https://doi.org/10.53656/ped21-6s.19mod

Резюме. The idea of this publication is to show how mathematical modeling presents dependence of \(\mathrm{CO}_{2}\) in the exhaust gases. Using quadratic function obtained results are with good approximation. The future below to hydrogen about marine uses. Mathematical modeling is the best way to show how we can make an experiment with small database and that with mathematical function we receive a full picture of problem that we research with data which can’t receive with real experiment.

Ключови думи: hydrogen; marine engine; modelling dependence of \(\mathrm{CO}_{2}\) in exhaust gases

Introduction

Modern marine engines are designed to improve the overall efficiency of the marine system (Feili et al. 2020). The introduction of new fuels such as hydrogen in maritime transport is considered a challenge due to the harsh environmental conditions in which the motor ship must operate (Jia et al. 2017). Any attempt to introduce a new fuel in the field of maritime transport must be accompanied by sufficient studies and experimental data to provide engineers and ship operators with the sufficient data on the new type of fuel used (Li et al. 2019; Miller et al. 2014; Miao et al. 2021; Sapra et al. 2020)

Objective and research methodologies

The purpose of this publication is to model the dependence of \(\mathrm{CO}_{2}\) contained in the exhaust gases on the amount of hydrogen gas supplied to the engine. The SKL 3NVD24 marine diesel engine was chosen as the object of the study. Place of the conducted experiments – Naval Academy “N. Vaptsarov” – Varna. The hydrogen experiment was performed with a VST 4C gas generator manufactured by Hydrogas.

The engine used is four-stroke, in-line, naturally aspirated. Piston stroke – 240 mm and cylinder diameter – 175 mm. The designation 3NVD24 indicates that the engine is 3-cylinder, N-means that the ratio of the stroke of the piston to the diameter of the cylinder – is less than 1.3. The letter sign V – indicates that the engine is four stroke and D – means that it is a diesel engine. The number after the designation is the stroke of the piston in centimeters. The SKL 3NVD24 engine was manufactured in 1965 at the Karl Libkner plant in Magdeburg in the former DDR. The SKL engine is shown on Figure 1. A hydrogen cell is shown on Figure 2.

The engine’s fuel system includes fuel filters, fuel pumps (one for each cylinder) and fuel valves. The engine oil system includes a crankshaft gear oil pump, coarse and fine filters and a double-acting manual piston pump for pre-coupling oil to the main and connection rod bearings.

The cooling system consists of two circuits, an open circuit in which the circulation of seawater is simulated and a closed circuit with fresh water. In case of damage to the cooling circuit with fresh water, the engine can also be cooled with sea water from the open circuit. A piston pump provides the incoming water to the open cooling circuit and a centrifugal pump provides cooling of the cylinder block and the cooling spaces of the cylinder head through water-water cooler. Both pumps are driven by the crankshaft via a gear drive. The engine is started with the help of compressed air at a nominal pressure of 30 bar and a minimum rotation pressure of 12 bar. The nominal speed is \(600 \mathrm{~min}^{-1}\) and the minimum speed is \(300 \mathrm{~min}^{-1}\). The rated power of the engine is 44.1 kW or 60 hp. The working volume of the cylinders is \(17.32 \mathrm{dm}^{3}\) (\(5.76 \mathrm{dm}^{3}\) for each cylinder). Stand KI2139B-GOSNITI is designed for testing engines with a nominal torque of \(25-40 \mathrm{~kg} / \mathrm{m}\) and a crankshaft speed of \(1500-3000 \mathrm{~min}^{-1}\). Since the operating frequency of the engine is \(300-600 \mathrm{~min}^{-1}\) to increase in conjunction with the electric brake an upshift is required. For this purpose, a multiplier with a gear ratio of \(1: 5\) is installed. The supply voltage of the stand is 380Vq the frequency is 50Hz. Its load capacity is 210kW. The breaking and torque-measuring device is a pendulum-type weighing mechanism.

This machine is an oxyhydrogen gas generator – VST 4C. It produces stoichiometric gas mixture composed of hydrogen and oxygen. The gas mixture is a useful product, which in turn is used to clean internal combustion engines of any types, size, power, fuel and purpose. The VST 4C is automatic and the operator must set the operating mode limits by providing a front-facing display for this purpose performing command and control functions. The gas generator is designed in accordance with the latest technologies and requirements for this type of machine. It is completely reliable and secure in operation (Table 1).

