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The numerical analysis of the effect of geometrical factors on natural gas ejector performance
Applied Thermal Engineering 59 (2013) 21e29
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The numerical analysis of the effect of geometrical factors on natural gas ejector performance WeiXiong Chen, DaoTong Chong*, JunJie Yan, JiPing Liu State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an 710049, China
h i g h l i g h t s Numerical investigation is carried out to analyze the natural gas ejector. The influence of two main geometry factors on ejector performance is investigated. The CFD visualization is applied to analyze the flow field and mixing process inside the ejector.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 September 2012 Accepted 21 April 2013 Available online 6 May 2013
Supersonic ejectors are applied to increase production and recovery from mature oil and gas fields. Compared to compressors, natural gas ejectors are a cost-effective way to boost the production of low pressure natural gas wells. In this study, two main ejector geometrical factors, the primary nozzle exit position (NXP) and the mixing tube length to diameter ratio (R), are investigated based on the CFD technique. Additionally, these two geometrical factors are proved to be influential factors with respect to ejector performance, including not only the entrainment ratio but also the pressure ratio. The numerical results show that the optimum NXP for the entrainment ratio varies from 3.6 to 7.2 mm, but for the pressure ratio, it is in the range of 1.2e7.2 mm. The optimum value R decreases with increasing primary flow pressure, and the optimum R for the entrainment ratio varies from 2 to 8, but for the pressure ratio, it is in the range of 3e7. The CFD technique is found to be an effective performance predictor and also provides an insightful understanding of the flow and mixing process within the ejector. This study may provide a beneficial reference for the design of supersonic ejectors and may be helpful for further applications in boosting natural gas production. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Natural gas ejector Geometrical factors Entrainment ratio Pressure ratio
1. Introduction The use of ejectors is not new with respect to compressible fluids. Ejectors are simple mechanical devices, which can employ a high pressure motive stream to entrain and accelerate a low pressure secondary stream. Ejectors were first used by LeBlanc in France before 1901. Their first wave of popularity came in the early 1930s, particularly for use in air conditioners. Today, in light of the exhaustible nature of fossil energy sources and with ever-increasing awareness of the need to protect the environment, in addition to pressures to do so, ejectors have become the focus of renewed interest in many scientific areas. They have been widely used in the engineering fields, such as “jet augmentor wings” in the aerospace area [1,2] and heat pumps in district-heating systems [3]. Additionally, due to the problems of
* Corresponding author. Tel./fax: þ86 29 82665741. E-mail address: [email protected] (D. Chong). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.04.036
global warming and ozone depletion, one of the most popular applications is steam jet refrigeration [4e6]. Our primary interest in this paper is the use of supersonic ejectors in boosting the production of low pressure natural gas. Generally, the production and pressure of gas wells gradually decrease with extended production lifetime, or, what is more serious, these wells may even be abandoned. Thus, it is important to maintain the production and to obtain the maximum recovery from gas wells when their pressures fall below the pipeline pressure or the pressure of the processing system. To maintain the production of low pressure wells, natural gas compressors have conventionally been used; these compressors are bulky and costly to operate and maintain. In contrast, supersonic ejectors have several advantages, such as the lack of moving parts, the relatively low capital cost, the simplicity of operation, the reliability and the low maintenance cost. The most important benefit is that ejectors can be powered by the energy of the high pressure gas well itself, which is usually wasted through choke valves, to boost the natural gas production. Despite
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Nomenclature d G L m N NXP P R RNG S t u Pi
diameter (m) natural gas volume flow rate under standard conditions (104 m3 per day) length (m) natural gas mass flow rate (kg/s) pressure ratio (%) primary nozzle exit position pressure (MPa) mixing tube length to diameter ratio renormalization group generalised source time (s) entrainment ratio (%) axial pressure (MPa)
the fact that natural gas ejectors have so many advantages for boosting the productivity of low pressure natural gas wells, they are not widely used in the natural gas industry because of their demonstrated low performance under present conditions. Because both the operational conditions and geometries significantly affect the ejector performance, a deeper understanding of ejector working principles and entrainment features is essential for improving the performance of the overall system. The effect of geometry on the ejector performance has been analysed by different researchers. First, Keenan et al. [7] proposed a 1-D constant pressure mixing ejector theory for analysing the ejector performance. Later, this model was improved by considering a real gas and thermodynamic irreversibility [8]. Munday and Bagster [9] postulated a fictive throat or “effective area” located at some location inside the mixing chamber. They assumed that the primary flow fans out without mixing the induced flow after it is discharged from the exit of the nozzle, and the mixing of the two flows begins with a uniform pressure after the hypothetical throat. Based on their assumptions, Huang et al. [10] further assumed that constant pressure mixing occurs inside the constant area section of the ejector and then set up a model to predict the performance when the ejector is at critical operation. These theoretical models are helpful in analysing the influence of certain ejector geometries, such as the mixing tube diameter, on the ejector performance. However, the effects of other important geometries, such as the primary nozzle exit position (NXP) and the mixing tube length to diameter ratio R (R ¼ Lmt/dmt), are not reflected in those theoretical models due to the limitations associated with the 1-D flow simplification. Due to the significance of these effects (NXP and R) on the ejector performance, many researchers have paid attention to investigate NXP and R. Keenan et al. [8] and Huang and Chen [11] experimentally investigated the effect of NXP on ejector performance and reported that the entrainment ratio decreased as the primary nozzle was moved away from the mixing tube. However, Aphornratana and Eames [12] indicated that the entrainment ratio increased as the primary nozzle was moved away from the mixing tube. Based on their numerical results, Rusly et al. [13] reported only a small influence of NXP on the entrainment ratio. Pianthong et al. [14] investigated the performance of an ejector with NXP varying from 15 mm to 10 mm, and their numerical results showed that the entrainment ratio increased slightly as the NXP was moved further from the inlet section. However, an increasing number of researchers recognises that there is an optimal NXP for obtaining optimal operation [15]. For the parameter R, the experimental results from Havelka et al. [16] showed that the
Greek symbols G generalised diffusion coefficient ε turbulent dissipation rate (m2/s3) q inclination (deg) k turbulent kinetic energy (m2/s2) r density (kg/m3) n specific volume (m3/kg) f generalised variables Subscripts c back pressure d diffuser H high motive pressure L low induced pressure mc mixing chamber mt mixing tube t throat of the primary nozzle
entrainment ratio increased as R was increased and then reached a plateau when the ratio was larger than 6; the same conclusion was obtained by the numerical results in Ref. [17]. However, the numerical results of Pianthong et al. [14] and Varga et al. [18] indicated that the constant area section length had no influence on the entrainment ratio but influenced the value of the critical back pressure. From these studies, it is clear that the optimum NXP and mixing tube length varied with the operational condition, and it is difficult to find a universal value that meets all of the conditions. As mentioned above, many investigations have been carried out to study the effects of geometrical factors on the ejector performance in various applications, but the studies on natural gas ejectors are relatively sparse. Sarshar et al. [19,20] indicated that the jet pumps were proven to be a cost effective manner in which to boost production and recovery from low pressure gas wells. In their experimental results, the entrainment ratio reached 78% when the high pressure, low pressure and discharged pressure were 5.5 MPa, 1.6 MPa and 2.0 MPa, respectively. Melancon [21] and Andreussi [22] also investigated its operational mechanism and economics. Recently, Chong et al. [23] carried out geometrical optimisation on the design condition to obtain the maximum pressure ratio. Chen et al. [24] made the geometrical optimisation to gain the maximum entrainment ratio on the design operation, and the effect of diffuser on the performance also involved which was ignored in Ref. [23]. In the application of a natural gas ejector, there are two important parameters; namely, they are the entrainment ratio and the pressure ratio, with the definitions given as follows:
Entrainment ratio : u ¼ mL =mH
(1)
Pressure ratio : N ¼ ðPc PL Þ=ðPH Pc Þ ¼ ðPH PL Þ=ðPH Pc Þ 1
(2)
As mentioned above, it is highly desirable to obtain the maximum total recovery from all gas wells and to maintain their production in the industry. Thus, an important issue is the boosting of production from lower pressure gas wells. This means that the optimum operation of an ejector should be defined as (1) the maximum entrainment ratio and (2) the maximum pressure ratio. However, previous studies mainly were focused on the maximum entrainment ratio. To deepen the understanding of ejector performance, the present paper is focused on the effects of the geometrical factors, NXP and R, on the entrainment ratio and pressure ratio.
