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Design and structure optimization of small-scale radial inflow turbine for organic Rankine cycle system
Energy Conversion and Management 199 (2019) 111940
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Design and structure optimization of small-scale radial inflow turbine for organic Rankine cycle system ⁎
T
⁎
Tan Wua,b, Long Shaoc, , Xinli Weia,b, Xinling Maa,b, , Guojie Zhanga,b a
School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou 450001, China Engineering Research Center of Energy Saving Technologies and Equipments on Thermal System, Ministry of Education (MOE), Zhengzhou 450001, China c College of Mechanical and Electrical Engineering, Henan Agricultural University, Zhengzhou 450002, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Waste heat recovery Organic Rankine cycle Radial inflow turbine Turbine design and optimization
The ORC (organic Rankine cycle) system has the advantages of simple structure, environmental friendliness, reliability and low capital cost. The expander is the key device of energy conversion in the ORC system, and its performance has a direct influence on that of the ORC. In this paper, a self-designed and manufactured radial inflow turbine is applied to low temperature waste heat power generation. The numerical model for the internal flow of the radial inflow turbine is established, and the numerical results show a better agreement with the experimental data. Firstly, the influence of blade stagger angles on nozzle performance is studied. The study finds that with the decrement of stagger angles under specific angle ranges, the velocity coefficient increases. However, the efficiency of the nozzle decreases sharply when the stagger angle exceeds 30°. Secondly, the influence of the blade profile on the efficiency of the rotor is investigated. The results indicate that with t increasing, the efficiency of the rotor firstly increases, then decreases quickly. It increases by 1% compared with that of the original rotor, when the t = 1.95. At last, the performance of the turbine is researched numerically. This paper discovers that total-to-static efficiency of the turbine increases by 1.7% compared with that of the original turbine. This research provides orientation and basis for the improvement of aerodynamic design and performance of radial inflow turbine. As for practical application, the study can provide certain reference for the structure and blade profile design of nozzles and rotors to further improve the performance, and to offer some data for the operational control and tests.
1. Introduction With the depletion of non-renewable energy and environmental deterioration, scientific energy utilization technologies are paid more and more attention all over the world. Organic Rankine cycle (ORC) is a recognized and effective method to convert low grade heat into power [1]. ORC can recover different kinds of low-grade heat, such as industrial waste heat [2], biomass sources [3], solar energy [4], geothermal sources [5], waste heat from engine exhaust [6], ocean thermal energy conversion [7]. It can increase the power supply while achieving energy and environmental sustainability at the same time. The main components of an ORC are evaporator, condenser, working fluid pump and expander [8]. The expander is an important energy conversion device in the ORC system. The organic working fluid enters the evaporator and becomes the superheated gas, and it pushes expander to realize conversion from thermal energy to mechanical energy. The isentropic efficiency of the expander directly affects the
⁎
overall performance and efficiency of the system [9]. According to different working principles, the expander is divided into two categories. One type is volumetric expander, which generally obtains enthalpy drop and pressure ratio by changing the inner volume of the working chamber, including screw expander [10], piston expander [11], scroll expander [12], and so on. The other is speed expander, which mainly includes axial flow turbine [13], radial inflow turbine [14] and centrifugal turbine [15]. The radial inflow turbine is characterized by the capacity to deal with large enthalpy drop at the low peripheral, low manufacturing cost and compact structure [16]. The radial inflow turbine is suitable for dry working fluids and isentropic working fluids. The rotational speed and expansion efficiency are relatively high [17]. Over the years, an increasing number of works have studied the optimization of radial inflow turbine design. Applying Computational Fluid Dynamics (CFD) to performance prediction, internal flow analysis and structural design of radial inflow turbine has already become a
Corresponding authors at: School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou 450001, China (X. Ma). E-mail addresses: [email protected] (L. Shao), [email protected] (X. Ma).
https://doi.org/10.1016/j.enconman.2019.111940 Received 7 March 2019; Received in revised form 16 July 2019; Accepted 13 August 2019 Available online 21 August 2019 0196-8904/ © 2019 Published by Elsevier Ltd.
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Nomenclature β c D Ḋ h Δh H L (l) ṁ N P R (r) s T u w W
absolute velocity, m/s diameter, m diameter ratio of blade, specific enthalpy, kJ/kg specific enthalpy drop, kJ/kg total enthalpy, kJ/kg length or blade height, m mass flow, kg/s rotational speed, rpm pressure, MPa radius, mm entropy, J/kg·K temperature, K rotor blade velocity, m/s relative velocity, m/s power, kW
θ v Ω η ρ ζ φ ψ
direction, degree relative flow angle with respect to the meridional direction, degree polar angle, degree velocity ratio, – degree of reaction, – efficiency, – density, kg/m3 loss coefficient, – nozzle velocity coefficient, – rotor blade velocity coefficient, –
Subscripts 1–6 u s t T
state point peripheral isentropic state total state turbine
Greek symbols α
absolute flow angle with respect to the meridional
evaluated by three-dimensional analysis using CFD. And the comparison between results of the one-dimensional design and CFD simulation was conducted. About the structure optimization of the turbine, Ssebabi et al. [24] connected the turbo expander to the generator with a magnetic coupler to achieve non-contact transmission and tested the performance of expander with air as the working fluid. The optimization of the rotor blade was carried out in consideration of parameters such as the number of rotor blades and the angle of the outlet airflow. In the study of nozzle blades, Razaaly et al. [25] adopted a two-dimensional highprecision turbulent computational fluid dynamics model and made the uncertainty measurement analysis of typical supersonic nozzle blades in ORC applications. In the analysis process, Kriging-based techniques were adopted. In the study of the loss model, Wu et al. [26] combined the preliminary design of the heat loss model with three-dimensional numerical simulation to optimize. A genetic algorithm based on turbine geometry optimization was designed, and the optimized specific speed and blade shape could increase the power output by 3.6%. The more detailed analysis and optimization of the ORC radial inflow turbine based on CFD need to be further investigated [19]. For the thermodynamic cycle in a kW-scale ORC system, this paper presents a one-dimensional design model. Design parameters and a finite element
crucial research method and an available verification for the one-dimensional model [18]. However, only a few past studies have focused on the CFD simulations of radial inflow turbine in organic Rankine cycles. According to a conclusion drawn by Xia et al. [19], the threedimension CFD results are in correspondence with the one-dimensional analysis, and the addition of splitter blade contributes to improving the performance of ORC radial inflow turbine. For the design of aerodynamic distribution, Zheng et al. [20] proposed a preliminary design and an evaluation method that combined the design of radial inflow turbine with the predicted variable operating conditions, and used the numerical simulation results and experimental data to verify it. Fiaschi et al. [21] made a three-dimensional analysis of the rotor with the geometry inputs calculated from one-dimensional design for a 5 kWORC radial-inflow turbine operating with R134a. The number and the geometry of the rotor blades were further refined by CFD approach. Li et al. [22] developed an aerodynamic and profile design system, in which a radial inflow turbine with R123 as the working fluid was designed and the numerical analysis was conducted. The simulation results indicated that the shock wave caused by the high expansion ratio in the nozzle was well controlled. With regard to identical design conditions, Kim et al. [23] proposed a novel method to design ORC radial-inflow turbine. The performance of a designed turbine was then
Fig. 1. Schematic diagram of an ORC system (left) and T-s diagram (right). 2
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analysis model are developed, so as to conduct a numerical study on aerodynamic layout design and performance of radial inflow turbine with R123 as the working fluid. Taking working fluid mass flow rate, turbine output power and isentropic efficiency as evaluation indexes, this paper compares experimental data [27] and simulated results, and it finds their change rules are basically consistent. It researches the optimization of the stagger angle, the number of nozzle blade and parabolic index, for further improving the operational efficiency of the turbine. The results provide some reference for the design of radial inflow turbine used in the ORC system. Fig. 3. Velocity triangles at rotor inlet and outlet.
2. Design and analysis of radial inflow turbine
outlet of the guider increases to c4, during which its pressure and temperature respectively decrease to P4 and T4. Then the gas enters into the rotor in the high-speed revolution at the relative speed of w4, and the peripheral velocity of blades is u4. The gas continues to expand to do work in the blades. The work done in the blades by every kilogram working fluid is marked as Δhu,4-5, named peripheral work. When the gas pressure in the outlet of blades decreases to P5, the temperature decreases to T5. The relative velocity of air flow in the outlet is named as w5, and its absolute velocity c5 is the vector sum of the velocity u5 and w5 in the point. Finally, the working fluid enters into the air or is transported to the pipeline through a diffuser or exhaust pipe. The flow condition of the gas in the inlet and outlet are expressed as velocity triangles at rotor inlet and outlet, as shown in Fig. 3. The flowchart of the in-house radial inflow turbine preliminary onedimensional aerodynamic design program is illustrated in Fig. 4. Based on it, the basic geometry of radial inflow turbine and its performance in the design are obtained. Detailed design requirements and chosen design parameters are included in the input data, for instance, the flow angles, the geometry ratios, the blade number and the nozzle design parameters by using Aungier’s method [29]. In addition, three non-dimensional parameters are considered in this method, such as the reaction Ω, the velocity ratio v, and the radius ratio r5/r4 [30]. Eqs. (1) and (2) state Ω and v, respectively.
