Research ArticleTheoretical Study of the Effect of InstrumentParameters on the Flow Field of Air-FlowImpacting Based Mechanochemical Synthesis

Yang Tao , Jun Lin, Zhao Zhang, Qiuting Guo, Jin Zuo, and Bo Lu

High Speed Aerodynamics Institute, China Aerodynamic Research and Development Center, Mianyang 621000, China

Correspondence should be addressed to Yang Tao; 50323222@qq.com

Received 3 January 2018; Revised 20 March 2018; Accepted 25 March 2018; Published 24 May 2018

Academic Editor: Jose C. Merchuk

Copyright © 2018 Yang Tao et al. )is is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

)e air-flow impacting based mechanochemical synthesis is an alternative strategy to traditional mechanochemical preparations,which has many advantages in terms of reaction temperature, preparation speed, and cleanness. Herein, we theoretically study theeffect of instrument parameters, including the axial position of physical target, the diameter difference between nozzle throat andsuction pipe, and divergence angles of uniform speed region, on the flow field of the air-flow impacting based mechanochemicalsynthesis. )e optimized parameters have been obtained. Under the optimal conditions, a stable and high-speed air flow isobtained, in which the speed can achieve a Mach number of approximately 2.6. )e high-speed air flow is able to easily carry thereacting substances to arrive at the physical target, triggering a chemical reaction. )ese findings undoubtedly provide a keyguideline for further development and application of the air-flow impacting based mechanochemical synthesis.

1. Introduction

)e mechanochemical synthesis has received more andmore attention due to its unique advantages such as sim-pleness, economy, and environmental friendliness [1]. It canfacilely proceed in the solid state without the use of solvents.A variety of substances spanning from organic compoundsto metal-organic frameworks to nanomaterials have beensuccessfully prepared using the mechanochemical synthesistechniques [1–7]. Traditionally, the mechanochemical syn-thesis is carried out by hand grinding, ball milling, and twinscrew extrusion [8–14]. However, these methods suffer frommany drawbacks. For instance, these methods will producea high temperature during the procedures, which are notsuitable to prepare thermally sensitive compounds. Addi-tionally, the preparation speed is limited at kg·h−1, makingthem insufficient to realize the large-scale synthesis.

In order to overcome these shortcomings, we recentlydeveloped a novel air-flow impacting basedmechanochemicalsynthesis [15]. In this strategy, the air flow can be acceleratedto a maximum velocity going up to 300–600m/s at room

temperature (approximately 25°C). When the reacting sub-stances are carried by the air flow with a supersonic speed,they will tempestuously collide with each other or a physicaltarget, accompanying that the mechanical energy effectivelyinitiates the chemical reaction. )e gaseous medium isemployed instead of physical ball, pestle, and screw, resultingin a more clean and renewable synthesis. More importantly, ithas been demonstrated that the air-flow impacting basedmechanochemical synthesis is able to achieve large-scale andfast preparation at kg·min−1 rates, which is at least sixty timesfaster than the traditional mechanochemical synthesismethods. Obviously, the performance of air-flow impactingbased mechanochemical synthesis is highly dependent on theair-flow field in the instrument. To better understand thepreparation process, it is highly desirable to study the air-flowfield in the instrument.

Here, we theoretically investigate the effect of aero-dynamic design parameters of the instrument on the flow fieldof the air-flow impacting based mechanochemical synthesis.Several instrument parameters, including the physical target,the diameter difference between nozzle throat inwall and

HindawiInternational Journal of Chemical EngineeringVolume 2018, Article ID 3061517, 6 pageshttps://doi.org/10.1155/2018/3061517

suction pipe of solid reaction particles, and divergence anglesof acceleration pipe, have been investigated. Based on theanalysis results, we obtain the optimized aerodynamic designparameters. �is work provides a guideline for the air-�owimpacting based mechanochemical synthesis.

2. Methods

2.1. Design of De Laval Nozzle. De Laval nozzle is employedto produce a high-speed air �ow with a supersonic speed.Isentropic �ow was assumed in the annular nozzle. �eproduced Mach number (Ma) is depended on the area ratioof exit surface and throat Aex/Athr, according to the fol-lowing equation [16, 17]:

Aex

Athr�

1Ma

2c + 1

1 +c− 12M2

a( )( )(c+1)/(2(c−1))

, (1)

where c is the ratio of speci�c heats, which is taken to beconstant of 1.4 for the diatomic gas molecules,Aex is the areaof the exhaust, and Athr is the area of the throat.

�e pressure ratio of the total pressure to the staticpressure at the intake side and exhaust side must maintaina high enough value, and the critical pressure ratio can bedetected by the following relationships [18–20]:

p0pex

�T0

Tex( )

c/(c−1)

� 1 +c− 12M2

a( )c/(c−1)

, (2)

where p0 and T0 are the total pressure and total temperatureat intake side and pex and Tex are the static pressure andstatic temperature at the exhaust side of the nozzle.

