1D turbine design would be then beneficial.

7 Conclusion

This paper is the first to present the full design process of a radial-inflow turbine working with R134a in high mass flow conditions for petrochemical applications. The thermodynamic cycle, the preliminary 1D design, the meanline analysis of the turbine, the steady-state 3D viscous simulations of the turbine at nominal condition and the prediction of the turbine’s off-design performance based on the designed mathematical model are finished. The main conclusions can be summarized as follows: (1) For the waste heat utilization in diesel refining process, the ORC system and the matched radial-inflow turbine is preliminarily designed. Its rotor inlet radius is 169.37 mm, the rated speed is 8000 rpm, the turbine power is 643 kW and the turbine efficiency is 81.6%. (2) The commercial software ANSYS-Vista RTD, Blade Gen, TurboGrid and CFX are used to perform a meanline design, create 3D geometry of one flow passage and conduct three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations respectively. (3) The designed radial-inflow turbine model is extremely reliable and accurate through the comparisons among the results of the preliminary design and CFD 28

analysis at the nominal condition. (4) Parametric studies were carried out highlighting the relative robustness of the design point over the variations of temperature, rotational speed and pressure ratio. The results also confirmed that the effects of rotational speed, inlet temperature and pressure ratio are less pronounced at the nominal conditions. Therefore, the nominal point is the most capable of handling a variation of rotational speed, temperature or pressure ratio while maintaining a relatively high efficiency over the range of variation. In this paper, a new theory for the ORC radial-inflow turbine design phases has been proposed by providing the thermodynamic cycle analysis, preliminary design tools, prediction code of off-design performance and CFD verification. Finally, the preliminary design tool coupled with the off-design performance analysis will be developed and applied to this candidate R134a radial-inflow turbine which can be useful to structural analysis and shape optimization.

Acknowledgement

The authors gratefully acknowledge the financial support by the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130201110037) and the National high-tech Research and development (Grant No. 2012AA053002).

29

References [1] J. Wang, Y. Dai, L. Gao, Exergy analyses and parametric optimizations for different cogeneration power plants in cement industry, Applied Energy, 86 (2009) 941-948. [2] D. Hu, Y. Zheng, Y. Wu, S. Li, Y. Dai, Off-design performance comparison of an organic Rankine cycle under different control strategies, Applied Energy, 156 (2015) 268-279. [3] O. Badr, S. Naik, P. O'Callaghan, S. Probert, Expansion machine for a low power-output steam Rankine-cycle engine, Applied Energy, 39 (1991) 93-116. [4] H.D.M. Hettiarachchi, M. Golubovic, W.M. Worek, Y. Ikegami, Optimum design criteria for an Organic Rankine cycle using low-temperature geothermal heat sources, Energy, 32 (2007) 1698-1706. [5] B. Saleh, G. Koglbauer, M. Wendland, J. Fischer, Working fluids for low-temperature organic Rankine cycles, Energy, 32 (2007) 1210-1221. [6] J. Facão, A.C. Oliveira, Analysis of energetic, design and operational criteria when choosing an adequate working fluid for small ORC systems, in: ASME 2009 International Mechanical Engineering Congress & Exposition, 2009, pp. 13-19. [7] T. Guo, H. Wang, S. Zhang, Fluid selection for a low-temperature geothermal organic Rankine cycle by energy and exergy, in: Power and Energy Engineering Conference (APPEEC), 2010 Asia-Pacific, IEEE, 2010, pp. 1-5. [8] H. Chen, D.Y. Goswami, E.K. Stefanakos, A review of thermodynamic cycles and working fluids for the conversion of low-grade heat, Renewable and sustainable energy reviews, 14 (2010) 3059-3067. [9] A. Toffolo, A. Lazzaretto, G. Manente, M. Paci, A multi-criteria approach for the optimal selection of working fluid and design parameters in Organic Rankine Cycle systems, Applied Energy, 121 (2014) 219-232. [10] C. Ventura, P. Jacobs, A. Rowlands, P. Petrie-Repar, E. Sauret, Preliminary Design and Performance Estimation of Radial Inflow Turbines: An Automated Approach, Journal of Fluids Engineering-Transactions of ASME, 134 (2012) 1-13. [11] A. Whitfield, The Preliminary Design of Radial Inflow Turbines, Journal of Turbomachinery, 112 (1990) 51. [12] A.M. Delgado-Torres, L. García-Rodríguez, Analysis and optimization of the low-temperature solar organic Rankine cycle (ORC), Energy Conversion and Management, 51 (2010) 2846-2856. [13] N. Shokati, F. Ranjbar, M. Yari, Exergoeconomic analysis and optimization of basic, dual-pressure and dual-fluid ORCs and Kalina geothermal power plants: A comparative study, Renewable Energy, 83 (2015) 527-542. [14] B.F. Tchanche, G. Lambrinos, A. Frangoudakis, G. Papadakis, Low-grade heat conversion into power using organic Rankine cycles–A review of various applications, 30

