ARTICLE

J. Cent. South Univ. (2019) 26: 2068-2076

DOI: https://doi.org/10.1007/s11771-019-4154-z

Effect of nozzle geometry on pressure drop in submerged gas injection

XIAO Jun-bing(肖俊兵)^{1, 2}, YAN Hong-jie(闫红杰)¹, Markus SCHUBERT²,Sebastian UNGER², LIU Liu(刘柳)¹, Eckhard SCHLEICHER², Uwe HAMPEL^{2, 3}

1. School of Energy Science and Engineering, Central South University, Changsha 410083, China;

2. Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328, Germany;

3. Chair of Imaging Techniques in Energy and Process Engineering, Technische UniversittDresden 01062, Germany

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Abstract: Submerged gas injection into liquid leads to complex multiphase flow, in which nozzle geometries are crucial important for the operational expenditure in terms of pressure drop. The influence of the nozzle geometry on pressure drop between nozzle inlet and outlet has been experimentally studied for different gas flow rates and bath depths. Nozzles with circular, gear-like and four-leaf cross-sectional shape have been studied. The results indicate that, besides the hydraulic diameter of the outlet, the orifice area and the perimeter of the nozzle tip also play significant roles. For the same superficial gas velocity, the average pressure drop from the four-leaf-shaped geometry is the least. The influence of bath depth was found negligible. A correlation for the modified Euler number considering the pressure drop is proposed depending on nozzle geometric parameterand on the modified Froude numberwith the hydraulic diameter of the nozzle d_o as characteristic length.

Key words: submerged gas injection; nozzle geometry; hydraulic diameter; pressure drop; modified Euler number

Cite this article as: XIAO Jun-bing, YAN Hong-jie, Markus SCHUBERT, Sebastian UNGER, LIU Liu, Eckhard SCHLEICHER, Uwe HAMPEL. Effect of nozzle geometry on pressure drop in submerged gas injection [J]. Journal of Central South University, 2019, 26(8): 2068-2076. DOI: https://doi.org/10.1007/s11771-019-4154-z.

1 Introduction

Submerged gas injection into liquids is encountered in many processes of chemical [1-3]{Harby, 2014 #139;Harby, 2017 #35;Liu, 2018 #865}, nuclear [4, 5] and metallurgical [5-9] industries. Such bottom-blowing technology is often utilized in metallurgical processes. Here, the gas injected through the nozzle into the molten bath transfers kinetic energy to promote the stirring and participates in the redox reaction [10]. The nozzle configuration is one of the key blowing devices [11-13], which is prone to erosion leading to brick damages [14, 15].

Many studies on pressure fluctuations at the nozzle outlet have been carried out to investigate nozzle erosion and wear of the refractory lining [16-19]. AOKI [16, 17] measured the static pressure at different distances from the nozzle outlet using pressure probes to investigate the nozzle outlet erosional effects on the pressure fluctuation. WEI et al [18, 19] studied the effect of the gas expansion on nozzle and refractory measuring the pressure (magnitude and frequency) via pressure sensor. Gas blowing rate, Tuyére number and position were found to influence erosion and lining wear caused by the aforementioned pressure. The influence of the submerged nozzle geometry on the pressure fluctuation, however, has hardly been studied so far.

For the bottom-blown smelting process, Shui-Kou-Shan (SKS) nozzles are being frequently used [20, 21]. They are designed with a central hole and one or two concentric rings of gas channels for the compressed air [22, 23] as shown in Figure 1(a). Simpler pipe-in-a-pipe nozzle designs were proposed by KAPUSTA et al [10] as shown on Figure 1(b). They concluded that smaller the flow channel, the higher the pressure required to guarantee the same smelting efficiency. It should be noted that the design of the bottom-blown nozzles is similar to the ones commonly used for top-blown processes [24, 25], where a short nozzle tip is connected with a long tube to limit the supply gas pressure. However, modifications of the tip geometry for the reduction of gas pressure drop through the nozzle in the bottom-blown process have not been in the focus of research and development so far.

In this work, the influence of the nozzle geometry on the pressure drop between nozzle inlet and outlet for different gas flow rates and bath depths is studied. Empirical correlations for predicting the pressure drop are proposed through dimensional analysis.

