Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study

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Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study Yi Zhang a, Xiaohang Qu a,b,*, Guanmin Zhang a,**, Xueli Leng a, Maocheng Tian a a

School of Energy and Power Engineering, Shandong University, Jinan 250061, Shandong, PR China Department of Energy and Power Engineering, Shandong University of Technology, Zibo 255000, Shandong, PR China

b

highlights
Effect of non-condensable gas on performance of ejector is experimentally studied.
A numerical method is proposed to predict the ejector performance.
Flow fields inside ejector are shown by simulation.
Mechanism of the influence of non-condensable gas is demonstrated.

article info

abstract

Article history:

An ejector containing phase changing gas-liquid flow process acts as a popular and deci-

Received 29 July 2019

sive device in multiple industrial applications, including the hydrogen production, elec-

Received in revised form

tricity production, fuel cells, refrigeration, petroleum industry and desalination systems.

29 August 2019

However, non-condensable gas is inevitable for the usual operation of phase-changing gas-

Accepted 29 September 2019

liquid ejector in the trigeneration or electrolyzer system for hydrogen production, and

Available online xxx

rarely research is concerned with this issue. In the present study, the effect of noncondensable gas contained in the condensable gas on the characteristics of gas-centered

Keywords:

water ejector is presented, with steam, water and air acting as the gas, liquid and non-

Steam-water ejector

condensable gas, respectively. Experimentally, the flow rate of steam is controlled to be

Hydrogen production

1.45 g/s with an absolute pressure of 120 kPa, the air flow rate varies from 0 to 0.14 g/s,

Gas-liquid flow

resulting in a non-condensable gas concentration ranging from 0 to 9%, and the resulted

Non-condensable gas

water flow rate at 100 kPa and 282.15 K changes from 34.7 to 37.3 g/s. Combined with the

Direct contact condensation (DCC)

numerical methods, the performance of ejector expressed in ejected water flow rate was found to increase firstly with a small amount of non-condensable gas, and decrease when the non-condensable gas reaches a certain amount. In addition, the distributions of multiple local flow parameters including pressure, condensation rate and gas volume fraction, velocity and temperature inside the ejector were shown for different non-condensable concentration, by which the mechanism for the change of ejector performance under varying non-condensable concentration was demonstrated. These findings are initiative

* Corresponding author. Department of Energy and Power Engineering, Shandong University of Technology, Zibo 255000, Shandong, PR China. ** Corresponding author. School of Energy and Power Engineering, Shandong University, Jinan 250061, Shandong, PR China. E-mail addresses: [email protected] (X. Qu), [email protected] (G. Zhang). https://doi.org/10.1016/j.ijhydene.2019.09.243 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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and insightful for the ejector design optimization in the trigeneration system for hydrogen production and the proposed numerical models can be utilized in analysis and design of steam ejector with non-condensable gas involved. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Nomenclature A CD d db D e ER H h k l m M Nu P Pr Q r Re T U v

Area Drag force coefficient Nozzle diameter Mean bubble diameter Diffusion coefficient Internal energy Entrainment ratio Enthalpy Heat transfer coefficient Isentropic component Length Mass flow rate Momentum transfer Nusselt number Pressure Prandtl number Energy transfer Volume fraction Reynolds number Temperature Velocity vector Velocity

Introduction With the rapid development of world economy, the contradiction between the pollutants caused by the extensive use of fossil fuels and the requirement of human beings for environment protection is becoming one of the main factors preventing social development. Therefore, the developing clean energy and the researching energy saving and emission reduction technology become worldwide issues which need to be solved urgently. It is common knowledge that hydrogen is a prospective, clean and sustainable energy carrier [1e3]. And thus hydrogen has been proposed as a unique alternative to fossil fuel [4,5]. According to the published references [4,6], numerous approaches have been proposed to produce hydrogen efficiently and economically using renewable energy sources, including the trigeneration system for hydrogen production [7e10], steam reforming for hydrogen production (including methanol steam [11], ethanol steam [12], methane steam [13], and natural gas [14]), and electrolyzer for hydrogen production [15]. In all the hydrogen production systems mentioned above, the trigeneration system is recognized as a promising hydrogen production approach. The main reason is that this

X x,y,z,t

Mass concentration Space and time location

Greek letters G Interphase mass transfer r Density m Molecular viscosity l Conductivity a Liquid phase b Gas phase Subscripts & Superscripts ave Averaged value cr Critical value D Drag TD Turbulence dispersion eff Effective value int Integrated value w Water a Air s Steam T Transpose of tensor total Total value a, b Liquid or gas phase

system can not only produce hydrogen energy, but also obtain other high value-added products (e.g. heat, cool, electricity, hot water, hot air and synthetic fuels) [4,7]. In this kind of hydrogen production system, the steam-water ejector (or shorten as steam ejector) is an important device which utilizes the steam of very high pressure and thus very high speed after expansion to entrain or pump water at low pressure [4,16,17]. In addition, the steam ejector has been also massively applied in other industrial fields, including the electrolyzer for hydrogen production [4], ejection system of condenser in a thermal power plant [18,19], exhausted heat recovery system [20,21], anode off-gas recirculation for solid oxide fuel cells [22e26], desalination systems [27], pre-heating system in petroleum industry [28] and refrigeration system [29e31]. Moreover, due to its advantages of simplicity, no moving parts, low maintenance cost and high reliability, the steam-water ejector is also claimed to be promising if incorporated in the safety system of the trigeneration system for power, hydrogen and freshwater production from high temperature gas-cooled reactor of nuclear power plants in the future [32,33]. And in the above systems, the gas-liquid twophase working state also occurs constantly in the steam ejectors. Hence, it is significantly important to study the

Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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performance of the gas-liquid ejector for the safety, reliability and efficiency of both the electrolyzer system for hydrogen production and the trigeneration for hydrogen production, power generation and cooling or heating. According to the reported literatures [34e38], the recent research attention has been mainly paid on the gas-liquid flow inside, particularly for cases involving phase change. The recent experimental research efforts and their respective test conditions and conclusions are summarized in Table 1. Like Table 1, the performance indicator of gas-liquid ejector in the trigeneration system for hydrogen production is usually also evaluated through the entrained liquid flow rate (or entrainment ratio, ER), compression ratio, and entrainment pressure, since these indicators are critical for the system where the ejectors are installed [10]. Most of previous researches focus on the influential factors on the performance of ejector operating under various structures, boundary conditions and parameters of working fluids [39e41]. Ejectors of multiple stages and multiple nozzles have also been developed and tested in order to further improve the performance [21]. Other than experimental and numerical methods, one-dimensional analytical model along with proper assumptions and simplifications have been built to predict the ejector performance, and exergy efficiency is usually taken as a comprehensive performance criterion [42e44]. In contrast to the simple structure, the gas-liquid two phase flow inside an ejector in the trigeneration system for hydrogen production is quite complex and hard to predict accurately, mainly because of the phase change occurring rapidly in a very limited space, for instance, the condensation shock wave [50e52]. In view of this, a lot of literatures concentrate on studying the gas jet direct contact condensation (DCC) in large liquid pool, which is the dominant process occurring inside a gas-liquid ejector [53,54]. The attention has mainly been paid on ejector performance, jet plume shape, length, stability and heat transfer inside the ejector [17,52,55e58] under different geometric structural parmeters, flow parmeters and liquid properties. Tashtoush et al. [17] reviewed the effect of various geometrical aspects on the ejector performance. Zheng et al. [59] studied the effects of phase change, transient flow, inlet and outlet parameters on the performance of gas-liquid two-phase ejector using CFD simulation, showing that the phase change has a significant effect on the performance of two-phase ejector, and the entrainment ratio increases and decreases with increasing liquid inlet velocity and mixture outlet pressure, respectively. Qiu et al. [56] proposed a method to obtain the heat transfer coefficient based on the observed features of the pressure oscillation of steam jet condensing in a subcooled water. Qu and Tian [57] demonstrated the addition of non-condensable gas in the steam bubble can deteriorate severely the condensation heat transfer rate and smooth the pressure fluctuations. For the condensation of steam jet, the suppression effects of non-condensable gas on both the heat transfer and pressure fluctuation were also reported by Zhao et al. [58] experimentally and Zhou et al. [60] numerically. To sum up, the non-condensable gas in the steam, air etc. can severely decrease the condensation heat transfer of DCC and

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impose adverse influence on applications like passive safety system of the trigeneration system for hydrogen production of the high temperature nuclear reactor and direct contact heat exchangers [55,57,58,60]. Accounting for the confinement effect of the channel on DCC, Xu et al. [61,62] studied the DCC process of steam jet flow in co-current or cross water flow, and it was found the flowing water could enhance significantly the condensation heat transfer process. Abe and Shibayama [49] experimentally investigated the distribution of velocity, temperature and pressure inside a watercentered steam ejector, and the condensation heat transfer rates was evaluated. Even if the studies have been abundant on gas-liquid phase changing ejectors in the trigeneration system for hydrogen production, some influencing factors have not been addressed sufficiently, one of which is the impact of non-condensable composition existing in gas phase. Due to system leakage, gas dissolution in liquid, chemical corrosion or nuclear reaction, non-condensable gas is frequently produced inevitably when applying steam-water ejector at different situations. In view of the conclusions from experiments of steam condensation heat transfer on a solid surface of a wall type heat exchanger, non-condensable gas creates huge heat resistance, deteriorates heat transfer rate and should be avoided during operation. However, to the authors’ knowledge, few public literatures report on the impact of the non-condensable gas on the performance of gas-liquid ejector in the trigeneration hydrogen production system, a special DCC heat exchanger which functions both heating the liquid and rising its pressure but without solid heat transfer surface. From the above, although there exist plenty of literatures concentrating on the analyses of steam-water ejector and the effects of non-condensable gas on the condensation characteristics of steam bubble or steam jet, few literatures concern on the non-condensable gas’ influence on a steam-water ejector in the trigeneration system for hydrogen production, where the DCC with non-condensable gas occurs in a confined channel. However, the non-condensable gas is inevitable and produces huge influence even with a tiny amount. The novelty of this research therefore lies on the exploration of noncondensable gas’s effect on the performance of steam-water ejector applied in the trigeneration system for hydrogen production. This study could help understand the operating characteristic of steam-water ejector applied in the trigeneration or electrolyzer system for hydrogen production when noncondensable gas is involved, with not only the external performance of ejector is to be given but also multiple internal flow fields explaining the external performance are to be analyzed. This paper is organized as follows. Firstly, the experimental facility to test the performance of ejector is described when air is contained in the steam under varying concentrations. The pressures of steam inlet, water inlet and outlet are controlled to be 120 kPa, 100 kPa and 1 atm respectively. And then based on the introduced methods and models, the numerical simulations were conducted to assist analyzing the experimental results. Subsequently, according to the results from both experiment and simulation, the

Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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influence of non-condensable gas on both ejector’s external performance and internal flow fields are shown. Finally, the main conclusions and perspectives are given.

