1. Introduction
Microbubble drag-reduction technology is a new powerful means of ship energy saving and emission reduction. Gas is injected into the boundary layer covering the ship bottom from a series of slots, nozzles, openings, or porous material flush with the surface designed to generate a bubble stream, so the flow downstream of the nozzles or outlets will form a mixture of microbubbles and water to reduce the skin-friction drag of the hull. The buoyancy of the bubbles pushes them towards the bottom of the hull within the turbulent boundary layer, and the ship motion sweeps them aft. Research [
1] has been carried out into the effect of injected bubble size and it has been proposed from laboratory tests that relatively small bubble diameter (0.3–0.5 mm) gives the best results. The drag reduction rate of microbubbles is generally about 25% [
2], which can effectively reduce the power consumption of the ship’s main engine. The surface vehicle can directly use air injection to form microbubbles, while the underwater vehicle can only choose other types of gas injection due to its isolation from the air. Therefore, the study of the influence of gas type on the efficiency of MBDR is of great significance for the reduction in skin friction drag of underwater vehicles.
It is generally believed that the mechanism of MBDR is the change in velocity gradient of the turbulent boundary layer caused by gas injection, which reduces the viscosity and density of local fluid, and thus reduces the turbulent kinetic energy and shear stress between water and wall [
3]. Moreover, the type of injected gas is also an important factor in microbubble drag reduction. McCormick [
4] reduced the viscous drag of a fully submerged rotating body by producing hydrogen gas on the hull by electrolysis. The experimental results showed that hydrogen microbubbles are very effective in reducing drag. Pal [
5] used flush-mounted hot-film probes to measure the shear stress fluctuations when air and helium were injected into the turbulent boundary layer, respectively. Deutsch and Castano [
6] measured the skin friction drag after gas injection into a turbulent boundary layer of a submerged axisymmetric body. It was found that the reduction in skin friction reduction increases with increasing free-stream speed. At high speeds, helium injection is more effective at reducing skin friction than air injection. Fontaine and Deutsch [
7] measured the effects of five different gases—air, helium, carbon dioxide, argon, and sulfur hexafluoride—on the microbubble skin friction reduction on an axisymmetric model. It was found that Sulfur hexafluoride is less effective in reducing drag, and helium has a better drag reduction effect than other gases. Deutsch [
8] used carbon dioxide as an injection to carry out experiments and studied the influence of surface roughness on microbubble drag reduction. The study took advantage of the solubility of carbon dioxide, which can minimize problems with mean velocity measurements and optical access. Zhu [
9] proposed a novel self-adaptive microbubble electrolysis control technique for the problem of stable, high-efficiency flow drag reduction for underwater vehicles. The flow drag reduction performance and mechanisms of microbubble arrays were investigated by experimental and numerical methods. Skudarnov [
10] introduced CO
2 gas as a species mass source and used numerical methods to assess the role of mixture density variation of microbubbles on the drag reduction rate. The numerical model proposed in the study only considered the convective diffusion process between injected gas and water and did not consider the interphase mass transfer process between soluble gas CO
2 and water during microbubble injection.
Numerical simulation is an effective method to study the microbubble drag reduction mechanism. For the turbulent motion with a low Reynolds number, more accurate results can be obtained by direct numerical simulation. Mattson and Mahesh [
11] presented the results from a one-way coupled, Euler–Lagrange direct numerical simulation of bubbles injected into a turbulent boundary layer. By analyzing the forces on the bubble, it was found that the carrier-fluid acceleration is the main reason for moving the bubbles away from the wall. Pang et al. [
12] established the Euler–Lagrange two-way coupling model and carried out a numerical study on MBDR of the flat plate. Direct numerical simulation was used to solve the velocity field of the liquid, and the Newton equation of motion was used to calculate the bubble trajectory. Rawat et al. [
13] numerically studied the interaction between a dispersed phase composed of microbubbles and a turbulent boundary layer flow. The Euler–Lagrange approach based on Direct Numerical Simulation of the continuous phase flow equations and a Lagrange tracking for the dispersed phase were used. The feedback effect of dispersed bubbles on the carrying flow was considered in this study. The local and temporal variations of bubble concentration and momentum source terms were considered in the mass and momentum balance equations. Velasco et al. [
14] used the Euler–Lagrange approach and the bidirectional coupling direct numerical simulation method to study the interaction between microbubbles and turbulence in vertical upward channel flow.
