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Research Paper
Aerodynamic design and numerical study for centrifugal turbine withdifferent shapes of volutes
Ying Wang, Xin Tan, Naian Wang, Diangui Huang
⇑
School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, ChinaShanghai Key Laboratory of Multiphase Flow and Heat Transfer of Power Engineering, Shanghai 200093, China
h i g h l i g h t s
Three-dimensional steady ﬂow for the designed centrifugal turbine was studied.
CFD simulation was conducted both in design and off-design conditions.
Volutes with three types of cross section shapes were designed and applied.
Aerodynamic performances are almost the same with three types of volutes.
The pear shaped volute shows slightly higher total efﬁciency than other types.
a r t i c l e i n f o
Article history:
Received 19 June 2017Revised 29 October 2017Accepted 20 November 2017Available online 21 November 2017
Keywords:
Centrifugal turbineNumerical simulationAerodynamic designVolute
a b s t r a c t
Centrifugal turbine presents good aerodynamic and geometric compatibility. The straight blade can bedirectly used without signiﬁcant effect on three dimensional ﬂow ﬁeld, and therefore the optimum valuesof the speed ratio and reaction degree can keep constant along the spanwise direction with higher turbineefﬁciency and simpler manufacturing. Furthermore, the closed impeller which is made by ﬁxing the bladetip using cover band shows larger impeller strength and is suitable for high-speed rotation. In recentyears, the centrifugal turbine with many potential advantages is gradually becoming a research hotspotin the ﬁeld of turbine. In this paper, three kinds of volutes with different cross section shapes weredesigned for a single-stage centrifugal turbine unit. Based on the CFD simulation in the whole ﬂowpassage, the analysis of three-dimensional steady ﬂow for the designed centrifugal turbine was carriedout under both of design and off-design conditions, and the following results were obtained: the aerody-namic performance of centrifugal turbines with three kinds of volutes are almost the same under both of design and off-design conditions. Besides, the pear shaped volute shows slightly higher total efﬁciency,and its overall efﬁciency, stage internal efﬁciency and power are 87.36%, 85.79% and 484.88 kW,respectively.
2017 Elsevier Ltd. All rights reserved.
1. Introduction
Turbine is a type of power machine to convert heat of workingmedium into mechanical energy and has been widely used in elec-tric power, petrochemical, aerospace, ships, locomotives and otherﬁelds. Normally, turbines can be divided into two types includingaxial ﬂow turbine and radial ﬂow turbine. Axial ﬂow turbine whichallows greater ﬂow rate and higher energy efﬁciency is normallydesigned into multistage type. In this way, the requirement of highexpansion ratio and power can be achieved. However, since therotational speeds at different radii show various values for axialﬂow turbine blade, the twisted blade has to be adopted. For thelong blade, the reaction ratios and speed ratios show large varia-tion from the blade root to blade tip. Thus, the long blade cannotbe designed or operated near the optimum reaction ratio andspeed ratio. Radial ﬂow turbines can be divided into two types:radial turbine and centrifugal turbine. The radial turbine is usuallyused in automobile turbocharging, low temperature powergeneration and micro gas turbine, etc. [1–4]. However, the existingcentrifugal turbine shows poor aerodynamic and geometric com-patibility. That is, along the ﬂow direction, the working substanceexpands constantly and the speciﬁc volume increases, while theperimeter of rotating surface in the runner decreases. Thus,the height of the blade along the radial direction increases rapidly.
https://doi.org/10.1016/j.applthermaleng.2017.11.0971359-4311/
2017 Elsevier Ltd. All rights reserved.
⇑
Corresponding author at: School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China.