W. Chen et al. / Applied Thermal Engineering 59 (2013) 21e29 Table 1 The properties of methane. Parameters
Unit
Values
Density Specific heat Thermal conductivity Viscosity Molecular weight
kg/m3 J/(kg K) W/(m K) kg/(m s) kg/kmol
Ideal gas model 2222 0.0332 1.087 105 16.04303
In the studies mentioned above, ejectors have been applied in natural gas production, but little has been reported regarding the geometrical factors of the natural gas ejector, even though these factors have tremendous influence on the ejector performance. Therefore, it is substantially important to investigate the trends and to give guidelines for NXP and R under a range of operational conditions and different geometries. In the present study, the two main geometrical factors of the natural gas ejector (NXP and R) are investigated numerically based on CFD. The work will be beneficial for the design of supersonic natural gas ejectors and will be helpful for the further applications of supersonic ejectors in natural gas fields. 2. The CFD model and validation 2.1. The CFD model In the present work, the commercial software Fluent 6.3.26 is used as the CFD solver. The flow inside the ejector is governed by the compressible steady-state turbulent form of the flow conservation equations. The flow and heat transfer processes in the natural gas ejector are considered to be axisymmetric, and the physical model could be treated as two-dimensional in cylindrical coordinates. Therefore, the ejector geometry establishes a 2-D domain in the Gambit 2.3. 16 with 21,167 cells, and the mesh is denser for the high velocity region. For variable density flows, the Favre averaged NaviereStokes equations are the most suitable in this work. The governing equations can be written as follows:
vðrfÞ=vt þ divðrV fÞ ¼ divðGgradfÞ þ S
(3)
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where 4 denotes different parameters, such as the velocity, the temperature, k, and ε. For different 4, the generalised diffusion coefficient G and the generalised source S have different expressions, which can be found in the literature [25]. Additionally, the RNG keε model is employed to simulate the turbulent flow, which has been proven to be a better predictor of performance than other models [13,17]. The working fluid in the model is methane. The density of the methane is obtained using the ideal gas equation. The other properties, such as the specific heat, the thermal conductivity, the viscosity and the molecular weight, are held constant, as listed in Table 1. Standard wall function is used in the near wall treatment, which gives reasonably accurate results for a wall bounded with a very high Reynolds number flow [14,15]. The boundary conditions of the primary flow and induced flow inlets are set as the “pressure inlet” conditions, and the outlet of the ejector is adopted as the “pressure outlet” condition. 2.2. Experimental validation The natural gas ejector has been applied in the Changqing gas field, China, to boost the production of low pressure natural gas. A typical ejector is presented in Fig. 1; this ejector consists of five main parts, including a primary nozzle (A), a secondary nozzle (B), a mixing chamber (C), a mixing tube (D) and a diffuser (E). Additionally, the important geometrical factors of the ejector are listed in Table 2, according to the research in Refs. [23,24]. Fig. 2 is a schematic diagram of the natural gas ejector typically installed in industrial applications. The motive gas from the high pressure well is first heated by the heater and then is accelerated into a supersonic state through the primary nozzle. The induced gas from the low pressure well is also first heated by the heater and then is entrained into the supersonic ejector through the secondary nozzle. The two streams are well-mixed in the mixing chamber and mixing tube, and then the mixed fluid is decelerated and recompressed in the diffuser to match the pipeline and transportation requirements. The flow rates of the induced and discharged natural gas are measured because of their relatively low pressures, and the flow rate of the motive gas is calculated as follows:
Fig. 1. A schematic diagram of the test rig.
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Table 2 The design parameters of the natural gas ejector. Parameters
Symbols
Unit
Result
Primary pressure Induced pressure Discharged pressure Throat diameter of primary nozzle Diameter of mixing tube Length of mixing tube Length of primary nozzle Inclination angle of diffuser Inclination angle of mixing chamber
PH PL Pc dt dmt Lmt LH
MPa MPa MPa mm mm mm mm deg deg
13 2 5.2 4.6 8.2 41 58 1.43 14
GH ¼ Gd GL
q2 q1
(4)
Then, the measured flow rates are converted to volume flow rates under the standard condition, and the mass entrainment ratio is also defined as
u ¼ mL =mH ¼ GL =GH
(5)
An uncertainty analysis is performed by applying the estimation method proposed by Moffat [26]. In the experiment, the temperature is measured by a K-type thermocouple (i.e., nickel chromiume nickel silicon) with an accuracy of 0.5 K. The gas flow rate is measured by Tancy vortex precession flow rates to 1% accuracy. The range of the gas flowmeter measuring the induced gas is (0e 4) 104 m3 per day, while the induced gas flow rate varies from 0.5 to 2.3 104 m3 per day in the experiment. The range of the gas flowmeter measuring the discharged gas is (0e10) 104 m3 per day, while the discharged gas flow rate is in the range of (4.4e 7.4) 104 m3 per day, The entrainment ratio is calculated by Equations (4) and (5), so the uncertainty of entrainment ratio is less than 13.5%. All the pressure transducers have the same accuracy of 1%, but different measuring ranges. The range of the pressure transducer measuring the induced gas and discharged gas is 0e 10 MPa, with the induced gas pressure varying from 1 to 5 MPa and the discharged gas pressure keeping constant at 5.2 MPa. The range of the pressure transducer measuring the motive gas is 0e20 MPa,
Fig. 3. The deviation comparison of entrainment ratios between the experimental and simulated results.
while the motive gas pressure varies from 10 to 14 MPa. The pressure ratio is calculated by Equation (2), so the uncertainty of pressure ratio is less than 15.9%. Fig. 3 presents the entrainment ratio obtained by experimental ejector (the design parameters are listed in Table 2) and by CFD simulation in which the motive pressure varies from 12 MPa to 14 MPa, the induced pressure is in the range of 2e4.5 MPa, and the back pressure is held constant at the value of 5.2 MPa. The results show that the numerical results agree well with the experimental data with a maximum deviation less than 11.06%. 3. Results and discussions Numerical method is applied to investigate the effects of NXP and R on the ejector performance, 39 ejectors with different geometrical factors are established in gambit. They are divided into six groups, as shown in Table 3, for the convenience of analysis.
