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Numerical investigation on the internal flow and the particle movement in the abrasive waterjet nozzle
Numerical investigation on the internal flow and the particle movement in the abrasive waterjet nozzle Xinping Long, Xiaofeng Ruan, Qi Liu, Zhengwen Chen, Shengxiong Xue, Ziquan Wu PII: DOI: Reference:
S0032-5910(16)30673-8 doi: 10.1016/j.powtec.2016.09.089 PTEC 11999
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
1 June 2016 14 September 2016 30 September 2016
Please cite this article as: Xinping Long, Xiaofeng Ruan, Qi Liu, Zhengwen Chen, Shengxiong Xue, Ziquan Wu, Numerical investigation on the internal flow and the particle movement in the abrasive waterjet nozzle, Powder Technology (2016), doi: 10.1016/j.powtec.2016.09.089
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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in the Abrasive Waterjet Nozzle
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Numerical Investigation on the Internal Flow and the Particle Movement
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Xinping Long.
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Wuhan University, Hubei, 430072 China;
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Xinping Long a*, Xiaofeng Ruan b, Qi Liu c Zhengwen Chen d, Shengxiong Xue e, Ziquan Wu f
Key Lab of Jet Theory and New Technology of Hubei Province, Hubei, 430072 China
Xiaofeng Ruan
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b
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[email protected]
Wuhan University, Hubei, 430072 China;
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Key Lab of Jet Theory and New Technology of Hubei Province, Hubei, 430072 China [email protected]
c
Qi Liu
Wuhan University, Hubei, 430072 China; Key Lab of Jet Theory and New Technology of Hubei Province, Hubei, 430072 China [email protected]
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Zhengwen Chen 1
ACCEPTED MANUSCRIPT Hefei General Machinery Research Institute, Hefei, 230071, China
Shengxiong Xue
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e
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[email protected]
Hefei General Machinery Research Institute, Hefei, 230071, China
Ziquan Wu
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f
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[email protected]
Shenyang All-Powerful Science and Technology Stock Co., Ltd, Shenyang, 110179, China
Corresponding author. Tel. and Fax number: +86-27-68774906(the same)
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*
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[email protected]
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E-mail address: [email protected]
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ACCEPTED MANUSCRIPT Abstract
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A better understanding of the Abrasive Waterjet (AWJ) nozzle internal multiphase flow is
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crucial for improving AWJ machining performance. Simulation of the internal flow and the
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particle movement in the abrasive entrained waterjet nozzle was conducted based upon the Euler-Lagrange approach and the Discrete Particle Model was used to calculate the
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abrasive particle trajectories. The particle shape factor and the energy loss due to particle-wall interactions were considered in the numerical model. The results indicate that
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a longer focus tube can reduce the particle circumferential movement and thus ensure the particles exiting the nozzle without large circumferential velocities. A decrease of particle
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shape factor will improve the particle acceleration process. The effects of particle density and particle diameter are analyzed. The reported results will provide guidance for AWJ
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applications and the design of AWJ nozzle.
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Keywords: Abrasive Waterjet (AWJ); CFD simulation; Multiphase flow; DPM
1. Introduction
The Pure Waterjet (PWJ) added with abrasive particles (e.g. silica or garnet), which is named as abrasive waterjet, can be utilized to machine a wide range of engineering materials. Generally, there are two types of abrasive waterjets [1]. The first type is called the Abrasive Slurry Jet (ASJ) where abrasive particles are premixed with water in a high pressure tank and generate the so called slurry. The resulting slurry is then directly pressurized and accelerated in a high pressure tube. The second one is called the Abrasive Waterjet (AWJ) where an entrainment system is used to feed abrasive particles. As shown in Fig.1, in the AWJ system, the abrasive particles and air enter into 3
ACCEPTED MANUSCRIPT the mixing chamber and then in the focusing tube the particles are accelerated by the high speed waterjet which is formed by the high pressure water ejecting from the orifice.
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In recent years, AWJ technology has developed rapidly and has been widely applied in numerous
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fields [2-5]. It has become an attractive technology due to its ability to cut both brittle and ductile materials without any influence on their microstructure [6]. Particularly, compared with conventional machining tools, AWJ machining has its distinct advantages of high machining
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versatility, high accuracy, no thermal effect and high flexibility. During the last decades, extensive
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studies have been conducted to investigate the characteristics of the jets, the shape topography formed by AWJ machining and cutting, and the energy transfer efficiency [5-11].
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As an important component of the AWJ equipment, the AWJ nozzle is crucial for improving
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machining quality and reducing energy consumption. It comes clear that the study of the nozzle
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parameters along with a deeper understanding of the characteristics of multiphase flow inside and outside the nozzle are essential in order to develop AWJ into an effective machining and cutting
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technique.
