1. Introduction
Microbubble drag reduction technology is a new and powerful means for ship energy conservation and emission reduction. Gas is injected into the boundary layer covering the bottom of the ship from a series of slots, nozzles, openings or porous material flush with the surface, designed to create a flow of bubbles, so the flow downstream of the nozzle or outlet will form a mixture of microbubbles and water to reduce the surface of the hull Frictional resistance. The buoyancy of the bubbles pushes them toward the bottom of the ship’s hull within the turbulent boundary layer, and the ship’s motion sweeps them aft.Research [1] The effect of injected bubble size has been studied, and laboratory tests have shown that relatively small bubble diameters (0.30.5 mm) give the best results.The drag reduction rate of microbubbles is generally around 25% [2], which can effectively reduce the power consumption of the ship’s main engine. Surface vehicles can directly use air injection to form microbubbles, while underwater vehicles can only choose other types of air injection methods because they are isolated from the air. Therefore, studying the effect of gas type on MBDR efficiency is of great significance for reducing the surface friction resistance of underwater vehicles.
It is generally believed that the mechanism of MBDR is that gas injection causes changes in the velocity gradient of the turbulent boundary layer, which reduces the viscosity and density of the local fluid, thereby reducing the turbulent kinetic energy and shear stress between the water and the wall. [3]. In addition, the type of injected gas is also an important factor in microbubble drag reduction.McCormick [4] The viscous drag of a fully submerged rotating body is reduced by generating hydrogen gas on the hull through electrolysis. Experimental results show that hydrogen microbubbles are very effective in reducing drag.friend [5] An embedded hot film probe was used to measure the shear stress fluctuations when air and helium were injected into the turbulent boundary layer, respectively.Deutsch and Castano [6] The surface friction resistance after gas injection into the turbulent boundary layer of an underwater axisymmetric body was measured. It was found that as the freestream velocity increases, the reduction in surface friction increases. At high speeds, helium injection is more effective at reducing surface friction than air injection.Fontaine and Deutsch [7] The effect of five different gases (air, helium, carbon dioxide, argon and sulfur hexafluoride) on microbubble surface friction reduction was measured on an axisymmetric model. It was found that sulfur hexafluoride has a poor drag reduction effect, while helium has a better drag reduction effect than other gases.German [8] Experiments were conducted using carbon dioxide as an injection agent to study the effect of surface roughness on microbubble drag reduction. The study takes advantage of the solubility of carbon dioxide, which minimizes problems with average velocity measurements and optical access.Zhu [9] Aiming at the problem of stable and efficient flow drag reduction for underwater vehicles, a new adaptive microbubble electrolysis control technology is proposed. The flow drag reduction performance and mechanism of microbubble arrays were studied experimentally and numerically.Skudanov [10] Introduce CO_{2} Gas is used as the material mass source, and numerical methods are used to evaluate the effect of density changes in the mixture of microbubbles on the drag reduction rate.The numerical model proposed in the study only considers the convection and diffusion process between the injected gas and water, and does not consider the interphase mass transfer process between the soluble gas CO_{2} and water during microbubble injection.
Numerical simulation is an effective method to study the drag reduction mechanism of microbubbles. For turbulent motion at low Reynolds numbers, more accurate results can be obtained through direct numerical simulation.Mattson and Mahesh [11] Results from oneway coupled EulerLagrangian direct numerical simulations of bubbles injected into a turbulent boundary layer are presented. By analyzing the force on the bubble, it was found that the acceleration of the carrier liquid is the main reason why the bubble moves away from the wall. Pang et al. [12] A EulerLagrange twoway coupling model was established, and a numerical study of flat MBDR was conducted. Direct numerical simulation is used to solve the liquid velocity field, and Newton’s equations of motion are used to calculate the bubble trajectory. Rawat et al. [13] The interaction between the dispersed phase consisting of microbubbles and the turbulent boundary layer flow is studied numerically. An EulerianLagrangian method based on direct numerical simulation of the continuous phase flow equation and Lagrangian tracking of the dispersed phase is used. This study considers the feedback effect of dispersed bubbles on the current carrying flow. Local and temporal variations of the bubble concentration and momentum source terms are considered in the mass and momentum balance equations. Velasco et al. [14] used the EulerLagrangian method and the twoway coupled direct numerical simulation method to study the interaction between microbubbles and turbulence in vertical upward channel flow.
For numerical studies of high Reynolds number turbulent motion, an appropriate turbulence model is usually selected to solve the governing equations. For the microbubble drag reduction process, establishing a microbubble coalescence and fragmentation model is one of the main research methods. Mohanarangam et al. [15] Based on the population equilibrium model, the MBDR of twodimensional plates was studied using multisize groups (MUSIG). The model considers interphase resistance and focuses on the impact of bubble merger and collapse on MBDR.Wei [16] The EulerEuler twophase flow model is used to simulate MBDR on bulk carriers. This model takes interphase resistance into account but ignores the effects of bubble deformation, coalescence, and collapse.Pang and Zhang [17] The mixed multiphase flow model combined with the population equilibrium model was used to study the MBDR of horizontal channel turbulent flow. The model describes the merger and collapse phenomena of bubble groups. Qin et al. [18] Based on the EulerEulerian twofluid model combined with the overall equilibrium model, the bubble flow along the flat plate was simulated. Merging and collapse of bubbles are considered, and drag and lift are fully modeled according to applicable closure models. Zhang et al. [19] A EulerLagrangian model that can simulate bubble merger and collapse is proposed. The bubble size distribution, bubble trajectory, bubbleinduced turbulence modulation mechanism and their relationship with the bubble size distribution were analyzed. For other microbubble drag reduction methods, Lyu et al. [20] A gasliquid twophase flow model based on the mixed flow model was proposed, and the MBDR process of the SUBOFF rotation model was numerically simulated. Wang et al. [21] A twoway coupled EulerLagrangian method based on large eddy simulations is used to study the MBDR mechanism in a fully developed turbulent boundary layer on a flat plate. Zhao et al. [22] The OpenFOAM framework is used to study twophase microbubble flow on an axisymmetric body.Numerical models include the EulerEulerian twofluid model with closed relations for interfacial momentum transfer to capture interfacial momentum transfer for multiphase flows, as well as the standard $k\u2013e$ OpenFOAM has a continuous phase model and a dispersed phase turbulence model internally.king [23] A numerical study of MBDR was conducted using a flat plate model, and the relationship between the Eulerian multiphase flow model and the mixed multiphase flow model was compared. The results show that the mixed multiphase flow model requires fewer meshes than the Eulerian multiphase flow model. The Eulerian multiphase flow model has high calculation accuracy, but the calculation time is long and the convergence is poor. The mixed multiphase flow model has short calculation time and good convergence, but has large errors.
To date, no similar MBDR numerical method considering gas solubility has been found in the published literature. This work defines the mass transfer rates of different types of gases in the gasliquid phase by writing UDFs in Fluent Fluid software, and studies the impact of gas types on MBDR. The gas types chosen were air, carbon dioxide, helium and argon. Eulerian multiphase flow model and Realized $k\u2013e$ The turbulence model is used to describe the turbulence problem of microbubble drag reduction caused by gas injection on an axisymmetric body. The population equilibrium model is used to describe the coalescence and collapse of bubbles. Calculate the equilibrium concentration of microbubble mixed flow using Henry’s theorem.The mass transfer coefficient is based on ${K}_{\mathrm{L}}$ This model combines the Higbee penetration theory and the velocityslip model. The local mass fraction of the mixed flow is solved by the convectiondiffusion equation. Finally, based on some working conditions of the water tunnel experiment, the drag reduction rate of different types of gases caused by microbubble injection was numerically calculated, as well as the impact of the solubility of different types of gases on the drag reduction rate during the microbubble injection process. Through comparative analysis with experimental data, The correctness of the proposed numerical model is verified.
5.in conclusion
In this study, a numerical method for MBDR considering gas solubility is proposed. A UDF was written to define the mass transfer velocity between the gas phase and the liquid phase during microbubble injection of different types of gases, and an MBDR numerical model of different types of gases was established. According to the experimental conditions, the MBDR of air, carbon dioxide, helium and argon was numerically studied, and the numerical simulation results were compared with the experimental data. Finally the following conclusions were drawn:
 (1)