E-mail address:
dghuang@usst.edu.cn (D. Huang).Applied Thermal Engineering 131 (2018) 472–485
Contents lists available at ScienceDirect
Applied Thermal Engineering
journal homepage: www.elsevier.com/locate/apthermeng
The corresponding impeller shows complex structure and ﬂowﬁeld, high manufacturing cost, small ﬂow rate and low efﬁciency.In 1949, centrifugal steam turbine was ﬁrst invented byLjungström [5], and had not been applied and studied for a longtime. Recently, with the development of organic Rankine cycle(ORC) system based on waste heat utilization technology [6], cen-trifugal turbine has been used again and gains good commercialpromotion [7–9]. Organic ﬂuid shows large molecular weights,low sound speed and low enthalpy drop. In the design of centrifu-gal turbine, by properly allocating parameters such as enthalpydrop in each stage, the centrifugal turbine can achieve stage efﬁ-ciency equivalent to an axial ﬂow turbine.Fig. 1 shows the structure schematic diagram of centrifugal tur-bine. The main components of a centrifugal turbine include inlet,stator cascade, rotor cascade, diffuser, volute and simple annularoutlet. The centrifugal turbine shows the following advantages:(1) In the expansion process, the working substance shows goodaerodynamic and geometric compatibility. That is, along the ﬂowdirection, the working substance expands constantly, the speciﬁcvolume increases, and the ﬂow passage area also increases syn-chronouslywith the increaseof radius. Thenthe heightof the bladealong the radial direction shows slow variation or even maintainsthe same. (2) Straight blades are adopted in the centrifugal turbine.The corresponding turbine can both design and operate at the opti-mum reaction degree and velocity ratio. There shows higher tur-bine efﬁciency and simpler blade manufacturing. Besides, byusing shroud, a closed impeller can be manufactured by ﬁxingthe topof the straightblade. This impelleris suitable for highspeedrotation, as the strength of the impeller is increased. Meanwhile,the ﬂow ﬁeld in cascade with straight blade shows relativelystrong two-dimensional (2D) characteristics, and lower three-dimensional (3D) effect. (3) Compared with radial turbine, the cen-trifugal turbine is easier to be designed into multi-stage typewhich can achieve higher efﬁciency by utilizing reheating andshows larger ﬂow rate compared with radial turbine. Because of the remarkable advantages of centrifugal turbine, it is necessaryto conduct a thorough and systematic study on its ﬂow mechanismand design method.Due to the world energy crisis and the urgent demand of energysaving and emission reduction, ORC low temperature waste heatutilization system has gained more attention. As the expander of ORC, the centrifugal turbine has attracted much attention in recentyears. Currently, the research of turbine mainly depends on theo-retical model, engineering test and numerical simulation. In1949, Ljungström [5] designed a twin inlet opposed centrifugalsteam turbine with power performed from hundreds of kilowattsto tens of megawatts. Owing to the cantilevered disk structure,the development of high power unit was limited due to the pro-cesses and materials in the circumstances. In 1998, Sekavcˇ nik[10] designed a single stage centrifugal turbine with ideal gas asworking substance, where one dimensional (1D) analysis and 3Dnumerical analysis of the aerodynamic characteristic for this tur-bine were carried out by using software of ASCﬂow. In 2004, Brun[11–13] from Southwestern Research Institute designed a newtype of centrifugal gas turbine by perfectly integrating centrifugalcompressor and centrifugal turbine on a turntable. In recent years,an Italy energy company named Exergy [7–9] designed an ORCcentrifugal turbine which has been widely and commercially
Nomenclature
a
1
half of horizontal axis of shroud elliptical arcs [mm]
a
2
half of horizontal axis of hub elliptical arcs [mm]
b
1
half of vertical axis of shroud elliptical arcs [mm]
b
2
half of vertical axis of hub elliptical arcs [mm]
c
0
ﬂow speed when entering the stator blade
c
1
ﬂow speed in stator [m/s]
c
2
outlet absolute velocity of rotor blade [m/s]
D
0
outlet diameter of inlet, is also the inlet diameter of theﬁrst stage stator blade [mm]
D
3
outlet diameter of vaneless diffuser [mm]
D
in
inlet diameter of inlet [mm]
D
out
outlet diameter of volute [mm]
D
2
/D
1
diameter ratio [mm]
G
mass ﬂow rate [kg s
1
]
G
u
airﬂow at the outlet of front guide vane
