Experimental and CFD analysis of nozzle position of subsonic ejector

Abstract

The influence of nozzle position on the performance of an ejector was analyzed qualitatively with free jet flow model. Experimental investigations and computational fluid dynamics (CFD) analysis of the nozzle position of the subsonic ejector were also conducted. The results show that there is an optimum nozzle position for the ejector. The ejecting coefficient reaches its maximum when the nozzle is positioned at the optimum and decreases when deviating. Moreover, the nozzle position of an ejector is not a fixed value, but is influenced greatly by the flow parameters. Considering the complexity of the ejector, CFD is reckoned as a useful tool in the design of ejectors.

Keywords

ejector / nozzle position / ejecting coefficient / CFD

Introduction

The ejector, also called jet pump when the internal flow is liquid, is a device sucking low-pressure flow or solid particulates by high-pressure flow without any aid of mechanical force. It includes a primary nozzle, suction chamber, mixing chamber, and diffuser, as shown in Fig. 1. The ejector is widely applied in many fields, such as oil recovery, steam refrigeration system, gas mixing, pneumatic conveying, etc, due to its simple structure and reliable operation.

The ejecting coefficient, one of the most important evaluation indicators for the function of the ejector, is defined as the mass flow ratio of the secondary flow to that of the primary flow. The design of the ejector is aimed at obtaining a maximum ejecting coefficient once operation parameters are determined. When subjected to fixed parameters such as primary flow pressure (p_p), secondary flow pressure (p_s) and ejector outlet pressure (p_m), the ejecting coefficient is determined by geometric parameters such as nozzle position (h, distance between nozzle outlet and mixing chamber inlet), nozzle outlet diameter (D_pn), and diameter of mixing chamber inlet (D_mc).

The nozzle position h has a great influence on the performance of the ejector. So far, the design and evaluation of the ejector have been based on 1-D analysis and Sokurov’s method has been frequently applied. Sokurov calculated the nozzle position of the ejector adopting the theory of subsonic free jet [1]. However, as the mixing process of the two flows is too complicated, the principle remains unclear until now. This method is still semi-empirical and it is difficult to conduct quantitative calculation on the design of different ejectors.

With the development of computer science, computational fluid dynamics (CFD) technique has become a useful tool for the design and analysis of fluid machinery. The essence of CFD lies in dividing the space into micro control volumes and on each volume, solving conservation equations of mass, momentum, energy, turbulence, etc. Thus, the distribution of velocity, pressure and temperature in the space is obtained respectively. As far as 1-D analysis is concerned, the field distribution is approximated by some characteristic values, e.g. the whole velocity/pressure field of the cross-section is substituted with the average velocity/pressure, as will bring on obvious deviation, so that various correction coefficients are brought in by experiments. The CFD analysis outshines 1-D analysis in theory, reducing the period and cost of the design, and has been applied in the analysis and design of the ejector.

Xu [2] has conducted a CFD analysis on supersonic steam-jet ejector and found that an optimum nozzle position exists. The ejecting coefficient decreases when deviating, especially when the optimum nozzle position is exceeded, resulting in a sharp deterioration of the ejector performance. Similar studies have been made by Li et al. [3] and Li [4] who obtained the same results as that of Ref. [2]. A CFD analysis of a supersonic gas ejector by Yang [5] shows that the ejecting coefficient decreases when h exceeds a certain value, and remains almost unchanged when h is below that value. A CFD analysis of an ejector using methanol as the working fluid by Riffat [6] shows that positioning the nozzle exit at least 0.21 of the length of the mixing chamber diameter upstream of the entrance of the mixing chamber has higher ejecting coefficient than moving it into the mixing chamber.

Researches on different types of ejectors get similar results that an optimum nozzle position exists. However, the cause of its existence remains unclear, and few papers present researches combining the experiment with CFD. An investigation on a subsonic ejector is conducted in this paper. The empirical theory of free jet is adopted to make a qualitative analysis on the nozzle position of the ejector. Experiments and CFD analysis are conducted, and good agreement is found between them. The experimental data received are mainly used for validation and optimization of the CFD model due to the limitations of the test apparatus. Further study is conducted by CFD.

Analysis

The basic principle of the ejector lies in enhancing the pressure of the secondary flow by the jet flow entrainment of the primary flow. Jet flow is common in engineering. In-depth study has already been made into the subsonic axisymmetric free jet and a lot of empirical formulas have been obtained. However, the primary flow in the ejector is a kind of confined jet flow. No universal empirical formula is available at the moment due to its complexity. According to the research by Abramovich, the flow field of confined jet is quite similar to that of free jet [7]. Sokurov got an ideal result in the design of the ejector according to the subsonic free jet theory [1]. Therefore, free jet theory is adopted in this paper to analyze the nozzle position of the ejector, with some modifications of the empirical coefficients.