The solubility of gases cannot be ignored during the MBDR process. The drag reduction rate of gases with higher solubility decreases slowly, while the drag reduction efficiency of gases with lower solubility is higher;
 (2)

When the injected gas volume flow rate is small, gas dissolution has a greater impact on the drag reduction rates of different types of gases. The greater the gas solubility, the greater the drag reduction ratio and the lower the drag reduction efficiency. When the injected gas volume flow rate is large, gas dissolution has less impact on the drag reduction rates of different types of gases;
 (3)

When the volume flow rate of the injected gas is small, for the same type of gas, if the volume flow rate of the injected gas is the same but the injection speed is different, the drag reduction ratio will also be different, and the greater the solubility of the gas, the greater the difference in drag reduction rate. .
By comparing the drag reduction ratio numerical simulation results with experimental data, it can be found that the volume flow rate of injected different types of gases has a gas saturation point, which is the dividing point between small volume flow rate and large volume flow rate. The injection gas volume flow rate is large. Moreover, due to differences in gas solubility, different types of gases have different volume flow rates at the gas saturation point. The existence of the gas saturation point only reflects the impact of gas injection speed on MBDR efficiency. This point is also the critical point when the MBDR state changes to the gas layer drag reduction state. In addition, in order to improve the calculation accuracy of the model, further research can be conducted from the following aspects: (1) Select an appropriate turbulence model according to the research conditions of the microbubble jet flow field. (2) In order to improve the simulation accuracy of the population balance model and the interphase mass transfer coefficient model, it is necessary to study the population distribution of the microbubble diameter produced during the gas injection process; (3) Study the interphase mass transfer rate during the microbubble injection process and analyze the microbubbles. The intrinsic relationship between bubble drag reduction and interphase mass transfer.