Based on the assumption of conservation of momentum in the focus tube during abrasive particles acceleration processes, Tazibt et al. [1] developed a general modelling to investigate the characteristics of particle velocity. Their model makes it possible to study the influence of entrainment of air on the particle acceleration process. However, since it is a one-dimensional, the theoretical model is insufficient to describe the particle velocity variations in the liquid-gas turbulent jet of three-dimensional flow. Also, this model did not take the effects of the abrasive particle sizes into consideration. Momber [12] carried out impact-force measurements and analyzed the energy transfer during the formation of high speed waterjets and during the mixing 4
ACCEPTED MANUSCRIPT and acceleration processes of abrasive particles. Coray et al. [13] measured the kinetic energy distribution of abrasive particles inside the 5:1 scale AWJ nozzle and analyzed the structure of the
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jet. It was found that the AWJ flow was a three phase flow which involved a strong mixing process
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among the liquid, gas and particles. Osman et al. [14] conducted experiments to investigate the hydrodynamic characteristic of the liquid-gas jet structure and introduced a schematic representation of the two phase jet flow along the focus tube. However, the abrasive particles were
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not considered in their experiments. It is noted that some measurements just can not be done at
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high operating pressures due to the strong liquid-solid interactions in the extremely small nozzle. For the study of such high speed internal flows, the computational fluid dynamics (CFD) has
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become increasingly important to obtain information that cannot or cannot easily be obtained
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experimentally [15, 16]. Relatively few studies have been published on three-dimensional
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simulation of AWJ nozzle. Prisco et al. [17] conducted 3D CFD-based modelling to study the internal flows in AWJ nozzle. Their model was based upon the Euler-Euler approach and did not
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consider the solid particle phase. Based upon Euler-Lagrange method, Yang et al. [18] numerically simulated the multiphase flows in the AWJ nozzle at ultra-high pressure and also predicted the wear rates of the internal nozzle walls. Basha et al. [19] employed CFD techniques to study the flow characteristics inside AWJ nozzle and their results confirmed that CFD could be utilized to explain the relationship between the nozzle parameters and AWJ performance. So far, the dynamic behaviors of AWJ and the water-air-particle interactions inside the nozzle remain to be fully investigated and researches on AWJ are far to reach a comprehensive understanding. It should be noted that the small characteristic dimensions of AWJ nozzle and the ultrahigh velocity, together with the aggressiveness of abrasive particles, make the experimental investigations of the waterjet 5
ACCEPTED MANUSCRIPT and particle motions inside the nozzle rather difficult [12-14]. Specifically, a better understanding of the multiphase flow in the AWJ nozzle is essential for enhancing AWJ machining and cutting
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performance, as well as for designing high performance AWJ nozzle and reducing energy
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consumption.
The present work is to investigate the internal water-air flow and the particle movement in the AWJ nozzle at 450 MPa operating condition on the basis of 3D Euler-Lagrange numerical
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simulation. The particle shape factor and the energy dissipation due to particle-wall interactions
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have been taken into consideration. The present study attempts to reveal the effects of particle parameters and particle inlet conditions on the particle movement in AWJ nozzle.
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2. Numerical model
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As shown in Fig. 1, the abrasive waterjet in the AWJ nozzle is made up of three phases which includes water, gas and abrasive particles. Since the volume fraction of abrasive particles is less
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than 10% [1], the Euler-Lagrange method is adopted for the current simulations.
2.1 The continuous phase
The water-air multiphase flow is simulated based upon the Volume of Fluid (VOF) model which is particularly suitable to track the interface between two or more immiscible fluids. The air phase is treated as the primary phase and the continuity equation for water phase can be written as
ui
w 0 xi
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(1)
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w
is the water phase volume fraction, ui denotes the velocities in the xi direction.
The primary air phase volume fraction
a can be directly obtained according to the
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(2)
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a 1 w
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following equation
A single momentum equation is solved for the mixture of water and air throughout the computational domain, and the resulting velocity field is shared between the two phases. The
x j
P ui u j ui 'u j ' FD xi x j x j xi x j
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ui u j
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momentum equation is given by
(3)
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where P is the static pressure shared by both phases, is the mixture dynamic viscosity, is
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the mixture density, FD denotes the drag force between the continuous phase and the disperse ' ' phase, - ui u j is the Reynolds stress term which is closed by the RNG k turbulence
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model [20] with near wall treatment in the current study.
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The mixture dynamic viscosity and the mixture density in Eq. (3) can be calculated as follows
where
a a w w
(4)
a a w w
(5)
a is the air dynamic viscosity, w is the water dynamic viscosity, a and w stand
for the air density and the water density respectively.
2.2 The disperse phase
The solid particles can be tracked in Lagrangian reference frame when the volume fraction is less than 10%. As the particle phase volume concentration is low, one-way coupling can be applied in the simulations, which indicates that particle movement is affected by the continuous phase while 7
ACCEPTED MANUSCRIPT the continuous phase is not affected by the particle flow. Also ， it is assumed that the particle-particle interactions and the particle rotations can be neglected in this study. Thus, particle
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trajectories were computed based upon the Discrete Particle Model (DPM). The drag force on the particle is modeled as
18 CD Rep u u p p d p2 24
dp u u p
(6)
(7)
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Rep
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where the particle Reynolds number Rep is defined as
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FD
where dp is the particle diameter, p is the particle density. CD in Eq.(6) is the drag coefficient
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which is given by[21]
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where
b3 Rep 24 (1 b1 Rep b2 ) Rep b4 Rep
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CD
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b1 exp(2.3288 6.4581 2.4486 2 ) b2 0.0964 0.5565 2 3 b3 exp(4.905 13.8944 18.4222 10.2599 ) b exp(1.4681 12.2584 20.7322 2 15.8855 3 ) 4
The particle sphericity or shape factor in Eq. (9) is defined as
(8)
(9)
s / S where s is the surface
area of a sphere having the same volume as the particle and S is the actual surface area of the particle. Thus, when the shape factor is less than one, it presents the solid particle is non-spherical. The decrease of shape factor indicates the increase of particle sharpness and contributes to a larger drag coefficient as shown in Fig. 2.