H
0
outlet width of inlet, is also the inlet blade height of theﬁrst stage stator blade [mm]
H
2
blade height at outlet for the last stage rotor blade [mm]
n
design speed [r/min]
O
center of the central streamline arc [–]
P
0
pressure when entering the stator blade
g
u
rotor efﬁciency [%]
q
2
outlet density of rotor blade [kg/m
3
]
q
3
density at the outlet of front guide vane [kg/m
3
]
s
restitution coefﬁcient of residual velocity
P
0
⁄
total inlet pressure [kPa]
P
1
temperature in stator
P
2
outlet backpressure [kPa]
r
radius of guiding cone at inlet [mm]
r
3
inlet diameter of volute [mm]
R
radius of the central streamline arc [mm]
R
1
arc radius of central streamline at outlet [mm]
R
2
shroud arc radius of simple annular outlet [mm]
R
3
hub arc radius of simple annular outlet [mm]
T
0
temperature when entering the stator blade
T
0
⁄
total inlet temperature [K]
T
1
pressure in stator [K]
T
2
temperature of moving impeller [K]
u
1
inlet rotor speed [m/s]
u
2
outlet rotor speed of moving impeller [m/s]
W
turbine power [kW]
w
1
relative speed [m/s]
w
2
relative velocity of moving impeller [m/s]
X
a
speed ratio [–]
Greek symbols
u
velocity coefﬁcient of stator blade [mm]
w
velocity coefﬁcient of rotor blade [mm]
X
reaction degree [mm]
Fig. 1.
Schematic diagrams of structure for centrifugal turbine [9].
Y. Wang et al./Applied Thermal Engineering 131 (2018) 472–485
473
applied on geothermal energy, biomass energy and industrialwaste heat. Pini, Persico and Casati [14–26] who cooperated withExergy investigated the ﬂow principle and ﬁeld of application fororganic Rankine centrifugal turbine. A set of aerodynamic designand optimization method of centrifugal turbine was developedand a series of studies on the aerodynamic performance of the cen-trifugal turbine were carried out. Welch [27–29] from an Americancompany named Energent designed a type of ORC centrifugal tur-bine by adopting straight blade with a mixture of ammonia andwater as working substance. The isentropic efﬁciency of commer-cial operation was close to 80%. A prototype of 50 kW was exhib-ited in Shanghai Industry Fair in 2010. Liu [30] conductedaerodynamic analysis for prototype and aerodynamic design for amodiﬁed single stage centrifugal turbine with low speed, high loadand large torque. Generally, although there were some foundationsfor the study of centrifugal turbine characteristics, the researchwas unclear, and the aerodynamic and geometric design of themain ﬂow passage components and the optimization of the ﬂowpath need further to be studied.In recent years, due to the rapid development of high-performance computer technology, computational ﬂuid dynamics(CFD) technology has been widely applied [31] and has becomeone of the main research methods in the ﬁeld of aerodynamics,ﬂuid mechanics, heat transfer, combustion, etc. In industry, CFDtechnology [32] with 3D and unsteady ﬂow numerical simulationcapability has become an important analysis tool for industrialdesign. There are speciﬁc problems that need to be addressed, suchas turbulence models and transition models [33]. However, thiswill not completely prevent us from using CFD tools to understandthe ﬂow mechanism of ﬂuids. CFD helps to provide information fordesigning ﬂuid models with higher performance. Through numer-ical optimization method, the information obtained from CFD sim-ulation helps to conduct optimal design for ﬂuid model.The main focus of optimal design for turbomachinery bladetype is to seek for the proﬁle parameters with best aerodynamicperformance, along with minimum ﬂow loss and maximum workcapacity as design goals under certain constraint conditions. Theaerodynamic optimization design method of turbomachinery isgenerally divided into direct and inverse ones. Although theinverse method requires relatively small amount of calculation,the ﬂow ﬁeld of design object as well as proper blade surfacepressure or velocity distribution should be provided by designers.In order to obtain turbomachinery with higher aerodynamicperformance, the direct optimization method is usually adoptedby researchers. Through using proper optimization algorithm andcontrol strategy, the iteration of geometric variables of turboma-chinery is conducted to optimize the aerodynamic shape of bladeproﬁle. The direct method reduces the reliance on experienceand shortens the design periods. Combined with CFD analysismethod, the optimal design of direct problem can achieve the bestobject