The schematic diagram of the organic Rankine cycle system is shown in Fig. 1. The liquid working fluid in the condenser gradually enters the evaporator after it is boosted by the pump. In the process, it absorbs heat from the heat source to become the saturated or the superheated vapor. Then the vapor flows into the turbine to generate power through expansion. Finally, the turbine exhaust is condensed to liquid by the condenser. The radial inflow turbine consists of three main components, including volute, nozzle and rotor, as illustrated in the right drawing in Fig. 2. The incoming fluid is accelerated and distributed uniformly around the periphery of the turbine via volute (1–2). Further acceleration and increase in the circumferential component of velocity are attained via the nozzle (2–3) before it enters the rotor. The space between the nozzle and rotor (3–4) makes the nozzle outlet possible to wake to mix out. Then the kinetic energy of the fluid is converted into mechanical energy of shaft as it expands through the rotor (4–5). The corresponding enthalpy-entropy diagram detailing the expansion process across the stage is shown in the left drawing in Fig. 2. The onedimensional aerodynamic design method of radial inflow turbine simplifies the expansion and flow of gas working flow as a univariate steady flow characterized by being adiabatic, axisymmetric and inviscid [28]. The thermodynamic properties, geometry parameters and flow features are determined at key stations throughout the stage as illustrated in Fig. 2. As the turbine works, the working fluid flows into the intake pipeline at certain speed c0, when its total pressure is marked as Pt1, total temperature as Tt1. The gas entering into the turbine firstly expands and accelerates in the nozzle. The process makes the speed of gas in the
Ω = Δhs,4 − 5/Δh s,1 − 5
(1)
v = u4 / cs = u4 / 2Δhs,1 − 5
(2)
where Δhs,4 −5 and Δhs,1 −5 respectively represent the isentropic specific
Fig. 2. Schematic of the radial inflow turbine meridional view (right), enthalpy-entropy diagram of the turbine expansion (left). 3
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the blade outlet. The axial efficiency of the turbine ηtur and its power Wtur are gained by Eqs. (10) and (11).
ηtur = (ηu − ζ friction ) ηm ηc ηe
(10)
Wtur = ṁ Δhs,1 − 5 ηtur
(11)
where ηm is mechanical efficiency, ηc is clearance loss efficiency, ηe is partial intake loss efficiency, and full air intake is 1. In this paper, following factors are taken into consideration, such as nozzle loss Δhloss,volute, passage loss Δhpassage, clearance loss Δhclearance, friction loss Δhfriction and exit loss Δhexit, as Eq. (12) [32]. The total-tostatic efficiency [33] is expressed in the form of enthalpy drop, defined as Eq. (13).
Δhloss = Δhloss,volute + Δh passage + Δhclearance + Δh friction + Δhexit
(12)
Δ
ηts =
enthalpy drop of the rotor and the stage, and cs is the spouting velocity. In line with the inlet total temperature Tt1 and the pressure Pt1, the total enthalpy ht1 and the entropy s1 are figured out by the REFPROP database, and the ideal enthalpy at the rotor outlet h5s can also be obtained by s1 and the outlet static pressure P5. As a result, the stage isentropic enthalpy drop Δhs,1 −5 is expressed by Eq. (3).
a=
zm ·t −1 = x m tan β = const
Therefore, Δhs,4 − 5 and u4 are gained by Eqs. (1) and (2), and then h4s and r4 are calculated by using Eqs. (4) and (5), respectively. (4)
r = 60000u/2πN
(5)
(6)
Δh friction ṁ Δh s,1 − 5
(7)
ζ friction =
where f is the friction coefficient of the disk, ρ4 is the density of working fluid in the blade inlet, and ṁ is the mass flow rate of the turbine. The peripheral work of the turbine Δhu,4-5 and the peripheral efficiency ηu of the radial inflow turbine are gained by Eq. (8), Eq.(9a) and Eq.(9b) [31].
Δh u,4 − 5 = ηu =
c42 − c52 u 2 − u52 w 2 − w42 + 4 + 5 2 2 2
Δh u,4 − 5 Δh s,1 − 5
(8)
(9a)
ηu 2 = 2ν (φ cos α4 1 − Ω − D4̇ ν + D4̇ ψ cos β5 2 Ω + φ2 (1 − Ω) + D4̇ ν 2 − 2νφ cos α4 1 − Ω )
(14)
(15)
When the design sets the heat source temperature to 393.15 K, the cold source temperature of 293.15 K, the evaporator temperature difference of 5 K, the condenser temperature difference of 3 K and other parameters are constant. When the unit power generation of hot fluid is the largest, the net output power is used as the evaluation index, the optimal evaporation temperature of ORC system is 344.7 K and the optimum condensation temperature is 301.09 K. There must be a suitable degree of subcooling and superheat in the organic working fluid. It is assumed that the superheat and subcooling of the working fluid in evaporator and condenser are both 5 K. Under the saturation pressure, the condenser outlet and the evaporator outlet temperatures are 296.09 K, 349.7 K, and the saturation pressures are 0.102 MPa, 0.392 MPa. The condensing pressure of the working fluid in the condenser is 0.102 MPa, the outlet temperature is 296.09 K, the working fluid evaporation pressure in the evaporator is 0.392 MPa, and the outlet temperature is 349.7 K. According to the optimized working condition parameters of the ORC system, the preliminary design of the radial inflow turbine is carried out with R123 as the working fluid. The design parameters for the turbine is shown in Table 1. A radial inflow turbine consists of a volute, a nozzle, an impeller and a diffuser. The main role of a volute is distributing flow evenly to the nozzle inlet, and it has an axisymmetric structure. Therefore, the volute is a spiral tube whose section evenly decreases along the flow direction. The cross section of the volute flow passage is a circle. The designed volute is shown in Fig. 5(a). The role of the nozzle is to convert heat into kinetic energy and to obtain the flow rate and flow direction required for the rotor inlet. A Nozzle is composed of a set number of equant-shaped blades which are equally spaced on a ring. In this radial inflow turbine, TC-4P blade profile [34] by Moscow Institute of Dynamics is adopted, as shown in Fig. 5(b). The organic vapor continues doing work by expansion in the impeller, and converts kinetic energy into mechanical energy for transmission to the generator. The impeller is also a certain set of equant-shaped blades which are uniformly distributed on a disk. According to the principle of one-dimensional flow,
where u is the peripheral velocity, r is the radius of rotor, and N is the rotational speed. Friction loss power of disk Δhfriction and its friction loss coefficient ζfriction are gained by Eqs. (6) and (7).
u 3 1 Δh friction = fρ4 r42 ⎛ 4 ⎞ 100 ⎝ ⎠ 1.36
1 (tgβh)−1 2
The blade outlet angle β and the parabolic index t will affect the rotor performance. In the case where h and β are known, the relationship between t and zm is calculated by Eq. (15).
(3)
h4s = h t1 − (1 − Ω)Δhs,1 − 5
(13)
where ηts denotes the total-to-static efficiency, Hs is the total enthalpy, and Δhloss is the loss enthalpy. According to the blade profile, the parabolic equation x=azt directly affects the blade structure and molding, including non-developable ruled parabolic surface. In the parabolic equation is given by Eq. (14).
Fig. 4. The flowchart of radial inflow turbine preliminary aerodynamic design.
Δhs,1 −5 = ht1 − h5s
Hs − ∑ hloss Hs
(9b)
where Ω is the degree of reaction, φ is nozzle velocity coefficient, ψ is rotor blade velocity coefficient, D4̇ is diameter ratio of the blade, α4 is absolute flow angle of the blade inlet, and β5 is relative flow angle of 4
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2.13 × 10−3 m3, and the corresponding value of in the condenser is 3.25 × 10−3 m3, as is shown in Fig. 8(a). The experimental system adopts the GC-DRY-60 electric heating and heat transfer oil furnace produced by Yancheng Gongchuang Electric Heating Equipment Co., Ltd. Following components are included in the facility, such as an electric heater, a high tank, an oil temperature control system, a hot oil pump, a liquid level meter and other auxiliary fittings, as is shown in Fig. 8(b). Its maximum heating power is 60 kW, and the actually-required heating can be adjusted by the temperature control system. The working fluid pump used in the experiment is hydraulic diaphragm type pump, JYMD-1000/2.5. Its major performance parameters are maximum flow 1000 L/h, maximum pressure 2.5 MPa, intake stroke 50 mm, and motor power 2.2 kW, as is shown in Fig. 8(c). The generator, the main facility for the electrical output of ORC system, is a three-phase AC permanent magnet synchronous generator at high speed (with rated power being 5 kW, rated speed being 12000 rpm). When operated under rated conditions, the generator is with efficiency of 90%, and its output voltage is proportional to the speed. The specially-developed reducer is used to adapt to the turbine and the generator. First-class gear transmission is adopted in the experiment, with a ratio of 5.304 and an external dimension of 200 mm × 131 mm × 220 mm. The reducer is connected to the turbine through a coupling. Experimental equipment consisting of a turbine, a reducer and a generator is shown in Fig. 8(d). The radial turbine used in the experiment is shown in Fig. 8(e). The power of resistance wires is used as the load to consume electrical energy from the generator. The load can be adjustable, as is shown in Fig. 8(f). In the data acquisition systems, following facilities are included, such as a Coriolis mass flow meter, an intelligent liquid turbine flow meter, an elliptical gear flow meter, a temperature sensor, a pressure sensor, an Agilent data acquisition instrument, an electrical parameter meter, and a computer. The Coriolis mass flow meter is installed at the outlet of the pump to measure the mass flow rate of the R123. The elliptical flow meter is installed in the heat source cycle to measure the volume flow of the heat transfer oil. An intelligent liquid turbine flow meter is installed in the condensing cycle to measure the flow of cooling water. A temperature sensor and a pressure sensor are separately installed at the inlet and outlet of the main equipment. The Agilent data acquisition device mainly keeps track on the temperature, pressure and working fluid flow in the thermal system. The electric parameter measuring instrument with a 10-second interrecord gap mainly records the frequency, the output voltage, the current and the electric power of the generator. The recorded data are summarized on the computer by software to check the performance of the generator. According to the temperature and pressure collected by the computer, the parameters including enthalpy and entropy of the R123 are obtained through the REFPROP 9.0 issued by NIST. The main experimental testing instruments are listed in Table 2.
Table 1 Main design parameters for the radial inflow turbine. Design parameter
Value
Turbine inlet temperature/K Turbine inlet pressure/MPa Turbine outlet pressure/MPa Mass flow rate/kg·s−1 Rotational speed/r·min−1 Degree of reaction Velocity ratio Rotor inlet diameter/mm Shroud diameter rotor outlet/mm Hub diameter at rotor outlet/mm Number of rotor blade Rotor blade height at the inlet/mm Nozzle inlet diameter/mm Nozzle outlet diameter/mm Number of nozzle blade Nozzle blade height/mm Turbine axial height/mm Turbine output/kW Turbine efficiency/%
345.15 0.393 0.102 0.111 54,950 0.45 0.69 50 34 19 12 1.8 70 56 17 1.6 15 1.68 68
(a) Volute
(b) Nozzle
(c) Impeller
(d) Radial inflow turbine
Fig. 5. Photograph of the radial inflow turbine.
based on the reverse design, the isosceles trapezoidal design method is proposed to get 3D meridional flow channel of the impeller. The blade shape of the impeller adopts non-developable parabolic surface profile. The developed impeller is shown in Fig. 5(c). Fig. 5(d) is the photograph of developed radial inflow turbine.
