Numerical Investigation on the Performance of ... - Science Direct

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ScienceDirect Energy Procedia 105 (2017) 4997 – 5004

The 8th International Conference on Applied Energy – ICAE2016

Numerical investigation on the performance of different primary nozzle structures in the supersonic ejector Kangkang Xue, Kaihua Li, Weixiong Chen*, Daotong Chong, Junjie Yan State Key Laboratory of Multiphase Flow in Power Engineering Xi’anJiaotongUniversity,Xi’an, Shaanxi, 710049, P.R. China

Abstract Computational fluid dynamics (CFD) technique is employed to investigate the effect of primary nozzle structures on the supersonic ejector performance. The performance of the supersonic ejectors with three different nozzle structures, including conical nozzle, petalage nozzle and crenation nozzle, have been compared under the same conditions. Compared with the ejector equipped with the conical nozzle, the entrainment ratio of petalage nozzle is slightly smaller, while the critical back pressure increases by 5.2%. Just the opposite, the entrainment ratio of crenation nozzle is slightly higher, and the critical back pressure would decrease by 2.1%. In addition, the effects of primary/induced fluid pressure on the flow field (pressure and Mach number along the ejector centerline) are observed and analyzed to explain the mixing process occurring inside the ejector. It finds out that the shape of the mixing layer in the supersonic ejector with different nozzles is different. © 2017 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy.

Keywords: Supersonic ejector; CFD; Primary nozzle; Entrainment ratio; Critical back pressure

1. Introduction Supersonic ejectors are economically feasible and environmentally-friendly gas dynamics devices, which could utilize the augmentation of momentum and energy from a supersonic primary flow to entrain and pump a secondary flow. Due to the simplicity in construction and operation, ejectors have been widely used in many regions, such as power, chemical, refrigeration, power plant and so on[1]. There are two main parameters to evaluate the ejector performance, named as entrainment ratio and critical back pressure. Entrainment ratio is the mass flow-ratio of the secondary flow to the primary flow, and critical back pressure means the final pressure with the ejector working at its maximum capability. For a long time, computational fluid dynamics (CFD) technique has proved to be an efficient tool in analyzing flow field and calculating ejector performance. There are also some investigations on the influence of the nozzle geometry on the ejector performance. Chang and Chen[2] experimentally apply a petal nozzle to enhance the performance of a steam-jet refrigeration system. Their experimental results indicated that the performance of an ejector with a petal nozzle was better than that with a conical nozzle

*Corresponding author. Tel.:86-29-82667753; Fax:86-29-82667753 E-mail address:[email protected].

1876-6102 © 2017 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. doi:10.1016/j.egypro.2017.03.1000

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Kangkang Xue et al. / Energy Procedia 105 (2017) 4997 – 5004

for a larger AR number. Narabayshi et al.[3] studied the flow of single and multi-nozzle jet pumps numerically and experimentally. It was shown that the peak efficiency of the improved jet pumps will be 36%. Ruangtrakoon et al. [4] investigated the effect of the primary nozzle geometries on the performance of an ejector used in the steam jet refrigeration cycle using CFD. It was found that shock’s position of the mixed fluid and the expansion angle of the primary fluid jet stream within the mixing chamber played a very important role on the ejector performance. Kong et al.[5] employed numerical simulations to investigate the effects of a chevron nozzle within the supersonic ejector. The results turned out that with a chevron nozzle in the supersonic ejector, the entrainment ratio was improved 14.8% in average, and the pressure recovery was increased 8.5% in average. As mentioned above, primary nozzle structures have an influence on entrainment performance both at critical mode and sub-critical mode operation, as well as the critical back pressure. Based on the method of numerical simulation, the impact of primary nozzle structure, including conical nozzle, petalage nozzle and crenation nozzle, on ejector performance would be analyzed. Then, a better understanding of the flow behavior inside the ejector, which has directly greater dependence in the performance of the ejector, will be acquired. Nomenclature X