2 Experimental

The schematic diagram of the experimental setup is shown in Figure 2. It includes a liquid vessel (hexagonal footprint, which inscribes a circle of 1.2 m diameter) open to the ambient environment at the top, a pressure transducer PT (Omega, PD23-V-0.2), a gas flow meter (Omega, FMA-2611A) and a data acquisition system DAS with a personal computer PC. The interchangeable nozzles were installed at the center of the vessel bottom. Tap water was used as the liquid phase filled to depths of 0.160 m, 0.200 m, 0.284 m, 0.360 m and 0.400 m.

The schematic diagram of the circular-shaped nozzle is shown in Figure 3(a). Compared to the previous studies [12, 13, 26], nozzle tips with different cross-sectional geometries including circular, gear and four-leaf shape were designed (Figure 3(b)). The stainless-steel nozzles were divided into upper and lower parts, i.e. nozzle tips with a length of 10 mm highlighted by the red dashed line and the hollow tube with identical geometry. The three-dimensional view of the gear-shaped nozzle is exemplarily shown in Figure 3(c).

Figure 1 Photographs of nozzles tips:

Figure 2 Schematic diagram of experimental setup

Figure 3 Nozzle designs:

The geometric parameters of the different nozzle geometries are summarized in Table 1.

Table 1 Geometric parameters of nozzle geometries

The cross-sectional area is available for the gas flow in the case of the gear-shaped geometry is almost the same as that of the four-leaf geometry. The perimeter of the cross-section available for the gas flow in the case of the circular shape is close to that of the four-leaf-shaped geometry. The hydraulic diameter of the nozzle outlet d_H at cross-section B-B in Figure 3 is obtained by

                            (1)

where A_oiand L_oi are, respecitively, the area and the perimeter of the orifice cross-section available for the gas flow and n is the total number of openings (index i).

The gas flow rate in the present study was selected to ensure equal modified Froude numbers at the nozzle tips in the model Fr_m (setup in this work) and in the prototype Fr_p (Figure 1(a)). The modified Froude number of the model is calculated according to

                            (2)

where ρ_gis the gas density; ρ_l is the liquid density and u_o is the gas superficial velocity at the nozzle outlet.

Due to the short length of the various nozzle geometries, changes in gas density are very small and can be neglected. Thus, the superficial gas velocity at the nozzle outlet is obtained dividing the gas flow rate at the nozzle inlet Q_inby the total area of the cross-sectional openings according to

                              (3)

The gas flow rate at the nozzle inlet for the model is

        (4)

where subscripts m and p refer to conditions of model and prototype, respectively.

In the present work, the pressure loss caused by viscous effects can be neglected, because of the smooth surface of the plastic pipe and the very short length of the stainless-steel nozzle tip. According to the operating parameters of the bottom-blown furnace, the range of the gas flow rate was set between 0.5×10^-3 m³/s and 1.83×10^-3 m³/s.

The gas superficial velocities at the nozzle outlet (Table 2) are calculated using Eq. (3). Due to the similar orifice area in the cases of gear-shaped and four-leaf-shaped nozzle, the gas superficial velocities are similar to a constant gas flow rate.

Table 2 Gas superficial velocities at nozzle outlet for different nozzle geometries

The pressure drop between nozzle inlet and outlet was measured via pressure transducer. The sensor connections were flush-mounted at the nozzle inlet plane and at the nozzle exit plane with 10 mm distance to the nozzle geometric centerline, respectively. Every measurement was conducted at a sampling rate of 1000 Hz for a total duration of 30 s. Every measurement was performed three times to ensure repeatability. Before the pressure measurement, the pressure transducer was calibrated using a pressure calibrator module (Druck Unomat-MCX II) and a hydraulic pump (Armano PS 600-P).

To assess the difference of the pressure drop behavior, the deviation of the pressure drop was calculated according to

                            (5)

where j represents the index of results from a certain bath depth and is the average pressure drop of all bath depths at a certain gas flow rate.

3 Results and discussion

For the circular nozzle tip, the variation of the mean pressure drop for different bath depths is plotted as a function of the gas flow rate in Figure 4. For a constant bath depth, the pressure drop increases with increasing gas flow rate following a power-law relationship. The influence of the bath depth, which defines the hydrostatic pressure, is negligible. The deviations of the pressure drop according to Eq. (5) for the circular-shaped geometry are summarized in Table 3, which gives evidence that the influence of the bath depth on the pressure drop is insignificant.