4. Numerical analysis of the flow in the radial inflow turbine For the geometry of the nozzle blade and the rotor blade of the radial inflow turbine, the single passage model is established by CFD, and the numerical simulation of the flow field in the turbine is carried out. The structure of the nozzle and rotor is optimized by studying the flow characteristics and aerodynamic properties of the turbine.
3. Experimental facility of the ORC system The schematic diagram of the ORC test rig is as shown in Fig. 6. The testing rig is presented in Fig. 7. The evaporator transfers heat energy of waste heat source to the organic working fluid and heats its liquid form into saturated gas or slightly superheated gas. The condenser transfers the heat of completed organic working fluid from the turbine to the cooling water. This process condenses the superheated organic vapor into saturated liquid or slightly subcooled liquid. In this platform, plate heat exchangers produced by SWEP (a company which professionally produces heat exchangers in Sweden) are used as the evaporator and the condenser. The volume of organic working fluid channel in the evaporator is
4.1. Single passage model of the turbine In consideration of the symmetry of the position between the nozzle blades, the flow conditions of the working fluid in the nozzle passage are basically the same. In order to obtain the calculation results, the single passage model of the nozzle is used for numerical calculation and research. The geometric model and structured grid of the blade are shown in Fig. 9. The geometrical structure, physical parameters and flow 5
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P
T
F
P
T
Speed
Generator Load M P
P
Turbine
T P
T
T Cooling Water
Heat Source Evaporator
P T
Condenser P
P T
T
F
T
P
Working fluid pump T
P
Fluid L reservoir
P
T
F
Fig. 6. Schematic diagram of ORC system.
model and experimental works in the published literature to evaluate the availability of the proposed off-design performance estimation methodology. These cases were chosen to offer reference for the proposed model via ample geometric data. The dependable and good quality of the presented thermodynamic data is another reason. The experimental data was obtained by Shao et al. [27] who used R123, a high dense organic fluid, as the working fluid. The boundary parameter of the single passage model was the experimental data of the turbine inlet and outlet, respectively. The corresponding calculated values are shown in Table 3. According to different working conditions, the calculation is conducted to obtain a group of results, and compared them with those results calculated in the experiment under same conditions, so as to verify the veracity under variable working conditions, as shown in Fig. 12. Based on the actual sequence of experiments, a number of observed values in every steady working condition is used for boundary conditions, and then calculations results are obtained. It could be observed that the results of simulation in the present
characteristics of the rotor are characterized by distinct periodicity. The Boolean operation is used to obtain the fluid region in the rotor. The rotor structural body and the fluid domain are shown in Fig. 10(a) and (b), respectively. In the meshing process, following components are divided more densely by the O-grid method, such as the rotor blade near wall surface, the blade leading edge boundary and the blade trailing edge boundary, so that y+ is about 3. According to the design parameters, mesh segmentation and mesh generation are performed on the flow passage. The structured grid of the rotor is shown in Fig. 11(a). Fig. 11(b) is a partially enlarged view of the leading edge of the rotor passage. Additional grid treatment is implemented and a detailed simulation is conducted for its flow field, so that the calculation accuracy can be effectively improved.
4.2. Validation The experiment compares the results of the proposed expander
Fig. 7. The testing rig based on the radial inflow turbine. 6
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(a) Evaporator and condenser
(b) Electric heating furnace Fig. 9. Nozzle model and grid.
rotating coordinate system is set to rotate about the Z-axis, and the rotating coordinate system is set to a stationary reference coordinate system with a turbine rotational speed of 54,950 r/min. The inlet and outlet boundary parameters are given according to designed conditions, as shown in Table 4. (d) Turbine with reducer and generator
(c) Pump
(e) Radial inflow turbine
4.4. Structural optimization of the nozzle blade The effects of the nozzle blade stagger angle on the peripheral velocity of the outlet are shown in Fig. 13. In general, as the peripheral velocity of the outlet increases, the turbine output increases accordingly. It can be seen that when the number of nozzle blade is constant, the peripheral velocity of the outlet gradually decreases as the stagger angle increases. When the stagger angle is constant, the peripheral velocity increases as the number of the nozzle blade increases. The effects of the nozzle blade stagger angle on the flow angle of the outlet are shown in Fig. 14. Within a reasonable range, reducing the flow angle of the blade can increase the turbine output. When the stagger angle is constant, as the number of blades increases, the outlet flow angle decreases, and the trend gradually becomes slow. It shows that the increasing quantity of blades leads to their growing guiding effect on the working fluid, but the effect of the nozzle blade on the latter is limited. When the number of blades is constant, the flow angle of the outlet increases as the stagger angle increases. The range of the flow angle is generally between 14° and 20°, which ensures the efficiency of the nozzle blade. Therefore, for a certain stagger angle, there is always a corresponding number of nozzle blade, so that the nozzle has higher efficiency. According to the analysis, when the stagger angle is 28° and the number of the nozzle blade is 17 or 19, the comprehensive performance is good. In order to avoid the resonance of the nozzle and the rotor, the number of the nozzle blade and the rotor blade are designed without common divisor. Therefore, a scheme with a stagger angle of 28° and a number of the nozzle blade of 19 is selected. The numerical calculation is shown in Table 5. Compared with the original nozzle blade, the optimized facility is featured with more excellent performance. Its peripheral velocity increased by 7.4% and the velocity coefficient
(f) Loads
Fig. 8. Major equipment and apparatus of the ORC system.
study are in good agreement with the experimental values. Following factors are selected as the evaluation indicators, such as the turbine output, isentropic efficiency and working fluid mass flow rate of the turbine, and the numerical results are slightly larger than the experimental measurement results. 4.3. Calculation method and boundary conditions In this paper, the Spalart-Allmaras model is taken for numerical calculation of the flow field of the nozzle blade and the rotor blade. The organic working fluid is kept in a gaseous state in the passage, and the calculation parameters are obtained by a physical database. The calculated organic working fluid is R123, and the turbine inlet and outlet surfaces are respectively set to pressure inlet and outlet. The surface generated by dividing passage is set to a periodic boundary condition, and the other surfaces are set to adiabatic solid wall conditions. The Table 2 Names and models of testing instrument. Measuring object
Instrument
Type
Range
Accuracy
Temperature Pressure
Thermal resistance Diffused silicon pressure transmitter
WZP Pt100 HX-L61
± (0.15 + 0.002 t)K ± 0.2%
Data collection Working fluid flow
Agilent data collector Coriolis flow meter Intelligent liquid turbine flow meter Oval gear flow meter Laser tachometer Electric parameter measuring instrument
34980A RHM04 RHE 14 YK-LWGY-25 YK-LC-20 DT-2857 8903D
73.15–773.15 K 0–1.6 MPa −0.1–0.4 MPa – 0–24 kg/min
Glass
HMI-1TT
0–10 m3/h 0.4–4 m3/h 2.5–99999 rpm 45–1000 Hz 0.1–60 A 5–500 V 0.5 W–30 kW —
± 0.5% ± 0.5% ± 0.05% ± 1.5 ± 1% ± 1% ± 1% —
Rotating speed Electric frequency Current Voltage Electric power Working condition
7
± 0.1%
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seen from Fig. 16(b) that the static pressure in the suction surface gradually decreases along the streamwise. At 80% of the blade height of the blade trailing edge, there is a local low pressure region and the distribution of isobars is complicated. In view of the pressure surface and suction surface of the blade, the effect of the wall surface on the flow characteristics is greater, and the overall static pressure decreases with the decrease of the blade height. The velocity distribution in the pressure surface, and the flow velocity gradually decreases from the leading edge to the trailing edge of the blade, as shown in Fig. 16(c). At the blade inlet, the isovelocity line is distributed more evenly, while at the 20% of blade height of the trailing edge, there is a local low-speed zone. The velocity gradually decreases along the streamwise, as shown in Fig. 16(d). The isovelocity line is curved to form a small low velocity region at the trailing edge of the blade. At the same time, the velocity near the hub is obviously lower than the number near the shroud. The velocity distribution on the blade is relatively uniform, and the working fluid flow state is better. It can be seen from Fig. 16(e) that the temperature in the blade pressure surface gradually decreases from the leading edge to the trailing edge of the blade. The temperature drop of the former changes markedly, while the temperature gradient of the latter is smaller, and the isotherm distribution of the blade inlet is more uniform. Overall, the blade is featured with excellent flow properties, but there is a certain flow loss at the trailing edge. In the future design of the rotor, some attention should be paid to the improvement of the trailing edge shape of the blade.
Fig. 10. Rotor geometry model.
Fig. 11. Rotor grid.
