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Numerical simulation and experimental validation of large pressure pulsation in reciprocating compressor
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2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, 2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, Sydney, Australia Sydney, Australia
Numerical simulation and experimental validation of large pressure 15th International Symposium on District Heating and Numerical The simulation and experimental validation ofCooling large pressure pulsation in reciprocating compressor pulsation in reciprocating compressor Assessing theQuan feasibility using Chang the heat a,b b a Yuan Li , Kai , Rui Wuaof , Yunfeng , Beidemand-outdoor Guoa,*, Bo Zhangb a,b b a a a,* b Yuan Li ,function Kai Quan ,for RuiaWu , Yunfeng Chang , Bei Guodemand , Bo Zhang temperature long-term district heat forecast School of Energy and Power Engineering, Xi'an Jiaotong University, No.28, Xianning West Road, Xi'an, 710049, P.R. China a
Sinopec ChuanEngineering, to Eastern China Gas Pipeline Wuhan, 430020, P.R.710049, China P.R. China School of Energy andSiPower Xi'an Transmission Jiaotong University, No.28,Co.Ltd., Xianning West Road, Xi'an, a,b,c a a b c c b Sinopec Si Chuan to Eastern China Transmission Gas Pipeline Co.Ltd., Wuhan, 430020, P.R. China
a
b
I. Andrić
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
a Abstract IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300the Nantes, A numerical model basedSystèmes on the Énergétiques one-dimensional unsteady flow theory was established to simulate largeFrance pulsation of the reciprocating compressor. simulation model was consisting of theory the single pipeline system, the straight pipe +volume A numerical model based The on the one-dimensional unsteady flow wasstraight established to simulate large pulsation of the chamber pipeline system and straight pipe + reducer pipeline of system. The models solved by using the twopipe steps+volume method reciprocating compressor. Thethe simulation model was consisting the single straight were pipeline system, the straight and the method characteristics. To validate simulation model, the experiment measure was done chamber pipelineofsystem and the straight pipe +the reducer pipeline system. The modelstowere solvedthe bypressure using thepulsation two steps method inAbstract different exhaust pressures, different rotate speeds and different pipeline systems. The waveforms of the simulation and and the method of characteristics. To validate the simulation model, the experiment to measure the pressure pulsationresults was done thedifferent experimental results were in good agreement andand all of the relative errors of theThe pressure unevenness belowresults 10%. The in exhaust pressures, different rotate speeds different pipeline systems. waveforms of the were simulation and District heating networks are commonly addressed in the literature as established one of the most for decreasing the simulation resultsresults were consistent with agreement the experiment results. model this effective paper wassolutions accurate. the experimental were in good and all of theThe relative errors of the in pressure unevenness were below 10%. The greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat simulation results were consistent with the experiment results. The model established in this paper was accurate. to the changed climate conditions ©sales. 2018 Due The Authors. Published by Elsevier Ltd. and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. © 2019 The Authors. Published by Elsevier Ltd. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018 The Authors. by Elsevier Ltd. This an open under the CCthe BY-NC-ND license The ismain scopeaccess of thisarticle paper is toresponsibility assess feasibility of using(https://creativecommons.org/licenses/by-nc-nd/4.0/) the heat demand outdoor temperature function for heat demand Selection under of the scientific committee of the–2nd International Conference on Energy and This is an and openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of as thea2nd International Conference on Energyofand forecast. The district of Alvalade, located in Lisbon (Portugal), was used case study. The district is consisted 665 Power, ICEP2018. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Power, ICEP2018. renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Keywords: Type your keywords here, separated by semicolons ; compared with results from a dynamic heat demand model, previously developed and validated by the authors. Keywords: Type your keywords here, separated by semicolons ; The results showed that when only weather change is considered, the margin of error could be acceptable for some applications error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.(the Introduction scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1. Introduction The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the The reciprocating is widely used induring the industry and season daily life to supercharge and conveyofthe gas. The decrease in the numbercompressor of heating hours of 22-139h the heating (depending on the combination weather and The reciprocating compressor is widely used in the industry and daily life to supercharge and convey the gas.on The results show the reciprocating compressor possesses some characters, including high thermal efficiency, good renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending the results reciprocating compressor possesses characters, including high thermal efficiency, good versatility andthe much application and so could on [1]. advancement of the compressor and an increase coupledshow scenarios). The values suggested beWith used the to some modify the function parameters for technology the scenarios considered, and versatility much of application and socompressors on [1]. Withhave the advancement the competitiveness. compressor technology andcompressors an increase demand production, the demand low-speed gradually lostoftheir Thus, the improve for theand accuracy heat estimations.