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ACCEPTED MANUSCRIPT 2.3 Particle-wall interactions
When particle enters into the AWJ nozzle, it may impact the internal nozzle wall and rebound
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several times. During this process, the particle momentum energy is dissipated due to the
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particle-wall interactions which can be modeled by introducing the coefficients of restitution (normal direction en and tangential direction et). The coefficients of restitution are defined as the
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ratio between the impact and the rebound velocity of particle and the rebound model [22] proposed by
en 0.988 0.78 0.19 2 0.024 3 0.027 4
(10)
denotes particle incidence angle.
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where
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e 1 0.78 0.84 2 0.21 3 0.028 4 0.022 5
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3. Physical model and boundary conditions
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Due to the presence of abrasive particle inlet tube, the geometry of AWJ nozzle is non-axisymmetrical. Thus, a three dimensional model is necessary to correctly simulate the
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internal flow. The AWJ nozzle used in the present study has an orifice diameter (D1) of 0.4 mm, abrasive inlet tube diameter (D2) of 3 mm, mixing chamber diameter (D3) of 5 mm, focus tube diameter (D) of 1 mm, and focus tube length (L) of 60 mm. The structured grid used for the CFD simulations are shown in Fig. 3. And the origin (0, 0, 0) of the coordinate system is set at the center of the start end of the straight part of the focus tube. A mesh refinement has been performed in the liquid-gas jet surface surrounding and around the orifice regions to improve the VOF surface tracking. Two mesh resolutions were tested with 1.2 million nodes and 1.5 million nodes respectively. It was found that the mesh-independent solutions could be obtained using the mesh
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ACCEPTED MANUSCRIPT with 1.2 million nodes. Thus, the mesh with 1.2 million nodes was adopted in the current simulation.
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For the continuous phase, the pressure inlet boundary condition is applied to the primary flow (air)
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as well as that of the secondary (water) flow, and a pressure outlet condition is assigned to outlet of free jet domain. The water pressure inlet pw is set to 450 MPa which is a typical operating pressure for ultrahigh pressure AWJ applications. In the current study, it is assumed that the air is
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naturally sucked into the mixing chamber by the Venturi effect. Thus, the air pressure Pa is set to
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0.101325 MPa (atmospheric pressure). The atmospheric pressure is also applied at the pressure outlet of the free jet domain. The no-slip velocity condition is imposed on the wall boundaries. For
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the particle phase, uniform velocities are applied at the abrasive particle inlet boundary with a
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specified particle mass flow of 5 g/s in all the simulation cases. And the maximum particle volume
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loading in our current simulations is less than 5%. About 4,000 particles were injected and analyzed in the cases. The outlet boundary is set as ‘escape’, which means that the trajectory
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tracking calculation is stopped once the particle reaches the boundary. And the particle-wall collisions are modeled using the aforementioned rebound model [22] .
4. Simulation procedure
In the current simulation, the control volume method (FVM) is applied to discretize the governing equations of continuous phase. The second order upwind scheme is used for the advection terms in the equations governing mass conservation, momentum and turbulence closure. The second order accurate QUICK scheme is employed to discretize the phase volume fraction. The PRESTO! algorithm is applied to approximate the pressure value. When the water-air flow field solution is
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ACCEPTED MANUSCRIPT obtained, abrasive particles are added into the multiphase flow through the abrasive inlet tube. Then, particle velocities and particle trajectories are calculated and statistically analyzed. The
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simulations were carried out using the commercial software Fluent 14.5.
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5. Results and Discussion
5.1 Flow field inside AWJ nozzle
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When the high pressure water passes through the orifice, the high speed waterjet is formed. Since
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the water phase is treated as incompressible in the numerical model, the theoretical water velocity can be directly calculated by the Bernoulli equation:
2 pw
vth
(11)
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w
where the inlet pressure of water pw is set as 450 MPa, and water density is 998.2 kg/m3. Thus, the
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theoretical Bernoulli velocity vth is 949.54 m/s which is in good consistent with the simulated value of 949.51 m/s.