function by constantly modifying the geometric proﬁleshape. Although this calculation method causes high computingcost, with the rapid development of computer technology in recentyears, great development has been achieved in the ﬁeld of turbo-machinery aerodynamic optimization design, especially on theaspect of multi-objective design and multiple work conditiondesign [33–35]. Currently, the optimization design of turboma-chinery has been developed to the stage of automatic optimizationdesign using large-scale optimization platform, such as IsightandWorkbench which are multidisciplinary optimization softwareplatform. The software which shows good integration andcomplete algorithm can link up with CAD/CAE/CFD and integrateexperimental design, approximate modeling and optimizationalgorithm as a whole [36–38].The study of turbulence is one of the most difﬁcult problems incomputational ﬂuid dynamics. There are three main methods toconduct numerical study of turbulence: Reynolds Time-AverageParameter Method (RANS), Large eddy simulation (LES) and Directnumerical simulation (DNS) method. Among these, the DNSmethod is limited to theoretical research due to the need of hugecomputing resources; the LES method has a certain prospect of engineering application, and it is still difﬁcult to popularize; theRANS method is widely used in Engineering due to less computa-tional resources and certain reliability. The software of CFX pro-vides both of RANS and LES methods [39].Centrifugal turbine is a new type of turbine, and it will have awide range of applications in energy utilization. How to design acentrifugal turbine with higher performance has become a hotresearch topic in recent years. In this paper, the volute and frontguide vane of a single stage centrifugal turbine is investigated withperformance study under both of design and off-design conditions.Besides, the performance is compared with the single stage cen-trifugal turbine with simple annular outlet and the same aerody-namic parameter, stage blade type and inlet.
2. Working principle of centrifugal turbine
Working substance enters the stator blade with ﬂow speed
c
0
,pressure
P
0
and temperature
T
0
, and it is expanded and acceleratedto
c
1
in stator. The heat energy of the working substance is con-verted to kinetic energy, and the temperature and pressure dropto
T
1
and
P
1
, respectively. After that, the working substance entersthe moving impeller with relative speed of
w
1
. For moving impel-ler, the inlet rotor speed is
u
1
and the working substance continuesto expand and do work where temperature and pressure drops to
T
2
and
P
2
, and relative velocity increases to
w
2
. The outlet rotorspeed of moving impeller is
u
2
. The working substance leaves themoving impeller with velocity of
c
2
and then enters the followingcomponents. The through-ﬂow geometric parameters are showedin Fig. 2 and the enthalpy entropy diagram for centrifugal turbineimpeller is showed in Fig. 3.
3. 1D aerodynamic parameters and blade proﬁle
One dimensional aerodynamic parameters of a single-stagecentrifugal turbine adopts the designing parameters in Refs.
Fig. 2.
Through-ﬂow geometric parameters of centrifugal turbine.474
Y. Wang et al./Applied Thermal Engineering 131 (2018) 472–485
[40,41], and the complete gas as working substance. The designparameters are showed in Table 1 and the main aerodynamicparameters and geometric parameters of a centrifugal turbine areshowed in Table 2. The velocity triangle of stage inlet and outletis showed in Fig. 4 and the parameter values for speed triangleare showed in Table 3.The stator blade and rotor blade adopt the optimized blade pro-ﬁle based on Ref. [42] with 32 stator blades and 43 rotor blades asshown in Fig. 5. The optimized values of stage aerodynamic perfor-mance of optimal design are showed in Table 3.
4. Size of stationary accessory ﬂow passage components
By taking centrifugal turbine with simple annular outlet as Ref.[43], the aerodynamic performance of centrifugal turbine withvolute outlet is studied. Both of the turbines have the same 1Daerodynamic parameters, stage blade proﬁle and inlet. As shownin Fig. 6, the main ﬂow passage components of centrifugal turbinewith volute outlet include stationary accessory ﬂow components(inlet, vaneless diffuser and outlet), stator blade and rotor blade,where the shapes of stator blade and rotor blade are showed inFig. 5. Besides, Fig. 7 shows the 3D ﬂow diagram of whole turbine.
