A Combined Experimental and Numerical Study of Shotcrete Jets and
Related Wet Spray Nozzles

In this research, the dynamics of wet spray nozzles with different geometries, used to accelerate shotcrete, are investigated on the basis of a suitable three-dimensional mathematical model and related numerical method. Simulations have been conducted in the frame of the SIMPLEC algorithm. The k-ε turbulence model has been used to account for turbulent effects. The study shows that when the angle of the convergent section is less than 3°, it has a scarce effect on the dynamics of the jet of shotcrete; with the increase of the convergence angle, the shotcrete jet velocity decreases and the nozzle wear increases; when this angle is greater than 6°, the concrete outlet jet velocity is very small and the nozzle can easily be blocked. Experimental results are in good agreement with the outcomes of the numerical simulations, which indicates that the used approach is reliable.


Introduction
Shotcrete or sprayed concrete, a cement-based mixture projected pneumatically in high velocities [1], is often used in various constructions, such as mine tunnels, railway and highway tunnels, and water conservancy culverts [2][3][4]. The flexibility of shotcrete makes it an effective alternative to conventional concrete in rock support, tunnel lining, and concrete repair. For example, the pneumatic projection allows shotcrete to be applied quickly on the uneven substrate surfaces, acting as excavation stabilization and arch lining in mines [5]. There is a problem of uneven injection and large amount of dust on the shotcrete construction site. Ulvestad et al. [6] ever indicated that mean exposures to total dust and respirable dust in shotcrete were significantly higher than in drillers (13.6, 3.4 mg/m 3 and 3.6, 1.2 mg/m 3 ). Georg et al. [7,8] compared the exposure situation of shotcrete dust in heading face between Swiss road tunnel and Munich subway tunnel with similar shotcrete and ventilation, results showed that the average fine dust concentration of road tunnel (13.2 mg/m 3 ) and subway tunnel (11.6 mg/m 3 ) was still higher in fact, what is more, the peak of dust concentration during shotcrete can reach up to more than 100 mg/m 3 for the road tunnel and up to 70 mg/m 3 for the subway tunnel. Praml et al. [9,10] measured dust concentration during the shotcrete in amine tunnel construction site. Results showed that the fine dust concentration were 4.2 mg/m 3 for mixer operator and 11.6 mg/m 3 for nozzleman. The peak loads of dust concentration can reach up to five times the mean value. These problems not only waste valuable wet spray materials, generate a large amount of dust, damage the support strength, reduce work efficiency, but also pose a threat to the health and safety of workers.
Currently, when it comes to shotcrete, a large amount of researches pay their attention on the pumpability and shootability of fresh concrete [11][12][13] or the mechanism of sprayed concrete [14,15]. Chen et al. [16] summarized the technologies for reducing cement dust during shotcrete from new process, new apparatus to new materials, as well as the pathological damage of cement dust. Zeng et al. [17] indicated that the magnetized water can enhance the strength of shotcrete by 10% or so, and reduce the dust density by 50% in comparison with the ordinary shotcrete. The rebound rate of shotcrete mixed with magnetized water is greatly improved compared with that of the ordinary water shotcrete.
At present, there are few researches on the structure of wet spray nozzles, and in those researches the range of nozzle convergence angle is large lacking certain certainty, which has a great effect on the performance of nozzle [18]. This paper studies the effect of the shrinkage angle of the wet sprayer's nozzle on the uniformity of concrete injection and the reduction of dust through theoretical analysis, numerical calculation and experimental research. Based on the numerical calculation results, the specimen is made. The correctness of the numerical simulation results is verified in the experimental research and then applied to engineering practice.

Wet Sprayer Working Principle and Structure Characteristics of Nozzle
The construction of wet shotcrete refers to a process in which cement, water and aggregates are fully stirred in a certain proportion in blender, then pumped or air-conveyed to the nozzles, and finally, the concrete is accelerated with compressed air at the nozzle [19,20]. The nozzle as the concrete exit is essential to the whole machine. In order to improve the technology and product quality of the wet sprayer, it is necessary to study the influence of the nozzle structure on the concrete flow in the nozzle. The nozzle is composed of convergent section, mixed core, air-induction ring, and connection snap ring, as shown in Fig. 1, In practice, the compressed air and the accelerating agent enter the nozzle from the air induction ring (part 2 in Fig. 1). The concrete is pushed to the straight pipe (part 1) through the alternate delivery cylinder, and fully and evenly mixed in the material-gas mixing core (part 3) with high pressured air entering through the air induction ring (part 2). The suspended concrete particles pass through the front convergent section (part 5) and are sprayed from the outlet (part 6) to the sprayed surface, completing the entire concrete spraying operation.