demand for flow production, therotate low-speed have lost in their the compressors with heavy and high speedcompressors have become the gradually main device thecompetitiveness. chemical and oilThus, industry. In practical © 2017 The flow Authors. by Elsevier Ltd. with heavy andPublished high rotate speed have the main device inThe thelarge chemical and oil In practical production, the high-speed compressors havebecome large pressure pulsation. pulsation hasindustry. much disadvantage. Peer-review under responsibility of the power Scientific Committee of The 15th Symposium onhas District production, high-speed compressors have large and pressure pulsation. The large pulsation much disadvantage. For example,the it makes the indicated increase the gas flowInternational decrease. And it accelerates the Heating wear ofand the gas Cooling. For example, it makes the indicated power increase and the gas flow decrease. And it accelerates the wear of the gas
Keywords:©Heat Forecast; Climatebychange 1876-6102 2018demand; The Authors. Published Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1876-6102 © 2018 The Authors. Published by Elsevier Ltd. Selection under responsibility of the scientific of the 2nd International Conference on Energy and Power, ICEP2018. This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 10.1016/j.egypro.2019.02.212
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Nomenclature U R X Z L0 p u ρ x t f
dimensionless velocity dimensionless density dimensionless distance dimensionless time reference length pressure velocity density distance time friction coefficient
valve and shorten life of the crankshafts. Therefore, it is of great significance to study the generation mechanism, to predict the changed trend and to master the effective method to control the pressure pulsation. There are two main methods for analyzing the pressure pulsation, one is the plane wave theory, and the other is the one-dimensional unsteady flow theory [2]. The plane wave theory method cannot fully describe the complex phenomenon in the pipeline. In addition, the airflow parameters in the pipeline are constant rather than the actual values, which leads to the low accuracy of the calculation results. The one-dimensional unsteady flow theory does not ignore the nonlinear factors when establishing the governing equation of gas flow in the pipeline, and also considers the influence of friction between the gas and the inner wall as well as the actual gas property [3]. More scholars have experimentally maintain that the unsteady flow theory is more in line with the actual situation, especially on the condition of large pulsation. Wendroff and Lax [4] proposed the Lax-Wendroff finite difference method to solve the gas flow equations, which serves as a theoretical underpinning for solving the one-dimensional unsteady compressible flow equations. Richtwyer and Morton[5] proposed a two-step Lax-Wendroff method, which greatly improves the computing power in the simulation. Besides, the characteristic line method of the uniform entropy correction theory is experimentally proved that it is in line with the actual situation[6]. A numerical method combines the two method is used widely to solve the one-dimensional unsteady flow equations: the method of characteristics is used on the boundary, and the Lax-Wendroff two-step method is used inside the pipeline. Most of the scholars use this method to simulate the airflow pulsation. For example, Liu and Sodel[7, 8] study the gas column resonance pressurization phenomenon of the variable speed compressor by this theory; Brun[9] write the pulsation calculation program by using this method, and analyzes the influence of the acoustic impedance and acoustic characteristics of the pipeline on the airflow pulsation. Stosic[10] used this method to enable the clearance size of a screw compressor for start-up and steady running conditions to be determined. Based on the one-dimensional unsteady flow theory, this paper establishes a model of the reciprocating compressor based on the method which combines the method of characteristics and the Lax-Wendroff two-step method. A program is written to simulate the pressure pulsation in 3 systems, the single straight pipeline, the straight pipe +volume chamber pipeline and the straight pipe + reducer pipeline. The experiments are also carried out to validate the simulation model in different exhaust pressures, different rotate speeds and different pipeline system. 2. Equations and solution method When the diameter of the pipeline is much smaller than the length of the pipeline, it can be considered that all of the parameters on any section are equal. So the flow can be simplified into the one-dimensional flow. So the fluid element can be taken as the research object. The mass equation, the momentum equation and the energy equation form the control equations of the one-dimensional unsteady flow theory. Continuous equation:
Yuan Li et al. / Energy Procedia 160 (2019) 606–613 Author name / Energy Procedia 00 (2018) 000–000
608 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
(𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌) +
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
(𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌) +
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
3
𝜌𝜌𝜌𝜌 = 0
(1)
(𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌2 + 𝑝𝑝𝑝𝑝) = 𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌
(2)
Momentum equation: 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
Energy equation: 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
𝑉𝑉𝑉𝑉 +
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
𝐺𝐺𝐺𝐺 = 𝐵𝐵𝐵𝐵
𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝑉𝑉 = �1 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 2 + 2
𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘−1
(3) 0 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 2 𝑓𝑓𝑓𝑓𝐿𝐿𝐿𝐿0 |𝑅𝑅𝑅𝑅|𝑅𝑅𝑅𝑅 2 −𝑅𝑅𝑅𝑅 𝐷𝐷𝐷𝐷 � , 𝐺𝐺𝐺𝐺 = �1 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 � , 𝐵𝐵𝐵𝐵 = � � 2 𝐿𝐿𝐿𝐿0 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝑃𝑃𝑃𝑃 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 3 𝐾𝐾𝐾𝐾−1 2 𝑎𝑎𝑎𝑎0
(4)
Those equations are the NPDE (Nonlinear Partial Differential Equations), which can’t get their analytic solutions and need to apply numerical method to reach the approximate solutions. In this paper, the two-step method and the characteristics method is combined to calculate the equations. The two-step method is used at the point inside the pipeline, and the method of characteristics is used at the boundary point. Figure 1 is the flow chart of the solution algorithm.
Fig. 1. Solution algorithm.