4.6. Profile optimization of the rotor blade Table 3 Results comparison between the experimental values and calculated values [27]. Parameter
Turbine inlet temperature Turbine inlet pressure Turbine outlet temperature Turbine outlet pressure Mass flow rate Turbine output Isentropic efficiency
Unit
Experimental value
Calculated value
Case1
Case2
Case3
Case1
Case2
Case3
K
393.7
391.3
393.8
393.3
390.6
393.4
MPa K
0.258 377.6
0.366 371.2
0.344 374.1
0.253 377.1
0.360 368.1
0.337 371.8
MPa kg/s kW %
0.115 0.201 2.278 80.6
0.165 0.273 2.914 76.4
0.085 0.248 2.746 78.2
0.115 0.213 2.512 86.2
0.167 0.289 3.013 85.3
0.087 0.262 2.988 85.9
In the design of the rotor, the value of t is given empirically in general, so there is some uncertainty. Therefore, it is necessary to find the optimal parabolic index t to make the flow state inside the rotor is optimal. By adjusting the value of the parabolic index t, different values of zm are obtained, and the numerical calculation of the flow field in the rotor is performed. The results are shown in Table 6. As can be seen from Table 5, the axial length of the rotor increases as the parabolic index t becomes larger. The rotor efficiency increases with the parabolic index t, and the impeller efficiency reaches the maximum when the optimal value is t = 1.95. The efficiency of the rotor increases firstly and then decreases with the increase of the parabolic index t. When the optimal value is 1.95, the rotor efficiency reaches the maximum. The velocity vector of 50% of the blade height flow surface is shown in Fig. 17. The comparison shows that there is an enormous difference between the flows of working fluid before and after optimization. In the flow passage before optimization, the working fluid moves substantially along the flow guiding direction after passing through 50% of the flow passage. The range of vortex near the optimized rotor inlet is significantly smaller than that of the original rotor, and the working fluid flows along the guiding direction at 35% of the flow passage. At 70% of the flow passage, the optimized velocity vector distribution is more uniform, indicating that the flow state of the main flow in the flow passage is good, and the expansion process can be successfully realized for most of the working fluid. The velocity vector of 50% of the blade height rotor inlet is shown in Fig. 18. There is a distinct bending phenomenon in the inlet velocity vector before optimization, but the optimized inlet velocity vector distribution is more uniform. It is concluded that the optimized rotor inlet flow performance is improved and the working fluid is substantially unaffected by the rotor inlet vortex.
increased by 1.12%. The total pressure distribution in the meridional plane of the nozzle blade is shown in Fig. 15. After the comparison of the pressure distribution before and after the optimization, the optimized pressure distribution is more reasonable. After optimization, the pressure drop gradients of static pressure and total pressure are closer to the throat area. The trend of the total pressure is basically consistent with the expansion process of the organic working fluid. Moreover, the optimized total outlet pressure distribution is relatively uniform, indicating that the optimization results are more reasonable.
4.5. Structural optimization of the rotor blade The pressure, velocity and temperature distribution in the rotor blade surface are illustrated in Fig. 16. It can be seen from Fig. 16(a) that the static pressure in the blade pressure surface gradually decreases from the leading edge to the trailing edge of the blade. At the 90% of blade height of the leading edge, part of the isobar is bent to form a small recirculation zone. With the streamwise being about 30% to 45% and the blade height being 70%, there is a range of low pressure regions. The isobars are generally evenly distributed, but they are strongly bent near the tip of the blade, causing flow losses. It can be
4.7. Optimization design of radial inflow turbine The numerical calculation of the turbine is carried out using the optimized nozzle and rotor models. The total-to-static efficiency is used as an indicator to analyze the original design and the optimized model of the turbine. In the turbine model, there are 12 rotor blades, 17 nozzle 8
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Fig. 12. Validation of the turbine model at diffident experimental conditions.
30
Parameter
Unit
Nozzle
Rotor
The The The The
K MPa K MPa
345.15 0.393 321.5 0.192
320.5 0.192 303.5 0.102
inlet temperature inlet pressure outlet temperature outlet pressure
Outlet flow angle (°)
Table 4 Boundary parameters setting.
Stagger angle (28°) Stagger angle (32°) Stagger angle (36°)
25
20
15
10 14
16
18
20
22
24
The nozzle blade number Fig. 14. Variations of the flow angle of the outlet versus the number of blades at different stagger angles. Table 5 Outlet parameters before and after the optimization.
Fig. 13. Variations of the peripheral velocity of the outlet versus the number of blades at different stagger angles.
9
Parameter
Unit
Before the optimization
After the optimization
Outlet velocity Outlet temperature Peripheral velocity of the outlet Outlet flow angle Velocity coefficient
m/s K m/s
152.683 320.62 137.504
158.473 320.12 147.679
° –
23.7 0.935
15.8 0.9455
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Table 6 Calculation results of different blade profiles.
a
Before the optimization
b
Parabolic index t
Axial length of rotor
Rotor efficiency
1.85 1.90 1.95 2.00 2.05 2.10
4.45 4.5 4.55 4.60 4.65 4.70
0.885 0.892 0.903 0.894 0.889 0.881
After the optimization
Fig. 15. The total pressure distribution in the meridional plane of the nozzle blade.
rotational speed of the rotor is set to 54,950 r/min, the nozzle flow passage is a stationary coordinate system. The interface boundary is used to connect the moving area to the static area, and the wall condition is set to the adiabatic wall condition. The static pressure distribution of the turbine before and after the optimization is shown in Fig. 19. The cross section at 50% of the blade height is selected for observation. The trends of corresponding working fluid flow before and after optimization are basically the same. After the working fluid passes through the throat of the nozzle blade, the pressure begins to decrease, as shown in Fig. 19(a). There is a high
blades and 19 optimized nozzle blades. The number of rotor single passage grids is 460,000, that of nozzle single passage grids is 200,000, and that of whole flow passage grids is about 8.3 million. The nozzle inlet takes the pressure boundary, the total pressure is 0.393 MPa, and the total temperature is 345.15 K. The rotor outlet takes the pressure boundary, the pressure is 0.102 MPa, and the working fluid is R123. The rotor flow passage adopts a rotating coordinate system, and the
Fig. 16. The distribution of pressure, velocity and temperature in the rotor blade surface. 10
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before and after optimization under the designed conditions are shown in Table 7. Although the expansion ratio is reduced, the total-to-static efficiency of the optimized turbine is increased by 1.7%. The optimized radial inflow turbine performance has been improved under designed conditions.
5. Conclusions In this paper, the flow field characteristics of the nozzle and the rotor of the radial inflow turbine are studied. The turbine is optimized by adjusting the stagger angle, the number of the nozzle blade and the parabolic index. This research provides orientation and basis for the improvement of aerodynamic design and performance of radial inflow turbine. As for practical application, the study can provide certain reference for the structure and blade profile design of nozzles and rotors to further improve the performance, and to offer some data for the operational control and tests. The results are shown as follows:
Fig. 17. The velocity vector of 50% of the blade height flow surface.
(1) Taking working fluid mass flow rate, turbine output power and isentropic efficiency as evaluation indexes, this paper compares experimental data and simulated results, and it finds their change rules are basically consistent. Difference between the calculated value of working flow and measured one is nearly 5.7%. Difference between these two values of output power and isentropic efficiency is no more than 10%. It indicates the reasonability of numerical calculation model and the reliability of the results. (2) Within a reasonable range, as the stagger angle of the nozzle blade decreases, the velocity coefficient continuously increases. Appropriately increasing the number of the nozzle blade can increase the peripheral velocity of the nozzle outlet and enhance the guiding effect of the nozzle. After the nozzle blade is optimized, the peripheral velocity increases by 7.4%, and the velocity coefficient increases by 1.12%. (3) The local high pressure zone is prone to occur near the leading edge of the rotor inlet, while there is a distinct flow vortex at the rotor outlet near the suction surface. Due to the action of the leading edge, trailing edge and wall of the blade, the local high pressure zone and vortex will cause a certain flow loss. When the optimal parabolic index is 1.95, the rotor efficiency increases by about 1%, and the maximum rotor efficiency is 90.3%. (4) After optimization of the turbine, the total-to-static efficiency increases by 1.7%, which indicates that the performance of the optimized radial inflow turbine is improved.
Fig. 18. The velocity vector of 50% of the blade height rotor inlet.
Fig. 19. The static pressure distribution of 50% of the blade height of turbine.
pressure region near the suction surface at the outlet of the nozzle blade, and a small amount of low pressure region is located near the pressure surface, which is consistent with the analysis result of the single passage. In the nozzle inlet region, the pressure of the working fluid is considerably lower than that in the blade. There is a localized high pressure region near the suction surface of the rotor inlet, which is related to the shape of the rotor inlet. The optimized turbine flow characteristics are superior in Fig. 19(b). The pressure drop gradient of the working fluid in the nozzle flow passage is obvious, and the high pressure region of the rotor inlet substantially disappears. The flow characteristics of the working fluid have been redistributed, which improved the performance of the turbine. The streamline distribution of 50% of the blade height of turbine before and after the optimization is shown in Fig. 20. The velocity streamline of the flow passage in the nozzle is the same, and it is smoother in the flow passage without obvious vortex. At the rotor inlet, there is a small amount of high velocity area, in the velocity streamline of the working fluid, and the velocity at the pressure surface is relatively higher. The velocity of the gas at the rotor outlet is significantly higher and there is no remarkable separation. Overall, there is a dramatical increase in the velocity of the airflow in the nozzle and rotor flow passage. The nozzle plays a major role in accelerating the working fluid, and the rotor plays a good guiding role. The calculation results of the performance parameters of the turbine
Declaration of Competing Interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
a
Before the optimization
b
After the optimization
Fig. 20. The streamline distribution of 50% of the blade height of turbine. 11
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Table 7 Comparison of performance parameters of turbine before and after optimization.