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To facilitate discussion, the cylindrical coordinate system is defined with ‘x’ for the axial direction and ‘r’ for the radial distance from the axial centerline, and the origin remains the same as shown in Fig. 3. Thus, the velocity are made up of axial velocity va, radial velocity vr and circumferential velocity vc. When the high pressure water ejects from the orifice, the high speed waterjet is formed and flows downstream into the mixing chamber, and the air phase is sucked inside by the Venturi phenomenon. The water-air multiphase flow inside the AWJ nozzle is rather complex as shown in Fig. 4. The air flow is comparatively uniform in the abrasive inlet tube. However, when the air enters into the mixing chamber, a swirl flow around the waterjet is formed due to the velocity 11
ACCEPTED MANUSCRIPT gradient between the two phases. This kind of flow develops into the focus tube and may drag the particles conduct circumferential movements and the resulted centrifugal force will increase the
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possibility of the collision of the particles with the local wall which will cause more energy
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dissipation. On the other hand, if the swirl flow is strong enough at the focus tube outlet, it may make some particles gain comparatively large circumferential velocities in the free jet region which will decrease the AWJ machining performance.
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The circumferential velocities of air phase at different cross sections are analyzed. As shown in
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Fig. 5, at the cross section of x=5 D, the peak value of circumferential velocity is more than 120 m/s. At the position of x=40 D, the circumferential velocity of air is less than 20 m/s, which
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indicates that the swirl flow is dissipated with the increased length of focus tube. The multiphase
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flow in the straight part of the focus tube is fully developed as illustrated in Fig. 6. The axial
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velocities at different positions almost collapse together and turn out to be the top-hat profiles. It should be mentioned that, although the presence of abrasive inlet tube makes the geometry of AWJ
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nozzle non-axisymmetric, the distributions of axial velocity in the focus tube are almost symmetrical and this phenomenon is also predicted by former investigators [17, 19].
5.2 Effect of particle shape factor
Fig. 7 shows the evolution of particles and waterjet velocities along the centerline of the AWJ nozzle. It indicates that there is a sudden decay in the waterjet velocity at the entrance of the focus tube. Once the waterjet flows further downstream into the focus tube, its velocity remains almost the same. Meanwhile, it can be seen in Fig. 7 that the abrasive particle velocities increase rapidly at the focus tube entrance. Further downstream, the increase of particle velocity along the focus tube is not obvious, and the particle velocity almost remains stable at the axial distance of 50 mm. 12
ACCEPTED MANUSCRIPT To account for the shape of abrasive particle, shape factor is changed to investigate dynamic behavior of particle with different sphericities. The increase in particle sharpness from
= 0.8 to
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= 0.6 results in different particle outlet velocities. With smaller shape factor, the particle velocity
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seems to increase more quickly and the final particle outlet velocity also gets higher. One possible explanation may be the larger drag force coefficient for smaller shape factor as shown in Fig. 2. Since the abrasive is non-spherical in real AWJ applications, the influence of shape factor on the
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particle outlet velocities deserves to be further studied. Fig. 8 gives the probability distribution of
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particle velocity at the focus outlet. The general probability distributions under the two different shape factors turn out to be similar. However, the smaller shape factor indicates a larger
= 0.6, the predicted mean outlet velocity is 814.7 m/s.
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while for
= 0.8 is 765.3 m/s,
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probability of high particle velocity. The predicted mean outlet velocity for
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5.3 Effect of particle density
As shown in Fig. 9, the increase of particle density tends to decrease particle velocity. When set
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the particle density as 2500 kg/m3, the particle velocity at the AWJ nozzle outlet is 827.1 m/s. Increase the particle density to 3000 kg/m3, the outlet velocity of particle decrease to 814.7 m/s. Further increase the particle density to 3500 kg/m3, the outlet particle velocity remains unchanged, which indicates that the particle can be effectively accelerated by waterjet in the focus tube. The probability distributions of outlet velocity with different particle densities are given in Fig. 10. Since the variations of particle outlet velocities are not significant, large density particles indicate stronger impact ability and are recommended for AWJ applications.
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Fig. 11 shows the particle velocity evolutions with different particle diameters. The smallest
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particle tends to be accelerated more effectively by the waterjet and can obtain higher velocity
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after traveling some distance in the focus tube. However, with the increase of particle diameter, the particle outlet velocity becomes smaller because of larger inertia. Thus, particle with smaller
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size indicates a larger outlet velocity and can improve AWJ machining ability.
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6. Conclusions
Numerical simulations based on Euler-Lagrange approach have been carried out to investigate the
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internal flow and the particle movement in the AWJ nozzle. The influence of particle shape and
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the energy loss due to particle-wall collisions are considered in the numerical model. The results
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show that the air phase near the entrance of the focus tube has a large circumferential velocity which lead to the circumferential movement of particles, and the induced centrifugal force will
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increase the possibility of the collision of the particles with the local wall. A longer focus tube can reduce the particle circumferential movement and thus ensure the particles exiting the nozzle without large circumferential velocities. A decrease of particle shape factor will improve the particle acceleration process. Large density particle with small diameter is recommended for AWJ applications.
Acknowledgement
This work was financially supported by National High Technology Research and Development Program 863 (2015AA043401)
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Graphical abstract
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Highlights he multiphase flow in Abrasive Waterjet (AWJ) nozzle was modeled. The particle motion in the nozzle was simulated. The effects of particle parameters were analyzed.