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3. Experiment Setup The experiment selected a V-type single stage reciprocating air compressor. The detailed parameters of the compressor are shown in the Table 1. One of the cylinders was chosen as the excitation source of the system. The pulsation pressure at the three points were measured in different exhaust pressures, different rotate speeds, and different pipeline system. Table 1. Parameters of the experimental compressor. Item
Value
Item
Value
Model
V-0.67/8
Rated rotate speed(r∙min-1)
980
Type
Single stage
Stroke(m)
0.06
Suction pressure(MPa)
1.013
Bore(m)
0.09
Rated Exhaust pressure(MPa)
0.8
Link length(m)
0.17
Rated power(kW)
5.5
Relative clearance volume(%)
6.9
The end of the pipeline is connected to a gasholder, the outlet of which installed a valve and a pressure gauge. The suction pressure is constant. The pressure inside the pipeline can be changed by adjusting the opening degree of the valve, and the pressure is set based on the pressure gauge. For this reason, the experiments reached different exhaust pressure. In order to measure the pressure pulsations in different rotate speeds, the motor of the compressor is connected to a frequency converter. By changing the output of the frequency converter, the operating rotate speeds varied too. Besides, a steel pipe with an inner diameter of 16mm and a length of 2m was selected. To facilitate the change of the piping system in the experiments, this pipe was cut into two 1m long pipes. One was connected to the exhaust, and the other one was connected to the gasholder. The two pipes were connected with three different part, including the connector, the volume chamber and the reducer, so they formed three pipeline system, the single straight pipeline system, the straight pipe +volume chamber pipeline system and the straight pipe + reducer pipeline system. The structural diagrams and the test points of the three systems are as shown in the Figure 2.
Fig. 2. Structural diagram.
4. Results 4.1. Different exhaust pressures A lot of experiments were done on different conditions. In this paper, the results of the single straight pipeline system in the rotate speed of 980r∙min-1 are shown. The exhaust pressures are 0.3MPa, 0.4MPa, 0.5MPa, respectively. The results of experiment and simulation are as follows in Figure 3. It can be seen that the waveforms of the simulation and the experiment are similar.
Yuan Li et al. / Energy Procedia 160 (2019) 606–613 Author name / Energy Procedia 00 (2018) 000–000
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5
(a) 0.3MPa, No.1
(b) 0.3MPa, No.2
(c) 0.3MPa, No.3
(d) 0.4MPa, No.1
(e) 0.4MPa, No.2
(f) 0.4MPa, No.3
(g) 0.5MPa, No.1
(h) 0.5MPa, No.2
(i) 0.5MPa, No.3
Fig. 3.Pressure pulsation of the single straight pipeline system in 980r∙min-1 in different exhaust pressure at different test points.
The Table 2 shows the comparison of the pressure unevenness between the simulation results and the experiment results at the test point 1. According to the pressure unevenness, the pressure pulsation in the experiment is large enough. Meanwhile the relative errors of the pressure unevenness between the simulation results and the experiment results in three different exhaust pressures are 7.91%, 1.00%, and 7.41%, all of which are below 10%. So in different exhaust pressures, the simulation results show a good agreement with the experiment results. Table 2. Pressure unevenness of the simulation and the experiment in different exhaust pressures. Exhaust pressure
Simulation
Experiment
Absolute error
Relative error
(MPa)
(%)
(%)
(%)
(%)
0.3
31.08
33.75
2.67
7.91
0.4
30.56
30.85
0.29
1.00
0.5
30.53
29.43
1.10
7.41
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4.2. Different rotate speeds The rotate speeds were set up as 369r/min, 496 r/min, 663 r/min, 814 r/min, 980 r/min and 1094 r/min. Figure 4 is the results of the test point 1 of the single straight pipe system when the exhaust pressure is 0.5 MPa. And in the Table 3, the pressure unevenness is also large enough. The relative errors are below basically 10. Obviously, not only the simulation waveforms are consistent with the experimental results, but also the relative errors of the pressure unevenness are small.
(a)369r∙min-1
(b) 496r∙min-1
(c)663 r∙min-1
(d)814r∙min-1
(e) 980r∙min-1
(f)1094 r∙min-1
Fig. 4.Pressure pulsation of the single straight pipeline system in 0.5MPa at test point 1 in different rotate speeds. Table 3. Pressure unevenness of the simulation and the experiment in different rotate speeds. Rotate speed
Simulation
Experiment
Absolute error
Relative error
(r∙min )
(%)
(%)
(%)
(%)
369
15.29
15.82
0.53
3.2
496
16.03
17.52
1.49
8.5
663
19.84
21.50
1.66
7.7
814
18.11
19.52
1.41
7.2
980
30.53
28.43
2.10
7.4
1094
23.71
25.12
2.41
5.6
-1
Besides, the paper analyses the maximum amplitudes of different frequencies in 663r∙min-1 by Fourier decomposition. It can be seen from the Table 4. The relative errors of the first three are small and the last five are big. But the max amplitudes of the last five are very small, which have little effect on the composed result. Thus, it is verified that in different rotate speeds, the results of the simulation are not only consistent with the experiment results in the time domain, but also in the frequency domain.
