Journal of Mechanical Science and Technology 30 (12) (2016) 5521~5527 www.springerlink.com/content/1738-494x(Print)/1976-3824(Online)
DOI 10.1007/s12206-016-1120-7
Analysis of performance for centrifugal steam compressor† Seung-Hwan Kang1, Changkook Ryu2 and Han Seo Ko2,* 1
Department of Mechanical Engineering, Graduate School, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon 16419, Korea 2 School of Mechanical Engineering, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon 16419, Korea (Manuscript Received May 11, 2016; Revised June 30, 2016; Accepted July 25, 2016)
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Abstract In this study, mean streamline and Computational fluid dynamics (CFD) analyses were performed to investigate the performance of a small centrifugal steam compressor using a latent heat recovery technology. The results from both analysis methods showed good agreement. The compression ratio and efficiency of steam were found to be related with those of air by comparing the compression performances of both gases. Thus, the compression performance of steam could be predicted by the compression performance of air using the developed dimensionless parameters. Keywords: Centrifugal compressor; CFD analysis; Characteristic compression prediction; Mean streamline analysis; Steam compression; Vaneless diffuser ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
In many industrial fields, hot steam is produced and wasted. If the energy of hot steam can be reused, the reduction of input energy and the increase of efficiency for the industrial process can be expected. One of the ways to reuse hot steam is to use latent heat recovery technology using steam compression. This technology is attributed to the principle that the saturation temperature of the vapor rises as its pressure increases, as shown in Fig. 1. After compressing the vapor produced by the process, the energy of the vapor is reused as a heat source for the process. Hong et al. [1] showed input energy reduction and the high energy efficiency using steam compression latent heat recovery technology in the process of fry-drying for fuel production from sewage sludge. In the process, desalination is also used for this technology. The heated and evaporated vapor from seawater or waste water is compressed, and the compressed vapor is condensed by heat exchange with the incoming sea water. One of the methods to compress vapor is Mechanical vapor recompression (MVR). The MVR system requires high compressing technology, and high reliability and durability. Thus, the centrifugal compressor is used for the MVR to satisfy these requirements. Since many variables of the centrifugal compressor design need to be considered, it is complex to predict its performance. Extending the limit causes the compressor to become noisy and vibrate, and can even break. Thus, *
Corresponding author. Tel.: +82 31 290 7453, Fax.: +82 31 290 5889 E-mail address:
[email protected] † Recommended by Associate Editor Simon Song © KSME & Springer 2016
P2
T (℃)
P1
Wcomp
T2 Qsteam T1
isentropic
1. Introduction
entropy Fig. 1. Process of steam compression and latent heat recovery.
it is important to study the characteristics of the compressor and determine a way to predict its performance. Mean streamline and numerical analyses were used to investigate the performance of the compressor. The mean streamline analysis based on the integral method was developed to calculate the change of flow along with a streamline from the inlet to the outlet of the compressor. Thus, it is also called one-dimensional (1D) analysis. This method is useful to analyze the ultimate state of the compressor. The numerical analysis, or Computational fluid dynamics (CFD) analysis, is based on the differential method which divides fluid into small elements and calculates the flow state of each element. The performance of the compressor is calculated using both methods, the results of which are verified.
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2. Calculation method
Cθ2b
2.1 Mean streamline analysis
Cθ2
The total work input into the rotating body is equal to the angular momentum change of the rotating body. To arrange the momentum integral equation by this relation, Euler’s equation is derived as follows [2-4]: w=
Wɺ τω ω = = mɺ ( r2Cθ 2 − rC 1 θ 1 ) = U 2Cθ 2 − U1Cθ 1 mɺ mɺ mɺ
U 2Cθ 2 . Cp
(3)
The outlet total pressure is calculated using the isentropic efficiency, which is defined as follows:
ηs =
∆h0,s ∆h0
=
h02,s − h01 h02 − h01
=
C p (T02,s − T01 ) C p (T02 − T01 )
T T01 02,s − 1 T . = 01 (T02 − T01 )
(4)
The isentropic efficiency calculated from the CFD was applied to the mean streamline analysis. Using Eq. (4), the isentropic temperature ratio is as follows: T02,s T01
= 1+
η s (T02 − T01 ) T01
.
(5)
In addition, the isentropic process relation can be obtained as follows. p02 T02,s = p01 T01
k k −1
.