Fig. 2. The schematic of the test system of the supersonic natural gas ejector.
W. Chen et al. / Applied Thermal Engineering 59 (2013) 21e29
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Table 3 The geometric variations of the ejector. Ejector groups
dmt (mm)
NXP (mm)
R
Group 1 Group2 Group 3 Group 4 Group 5 Group 6
8.2 8.2 8.2 8.2 8.2 8.2
0, 1.2, 2.4, 3.6, 4.8, 6, 7.2 0, 1.2, 2.4, 3.6, 4.8, 6, 7.2 0, 1.2, 2.4, 3.6, 4.8, 6, 7.2 0 3.6 6.0
3 5 7 2, 3, 4, 5, 6, 7, 8, 9, 10 2, 3, 4, 5, 6, 7, 8, 9, 10 2, 3, 4, 5, 6, 7, 8, 9, 10
Generally, in the operation of natural gas ejectors, the back pressure is determined by the transportation pipeline back pressure; hence the pressure is usually constant, and in the present paper, it is equal to 5.2 MPa. To achieve maximum recovery from the gas wells, the performance is enhanced when the ejector operates with lower induced pressure. According to Equation (2), the maximum pressure ratio is obtained by achieving the lowest induced pressure or the maximum back pressure. Therefore, the value of the maximum back pressure could lead to the maximum pressure ratio while the primary and induced pressures are constant. 3.1. The effect of NXP on the ejector performance In the investigation, the ejector performance is presented as the NXP is varied at different operations. Additionally, the results are shown in Fig. 4aec. As shown in Fig. 4a (group 1), the entrainment ratio first decreases at NXP ¼ 1.2 mm and then increases linearly with NXP when the primary pressure is 12 MPa. Then, as R is increased to 5, the entrainment ratio nearly increases with the NXP, as shown in Fig. 4b (group 2). However, when R is 7 in Fig. 4c (group 3), the entrainment ratio increases and reaches a maximum value when the NXP is larger than 3.6 mm. When the primary pressure is 13 MPa and R is 3, the entrainment ratio increases linearly with NXP. Then, with increasing mixing tube length, the entrainment ratio first increases to a peak value at NXP ¼ 3.6 mm and then slightly decreases. When the primary pressure is 14 MPa, the entrainment ratio always reaches a maximum value at NXP ¼ 4.8 mm and then slightly decreases. The pressure ratio always has an optimum NXP value of 1.2 mm for different R when the primary pressure is 14 MPa. For a primary pressure of 13 MPa, the pressure ratio also has an optimum NXP value at 3.6 mm when R is less than 7. However, the pressure ratio reaches a maximum value at NXP ¼ 2.4 mm when R is equal to 7, as shown in Fig. 4c. When the primary pressure is 12 MPa, the pressure ratio increases with the NXP for different values of R. The CFD visualisation is applied to simulate the flow field inside the ejector. When the primary flow discharges into the mixing chamber, it continues to expand because of the higher pressure than that in the mixing chamber. The first series of oblique shocks and expansion waves are induced, which is called the “diamond wave” or “shock train”. The high velocity difference between the two streams induces the semi-separation, and the shear stress layer is presented. Then, the converging duct for the induced flow is formed between the wall and the primary flow jet core [9]. The shear stress accelerates the induced flow; conversely, the shear mixing and the viscosity of the fluid cause the diamond wave to decay. Subsequently, the primary flow jet core is at a lower supersonic velocity (compared with the velocity at the exit of the nozzle), and the diamond wave violence is reduced. This leads to a relatively smooth jet core, and the secondary flow is accelerated to a sonic velocity and then choked. Later, either at the beginning of the diffuser or at the end of the mixing tube, which is usually called
Fig. 4. The effect of the primary nozzle exit position on the ejector performances of (a) group 1, (b) group 2 and (c) group 3.
the “shock position,” a non-uniform stream produces the second series of oblique shock waves. Furthermore, the static pressure gradually recovers to the back pressure. Additionally, the place corresponding to the sonic velocity is usually named the “choking position”, and the annulus area between the primary jet core and the wall at this position is called the “effective area”, which is widely used in 1-D model theory [10,17,27]. The entrainment ratio increases with increasing “effective area”. As shown in Fig. 5, when NXP ¼ 0 mm, it is clear that the sonic line is not very close to the wall, and the entrainment ratio is still sensitive to the back
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Fig. 5. The sonic line in the mixing tube for different NXP (ejectors in group 2).
Fig. 7. The static pressure distribution along the centreline for different NXP (ejectors in group 2).
pressure, hence the ejector works on the sub-critical mode (has been checked). When the NXP increases, the sonic line changes. As shown in the figure, the sonic line location is more closer to the wall, and there exists a maximum value with the increase of NXP, which means that the ejector is at critical operation. It can be clearly seen that the annulus effective area for induced flow between the primary jet core and the wall of NXP ¼ 3.6 mm is larger than that of NXP ¼ 7.2 mm. These findings can explain that the entrainment ratio when NXP ¼ 3.6 mm is larger than that when NXP ¼ 7.2 mm. Fig. 6 presents the flow visualisation inside the ejector, and Fig. 7 shows the axial pressure distribution for different NXPs on ejector group 2. When the primary flow discharges into the mixing chamber, it continues to expand because of the higher pressure than that in the mixing chamber. The first series of oblique shocks and expansion waves are induced, which is called the “diamond wave” or “shock train”. Either at the beginning of the diffuser or at the end of the mixing tube, which is usually called the “shock position”, a non-uniform stream produces the second series of
oblique shock waves. Because of these two series of oblique shock waves, there exists drastic pressure oscillation. As shown in the figures, when NXP equals 0, the second series of oblique shocks has combined with the first series of oblique shocks. This means that the back flow information can travel back and affect the upstream flow field, so the induced flow is no longer choked, and the ejector is on sub-critical operation. Compared with the operation when NXP is 3.6 and 7.2 mm, it could easily be determined that the second series of oblique shocks is more flattened when NXP ¼ 3.6 mm than that when NXP ¼ 7.2 mm. This means that better mixing happens inside the ejector and causes the smaller velocity difference between the primary jet flow and the induced flow. Thus, the mixed stream is more uniform. Therefore, a reduced compression effect is required, and the shock position moves downstream. As shown in the figures, the shock position when NXP ¼ 3.6 mm is closer to the entrance of the diffuser than that when NXP ¼ 7.2 mm. In conclusion, the ejector with NXP ¼ 3.6 mm can be obtained at a higher critical back pressure and pressure ratio than that with NXP ¼ 7.2 mm.
