Advances in Fluid Mechanics: Computing and Mathematical Models, Turbulence, Fluid Theory Applications

This paper reviews the application of computing and their mathematical principles in fluid mechanics, turbulence, and fluid mechanics. Specifically, it includes the application of computer software in fluid mechanics, the application of mathematical principles in fluid mechanics, the mathematical model in turbulence, the specific application of turbulence model, the application of fluid mechanics in engineering, and the application of fluid mechanics in simulation technology. The comparison and analysis of the similarities and differences in various applications are made to provide theoretical guidance for the researchers engaged in the research of fluid mechanics.


Introduction
Fluid mechanics studies the laws of interaction and flow when the fluid itself is at rest and in motion under the action of various forces and when there is relative motion between fluid and solid boundary walls [1].
Computer science and its mathematics have relevant applications in fluid mechanics, and fluid mechanics also has many application values in engineering and chemistry, among which one kind of branch is more representative, such as turbulence, turbulence is a flow characterized by recirculation, eddy current, and obvious randomness, and it also has cross-application with mathematical models and computing [4] [5].
This paper reviews the application of computing and their mathematical principles in fluid mechanics, turbulence, and fluid mechanics.Specifically, it includes the application of computer software in fluid mechanics, the application of mathematical principles in fluid mechanics, the mathematical model in turbulence, the specific application of turbulence model, the application of fluid mechanics in engineering, and the application of fluid mechanics in simulation technology.The comparison and analysis of the similarities and differences in various applications are made to provide theoretical guidance for the researchers engaged in the research of fluid mechanics.

Application of computer software in fluid mechanics
The application of computer software simulation in fluid mechanics has provided a lot of convenience for engineering.Li et al. have brought many changes to computational fluid dynamics (CFD) by using The improvement of volume flow has always been a key research direction in engineering and scientific research.The technology of reducing flow energy loss by changing external conditions is developing and improving day by day.However, the appearance of particle image velocimetry (PIV) changes the analysis Angle.As a flow field display technology, PIV can help people obtain the internal information of fluid flow clearly and accurately, and has the advantages of non-contact and no interference to flow.Han et al. introduced the composition of the PIV system, expounded its application in turbulence theory, and pointed out that it has a bright prospect in pipeline flow application [6].

Application of mathematical principles to fluid mechanics
The application of mathematics and its physics principle in fluid mechanics can meet the accuracy and objectivity of engineering application to a certain extent.Lu et al. constructed a computational fluid dynamics post-processing method in the numerical simulation to perform power decomposition on the flow field.Theoretically, the method is based on the work-based method to calculate each power item in the flow field and track the change of the power, so as to quantitatively analyze the power conversion process in the simulated flow field.The power decomposition method is adopted to provide a new idea for the aerodynamic design of aircraft with integrated flight-push [7].Shi et al. used the principle of minimum entropy increase in non-equilibrium thermodynamics to analyze the characteristics of laminar and turbulent flows when they approach the stationary state of thermodynamic equilibrium.Especially in turbulent flow, some empirical assumptions have been abandoned.It is pointed out that the distribution of velocity and temperature can be derived from the minimum entropy increment principle when the flow is in local mechanical equilibrium.Conversely, it also reveals the mechanism that fully developed turbulence follows the principle of minimum entropy increase.[9].analyzed the flow field characteristics of the turbulent mill by numerical simulation, revealed the crushing mechanism of the turbulent mill, improved operation efficiency and optimized its design.

Specific application of turbulence model
The specific application of the turbulence model is mainly reflected in the application of engineering.

The application of fluid mechanics
The application of fluid mechanics is mainly embodied in engineering and simulation technology, which solves many practical problems and provides convenience for engineering applications.

Specific application of turbulence model
The application of fluid mechanics in engineering is reflected in many aspects.For example, Yang et al. introduced the application of hydrostatics and fluid dynamics in hydraulic engineering technology and explained the very important role of fluid mechanics theory in hydraulic engineering.The principle of fluid mechanics is used to explain the problems in hydraulic technology, and the solution to these problems can not be separated from the development of fluid mechanics [11].Chen et al. analyzed the movement of fluid in some typical beneficiation equipment, expounded the importance of fluid mechanics to the development of beneficiation, and explained the characteristics of fluid mechanics in beneficiation and the fluid mechanics problems faced in beneficiation [12].
Zhou et al discussed the application of computational fluid dynamics (CFD) to study indoor airflow due to heating, ventilation, air conditioning (HVAC) systems, and fire.Three key elements in the CFD model are pointed out.The temperature distribution in the fire development stage is simulated in a small room with a forced ventilation system, and the results under four ventilation conditions are illustrated graphically [13].Zhou, Han, et al [14].described some of the work carried out by the aero-engine Aero-Thermal Key Laboratory to make computational fluid dynamics more effective in the field of aspirated propulsion.