Mathematical Formulation
According to the working principle of the wet sprayer, the concrete mass is accelerated in the nozzle by the compressed air, and run in an axially-accelerated manner in the suspended state. At the same time, there is a circumferential rotational motion [21,22]. That is to say, the concrete mass is in a spiral motion in space and the axial and tangential forces are complex in the spraying process. However, the gravity and the levitation force balance each other in the vertical direction during the horizontal spray of concrete particles. The tangential force in the circumferential direction only produces a tangential rotational motion, without any effect on the axial movement of the concrete. Thus, the tangential force can be ignored when analyzing the axial movement of the concrete. The forces acting on the concrete mass mainly include the axial flow thrust F R and the frictional resistance T of the nozzle inner wall. Fig. 2 briefly illustrates the forces on the concrete mass in horizontal pipes in dl section [23,24].
Airflow thrust Eq. (1): where C s refers to the flow resistance coefficient; A s is the total frontal area of concrete particle mass in dl section, m 2 ; q a is the air density, kg/m 3 ; v a , the air velocity, m/s; v s , the transportation speed for concrete mass, m/s. Pipe wall resistance Eq. (2): where λ s refers to the resistance coefficient of concrete mass, and A is the cross section area. Since: According to the previous analysis, the airflow resistance of the shotcrete particles is within the Newton resistance zone, i.e., K = 0, thus it can be obtained: Namely: According to Newton's second law: M s dv s dt , and combined it with Eq. (2): where v n stands for the suspension velocity, m/s; λ s , flow resistance coefficient; D, inner diameter of the nozzle, mm; and θ, convergence angle of the convergent section,°.
The Eq. (8) is the differential equation of the motion of concrete mass in horizontal nozzle, which reflects the change of actual velocity of the concrete with time in the spraying process, that is, with the increase of time, the actual velocity of the concrete mass will accelerate from pumping speed to stable speed. The factors which affect the spray velocity of concrete include the convergence angle θ of the nozzle's convergent section, the suspension velocity v n of the concrete mass, the airflow velocity v a , and the flow resistance coefficient λ s of the concrete mass. Among them, the convergence angle of the convergent section of the nozzle is crucial to the spray velocity of the concrete mass. The motion of the concrete flow in the nozzle can be described in this way. The concrete mass is pumped into the nozzle inlet, and under the action of high-pressure wind, the decelerating acceleration movement is performed. When the material mass acceleration is zero, the energy exchange between high pressure air and concrete mass ends. At that moment, the concrete mass gains the highest speed, and the material mass is in evenness motion.
The material mass can be considered to be an incompressible fluid due to neglecting the compressibility effects. The governing equations for the flow in the nozzle can be written as follow: Continuity equation where q is the fluid density, kg m 3 ; u i ; u j are the fluid velocity of the unit body at the i and j direction respectively, m/s; p is the static pressure, Pa; s ij is the stress tensor, Pa; qg i are the gravitational body force, N m 3 ; F i is a momentum source term, N m 3 . In the calculation area, no external force is involved, thus the momentum source term F i ¼ 0.