Fig. 6. The mach number field for different NXP (ejectors in group 2).
W. Chen et al. / Applied Thermal Engineering 59 (2013) 21e29
3.2. The effect of R on the ejector performance Fig. 8a (group 4) shows the relationship of the ejector performance with the throat length at different motive pressures. As shown in Fig. 8a, the entrainment ratio and pressure ratio first increase and then reach a plateau with the increase of R. The optimal R value for the maximum entrainment ratio is 9 when the motive pressure is 12 MPa, but decreases to 3 when the motive pressure is 14 MPa. However, the optimal value for the maximum pressure ratio is in the range of 3e8.
Fig. 8. The effect of mixing tube length on the ejector performances of (a) group 4, (b) group 5 and (c) group 6.
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Fig. 8b (group 5) and 8c (group 6) present the effect of R on the performance of the ejector at different values of NXP. In Fig. 8b and c, the same tendency has been found for different NXP. It can be identified from Fig. 8b that the optimal values for the entrainment ratio and pressure ratio are in the range of 3e8 and 3e7, respectively. In Fig. 8c, the optimal values for the entrainment ratio and pressure ratio are in the range of 2e8 and 3e7, respectively. From Fig. 8aec, it can be concluded that there exists an optimal R for the entrainment ratio and pressure ratio, but the optimal value decreases with the increase of motive pressure. To gain further insight into this phenomenon, the CFD visualisation is used to analyse the flow field inside the ejector in group 5. Fig. 9 shows the sonic line location of the ejector, while the length of the mixing tube varies. When R ¼ 3, it is clear that the sonic line is not very close to the wall, and the entrainment ratio is still sensitive to the back pressure, so the ejector works in the subcritical mode. When the length of the mixing tube is increased, the sonic line location will change. As shown in the figure, the sonic line location reaches a maximum value. The annulus effective area of the induced flow of R ¼ 5 is similar to that of R ¼ 7, as shown in Fig. 9. It can be easily concluded that the entrainment ratio remains constant when R is larger than a certain value. Fig. 10 presents the flow visualisation inside the ejector, and Fig. 11 shows the axial pressure distribution for different mixing tube lengths. The second series of oblique shocks travels upstream and combines with the first series of oblique shocks, as shown in Fig. 11, when R ¼ 3, the ejector is in sub-critical operation. With the increase of mixing tube length, the better mixing effect happens between the primary and induced flows because of the longer contact time and leads to the smaller speed difference between the primary and induced flows. Thus, the mixed stream is more uniform, and the ejector can be operated at a higher back pressure and can gain a higher pressure ratio. However, when R is greater than 5, the pressure ratio decreases. As shown in Fig. 11, the shock position when R ¼ 5 is closer to the entrance of the diffuser than that when R ¼ 10. This is because, as the mixing tube length is increased, the pressure loss increases due to the interaction of the flow with the viscous boundary layer in the ejector. Additionally, it is believed that the loss increases with the mixing tube length. This situation leads to the upstream movement of the shock position. In
Fig. 9. The sonic line in the mixing tube for different mixing tube lengths (ejectors in group 5).
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Fig. 10. The mach number field for different mixing tube lengths (ejectors in group 5).
2. The mixing tube length not only affects on the pressure ratio but also on the entrainment ratio. When the primary pressure is 12 MPa, the entrainment ratio and pressure ratio are sensitive with the mixing tube length. For the other two primary pressures, the entrainment ratio and pressure ratio increase up and reach a plateau with the increase of mixing tube length. Additionally, the optimum value R decreases with the increase of primary flow pressure, and the optimum R for entrainment ratio is varied from 2 to 8, but for the pressure ratio, it is in the range of 3e7.
Fig. 11. The static pressure distribution along the centreline for different mixing tube lengths (ejectors in group 5).
These results show that the numerical simulation approach provides an effective alternative in the study of ejector performance. Further, the CFD visualisation also provides a detailed flow field and a good explanation of the flow structure inside the ejector. In conclusion, the geometrical factors (NXP and R) should be carefully and properly selected to obtain the optimal ejector operation. The results offered in this paper may provide a beneficial reference for the design and assist in further applications in boosting low pressure natural gas production using the supersonic ejector. Acknowledgements
conclusion, an ejector with the length to diameter ratio of 5 can obtain a higher critical back pressure and pressure ratio than that with the length to diameter ratio of 10. 4. Conclusions In this work, the two main geometrical factors: primary nozzle exit position (NXP) and mixing tube length to diameter ratio (R) are investigated on natural gas ejector for boosting low pressure natural gas production by the CFD technique. The effects of these two geometrical factors on the ejector performance (entrainment ratio and pressure ratio) are carefully studied under different operating conditions, and the CFD visualisation is applied to analyse the detailed flow field inside the ejector. The main results can be summarised as follows: 1. NXP plays an important role on the ejector performance, it should be properly determined to make the ejector work on the optimal operation. Normally, there is always an optimum NXP. The optimum value decreases with the increase of primary flow pressure, and the optimum NXP for entrainment ratio is varied from 3.6 to 7.2 mm, but for the pressure ratio, it is in the range of 1.2e7.2 mm.
This work was supported by the National Natural Science Foundation of China (No. 51006081 and No. 51125027) and the National Basic Research Program of China (973 Program) (No. 2009CB219803). References [1] M. Alperin, J.J. Wu, Thrust augmenting ejector, part I, AIAA J. 21 (10) (1983) 1428e1436. [2] M. Alperin, J.J. Wu, Thrust augmenting ejector, part II, AIAA J. 21 (12) (1983) 1698e1706. [3] J.J. Yan, S.F. Shao, J.P. Liu, Z. Zhang, Experiment and analysis on performance of steam-driven jet injector for district-heating system, Appl. Therm. Eng. 25 (2005) 1153e1167. [4] D.W. Sun, I.W. Eames, Recent developments in the design theories and applications of ejectorsda review, J. Inst. Energy 68 (1995) 65e79. [5] K. Chunnanond, S. Aphornratana, Ejectors: applications in refrigeration technology, Renewable Sustainable Energy Rev. 8 (2004) 129e155. [6] Y. Bartosiewicz, Z. Aidoun, Y. Mercadier, Numerical assessment of ejector operation for refrigeration applications based on CFD, Appl. Therm. Eng. 26 (2006) 604e612. [7] J.H. Keenan, E.P. Neumann, A simple air ejector, J. Appl. Mech. Trans. ASME 64 (1942) A75eA81. [8] J.H. Keenan, E.P. Neumann, F. Lustwerk, An investigation of ejector design by analysis and experiment, J. Appl. Mech. Trans. ASME 17 (1950) 299e309. [9] J.T. Munday, D.F. Bagster, A new ejector theory applied to steam jet refrigeration, Ind. Eng. Chem. Process Des. Dev. 16 (1977) 442e449.