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S0032-5910(16)30673-8 doi: 10.1016/j.powtec.2016.09.089 PTEC 11999
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
1 June 2016 14 September 2016 30 September 2016
Please cite this article as: Xinping Long, Xiaofeng Ruan, Qi Liu, Zhengwen Chen, Shengxiong Xue, Ziquan Wu, Numerical investigation on the internal flow and the particle movement in the abrasive waterjet nozzle, Powder Technology (2016), doi: 10.1016/j.powtec.2016.09.089
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
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in the Abrasive Waterjet Nozzle
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Numerical Investigation on the Internal Flow and the Particle Movement
a
Xinping Long.
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Wuhan University, Hubei, 430072 China;
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Xinping Long a*, Xiaofeng Ruan b, Qi Liu c Zhengwen Chen d, Shengxiong Xue e, Ziquan Wu f
Key Lab of Jet Theory and New Technology of Hubei Province, Hubei, 430072 China
Xiaofeng Ruan
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b
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[email protected]
Wuhan University, Hubei, 430072 China;
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Key Lab of Jet Theory and New Technology of Hubei Province, Hubei, 430072 China [email protected]
c
Qi Liu
Wuhan University, Hubei, 430072 China; Key Lab of Jet Theory and New Technology of Hubei Province, Hubei, 430072 China [email protected]
d
Zhengwen Chen 1
ACCEPTED MANUSCRIPT Hefei General Machinery Research Institute, Hefei, 230071, China
Shengxiong Xue
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e
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[email protected]
Hefei General Machinery Research Institute, Hefei, 230071, China
Ziquan Wu
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f
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[email protected]
Shenyang All-Powerful Science and Technology Stock Co., Ltd, Shenyang, 110179, China
Corresponding author. Tel. and Fax number: +86-27-68774906(the same)
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[email protected]
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E-mail address: [email protected]
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ACCEPTED MANUSCRIPT Abstract
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A better understanding of the Abrasive Waterjet (AWJ) nozzle internal multiphase flow is
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crucial for improving AWJ machining performance. Simulation of the internal flow and the
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particle movement in the abrasive entrained waterjet nozzle was conducted based upon the Euler-Lagrange approach and the Discrete Particle Model was used to calculate the
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abrasive particle trajectories. The particle shape factor and the energy loss due to particle-wall interactions were considered in the numerical model. The results indicate that
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a longer focus tube can reduce the particle circumferential movement and thus ensure the particles exiting the nozzle without large circumferential velocities. A decrease of particle
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shape factor will improve the particle acceleration process. The effects of particle density and particle diameter are analyzed. The reported results will provide guidance for AWJ
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applications and the design of AWJ nozzle.
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Keywords: Abrasive Waterjet (AWJ); CFD simulation; Multiphase flow; DPM
1. Introduction
The Pure Waterjet (PWJ) added with abrasive particles (e.g. silica or garnet), which is named as abrasive waterjet, can be utilized to machine a wide range of engineering materials. Generally, there are two types of abrasive waterjets [1]. The first type is called the Abrasive Slurry Jet (ASJ) where abrasive particles are premixed with water in a high pressure tank and generate the so called slurry. The resulting slurry is then directly pressurized and accelerated in a high pressure tube. The second one is called the Abrasive Waterjet (AWJ) where an entrainment system is used to feed abrasive particles. As shown in Fig.1, in the AWJ system, the abrasive particles and air enter into 3
ACCEPTED MANUSCRIPT the mixing chamber and then in the focusing tube the particles are accelerated by the high speed waterjet which is formed by the high pressure water ejecting from the orifice.
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In recent years, AWJ technology has developed rapidly and has been widely applied in numerous
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fields [2-5]. It has become an attractive technology due to its ability to cut both brittle and ductile materials without any influence on their microstructure [6]. Particularly, compared with conventional machining tools, AWJ machining has its distinct advantages of high machining
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versatility, high accuracy, no thermal effect and high flexibility. During the last decades, extensive
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studies have been conducted to investigate the characteristics of the jets, the shape topography formed by AWJ machining and cutting, and the energy transfer efficiency [5-11].
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As an important component of the AWJ equipment, the AWJ nozzle is crucial for improving
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machining quality and reducing energy consumption. It comes clear that the study of the nozzle
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parameters along with a deeper understanding of the characteristics of multiphase flow inside and outside the nozzle are essential in order to develop AWJ into an effective machining and cutting
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technique.