Before the optimization After the optimization
Expansion ratio
Outlet temperature
Total-to-static efficiency
3.85 3.81
303.52 305.47
0.863 0.880
Acknowledgements
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This work was supported by the Funding Plan for Key Research Projects of Henan Province Higher Education Institutions in 2018 (No. 18B620002); Funding Plan for Key Research Projects of Henan Province Higher Education Institutions in 2019 (No. 19A480005). The financial support is gratefully acknowledged. References [1] Pethurajan V, Sivan S, Joy GC. Issues, comparisons, turbine selections and applications – an overview in organic Rankine cycle. Energy Convers. Manage. 2018;166:474–88. [2] Shao L, Ma XL, Wei XL, et al. Design and experimental study of a small-sized organic Rankine cycle system under various cooling conditions. Energy 2017:130. [3] Boyaghchi FA, Chavoshi M, Sabeti V. Multi-generation system incorporated with PEM electrolyzer and dual ORC based on biomass gasification waste heat recovery: exergetic, economic and environmental impact optimizations. Energy 2018;145:38–51. [4] Zhao L, Zhang Y, Deng S, et al. Solar driven ORC-based CCHP: comparative performance analysis between sequential and parallel system configurations. Appl. Therm. Eng. 2018;131:696–706. [5] Imran M, Usman M, Park BS, et al. Comparative assessment of Organic Rankine Cycle integration for low temperature geothermal heat source applications. Energy 2016;102:473–90. [6] Liu P, Shu G, Tian H, et al. Alkanes based two-stage expansion with interheating Organic Rankine cycle for multi-waste heat recovery of truck diesel engine. Energy 2018;147:337–50. [7] Wang M, Jing R, Zhang H, et al. An innovative Organic Rankine Cycle (ORC) based Ocean Thermal Energy Conversion (OTEC) system with performance simulation and multi-objective optimization. Appl. Therm. Eng. 2018;145:743–54. [8] Park BS, Usman M, Imran M, et al. Review of Organic Rankine Cycle experimental data trends. Energy Convers. Manage. 2018;173:679–91. [9] Pantano F, Capata R. Expander Selection for an on board ORC energy recovery system. Energy 2017;141:1084–96. [10] Ziviani D, Gusev S, Lecompte S, et al. Optimizing the performance of small-scale organic Rankine cycle that utilizes a single-screw expander. Appl. Energy 2017;189:416–32. [11] Hou X, Zhang H, Xu Y, et al. External load resistance effect on the free piston expander-linear generator for organic Rankine cycle waste heat recovery system. Appl. Energy 2018;212:1252–61. [12] Song P, Wei M, Zhang Y, et al. The impact of a bilateral symmetric discharge structure on the performance of a scroll expander for ORC power generation system. Energy 2018;158:458–70. [13] Ayad M, Jubori A. An innovative small-scale two-stage axial turbine for low-temperature organic Rankine cycle. Energy Convers. Manage. 2017;144:18–33. [14] Guillaume L, Legros A, Desideri A, et al. Performance of a radial-inflow turbine integrated in an ORC system and designed for a WHR on truck application: an experimental comparison between R245fa and R1233zd. Appl. Energy
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Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Design and structure optimization of small-scale radial inflow turbine for organic Rankine cycle system ⁎
T
⁎
Tan Wua,b, Long Shaoc, , Xinli Weia,b, Xinling Maa,b, , Guojie Zhanga,b a
School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou 450001, China Engineering Research Center of Energy Saving Technologies and Equipments on Thermal System, Ministry of Education (MOE), Zhengzhou 450001, China c College of Mechanical and Electrical Engineering, Henan Agricultural University, Zhengzhou 450002, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Waste heat recovery Organic Rankine cycle Radial inflow turbine Turbine design and optimization
The ORC (organic Rankine cycle) system has the advantages of simple structure, environmental friendliness, reliability and low capital cost. The expander is the key device of energy conversion in the ORC system, and its performance has a direct influence on that of the ORC. In this paper, a self-designed and manufactured radial inflow turbine is applied to low temperature waste heat power generation. The numerical model for the internal flow of the radial inflow turbine is established, and the numerical results show a better agreement with the experimental data. Firstly, the influence of blade stagger angles on nozzle performance is studied. The study finds that with the decrement of stagger angles under specific angle ranges, the velocity coefficient increases. However, the efficiency of the nozzle decreases sharply when the stagger angle exceeds 30°. Secondly, the influence of the blade profile on the efficiency of the rotor is investigated. The results indicate that with t increasing, the efficiency of the rotor firstly increases, then decreases quickly. It increases by 1% compared with that of the original rotor, when the t = 1.95. At last, the performance of the turbine is researched numerically. This paper discovers that total-to-static efficiency of the turbine increases by 1.7% compared with that of the original turbine. This research provides orientation and basis for the improvement of aerodynamic design and performance of radial inflow turbine. As for practical application, the study can provide certain reference for the structure and blade profile design of nozzles and rotors to further improve the performance, and to offer some data for the operational control and tests.
1. Introduction With the depletion of non-renewable energy and environmental deterioration, scientific energy utilization technologies are paid more and more attention all over the world. Organic Rankine cycle (ORC) is a recognized and effective method to convert low grade heat into power [1]. ORC can recover different kinds of low-grade heat, such as industrial waste heat [2], biomass sources [3], solar energy [4], geothermal sources [5], waste heat from engine exhaust [6], ocean thermal energy conversion [7]. It can increase the power supply while achieving energy and environmental sustainability at the same time. The main components of an ORC are evaporator, condenser, working fluid pump and expander [8]. The expander is an important energy conversion device in the ORC system. The organic working fluid enters the evaporator and becomes the superheated gas, and it pushes expander to realize conversion from thermal energy to mechanical energy. The isentropic efficiency of the expander directly affects the
⁎
overall performance and efficiency of the system [9]. According to different working principles, the expander is divided into two categories. One type is volumetric expander, which generally obtains enthalpy drop and pressure ratio by changing the inner volume of the working chamber, including screw expander [10], piston expander [11], scroll expander [12], and so on. The other is speed expander, which mainly includes axial flow turbine [13], radial inflow turbine [14] and centrifugal turbine [15]. The radial inflow turbine is characterized by the capacity to deal with large enthalpy drop at the low peripheral, low manufacturing cost and compact structure [16]. The radial inflow turbine is suitable for dry working fluids and isentropic working fluids. The rotational speed and expansion efficiency are relatively high [17]. Over the years, an increasing number of works have studied the optimization of radial inflow turbine design. Applying Computational Fluid Dynamics (CFD) to performance prediction, internal flow analysis and structural design of radial inflow turbine has already become a
Corresponding authors at: School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou 450001, China (X. Ma). E-mail addresses: [email protected] (L. Shao), [email protected] (X. Ma).
https://doi.org/10.1016/j.enconman.2019.111940 Received 7 March 2019; Received in revised form 16 July 2019; Accepted 13 August 2019 Available online 21 August 2019 0196-8904/ © 2019 Published by Elsevier Ltd.
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Nomenclature β c D Ḋ h Δh H L (l) ṁ N P R (r) s T u w W
absolute velocity, m/s diameter, m diameter ratio of blade, specific enthalpy, kJ/kg specific enthalpy drop, kJ/kg total enthalpy, kJ/kg length or blade height, m mass flow, kg/s rotational speed, rpm pressure, MPa radius, mm entropy, J/kg·K temperature, K rotor blade velocity, m/s relative velocity, m/s power, kW
θ v Ω η ρ ζ φ ψ
direction, degree relative flow angle with respect to the meridional direction, degree polar angle, degree velocity ratio, – degree of reaction, – efficiency, – density, kg/m3 loss coefficient, – nozzle velocity coefficient, – rotor blade velocity coefficient, –
Subscripts 1–6 u s t T
state point peripheral isentropic state total state turbine
Greek symbols α
absolute flow angle with respect to the meridional
evaluated by three-dimensional analysis using CFD. And the comparison between results of the one-dimensional design and CFD simulation was conducted. About the structure optimization of the turbine, Ssebabi et al. [24] connected the turbo expander to the generator with a magnetic coupler to achieve non-contact transmission and tested the performance of expander with air as the working fluid. The optimization of the rotor blade was carried out in consideration of parameters such as the number of rotor blades and the angle of the outlet airflow. In the study of nozzle blades, Razaaly et al. [25] adopted a two-dimensional highprecision turbulent computational fluid dynamics model and made the uncertainty measurement analysis of typical supersonic nozzle blades in ORC applications. In the analysis process, Kriging-based techniques were adopted. In the study of the loss model, Wu et al. [26] combined the preliminary design of the heat loss model with three-dimensional numerical simulation to optimize. A genetic algorithm based on turbine geometry optimization was designed, and the optimized specific speed and blade shape could increase the power output by 3.6%. The more detailed analysis and optimization of the ORC radial inflow turbine based on CFD need to be further investigated [19]. For the thermodynamic cycle in a kW-scale ORC system, this paper presents a one-dimensional design model. Design parameters and a finite element
crucial research method and an available verification for the one-dimensional model [18]. However, only a few past studies have focused on the CFD simulations of radial inflow turbine in organic Rankine cycles. According to a conclusion drawn by Xia et al. [19], the threedimension CFD results are in correspondence with the one-dimensional analysis, and the addition of splitter blade contributes to improving the performance of ORC radial inflow turbine. For the design of aerodynamic distribution, Zheng et al. [20] proposed a preliminary design and an evaluation method that combined the design of radial inflow turbine with the predicted variable operating conditions, and used the numerical simulation results and experimental data to verify it. Fiaschi et al. [21] made a three-dimensional analysis of the rotor with the geometry inputs calculated from one-dimensional design for a 5 kWORC radial-inflow turbine operating with R134a. The number and the geometry of the rotor blades were further refined by CFD approach. Li et al. [22] developed an aerodynamic and profile design system, in which a radial inflow turbine with R123 as the working fluid was designed and the numerical analysis was conducted. The simulation results indicated that the shock wave caused by the high expansion ratio in the nozzle was well controlled. With regard to identical design conditions, Kim et al. [23] proposed a novel method to design ORC radial-inflow turbine. The performance of a designed turbine was then
Fig. 1. Schematic diagram of an ORC system (left) and T-s diagram (right). 2
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analysis model are developed, so as to conduct a numerical study on aerodynamic layout design and performance of radial inflow turbine with R123 as the working fluid. Taking working fluid mass flow rate, turbine output power and isentropic efficiency as evaluation indexes, this paper compares experimental data [27] and simulated results, and it finds their change rules are basically consistent. It researches the optimization of the stagger angle, the number of nozzle blade and parabolic index, for further improving the operational efficiency of the turbine. The results provide some reference for the design of radial inflow turbine used in the ORC system. Fig. 3. Velocity triangles at rotor inlet and outlet.
2. Design and analysis of radial inflow turbine
outlet of the guider increases to c4, during which its pressure and temperature respectively decrease to P4 and T4. Then the gas enters into the rotor in the high-speed revolution at the relative speed of w4, and the peripheral velocity of blades is u4. The gas continues to expand to do work in the blades. The work done in the blades by every kilogram working fluid is marked as Δhu,4-5, named peripheral work. When the gas pressure in the outlet of blades decreases to P5, the temperature decreases to T5. The relative velocity of air flow in the outlet is named as w5, and its absolute velocity c5 is the vector sum of the velocity u5 and w5 in the point. Finally, the working fluid enters into the air or is transported to the pipeline through a diffuser or exhaust pipe. The flow condition of the gas in the inlet and outlet are expressed as velocity triangles at rotor inlet and outlet, as shown in Fig. 3. The flowchart of the in-house radial inflow turbine preliminary onedimensional aerodynamic design program is illustrated in Fig. 4. Based on it, the basic geometry of radial inflow turbine and its performance in the design are obtained. Detailed design requirements and chosen design parameters are included in the input data, for instance, the flow angles, the geometry ratios, the blade number and the nozzle design parameters by using Aungier’s method [29]. In addition, three non-dimensional parameters are considered in this method, such as the reaction Ω, the velocity ratio v, and the radius ratio r5/r4 [30]. Eqs. (1) and (2) state Ω and v, respectively.