N
Fig. 2. Triangle of impeller exit velocity.
(2)
Thus, T02 = T01 +
Cm2
(1)
where τ and ω are the torque and angular velocity, respectively, and U and Cθ are the impeller velocity and the absolute tangential flow velocity, respectively. The work input into the impeller is equal to the enthalpy change of the fluid. If the inlet tangential velocity Cθ1 is zero, then the outlet total temperature is derived as follows: h02 − h01 = C p (T02 − T01 ) = U 2Cθ 2 − U1Cθ 1 = U 2Cθ 2 .
Cslip
(6)
The fluid does not follow along the angle of the blade at the outlet due to the slip of the fluid. As shown in Fig. 2, the outlet flow angle β 2 differs from the blade angle β 2 b . Thus, the slip factor can be defined using the ratio of the actual tangential flow velocity to the ideal tangential velocity by the blade angle, σ slip = Cθ 2 / Cθ 2b . The slip factor has been calculated by many researchers, and among them, slip factor equations of Stodola, Stanitz, Wiesner and Paeng were used in this study [2-8]. Sto-
dola first proposed the slip velocity and slip factor. Stanitz’s slip factor is particularly applicable to the straight radial bladed impellers. Wiesner devised an empirical expression based on Buseman’s slip factor, which is a universally accurate method for the centrifugal impellers over the entire range of the practical parameters widely used in practice. Paeng’s slip factor was obtained from a new relative eddy model in a recent study. These slip factors are as follows [2-9]: Stodola’s slip factor: (π / Z ) cos β 2b σ slip = 1 − 1 − φ2 tan β 2b
(7)
where φ2 = C m 2 / U 2 .
(8)
Stanitz’s slip factor: 0.63π / Z . σ slip = 1 − 1 − φ2 tan β 2 b
(9)
Wiesner’s slip factor: cos β 2 / Z 0.7 σ slip = 1 − 1 − φ2 tan β 2b and Paeng’s slip factor: fα σ slip = 1 − 1 − φ2 tan β 2b
(10)
(11)
where π sin cos β 2b Z α= π 1 + sin cos β 2 b Z
(12)
S.-H. Kang et al. / Journal of Mechanical Science and Technology 30 (12) (2016) 5521~5527
Selecting N , D and ρ01 as common factors, the relation above is rearranged with five dimensionless groups as follows:
Calculate inlet velocity and mass flow rate at each RPM Calculate T , p and ρ at inlet
mɺ ∆h0 s P ρ 01 ND 2 ND , , fn , , , k = η ρ ND 3 N 2D2 a01 ρ 01 N 3 D5 µ 01
Assume ρ New ρ
no
ɺ 01 mɺ RT01 1 mɺ mɺ mRT . = = = 3 2 2 ρ 01 ND ρ 01a01 D p01D 2 p01 kRT01 D k
yes
Fig. 3. Flow chart of algorithm for compressing performance.
∆h0 s = C p (T02 s
and correction factor f
(
(17)
And according to Eqs. (2) and (6)
Result
f = f 0( Z ) + A( Z ) exp β 2b / B( Z )
(16)
where P / ( ρ 01 ٛN 3 D 5 ) refers to the power coefficient Pˆ and mɺ / ρ01 ND 3 refers to the mass flow coefficient. The dimensionless mass flow coefficient is rearranged with the equation of state as follows:
Calculate T , p and ρ at outlet
New ρ identical with assumed ρ ?
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)
(13)
f 0( Z ) = 0.833 + 0.21exp ( − Z 3 / 32.3)
A( Z ) = 0.024 1 − exp ( − Z 4.1 / 336 ) ٛ
(14)
The following algorithm as Fig. 3 was developed in order to predict the compressing performance by the revolution of the impeller. 2.2 Dimensionless group The important parameters for a compressor are pressure and temperature. The subscript 0 refers to the total condition or the stagnation condition, and the subscripts 1 and 2 refer to the properties at the inlet and outlet of the turbo-machine, respectively. D refers to the diameter or the characteristic length of the impeller, and N refers to the revolution of the impeller. When isentropic enthalpy change ∆h0 s , efficiency η , and power P are set as performance parameters of the turbomachine, the performance parameter of compressible fluid is the function of variables as follows [2-4]: ∆h0 s , η , P = f ( µ , N , D, mɺ , ρ 01 , a01 , k )
(15)
where a is the speed of sound and k is the specific heat ratio.