Numerical Simulation and Boundary Condition
After the mesh is generated in ICEM ® , the computational fluid dynamics (CFD) software ANSYS FLUENT ® is used for numerical simulation. The whole nozzle is set up as a system of three-dimensional, incompressible, viscous, and turbulent flow with steady calculation. This research only focuses on the movement of the working medium, excluding the temperature change of the working medium, the hydration reaction of the cement, and the change of the internal energy of the working medium. All the components of the nozzle are rigid, ignoring the deformation caused by the interaction between the solid wall forming the flow area and the working medium. The discretization scheme of the governing equation is first-order upwind scheme. SIMPLE solver is used to solve Pressure-Velocity Coupling. The Pressure Interpolation uses PRESTO! Scheme [25,26]. The max iteration number is 4000, and the convergence is assumed with all residues less than 10 −5 .
The Operating environment is 101325 Pa; density of concrete particles is 2500 kg/m 3 ; concrete dynamic viscosity is 32 N·s/m 2 ; water-cement ratio is 0.48; thermal conductivity is 1.28 W/m°C; specific heat capacity is 970 J/(kg·K). The RNG k-ε model is more reliable and accurate than the standard k-ε model. What's more, since the high-pressure air supply process of the concrete pile mass is in the square area of turbulent flow resistance and the turbulence is a fully developed strong turbulent turbulence with large intensity, the RNG k-ε model is more suitable. Therefore, this study used the RNG k-ε turbulent model to resolve the flow equations [27,28].
Concrete inlet conditions is adjustable where the velocity boundary condition can be implemented. Considering the actual conditions of the wet sprayer, the spray capacity of wet sprayer is 7 m 3 /h, and concrete flow direction is perpendicular to the nozzle inlet cross section, i.e., u y = u z = 0, u int_concrete = u x =7/πD 1 2 , where D 1 refers to the nozzle inlet cross section. The hydraulic diameter is 64 mm. The air inlet boundary conditions, considering the practical operating conditions, are selected as the pressure inlet pressure_inlet. The air flow direction is perpendicular to the air inlet section of the nozzle mixing chamber, i.e., u y = u x = 0, u int_air = u x . The field work wind pressure is 0.5 MPa [29], while the hydraulic diameter is 6 mm. The nozzle outlet boundary conditions are selected to be free outlet Outflow. The fluid Reynolds number and turbulence intensity can be solved with Re = u int ρd/γ and I = 0.16 (Re) −1/8 .

Geometry Model
The nozzle model is composed of a front convergent section, a middle mixing core, an air-induction ring, and a connecting ring, as shown in Fig. 1. The main parameters are listed in Tab. 1.

Mesh Independence Study
The quality of mesh has great effects on the speed and accuracy of the simulation. The model adopts a hexahedral core meshing format at the inlet of the concrete and the outlet of the mixed fluid to improve the accuracy of meshing. Due to the presence of 20 high-pressure air inlets in the intermediate mixing chamber, the model structure is complex. Therefore, an unstructured grid division format is used to ensure a reasonable balance between calculation accuracy and computational resources. The computational domain mesh and mesh quality are presented in Fig. 3. The mesh independence of the model has been studied. The Max element of size 0.0010 m, 0.0015 m, 0.0020 m, 0.0025 m and 0.0030 m has been selected respectively for meshing, according to the meshing pattern mentioned above. When the cell size is 0.0030 m, the total of 738665 grid points are used to mesh the entire geometry. When the cell size is 0.0020, the total number of grid points is 1454508. When the cell size is 0.0010, the number of that is 2855213. Given that mean velocity of the outlet is an important comprehensive parameter, the mean velocity is chosen as the evaluation index. As shown in Fig. 4, when the number of grid points is more than 1.4 million, the rate of change of mean velocity is less than 0.5%. In this paper, the cell size is 0.0020 m. A total of 1454508 grid points are used to mesh the entire geometry.

Numerical Calculation Results
In this study, modelling and numerical calculations were conducted with the convergency angles of convergent sections of 3°, 4°, 5°, 6°, and 7°respectively. Fig. 5 shows the flow velocity isogram when the convergency angle of convergent section θ is 4°.

Analysis of Resultant Velocity of Outlet Section
Under the condition that the air pressure of the wet sprayer and the pumping pressure of the concrete are constant, the greater the outlet velocity of the concrete jet is, the less energy consumption of the contact between the concrete mass and the inner wall surface of the nozzle, and the small the wear of the nozzle will be. The average speed of the outlet section U (Eq. (11)) is regarded as an assessment index for the analysis of the outlet section velocity field, in the analysis of the average velocity of outlet section where U i refers to the velocity of collection points in outlet section, m/s; and U is the mean velocity of collection points in outlet section, m/s.
Tab. 2 presents the mean velocity values of the outlet section collection points with various convergency angles of different nozzle models. Import the mean data into Origin9 ® to fit the data curve, as shown in Fig. 7. It can be seen that when the convergence angle of the convergent section is less than 3°, it can be considered that the concrete mass is transported in an approximately equal straight pipe, and the concrete outlet speed does not change much;  when the convergence angle of convergent section is greater than 6°, the concrete transport velocity is very small and the nozzles are easily blocked.