Renewable and sustainable energy reviews, 15 (2011) 3963-3979. [15] F. Campana, M. Bianchi, L. Branchini, A. De Pascale, A. Peretto, M. Baresi, A. Fermi, N. Rossetti, R. Vescovo, ORC waste heat recovery in European energy intensive industries: Energy and GHG savings, Energy Conversion and Management, 76 (2013) 244-252. [16] D. Wei, X. Lu, Z. Lu, J. Gu, Dynamic modeling and simulation of an Organic Rankine Cycle (ORC) system for waste heat recovery, Applied Thermal Engineering, 28 (2008) 1216-1224. [17] R.H. Aungier, Aerodynamic Performance Analysis of Axial-Flow Turbines, in: Turbine Aerodynamics: Axial-Flow and Radial-Flow Turbine Design and Analysis, ASME Press, 2006. [18] D. Pasquale, A. Ghidoni, S. Rebay, Shape optimization of an organic rankine cycle radial turbine nozzle, Journal of Engineering for Gas Turbines and Power, 135 (2013) 042308. [19] L. Mueller, Z. Alsalihi, T. Verstraete, Multidisciplinary optimization of a turbocharger radial turbine, Journal of Turbomachinery, 135 (2013) 021022. [20] P. Colonna, S. Rebay, J. Harinck, A. Guardone, Real-gas effects in ORC turbine flow simulations: influence of thermodynamic models on flow fields and performance parameters, in: ECCOMAS CFD 2006: Proceedings of the European Conference on Computational Fluid Dynamics, Egmond aan Zee, The Netherlands, September 5-8, 2006, Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS), 2006. [21] E. Sauret, Y. Gu, Three-dimensional off-design numerical analysis of an organic Rankine cycle radial-inflow turbine, Applied Energy, 135 (2014) 202-211. [22] P. Klonowicz, A. Borsukiewicz-Gozdur, P. Hanausek, W. Kryłłowicz, D. Brüggemann, Design and performance measurements of an organic vapour turbine, Applied Thermal Engineering, 63 (2014) 297-303. [23] S.-Y. Cho, C.-H. Cho, K.-Y. Ahn, Y.D. Lee, A study of the optimal operating conditions in the organic Rankine cycle using a turbo-expander for fluctuations of the available thermal energy, Energy, 64 (2014) 900-911. [24] E. Sauret, A.S. Rowlands, Candidate radial-inflow turbines and high-density working fluids for geothermal power systems, Energy, 36 (2011) 4460-4467. [25] H.M. Hettiarachchi, M. Golubovic, W.M. Worek, Y. Ikegami, Optimum design criteria for an organic Rankine cycle using low-temperature geothermal heat sources, Energy, 32 (2007) 1698-1706. [26] F. Marcuccilli, D. Thiolet, Optimizing binary cycles thanks to radial inflow turbines, in: Proceedings world geothermal congress, 2010. [27] T. Hung, S. Wang, C. Kuo, B. Pei, K. Tsai, A study of organic working fluids on system efficiency of an ORC using low-grade energy sources, Energy, 35 (2010) 1403-1411. [28] A. Schuster, S. Karellas, R. Aumann, Efficiency optimization potential in 31