As shown in Fig. 2, the diameter of the jet flow cross section increases gradually because of the secondary flow entrained by the primary flow, assuming the primary flow jets out from the nozzle with uniform distribution of velocity (u₀). The extension of jet flow boundary connects the axis at point O, which is known as jet stagnation point. The angle θ is the jet spread angle. A conical region near the nozzle, where the flow velocity remains u₀, is the jet core region. Between the jet core region and the jet flow boundary, there is the jet entrainment region, where the primary flow is entraining the secondary flow and mixing with each other. In the fully turbulent region, the two flows gradually merge into one. Experimental investigations have been made by Abramovich on the free jet, and a semi-empirical formula for the spread angle is obtained [8]:

(1)\tan \theta =\mathrm{3.4}\alpha .

α in Eq. (1) is the turbulence number. It explains the capability of jet flow for entraining the surrounding flow, and is related to the turbulence intensity and the velocity uniformity of the jet flow exit. The stronger the turbulence intensity is, the more non-uniform the velocity is, and the bigger α and θ will be.

When θ is fixed, the radius of jet cross section can be expressed as follows [8]:

(2){\displaystyle \frac{R_{\mathrm{js}}}{R_{\mathrm{jn}}}}=\mathrm{1}+\mathrm{3.4}{\displaystyle \frac{\alpha S}{R_{\mathrm{jn}}}},

where S refers to the distance between the selected jet cross section and nozzle exit, R_js is the radius of jet cross section, and R_jn is the radius of jet nozzle exit.

When the nozzle is located at the position shown in Fig. 2, R_js equals the radius of the mixing chamber inlet. According to Eq. (2), D_pn, D_mc, and L (the distance between nozzle exit and mixing chamber inlet) can be expressed as

(3){\displaystyle \frac{D_{\mathrm{mc}}}{D_{\mathrm{pn}}}}=\mathrm{1}+\mathrm{6.8}{\displaystyle \frac{\alpha L}{D_{\mathrm{pn}}}}.

L is computed using Eq. (3):

(4)L=({\displaystyle \frac{D_{\mathrm{mc}}}{D_{\mathrm{pn}}}}-1)\times {\displaystyle \frac{D_{\mathrm{pn}}}{\mathrm{6.8}\alpha }}.

When h equals L, the primary flow entraining the secondary flow will scarcely be influenced by the walls of the mixing chamber and suction chamber. The mixing process finishes in the suction chamber with a broader space, and the ejecting coefficient reaches its maximum. The ejecting coefficient will go down when h deviates from L, as shown in Figs. 3 and 4.

Figure 3 illustrates the flow field in the suction chamber in case h is below L, when the two flows will have their mixing process partly finished in the mixing chamber, being subjected to the constraint of the wall there. Meanwhile, the section area of the secondary flow is reduced in Fig. 3 compared with that in Fig. 2, as is similar to the throttling effect. The smaller h is, the more effective the throttling effect will be. Throttling effect increases the resistance of the secondary flow entering the mixing chamber, and is more effective with the increase of flow velocity.

Figure 4 depicts the case of h above L, when the diameter of the jet section at the mixing chamber inlet is bigger than D_mc. The jet impinges against the wall of the suction chamber and produces swirl flow there. The swirl flow obstructs the secondary flow from mixing with the primary flow and deteriorates the performance of the ejector. Besides, it will grow worse with the increase of h. In extreme cases, the ejecting coefficient will be a negative value when the primary flow reverses into the secondary flow.

According to Refs. [2-6] and the analysis above, the conclusion is drawn that there is an optimum nozzle position for the ejector. As for the subsonic ejector in this paper, the optimum value is L in Eq. (4), which is determined by α. However, currently, α can only be obtained from experiments. Sokurov’s research on the subsonic ejector shows that α is between 0.07 and 0.09 [1]. Besides, it takes a long time and a lot of money to conduct such experiments. Therefore, a combination of experiments and CFD analysis is applied to decide the proper nozzle position in this paper.