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Table 4. The max amplitude in different frequencies in 663r∙min-1. Simulation
Experiment
Relative
Frequency
Max amplitude
Frequency
Max amplitude
error
(Hz)
(kPa)
(Hz)
(kPa)
(%)
11.04
5.696
11.05
5.11
10.3
22.08
11.947
22.10
11.07
7.3
33.12
37.220
33.15
35.43
4.8
44.16
10.472
44.20
5.595
46.5
55.20
5.243
55.25
2.240
57.2
66.24
2.128
66.30
1.730
18.7
77.28
1.147
77.35
0.658
42.6
88.33
0.664
88.40
0.516
22.2
4.3. Different pipe systems In the experiment, three different pipeline systems are designed, which are the single straight pipeline system, the straight pipe +volume chamber pipeline system and the straight pipe + reducer pipeline system. The analysis of the single straight pipe system has been carried out in the chapter 4.2 and chapter 4.3. The Figure 5 shows the results of the straight pipe +volume chamber pipeline system. The exhaust pressure is 0.4 MPa and the rotate speed is 814r∙min-1. It can be seen the waveforms of the simulation results are well matched with the experiment results. The two waveforms have little difference in the phase and the amplitude.
(a)No.1
(b) No.2
(c)No.3
Fig. 5.Pressure pulsation of the straight pipe +volume chamber pipeline system in 0.4MPa in 814 r∙min-1 at different test points.
The Table 5 shows the pressure unevenness of the simulation and the experiment. The relative errors of the pressure unevenness between the simulation results and the experiment results at three test points are 9.7%, 2.4%, and 1.7%, respectively. All of the relative errors are below 10%. The simulation results is accurate in the straight pipe +volume chamber pipeline system. Table 5. Pressure unevenness of the straight pipe +volume chamber pipeline system. Test point number
Simulation
Experiment
Absolute error
Relative error
(%)
(%)
(%)
(%)
1
21.1
23.6
2.5
9.7
2
20.2
20.7
0.5
2.4
3
18.6
18.7
0.2
1.7
The Figure 6 is the result of the straight pipe + reducer pipe system. The exhaust pressure is 0.4 MPa and the rotational speed is 814r/min, too. The waveforms of the simulation results are similar to the test results. The Table 5
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shows the relative errors of the pressure unevenness between the simulation results and the experiment results at three test points are 3.4%, 7.6%, and 9.8%, respectively. All of the relative errors are below 10%. To sum up, the simulation model is valid in the straight pipe + reducer pipe system.
(a)No.1
(b) No.2
(c)No.3
Fig. 6.Pressure pulsation of the straight pipe + reducer pipe system in 0.4MPa in 814 r∙min-1 at different test points. Table 6. Pressure unevenness of the straight pipe +volume chamber pipeline system. Test point number
Simulation
Experiment
Absolute error
Relative errer
(%)
(%)
(%)
(%)
1
19.7
20.3
0.7
3.4
2
12.2
13.2
1.0
7.6
3
11.1
12.3
1.2
9.8
5. Conclusion In this paper, the numerical simulation and experimental research of the large pulsating are carried out in a reciprocating compressor. Based on the one-dimensional unsteady flow theory, the model of the single straight pipeline system, the straight pipe +volume chamber pipeline system and the straight pipe + reducer pipeline system are established. The simulation is programing. On the condition of different exhaust pressures, different rotate speeds and different piping systems, the waveforms of the simulation results and the experimental results are in good agreement. And the relative errors of the pressure unevenness are below 10%. The simulation model is valid, which can be used in analyzing the pulsation of the reciprocating compressors. References [1] ZhaoLin, XiongPo, WANG, ZanShe, FENG, & ShiYu, et al. (2011). Methods for large reciprocating compressor capacity control: a review based on pulse signal concept. Science Bulletin, 56(19), 1967-1974. [2] Chaoji CHEN, Maolin CAI, Zongxia JIAO. Vibration in pneumatic piping systems. Chinese Hydraulics & Pneumatics, 2007(1):3-7. [3] Xin, L. I., & Xiao, Q. G. (2008). Study on the pulsation of reciprocating compressor. Compressor Technology. [4] Chen, & Jing‐Bo. (2010). Lax‐wendroff and nyström methods for seismic modelling. Geophysical Prospecting, 57(6), 931-941. [5] Mériaux, C. A., Zemach, T., Kurzbesson, C. B., & Ungarish, M. (2016). The propagation of particulate gravity currents in a v-shaped triangular cross section channel: lock-release experiments and shallow-water numerical simulations. Physics of Fluids, 28(3), 785-110. [6] Yang, Bing, Jia-hai, & HUANG. (2016). The research of fluid-solid coupling vibration characteristics of axial piston pump based on the method of characteristic line-fast fourier transform. Machine Tool & Hydraulics(6), 47-52. [7] Liu Z, Soedel W. Using a gas dynamic model to predict the supercharging phenomenon in a variable speed compressor. The 1994 International Compressor Engineering Conference at Purdue: Purdue University, W Ladayette, IN, USA, 1994:491-497. [8] Liu Z, Soedel W. Performance study of a variable speed compressor with special attention to supercharging effect. The 1994 International Compressor Engineering Conference at Purdue: Purdue University, W Ladayette, IN, USA, 1994:499-506. [9] Brun K, Nored MG, Kurz R. Impact of piping impedance and acoustic characteristics on centrifugal compressor surge and operating range[J]. Journal of Engineering for Gas Turbines and Power, 2014, 137(3):032603. [10] Stosic, N. (2015). On heat transfer in screw compressors. International Journal of Heat & Fluid Flow, 51, 285-297.