The schematic diagram of the organic Rankine cycle system is shown in Fig. 1. The liquid working fluid in the condenser gradually enters the evaporator after it is boosted by the pump. In the process, it absorbs heat from the heat source to become the saturated or the superheated vapor. Then the vapor flows into the turbine to generate power through expansion. Finally, the turbine exhaust is condensed to liquid by the condenser. The radial inflow turbine consists of three main components, including volute, nozzle and rotor, as illustrated in the right drawing in Fig. 2. The incoming fluid is accelerated and distributed uniformly around the periphery of the turbine via volute (1–2). Further acceleration and increase in the circumferential component of velocity are attained via the nozzle (2–3) before it enters the rotor. The space between the nozzle and rotor (3–4) makes the nozzle outlet possible to wake to mix out. Then the kinetic energy of the fluid is converted into mechanical energy of shaft as it expands through the rotor (4–5). The corresponding enthalpy-entropy diagram detailing the expansion process across the stage is shown in the left drawing in Fig. 2. The onedimensional aerodynamic design method of radial inflow turbine simplifies the expansion and flow of gas working flow as a univariate steady flow characterized by being adiabatic, axisymmetric and inviscid [28]. The thermodynamic properties, geometry parameters and flow features are determined at key stations throughout the stage as illustrated in Fig. 2. As the turbine works, the working fluid flows into the intake pipeline at certain speed c0, when its total pressure is marked as Pt1, total temperature as Tt1. The gas entering into the turbine firstly expands and accelerates in the nozzle. The process makes the speed of gas in the
Ω = Δhs,4 − 5/Δh s,1 − 5
(1)
v = u4 / cs = u4 / 2Δhs,1 − 5
(2)
where Δhs,4 −5 and Δhs,1 −5 respectively represent the isentropic specific
Fig. 2. Schematic of the radial inflow turbine meridional view (right), enthalpy-entropy diagram of the turbine expansion (left). 3
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the blade outlet. The axial efficiency of the turbine ηtur and its power Wtur are gained by Eqs. (10) and (11).
ηtur = (ηu − ζ friction ) ηm ηc ηe
(10)
Wtur = ṁ Δhs,1 − 5 ηtur
(11)
where ηm is mechanical efficiency, ηc is clearance loss efficiency, ηe is partial intake loss efficiency, and full air intake is 1. In this paper, following factors are taken into consideration, such as nozzle loss Δhloss,volute, passage loss Δhpassage, clearance loss Δhclearance, friction loss Δhfriction and exit loss Δhexit, as Eq. (12) [32]. The total-tostatic efficiency [33] is expressed in the form of enthalpy drop, defined as Eq. (13).
Δhloss = Δhloss,volute + Δh passage + Δhclearance + Δh friction + Δhexit
(12)
Δ
ηts =
enthalpy drop of the rotor and the stage, and cs is the spouting velocity. In line with the inlet total temperature Tt1 and the pressure Pt1, the total enthalpy ht1 and the entropy s1 are figured out by the REFPROP database, and the ideal enthalpy at the rotor outlet h5s can also be obtained by s1 and the outlet static pressure P5. As a result, the stage isentropic enthalpy drop Δhs,1 −5 is expressed by Eq. (3).
a=
zm ·t −1 = x m tan β = const
Therefore, Δhs,4 − 5 and u4 are gained by Eqs. (1) and (2), and then h4s and r4 are calculated by using Eqs. (4) and (5), respectively. (4)
r = 60000u/2πN
(5)
(6)
Δh friction ṁ Δh s,1 − 5
(7)
ζ friction =
where f is the friction coefficient of the disk, ρ4 is the density of working fluid in the blade inlet, and ṁ is the mass flow rate of the turbine. The peripheral work of the turbine Δhu,4-5 and the peripheral efficiency ηu of the radial inflow turbine are gained by Eq. (8), Eq.(9a) and Eq.(9b) [31].
Δh u,4 − 5 = ηu =
c42 − c52 u 2 − u52 w 2 − w42 + 4 + 5 2 2 2
Δh u,4 − 5 Δh s,1 − 5
(8)
(9a)
ηu 2 = 2ν (φ cos α4 1 − Ω − D4̇ ν + D4̇ ψ cos β5 2 Ω + φ2 (1 − Ω) + D4̇ ν 2 − 2νφ cos α4 1 − Ω )
(14)
(15)
When the design sets the heat source temperature to 393.15 K, the cold source temperature of 293.15 K, the evaporator temperature difference of 5 K, the condenser temperature difference of 3 K and other parameters are constant. When the unit power generation of hot fluid is the largest, the net output power is used as the evaluation index, the optimal evaporation temperature of ORC system is 344.7 K and the optimum condensation temperature is 301.09 K. There must be a suitable degree of subcooling and superheat in the organic working fluid. It is assumed that the superheat and subcooling of the working fluid in evaporator and condenser are both 5 K. Under the saturation pressure, the condenser outlet and the evaporator outlet temperatures are 296.09 K, 349.7 K, and the saturation pressures are 0.102 MPa, 0.392 MPa. The condensing pressure of the working fluid in the condenser is 0.102 MPa, the outlet temperature is 296.09 K, the working fluid evaporation pressure in the evaporator is 0.392 MPa, and the outlet temperature is 349.7 K. According to the optimized working condition parameters of the ORC system, the preliminary design of the radial inflow turbine is carried out with R123 as the working fluid. The design parameters for the turbine is shown in Table 1. A radial inflow turbine consists of a volute, a nozzle, an impeller and a diffuser. The main role of a volute is distributing flow evenly to the nozzle inlet, and it has an axisymmetric structure. Therefore, the volute is a spiral tube whose section evenly decreases along the flow direction. The cross section of the volute flow passage is a circle. The designed volute is shown in Fig. 5(a). The role of the nozzle is to convert heat into kinetic energy and to obtain the flow rate and flow direction required for the rotor inlet. A Nozzle is composed of a set number of equant-shaped blades which are equally spaced on a ring. In this radial inflow turbine, TC-4P blade profile [34] by Moscow Institute of Dynamics is adopted, as shown in Fig. 5(b). The organic vapor continues doing work by expansion in the impeller, and converts kinetic energy into mechanical energy for transmission to the generator. The impeller is also a certain set of equant-shaped blades which are uniformly distributed on a disk. According to the principle of one-dimensional flow,
where u is the peripheral velocity, r is the radius of rotor, and N is the rotational speed. Friction loss power of disk Δhfriction and its friction loss coefficient ζfriction are gained by Eqs. (6) and (7).
u 3 1 Δh friction = fρ4 r42 ⎛ 4 ⎞ 100 ⎝ ⎠ 1.36
1 (tgβh)−1 2
The blade outlet angle β and the parabolic index t will affect the rotor performance. In the case where h and β are known, the relationship between t and zm is calculated by Eq. (15).
(3)
h4s = h t1 − (1 − Ω)Δhs,1 − 5
(13)
where ηts denotes the total-to-static efficiency, Hs is the total enthalpy, and Δhloss is the loss enthalpy. According to the blade profile, the parabolic equation x=azt directly affects the blade structure and molding, including non-developable ruled parabolic surface. In the parabolic equation is given by Eq. (14).
Fig. 4. The flowchart of radial inflow turbine preliminary aerodynamic design.
Δhs,1 −5 = ht1 − h5s
Hs − ∑ hloss Hs
(9b)
where Ω is the degree of reaction, φ is nozzle velocity coefficient, ψ is rotor blade velocity coefficient, D4̇ is diameter ratio of the blade, α4 is absolute flow angle of the blade inlet, and β5 is relative flow angle of 4
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2.13 × 10−3 m3, and the corresponding value of in the condenser is 3.25 × 10−3 m3, as is shown in Fig. 8(a). The experimental system adopts the GC-DRY-60 electric heating and heat transfer oil furnace produced by Yancheng Gongchuang Electric Heating Equipment Co., Ltd. Following components are included in the facility, such as an electric heater, a high tank, an oil temperature control system, a hot oil pump, a liquid level meter and other auxiliary fittings, as is shown in Fig. 8(b). Its maximum heating power is 60 kW, and the actually-required heating can be adjusted by the temperature control system. The working fluid pump used in the experiment is hydraulic diaphragm type pump, JYMD-1000/2.5. Its major performance parameters are maximum flow 1000 L/h, maximum pressure 2.5 MPa, intake stroke 50 mm, and motor power 2.2 kW, as is shown in Fig. 8(c). The generator, the main facility for the electrical output of ORC system, is a three-phase AC permanent magnet synchronous generator at high speed (with rated power being 5 kW, rated speed being 12000 rpm). When operated under rated conditions, the generator is with efficiency of 90%, and its output voltage is proportional to the speed. The specially-developed reducer is used to adapt to the turbine and the generator. First-class gear transmission is adopted in the experiment, with a ratio of 5.304 and an external dimension of 200 mm × 131 mm × 220 mm. The reducer is connected to the turbine through a coupling. Experimental equipment consisting of a turbine, a reducer and a generator is shown in Fig. 8(d). The radial turbine used in the experiment is shown in Fig. 8(e). The power of resistance wires is used as the load to consume electrical energy from the generator. The load can be adjustable, as is shown in Fig. 8(f). In the data acquisition systems, following facilities are included, such as a Coriolis mass flow meter, an intelligent liquid turbine flow meter, an elliptical gear flow meter, a temperature sensor, a pressure sensor, an Agilent data acquisition instrument, an electrical parameter meter, and a computer. The Coriolis mass flow meter is installed at the outlet of the pump to measure the mass flow rate of the R123. The elliptical flow meter is installed in the heat source cycle to measure the volume flow of the heat transfer oil. An intelligent liquid turbine flow meter is installed in the condensing cycle to measure the flow of cooling water. A temperature sensor and a pressure sensor are separately installed at the inlet and outlet of the main equipment. The Agilent data acquisition device mainly keeps track on the temperature, pressure and working fluid flow in the thermal system. The electric parameter measuring instrument with a 10-second interrecord gap mainly records the frequency, the output voltage, the current and the electric power of the generator. The recorded data are summarized on the computer by software to check the performance of the generator. According to the temperature and pressure collected by the computer, the parameters including enthalpy and entropy of the R123 are obtained through the REFPROP 9.0 issued by NIST. The main experimental testing instruments are listed in Table 2.