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[19] M.M. Sarshar, Boosting production from low-pressure oil and gas fields: a revolution in hydrocarbon production, Philos. Trans. R. Soc. A 357 (1999) 921e941. [20] M.M. Sarshar, N. Beg, I. Andrews, The Applications of Jet Pumps as a Costeffective Way to Enhance Gas Production and Recovery, in: Proceedings, Indonesian Petroleum Association Twenty-Ninth Annual Convention & Exhibition, Oct. 2003. [21] K. Melancon, J. Nunn, Ejector vapor recovery unit reliably and economically recovers vent and flash gas, World Oil 225 (11) (2004) 75e76. [22] P. Andreussi, S. Sodini, V. Faluomi, P. Ciandri, A. Ansiati, F. Paone, C. Battaia, G. De Ghetto, in: Multiphase Ejector to Boost Production: First Application in the Gulf of Mexico, Offshore Technology Conference (May 2003). Houston, Texas, USA. [23] D.T. Chong, J.J. Yan, G.S. Wu, J.P. Liu, Structural optimization and experimental investigation of supersonic ejectors for boosting low pressure natural gas, Appl. Therm. Eng. 29 (2009) 2799e2807. [24] W.X. Chen, D.T. Chong, J.J. Yan, J.P. Liu, Numerical optimization on the geometrical factors of natural gas ejectors, Int. J. Therm. Sci. 50 (8) (2011) 1554e1561. [25] W.Q. Tao, Numerical Heat Transfer, second ed., Xi’an Jiaotong University Press, Xi’an, 2001. [26] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1) (1988) 3e17. [27] A. Hemidi, F. Henry, S. Leclaire, J.M. Seynhaeve, Y. Bartosiewicz, CFD analysis of a supersonic air ejector. Part I: experimental validation of single-phase and two-phase operation, Appl. Therm. Eng. 29 (2009) 2990e2998.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
The numerical analysis of the effect of geometrical factors on natural gas ejector performance WeiXiong Chen, DaoTong Chong*, JunJie Yan, JiPing Liu State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an 710049, China
h i g h l i g h t s Numerical investigation is carried out to analyze the natural gas ejector. The influence of two main geometry factors on ejector performance is investigated. The CFD visualization is applied to analyze the flow field and mixing process inside the ejector.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 September 2012 Accepted 21 April 2013 Available online 6 May 2013
Supersonic ejectors are applied to increase production and recovery from mature oil and gas fields. Compared to compressors, natural gas ejectors are a cost-effective way to boost the production of low pressure natural gas wells. In this study, two main ejector geometrical factors, the primary nozzle exit position (NXP) and the mixing tube length to diameter ratio (R), are investigated based on the CFD technique. Additionally, these two geometrical factors are proved to be influential factors with respect to ejector performance, including not only the entrainment ratio but also the pressure ratio. The numerical results show that the optimum NXP for the entrainment ratio varies from 3.6 to 7.2 mm, but for the pressure ratio, it is in the range of 1.2e7.2 mm. The optimum value R decreases with increasing primary flow pressure, and the optimum R for the entrainment ratio varies from 2 to 8, but for the pressure ratio, it is in the range of 3e7. The CFD technique is found to be an effective performance predictor and also provides an insightful understanding of the flow and mixing process within the ejector. This study may provide a beneficial reference for the design of supersonic ejectors and may be helpful for further applications in boosting natural gas production. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Natural gas ejector Geometrical factors Entrainment ratio Pressure ratio
1. Introduction The use of ejectors is not new with respect to compressible fluids. Ejectors are simple mechanical devices, which can employ a high pressure motive stream to entrain and accelerate a low pressure secondary stream. Ejectors were first used by LeBlanc in France before 1901. Their first wave of popularity came in the early 1930s, particularly for use in air conditioners. Today, in light of the exhaustible nature of fossil energy sources and with ever-increasing awareness of the need to protect the environment, in addition to pressures to do so, ejectors have become the focus of renewed interest in many scientific areas. They have been widely used in the engineering fields, such as “jet augmentor wings” in the aerospace area [1,2] and heat pumps in district-heating systems [3]. Additionally, due to the problems of
* Corresponding author. Tel./fax: þ86 29 82665741. E-mail address: [email protected] (D. Chong). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.04.036
global warming and ozone depletion, one of the most popular applications is steam jet refrigeration [4e6]. Our primary interest in this paper is the use of supersonic ejectors in boosting the production of low pressure natural gas. Generally, the production and pressure of gas wells gradually decrease with extended production lifetime, or, what is more serious, these wells may even be abandoned. Thus, it is important to maintain the production and to obtain the maximum recovery from gas wells when their pressures fall below the pipeline pressure or the pressure of the processing system. To maintain the production of low pressure wells, natural gas compressors have conventionally been used; these compressors are bulky and costly to operate and maintain. In contrast, supersonic ejectors have several advantages, such as the lack of moving parts, the relatively low capital cost, the simplicity of operation, the reliability and the low maintenance cost. The most important benefit is that ejectors can be powered by the energy of the high pressure gas well itself, which is usually wasted through choke valves, to boost the natural gas production. Despite
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W. Chen et al. / Applied Thermal Engineering 59 (2013) 21e29
Nomenclature d G L m N NXP P R RNG S t u Pi
diameter (m) natural gas volume flow rate under standard conditions (104 m3 per day) length (m) natural gas mass flow rate (kg/s) pressure ratio (%) primary nozzle exit position pressure (MPa) mixing tube length to diameter ratio renormalization group generalised source time (s) entrainment ratio (%) axial pressure (MPa)
the fact that natural gas ejectors have so many advantages for boosting the productivity of low pressure natural gas wells, they are not widely used in the natural gas industry because of their demonstrated low performance under present conditions. Because both the operational conditions and geometries significantly affect the ejector performance, a deeper understanding of ejector working principles and entrainment features is essential for improving the performance of the overall system. The effect of geometry on the ejector performance has been analysed by different researchers. First, Keenan et al. [7] proposed a 1-D constant pressure mixing ejector theory for analysing the ejector performance. Later, this model was improved by considering a real gas and thermodynamic irreversibility [8]. Munday and Bagster [9] postulated a fictive throat or “effective area” located at some location inside the mixing chamber. They assumed that the primary flow fans out without mixing the induced flow after it is discharged from the exit of the nozzle, and the mixing of the two flows begins with a uniform pressure after the hypothetical throat. Based on their assumptions, Huang et al. [10] further assumed that constant pressure mixing occurs inside the constant area section of the ejector and then set up a model to predict the performance when the ejector is at critical operation. These theoretical models are helpful in analysing the influence of certain ejector geometries, such as the mixing tube diameter, on the ejector performance. However, the effects of other important geometries, such as the primary nozzle exit position (NXP) and the mixing tube length to diameter ratio R (R ¼ Lmt/dmt), are not reflected in those theoretical models due to the limitations associated with the 1-D flow simplification. Due to the significance of these effects (NXP and R) on the ejector performance, many researchers have paid attention to investigate NXP and R. Keenan et al. [8] and Huang and Chen [11] experimentally investigated the effect of NXP on ejector performance and reported that the entrainment ratio decreased as the primary nozzle was moved away from the mixing tube. However, Aphornratana and Eames [12] indicated that the entrainment ratio increased as the primary nozzle was moved away from the mixing tube. Based on their numerical results, Rusly et al. [13] reported only a small influence of NXP on the entrainment ratio. Pianthong et al. [14] investigated the performance of an ejector with NXP varying from 15 mm to 10 mm, and their numerical results showed that the entrainment ratio increased slightly as the NXP was moved further from the inlet section. However, an increasing number of researchers recognises that there is an optimal NXP for obtaining optimal operation [15]. For the parameter R, the experimental results from Havelka et al. [16] showed that the