Experimentation

copper rod, and hence this part can be regarded as smooth channel. As an estimation to judge if the flow at the nozzle exit is subsonic or supersonic, the steam was assumed to be ideal gas experiencing isentropic expansion in the nozzle. So, the critical pressure ratio can be expressed as: k k1  Pcr 2 ¼ kþ1 Ptotal

Ejector structure and experimental loop The shape and dimensions of the ejector used in the trigeneration system for hydrogen production in this study were determined based on the best practice guidelines indicated by the performance optimization studies for steam-water ejector (including references [39e41]), with consideration of the limitation of the capacity of our steam generator. The structure of the steam-water ejector including steam inlet, water inlet, mixing chamber (convergent tube), throat and diffuser (divergent tube) are given in Fig. 1. Meanwhile, it can be also seen from Fig. 1 that the dimensions of different parts employed in this experiment. In order to conveniently change the ejector structure and parts’ sizes when designing the experimental ejector, the different parts of ejector were manufactured separately and could be assembled or disassembled easily, as shown in Fig. 2. The effective length of mixing chamber was specially designed and equal to the distance between nozzle tip and throat inlet. The primary nozzle lip supposed to be as sharp as possible to ensure high efficiency, but a thick nozzle lip (3 mm) was designed instead to prevent the steam from condensing in advance of contacting secondary flow. The continuous converging-diverging part which composes the mixing chamber, throat, diffuser and the screw threads in both ends (as shown in Fig. 2(a)) was manufactured using CNC (Computer Numerical Control) lathe and grinding from a one-piece

(1)

For water steam k equals 1.3, so Pcr/Ptotal equals 0.5457. The smallest actual pressure ratio of nozzle exit to total pressure was estimated to be: P 97kPa ¼ 0:808 ¼ Ptotal 120kPa

(2)

where the P was chosen to be the smallest possible pressure shown in Fig. 10. Although the above estimation changes slightly when the steam is mixed with air, the Pexit is still far larger than Pcr. Besides, the nozzle is in convergent shape which prevents the gas from expanding into supersonic regime. As a result, subsonic primary flow was expected at the nozzle exit. Fig. 3(a, b) show the real photo and schematic diagram of the experimental system of steam ejector, respectively. As shown in Fig. 3(b), the experimental loop consists of a steam generator, an air compressor, a water tank, a data acquisition system and an associated equipment for flow control and measurement. To mitigate flow rate measurement disturbance from the motor oscillation, no water pump is installed in the water loop. Instead, a water tank with constant water level was placed two meters above the water inlet of steam ejector. The water inlet pressure was then kept constant during the process of all experimental runs by

Table 1 e Experiment studies on steam-water ejector. Authors

Type

Ps (MPa) Pw (MPa) Tw ( C)

Miyazaki [34]

Water-centered 0.067e0.55 0.11e0.4

Cattadori [35]

Steam-centered 2.5e8.7

0.2e0.26

Narabayashi [36] Water-centered 0.13

0.17

Deberne [45]

Water-centered 0.01e0.12

0e0.2

Deberne [46]

Water-centered 0.6

0.2

Shimizu [47]

Water-centered 0.1

e

Trela [44] Li [48] Shah [37]

Steam-centered 0.5 Water-centered 0.05e0.25 Steam-centered 0.14e0.22

e 0.4e1 0.096

Abe [49]

Water-centered 0.1e0.2

e

Miwa [38]

Water-centered 0.18e0.63

e

Main conclusion

8.5e59

Equivalent heat transfer coefficient in mixing chamber is related to the relative velocity and water temperature. Nu was proposed as a function of Re. 15e37 Ejector efficiency decreases with increasing water pressure or temperature. Steam consumption ratio was defined. 20e33 Stable team velocity at the entrance of mixing chamber was obtained and self-similarity was found for the interphase momentum and heat transfer. 15e110 Back pressure is limited with constant steam pressure. A wider operating boundary conditions can be obtained at lower water pressure. 15.2 Dispersed flow pattern forms at the entrance of mixing chamber. Relative velocity between fluids decrease along the flow path. Gas volume fraction reaches a value of 0.9 at the throat. 20e35 Wave speed increases with increasing steam flow rate. Increasing water flow rate can strengthen the wave but wave speed and length remains unchanged. 15e20 Exergy efficiency decreases with increasing ER. 18e70 ER increases with length of mixing chamber, and there exists a best length. 17 Under constant steam pressure and increasing water pressure, ER and water flow rate increase, but suction lift decreases. e Back pressure increases with increasing steam pressure but remains constant with varying water flow rate. Compression ratio remains constant with different steam pressure or water flow rate. 22 Quick-start up capability was demonstrated and minimum steam inlet pressure and liquid flow rate was shown.

Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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adjusting the valve before water inlet manually when other flow parameters change. By doing so, the performance of steam ejector can be indicated by water flow rate of the water inlet. The steam generated from steam generator was at saturation condition corresponding to a pressure as high as 0.5 MPa. Its pressure was reduced to 120 kPa by a throttle valve before mixing with the air from the air compressor. The maximum pressure and volumetric flow rate of the air compressor was 0.6 MPa and 60 L/min, respectively, and air pressure was also reduced before mixing with steam. To prevent the steam from condensing before reaching the steam ejector, the air was warmed up by electrical heating tape covering the air pipe and all the pipes including the steam ejector were covered by insulation materials. During the experiments, the pressure and temperature at the entrance of steam inlet were monitored to ensure the mixture gas was at 120 kPa saturated. All the pressure, temperature and flow rate signals were collected by a PC.

Experimental procedures Before experiment, deionized water in the steam generator was heated and kept boiling at a pressure of 0.5 MPa for 2 h for degassing to eliminate the non-condensable concentration errors caused by the dissolved gas in the water. During each experiment run, the steam inlet pressure and steam flow rate was kept constant and their values were monitored by a vortex type steam flow meter and a T-type thermocouple respectively. The air flow rate can be measured by a rotortype flow meter and its value was increased from 0 to 0.14 g/s, resulting in an air concentration in the steam from 0 to 9%. The pressure at the water inlet was adjusted manually to stay at a constant of 100 kPa value when air concentration varies. The experiment was designed to study the influence of non-condensable air mixed in the steam on the injected water flow rate. Hence, only one set of steam parameters and one set of water parameters were tested and the resulted water flow rated was expected to change with the air concentration. For each test runs, measurement of the air flow rate and the resulted water flow rate were conducted 60 times during one minute after all the test parameters reach a steady state. The averaged value of all the 60 measurements were taken as the final recording data of air and water flow rate and used for the subsequent analysis.

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Fig. 2 e The steam ejector before and after assembling.

Experimental ranges and uncertainty analysis According to the published reference [63], the uncertainty results include the effects of observed scatter in the measured data and the reported accuracy of the instruments used for measurements. To be specific, (1) the temperatures were measured by the T-type thermocouples with joint diameter of 0.2 mm with instrument errors of 0.1 K and the random error was estimated to be 0.1 K, resulting in a total uncertainty of 0.2 K. (2) The pressure transducers were used with a full scale error of 0.5% (0e150 kPa). Considering the observation error, the whole pressure uncertainty was determined to be 1 kPa. (3) The air flow rate was measured using the rotor-type flow meter with accuracy class of 2.5 and since the random error was very small compared with instrument error, the uncertainty of air flow rate was 2.5%. (4) The mass flow rate of steam by the vortex-type flow meter consists of instrument uncertainty of 0.5% and random uncertainty of 0.5%. (5) The mass flow rate of the water was measured by the coriolis-type mass flow meter. According to the instructions, its accuracy was 0.2% and the random error was relatively small and thus neglected. The uncertainty or errors for dimensions of ejector and operating flow conditions along with the experimental ranges are summarized in Table 2. The physical properties of air, steam and water at the ejector inlets flow conditions are summarized in Table 3. Since the range of the resulted water flow rate is small, the entrainment ratio (ER) expressed as dividing the water flow rate by the steam flow rate is of a very high uncertainty. Therefore, the performance of ejector is indicated by the water flow rate instead of ER in this research.

Fig. 1 e The structure and dimension of steam-water ejector.

Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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Fig. 3 e Real photo (a) and schematic diagram (b) of the experimental system of steam ejector.

Fig. 4 e Mesh generated by ICEM.

Numerical method Computer fluid dynamics (CFD) has been adopted a lot recently in researching gas-liquid two phase flow and shows superiority than experiment in analyzing flow details. Since the specific gas-liquid flow in the steam ejector is hard to be

Fig. 5 e Mesh independency.

visualized by the experiment, this study utilized CFX, a commercial CFD software, to help analyze the flow situations inside a steam ejector. Note the numerical solver CFX and grid generation tool ICEM were both from ANSYS version 18.2.

Fig. 6 e Comparison of the experimental and simulated water flow rate.

Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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Fig. 7 e Contours of condensation rate.

Numerical models The volume fraction, continuity, momentum and energy equations for both gas-phase and liquid-phase were solved using Euler-Euler two-fluid model in this study. These equations for primary liquid phase a are given as follow: Eqs. (3)e(6). Of note, the forms of all equations for secondary gas phase b are identical to those of primary liquid phase a, and thereby not repeated to describe here. v þ ðra ra Þ þ Vðra ra Ua Þ ¼ Gþ ba  Gab vt

(3)

respectively; M is the interphase momentum transfer term; and Q is the interphase heat transfer term. Meanwhile, considering that the gas-phase b is composed of non-condensable air and condensable steam (denoted as s), the species transport model should be incorporated into the simulation. It should be noted that the species equation of steam in the gas-phase b was only considered and given here, since the mass fractions of two components sum up to one.
v ðrb rb YSb Þ þ Vðrb rb Ub YSb Þ ¼ V rb rb DeffSb ðVYSb Þ þ SSb vt

where YSb, Sb and DeffSb are the mass fraction of steam in the

        T    v þ ra ra Ua þ V ra ra Ua 5Ua ¼ ra Vpa þ V ra meffa VUa þ VUa þ Gþ ba Ub  Gab Ua þ SMa þ Ma vt


v þ ðra ra ea Þ þ Vðra ra Ua ea Þ ¼ Vðra la Ta Þ þ Gþ ba eb  Gab ea þ Qa þ SEa vt (5) ra þ rb ¼ 1