supercritical Organic Rankine Cycles, Energy, 35 (2010) 1033-1039. [29] E. Lemmon, M. Huber, M. McLinden, NIST thermodynamic and transport properties of refrigerants and refrigerant mixtures (REFPROP) version 8.0, in, NIST, 2007. [30] F. Marcuccilli, S. Zouaghi, Radial inflow turbines for Kalina and organic Rankine cycles, system, 2 (2007) 1. [31] E. Sauret, Open design of high pressure ratio radial-inflow turbine for academic validation, in: ASME 2012 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, 2012, pp. 3183-3197. [32] H. Moustapha, M.F. Zelesky, N.C. Baines, D. Japikse, Axial and radial turbines, Concepts NREC White River Junction, VT, 2003. [33] A.J. Glassman, Turbine Design and Application. NASA SP-290, NASA Special Publication, 290 (1972). [34] C.A. Wasserbauer, A.J. Glassman, Fortran program for predicting off-design performance of radial-inflow turbines, (1975). [35] A. Romagnoli, R. Martinez-Botas, Performance prediction of a nozzled and nozzleless mixed-flow turbine in steady conditions, International Journal of Mechanical Sciences, 53 (2011) 557-574. [36] L. Pan, H. Wang, Improved analysis of Organic Rankine Cycle based on radial flow turbine, Applied thermal engineering, 61 (2013) 606-615. [37] C.A. Ventura, P.A. Jacobs, A.S. Rowlands, P. Petrie-Repar, E. Sauret, Preliminary design and performance estimation of radial inflow turbines: An automated approach, Journal of Fluids Engineering, 134 (2012) 031102. [38] M. Odabaee, E. Sauret, K. Hooman, Computational fluid dynamics simulation and turbomachinery code validation of a high pressure ratio radial-inflow turbine, in: 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2014), HEFAT, 2014. [39] P.C. Rocha, H.B. Rocha, F.M. Carneiro, M.V. da Silva, A.V. Bueno, k–ω SST (shear stress transport) turbulence model calibration: A case study on a small scale horizontal axis wind turbine, Energy, 65 (2014) 412-418. [40] P. Louda, P. Sváček, J. Fořt, J. Fürst, J. Halama, K. Kozel, Numerical simulation of turbine cascade flow with blade-fluid heat exchange, Applied Mathematics and Computation, 219 (2013) 7206-7214. [41] A. Agrawal, A.A. Cornelio, D. Limperich, Investigation of Cubic EOS Models for HFO-1234yf Refrigerant Used In Automotive application, (2012). [42] C. Ansys, ANSYS CFX-solver theory guide, ANSYS CFX Release, 11 (2009) 69-118. [43] R.C. Reid, J.M. Prausnitz, B.E. Poling, The properties of gases and liquids, (1987). [44] J.S. Brown, Predicting performance of refrigerants using the Peng–Robinson 32

equation of state, International Journal of Refrigeration, 30 (2007) 1319-1328. [45] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST reference fluid thermodynamic and transport properties–REFPROP, in, Version, 2002. [46] A.P. Wheeler, J. Ong, The role of dense gas dynamics on organic rankine cycle turbine performance, Journal of Engineering for Gas Turbines and Power, 135 (2013) 102603. [47] M. Pini, G. Persico, E. Casati, V. Dossena, Preliminary design of a centrifugal turbine for organic rankine cycle applications, Journal of Engineering for Gas Turbines and Power, 135 (2013) 042312. [48] Y. Li, X.-d. Ren, Investigation of the organic Rankine cycle (ORC) system and the radial-inflow turbine design, Applied Thermal Engineering, 96 (2016) 547-554. Figure captions Fig. 1. Configuration of ORC system including sketch of the radial inflow turbine. Fig.2. Schematic of the rotor velocity triangles (left) and enthalpy-entropy diagram of the turbine expansion (right). Fig.3. Flow chart of the turbine preliminary design and 3D modeling. Fig. 4. 3D view of the full 3D radial inflow turbine (stator and rotor blades). Fig. 5. 3D view of mesh generated for rotor blade flow passage. Fig. 6. 3Dview of mesh generated for stator blade flow passage. Fig. 7. Meridional view of a) Static temperature, b) static pressure, c) Mach number for the nominal condition. Fig. 8. Validation of the 1D turbine model at off-design conditions. Fig. 9. Evolution of the total-to-static efficiency with the total inlet temperature at three different rotational speeds. Fig. 10. Evolution of the total-to-static efficiency with the rotational speed at three different inlet temperatures. 33

Fig. 11. Variation of the turbine power with the total inlet temperature at three different rotational speeds. Fig. 12. Variation of the turbine power with the rotational speed at three different inlet temperatures. Fig. 13. Variation of the total-to-static efficiency with the total-to-static pressure ratio at three different inlet temperatures for the nominal rotational speed. Fig. 14. Variation of the total-to-static efficiency with the total-to-static pressure ratio at three different rotational speeds for the nominal inlet temperature.