Greek symbols G generalised diffusion coefficient ε turbulent dissipation rate (m2/s3) q inclination (deg) k turbulent kinetic energy (m2/s2) r density (kg/m3) n specific volume (m3/kg) f generalised variables Subscripts c back pressure d diffuser H high motive pressure L low induced pressure mc mixing chamber mt mixing tube t throat of the primary nozzle
entrainment ratio increased as R was increased and then reached a plateau when the ratio was larger than 6; the same conclusion was obtained by the numerical results in Ref. [17]. However, the numerical results of Pianthong et al. [14] and Varga et al. [18] indicated that the constant area section length had no influence on the entrainment ratio but influenced the value of the critical back pressure. From these studies, it is clear that the optimum NXP and mixing tube length varied with the operational condition, and it is difficult to find a universal value that meets all of the conditions. As mentioned above, many investigations have been carried out to study the effects of geometrical factors on the ejector performance in various applications, but the studies on natural gas ejectors are relatively sparse. Sarshar et al. [19,20] indicated that the jet pumps were proven to be a cost effective manner in which to boost production and recovery from low pressure gas wells. In their experimental results, the entrainment ratio reached 78% when the high pressure, low pressure and discharged pressure were 5.5 MPa, 1.6 MPa and 2.0 MPa, respectively. Melancon [21] and Andreussi [22] also investigated its operational mechanism and economics. Recently, Chong et al. [23] carried out geometrical optimisation on the design condition to obtain the maximum pressure ratio. Chen et al. [24] made the geometrical optimisation to gain the maximum entrainment ratio on the design operation, and the effect of diffuser on the performance also involved which was ignored in Ref. [23]. In the application of a natural gas ejector, there are two important parameters; namely, they are the entrainment ratio and the pressure ratio, with the definitions given as follows:
Entrainment ratio : u ¼ mL =mH
(1)
Pressure ratio : N ¼ ðPc PL Þ=ðPH Pc Þ ¼ ðPH PL Þ=ðPH Pc Þ 1
(2)
As mentioned above, it is highly desirable to obtain the maximum total recovery from all gas wells and to maintain their production in the industry. Thus, an important issue is the boosting of production from lower pressure gas wells. This means that the optimum operation of an ejector should be defined as (1) the maximum entrainment ratio and (2) the maximum pressure ratio. However, previous studies mainly were focused on the maximum entrainment ratio. To deepen the understanding of ejector performance, the present paper is focused on the effects of the geometrical factors, NXP and R, on the entrainment ratio and pressure ratio.
W. Chen et al. / Applied Thermal Engineering 59 (2013) 21e29 Table 1 The properties of methane. Parameters
Unit
Values
Density Specific heat Thermal conductivity Viscosity Molecular weight
kg/m3 J/(kg K) W/(m K) kg/(m s) kg/kmol
Ideal gas model 2222 0.0332 1.087 105 16.04303
In the studies mentioned above, ejectors have been applied in natural gas production, but little has been reported regarding the geometrical factors of the natural gas ejector, even though these factors have tremendous influence on the ejector performance. Therefore, it is substantially important to investigate the trends and to give guidelines for NXP and R under a range of operational conditions and different geometries. In the present study, the two main geometrical factors of the natural gas ejector (NXP and R) are investigated numerically based on CFD. The work will be beneficial for the design of supersonic natural gas ejectors and will be helpful for the further applications of supersonic ejectors in natural gas fields. 2. The CFD model and validation 2.1. The CFD model In the present work, the commercial software Fluent 6.3.26 is used as the CFD solver. The flow inside the ejector is governed by the compressible steady-state turbulent form of the flow conservation equations. The flow and heat transfer processes in the natural gas ejector are considered to be axisymmetric, and the physical model could be treated as two-dimensional in cylindrical coordinates. Therefore, the ejector geometry establishes a 2-D domain in the Gambit 2.3. 16 with 21,167 cells, and the mesh is denser for the high velocity region. For variable density flows, the Favre averaged NaviereStokes equations are the most suitable in this work. The governing equations can be written as follows:
vðrfÞ=vt þ divðrV fÞ ¼ divðGgradfÞ þ S
(3)
23
where 4 denotes different parameters, such as the velocity, the temperature, k, and ε. For different 4, the generalised diffusion coefficient G and the generalised source S have different expressions, which can be found in the literature [25]. Additionally, the RNG keε model is employed to simulate the turbulent flow, which has been proven to be a better predictor of performance than other models [13,17]. The working fluid in the model is methane. The density of the methane is obtained using the ideal gas equation. The other properties, such as the specific heat, the thermal conductivity, the viscosity and the molecular weight, are held constant, as listed in Table 1. Standard wall function is used in the near wall treatment, which gives reasonably accurate results for a wall bounded with a very high Reynolds number flow [14,15]. The boundary conditions of the primary flow and induced flow inlets are set as the “pressure inlet” conditions, and the outlet of the ejector is adopted as the “pressure outlet” condition. 2.2. Experimental validation The natural gas ejector has been applied in the Changqing gas field, China, to boost the production of low pressure natural gas. A typical ejector is presented in Fig. 1; this ejector consists of five main parts, including a primary nozzle (A), a secondary nozzle (B), a mixing chamber (C), a mixing tube (D) and a diffuser (E). Additionally, the important geometrical factors of the ejector are listed in Table 2, according to the research in Refs. [23,24]. Fig. 2 is a schematic diagram of the natural gas ejector typically installed in industrial applications. The motive gas from the high pressure well is first heated by the heater and then is accelerated into a supersonic state through the primary nozzle. The induced gas from the low pressure well is also first heated by the heater and then is entrained into the supersonic ejector through the secondary nozzle. The two streams are well-mixed in the mixing chamber and mixing tube, and then the mixed fluid is decelerated and recompressed in the diffuser to match the pipeline and transportation requirements. The flow rates of the induced and discharged natural gas are measured because of their relatively low pressures, and the flow rate of the motive gas is calculated as follows:
Fig. 1. A schematic diagram of the test rig.