Experimental investigation

The schematic diagram of the test system, mainly including the ejector model, two fans, three valves and some measuring instruments, is shown in Fig. 5. Both of the fans are centrifugal, with a maximum pressure of 15 kPa on the high pressure fan and 6 kPa on the low pressure fan. The ejector nozzle is convergent, with an exit diameter (D_pn) of 50 mm. The mixing chamber is a straight pipe (D_mc=76 mm, L=350 mm). The nozzle of the primary flow is adjustable, and as a result, the value of h can be changed easily. The flow pressure and the volume flow rate at the inlets are adjusted by Valve 1 and Valve 2, while the pressure at the outlet is adjusted by Valve 3. Considering the loss of resistance from the rotameter, the volume flow rate is obtained indirectly by measuring the velocity of the flow. The velocity is measured by Pitot tubes with the readings taken from the inclined manometer. For a better comparison between experiments and CFD analysis, five manometers have been set in the test system to measure the pressure of five representative points.

In the experiments, h is adjusted by changing the nozzle position. When h is fixed, the three valves are adjusted to change p_p, p_s and p_m. Noting the volume flow rate of primary flow (Q_p) and that of the secondary flow (Q_s), the ejecting coefficient is obtained as n = Q_s /Q_p .

CFD analysis

The 3-D model and the Tet/Hybrid mesh (the mesh density in the figure is 1/64 of that in practice for a better view) are shown in Fig. 6. The finite volume method (FVM) of second order accuracy is adopted to do spatial dispersion on the control equation. Segregated solver and SIMPLE computation method are applied to couple the pressure and the velocity. The air density is calculated according to compressible ideal gas, and the viscosity is expressed in the form of temperature exponential function in view of the impact of viscous heating. The inlet boundaries are defined as pressure inlet, and the outlet as pressure outlet. The no-slip boundary condition is selected as the wall boundary, and proper wall roughness is given as well. Fixed temperature thermal boundary condition is modeled at walls. The turbulence models available are mostly set in Standard κ-ϵ model [2-5]. RNG κ-ϵ turbulence model can fully simulate the swirl and separation flows. Riffat finds that the RNG κ-ϵ turbulence model can work out a better calculation result consistent with the experiment, and it takes less running time than other turbulence models [6]. Table 1 shows that the ejecting coefficient increases with the increase of p_s when the other parameters are fixed. The CFD results with RNG κ-ϵ model show better agreement with the experiments, while the results with standard κ-ϵ model are much higher. The conclusion is the same as that of Riffat, thus RNG κ-ϵ turbulence model is adopted in this paper.

The CFD analysis is conducted in two steps. First, the same condition as that in the experiments is simulated. The CFD model is validated and optimized with the experimental data. Then, more data is analyzed, which is difficult to obtain in the experiments.

Results and discussion

In the experiments, p_p (=14 kPa) and p_m (=9 kPa) are fixed, while p_s is adjustable. After p_s is determined, the primary flow nozzle is adjusted (set h at 0, 20, 40, 60, and 80 mm separately) to analyze the impact of h on the ejecting coefficient (n).

When p_s is set at 3.5 kPa, the secondary flow is too slight to be measured when h is 60 mm. With the increase of h to 80 mm, the primary flow reverses into the secondary flow. Figure 7 illustrates the trend of the ejecting coefficient when h is adjusted at 0 mm, 20 mm and 40 mm respectively, and p_s is set at 3.5 kPa and 4.5 kPa separately. It can be seen that n reaches its maximum when h is 20 mm and decreases when h is 0 mm or 40 mm. It is known from previous analysis, that the optimum value of h lies between 0 mm and 40 mm. The experiments mentioned above only define the scope of h, so more experiments are needed to determine its accurate value. Regarding the difficulty in moving and positioning the nozzle, CFD analysis is adopted instead of experiments.

Although CFD analyses on different ejectors have been done by some researchers, the effectiveness of the CFD analysis remains to be verified by experiments. A comparison of the experimental data and corresponding CFD results, as shown in Fig. 7, indicates that they are almost the same in tendency, but CFD results have greater values. One of the reasons for the deviation is that CFD analysis is conducted under ideal conditions, while there might be errors in the experiments, such as leakage loss, manufacturing errors, fluctuation of flow pressure, etc. Another reason might lie in the low precision of the measuring devices, resulting in the increase of error, especially when the volume flow rate is slight.