axial distance, mm

P

pressure, MPa

Greek symbols Ȧ

entrainment ratio

Subscripts H

high-pressure/primary flow

L

low-pressure/secondary flow

B

back pressures

2. Numerical model CFD technique was divided into two main parts: building a physical model and solving the set of mathematical equations. The physical model is created and divided as grid elements using commercial software, Gambit 2.3. For solving the equations, the commercial CFD software, FLUENT 6.3 was used to solve the mathematical model to simulate the flow inside ejector. 2.1 physical model Fig.1 shows the schematic diagram of the ejector. In the Fig.2, The geometrical configurations of the three primary nozzles are shown, including (a) conical nozzle, (b) petalage nozzle, (c) crenation nozzle, and the parameters are presented in Table 1. These nozzles only differ in the outlet-shape of primary nozzle, but the other parameters of these ejectors are the same. For example, these nozzles have the same area ratio, the constant area throat of mixing chamber to that of the nozzle throat, which equals to 3.24, and the throat diameter of primary nozzle is 10.0 mm. The length of the ejector throat equals six times its diameter (18.0 mm). And NXP is all 6 mm. More importantly, the total exit area of the three different nozzles remains the same such that the average exit Mach number (according to the isentropic area relation) is the same. As is shown in Fig. 3, due to the symmetry of the structure, the grid elements with a quarter of the area of the ejector are created in the form of a quadrilateral of about 2 million elements. The

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dense grid elements are focused on the area where the expanded wave and the mixing behaviors of two fluids are expected to occur. In addition, the near wall boundary layer is also defined so that the flow close to the ejector’s wall was more realistic.

Fig. 1 schematic diagram of the ejector Table 1the main design parameters of the ejector Parameters inlet diameter of primary nozzle Dp1/mm

Result 20

Throat diameter of primary nozzle Dp2/mm

10

outlet diameter of primary nozzle Dp3/mm

11.2

Throat diameter of mixing chamber Dm/mm

18

outlet diameter of diffuser Dd/mm

34

Contraction length of primary nozzle Lp1/mm

25

throat length of primary nozzle Lp2/mm

5

diffusion length of primary nozzle Lp3/mm

7

NXP/mm

6

Length of mixing chamber Lm/mm

108

Length of diffuser Ld/mm

182

contraction Angle of Mixing chamberĮ/ °

14.8

angle of diffuserȕ/ °

2.5

Fig. 2. Photographs of different nozzle structures of the supersonic nozzles. (a) Conical nozzle. (b) Petalage nozzle. (c) Crenation nozzle.

Fig. 3. Mesh generation for natural gas ejector.