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Table 2 The design parameters of the natural gas ejector. Parameters
Symbols
Unit
Result
Primary pressure Induced pressure Discharged pressure Throat diameter of primary nozzle Diameter of mixing tube Length of mixing tube Length of primary nozzle Inclination angle of diffuser Inclination angle of mixing chamber
PH PL Pc dt dmt Lmt LH
MPa MPa MPa mm mm mm mm deg deg
13 2 5.2 4.6 8.2 41 58 1.43 14
GH ¼ Gd GL
q2 q1
(4)
Then, the measured flow rates are converted to volume flow rates under the standard condition, and the mass entrainment ratio is also defined as
u ¼ mL =mH ¼ GL =GH
(5)
An uncertainty analysis is performed by applying the estimation method proposed by Moffat [26]. In the experiment, the temperature is measured by a K-type thermocouple (i.e., nickel chromiume nickel silicon) with an accuracy of 0.5 K. The gas flow rate is measured by Tancy vortex precession flow rates to 1% accuracy. The range of the gas flowmeter measuring the induced gas is (0e 4) 104 m3 per day, while the induced gas flow rate varies from 0.5 to 2.3 104 m3 per day in the experiment. The range of the gas flowmeter measuring the discharged gas is (0e10) 104 m3 per day, while the discharged gas flow rate is in the range of (4.4e 7.4) 104 m3 per day, The entrainment ratio is calculated by Equations (4) and (5), so the uncertainty of entrainment ratio is less than 13.5%. All the pressure transducers have the same accuracy of 1%, but different measuring ranges. The range of the pressure transducer measuring the induced gas and discharged gas is 0e 10 MPa, with the induced gas pressure varying from 1 to 5 MPa and the discharged gas pressure keeping constant at 5.2 MPa. The range of the pressure transducer measuring the motive gas is 0e20 MPa,
Fig. 3. The deviation comparison of entrainment ratios between the experimental and simulated results.
while the motive gas pressure varies from 10 to 14 MPa. The pressure ratio is calculated by Equation (2), so the uncertainty of pressure ratio is less than 15.9%. Fig. 3 presents the entrainment ratio obtained by experimental ejector (the design parameters are listed in Table 2) and by CFD simulation in which the motive pressure varies from 12 MPa to 14 MPa, the induced pressure is in the range of 2e4.5 MPa, and the back pressure is held constant at the value of 5.2 MPa. The results show that the numerical results agree well with the experimental data with a maximum deviation less than 11.06%. 3. Results and discussions Numerical method is applied to investigate the effects of NXP and R on the ejector performance, 39 ejectors with different geometrical factors are established in gambit. They are divided into six groups, as shown in Table 3, for the convenience of analysis.
Fig. 2. The schematic of the test system of the supersonic natural gas ejector.
W. Chen et al. / Applied Thermal Engineering 59 (2013) 21e29
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Table 3 The geometric variations of the ejector. Ejector groups
dmt (mm)
NXP (mm)
R
Group 1 Group2 Group 3 Group 4 Group 5 Group 6
8.2 8.2 8.2 8.2 8.2 8.2
0, 1.2, 2.4, 3.6, 4.8, 6, 7.2 0, 1.2, 2.4, 3.6, 4.8, 6, 7.2 0, 1.2, 2.4, 3.6, 4.8, 6, 7.2 0 3.6 6.0
3 5 7 2, 3, 4, 5, 6, 7, 8, 9, 10 2, 3, 4, 5, 6, 7, 8, 9, 10 2, 3, 4, 5, 6, 7, 8, 9, 10
Generally, in the operation of natural gas ejectors, the back pressure is determined by the transportation pipeline back pressure; hence the pressure is usually constant, and in the present paper, it is equal to 5.2 MPa. To achieve maximum recovery from the gas wells, the performance is enhanced when the ejector operates with lower induced pressure. According to Equation (2), the maximum pressure ratio is obtained by achieving the lowest induced pressure or the maximum back pressure. Therefore, the value of the maximum back pressure could lead to the maximum pressure ratio while the primary and induced pressures are constant. 3.1. The effect of NXP on the ejector performance In the investigation, the ejector performance is presented as the NXP is varied at different operations. Additionally, the results are shown in Fig. 4aec. As shown in Fig. 4a (group 1), the entrainment ratio first decreases at NXP ¼ 1.2 mm and then increases linearly with NXP when the primary pressure is 12 MPa. Then, as R is increased to 5, the entrainment ratio nearly increases with the NXP, as shown in Fig. 4b (group 2). However, when R is 7 in Fig. 4c (group 3), the entrainment ratio increases and reaches a maximum value when the NXP is larger than 3.6 mm. When the primary pressure is 13 MPa and R is 3, the entrainment ratio increases linearly with NXP. Then, with increasing mixing tube length, the entrainment ratio first increases to a peak value at NXP ¼ 3.6 mm and then slightly decreases. When the primary pressure is 14 MPa, the entrainment ratio always reaches a maximum value at NXP ¼ 4.8 mm and then slightly decreases. The pressure ratio always has an optimum NXP value of 1.2 mm for different R when the primary pressure is 14 MPa. For a primary pressure of 13 MPa, the pressure ratio also has an optimum NXP value at 3.6 mm when R is less than 7. However, the pressure ratio reaches a maximum value at NXP ¼ 2.4 mm when R is equal to 7, as shown in Fig. 4c. When the primary pressure is 12 MPa, the pressure ratio increases with the NXP for different values of R. The CFD visualisation is applied to simulate the flow field inside the ejector. When the primary flow discharges into the mixing chamber, it continues to expand because of the higher pressure than that in the mixing chamber. The first series of oblique shocks and expansion waves are induced, which is called the “diamond wave” or “shock train”. The high velocity difference between the two streams induces the semi-separation, and the shear stress layer is presented. Then, the converging duct for the induced flow is formed between the wall and the primary flow jet core [9]. The shear stress accelerates the induced flow; conversely, the shear mixing and the viscosity of the fluid cause the diamond wave to decay. Subsequently, the primary flow jet core is at a lower supersonic velocity (compared with the velocity at the exit of the nozzle), and the diamond wave violence is reduced. This leads to a relatively smooth jet core, and the secondary flow is accelerated to a sonic velocity and then choked. Later, either at the beginning of the diffuser or at the end of the mixing tube, which is usually called
Fig. 4. The effect of the primary nozzle exit position on the ejector performances of (a) group 1, (b) group 2 and (c) group 3.
the “shock position,” a non-uniform stream produces the second series of oblique shock waves. Furthermore, the static pressure gradually recovers to the back pressure. Additionally, the place corresponding to the sonic velocity is usually named the “choking position”, and the annulus area between the primary jet core and the wall at this position is called the “effective area”, which is widely used in 1-D model theory [10,17,27]. The entrainment ratio increases with increasing “effective area”. As shown in Fig. 5, when NXP ¼ 0 mm, it is clear that the sonic line is not very close to the wall, and the entrainment ratio is still sensitive to the back
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Fig. 5. The sonic line in the mixing tube for different NXP (ejectors in group 2).