(7)

(6)

where ra is the volume fraction of liquid-phase; ra is the liquid density; Ua is the velocity vector of liquid-phase; SMa is the external momentum source term of liquid-phase; SEa is the external energy source term of liquid-phase, meffa is the effective dynamic viscosity; and ea is the internal energy of liquid-phase. While Gþ ba and Gþ ab are the mass transfer from phase b to phase a and from phase a to phase b,

(4)

gas-phase b, species source term and effective kinematic diffusion coefficient, respectively. Since air in the gas-phase b is the non-condensable gas, the species source term was defined to be equal to the mass transfer between the liquidphase a and the gas-liquid b, as shown in Eq. (13). The effective kinematic diffusion coefficient consists of molecular component which was taken as a constant with value of 2.88  105 m2/s, and turbulent component which was accounted by the turbulence model. The condensation model presented in the published references [40,60,64] is used to model the DCC of steam and air mixture. The main difference from condensation model of pure steam stems from this fact that in the steam condensation model with non-condensable gas, the temperature at the

Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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Table 2 e Experimental ranges and errors. Measurement Nozzle diameter d Mixing chamber length l Water temperature Tw Air mass flow rate ma Steam mass flow rate mv Gas inlet pressure Air concentration Xa Resulted water flow rate mw

Aab ¼ Fig. 8 e Distribution of steam condensation rate.

interface is assumed to be equal to the saturation temperature corresponding to local partial steam pressure. The interface area between the liquid-phase a and the gas-liquid b per unit volume is define as follows:

Error or uncertainty ±0.1 mm ±0.5 mm ±0.2 K 2.5% 1.0% ±1 kPa 5% 0.2%

6rb db

(8)

where db is the bubble diameter of the gas-phase b. It is common knowledge that the internal flow structure of steam ejector is extremely complex. This results in the fact that it is difficult to accurately measure the distribution of bubble diameter. As a result, in this study, a mean value of 2 mm is used instead based on several trial simulations with different mean bubble diameter. This treatment method might have led to a deviation between the experimental and the simulation result. To verify the reliability and feasibility of this method, the further investigation is being under progress. The gas-liquid interphase momentum source term M presented in Eq. (4) is usually composed of five forces including interphase drag force, turbulence dispersion force, lift force, virtual mass force and wall lubrication force. In this study, considering that the interphase drag force MD and the turbulence dispersion force MTD are found dominant, so other three forces are neglected. Among them, the drag force MDa between the gas-liquid two phases can be calculated according to Eq. (9): MDa ¼  MDb ¼

Fig. 9 e Distribution of gas volume faction.

Range 4 mm 40 mm 282.15 K 0e0.14 g/s 1.45 g/s 120 kPa 0e9% 34.7e37.3 g/s

3 CD rb ra jUb  Ua jðUb  Ua Þ 4 db

(9)

where CD is drag force coefficient, and it can be calculated by the Schiller-Naumann drag model [65]:  
24 1 þ 0:15Re0:687 ; 0:44 CD ¼ max Re

(10)

Table 3 e Physical properties of fluids before entering into the experimental ejector. Fluids

Fig. 10 e Pressure distribution with varying air concentration.

Density (kg/ m3) Viscosity (105 Pa s) Thermal conductivity (W/(m$K)) Surface tension (N/ m)

Air at 120 kPa and 293 K

Steam at 120 kPa, saturation

Water at 100 kPa and 282.15 K

1.427

0.7001

999.8

1.82

1.24

134

0.0259

0.02505

0.577

e

e

0.0728 (293 K, 1 atm)

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The turbulence dispersion force MTD is calculated using the Lopez de Bertodano model [66] Eq. (11): MTDa ¼  MTDb ¼ CTD ra ka Vra

(11)

The interphase heat transfer term Q presented in Eq. (5) is obtained by two-resistance model. In this model, the thermal resistance of the gas side is considered to be zero, meaning the temperature Ts at the gas-liquid interface is equal to that Tb of the gas-phase. As a result, the heat transfer rate per unit volume in the continuous phase can be calculated as: Qa ¼ ha Aab ðTs  Ta Þ

(12)

For the condensation model of pure steam in water, the specific enthalpy of steam at the total pressure of gas is used to calculate the energy releasing during steam condensation, and the saturation temperature corresponding to the total pressure of gas is used to calculate the temperature difference between the gas-liquid two phases. Different from the condensation model of pure steam, when calculating condensation rate of steam with non-condensable gas, the specific enthalpy Hsb of the steam in the gas phase is employed to replace the saturation temperature Ts at the local partial pressure of steam. The purpose of this treatment is to take into account the effect of non-condensable gas on the condensation in the model equation. Mathematically, both the mass transfer rate G in Eq. (3) from the gas-phase b to the liquid-phase a per unit volume and the species source term Ssb in Eq. (7) are equal to the steam condensation rate in the steam-air mixture: Gab ¼  SSb ¼

Qa ha Aab ðTs  Ta Þ ¼ HSb  Hw HSb  Hw

(13)

here, Hw denotes the specific enthalpy of liquid-phase at the gas-liquid interface temperature. By Eq. (13), the condensation rate of steam from steam-air mixture can be legitimately estimated, and this is the main novelty of this paper to model equations. ha is the heat transfer coefficient at the liquidpahse side, and it can be calculated using Hughmark model [67] as follows: ha ¼

la Nua db 

Nua ¼

2:0 þ 0:6Re0:5 Pr0:33 ; 0  Re < 776:06; 0  Pr < 250 2:0 þ 0:27Re0:62 Pr0:33 ; 776:06  Re; 0  Pr < 250

(14)

(15)

Since SST k-u model has both the merit of k-e model in the main stream and the merit of k-u model close to the wall, SST k-u model in combination with enhanced wall treatment was used to account for all the turbulent simulations. This model has been shown to predict accurately the velocity and heat transfer at near wall region. Moreover, the turbulence quantities agree well with experimental results verifying the efficiency and accuracy of this model.