(18)
thus, ∆h0 s ∆h = 02s ∝ f ( p02 / p01 ٛ) N 2D2 a01
where
B( Z ) = 24.2 1 − exp ( − Z 1.311 / 3.04 ) .
k −1 p02 k − T01 ) = C pT01 − 1 p01
(19)
which means that the enthalpy change is a function of pressure ratio so that the pressure ratio could be a performance parameter. Therefore, the pressure ratio, efficiency, and power coefficient are defined as a function of the dimensionless group as follows: mɺ RT01 p02 ND , η , Pˆ = f , Re, , k. 2 p01 D p01 RT01
(20)
According to the relation above, the dimensionless mass flow rate is defined as:
Φ=
mɺ RT01 p01D 2
(21)
and the dimensionless revolution is: Ω=
ND . RT01
(22)
Using the dimensionless mass flow rate and revolution, the compressors for steam and air would show identical performances.
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Mass flow rate [kg/s]
0.2
0.15
0.1
0.05
0
(a) Front view
1
2
3
4
5 rpm
6
7
8
(b) Side view
9 4
x 10
Fig. 6. Mass flow rate calculated by mean streamline analysis. Fig. 4. Configuration of impeller.
rpm to 85000 rpm was calculated as shown in Fig. 6. AnsysCFX was used for the CFD analysis. 3.3 Comparison by dimensionless group
Fig. 5. Mesh generation for considered model by TurboGrid.
3. Numerical analysis 3.1 Shape A small centrifugal compressor with a vaneless diffuser was considered in this study. The impeller has a diameter of 102.4 mm and 12 backward blades including 6 main blades and 6 splitter blades. The inlet blade angle is 50.4° and the outlet blade angle is 28.0°, as shown in Fig. 4. The control volume has an axisymmetric area for the impeller and the diffuser. Thus, the model consists of only two blades, a main blade and a splitter blade, which made the analysis simple and quick using the rotational periodicity. The analysis using the simple model shows the same results as those of the total model. One passage model for the impeller and diffuser has about 140000 nodes with appropriate size for each mesh considering the boundary layer for each surface as shown in Fig. 5. The mesh was generated by Ansys TurboGrid. 3.2 Boundary condition For the inlet condition, the atmospheric condition with 26.85 °C and 101.3 kPa was assumed for air while 120 °C and 150 kPa were set for steam. The calculation can be performed in one of two ways. (1) Various mass flow rates can be calculated at a fixed rpm. This is a conventional way to analyze the performance of the compressor. (2) Various rpms are calculated assuming that the gas is sucked into the inlet along with the inlet blade angle. Then, the relative inlet velocity and its mass flow rate can be obtained. The former was considered for the comparison between air and steam using the dimensionless parameter. The latter was considered for the comparison between the mean streamline and CFD analyses. The mass flow rate according to the revolution from 10000
The pressure ratio and the efficiency of the compressor are functions of the dimensionless mass flow rate and dimensionless revolution, respectively. Thus, it is proposed that by setting dimensionless parameters, the performance of a fluid can be predicted by using the compressing performance data of another fluid in an identical compressor shape. At the fixed revolution, a dimensionless mass flow rate conversion coefficient is defined as follows: RT01
Φ fluid =
(23)
p01 D 2
which is derived from the dimensionless mass flow rate, Eq. (21) as follows: Φ = mɺ ×
RT01 p01D 2
= mɺ × Φ fluid .
(24)
Substituting the dimension of the compressor and the inlet condition of the fluid into Eq. (23), each dimensionless flow coefficient can be calculated. The gas constant of air, Rair = 287.042 J/kg-K, the gas constant of steam, Rsteam= 461.523 J/kg-K, and D is the outer diameter of the impeller. The conditions of each conversion coefficient are as follows: Φair = 0.27620 Φsteam = 0.27082.
(25) (26)
The difference between the dimensionless flow conversion coefficients of air and steam is within 2 %, thus both fluid flow ranges are expected to be similar. Likewise, the dimensionless revolution conversion coefficient can be defined as follows: Ω fluid =
D 2π 60 s RT01
(27)
which was derived from the dimensionless revolution, Eq. (22).
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Table 1. Transformed rpm for steam corresponding to rpm for air.