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2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, 2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, Sydney, Australia Sydney, Australia
Numerical simulation and experimental validation of large pressure 15th International Symposium on District Heating and Numerical The simulation and experimental validation ofCooling large pressure pulsation in reciprocating compressor pulsation in reciprocating compressor Assessing theQuan feasibility using Chang the heat a,b b a Yuan Li , Kai , Rui Wuaof , Yunfeng , Beidemand-outdoor Guoa,*, Bo Zhangb a,b b a a a,* b Yuan Li ,function Kai Quan ,for RuiaWu , Yunfeng Chang , Bei Guodemand , Bo Zhang temperature long-term district heat forecast School of Energy and Power Engineering, Xi'an Jiaotong University, No.28, Xianning West Road, Xi'an, 710049, P.R. China a
Sinopec ChuanEngineering, to Eastern China Gas Pipeline Wuhan, 430020, P.R.710049, China P.R. China School of Energy andSiPower Xi'an Transmission Jiaotong University, No.28,Co.Ltd., Xianning West Road, Xi'an, a,b,c a a b c c b Sinopec Si Chuan to Eastern China Transmission Gas Pipeline Co.Ltd., Wuhan, 430020, P.R. China
a
b
I. Andrić
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
a Abstract IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300the Nantes, A numerical model basedSystèmes on the Énergétiques one-dimensional unsteady flow theory was established to simulate largeFrance pulsation of the reciprocating compressor. simulation model was consisting of theory the single pipeline system, the straight pipe +volume A numerical model based The on the one-dimensional unsteady flow wasstraight established to simulate large pulsation of the chamber pipeline system and straight pipe + reducer pipeline of system. The models solved by using the twopipe steps+volume method reciprocating compressor. Thethe simulation model was consisting the single straight were pipeline system, the straight and the method characteristics. To validate simulation model, the experiment measure was done chamber pipelineofsystem and the straight pipe +the reducer pipeline system. The modelstowere solvedthe bypressure using thepulsation two steps method inAbstract different exhaust pressures, different rotate speeds and different pipeline systems. The waveforms of the simulation and and the method of characteristics. To validate the simulation model, the experiment to measure the pressure pulsationresults was done thedifferent experimental results were in good agreement andand all of the relative errors of theThe pressure unevenness belowresults 10%. The in exhaust pressures, different rotate speeds different pipeline systems. waveforms of the were simulation and District heating networks are commonly addressed in the literature as established one of the most for decreasing the simulation resultsresults were consistent with agreement the experiment results. model this effective paper wassolutions accurate. the experimental were in good and all of theThe relative errors of the in pressure unevenness were below 10%. The greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat simulation results were consistent with the experiment results. The model established in this paper was accurate. to the changed climate conditions ©sales. 2018 Due The Authors. Published by Elsevier Ltd. and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. © 2019 The Authors. Published by Elsevier Ltd. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018 The Authors. by Elsevier Ltd. This an open under the CCthe BY-NC-ND license The ismain scopeaccess of thisarticle paper is toresponsibility assess feasibility of using(https://creativecommons.org/licenses/by-nc-nd/4.0/) the heat demand outdoor temperature function for heat demand Selection under of the scientific committee of the–2nd International Conference on Energy and This is an and openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of as thea2nd International Conference on Energyofand forecast. The district of Alvalade, located in Lisbon (Portugal), was used case study. The district is consisted 665 Power, ICEP2018. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Power, ICEP2018. renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Keywords: Type your keywords here, separated by semicolons ; compared with results from a dynamic heat demand model, previously developed and validated by the authors. Keywords: Type your keywords here, separated by semicolons ; The results showed that when only weather change is considered, the margin of error could be acceptable for some applications error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.(the Introduction scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1. Introduction The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the The reciprocating is widely used induring the industry and season daily life to supercharge and conveyofthe gas. The decrease in the numbercompressor of heating hours of 22-139h the heating (depending on the combination weather and The reciprocating compressor is widely used in the industry and daily life to supercharge and convey the gas.on The results show the reciprocating compressor possesses some characters, including high thermal efficiency, good renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending the results reciprocating compressor possesses characters, including high thermal efficiency, good versatility andthe much application and so could on [1]. advancement of the compressor and an increase coupledshow scenarios). The values suggested beWith used the to some modify the function parameters for technology the scenarios considered, and versatility much of application and socompressors on [1]. Withhave the advancement the competitiveness. compressor technology andcompressors an increase demand production, the demand low-speed gradually lostoftheir Thus, the improve for theand accuracy heat estimations.