Computational mesh and boundary conditions In computation domain, steam nozzle diameter and mixing chamber length were fixed at 4 mm and 40 mm respectively, and all other sizes were the same with the experiment. The

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mesh consisting of elements of all hexahedral shape was generated using ICEM, as seen in Fig. 4. To guarantee the mesh quality, the part of water inlet which is perpendicular to the main ejector body was simplified in the simulation. This simplification would produce symmetry water flow field around the outside of primary nozzle which is not the case in experiment. However, considering the much faster primary gas flow than water flow and the intensive flow turbulence and condensation when two streams contact, the influence of this water flow symmetry or asymmetry was deemed to be minor and this can be justified by the comparison in the following section Performance of ejector under the influence of non-condensable gas. Grid independence check was done with mesh elements of 96324, 141376, and 248332. With meshes of three different number of cells, the pressure distribution along the axis of steam ejector is compared in Fig. 5. It can be seen form Fig. 5 that the deviation among the three meshes are very small, thus the number of mesh used in this simulation is sufficient. Besides, the results with different meshes showed a calculated water flow rate discrepancy of less than 0.5%. Taking both the computational time and accuracy costs into consideration, the mesh with a total cell number of 141376 is applied in following studies. In CFX, a mass flow rate boundary condition with varying concentration of air was applied at the steam inlet, and the temperature was set as the saturation temperature according to partial pressure of steam. For all the simulation cases in this section, the steam mass flow rate and water inlet temperature were 1.45 g/s and 282.15 K, respectively. A pressure outlet condition of 1atm was set at the ejector outlet. The computational domain was initialized with being full of water, zero velocity and uniform temperature. The properties of the steam and water were taken from the IAPWS-IF-1997 (International Association for the Properties of Water and Steam Industrial Formulation 1997). And air was taken as ideal gas when calculating its density. The details of simulation corresponding to the experiment can be seen in Table 4. Since stable results was expected, the simulation was treated as non-transient. Double precision solver was used and all the equations was discretized by high order scheme. During simulation, ejector outlet flow rate was monitored and only when the monitored parameters reached a constant value and residuals for all equations fell down 106 was the simulation considered converged. With a computer of 32 G RAM and 16 cores of 2.4 GHz, each simulation needs around 24 h.

Results and discussion Performance of ejector under the influence of noncondensable gas Fig. 6 gives the change of experimental and simulated water flow rate when the air concentration in the steam increases from 0 to 10%. As shown in Fig. 6, the water flow rate increases firstly with the air concentration until a certain value after which the water flow rate starts to decrease with the air concentration. The simulation predicted variation of the water flow rate as a function of air concentration is in well

Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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Distribution of flow fields

Table 4 e Simulation details corresponding to experiment. Item

Range

Nozzle diameter d Mixing chamber length l Steam mass flow rate mv Steam temperature Air concentration Xa Water inlet temperature Tw Water inlet pressure Outlet pressure

4 mm 40 mm 1.45 g/s Saturation 0e10% 282.15 K 100 kPa 1 atm

agreement with experiment except for deviation from two aspects: (1) the water flow rate was under predicted in the simulation and this discrepancy decrease from about 3% to 1% as the air concentration increases. (2) the value of air concentration where water flow rate reaches its maximum predicted by simulation is 3% in contrast to 2% from experiment and since the increment of air concentration in simulation is 1%, this deviation is acceptable. Therefore, it can be concluded that the simulation model has successfully predicted the ejector performance and be able to capture the influence mechanism of noncondensable gas on the performance of steam ejector. The minor deviation in Fig. 6 may be attributed to the usage of mean bubble diameter as described in section Numerical models and by Eq. (8), and precise modelling of the bubble size distribution in two-phase flow are considered necessary to tackle this deviation. One possible solution to the change of flow pattern and bubble size would be the multifluid and multi-size group treatment of gas-liquid flow by € nsch [68]. Ha The local distribution of condensation rate, gas volume fraction, pressure and drag force were not measured by the current experiment facility. Shah et al. [39,40] have employed a similar numerical method to study the performance of a steam-water ejector, except the steam was pure without noncondensable gas, and it has been proved by them the numerical method could well predict the distribution of pressure, gas void fraction and condensation rate inside ejector. Besides, the intention of the current research focuses on the external performance of steam ejector. As a result, the distribution of flow fields inside the ejector shown in the following subsections are only based on numerical simulation.