34

Table captions Table 1. Recent numerical simulations of ORC turbines. Table 2. The overall performance of ORC cycles for petrochemical applications. Table 3. Thermodynamic data required for the turbine design obtained from the R134a ORC cycle analysis. Table 4. Parameter scope of the radial inflow turbine. Table 5. Preliminary design data of R134a radial turbine. Table 6. Radial-inflow turbine 3D geometric dimensions. Table 7. Comparison of steady values under different number of cells Table 8. Comparison of the meanline analyses and the present 3D CFD simulations. Table 9. Comparison between reference[21] and 1D turbine model. Table 10. Comparison between the nominal point and best efficiency point.

35

Table 1. Recent numerical simulations of ORC turbines Author

Working

Simulation

Geometry

Quasi-3D

Radial turbine nozzle

fluid Wheeler

and Pentane

Ong [46]

R245fa

Viscous

Pini et al. [47]

Siloxane

Pseudo-3D

3-Stage

MDM

Throughflow

Centrifugal turbine

Hu et al. [2]

R245fa

1D Viscous

Radial-inflow turbine

Cho et al. [23]

R245fa

3D Viscous

Impulse radial turbine

and

Vaneless nozzle Sauret and Gu R143a

3D Viscous

Radial-inflow turbine

3D Viscous

Radial-inflow turbine

[21] Li and Ren [48]

R123

36

6-stage

Table 2. The overall performance of ORC cycles for petrochemical applications Item

Value

Diesel flow rate/temperature

30.56 kg/s, 418 K

Mass flow rate of R134a

40.34 kg/s

Heat exchanger DT

5K

Evaporating pressure

2500 kPa

Turbine inlet temperature

355.73 K

Condensing temperature/pressure

310K, 950 kPa

Turbine efficiency

82%

Pump efficiency

72%

Cycle efficiency

7.12%

Turbine shaft power

640 kW

Net power

515 kW

Table 3. Thermodynamic data required for the turbine design obtained from the R134a ORC cycle analysis Variables

(kPa) 2500

(kPa) 950

37

(K) 360

(kW) 640

Table 4. Parameter scope of the radial inflow turbine Design variables

Limited variables

α2 (°)

20~30

b2/r2

0.04~0.34

β2 (°)

80~110

r4,tip/r3

<0.90

r4/r3

0.35~0.7

r4,hub/r3

>0.10

β4 (°)

20~45

U/C0

0.63~0.72

N (rpm)

<10000

W (kW)

643 Table 5. Preliminary design data of R134a radial turbine

Global variables

Geometric parameters

(-)

2.58

(-)

16

(-)

2.63

(-)

19

(kg/s)

40.34



(%)

80



(%)

81.6

(rpm)

8000

W (kW)

643

(-)

0.711

38

Table 6. Radial-inflow turbine 3D geometric dimensions Nozzle (mm)

Rotor 194.78

(mm)

Diffuser 169.37

(mm)

110.0

(mm)

50.8

Blade height (mm)

13.23

Inlet blade height (mm)

13.23

TE thickness (mm)

1

TE thickness (mm)

1

178.28

Axial length (%)

35

(mm)

(deg)

0

(deg)

0

(deg)

16.8

(deg)

33.2

Clearances (mm): Axial

0.3

Radial

0.3

39

Axial length (%)

41

Table 7. Comparison of steady values under different number of cells Physical quantity

106×104

155×104

212×104

(kg/s)

40.3

40.9

40.8

(%)

86.3

84.3

85.2

(%)

87.2

85.2

86.1

678.8

669.9

677.6

(kPa)

2498.62

2493.35

2495.24

(K)

360.12

359.89

360.12

0.742

0.744

0.743

(-)

0.285

0.286

0.285

(kPa)

980.1

980.6

980.5

(K)