Table 1 Main design parameters for the radial inflow turbine. Design parameter
Value
Turbine inlet temperature/K Turbine inlet pressure/MPa Turbine outlet pressure/MPa Mass flow rate/kg·s−1 Rotational speed/r·min−1 Degree of reaction Velocity ratio Rotor inlet diameter/mm Shroud diameter rotor outlet/mm Hub diameter at rotor outlet/mm Number of rotor blade Rotor blade height at the inlet/mm Nozzle inlet diameter/mm Nozzle outlet diameter/mm Number of nozzle blade Nozzle blade height/mm Turbine axial height/mm Turbine output/kW Turbine efficiency/%
345.15 0.393 0.102 0.111 54,950 0.45 0.69 50 34 19 12 1.8 70 56 17 1.6 15 1.68 68
(a) Volute
(b) Nozzle
(c) Impeller
(d) Radial inflow turbine
Fig. 5. Photograph of the radial inflow turbine.
based on the reverse design, the isosceles trapezoidal design method is proposed to get 3D meridional flow channel of the impeller. The blade shape of the impeller adopts non-developable parabolic surface profile. The developed impeller is shown in Fig. 5(c). Fig. 5(d) is the photograph of developed radial inflow turbine.
4. Numerical analysis of the flow in the radial inflow turbine For the geometry of the nozzle blade and the rotor blade of the radial inflow turbine, the single passage model is established by CFD, and the numerical simulation of the flow field in the turbine is carried out. The structure of the nozzle and rotor is optimized by studying the flow characteristics and aerodynamic properties of the turbine.
3. Experimental facility of the ORC system The schematic diagram of the ORC test rig is as shown in Fig. 6. The testing rig is presented in Fig. 7. The evaporator transfers heat energy of waste heat source to the organic working fluid and heats its liquid form into saturated gas or slightly superheated gas. The condenser transfers the heat of completed organic working fluid from the turbine to the cooling water. This process condenses the superheated organic vapor into saturated liquid or slightly subcooled liquid. In this platform, plate heat exchangers produced by SWEP (a company which professionally produces heat exchangers in Sweden) are used as the evaporator and the condenser. The volume of organic working fluid channel in the evaporator is
4.1. Single passage model of the turbine In consideration of the symmetry of the position between the nozzle blades, the flow conditions of the working fluid in the nozzle passage are basically the same. In order to obtain the calculation results, the single passage model of the nozzle is used for numerical calculation and research. The geometric model and structured grid of the blade are shown in Fig. 9. The geometrical structure, physical parameters and flow 5
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P
T
F
P
T
Speed
Generator Load M P
P
Turbine
T P
T
T Cooling Water
Heat Source Evaporator
P T
Condenser P
P T
T
F
T
P
Working fluid pump T
P
Fluid L reservoir
P
T
F
Fig. 6. Schematic diagram of ORC system.
model and experimental works in the published literature to evaluate the availability of the proposed off-design performance estimation methodology. These cases were chosen to offer reference for the proposed model via ample geometric data. The dependable and good quality of the presented thermodynamic data is another reason. The experimental data was obtained by Shao et al. [27] who used R123, a high dense organic fluid, as the working fluid. The boundary parameter of the single passage model was the experimental data of the turbine inlet and outlet, respectively. The corresponding calculated values are shown in Table 3. According to different working conditions, the calculation is conducted to obtain a group of results, and compared them with those results calculated in the experiment under same conditions, so as to verify the veracity under variable working conditions, as shown in Fig. 12. Based on the actual sequence of experiments, a number of observed values in every steady working condition is used for boundary conditions, and then calculations results are obtained. It could be observed that the results of simulation in the present
characteristics of the rotor are characterized by distinct periodicity. The Boolean operation is used to obtain the fluid region in the rotor. The rotor structural body and the fluid domain are shown in Fig. 10(a) and (b), respectively. In the meshing process, following components are divided more densely by the O-grid method, such as the rotor blade near wall surface, the blade leading edge boundary and the blade trailing edge boundary, so that y+ is about 3. According to the design parameters, mesh segmentation and mesh generation are performed on the flow passage. The structured grid of the rotor is shown in Fig. 11(a). Fig. 11(b) is a partially enlarged view of the leading edge of the rotor passage. Additional grid treatment is implemented and a detailed simulation is conducted for its flow field, so that the calculation accuracy can be effectively improved.
4.2. Validation The experiment compares the results of the proposed expander
Fig. 7. The testing rig based on the radial inflow turbine. 6
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(a) Evaporator and condenser
(b) Electric heating furnace Fig. 9. Nozzle model and grid.
rotating coordinate system is set to rotate about the Z-axis, and the rotating coordinate system is set to a stationary reference coordinate system with a turbine rotational speed of 54,950 r/min. The inlet and outlet boundary parameters are given according to designed conditions, as shown in Table 4. (d) Turbine with reducer and generator
(c) Pump
(e) Radial inflow turbine
4.4. Structural optimization of the nozzle blade The effects of the nozzle blade stagger angle on the peripheral velocity of the outlet are shown in Fig. 13. In general, as the peripheral velocity of the outlet increases, the turbine output increases accordingly. It can be seen that when the number of nozzle blade is constant, the peripheral velocity of the outlet gradually decreases as the stagger angle increases. When the stagger angle is constant, the peripheral velocity increases as the number of the nozzle blade increases. The effects of the nozzle blade stagger angle on the flow angle of the outlet are shown in Fig. 14. Within a reasonable range, reducing the flow angle of the blade can increase the turbine output. When the stagger angle is constant, as the number of blades increases, the outlet flow angle decreases, and the trend gradually becomes slow. It shows that the increasing quantity of blades leads to their growing guiding effect on the working fluid, but the effect of the nozzle blade on the latter is limited. When the number of blades is constant, the flow angle of the outlet increases as the stagger angle increases. The range of the flow angle is generally between 14° and 20°, which ensures the efficiency of the nozzle blade. Therefore, for a certain stagger angle, there is always a corresponding number of nozzle blade, so that the nozzle has higher efficiency. According to the analysis, when the stagger angle is 28° and the number of the nozzle blade is 17 or 19, the comprehensive performance is good. In order to avoid the resonance of the nozzle and the rotor, the number of the nozzle blade and the rotor blade are designed without common divisor. Therefore, a scheme with a stagger angle of 28° and a number of the nozzle blade of 19 is selected. The numerical calculation is shown in Table 5. Compared with the original nozzle blade, the optimized facility is featured with more excellent performance. Its peripheral velocity increased by 7.4% and the velocity coefficient
(f) Loads
Fig. 8. Major equipment and apparatus of the ORC system.
study are in good agreement with the experimental values. Following factors are selected as the evaluation indicators, such as the turbine output, isentropic efficiency and working fluid mass flow rate of the turbine, and the numerical results are slightly larger than the experimental measurement results. 4.3. Calculation method and boundary conditions In this paper, the Spalart-Allmaras model is taken for numerical calculation of the flow field of the nozzle blade and the rotor blade. The organic working fluid is kept in a gaseous state in the passage, and the calculation parameters are obtained by a physical database. The calculated organic working fluid is R123, and the turbine inlet and outlet surfaces are respectively set to pressure inlet and outlet. The surface generated by dividing passage is set to a periodic boundary condition, and the other surfaces are set to adiabatic solid wall conditions. The Table 2 Names and models of testing instrument. Measuring object
Instrument
Type
Range
Accuracy
Temperature Pressure
Thermal resistance Diffused silicon pressure transmitter
WZP Pt100 HX-L61
± (0.15 + 0.002 t)K ± 0.2%
Data collection Working fluid flow
Agilent data collector Coriolis flow meter Intelligent liquid turbine flow meter Oval gear flow meter Laser tachometer Electric parameter measuring instrument
34980A RHM04 RHE 14 YK-LWGY-25 YK-LC-20 DT-2857 8903D
73.15–773.15 K 0–1.6 MPa −0.1–0.4 MPa – 0–24 kg/min
Glass
HMI-1TT
0–10 m3/h 0.4–4 m3/h 2.5–99999 rpm 45–1000 Hz 0.1–60 A 5–500 V 0.5 W–30 kW —
± 0.5% ± 0.5% ± 0.05% ± 1.5 ± 1% ± 1% ± 1% —
Rotating speed Electric frequency Current Voltage Electric power Working condition
7
± 0.1%
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seen from Fig. 16(b) that the static pressure in the suction surface gradually decreases along the streamwise. At 80% of the blade height of the blade trailing edge, there is a local low pressure region and the distribution of isobars is complicated. In view of the pressure surface and suction surface of the blade, the effect of the wall surface on the flow characteristics is greater, and the overall static pressure decreases with the decrease of the blade height. The velocity distribution in the pressure surface, and the flow velocity gradually decreases from the leading edge to the trailing edge of the blade, as shown in Fig. 16(c). At the blade inlet, the isovelocity line is distributed more evenly, while at the 20% of blade height of the trailing edge, there is a local low-speed zone. The velocity gradually decreases along the streamwise, as shown in Fig. 16(d). The isovelocity line is curved to form a small low velocity region at the trailing edge of the blade. At the same time, the velocity near the hub is obviously lower than the number near the shroud. The velocity distribution on the blade is relatively uniform, and the working fluid flow state is better. It can be seen from Fig. 16(e) that the temperature in the blade pressure surface gradually decreases from the leading edge to the trailing edge of the blade. The temperature drop of the former changes markedly, while the temperature gradient of the latter is smaller, and the isotherm distribution of the blade inlet is more uniform. Overall, the blade is featured with excellent flow properties, but there is a certain flow loss at the trailing edge. In the future design of the rotor, some attention should be paid to the improvement of the trailing edge shape of the blade.