Fig. 7. The static pressure distribution along the centreline for different NXP (ejectors in group 2).
pressure, hence the ejector works on the sub-critical mode (has been checked). When the NXP increases, the sonic line changes. As shown in the figure, the sonic line location is more closer to the wall, and there exists a maximum value with the increase of NXP, which means that the ejector is at critical operation. It can be clearly seen that the annulus effective area for induced flow between the primary jet core and the wall of NXP ¼ 3.6 mm is larger than that of NXP ¼ 7.2 mm. These findings can explain that the entrainment ratio when NXP ¼ 3.6 mm is larger than that when NXP ¼ 7.2 mm. Fig. 6 presents the flow visualisation inside the ejector, and Fig. 7 shows the axial pressure distribution for different NXPs on ejector group 2. When the primary flow discharges into the mixing chamber, it continues to expand because of the higher pressure than that in the mixing chamber. The first series of oblique shocks and expansion waves are induced, which is called the “diamond wave” or “shock train”. Either at the beginning of the diffuser or at the end of the mixing tube, which is usually called the “shock position”, a non-uniform stream produces the second series of
oblique shock waves. Because of these two series of oblique shock waves, there exists drastic pressure oscillation. As shown in the figures, when NXP equals 0, the second series of oblique shocks has combined with the first series of oblique shocks. This means that the back flow information can travel back and affect the upstream flow field, so the induced flow is no longer choked, and the ejector is on sub-critical operation. Compared with the operation when NXP is 3.6 and 7.2 mm, it could easily be determined that the second series of oblique shocks is more flattened when NXP ¼ 3.6 mm than that when NXP ¼ 7.2 mm. This means that better mixing happens inside the ejector and causes the smaller velocity difference between the primary jet flow and the induced flow. Thus, the mixed stream is more uniform. Therefore, a reduced compression effect is required, and the shock position moves downstream. As shown in the figures, the shock position when NXP ¼ 3.6 mm is closer to the entrance of the diffuser than that when NXP ¼ 7.2 mm. In conclusion, the ejector with NXP ¼ 3.6 mm can be obtained at a higher critical back pressure and pressure ratio than that with NXP ¼ 7.2 mm.
Fig. 6. The mach number field for different NXP (ejectors in group 2).
W. Chen et al. / Applied Thermal Engineering 59 (2013) 21e29
3.2. The effect of R on the ejector performance Fig. 8a (group 4) shows the relationship of the ejector performance with the throat length at different motive pressures. As shown in Fig. 8a, the entrainment ratio and pressure ratio first increase and then reach a plateau with the increase of R. The optimal R value for the maximum entrainment ratio is 9 when the motive pressure is 12 MPa, but decreases to 3 when the motive pressure is 14 MPa. However, the optimal value for the maximum pressure ratio is in the range of 3e8.
Fig. 8. The effect of mixing tube length on the ejector performances of (a) group 4, (b) group 5 and (c) group 6.
27
Fig. 8b (group 5) and 8c (group 6) present the effect of R on the performance of the ejector at different values of NXP. In Fig. 8b and c, the same tendency has been found for different NXP. It can be identified from Fig. 8b that the optimal values for the entrainment ratio and pressure ratio are in the range of 3e8 and 3e7, respectively. In Fig. 8c, the optimal values for the entrainment ratio and pressure ratio are in the range of 2e8 and 3e7, respectively. From Fig. 8aec, it can be concluded that there exists an optimal R for the entrainment ratio and pressure ratio, but the optimal value decreases with the increase of motive pressure. To gain further insight into this phenomenon, the CFD visualisation is used to analyse the flow field inside the ejector in group 5. Fig. 9 shows the sonic line location of the ejector, while the length of the mixing tube varies. When R ¼ 3, it is clear that the sonic line is not very close to the wall, and the entrainment ratio is still sensitive to the back pressure, so the ejector works in the subcritical mode. When the length of the mixing tube is increased, the sonic line location will change. As shown in the figure, the sonic line location reaches a maximum value. The annulus effective area of the induced flow of R ¼ 5 is similar to that of R ¼ 7, as shown in Fig. 9. It can be easily concluded that the entrainment ratio remains constant when R is larger than a certain value. Fig. 10 presents the flow visualisation inside the ejector, and Fig. 11 shows the axial pressure distribution for different mixing tube lengths. The second series of oblique shocks travels upstream and combines with the first series of oblique shocks, as shown in Fig. 11, when R ¼ 3, the ejector is in sub-critical operation. With the increase of mixing tube length, the better mixing effect happens between the primary and induced flows because of the longer contact time and leads to the smaller speed difference between the primary and induced flows. Thus, the mixed stream is more uniform, and the ejector can be operated at a higher back pressure and can gain a higher pressure ratio. However, when R is greater than 5, the pressure ratio decreases. As shown in Fig. 11, the shock position when R ¼ 5 is closer to the entrance of the diffuser than that when R ¼ 10. This is because, as the mixing tube length is increased, the pressure loss increases due to the interaction of the flow with the viscous boundary layer in the ejector. Additionally, it is believed that the loss increases with the mixing tube length. This situation leads to the upstream movement of the shock position. In
Fig. 9. The sonic line in the mixing tube for different mixing tube lengths (ejectors in group 5).
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W. Chen et al. / Applied Thermal Engineering 59 (2013) 21e29
Fig. 10. The mach number field for different mixing tube lengths (ejectors in group 5).
2. The mixing tube length not only affects on the pressure ratio but also on the entrainment ratio. When the primary pressure is 12 MPa, the entrainment ratio and pressure ratio are sensitive with the mixing tube length. For the other two primary pressures, the entrainment ratio and pressure ratio increase up and reach a plateau with the increase of mixing tube length. Additionally, the optimum value R decreases with the increase of primary flow pressure, and the optimum R for entrainment ratio is varied from 2 to 8, but for the pressure ratio, it is in the range of 3e7.
Fig. 11. The static pressure distribution along the centreline for different mixing tube lengths (ejectors in group 5).
These results show that the numerical simulation approach provides an effective alternative in the study of ejector performance. Further, the CFD visualisation also provides a detailed flow field and a good explanation of the flow structure inside the ejector. In conclusion, the geometrical factors (NXP and R) should be carefully and properly selected to obtain the optimal ejector operation. The results offered in this paper may provide a beneficial reference for the design and assist in further applications in boosting low pressure natural gas production using the supersonic ejector. Acknowledgements
conclusion, an ejector with the length to diameter ratio of 5 can obtain a higher critical back pressure and pressure ratio than that with the length to diameter ratio of 10. 4. Conclusions In this work, the two main geometrical factors: primary nozzle exit position (NXP) and mixing tube length to diameter ratio (R) are investigated on natural gas ejector for boosting low pressure natural gas production by the CFD technique. The effects of these two geometrical factors on the ejector performance (entrainment ratio and pressure ratio) are carefully studied under different operating conditions, and the CFD visualisation is applied to analyse the detailed flow field inside the ejector. The main results can be summarised as follows: 1. NXP plays an important role on the ejector performance, it should be properly determined to make the ejector work on the optimal operation. Normally, there is always an optimum NXP. The optimum value decreases with the increase of primary flow pressure, and the optimum NXP for entrainment ratio is varied from 3.6 to 7.2 mm, but for the pressure ratio, it is in the range of 1.2e7.2 mm.
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