demand for flow production, therotate low-speed have lost in their the compressors with heavy and high speedcompressors have become the gradually main device thecompetitiveness. chemical and oilThus, industry. In practical © 2017 The flow Authors. by Elsevier Ltd. with heavy andPublished high rotate speed have the main device inThe thelarge chemical and oil In practical production, the high-speed compressors havebecome large pressure pulsation. pulsation hasindustry. much disadvantage. Peer-review under responsibility of the power Scientific Committee of The 15th Symposium onhas District production, high-speed compressors have large and pressure pulsation. The large pulsation much disadvantage. For example,the it makes the indicated increase the gas flowInternational decrease. And it accelerates the Heating wear ofand the gas Cooling. For example, it makes the indicated power increase and the gas flow decrease. And it accelerates the wear of the gas
Keywords:©Heat Forecast; Climatebychange 1876-6102 2018demand; The Authors. Published Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1876-6102 © 2018 The Authors. Published by Elsevier Ltd. Selection under responsibility of the scientific of the 2nd International Conference on Energy and Power, ICEP2018. This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 10.1016/j.egypro.2019.02.212
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Nomenclature U R X Z L0 p u ρ x t f
dimensionless velocity dimensionless density dimensionless distance dimensionless time reference length pressure velocity density distance time friction coefficient
valve and shorten life of the crankshafts. Therefore, it is of great significance to study the generation mechanism, to predict the changed trend and to master the effective method to control the pressure pulsation. There are two main methods for analyzing the pressure pulsation, one is the plane wave theory, and the other is the one-dimensional unsteady flow theory [2]. The plane wave theory method cannot fully describe the complex phenomenon in the pipeline. In addition, the airflow parameters in the pipeline are constant rather than the actual values, which leads to the low accuracy of the calculation results. The one-dimensional unsteady flow theory does not ignore the nonlinear factors when establishing the governing equation of gas flow in the pipeline, and also considers the influence of friction between the gas and the inner wall as well as the actual gas property [3]. More scholars have experimentally maintain that the unsteady flow theory is more in line with the actual situation, especially on the condition of large pulsation. Wendroff and Lax [4] proposed the Lax-Wendroff finite difference method to solve the gas flow equations, which serves as a theoretical underpinning for solving the one-dimensional unsteady compressible flow equations. Richtwyer and Morton[5] proposed a two-step Lax-Wendroff method, which greatly improves the computing power in the simulation. Besides, the characteristic line method of the uniform entropy correction theory is experimentally proved that it is in line with the actual situation[6]. A numerical method combines the two method is used widely to solve the one-dimensional unsteady flow equations: the method of characteristics is used on the boundary, and the Lax-Wendroff two-step method is used inside the pipeline. Most of the scholars use this method to simulate the airflow pulsation. For example, Liu and Sodel[7, 8] study the gas column resonance pressurization phenomenon of the variable speed compressor by this theory; Brun[9] write the pulsation calculation program by using this method, and analyzes the influence of the acoustic impedance and acoustic characteristics of the pipeline on the airflow pulsation. Stosic[10] used this method to enable the clearance size of a screw compressor for start-up and steady running conditions to be determined. Based on the one-dimensional unsteady flow theory, this paper establishes a model of the reciprocating compressor based on the method which combines the method of characteristics and the Lax-Wendroff two-step method. A program is written to simulate the pressure pulsation in 3 systems, the single straight pipeline, the straight pipe +volume chamber pipeline and the straight pipe + reducer pipeline. The experiments are also carried out to validate the simulation model in different exhaust pressures, different rotate speeds and different pipeline system. 2. Equations and solution method When the diameter of the pipeline is much smaller than the length of the pipeline, it can be considered that all of the parameters on any section are equal. So the flow can be simplified into the one-dimensional flow. So the fluid element can be taken as the research object. The mass equation, the momentum equation and the energy equation form the control equations of the one-dimensional unsteady flow theory. Continuous equation:
Yuan Li et al. / Energy Procedia 160 (2019) 606–613 Author name / Energy Procedia 00 (2018) 000–000
608 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
(𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌) +
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
(𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌) +
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
3
𝜌𝜌𝜌𝜌 = 0
(1)
(𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌2 + 𝑝𝑝𝑝𝑝) = 𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌
(2)
Momentum equation: 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
Energy equation: 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
𝑉𝑉𝑉𝑉 +
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕
𝐺𝐺𝐺𝐺 = 𝐵𝐵𝐵𝐵
𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝑉𝑉 = �1 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 2 + 2
𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘−1
(3) 0 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 2 𝑓𝑓𝑓𝑓𝐿𝐿𝐿𝐿0 |𝑅𝑅𝑅𝑅|𝑅𝑅𝑅𝑅 2 −𝑅𝑅𝑅𝑅 𝐷𝐷𝐷𝐷 � , 𝐺𝐺𝐺𝐺 = �1 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 � , 𝐵𝐵𝐵𝐵 = � � 2 𝐿𝐿𝐿𝐿0 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝑃𝑃𝑃𝑃 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 3 𝐾𝐾𝐾𝐾−1 2 𝑎𝑎𝑎𝑎0
(4)
Those equations are the NPDE (Nonlinear Partial Differential Equations), which can’t get their analytic solutions and need to apply numerical method to reach the approximate solutions. In this paper, the two-step method and the characteristics method is combined to calculate the equations. The two-step method is used at the point inside the pipeline, and the method of characteristics is used at the boundary point. Figure 1 is the flow chart of the solution algorithm.
Fig. 1. Solution algorithm.