The experiment was performed while maintaining the same engine temperature, with a change in the amount of gas supplied (by changing the current of the hydrogen cell) and registration of the components of the exhaust gases. The experiment is performed at rated speed and without load. It is necessary to specify that all tests and the accompanying conclusions refer only to the specific type of hydrogen cell and the respective engine. Their summary on other conditions can only be of a principled nature.

Research method: in the performed research, a significant difference in the data was found, due to the selected factors and to external disturbances (Bakalova et al. 2020). An experimental – statistical method – regression analysis was chosen for processing the experimental material. Excerpts from 9 experiments were used. Obtaining qualitative regression models was achieved after performing the following a two-step procedure: determining the parameters of a pre-selected structure of the model and statistical analysis of the results (Bakalova 2020). The finally selected model can be used to predict the effect of the fuel- hydrogen mixture on the exhaust components. Due to the nature of hydrogen cell operation, a regression dependence of the change in the amount of hydrogen gas on the strength of the electric current was obtained at the beginning of the study. In all subsequent studies, the amount of hydrogen gas was taken as a factor and the content of gases was taken as a starting point. The results of the research are presented in Table 2.

Table 3 contains the values of the hydrogen gas in the nine experimental trials.

The results of the application of the regression analyses are given in Table 4.

The analysis of the data from the table shows that of the three adequate models with minimal standard error is the second model /quadratic function. It is adequate and with a maximum correlation coefficient. This model satisfies the conditions for applying regression analysis: no correlation of the residues, constant value of the variance, normal distribution of the residues eidues \(\mathrm{e}_{\mathrm{i}}\) and \(\sum e_{i} \equiv 3.004 e-012\), value assumed to be zero. It is finally chosen to approximate the data and the dependence: the amount of \(\mathrm{CO}_{2}\) contained in the exhaust gases from the hydrogen gas supplied to the engine. The graph below shows for comparison the real experimental data (*) and those obtained by the model (-), which shows a good approximation.

Conclusions

In conclusion, we can summarize that the mathematical modeling shows that a very good approximation is obtained between the data from the real experiment and those obtained during the mathematical processing. The quadric function is adequate with a maximum correlation coefficient.

REFERENCES

Bakalova, R., Mihalev, D., 2020. Identification of the dynamics of the ratio of foreign direct investment in the northeast region of Varna to the total, through one-factor regression models. V International Scientific Conference, 54 – 57. Summer session "INDUSTRY 4.0“, volume 1/8 [June 2020]

Bakalova, R. 2020. Identification of the relation of the foreign direct investments in the South-Eastern region of Burgas to the general ones, through one-factor regression models. V International Scientific Conference, 58 – 61. Summer session "INDUSTRY 4.0“, volume 1/8 [June 2020].

Feili M., Rostamzadeh H., Parikhani T., 2020. Hydrogen extraction from a new integrated trigeneration system working with zeotropic mixture, using waste heat of a marine diesel engine.

Jia P., Li G., Liang J., Zhang Z. & Zhong G., 2017. Numerical study of exhaust reforming characteristics on hydrogen production for a marine engine fueled with LNG.

Li, G., Liang, J., Long, Y., Zhang Z. & Zhang, X., 2019. Performance and emissions characteristics of a lean-burn marine natural gas engine with the addition of hydrogen-rich reformate.

Miller, JW., Pan, H., Princevac, M. & Pournazeri, S., 2014. Effect of hydrogen addition on criteria and greenhouse gas emissions for a marine diesel engine.

Miao, H., Xia, L., Wang, F., Wang, L. & Zhang, H., 2021. Design and optimization of hydrogen production by solid oxide electrolyzer with marine engine waste heat recovery and ORC cycle.

Sapra, H., Godjevac, M., De Vos, P. & Van Sluijs, W., 2020. Hydrogennatural gas combustion in a marine lean-burn SI engine: A comparitive analysis of Seiliger and double Wiebe function-based zero–dimensional modelling.