Figure 8 shows the variation of ejecting coefficient with the change of p_s (h=20 mm, p_p=14 kPa, and p_m=9 kPa). The CFD results agree with the experiments that the ejecting coefficient increases with the increase of p_s. The agreement is getting closer especially when the ejecting coefficient is increasing, resulting from the fact that the errors of measurement is reduced with the increase of volume flow rate. Figure 8 demonstrates in one aspect that one of the important factors of deviation between the CFD analysis and experiments lies in the errors of measuring devices. It is necessary to contrast the pressure in the CFD analysis and that in the experiments to verify the feasibility of CFD in the analysis of the ejector. It is very simple to measure the pressure in the experiments. The experimental data of pressure is more reliable than that of volume flow rate. In the mixing chamber, the primary flow and the secondary flow exchange their energy and momentum with sharp changes in pressure. The static pressure at the inlet (p_im) and the outlet (p_om) of the mixing chamber are measured in the experiments. Figure 9 demonstrates the trend of p_im and p_om with the change of p_s (h =20 mm, p_p=14 kPa, and p_m=9 kPa). According to Fig. 9, the CFD results are similar to that of the experiments, which proves that CFD is capable of simulating the complicated changes of pressure in the mixing chamber. A summary of Figs. 7 and 8 and 9 proves it feasible to simulate the subsonic ejector with CFD.

Figure 10 illustrates the CFD results of the impact of h on the ejecting coefficient with different p_s. It can be seen clearly that the ejecting coefficient goes up with the increase of p_s and an optimum h exists with fixed flow parameter. When h is at its optimum, the ejecting coefficient reaches its maximum. The optimum h is not constant but variable under the influence of p_s. The higher p_s is, the bigger the optimum h will be. When p_s is higher than 10 kPa, the curve is uniformly increasing, which shows that the optimum h is more than 40 mm.

Similar to what is shown in Fig. 10, n in Fig. 11 goes up with the increase of p_p. In case the flow parameter is fixed, an optimum h exists, which also increases with the increase of p_p.

Figure 12 shows the CFD analysis of the impact of p_m on the ejecting coefficient and the optimum h, which is similar to Figs. 10 and 11, showing that an optimum h exists and is variable with the influence of flow pressure. The ejecting coefficient goes up with the increase of p_p and p_s or the decrease of p_m, while the optimum h increases.

CFD analysis on the ejector gets not only the general data, but also the flow field and the pressure field which is difficult to obtain in experiments. Fixing the flow parameters (p_p =14 kPa, p_s =3.5 kPa, p_m =9 kPa), and adjusting h at 20 mm, the flow field in the ejector is shown in Fig. 13. Enlarged view of the flow field at the inlet of the secondary flow and the mixing chamber is presented in Fig. 14.

The condition that the ejecting coefficient reaches its maximum shown in Fig. 14 is similar to that shown in Fig. 2. The mixing process of the primary flow and the secondary flow almost finishes in the suction chamber. The mixed jet flow diameter at the inlet of mixing chamber equals D_mc. As shown in Fig. 14 (a), no swirl flow is generated and the flow field is ideal. As shown in Fig. 14 (b), the secondary flow flows into the ejector smoothly.

Adjusting h at 0 mm, the flow field of the ejector is shown in Fig. 15, which presents similar characteristics with that in Fig. 3. The mixing process of the two flows finishes in the mixing chamber with resistance from the constraint of the chamber wall. Slight swirl flow is generated in the mixing chamber, resulting in the decrease of the ejecting coefficient.

Figure 16 (a) shows the similar phenomenon with that in Fig. 4. The jet diameter at the mixing chamber inlet will be bigger than D_mc if h is above its optimum value, with the jet impinging against the wall of suction chamber to produce swirl flow. The bigger h is, the more intensive the swirl flow will be. If h is much too big, the primary flow will reverse into the secondary flow, as shown in Fig. 16 (b).

Conclusions

Experimental investigation and CFD analysis of the subsonic ejector was conducted. Good agreement is reached between the experimental findings and the CFD results. Therefore, it is feasible to satisfy the precision requirements in engineering practice by means of CFD on the ejector instead of experiments.

The influence of the nozzle position on the performance of the ejector is analyzed using the free jet model. The analysis helps in understanding the experimental results. It is qualitative as the free jet model is semi-empirical. Precise analysis and prediction of the ejector with free jet model involve massive experiments to modify relevant coefficients.

The nozzle position of the ejector influences the ejecting coefficient a lot. The optimum nozzle position of the subsonic ejector exists when the flow and other geometry parameters are fixed. The ejecting coefficient will reach its maximum when setting the nozzle at the optimum position, and decrease when deviating.

The optimum nozzle position of an ejector is not constant; but is a variable, influenced greatly by the flow parameters. When the changes of pressure favor the increase of the ejecting coefficient, the optimum h will increase accordingly.

References

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[4] Li H J. Study of the performance, configuration and particular flow phenomena of an ejector. Dissertation for the Doctoral Degree. Dalian: Dalian University of Technology, 2004 (in Chinese)

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[8] Zhang G Q, Wu J M. Hydromechanics. Beijing: China Machine Press, 2005 (in Chinese)

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