Similar to centrifugal compressor, the inlet introduces gas intothe turbine. This paper adopts the inlet structure as shown inFig. 8 which shows advantages including uniform and axial sym-metry air input, low ﬂow loss and simple and compact structure.Moreover, this paper adopts the central streamline method recom-mended by Ref. [43] to design inlet, as shown in Fig. 9. The central
streamline is the 1/4 arc which is tangent to the axial and radialdirections, and both of the hubline and shroud line adopt the 1/4ellipse with the same center of the arc. Fig. 10 shows the 3D axialcross-section of inlet. The structure and design of inlet are similarto Figs. 8 and 9. According to Ref. [43], the deﬁnition of each size is
showed in Table 4.The structure and design of vaneless diffuser is similar toFig. 11. The optimum outlet section diameter D
3
of vaneless dif-fuser is the result fromthe game betweenthe speed reduction withdiffuser and the frictional heating. According to the recommendedvalue from Ref. [43], the optimum diameter of vaneless diffuser is
D
3
= 1.03
⁄
D
2
= 734 mm. The structure and design of outlet is sim-ilar to Fig. 12, and the corresponding values are showed in Table 5
based on Ref. [43].
5. Design for front guide vane of volute
The design of volute and its front guide vane for a single stagecentrifugal turbine is conducted. Besides, the performance of thissingle stage centrifugal turbine is investigated under both of thedesign and off-design conditions. The results are compared withperformance of single stage centrifugal turbine with simple annu-lar outlet and the same aerodynamic parameters and geometricparameters.In order to achieve higher stage efﬁciency, the absolute ﬂowangle at the outlet of rotor blades is usually close to 90
. If theair ﬂows directly into the volute with this angle, then the outlinesize of the volute would be very large. Therefore, the front guidevane plays a role to deﬂect the absolute ﬂow angle which is closeto 90
to the designed volute inlet angle. The inlet angle in thispaper is set as 30
.The modeling of front guide vane of volute is conducted withSoftware BladeGen. The front guide vanes are designed as straightand thin plates with the same thickness of 2 mm. The inlet diam-eter is 714 mm, the inlet blade height is 40 mm, the outlet diame-ter is 794 mm, and the outlet blade height is 50 mm. The tangentangle of the camber line varies linearly from the inlet to the outlet.
Table 1
Design parameters of centrifugal turbine.
Parameters 1D value [32] Optimal value [33] Unit
Total inlet temperature
T
0
*
550 550 KTotal inlet pressure
P
0
*
320 320 kPaOutlet backpressure
P
2
200 206.934 kPaDesign speed
n
6000 6000 r/minMass ﬂow rate
G
8 8 kg.s
1
Turbine power
W
480 470 kWRotor efﬁciency
g
u
86.59 88.73 %
Table 2
Main aerodynamic parameters and geometric parameters of a centrifugal turbine.
Parameters Values Unit Parameters Values UnitSpeed ratio
X
a
0.52 [–] Outlet mach number of stator blade
M
0.722 [–]Reaction degree
X
0.2 [–] Blade height
H
40 mmDiameter ratio
D
2
/D
1
1.15 [–] Inlet diameter of stator blade
D
0
528.9 mmOutlet pressure of stationary blade
P
1
220 kPa Outlet diameter of stator blade
D
11
616.3 mmVelocity coefﬁcient of stator blade
u
0.97 [–] Inlet diameter of rotor blade
D
12
621.3 mmVelocity coefﬁcient of rotor blade
w
0.93 [–] Outlet diameter of rotor blade
D
2
708.8 mm
Fig. 4.
Schematic diagram of velocity triangle.
Fig. 3.
Enthalpy entropy diagram for centrifugal turbine impeller.
Y. Wang et al./Applied Thermal Engineering 131 (2018) 472–485
475

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