C2 CFD
350
30000
40000
50000
Dimensionless revolutions
1.0963
1.4617
1.8271
2.1925
Transformed RPM for steam
43547
58063
72579
87095
Ω=N×
2π D D = rpm × = rpm × Ω fluid . 60 s RT01 RT01
C2 1D,Stanitz
60000
C2 1D,Stodola
300 Outlet velocity [m/s]
RPM for air analysis
(28)
C2 1D,Wiesner C2 1D, Paeng
250 200 150 100 50
Substituting each condition into Eq. (27), the dimensionless revolution conversion coefficients can be calculated as follows: Ωair = 3.6542×10-5 Ωsteam= 2.5174×10-5.
0
1
2
3
4
5 rpm
6
7
8
9 4
x 10
Fig. 7. Impeller outlet velocity by mean streamline (1D) and CFD analyses.
(29) (30)
If performance data or a characteristic curve of a compressor is obtained with respect to air using either the numerical analysis or the experiment, the data of another fluid, such as the operating range of the flow rate or the revolution, can be obtained using the conversion coefficients. In the case of the mass flow rate, the operating flow range of steam is predicted from the performance result of air at a fixed rpm using the following relation, mɺ steam = mɺ air ×
Φ air . Φ steam
(31)
In addition, in the case of the revolution, the following relation shows the operating revolution for steam predicted from the performance result of air:
Fig. 8. Total pressure ratios by mean streamline (1D) and CFD analyses. 1.7 Tr CFD Tr 1D,Stanitz Tr 1D,Stodola Tr 1D,Wiesner Tr 1D, Paeng
rpmsteam = rpmair ×
Ω air . Ω steam
(32)
The above relations can be used to calculate the revolution for steam corresponding to that for air at the same condition as shown in Table 1.
4. Results and discussion 4.1 Comparison between mean streamline and CFD analyses The outlet velocity, total pressure ratio, and total temperature ratio of the impeller obtained by both analysis methods are shown in Figs. 7-9, respectively. As a result, the coefficients of Stanitz, Wiesner and Paeng were relatively close to the CFD result to predict the outlet velocity, while Stodola’s coefficient was very close to the CFD result for prediction of the pressure ratio and temperature ratio. Especially, three results from Stanitz, Wiesner, and Paeng’s calculation showed very good agreement each other. The slip factors were developed using the experimental results, while Stodola’s coefficient was obtained based on the theoretical derivation so that it
Total Temperature Ratio
1.6
1.5
1.4
1.3
1.2
1.1
1
1
2
3
4
5 rpm
6
7
8
9 4
x 10
Fig. 9. Total temperature ratios by mean streamline (1D) and CFD analyses.
showed the best agreement with the CFD results. 4.2 Steam compression The air compression with various mass flow rates at the fixed revolutions of 30000 rpm, 40000 rpm, 50000 rpm and 60000 rpm was analyzed and the total pressure ratio and isentropic efficiency from the inlet to the diffuser outlet are shown
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Fig. 10. Total pressure ratios for air and steam using one passage model.
Fig. 12. Relative Mach number in 50 % span view for air at 0.186 kg/s and 60000 rpm.
ber distribution according to the relative velocity in the 50 % span view of the impeller and diffuser at the condition of 60000 rpm and the mass flow rate of air of 0.186 kg/s. The choke occurred at the leading edge of the splitter blade so that the splitter blade could reduce the width of the passage in the impeller. Over Mach 1, the flow rate did not increase any further, and the compressing efficiency and performance decreased greatly. Fig. 11. Total isentropic efficiency for air and steam using one passage model.