Also, the various parts of the De Laval nozzle, includingconverge section, diverge section, and uniform speed sec-tion, are calculated to obtain the physical appearance such assize, length, and angle through a series of equations as shownin the supporting information (available here). To ensurethat the theoretical Mach number can reach 3, the physicalsizes of the De Laval nozzle are as follows: converge section(length: 40mm, diameter: 9.26mm), throat diameter(3mm), and diverge section (length: 24.69mm, diameter:6.17mm).

2.2.Numerical Simulation. We employ the commercial CFDcode Fluent 6.3 for the numerical simulation based on theabove-mentioned De Laval nozzle and variable instrumentalparameters as mentioned in our manuscript. �e compu-tational analysis uses the Navier–Stokes equations, whichcan be written in a conservational form as follows [21]:

zρzt+

z

zxjρuj( ) � 0, (3)

z ρui( )zt

+z

zxjρuiuj + δijp( ) �

zτijzxj

, (4)

z(ρE)zt

+z

zxjρHuj( ) �

z

zxjτijui + λ

zT

zxj( ), (5)

where ρ, p, and T denote �ow density, pressure, and tem-perature, respectively; uj is the velocity component along theCartesian coordinate xj;E andH are the total energy and thetotal enthalpy per unit volume, respectively; τij is the stresstensor; λ is the heat transfer coe�cient; and δij is theKronecker delta. �e equation of state of ideal gas is in-troduced to close the system.

�e RANS equations with the k-ω SST turbulence modelare used for the computational analysis. �e SST turbulencemodel is employed for high-accuracy boundary-layer sim-ulation. It is a hybrid method that couples the standard k-εand k-ω models in an e�cient manner, with the k-ω modelused in the near-wall region and the standard k-ε model inthe far-�eld region, blending them together at the interfacebetween the regions. It includes the modeling of transport ofshear stress via a modi�ed de�nition of the turbulentviscosity.

�e pressure inlet boundary conditions were used at theintakes of the nozzle and suction pipe. �e pressure outletboundary condition was applied at the exit. �e no-slippedwall was used for all of the solid walls. Moreover, all wallswere assumed as ideal rigid solid surfaces without de-formation during the collision. �e overall analysis of the�ow �eld of air-�ow impacting based mechanochemicalsynthesis was carried out on ANSYS 16.0.

3. Results and Discussion

3.1. �e Structure of the Air-Flow Impacting Instrument.As shown in Figure 1, the air-�ow impacting instrument isconsisting of suction pipe, convergent region, di�usionregion, uniform speed region, and a physical target. Whencompressed air is injected into this instrument, the air isaccelerated to a subsonic speed in the convergent region.�espeed of the air is further increased to the supersonic speedin the di�usion region. �e high-speed air can carry thereacting substances to collide with a physical target, trig-gering a chemical reaction.�e speed of the air is a key factorfor the chemical preparation, which is mainly dependent onthe diameter di�erence between nozzle throat and suctionpipe, the position of the physical target, and the divergenceangles.

3.2. Optimization of Aerodynamic Design Parameters for theFlow Field. To describe the speed of the air �ow, the Machnumber is introduced, which is expressed as Ma � u/c,where u is the local �ow velocity with respect to the boundariesand c represents the speed of sound in the medium. It can beexpressed as c �

����cRT√

, where c is the adiabatic exponent of

Convergent region

Diffusion region

Uniform speed region

Target

GasSuction pipe

Figure 1: Schematic representation of the air-�ow impacting basedmechanochemical synthesis instrument.

2 International Journal of Chemical Engineering

air, R is the gas constant, and T is the thermodynamic tem-perature [22]. We can solve the Navier–Stokes equations (5) toobtain the T at di�erent positions, which are further employedfor calculating c. �e e�ect of the diameter di�erence betweennozzle throat and suction pipe (ΔR) on the �ow �eld is �rstlyinvestigated. As shown in Figure 2, when the value of the ΔR islower than 0.5mm, the speed of the compressed air quicklydecreases to a sonic speed after spraying. Additionally, if theΔR is above 2.5mm, the air �ow is apt to form a curved shockwave, which is unstable (Figure 2(b)). �erefore, in order toobtain a stable high-speed air �ow, the value of the ΔR shouldbe kept in the range of 1.0-2.0mm.

Apart from the diameter di�erence between throatinwall and suction pipe ΔR, the axial position of the physicaltarget apart from the spraying outlet is another important

factor. As displayed in Figure 3(a), it cannot obtain a stable�ow �eld in the absence of the physical target, and the speedof the air �ow is relatively low. As the physical target isplaced in the instrument, a stable and high-speed air �owcan be obtained as shown in Figures 3(b)–3(e). Nevertheless,the physical target is also able to disturb the �ow �eld of theair �ow if it is too near the spraying outlet (Figures 3(f)–3(h)).Simultaneously, under this condition, it can result in localcongestion, leading to moving the curved shock wave for-ward. While the distance between the physical target and thespraying outlet is in the range from 395 to 410mm, a stableand high-speed air �ow can be obtained, and the average ofMa is approximately 2.6. �erefore, the optimized axial dis-tance between the physical target and the spraying outlet isranging from 395 to 410mm.