Fig. 10. Rotor geometry model.
Fig. 11. Rotor grid.
4.6. Profile optimization of the rotor blade Table 3 Results comparison between the experimental values and calculated values [27]. Parameter
Turbine inlet temperature Turbine inlet pressure Turbine outlet temperature Turbine outlet pressure Mass flow rate Turbine output Isentropic efficiency
Unit
Experimental value
Calculated value
Case1
Case2
Case3
Case1
Case2
Case3
K
393.7
391.3
393.8
393.3
390.6
393.4
MPa K
0.258 377.6
0.366 371.2
0.344 374.1
0.253 377.1
0.360 368.1
0.337 371.8
MPa kg/s kW %
0.115 0.201 2.278 80.6
0.165 0.273 2.914 76.4
0.085 0.248 2.746 78.2
0.115 0.213 2.512 86.2
0.167 0.289 3.013 85.3
0.087 0.262 2.988 85.9
In the design of the rotor, the value of t is given empirically in general, so there is some uncertainty. Therefore, it is necessary to find the optimal parabolic index t to make the flow state inside the rotor is optimal. By adjusting the value of the parabolic index t, different values of zm are obtained, and the numerical calculation of the flow field in the rotor is performed. The results are shown in Table 6. As can be seen from Table 5, the axial length of the rotor increases as the parabolic index t becomes larger. The rotor efficiency increases with the parabolic index t, and the impeller efficiency reaches the maximum when the optimal value is t = 1.95. The efficiency of the rotor increases firstly and then decreases with the increase of the parabolic index t. When the optimal value is 1.95, the rotor efficiency reaches the maximum. The velocity vector of 50% of the blade height flow surface is shown in Fig. 17. The comparison shows that there is an enormous difference between the flows of working fluid before and after optimization. In the flow passage before optimization, the working fluid moves substantially along the flow guiding direction after passing through 50% of the flow passage. The range of vortex near the optimized rotor inlet is significantly smaller than that of the original rotor, and the working fluid flows along the guiding direction at 35% of the flow passage. At 70% of the flow passage, the optimized velocity vector distribution is more uniform, indicating that the flow state of the main flow in the flow passage is good, and the expansion process can be successfully realized for most of the working fluid. The velocity vector of 50% of the blade height rotor inlet is shown in Fig. 18. There is a distinct bending phenomenon in the inlet velocity vector before optimization, but the optimized inlet velocity vector distribution is more uniform. It is concluded that the optimized rotor inlet flow performance is improved and the working fluid is substantially unaffected by the rotor inlet vortex.
increased by 1.12%. The total pressure distribution in the meridional plane of the nozzle blade is shown in Fig. 15. After the comparison of the pressure distribution before and after the optimization, the optimized pressure distribution is more reasonable. After optimization, the pressure drop gradients of static pressure and total pressure are closer to the throat area. The trend of the total pressure is basically consistent with the expansion process of the organic working fluid. Moreover, the optimized total outlet pressure distribution is relatively uniform, indicating that the optimization results are more reasonable.
4.5. Structural optimization of the rotor blade The pressure, velocity and temperature distribution in the rotor blade surface are illustrated in Fig. 16. It can be seen from Fig. 16(a) that the static pressure in the blade pressure surface gradually decreases from the leading edge to the trailing edge of the blade. At the 90% of blade height of the leading edge, part of the isobar is bent to form a small recirculation zone. With the streamwise being about 30% to 45% and the blade height being 70%, there is a range of low pressure regions. The isobars are generally evenly distributed, but they are strongly bent near the tip of the blade, causing flow losses. It can be
4.7. Optimization design of radial inflow turbine The numerical calculation of the turbine is carried out using the optimized nozzle and rotor models. The total-to-static efficiency is used as an indicator to analyze the original design and the optimized model of the turbine. In the turbine model, there are 12 rotor blades, 17 nozzle 8
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Fig. 12. Validation of the turbine model at diffident experimental conditions.
30
Parameter
Unit
Nozzle
Rotor
The The The The
K MPa K MPa
345.15 0.393 321.5 0.192
320.5 0.192 303.5 0.102
inlet temperature inlet pressure outlet temperature outlet pressure
Outlet flow angle (°)
Table 4 Boundary parameters setting.
Stagger angle (28°) Stagger angle (32°) Stagger angle (36°)
25
20
15
10 14
16
18
20
22
24
The nozzle blade number Fig. 14. Variations of the flow angle of the outlet versus the number of blades at different stagger angles. Table 5 Outlet parameters before and after the optimization.
Fig. 13. Variations of the peripheral velocity of the outlet versus the number of blades at different stagger angles.
9
Parameter
Unit
Before the optimization
After the optimization
Outlet velocity Outlet temperature Peripheral velocity of the outlet Outlet flow angle Velocity coefficient
m/s K m/s
152.683 320.62 137.504
158.473 320.12 147.679
° –
23.7 0.935
15.8 0.9455
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Table 6 Calculation results of different blade profiles.
a
Before the optimization
b
Parabolic index t
Axial length of rotor
Rotor efficiency
1.85 1.90 1.95 2.00 2.05 2.10
4.45 4.5 4.55 4.60 4.65 4.70
0.885 0.892 0.903 0.894 0.889 0.881
After the optimization
Fig. 15. The total pressure distribution in the meridional plane of the nozzle blade.
rotational speed of the rotor is set to 54,950 r/min, the nozzle flow passage is a stationary coordinate system. The interface boundary is used to connect the moving area to the static area, and the wall condition is set to the adiabatic wall condition. The static pressure distribution of the turbine before and after the optimization is shown in Fig. 19. The cross section at 50% of the blade height is selected for observation. The trends of corresponding working fluid flow before and after optimization are basically the same. After the working fluid passes through the throat of the nozzle blade, the pressure begins to decrease, as shown in Fig. 19(a). There is a high
blades and 19 optimized nozzle blades. The number of rotor single passage grids is 460,000, that of nozzle single passage grids is 200,000, and that of whole flow passage grids is about 8.3 million. The nozzle inlet takes the pressure boundary, the total pressure is 0.393 MPa, and the total temperature is 345.15 K. The rotor outlet takes the pressure boundary, the pressure is 0.102 MPa, and the working fluid is R123. The rotor flow passage adopts a rotating coordinate system, and the
Fig. 16. The distribution of pressure, velocity and temperature in the rotor blade surface. 10
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before and after optimization under the designed conditions are shown in Table 7. Although the expansion ratio is reduced, the total-to-static efficiency of the optimized turbine is increased by 1.7%. The optimized radial inflow turbine performance has been improved under designed conditions.
5. Conclusions In this paper, the flow field characteristics of the nozzle and the rotor of the radial inflow turbine are studied. The turbine is optimized by adjusting the stagger angle, the number of the nozzle blade and the parabolic index. This research provides orientation and basis for the improvement of aerodynamic design and performance of radial inflow turbine. As for practical application, the study can provide certain reference for the structure and blade profile design of nozzles and rotors to further improve the performance, and to offer some data for the operational control and tests. The results are shown as follows:
Fig. 17. The velocity vector of 50% of the blade height flow surface.
(1) Taking working fluid mass flow rate, turbine output power and isentropic efficiency as evaluation indexes, this paper compares experimental data and simulated results, and it finds their change rules are basically consistent. Difference between the calculated value of working flow and measured one is nearly 5.7%. Difference between these two values of output power and isentropic efficiency is no more than 10%. It indicates the reasonability of numerical calculation model and the reliability of the results. (2) Within a reasonable range, as the stagger angle of the nozzle blade decreases, the velocity coefficient continuously increases. Appropriately increasing the number of the nozzle blade can increase the peripheral velocity of the nozzle outlet and enhance the guiding effect of the nozzle. After the nozzle blade is optimized, the peripheral velocity increases by 7.4%, and the velocity coefficient increases by 1.12%. (3) The local high pressure zone is prone to occur near the leading edge of the rotor inlet, while there is a distinct flow vortex at the rotor outlet near the suction surface. Due to the action of the leading edge, trailing edge and wall of the blade, the local high pressure zone and vortex will cause a certain flow loss. When the optimal parabolic index is 1.95, the rotor efficiency increases by about 1%, and the maximum rotor efficiency is 90.3%. (4) After optimization of the turbine, the total-to-static efficiency increases by 1.7%, which indicates that the performance of the optimized radial inflow turbine is improved.
Fig. 18. The velocity vector of 50% of the blade height rotor inlet.
Fig. 19. The static pressure distribution of 50% of the blade height of turbine.
pressure region near the suction surface at the outlet of the nozzle blade, and a small amount of low pressure region is located near the pressure surface, which is consistent with the analysis result of the single passage. In the nozzle inlet region, the pressure of the working fluid is considerably lower than that in the blade. There is a localized high pressure region near the suction surface of the rotor inlet, which is related to the shape of the rotor inlet. The optimized turbine flow characteristics are superior in Fig. 19(b). The pressure drop gradient of the working fluid in the nozzle flow passage is obvious, and the high pressure region of the rotor inlet substantially disappears. The flow characteristics of the working fluid have been redistributed, which improved the performance of the turbine. The streamline distribution of 50% of the blade height of turbine before and after the optimization is shown in Fig. 20. The velocity streamline of the flow passage in the nozzle is the same, and it is smoother in the flow passage without obvious vortex. At the rotor inlet, there is a small amount of high velocity area, in the velocity streamline of the working fluid, and the velocity at the pressure surface is relatively higher. The velocity of the gas at the rotor outlet is significantly higher and there is no remarkable separation. Overall, there is a dramatical increase in the velocity of the airflow in the nozzle and rotor flow passage. The nozzle plays a major role in accelerating the working fluid, and the rotor plays a good guiding role. The calculation results of the performance parameters of the turbine
Declaration of Competing Interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
a
Before the optimization
b
After the optimization
Fig. 20. The streamline distribution of 50% of the blade height of turbine. 11
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Table 7 Comparison of performance parameters of turbine before and after optimization.
Before the optimization After the optimization
Expansion ratio
Outlet temperature
Total-to-static efficiency
3.85 3.81
303.52 305.47
0.863 0.880
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