in Figs. 10 and 11. The stream compression with various mass flow rates at fixed revolutions of 43547 rpm, 58063 rpm, 72579 rpm and 87095 rpm, which were transformed from the revolutions for the air compression using the conversion coefficients, was also investigated and the results are plotted on the same graphs as those showing the results for air. The total pressure ratio and isentropic efficiency of air and steam compressions, which were rearranged by the dimensionless parameters, showed very good agreement. Thus, it was proved that the compressing performance for a fluid could be predicted from the performance data of another fluid in the case of various fluids used for the same compressor. The total pressure ratio and temperature ratio increased as the mass flow rate decreased, while the efficiency increased up to the maximum point, and then decreased. At a certain low mass flow rate, the CFD analysis did not give a result since the performance of the compressor entered the unstable region, called the surge region, after the maximum efficiency. Thus, the maximum point can be the design point of the compressor. Each curve decreased rapidly at the high mass flow rate for the total pressure ratio and isentropic efficiency because the speed of the current increased as the flow rate increased and the choke occurred at the narrow area in the compressor, which induced failure. Fig. 12 shows the Mach num-
5. Conclusions In this study, mean streamline analysis and CFD analysis with respect to air were performed and compared to observe the characteristics of the small centrifugal compressor. The result of the mean streamline analysis showed good agreement with that of the CFD analysis. It was confirmed that the performance of the compressor was the function of the dimensionless mass flow rate and the dimensionless revolution regardless of the sort of fluid by comparing the CFD results between air and steam. It was also proposed that the performance data of a fluid could be predicted by the data of another fluid because the analysis results proved that the total pressure ratio and the isentropic efficiency of the compressor could be predicted from the data of another fluid using the dimensionless parameters. It was observed that the choke occurred at the high mass flow rate in the compressor so that the flow rate could not increase. The CFD analysis showed a narrow area where the choke occurred visually at the leading edge of the splitter blade.
Acknowledgment This study was supported by the New & Renewable Energy Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant (No. 20103020100010) funded by the Korea Ministry of Knowledge Economy.
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Nomenclature-----------------------------------------------------------------------a C Cp D h k ṁ N P p R r Re T U w Ẇ Z β η ρ σ τ Φ Ω ω
: Speed of sound : Absolute velocity of fluid [m/s] : Specific heat at constant pressure [J/kg·K] : Diameter [m] : Enthalpy [J/kg] : Specific heat ratio : Mass flow rate [kg/s] : Revolution : Power : Pressure [Pa] : Gas constant [J/kg·K] : Radius of impeller [m] : Reynolds number : Temperature [K] : Velocity of impeller [m/s] : Work per unit mass [J/kg] : Power [J/s] : Number of blades of impeller : Angle of relative velocity : Efficiency : Density [kg/m3] : Slip factor : Torque [N·m] : Dimensionless mass flow rate : Dimensionless revolution : Angular velocity [rad/s]
References [1] S. Hong, C. Ryu, H. S. Ko, T. I. Ohm and J. S. Chae, Process consideration of fry-drying combined with steam compression for efficient fuel production from sewage sludge, Appl. Energy, 103 (2013) 468-476. [2] S. L. Dixon, Fluid mechanics, thermodynamics of turbomachinery, 5th Ed., Elsevier Butterworth-Heinemann, Amsterdam, Boston (2005).
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[3] D. Japikse and N. C. Baines, Introduction to turbomachinery, Concepts ETI ; Oxford University Press, Norwich, Vt. : Oxford (1994). [4] A. T. Sayers, Hydraulic and compressible flow turbomachines, McGraw-Hill, London ; New York (1990). [5] F. J. Wiesner, A review of slip factors for centrifugal impellers, J. Eng. for Gas Turbines and Power, 89 (1967) 558-566. [6] K. S. Paeng and M. K. Chung, A new slip factor for centrifugal impellers, Proc. Inst. Mech. Eng. Part A J. Power Eng., 215 (2001) 645-649. [7] H. W. Oh, E. S. Yoon and M. K. Chung, An optimum set of loss models for performance prediction of centrifugal compressors, Proc. Inst. Mech. Eng. Part A J. Power Eng., 211 (1997) 331-338. [8] M. N. Šarevski and V. N. Šarevski, Characteristics of water vapor turbocompressors applied in refrigeration and heat pump systems, Int. J. Refrig., 35 (2012) 1484-1496. [9] Y.-S. Yoon and S. J. Song, Analysis and measurement of the impact of diffuser width on rotating stall in centrifugal compressors, J. Mech. Sci. and Tech., 28 (2014) 895-905.
Han Seo Ko is a Professor in the School of Mechanical Engineering, Sungkyunkwan University. He received his Ph.D. in Mechanical Engineering in 1998 from Texas A&M University. His research interests are flow control, microfluidics, optical tomography, micro-droplet ejection and heat and mass control. Seung-Hwan Kang is a Ph.D. student in the Department of Mechanical Engineering, Sungkyunkwan University. His research interests are computational fluid dynamics (CFD) and radiation heat transfer.