Distribution of the flow fields including pressure and void fraction are important reflection of the flow and heat transfer process occurring inside the ejector. By simulation, these flow fields can be obtained. The distribution contours of condensation rate at four air concentrations are shown in Fig. 7. The distributions of condensation rate, gas volume fraction and pressure along the axis of the ejector are shown in Figs. 8e10, respectively. Since these quantities in the steam nozzle show no obvious difference, the abscissa in these figures start from the exit of the steam nozzle. From Fig. 7, we can see the maximum value of the condensation rate in the whole domain decreases from 3252 to 2340 kg/(m3$s), as the air concentration increase from 0 to 10%, indicating deteriorated condensation heat transfer because of non-condensable air. Meanwhile, the shape of the condensing jet inside the convergent tube can be found to enlarge with increasing air concentration. As shown in Fig. 8, the quantitively variation of condensation rate along the ejector axis reaches the highest peak value in the end of the convergent tube and then this peak value decreases and moves towards rear part with increasing air concentration. From the above, it can be concluded the addition of air in the steam severely resists the heat transfer between water and steam. Due to the reduced condensation heat transfer rate, it is probably the gas cannot finish condensing in the convergent tube and extends to the throat and divergent tube. This is demonstrated by Fig. 9, where the gas volume fraction for case of pure steam reaches almost zero in the convergent tube and that for case with even only one percent of air remains higher than 0.5 at the entrance of throat and continue to decrease slowly in the divergent tube. Moreover, the gas volume fraction maintains unchanged in the divergent tube for very high air concentration. This is a combined effect of the enlarging flow area of divergent tube and the decreasing condensation rate. From Fig. 10, it can be seen that the pressure fluctuations inside are obviously suppressed when air is added into the steam, even with only one percent. The fluctuations become weaker and weaker and the magnitude of the change becomes smaller and smaller for the constant increment of the air concentration. This phenomenon is the most evident in the convergent tube where most of steam condenses. Therefore, the suppression of the fluctuations may be resulted from the

Fig. 11 e Velocity contours after steam ejection. (a) gas velocity, (b) water velocity, (c) gas Mach number. Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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Fig. 12 e Water temperature contours after steam injection.

reduced velocity changing rate stemming from the reduced condensation rate of steam. Furtherly, suppression effect of non-condensable gas on pressure fluctuations inside steam ejector is in agreement the CFD study of Zhou [60], where the pressure oscillations was found to be attenuated with the increase of air in the ejected steam. Since a two-fluid two phase model was used, two fields of velocity will be obtained, with one for gas phase and another for liquid phase. The velocity fields for gas and water with the increase of air concentration are shown in Fig. 11(a, b), along with the Mach number (defined as the ratio of local velocity to local sound speed) for gas velocity, as shown in Fig. 11 (c). Since the abrupt change of velocities are mainly limited in the nozzle and mixing chamber, the divergent tube of the ejector is cropped away in Fig. 11. As expected, the gas velocity is always higher than the water velocity for varying air concentration, because the gas and liquid are chosen to be the primary and secondary phases, respectively. As a result of the decreased condensation rate with increasing air concentration, the length of the jet formed by velocity and the maximum velocity in the contours also decrease, as shown in Fig. 11 (a) and (b). The contours of Mach number shown Fig. 11 (c) indicate that the flow fields of the ejector, including the part inside primary nozzle, are subsonic. The maximum Mach

number for each simulation case decreases with the increasing air concentration, and the maximum value for all cases is 0.46. The temperature change of the fluid mainly occurs where the condensation heat transfer occurs, so the temperature contours of water inside the mixing chamber and throat along the increase of air concentration are shown in Fig. 12. The water is heated by the condensation of steam and its temperature keeps increasing along the flow direction, and when the condensation finishes in the throat (see Fig. 7), the water temperature also stops increasing. When the air concentration is low, the temperature increases mainly in the mixing chamber. And then with the increase of air concentration, the temperature increases until the throat. This is in accordance with the distribution of condensation rate.

Distribution of turbulence kinetic energy and wall shear stress The contours of turbulence kinetic energy inside the ejector mixing chamber at different air concentrations are shown in Fig. 13. The maximum values of turbulence kinetic energy for each air concentration are also indicated above each of the ten individual images in Fig. 13. It can be seen the

Fig. 13 e Contours of turbulence kinetic energy. Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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Fig. 14 e Contours of wall shear stress.

turbulence is the strongest in the center of the steam jet. With increasing the air concentration, the turbulence is getting weak gradually. Meanwhile, the jet formed by the turbulence kinetic energy contours gets longer with increased air concentration. This is consistent with the fact of decreased condensation rate, which results in weak velocity turbulence. The shear stress contours at the ejector wall are demonstrated in Fig. 14. Since the wall shear stress before the mixing of gas and liquid is small, only the ejector mixing chamber, throat and divergent tube are demonstrated. The largest wall shear stress emerges at the entrance of ejector throat for all cases except when the gas is pure steam. It can be seen the wall shear stress for pure steam is distinctly small in comparison with cases of steam mixed with air. In contrast, a gradual increase of wall shear stress can be observed for the increasing air concentration. This is because as the air concentration increases, the condensation rate decreases, the jet plume formed by the gas phase enlarges and puts more pressure against the ejector wall.