Figure 4 Mean pressure drop from circular-shaped geometry for different bath depths

The variation of the mean pressure drop at different gas flow rates is presented as a function of the hydraulic diameter of the nozzle in Figure 5(a). For constant gas flow rate, the mean pressure drop decreases with the increase of hydraulic diameter. This is because the smaller the hydraulic diameter, the higher the pressure drop is. Furthermore, the mean pressure drop in the case of different nozzle geometries at a bath depth of 160 mm is plotted in Figure 5(b). The mean pressure drop of the four-leaf geometry is higher than that of the circular geometry, indicating that for similar cross-sectional perimeter for the gas flow (Table 1), the pressure drop decreases with increasing cross-sectional area. The mean pressure drop of the gear-shaped nozzle is higher than that of the four-leaf nozzle. This indicates that, at the same cross-sectional area available for the gas flow (Table 1), the pressure drop increases with the increase of the total perimeter. The reason for this is that for the same cross-sectional area available for the gas flow, the shape of the nozzle geometry becomes more complex with increasing perimeter. Furthermore, the difference of the pressure drop between gear shape and circular shape is greater than that between four-leaf shape and circular shape. This indicates that, at the same gas flow rate, the pressure drop for the gear shape is much higher than that for four-leaf shape. This is consistent with the conclusions from KAPUSTA et al [10], who found that the smaller the flow channel, the higher the pressure required to reach a certain velocity. Thus, compared with the gear shape, the four-leaf shape reduces the pressure drop at the same gas flow rate.

Table 3 Deviation of pressure drop for circular tip geometry

Figure 5 Pressure drop result:

The average pressure drop, obtained by averaging the mean pressure drop for different bath depths, is shown as a function of the superficial gas velocity at the nozzle outlet in Figure 6. The average pressure drop increases with the increasing superficial gas velocity. The average pressure drops from circular and gear-shaped geometry are similar, which explains the wide application of the gear-shaped geometry in the industry [10, 14]. However, the application of the nozzle with the four-leaf shaped geometry is an attempt to further reduce the pressure drop.

Figure 6 Average pressure drop for different nozzle geometries

4 Empirical correlations

The pressure drop ΔP is mainly governed by gas flow rate Q, gas density ρ_g, total orifice perimeter L_o, total orifice opening area A_oand hydraulic diameter d_o according to

                (6)

In this work, a correlation for ΔP was developed on the basis of the Buckingham π theorem. In Eq. (6), the six parameters were expressed in terms of the three independent physical units M, L and T. The Buckingham π theorem states that Eq. (6) can be rescaled into an equivalent dimensionless relationship with only seven dimensionless parameters. In this work, the variables Q, ρ_g and d_o were selected as independent physical units, thus, the dimensionless parameters can be written as

                          (7)

                          (8)

                          (9)

                        (10)

Substituting the physical variables with the basic dimension units in Eq. (7) results in

                (11)

Since π₁ is a combination of the dimensionless groups, the exponents a₁, b₁, c₁ must satisfy Eqs. (12) to (14) according to

(for M)                          (12)

(for L)                 (13)

c₁=0(for T)                             (14)

Accordingly, a₁=-2 and Eq. (7) becomes

                               (15)

π₂, π₃ and π₄were obtained in a similar way. Then, the group of dimensionless parameters is

,     (16)

Because π₁ and π₃ are dimensionless parameters, their combination is also dimensionless and can be expressed as

                          (17)

This parameter can be used to describe the shape of the nozzle geometry, which is similar to the circularity [27, 28]. Besides, π₂ is the modified Froude number with the hydraulic diameter d_o as the characteristic length [29, 30]. π₄ is the modified Euler number which is a function of the dimensionless parameters according to

                       (18)

Thus, the expressions of the modified Euler number Eu′can be written as

                   (19)

where k₀, k₁and k₂are unknown constants. These unknown constants are determined applying the least-square fitting method using the experimental data. The results and evaluation indicators are summarized in Table 4. It can be concluded that, the correlation can give good prediction under the experimental conditions, based on the low standard deviation StD and high coefficient of determination R².

Table 4 Fitting results of the parameters and evaluation indicators

5 Conclusions

The effect of the nozzle geometry on pressure drop between nozzle inlet and outlet has been studied using different gas flow rates and bath depths through experiments. Nozzles with circular, gear-like and four-leaf cross-sectional shape have been adapted. The main conclusions are

1) The effect of the gas flow rate on the pressure drop between nozzle inlet and outlet is remarkable and follows a power-law relationship. The influence of the bath depth is negligible.