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3. Experiment Setup The experiment selected a V-type single stage reciprocating air compressor. The detailed parameters of the compressor are shown in the Table 1. One of the cylinders was chosen as the excitation source of the system. The pulsation pressure at the three points were measured in different exhaust pressures, different rotate speeds, and different pipeline system. Table 1. Parameters of the experimental compressor. Item
Value
Item
Value
Model
V-0.67/8
Rated rotate speed(r∙min-1)
980
Type
Single stage
Stroke(m)
0.06
Suction pressure(MPa)
1.013
Bore(m)
0.09
Rated Exhaust pressure(MPa)
0.8
Link length(m)
0.17
Rated power(kW)
5.5
Relative clearance volume(%)
6.9
The end of the pipeline is connected to a gasholder, the outlet of which installed a valve and a pressure gauge. The suction pressure is constant. The pressure inside the pipeline can be changed by adjusting the opening degree of the valve, and the pressure is set based on the pressure gauge. For this reason, the experiments reached different exhaust pressure. In order to measure the pressure pulsations in different rotate speeds, the motor of the compressor is connected to a frequency converter. By changing the output of the frequency converter, the operating rotate speeds varied too. Besides, a steel pipe with an inner diameter of 16mm and a length of 2m was selected. To facilitate the change of the piping system in the experiments, this pipe was cut into two 1m long pipes. One was connected to the exhaust, and the other one was connected to the gasholder. The two pipes were connected with three different part, including the connector, the volume chamber and the reducer, so they formed three pipeline system, the single straight pipeline system, the straight pipe +volume chamber pipeline system and the straight pipe + reducer pipeline system. The structural diagrams and the test points of the three systems are as shown in the Figure 2.
Fig. 2. Structural diagram.
4. Results 4.1. Different exhaust pressures A lot of experiments were done on different conditions. In this paper, the results of the single straight pipeline system in the rotate speed of 980r∙min-1 are shown. The exhaust pressures are 0.3MPa, 0.4MPa, 0.5MPa, respectively. The results of experiment and simulation are as follows in Figure 3. It can be seen that the waveforms of the simulation and the experiment are similar.
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(a) 0.3MPa, No.1
(b) 0.3MPa, No.2
(c) 0.3MPa, No.3
(d) 0.4MPa, No.1
(e) 0.4MPa, No.2
(f) 0.4MPa, No.3
(g) 0.5MPa, No.1
(h) 0.5MPa, No.2
(i) 0.5MPa, No.3
Fig. 3.Pressure pulsation of the single straight pipeline system in 980r∙min-1 in different exhaust pressure at different test points.
The Table 2 shows the comparison of the pressure unevenness between the simulation results and the experiment results at the test point 1. According to the pressure unevenness, the pressure pulsation in the experiment is large enough. Meanwhile the relative errors of the pressure unevenness between the simulation results and the experiment results in three different exhaust pressures are 7.91%, 1.00%, and 7.41%, all of which are below 10%. So in different exhaust pressures, the simulation results show a good agreement with the experiment results. Table 2. Pressure unevenness of the simulation and the experiment in different exhaust pressures. Exhaust pressure
Simulation
Experiment
Absolute error
Relative error
(MPa)
(%)
(%)
(%)
(%)
0.3
31.08
33.75
2.67
7.91
0.4
30.56
30.85
0.29
1.00
0.5
30.53
29.43
1.10
7.41
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4.2. Different rotate speeds The rotate speeds were set up as 369r/min, 496 r/min, 663 r/min, 814 r/min, 980 r/min and 1094 r/min. Figure 4 is the results of the test point 1 of the single straight pipe system when the exhaust pressure is 0.5 MPa. And in the Table 3, the pressure unevenness is also large enough. The relative errors are below basically 10. Obviously, not only the simulation waveforms are consistent with the experimental results, but also the relative errors of the pressure unevenness are small.
(a)369r∙min-1
(b) 496r∙min-1
(c)663 r∙min-1
(d)814r∙min-1
(e) 980r∙min-1
(f)1094 r∙min-1
Fig. 4.Pressure pulsation of the single straight pipeline system in 0.5MPa at test point 1 in different rotate speeds. Table 3. Pressure unevenness of the simulation and the experiment in different rotate speeds. Rotate speed
Simulation
Experiment
Absolute error
Relative error
(r∙min )
(%)
(%)
(%)
(%)
369
15.29
15.82
0.53
3.2
496
16.03
17.52
1.49
8.5
663
19.84
21.50
1.66
7.7
814
18.11
19.52
1.41
7.2
980
30.53
28.43
2.10
7.4
1094
23.71
25.12
2.41
5.6
-1
Besides, the paper analyses the maximum amplitudes of different frequencies in 663r∙min-1 by Fourier decomposition. It can be seen from the Table 4. The relative errors of the first three are small and the last five are big. But the max amplitudes of the last five are very small, which have little effect on the composed result. Thus, it is verified that in different rotate speeds, the results of the simulation are not only consistent with the experiment results in the time domain, but also in the frequency domain.