Mechanism of the influence of non-condensable gas The gas volume fraction or void fraction distribution inside the steam ejector is shown in Fig. 15, with the air concentration increasing from 0 to 10% from the left to right. Along with the increasing non-condensable gas concentration, it is shown that the gas occupies more and more space inside the steam ejector, indicating a reduced condensation rate of the steam. In contrast to the deterioration effect of air to the condensation heat transfer, the interfacial area between liquid and gas is enlarged due to the addition of air. This is resulted from the factor that the reduced condensation rate requires larger interface area to finish condensing of steam. This can also be demonstrated by Fig. 16, where the total interface area Aint representing the sum of all the interface area is shown with the variation of air concentration. Aint can be obtained by integrating the interface area density throughout the calculation domain, as shown by Eq. (16). However, due to the limited space of the mixing chamber, the Aint increases at a slower manner when the air concentration reaches a higher value.

Fig. 15 e Gas volume fraction in the steam ejector. Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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Fig. 16 e Total interface area with varying air concentration.

Aint ¼ ∭ Aab dxdydz

Fig. 18 e Variation of total drag force along air concentration.

(16)

Two quantities, averaged liquid velocity vaave and nominal liquid flow cross sectional area Aa, were defined by Eqs. (17) and (18) in order to explain the variation trend of water flow rate with air concentration. va is calculated as the total momentum of water inside the ejector divided by the total mass of water and Aa can be regarded as a virtual cross-sectional area through which water flows. It is worth noting that Aa is not a physically existed area but a reflection of the space inside ejector which is occupied by water. The variations of vaave and Aa with increasing air concentration are shown in Fig. 17. It can be seen that vaave increases and Aa decreases both monotonously with increasing air concentration. This is mainly caused by the enlarged gas jet plume and limited size of the mixing chamber. vaave ¼

Aa ¼

∭ ra va ra dxdydz ∭ ra ra dxdydz

mw ra vaave

13

(17)

(18)

From the above, on the one hand, with the increase of air concentration in steam the size of gas jet plume and gas-liquid contact area in the mixing chamber of ejector increases because of the reduced condensation rate, as shown in Figs. 15 and 16. This is beneficial to the shear force between the gas and liquid and functions to improve the ejector performance (improve water flow rate). On the other hand, the shrinkage of flow area for water acts to prevent the water flow rate from increasing continuously as air concentration increases as shown in Fig. 17, and hence is an adverse factor for the improvement of ejector performance. As a result, under the influence of both enlarged interfacial area and reduced water flow area, the ejector performance is bound to reach its best at a certain amount of non-condensable gas. As shown in Fig. 18, the total drag force (defined by Eq. (19)) increases firstly with the air concentration and after a certain point decreases with further increase of air concentration, and this variation is accordant with the variation of water flow rate. As a result, the total drag force integrated throughout the ejector was found to be a representative of ejector performance. FD ¼ ∭

3 CD rb r ðUb  Ua Þ2 dxdydz 4 db a

(19)

Conclusions The effect of non-condensable gas (e.g. air) on the performance of steam-water ejector used in the trigeneration system for hydrogen production was studied experimentally. Meanwhile, a numerical method to predict the performance of the steam-water ejector with non-condensable gas was established. By the numerical method, the local flow parameters distribution under different air concentrations were shown, and the mechanism of the influence of noncondensable gas was explained. The main conclusions are as follows:

Fig. 17 e Variation of averaged liquid velocity and nominal liquid flow area along air concentration.

(1) The performance of ejector indicated by entrained water flow rate is improved for a small amount of non-

Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243

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condensable gas but deteriorated with even higher values. A change of entrained water flow rate of 8% can be observed with the change of non-condensable gas concentration. The effect of non-condensable gas on steam ejector was found to be positive when air concentration is low and negative when the concentration increases to a certain amount, whose specific value is related to the ejector structure and boundary conditions. (2) With the increase of air concentration from 0 to 10%, the condensation heat transfer deteriorates, the maximum condensation rate in the whole flow field decrease from 3252 to 2340 kg/(m3$s), and the peak value in the axis direction decreases and moves towards the end of ejector. The gas volume occupation enlarges and was found to extend from the end of convergent tube to divergent tube. The pressure fluctuations along the steam-ejector was suppressed due to oscillation suppression effect of non-condensable gas. The maximum velocities for both gas and water in the ejector flow field decrease with increasing air concentration. The jets formed by these velocities’ contours enlarge due to the decreased condensation rate. The distribution of condensation rate can also be correctly reflected by the water temperature distribution inside the ejector convergent tube. (3) The turbulence kinetic energy inside ejector in the trigeneration hydrogen production system gets weaker with the increasing air concentration, whereas the wall shear stress gets stronger with the increasing air concentration with its maximum value emerging at the entrance of ejector throat. (4) Through the numerical analysis of the gas-liquid interfacial area, liquid flow area and drag force, the effect of non-condensable gas on the ejector performance is shown to result from the competitive factors of the enlarged gas-liquid interface contact area (positive factor) and the reduced water flow cross sectional area (negative factor) due to the decreased steam condensation rate inside the steam ejector. The integral drag force between phases changes among 54.8 N and 56.4 N and the variation is accordant with the variation of ejector performance. Furthermore, to provide a further validation of numerical model, the experiments of both the wider range of flow conditions and the ejector of larger size should be performed in the future. In particular, in aspects of validating the distribution of local flow parameters, a more advanced measurement technique will be required.

Acknowledgements The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (Grant No. 51806128, No. 51576115 and No. 51676114) and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019BEE008 and No. ZR2016EEM26).

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Please cite this article as: Zhang Y et al., Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study, International Journal of Hydrogen Energy, https://doi.org/ 10.1016/j.ijhydene.2019.09.243