Based on the assumption of conservation of momentum in the focus tube during abrasive particles acceleration processes, Tazibt et al. [1] developed a general modelling to investigate the characteristics of particle velocity. Their model makes it possible to study the influence of entrainment of air on the particle acceleration process. However, since it is a one-dimensional, the theoretical model is insufficient to describe the particle velocity variations in the liquid-gas turbulent jet of three-dimensional flow. Also, this model did not take the effects of the abrasive particle sizes into consideration. Momber [12] carried out impact-force measurements and analyzed the energy transfer during the formation of high speed waterjets and during the mixing 4
ACCEPTED MANUSCRIPT and acceleration processes of abrasive particles. Coray et al. [13] measured the kinetic energy distribution of abrasive particles inside the 5:1 scale AWJ nozzle and analyzed the structure of the
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jet. It was found that the AWJ flow was a three phase flow which involved a strong mixing process
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among the liquid, gas and particles. Osman et al. [14] conducted experiments to investigate the hydrodynamic characteristic of the liquid-gas jet structure and introduced a schematic representation of the two phase jet flow along the focus tube. However, the abrasive particles were
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not considered in their experiments. It is noted that some measurements just can not be done at
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high operating pressures due to the strong liquid-solid interactions in the extremely small nozzle. For the study of such high speed internal flows, the computational fluid dynamics (CFD) has
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become increasingly important to obtain information that cannot or cannot easily be obtained
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experimentally [15, 16]. Relatively few studies have been published on three-dimensional
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simulation of AWJ nozzle. Prisco et al. [17] conducted 3D CFD-based modelling to study the internal flows in AWJ nozzle. Their model was based upon the Euler-Euler approach and did not
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consider the solid particle phase. Based upon Euler-Lagrange method, Yang et al. [18] numerically simulated the multiphase flows in the AWJ nozzle at ultra-high pressure and also predicted the wear rates of the internal nozzle walls. Basha et al. [19] employed CFD techniques to study the flow characteristics inside AWJ nozzle and their results confirmed that CFD could be utilized to explain the relationship between the nozzle parameters and AWJ performance. So far, the dynamic behaviors of AWJ and the water-air-particle interactions inside the nozzle remain to be fully investigated and researches on AWJ are far to reach a comprehensive understanding. It should be noted that the small characteristic dimensions of AWJ nozzle and the ultrahigh velocity, together with the aggressiveness of abrasive particles, make the experimental investigations of the waterjet 5
ACCEPTED MANUSCRIPT and particle motions inside the nozzle rather difficult [12-14]. Specifically, a better understanding of the multiphase flow in the AWJ nozzle is essential for enhancing AWJ machining and cutting
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performance, as well as for designing high performance AWJ nozzle and reducing energy
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consumption.
The present work is to investigate the internal water-air flow and the particle movement in the AWJ nozzle at 450 MPa operating condition on the basis of 3D Euler-Lagrange numerical
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simulation. The particle shape factor and the energy dissipation due to particle-wall interactions
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have been taken into consideration. The present study attempts to reveal the effects of particle parameters and particle inlet conditions on the particle movement in AWJ nozzle.
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2. Numerical model
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As shown in Fig. 1, the abrasive waterjet in the AWJ nozzle is made up of three phases which includes water, gas and abrasive particles. Since the volume fraction of abrasive particles is less
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than 10% [1], the Euler-Lagrange method is adopted for the current simulations.
2.1 The continuous phase
The water-air multiphase flow is simulated based upon the Volume of Fluid (VOF) model which is particularly suitable to track the interface between two or more immiscible fluids. The air phase is treated as the primary phase and the continuity equation for water phase can be written as
ui
w 0 xi
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(1)
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w
is the water phase volume fraction, ui denotes the velocities in the xi direction.
The primary air phase volume fraction
a can be directly obtained according to the
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(2)
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a 1 w
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following equation
A single momentum equation is solved for the mixture of water and air throughout the computational domain, and the resulting velocity field is shared between the two phases. The
x j
P ui u j ui 'u j ' FD xi x j x j xi x j
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ui u j
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momentum equation is given by
(3)
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where P is the static pressure shared by both phases, is the mixture dynamic viscosity, is
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the mixture density, FD denotes the drag force between the continuous phase and the disperse ' ' phase, - ui u j is the Reynolds stress term which is closed by the RNG k turbulence
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model [20] with near wall treatment in the current study.
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The mixture dynamic viscosity and the mixture density in Eq. (3) can be calculated as follows
where
a a w w
(4)
a a w w
(5)
a is the air dynamic viscosity, w is the water dynamic viscosity, a and w stand
for the air density and the water density respectively.
2.2 The disperse phase
The solid particles can be tracked in Lagrangian reference frame when the volume fraction is less than 10%. As the particle phase volume concentration is low, one-way coupling can be applied in the simulations, which indicates that particle movement is affected by the continuous phase while 7
ACCEPTED MANUSCRIPT the continuous phase is not affected by the particle flow. Also ， it is assumed that the particle-particle interactions and the particle rotations can be neglected in this study. Thus, particle
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trajectories were computed based upon the Discrete Particle Model (DPM). The drag force on the particle is modeled as
18 CD Rep u u p p d p2 24
dp u u p
(6)
(7)
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Rep
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where the particle Reynolds number Rep is defined as
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FD
where dp is the particle diameter, p is the particle density. CD in Eq.(6) is the drag coefficient
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which is given by[21]
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where
b3 Rep 24 (1 b1 Rep b2 ) Rep b4 Rep
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CD
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b1 exp(2.3288 6.4581 2.4486 2 ) b2 0.0964 0.5565 2 3 b3 exp(4.905 13.8944 18.4222 10.2599 ) b exp(1.4681 12.2584 20.7322 2 15.8855 3 ) 4
The particle sphericity or shape factor in Eq. (9) is defined as
(8)
(9)
s / S where s is the surface
area of a sphere having the same volume as the particle and S is the actual surface area of the particle. Thus, when the shape factor is less than one, it presents the solid particle is non-spherical. The decrease of shape factor indicates the increase of particle sharpness and contributes to a larger drag coefficient as shown in Fig. 2.