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2.2 Modeling

Approach

The CFD software -Fluent 6.3 version is adopted to deal with the compressible Navier-Stokes equations governing the supersonic ejector flow field. The governing equations could be listed as follows˖ μ(ߩ‫)׎‬Τ߲‫ ݐ‬+ ݀݅‫(ݒ݅݀ = )׎ܸߩ(ݒ‬Ȟ݃‫ )׎݀ܽݎ‬+ ܵ In above equations, ‫ ׎‬represents different parameters, for example the velocity, the temperature, and so RQ7KHJHQHUDOL]HGGLIIXVLRQFRHIILFLHQWīDQGWKHJHQHUDOL]HGVRXUFH6KDYHWKHUHODWHGH[SUHVVLRQVIRU the corresponding ‫׎‬, which can be found in the literature [6]. In this study, the working fluid in the model is air, the density of which is obtained using the ideal gas equation. The density-based implicit solver is selected to solve the governing equations, which have been proven to be suitable for a supersonic flow field [7] and the flow is set based on steady-state. Additionally, RNG k-İPRGHOLVHPSOR\HGWRVLPXODWHWKHWXUEXOHQWIORZ$QGWKHVWDQGDUGZDOOIXQFWLRQLVDGRSWHGWR deal with the flow characteristic adjacent to the wall [8]. The boundary conditions of the primary/induced flow inlets are set as the “pressure inlet” conditions, and the outlet of the ejector is adopted as the “pressure outlet” condition. All discretizations are selected as second order upwind schemes. In this study, the solution is considered as converged when the two following converging criteria are satisfied. On the one hand, it had to be shown that mass flow rates at the induced flow inlets in the calculation domain are stable. On the other hand, every residual of the calculation must be lower than 10-6 after 50,000 iterations) in order to ensure that the solution from the simulation is accurate. 3 Results and discussion The three different operational modes for ejectors are the critical mode, sub-critical mode and back flow mode. Both critical back pressure DQG HQWUDLQPHQW UDWLR Ȧ DUH WKH PRVW LPSRUWDQW LQGLFDWRUV IRU evaluating the operation performance of ejectors. The higher critical back pressure and entrainment ratios imply a better ejector performance. The entrainment ratio keeps a constant value in the critical mode while it decreases rapidly with the increase of the back pressure in the subcritical mode, which can be seen in Fig. 4. Meanwhile, Fig. 4 depicts the relations between entrainment ratio and back pressure with different primary nozzles, when the primary flow pressure PH is 0.45MPa and the secondary flow pressure PL is 0.12MPa. It could find out that entrainment ratio of the ejector with a crenation nozzle has the maximum value, while entrainment ratio of the ejector a petalage nozzle has the minimum value, when they are always under the critical mode condition. However, critical back pressure of the ejector with a petalage nozzle is much higher than that of the ejector with both a conical nozzle and a crenation nozzle, and critical back pressure of the ejector with a conical nozzle is much higher than that of the ejector with a crenation nozzle. Meanwhile, critical back pressure has the opposite variation, the ejector with a petalage nozzle is 5.2% bigger than that of the ejector with a conical nozzle, while critical back pressure of the ejector with a crenation nozzle is 2.1% smaller than that of the ejector with a conical nozzle. Further, in order to understand the three-dimensional flow structure of the ejector, images are selected at eight surfaces located at X=37, 50, 70, 90, 110, 130, 150 and 170mm downstream of the ejector exit, which capture critical sections of the flow picture seen in the stream wise section. Fig. 5 depicts contours of Mach number distribution in the mixing chamber of the ejectors (starting from nozzle exit X=37mm) between the conical nozzle, the petalage nozzle and the crenation nozzle. When the primary pressure is 0.45MPa, and the induced pressure is 0.12MPa, and the back pressure is 0.18MPa. The mixing layer from the conical supersonic nozzle (Fig. 5(a)) is visible as circular rings which expand in width, as well as thickness according to the growth of the primary flow boundary and the thickness of the mixing layer. For the petalage nozzle (Fig. 5(b)), the mixing layer is also visible as the shape of “+”, which becomes more


and more bigger along the ejector centerline, until the angle of the shape of “+”contacting with the wall of the ejector. Consider the crenation nozzle (Fig. 5(b)), when X=50mm and 70 mm, the mixing layer is visible as the shape of the crenation. However, when away from X=90mm, the mixing layer become from the shape of the crenation to that of square. Thus, in the near field of the nozzle, the variation of the shape produces significant perturbations to the mixing layer which can lead to enhancement of entrainment and mixing.

)LJ(QWUDLQPHQWUDWLRȦYHUVXVEDFNSUHVVXUHIRUGLIIHUHQWQR]]OHV

Fig. 5. Contours of Mach number distribution in the mixing chamber of the ejectors away from nozzle exit.

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Meanwhile, Fig. 6 depicts pressure distribution along the ejector centerline and Fig. 7 depicts Mach number distribution along the ejector centerline. In Fig.6 and Fig.7, the region between the nozzle exit and the ejector throat inlet, which is usually called as NXP, both the Mach number and static pressure at the ejector centerline fluctuate while the flow flows through the mixing chamber. According to Fig.6 and Fig.7, it is observed that the fluctuation level of the Mach number and static pressure at nozzle exit with a crenation nozzle is greater than that with both a conical nozzle and a petalage nozzle, which enhances the performance of the entrainment of the ejector with a crenation nozzle. On the other hand, in Fig. 7, by compare with the ejector with a conical nozzle, the Mach number of the ejector exit with a petalage nozzle is 29.7% smaller and the Mach number of the ejector exit with a crenation nozzle is 7.5% bigger. This indicates that the decrease of the Mach number of the ejector exit can promote the pressure recovery of the ejector diffuser. Therefore, the critical back pressure of the ejector with a petalage nozzle could largen.