Analysis of Volume Fraction of Concrete Phase in Outlet Section
The distribution of the volume fraction of the concrete phase at the outlet of the nozzle is an important factor for judging the mixing effect of the nozzle structure on the mixed fluid. A reasonable distribution of the volume fraction of the concrete phase reflects the good mixing effect of the mixed fluid. In the past, the judgment of the mixing effect of the shotcrete flow can only be expressed indirectly based on the rebound rate of the sprayed wall surface. Through numerical simulation software analysis, the volume fraction of the concrete phase at the nozzle outlet of the mixed fluid is shown in Fig. 8.   In order to objectively reflect the degree of mixing, both the standard deviation and the mean value are taken into account.
1. The degree of dispersion represents the ratio of the standard deviation to the measured mean value. The percentage expression is where S refers to the Standard deviation; and x is the arithmetic mean of volume fraction.
2. Evenness represents the degree to which a set of measurements approaches the mean value of the measurements. The mathematical expression is The essence of dispersion and evenness is same, but just two different perspectives.
The analysis of the volume fraction of the concrete phase in the outlet section shows that both high concentration of concrete and low concentration fluctuation along the center of the nozzle are required in construction. Thus, suitable statistics to characterize this comprehensive evaluation index is necessary.
Define the comprehensive evaluation index Q as the product of the evenness and the measured mean values: From Tab. 3, it can be seen that the best sample of the outlet section concrete spray evenness is the model with the convergence angle of 6°in the convergent section.

Test System
Due to the limitation of test conditions, it is very difficult to directly measure the mixing quality of the concrete flow in the nozzle. Therefore, this study employed the method of measuring the impact force of the water jet flow abrasive on the object to indirectly determine the quality of the jet, and set up a shotcrete impact force distribution test system. Based on the field conditions of wet shotcrete as shown in Fig. 9, an effective concrete spray force distribution test scheme is proposed by using LabVIEW ® to curve the input and output characteristics of the sensor, and analyzing and processing the test data [30].

Sensor Layout
In order to measure the distribution of shotcrete impact force, a force transducer array system was designed. According to the characteristics of the central symmetrical structure of the shotcrete impact diffuse surface, taking into account the reduction of the test cost, 11 pressure transmitter collection points were arranged along a horizontal axis (−500 mm-500 mm) at a distance of 1000 mm × 1000 mm, as shown in Fig. 10, and fixed with nuts and the gaps were sealed with caulking glue. Collection points were evenly represented. The pressure transmitters in the array were numbered according to the distance from the centre of the bottom plate for the convenience of following test. From left to right, they were

Nozzle Models Production and Testing
According to the previous analysis, the nozzle models with convergence angles of 4°, 5°, and 6°were fabricated as shown in Fig. 12, and field tests were conducted. Fig. 13 shows the site of field test of shotcrete impact force test system. Setting LabVIEW, the sampling frequency is 1000, which means that it is collected 1000 times per second. Since the output signal of the transmitter is 0-5 V and the range is 0.5 MPa, the output pressure and voltage conversion formula is shown as Eq. (15).
Multiple groups of test data have been obtained by replacing the convergent section to obtain. The test data are shown in Tab. 4.   The processed mean data was imported into Origin9 ® for data curve fitting, the results being showed in Fig. 14.
The distribution rule of the fitting curve is consistent with that of the volume fraction curve of the concrete phase of the nozzle outlet section shown in Fig. 8.
Based on the above analysis, Q values of nozzle models with different convergence angles in the convergent section were calculated, as showing in Tab. 5.
By calculating Q value of the comprehensive evaluation index, the nozzle model with convergence angle of 6°in convergent section and Q value of more than 5°and 4°has the best performed, which is consistent with the theoretical analysis and numerical calculation results. The nozzle model with the convergence angle of 6°in convergent section has good shotcrete evenness and the test results is satisfactory.  Figure 14: Mean test data curve of convergent section of different nozzle models

Conclusion
In this study, the combination of numerical calculation and experimental research was employed to study the effect of the nozzle's convergence angle on the spraying performance of the concrete. According to the numerical calculation results, nozzle models were produced, and the shotcrete distribution test system was established to verify the numerical simulation, which then was applied to engineering practice. The study shows that when the convergence angle of the convergent section is less than 3°, the convergence angle has little effect on the shotcrete mass; with the increase of the convergence angle, the shotcrete mass jet velocity decreases and the nozzle wear increases; when the convergent section convergence angle is greater than 6°, the concrete outlet jet velocity is very small and the nozzle is easily blocked. The shotcrete impact force distribution test system was designed and assembled in line with the conditions of the wet shotcrete construction site, which can correctly collect the impact force of the sprayed surface and analyze the nozzle spray evenness. The test system provides an effective solution for on-site testing of the spraying performance of the wet sprayer nozzle. The force distribution test has a good consistence with the numerical simulation results.