∆R (mm)

Suction pipe

�roat

(a)

∆R = 0.5

∆R = 1.0

∆R = 2.0

∆R = 2.5

∆R = 1.5

Mach number: 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

–0.1 0 0.1 0.2 0.3 0.4X (m)

(b)

Figure 2: (a)�e front view of the throat and suction pipe. (b) E�ect of the diameter di�erence between nozzle throat and suction pipe (ΔR)on the �ow �eld of the air �ow.

Target3.63.43.232.82.62.42.221.81.61.41.210.80.60.40.2

Ma

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 3: Cross-sectional �ow �eld of air �ow in the absence (a) and presence of a physical target placed under di�erent positions: (b) 410,(c) 405, (d) 400, (e) 395, (f) 390, (g) 385, and (h) 381mm.

International Journal of Chemical Engineering 3

In order to avoid the appearance of strong shock waveand keep a high air �ow, the divergence angle is introducedin the uniform speed region as shown in Figure 4(a). �ee�ect of the divergence angle on the axial speed (Uaxis) isexamined at a Ma of 3. �e high Ma can promote thecollisional processes, which e�ectively initiates the chemicalreaction. In the present stage, it is very di�cult to achieve theequipment with the Ma number of more than 3 because ofthe limitations in terms of materials, carrier gas, andpressure. It can be seen that the absence of the divergenceangle is able to result in gas congestion and a fast decrease ofthe Uaxis, which decreases to the subsonic speed. �is resultcon�rms that the introduction of the divergence angle isquite necessary. In addition, with the increasing the di-vergence angle from 0.1° to 0.3°, the value of the Uaxisgradually increases and reaches a stable value at 0.3°.However, when the divergence angle is larger than 0.3°, theunstable shock wave appears in the end of the uniform speedregion. Accordingly, the optimized divergence angle is 0.3°to obtain a stable and high-speed air �ow.

3.3. Distribution of Air-Flow Field. Under the optimalaerodynamic design parameters, we further investigate thedistribution of air-�ow �eld in the air-�ow impacting basedmechanochemical synthesis instrument. As indicated in

Figure 5, the high pressure gas is accelerated in the con-vergent region, and the gas achieves a relatively high speed.Besides, an extremely relative static pressure (P/Pref� 0.1,where P and Pref are the local static pressures and referencepressure with mean value of 1 atm, resp.) is obtained in theexit of the suction pipe. �e great pressure di�erence is in

End of nozzle Positionof target

µAxis

Uniform speed region

Ma = 3

(a)

Uax

is (m

/s)

X (m)–0.1 0 0.1 0.2 0.3 0.4

0

100

200

300

400

500

600

700 Suctionpipe Uniform speed region

0.6°0.5°0.4°

0.3°0.2°

0.1°0.0°

(b)

Figure 4: (a) �e scheme for the divergence angle (μ). (b) �erelationship between the axis speed (Uaxis) and the divergence anglefrom 0° to 0.6° in the uniform speed region.

Mach number: 0.4 0.8 1.2 21.6 2.4

0.43 0.44 0.460.45X

(a)

0.45X

Axial velocity: 0 100 200 300 400 500

(b)

X (m)

P/P r

ef

–0.1 0 0.1 0.2 0.3 0.4

0.2

0.4

0.6

0.8

1

Inject tube Accelerating ductTarget0.4 0.4050.410.4150.42

400

600

0.4

0.8

VelocityPressure

800

700

600

500

400

300

200

100

0

Uax

is (m

/s)

(c)

Figure 5: (a, b) �e distribution of air-�ow �eld at the di�usionregion and the physical target. (c) �e velocity and pressure versusthe position at the axis line, where P and Pref represent the localstatic pressures and reference pressure with mean value of 1 atm.

4 International Journal of Chemical Engineering

favor of the injection of various reaction substances into thereaction instrument. Furthermore, the low-speed air flowfrom the suction pipe is carried by the air flow with a highspeed in the diffusion region, which crosses over the uniformspeed region. Eventually, a high-speed air flow and strongbow shock wave are formed near the physical target. )emaximum speed of the air flow is about 550m/s with a localMa of 2.6, which is capable of supplying mechanochemicalenergy for powerful effective chemical preparation.

4. Conclusions

In summary, we investigate the effect of the instrumentparameters, such as the physical target, the diameter dif-ference between throat inwall and suction pipe, and thedivergence angles, on the flow field of air-flow impactingbased mechanochemical synthesis. )e results illustrate thatthese parameters strongly affect the speed of air flow. )eaverage Ma of the air flow can reach 2.6. Additionally, the airflow with a high speed forms a stable flow field, which cancarry the reaction substances to collide with the physicaltarget, inducing a chemical reaction. )ese findings mayserve as a guide to the air-flow impacting based mecha-nochemical synthesis and further broaden the applicationfield of the mechanochemical synthesis.

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper.

Acknowledgments

)e support of this research by the National Natural ScienceFoundation of China (Grant no. 51327804) is gratefullyacknowledged.

Supplementary Materials

Figure S1: the structure of De Laval nozzle. Figures S2 and S3:the corresponding theoretical calculations. (SupplementaryMaterials)

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