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ACCEPTED MANUSCRIPT 2.3 Particle-wall interactions
When particle enters into the AWJ nozzle, it may impact the internal nozzle wall and rebound
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several times. During this process, the particle momentum energy is dissipated due to the
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particle-wall interactions which can be modeled by introducing the coefficients of restitution (normal direction en and tangential direction et). The coefficients of restitution are defined as the
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ratio between the impact and the rebound velocity of particle and the rebound model [22] proposed by
en 0.988 0.78 0.19 2 0.024 3 0.027 4
(10)
denotes particle incidence angle.
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where
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e 1 0.78 0.84 2 0.21 3 0.028 4 0.022 5
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3. Physical model and boundary conditions
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Due to the presence of abrasive particle inlet tube, the geometry of AWJ nozzle is non-axisymmetrical. Thus, a three dimensional model is necessary to correctly simulate the
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internal flow. The AWJ nozzle used in the present study has an orifice diameter (D1) of 0.4 mm, abrasive inlet tube diameter (D2) of 3 mm, mixing chamber diameter (D3) of 5 mm, focus tube diameter (D) of 1 mm, and focus tube length (L) of 60 mm. The structured grid used for the CFD simulations are shown in Fig. 3. And the origin (0, 0, 0) of the coordinate system is set at the center of the start end of the straight part of the focus tube. A mesh refinement has been performed in the liquid-gas jet surface surrounding and around the orifice regions to improve the VOF surface tracking. Two mesh resolutions were tested with 1.2 million nodes and 1.5 million nodes respectively. It was found that the mesh-independent solutions could be obtained using the mesh
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ACCEPTED MANUSCRIPT with 1.2 million nodes. Thus, the mesh with 1.2 million nodes was adopted in the current simulation.
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For the continuous phase, the pressure inlet boundary condition is applied to the primary flow (air)
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as well as that of the secondary (water) flow, and a pressure outlet condition is assigned to outlet of free jet domain. The water pressure inlet pw is set to 450 MPa which is a typical operating pressure for ultrahigh pressure AWJ applications. In the current study, it is assumed that the air is
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naturally sucked into the mixing chamber by the Venturi effect. Thus, the air pressure Pa is set to
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0.101325 MPa (atmospheric pressure). The atmospheric pressure is also applied at the pressure outlet of the free jet domain. The no-slip velocity condition is imposed on the wall boundaries. For
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the particle phase, uniform velocities are applied at the abrasive particle inlet boundary with a
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specified particle mass flow of 5 g/s in all the simulation cases. And the maximum particle volume
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loading in our current simulations is less than 5%. About 4,000 particles were injected and analyzed in the cases. The outlet boundary is set as ‘escape’, which means that the trajectory
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tracking calculation is stopped once the particle reaches the boundary. And the particle-wall collisions are modeled using the aforementioned rebound model [22] .
4. Simulation procedure
In the current simulation, the control volume method (FVM) is applied to discretize the governing equations of continuous phase. The second order upwind scheme is used for the advection terms in the equations governing mass conservation, momentum and turbulence closure. The second order accurate QUICK scheme is employed to discretize the phase volume fraction. The PRESTO! algorithm is applied to approximate the pressure value. When the water-air flow field solution is
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ACCEPTED MANUSCRIPT obtained, abrasive particles are added into the multiphase flow through the abrasive inlet tube. Then, particle velocities and particle trajectories are calculated and statistically analyzed. The
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simulations were carried out using the commercial software Fluent 14.5.
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5. Results and Discussion
5.1 Flow field inside AWJ nozzle
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When the high pressure water passes through the orifice, the high speed waterjet is formed. Since
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the water phase is treated as incompressible in the numerical model, the theoretical water velocity can be directly calculated by the Bernoulli equation:
2 pw
vth
(11)
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w
where the inlet pressure of water pw is set as 450 MPa, and water density is 998.2 kg/m3. Thus, the
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theoretical Bernoulli velocity vth is 949.54 m/s which is in good consistent with the simulated value of 949.51 m/s.
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To facilitate discussion, the cylindrical coordinate system is defined with ‘x’ for the axial direction and ‘r’ for the radial distance from the axial centerline, and the origin remains the same as shown in Fig. 3. Thus, the velocity are made up of axial velocity va, radial velocity vr and circumferential velocity vc. When the high pressure water ejects from the orifice, the high speed waterjet is formed and flows downstream into the mixing chamber, and the air phase is sucked inside by the Venturi phenomenon. The water-air multiphase flow inside the AWJ nozzle is rather complex as shown in Fig. 4. The air flow is comparatively uniform in the abrasive inlet tube. However, when the air enters into the mixing chamber, a swirl flow around the waterjet is formed due to the velocity 11
ACCEPTED MANUSCRIPT gradient between the two phases. This kind of flow develops into the focus tube and may drag the particles conduct circumferential movements and the resulted centrifugal force will increase the
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possibility of the collision of the particles with the local wall which will cause more energy
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dissipation. On the other hand, if the swirl flow is strong enough at the focus tube outlet, it may make some particles gain comparatively large circumferential velocities in the free jet region which will decrease the AWJ machining performance.