319.8

320.02

320.1

Global Variables

W (kW) Stator inlet

Rotor inlet (-) Rotor outlet

40

Table 8. Comparison of the meanline analyses and the present 3D CFD simulations Preliminary design Variables

Turbine model

Present CFD

(ANSYS-Vista RTD)

Global variables (-)

2.58

2.53

2.54

(-)

2.63

2.63

2.63

(kg/s)

40.34

41.10

40.9

(%)

80.0

79.9

84.3

(%)

81.7

81.7

85.2

643.7

641.2

669.9

(kPa)

2500

2500

2493.35

(K)

360

360

359.89

(kJ/kg)

444.3

444.3

444.3

0.744

0.743

0.744

(-)

0.273

0.304

0.286

(kPa)

969.0

988.6

980.6

(K)

320.2

320.9

320.02

(kJ/kg)

428.4

428.7

427.92

W (kW) Stator inlet

Rotor inlet (-) Rotor outlet

41

Table 9. Comparison between reference[21] and 1D turbine model Variables

Reference[21]

Turbine model

Deviation

8000

8000

(kPa)

5000

5000

(K)

413

413

(kPa)

1835

1835

(kg/s)

17.06

16.55

2.98%

(%)

83.5

83.93

0.51%

421.5

413.22

1.96%

Fixed Value (rpm)

Performance

W (kW)

Table 10. Comparison between the nominal point and best efficiency point Variables

Nominal point

Best efficiency point

(%)

79.9

83.0

(-)

2.63

2.1

(K)

360

360

(kg/s)

41.10

34.68

(rpm)

8000

8000

W (kW)

641.2

472.3

42

43

Turbine

Evaporator

Diesel

Radial inflow turbine

Condenser

Production

Pump

Cooling water

δz

Stator Vaneless space

Fluid reservoir Rotor

Recycling

r1 r2 r3

δr b4 r4,tip r4,hub

r4

Fig.1. Configuration of ORC system including sketch of the radial inflow turbine.

P1

Rotor inlet

α3

C3

β3 W3

U3

Rotor outlet

β4

α4 C4

U4

Enthalpy (J/kg)

1 2s

P2 P3

2

Nozzle Vaneless space

3 3s t4 t4s

W3

Pt4

Rotor

4 P4

4s Entropy (J/kg·K)

Fig.2. Schematic of the rotor velocity triangles (left) and enthalpy-entropy diagram of the turbine expansion (right).

44

Start

Thermodynamic design and performance analysis of ORC

Read Turbine areodynamics input (PTin, TTin, m, ΠT-T , ω, U/C0)

Read Turbine geometry input (Number of vanes, axial length)

Loss correlations

Calculate ANSYS Vista-RTD

Read Geometry dimensions

Model ANSYS BladeGen 3D geometry

End

Fig.3. Flow chart of the turbine preliminary design and 3D modeling.

45

Fig.4. 3D view of the full 3D radial inflow turbine (stator and rotor blades).

Psout=950kPa

Fig.5. 3D view of mesh generated for rotor blade flow passage.

46

PTin=2500kPa, TTin=360K

Fig.6. 3Dview of mesh generated for stator blade flow passage.

(a)

(b)

(c) 47

Fig.7. Meridional view of a) Static temperature, b) static pressure, c) Mach number for the nominal condition.

Fig. 8. Validation of the 1D turbine model at off-design conditions.

48

Fig. 9. Evolution of the total-to-static efficiency with the total inlet temperature at three different rotational speeds.

49

Fig. 10. Evolution of the total-to-static efficiency with the rotational speed at three different inlet temperatures.

Fig. 11. Variation of the turbine power with the total inlet temperature at three different rotational speeds.

50

Fig. 12. Variation of the turbine power with the rotational speed at three different inlet temperatures.

51

Fig. 13. Variation of the total-to-static efficiency with the total-to-static pressure ratio at three different inlet temperatures for the nominal rotational speed.

Fig. 14. Variation of the total-to-static efficiency with the total-to-static pressure ratio at three different rotational speeds for the nominal inlet temperature.

52

Highlights

1. The complete design process of a R134a 640 kW radial-inflow turbine is finished. 2. 3D viscous simulation is presented and discussed at the nominal condition. 3. The turbine’s off-design performance prediction model is established and analyzed. 4. The parametric studies show that the design point has better robustness.

53