2) The hydraulic diameter, the outlet area and perimeter affect the pressure drop significantly. It can be summarized that the more the cross-sectional area available for the gas flow, the less the pressure drop at the same cross-sectional perimeter is. The more the perimeter, the more the pressure drop at the same cross-sectional area is available for the gas flow.

3) For the same superficial gas velocity, the average pressure drop from the four-leaf-shaped geometry is the least in the present work.

4) Through dimensional analysis, a correlation for the modified Euler number considering the pressure drop has been proposed depending on nozzle geometric parameter and on the modified Froude number with the hydraulic diameter d_o as characteristic length. The proposed correlation is good in replicating the experimental data.

Nomenclature

a₁, a₂, a₃, a₄

Unknown exponents

A_o

Total open orifice area, m²

A_oi

Area of the orifice cross-section available for the gas flow, m²

A_oi,m

Area of the orifice cross-section in the model, m²

A_oi,p

Area of the orifice cross-section in the prototype, m²

b₁, b₂, b₃, b₄

Unknown exponents

c₁, c₂, c₃, c₄

Unknown exponents

d_o

Hydraulic diameter of the nozzle tip, m

d_o,m

Hydraulic diameter in the model, m

d_o,p

Hydraulic diameter in the prototype, m

Eu

Modified Euler number

Fr_m

Modified Froude number of the model

Fr_p

Modified Froude number of the prototype

g

Gravitational acceleration, m/s²

i

Number of specified orifice

j

Index of results from a certain bath depth

k₀, k₁, k₂

Unknown constants

L_o

Total perimeter of the orifice cross-section, m

L_oi

Perimeter of the orifice cross-section available for the gas flow, m

n

Total number of the orifices

ΔP

Pressure drop, kPa

ΔP_j

Pressure drop from a certain bath depth, kPa

Average pressure drop of all bath depths, kPa

Q, Q_in

Gas flow rate at nozzle inlet, m³/s

Q_in,m

Gas flow rate at nozzle inlet in the model, m³/s

Q_in,p

Gas flow rate at nozzle inlet in the prototype, m³/s

u_o

Superficial gas velocity at nozzle outlet, m/s

Greek letters

ρ

Fluid density, kg/m³

ρ_g

Gas density, kg/m³

ρ_g,m

Gas density in the model, kg/m³

ρ_g,p

Gas density in the prototype, kg/m³

ρ_l

Liquid density, kg/m³

ρ_l,m

Liquid density in the model, kg/m³

ρ_l,p

Liquid density in the prototype, kg/m³

σ

Pressure drop deviation

π₁, π₂, π₃, π₄, π₅

Dimensionless parameter

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(Edited by ZHENG Yu-tong)

中文导读

喷嘴结构对浸没式气体喷吹过程压降的影响

摘要：浸没式气体喷吹进入液体中引起复杂多相流动，其中喷嘴的结构对压降方面的操作费用至关重要。本文使用了具有圆形、齿轮状和四叶截面形状的喷嘴结构，研究了不同气体流量和溶池深度下喷嘴结构对喷嘴进出口间压降的影响。结果表明，除喷孔出口处水力直径外，喷孔出口处面积和周长也对压降有重要作用。对于相同的气相表观气速，四叶形几何结构条件下的平均压降最小。溶池深度对压降的影响可以忽略不计。提出了一个与压力降相关的修正欧拉数的经验式，该式取决于喷嘴结构参数和特征长度为水力直径d_o的修正弗劳德数。

关键词：浸没式气体喷吹；喷嘴结构；水力直径；压降；修正欧拉数

Foundation item: Project(51676211) supported by the National Natural Science Foundation of China; Project(2017SK2253) supported by the Key R&D Plan of Hunan Province of China; Project(2015zzts044) supported by Fundamental Research Funds for the Central Universities, China; Project(201606370092) supported by the China Scholarship Council

Received date: 2019-05-29; Accepted date: 2019-07-19

Corresponding author: YAN Hong-jie, PhD, Professor; Tel: +86-13873102530; E-mail: s-rfy@csu.edu.cn; ORCID: 0000-0002-9573- 0465; Markus SCHUBERT, PhD; Tel: +49-351-260-2627; E-mail: m.schubert@hzdr.de; ORCID: 0000-0002- 6218-0989