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Table 4. The max amplitude in different frequencies in 663r∙min-1. Simulation
Experiment
Relative
Frequency
Max amplitude
Frequency
Max amplitude
error
(Hz)
(kPa)
(Hz)
(kPa)
(%)
11.04
5.696
11.05
5.11
10.3
22.08
11.947
22.10
11.07
7.3
33.12
37.220
33.15
35.43
4.8
44.16
10.472
44.20
5.595
46.5
55.20
5.243
55.25
2.240
57.2
66.24
2.128
66.30
1.730
18.7
77.28
1.147
77.35
0.658
42.6
88.33
0.664
88.40
0.516
22.2
4.3. Different pipe systems In the experiment, three different pipeline systems are designed, which are the single straight pipeline system, the straight pipe +volume chamber pipeline system and the straight pipe + reducer pipeline system. The analysis of the single straight pipe system has been carried out in the chapter 4.2 and chapter 4.3. The Figure 5 shows the results of the straight pipe +volume chamber pipeline system. The exhaust pressure is 0.4 MPa and the rotate speed is 814r∙min-1. It can be seen the waveforms of the simulation results are well matched with the experiment results. The two waveforms have little difference in the phase and the amplitude.
(a)No.1
(b) No.2
(c)No.3
Fig. 5.Pressure pulsation of the straight pipe +volume chamber pipeline system in 0.4MPa in 814 r∙min-1 at different test points.
The Table 5 shows the pressure unevenness of the simulation and the experiment. The relative errors of the pressure unevenness between the simulation results and the experiment results at three test points are 9.7%, 2.4%, and 1.7%, respectively. All of the relative errors are below 10%. The simulation results is accurate in the straight pipe +volume chamber pipeline system. Table 5. Pressure unevenness of the straight pipe +volume chamber pipeline system. Test point number
Simulation
Experiment
Absolute error
Relative error
(%)
(%)
(%)
(%)
1
21.1
23.6
2.5
9.7
2
20.2
20.7
0.5
2.4
3
18.6
18.7
0.2
1.7
The Figure 6 is the result of the straight pipe + reducer pipe system. The exhaust pressure is 0.4 MPa and the rotational speed is 814r/min, too. The waveforms of the simulation results are similar to the test results. The Table 5
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shows the relative errors of the pressure unevenness between the simulation results and the experiment results at three test points are 3.4%, 7.6%, and 9.8%, respectively. All of the relative errors are below 10%. To sum up, the simulation model is valid in the straight pipe + reducer pipe system.
(a)No.1
(b) No.2
(c)No.3
Fig. 6.Pressure pulsation of the straight pipe + reducer pipe system in 0.4MPa in 814 r∙min-1 at different test points. Table 6. Pressure unevenness of the straight pipe +volume chamber pipeline system. Test point number
Simulation
Experiment
Absolute error
Relative errer
(%)
(%)
(%)
(%)
1
19.7
20.3
0.7
3.4
2
12.2
13.2
1.0
7.6
3
11.1
12.3
1.2
9.8
5. Conclusion In this paper, the numerical simulation and experimental research of the large pulsating are carried out in a reciprocating compressor. Based on the one-dimensional unsteady flow theory, the model of the single straight pipeline system, the straight pipe +volume chamber pipeline system and the straight pipe + reducer pipeline system are established. The simulation is programing. On the condition of different exhaust pressures, different rotate speeds and different piping systems, the waveforms of the simulation results and the experimental results are in good agreement. And the relative errors of the pressure unevenness are below 10%. The simulation model is valid, which can be used in analyzing the pulsation of the reciprocating compressors. References [1] ZhaoLin, XiongPo, WANG, ZanShe, FENG, & ShiYu, et al. (2011). Methods for large reciprocating compressor capacity control: a review based on pulse signal concept. Science Bulletin, 56(19), 1967-1974. [2] Chaoji CHEN, Maolin CAI, Zongxia JIAO. Vibration in pneumatic piping systems. Chinese Hydraulics & Pneumatics, 2007(1):3-7. [3] Xin, L. I., & Xiao, Q. G. (2008). Study on the pulsation of reciprocating compressor. Compressor Technology. [4] Chen, & Jing‐Bo. (2010). Lax‐wendroff and nyström methods for seismic modelling. Geophysical Prospecting, 57(6), 931-941. [5] Mériaux, C. A., Zemach, T., Kurzbesson, C. B., & Ungarish, M. (2016). The propagation of particulate gravity currents in a v-shaped triangular cross section channel: lock-release experiments and shallow-water numerical simulations. Physics of Fluids, 28(3), 785-110. [6] Yang, Bing, Jia-hai, & HUANG. (2016). The research of fluid-solid coupling vibration characteristics of axial piston pump based on the method of characteristic line-fast fourier transform. Machine Tool & Hydraulics(6), 47-52. [7] Liu Z, Soedel W. Using a gas dynamic model to predict the supercharging phenomenon in a variable speed compressor. The 1994 International Compressor Engineering Conference at Purdue: Purdue University, W Ladayette, IN, USA, 1994:491-497. [8] Liu Z, Soedel W. Performance study of a variable speed compressor with special attention to supercharging effect. The 1994 International Compressor Engineering Conference at Purdue: Purdue University, W Ladayette, IN, USA, 1994:499-506. [9] Brun K, Nored MG, Kurz R. Impact of piping impedance and acoustic characteristics on centrifugal compressor surge and operating range[J]. Journal of Engineering for Gas Turbines and Power, 2014, 137(3):032603. [10] Stosic, N. (2015). On heat transfer in screw compressors. International Journal of Heat & Fluid Flow, 51, 285-297.