Fig. 6.Pressure distribution along the ejector centreline.

Fig. 7.Mach number distribution along the ejector centreline.

As mentioned in Introduction, the ejector with a crenation nozzle could enhance the entrainment performance at the critical mode. Thus, it's necessary to study and obtain the impact of the ejector performance with different nozzle under both different primary inlet pressures and different induced inlet pressures. Fig.8 presents that the entrainment ratio varies with different induced pressures under different nozzles. When PH=0.45MPa, PB=0.18MPa, with the increase of PL, the entrainment ratio always increases. Meanwhile, when PL=0.10MPa, 0.12 MPa and 0.14MPa respectively, entrainment ratio of the ejector with a crenation nozzle is slightly higher for the ejector with a conical nozzle and a petalage nozzle. Fig.9depicts the variation of the entrainment ratio varies with different primary pressures under different


nozzles. When PL =0.12MPa, PB=0.18MPa, with the increase of PH, the entrainment ratio always decreases. At the same time, when PH=0.40MPa, 0.45 MPa and 0.50MPa respectively, entrainment ratio of the ejector with a crenation nozzle is also slightly higher for the ejector with a conical nozzle and a petalage nozzle.

Fig. 8 Variation of entrainment ratio different induced inlet pressures with different nozzles

Fig. 9 Variation of entrainment ratio different primary inlet pressures with different nozzles

4 Conclusions In the present study, the computational fluid dynamics (CFD) technique has been used to analyze and calculate ejector performance with different nozzles. Meanwhile, the detailed flow field inside the ejector has been analyzed through the CFD visualization. The influence with different nozzle under both different primary inlet pressures and different induced inlet pressures is also analyzed. The main conclusion could be concluded as follows: 1. Entrainment ratio of the ejector with a crenation nozzle is slightly higher for the ejector with a conical nozzle while entrainment ratio of the ejector with a conical nozzle is slightly higher for the ejector with a petalage nozzle under the critical mode condition. 2. By compare with the ejector with a conical nozzle, critical back pressure of the ejector with a petalage nozzle is 5.2% bigger and critical back pressure of the ejector with a crenation nozzle is 2.1% smaller. Acknowledgements This work was supported by Postdoctoral Science Foundation of China (No. 2014M552441) and Fundamental Research Funds for the Central Universities and National Natural Science Foundation References [1] K. Chunnanond, S. Aphornratana, Ejectors: applications in refrigeration technology, Renew. Sustain. Energy Rev. 8 (2004) 129155. [2] Y.J. Chang, Y.M. Chen, Enhancement of a steam-jet refrigerator using a novel application of the petal nozzle, Exp. Therm. Fluid Sci. 22 (2000) 203-211. [3] T. Narabayashi, Y. Yamazaki, H. Kobayashi, T. Shakouchi, Flow analysis for single and multi-nozzle jet pump, JSME Ser. B. 49 (4) (2006) 933e939. [4]N. Ruangtrakoon, T. Thongtip, S. Aphornratana, T. Sriveerakul, CFD simulation on the effect of primary nozzle geometries for a

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steam ejector in refrigeration cycle, International Journal of Thermal Sciences.63 (2013) 133-145 [5] F. Kong, J. Yingzi, T. Setoguchi, Heuy Dong Kim, Numerical analysis of chevron nozzle effects on performance of the supersonic ejector-diffusersystem, J. Therm. Sci. 22 (5) (2013) 459-466. [6] W.Q. Tao. Numerical heat transfer, 2nd edition. Xi’an Jiaotong University Press, Xi’an, 2001. [7] T. Sriveerakul, S. Aphornratana, K. Chunnanond, Performance prediction ofsteam ejector using computational fluid dynamics: Part 1. Validation of the CFD results, International Journal of Thermal Sciences 46 (8) (2007) 812-822. [8] W.X. Chen, J.J. Yan, D.T. Chong, J.P. Liu, The numerical analysis of the effect of geometrical factors on natural gas ejector performance. Applied Thermal Engineering 59 (1-2) (2013) 21-29.