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Velocity Flow Field Characteristic on Nozzle Cavity using Central Composite Design of Computational Method for Dry Ice Blasting System

In the development of dry ice blasting nozzle geometry, the critical process parameters depend on particle jet velocity. However, very few researchers have attempted sensitivity on the velocity flow area of specific nozzle geometric parameters. A numerical simulation approach was performed in this paper using Ansys Fluent to investigate different nozzle parameters on the velocity flow field. A two-dimensional model is solved iteratively using averaged Navier-Stokes under Eulerian flow description. It was found that the velocity value increases that reach 550 m/s with an increment of the nozzle area ratio of up to 20 without influencing convergent angle and the velocity magnitude drop linearly from 525 m/s to 505 m/s in with the rise of divergent length that swell up to 700 mm and with constant convergent angle and convergent length.


Introduction
Industrial pollution is a massive challenge faced by a process operator due to impurities present in the system, resulting in a decrease in efficiency [1]. Due to this scenario, various removal method has been carefully design. Dry ice blasting is one of the successful removal process implemented by cleaning industries. This cleaning method characterized by non-humidity cleaning conditions and free from any secondary waste after the process compared to another conventional blasting system [2].
In addition to green environmental impact, the system is a reasonably cheap and safe cleaning method; however, one of its drawbacks directly relates to the lowest particle speed from the nozzle outlet [3]. The nozzle is a vital component of the dry ice blasting productivity. Due to this issue, many researchers began to investigate and optimize the nozzle efficiency. The subsequent finding found that the nozzle geometry influences the two-phase flow outlet and the cleaning speed [4]. From the designing process point of view, very few researchers have attempted to respond to nozzle parameters on particle velocity speed, especially using a systematic approach [5,6]. They behind this is that the study of threedimensional model requires high computation load and longer time to achieve convergent status as the process involves high-speed compressible flow with the interaction of discrete particle model [7].
Therefore, this research employs two-dimensional model to ease computational load by using the averaged Navier-Stokes equations under Eulerian flow description. This study would consider the effect  [8]. Results are presented in term of response surface chart between particle velocity magnitude and nozzle geometric parameters.

Geometrical Modelling
The model of nozzle geometry was created by Ansys design modeller, which directly refer to a previous literature study [6,9]. The boundary condition and the nozzle dimension are demonstrated in Table 1

Mesh of Nozzle and Central Composite Design
Computational calculation employs a finite volume method while the domain creation discretized using Ansys Mesh Modeller. The nozzle geometry consists of three major sections, namely convergent, throat and divergent section. These sections are essential for mesh refinement, especially near the throat region [10]. Throat region requires edge sizing method as the area has a narrower cross-sectional area that will cause a rapid change in velocity and pressure [11,12]. Any geometrical changes such as corner and cross-sectional area reduction need a small mesh element in which these regions have the highest changes in elemental gradient [13,14]. The domain near cylindrical and rectangular employs proximity and curvature mesh element [15,16]. The mesh quality must refer to mesh metric spectrum skewness where highest skewness gives bad accuracy in solving the solution [17]. Response surface chart plotted from variable nozzle parameters 3 was based on response surface methodology in which the design of the experiment utilised the central composite design approach. This method is useful for building a second order, which is a quadratic model for the response variable, without completing the three-level factorial design [18].

Governing Equation
The particle's governing equation to fluid interaction can be analysed via averaged Navier-Stokes equation under Eulerian flow description that is written in their compact Cartesian form as follows.
However, the turbulence models relate to the Boussinesq hypothesis in this research. Following the eddy viscosity assumption,െߩ‫ݑ‬Ԣ ప ‫ݑ‬Ԣ ఫ തതതതതതത , and the average Reynolds stress tensor is proportional to the mean deformation rate tensor. Figure 2 presents the response surface analysis of different nozzle geometry concerning the particle flow field at the nozzle outlet section. Figure 2a on the other hand, shows the velocity value increases that reach 550 m/s with an increment of the nozzle area ratio of up to 20 without influencing convergent angle. Besides, Figure 2b demonstrates the response of convergent angle and convergent length toward the particle velocity magnitude. The velocity flow field reaches a constant value of approximately 510 m/s for all convergent angles and length ranges. Figure 2c shows the response of convergent length and the nozzle area ratio against the velocity. The velocity trend increases with the rise of nozzle area ratio with constant convergent length. Figure  2d highlights a response surface's result for divergent length with a convergent angle concerning velocity magnitude. The velocity magnitude drops linearly from 525 m/s to 505 m/s in with the rise of divergent length swell up to 700 mm and with constant convergent angle and convergent length, as shown in Figure 2e. Furthermore, Figure 2f presents the trend of velocity increases quadratically with a further rise of nozzle area ratio that reach maximum to around 575 m/s with nozzle area ratio and divergent lengths of 20 and 300 mm respectively.

Conclusions
Response surface analysis using central composite design of experiment was simulated and analyzed by the steady flow of 2D single-hose dry ice blasting nozzle geometry. In the present study, a simulation has been carried out on four input variables and output parameters. Based on the simulation results, it was found that: • Velocity value increases that reach 550 m/s with an increment of the nozzle area ratio of up to 20 without influencing the convergent angle. • The velocity flow field reaches a constant value of approximately 510 m/s for all convergent angles and length ranges. • The velocity magnitude drops linearly from 525 m/s to 505 m/s in with the rise of divergent length that swell up to 700 mm and with constant convergent angle and convergent length. Apart from quantitative conclusion presented above, some future works can be extended from this research. The experimental approach can be made to solidify the result finding with supporting theoretical justification. Apart from that, a dimensional analysis could be done to determine the relationship of various nozzle geometry based on the result finding in this paper. Thus, the reader can correlate the common dimensionless parameter for standardized designing process.