For the numerical study of the turbulent motion with a high Reynolds number, a suitable turbulence model is usually chosen to solve the governing equation. Aiming at the drag reduction process using microbubbles, it is one of the main research methods to establish the microbubble coalescence and fragmentation models. Mohanarangam et al. [
15] studied MBDR of two-dimensional plates using multi-size groups (MUSIG) based on population balance models. The model took into account the interphase drag and focused on the effect of bubble coalesce and breakup on MBDR. Wei [
16] used Euler–Euler two-phase flow model to simulate MBDR on a bulk carrier. The model considered the interphase resistance, but ignored the influence of bubble deformation, coalescence and breakup. Pang and Zhang [
17] used a mixture multiphase flow model combined with the population balance model to study MBDR of horizontal channel turbulence, and the model described the coalescence and breakup phenomena of the bubble groups. Qin et al. [
18] simulated the bubbly flow along the flat plate based on Eulerian–Eulerian two-fluid modeling combined with a population balance model. Bubble coalescence and breakup were considered and drag and lift were fully modeled based on applicable closure models. Zhang et al. [
19] proposed an Euler–Lagrange model that can simulate bubble coalescence and breakup. The bubble-size distribution, the bubble trajectory, and the mechanism of bubble induced turbulence modulation and its relationship with bubble-size distribution were analyzed. For other methods of microbubble drag reduction, Lyu et al. [
20] proposed a gas–liquid two-phase flow model based on the mixed-flow model, and numerically simulated the MBDR process of the SUBOFF rotating model. Wang et al. [
21] used a two-way coupled Euler–Lagrange approach based on a large eddy simulation to study the MBDR mechanism in a fully developed turbulent boundary layer over a flat-plate. Zhao et al. [
22] used an OpenFOAM frame to study the two-phase micro-bubble flow over an axisymmetric body. The numerical models included an Eulerian–Eulerian two-fluid model with closure relationships for the interfacial momentum transfer to capture the interfacial momentum transfer of multiphase flows, and a standard
model for the continuous phase and one turbulence model inside the OpenFOAM for the dispersed phase. Wang [
23] numerically studied MBDR by using a flat-plate model, and compared the relationship between the Eulerian multiphase flow model and the mixed multiphase flow model. The results indicated that the mixed multiphase flow model requires less mesh than the Eulerian multiphase flow model. Eulerian multiphase flow model has high calculation accuracy, but long calculation time and poor convergence. The calculation time of the mixed multiphase flow model is short, the convergence is good, but the error is large.
So far, no similar numerical method for MBDR considering gas solubility has been found in the published literature. In this work, by writing UDF in fluent fluid software, the mass transfer velocity of different types of gases in the gas–liquid phase is defined, and the influence of gas types on MBDR is studied. The types of gases selected are air, carbon dioxide, helium and argon. The Euler multiphase flow model and Realizable turbulence model are used to describe the turbulence problems of microbubble drag reduction caused by gas injection on an axisymmetric body. The population balance model is used to describe the coalescence and breakup of bubbles. Henry theorem is used to calculate the equilibrium concentration of the microbubble mixed flow. The mass transfer coefficient is based on the model which combines the Higbie permeation theory and the velocity slip model. The local mass fraction of the mixed flow is solved by the convection–diffusion equation. Finally, the drag reduction ratio of microbubble injection for different types of gases is calculated numerically according to some working conditions of the water tunnel experiment, and the influence of the solubility of different types of gas on the drag reduction rate during the process of microbubble injection is analyzed by comparing with the experimental data, and the correctness of the numerical models proposed is verified.
5. Conclusions
In this study, a numerical method for MBDR considering gas solubility is presented. A UDF is written to define the mass transfer velocity between the gas and liquid phase during microbubble injection of different types of gases, and the numerical models for MBDR of different types of gases are established. According to the experimental conditions, the numerical studies on MBDR of air, carbon dioxide, helium and argon are carried out, and the numerical simulation results and experimental data are compared and analyzed. Finally, the following conclusions are reached:
- (1)
Gas solubility cannot be ignored in the process of MBDR. The drag reduction ratio of gas with greater solubility decreases more slowly, and the drag reduction efficiency of gas with smaller solubility is higher;
- (2)
When the volume flow rate of injected gas is small, gas dissolution has a great influence on the drag reduction ratio of different types of gases. The larger the solubility of gas, the larger the drag reduction ratio and the lower the drag reduction efficiency. When the volume flow rate of injected gas is large, the influence of gas dissolution on drag reduction ratio of different types of gases is small;
- (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 is also different, and the greater the solubility of the gas, the greater the difference in the drag reduction ratio.
By comparing the numerical simulation results of the drag reduction ratio with the experimental data, it can be found that the volume flow rate of different types of gases injected has a gas saturation point, which is the dividing point between a small volume flow rate and the large volume flow rate of injected gas. Moreover, due to the difference in gas solubility, the volume flow rate of different types of gases at the gas saturation point is different. The existence of the gas saturation point only reflects the influence of the gas injection speed on the MBDR efficiency, and this point is also the critical point of the transition from MBDR state to the gas-layer drag-reduction state. In addition, in order to improve the calculation accuracy of the proposed model, further research can be carried out from the following aspects: (1) According to the study condition of the microbubble injection flow field, the appropriate turbulence model can be selected. (2) In order to improve the simulation accuracy of the population balance model and the interphase mass transfer coefficient model, the population distribution of the microbubble diameter generated during gas injection should be studied; and (3) the interphase mass transfer rate during microbubble injection is investigated, and the internal relationship between microbubble drag reduction and interphase mass transfer can be analyzed.