Application of fluid mechanics to simulation technology
The application of fluid dynamics in simulation is mainly reflected in engineering, chemistry, biology, and many other aspects.For example, Shi introduces the computational fluid dynamics (CFD) method in the field of CVD to conduct numerical simulation research on the CVD process, which can effectively reduce the research and development cost and improve deposition efficiency, etc [15].Then, ANSYS Fluent software is taken as an example.The computational fluid dynamics simulation analysis method is briefly described, as shown in Figure 4.

Conclusion
This paper reviews the application of computing and their mathematical principles in fluid mechanics, turbulence, and fluid mechanics.Specifically, it includes the application of computer software in fluid mechanics, the application of mathematical principles in fluid mechanics, the mathematical model in turbulence, the specific application of turbulence model, the application of fluid mechanics in engineering, and the application of fluid mechanics in simulation technology.The comparison and analysis of the similarities and differences in various applications are made to provide theoretical guidance for the researchers engaged in the research of fluid mechanics.

1 .
Mathematical models in turbulenceMathematical modeling is a common method in hydrodynamic turbulence, which can be used to solve difficult problems in turbulence[8].Su et al. used a four-equation model to transport turbulent Prandtl number (Pr_t) by introducing dynamic and thermal turbulence time scale to improve the numerical heat transfer accuracy of liquid lead-bismuth.The study can provide a reference for the study of turbulent heat transfer mechanism of liquid lead-bismuth, and provide data support and solution program for the design and safety evaluation of rod bundle assembly for Ci ADS liquid lead-bismuth cooling winding.By simulating Laval nozzle flow field, Yang et al. obtained accurate and efficient results.Using numerical simulation method, the S-A, k-ε, k-ω turbulence models of compressible viscous flow were compared in many aspects, such as convergence rate, mass flow error and Mach number error.Finally, it is concluded that it is effective to use k-ω turbulence model for numerical simulation of Laval nozzle.Residuals of S-A, k-ε and k-ω turbulence models are shown in Figure 2 below.Jiang, by comparing the standard k-ε model, CHEN-KIMk-ε model and RNGk-ε model, The three models were used for CFD simulation of indoor air return zone of HVAC.The results show that there is little difference between the simulation results of CHEN-KIMk-ε model and RNGk-ε model, but both of them are better than the standard k-ε model.The coefficients of the three turbulence models are shown in Table1 below.

Figure 2 .
Figure 2. (a) Residual diagram of K-w turbulence model, (b) K-e, (c)S-A Similarly, Zhou et al. derived the flow governing equation in the form of tensor and the discrete form of the pressure correction equation in the two-dimensional arbitrary curvilinear coordinate system, and applied the SIMPLE algorithm to solve the coupling of pressure and velocity to solve the Navier-Stokes equation numerically with pressure as the main solving variable.On this basis, a program is written to calculate the compressible and incompressible two-dimensional turbulent flow field.Ren et al. discussed the SIMPLE algorithm of numerical simulation and related technical details in numerical simulation, compiled the corresponding numerical simulation program of turbulent flow, and applied it in the For example, Ma et al. discussed the selection method of the turbulence model in ship CFD.The numerical calculation of the flow field around container ships, oil tankers, and bulk carriers is carried out by using the standard k-ε model, RNGk-ε model, Realizablek-ε model, standard k-ω model, and SSTk-ω model respectively.Some meaningful conclusions are obtained through the flow field analysis and comparison with the experimental results.fig.3shows the pressure cloud maps of bow and stern flow around container ships simulated by different turbulence models.In addition, multiphase turbulent reactive flow widely exists in thermal energy, aerospace, aviation, nuclear energy, chemical engineering, metallurgy, petroleum, and other engineering, as well as water environment and atmospheric environment.environment[10].

Figure 3 .
Figure 3. the smooth pressure cloud image of the bow and stern flow around a container ship simulated by different turbulence models

Figure 4 .
Figure 4. (a) the smooth pressure cloud image of the bow and stern flow around a container ship simulated by different turbulence models (b) Contour map of mass fraction distribution of main components in the synthesis of molten SiO2 by a CVD method

Figure 5 .
Figure 5. simulation flow of ship maneuvering motion based on computational fluid dynamics

Table 1 .
Coefficients in three turbulence models