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The circumferential velocities of air phase at different cross sections are analyzed. As shown in
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Fig. 5, at the cross section of x=5 D, the peak value of circumferential velocity is more than 120 m/s. At the position of x=40 D, the circumferential velocity of air is less than 20 m/s, which
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indicates that the swirl flow is dissipated with the increased length of focus tube. The multiphase
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flow in the straight part of the focus tube is fully developed as illustrated in Fig. 6. The axial
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velocities at different positions almost collapse together and turn out to be the top-hat profiles. It should be mentioned that, although the presence of abrasive inlet tube makes the geometry of AWJ
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nozzle non-axisymmetric, the distributions of axial velocity in the focus tube are almost symmetrical and this phenomenon is also predicted by former investigators [17, 19].
5.2 Effect of particle shape factor
Fig. 7 shows the evolution of particles and waterjet velocities along the centerline of the AWJ nozzle. It indicates that there is a sudden decay in the waterjet velocity at the entrance of the focus tube. Once the waterjet flows further downstream into the focus tube, its velocity remains almost the same. Meanwhile, it can be seen in Fig. 7 that the abrasive particle velocities increase rapidly at the focus tube entrance. Further downstream, the increase of particle velocity along the focus tube is not obvious, and the particle velocity almost remains stable at the axial distance of 50 mm. 12
ACCEPTED MANUSCRIPT To account for the shape of abrasive particle, shape factor is changed to investigate dynamic behavior of particle with different sphericities. The increase in particle sharpness from
= 0.8 to
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= 0.6 results in different particle outlet velocities. With smaller shape factor, the particle velocity
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seems to increase more quickly and the final particle outlet velocity also gets higher. One possible explanation may be the larger drag force coefficient for smaller shape factor as shown in Fig. 2. Since the abrasive is non-spherical in real AWJ applications, the influence of shape factor on the
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particle outlet velocities deserves to be further studied. Fig. 8 gives the probability distribution of
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particle velocity at the focus outlet. The general probability distributions under the two different shape factors turn out to be similar. However, the smaller shape factor indicates a larger
= 0.6, the predicted mean outlet velocity is 814.7 m/s.
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while for
= 0.8 is 765.3 m/s,
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probability of high particle velocity. The predicted mean outlet velocity for
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5.3 Effect of particle density
As shown in Fig. 9, the increase of particle density tends to decrease particle velocity. When set
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the particle density as 2500 kg/m3, the particle velocity at the AWJ nozzle outlet is 827.1 m/s. Increase the particle density to 3000 kg/m3, the outlet velocity of particle decrease to 814.7 m/s. Further increase the particle density to 3500 kg/m3, the outlet particle velocity remains unchanged, which indicates that the particle can be effectively accelerated by waterjet in the focus tube. The probability distributions of outlet velocity with different particle densities are given in Fig. 10. Since the variations of particle outlet velocities are not significant, large density particles indicate stronger impact ability and are recommended for AWJ applications.
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ACCEPTED MANUSCRIPT 5.4 Effect of particle diameter
Fig. 11 shows the particle velocity evolutions with different particle diameters. The smallest
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particle tends to be accelerated more effectively by the waterjet and can obtain higher velocity
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after traveling some distance in the focus tube. However, with the increase of particle diameter, the particle outlet velocity becomes smaller because of larger inertia. Thus, particle with smaller
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size indicates a larger outlet velocity and can improve AWJ machining ability.
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6. Conclusions
Numerical simulations based on Euler-Lagrange approach have been carried out to investigate the
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internal flow and the particle movement in the AWJ nozzle. The influence of particle shape and
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the energy loss due to particle-wall collisions are considered in the numerical model. The results
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show that the air phase near the entrance of the focus tube has a large circumferential velocity which lead to the circumferential movement of particles, and the induced centrifugal force will
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increase the possibility of the collision of the particles with the local wall. A longer focus tube can reduce the particle circumferential movement and thus ensure the particles exiting the nozzle without large circumferential velocities. A decrease of particle shape factor will improve the particle acceleration process. Large density particle with small diameter is recommended for AWJ applications.
Acknowledgement
This work was financially supported by National High Technology Research and Development Program 863 (2015AA043401)
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ACCEPTED MANUSCRIPT [18] M. Yang, Y. Wang, C. Kang, Y.U. Feng, Multiphase Flow and Wear in the Cutting Head of Ultra-high Pressure Abrasive Water Jet, Chinese Journal of Mechanical Engineering, 22 (2009) 729-734. [19] A.T. Basha, M. Annoni, M. Monno, F. Inzoli, Investigation of the hydrodynamic characteristics of
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[21] A. Haider, O. Levenspiel, Drag Coefficient and Terminal Velocity of Spherical and Non-Spherical [22] A. Forder, M. Thew, D. Harrison, A numerical investigation of solid particle erosion experienced
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Graphical abstract
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Highlights he multiphase flow in Abrasive Waterjet (AWJ) nozzle was modeled. The particle motion in the nozzle was simulated. The effects of particle parameters were analyzed.
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