Fuel Consumption Rate Optimization Analysis of Dual-fuel Marine Diesel Engines Based on Orthogonal Design

To investigate the influence of diesel engine operating matching parameters on the comprehensive fuel consumption rate of butanol-diesel dual-fuel engines, a high-pressure combustion chamber cycle model of a 4190ZLC-2 marine medium-speed diesel engine was established using AVL-FIRE simulation software. After establishing the optimum blending ratio of butanol, the fuel system parameters were optimized using a one-time regression orthogonal experimental design method, and a mathematical model for fuel consumption rate prediction was constructed to find the combination of parameters with the lowest fuel consumption rate as the target. The study shows that inlet pressure has the greatest influence on the fuel consumption rate, followed by EGR and inlet air temperature. The lowest fuel consumption rate was achieved by combining the following parameters: (butanol blending ratio of 20%, EGR rate 0, inlet pressure 0.233 MPa, inlet temperature 325.15 K, Injection advance angle 22.6 °CA, the diameter of oil injection hole (0.26 mm); after optimization, the fuel consumption rate was reduced by 9.96% compared to the original machine.


Introduction
Finding new alternative fuels is an effective way to save energy and reduce emissions [1] .Butanol, as a new alternative fuel of the second generation, has the advantages of high calorific value and is non-corrosive to pipelines [2][3] .Yao Mingfa et al. [4] blended butanol in a heavy-duty diesel engine and conducted several injection tests, which showed that the blending of butanol in diesel fuel increased NOx emissions, but a significant reduction in carbon soot and CO.Ogyzhan Dogan et al. [5] blended different proportions of butanol in a high-speed diesel engine, and the combustion results showed that the fuel consumption rate increased with increasing butanol blending ratio, exhaust temperature decreased, NOx did not change significantly, but carbon monoxide and carbon soot emissions decreased significantly.Therefore, in this paper, the AVL-FIRE software is used to construct a high-pressure cycle model of the combustion chamber.The parameters are simulated and matched by one-time regression orthogonal tests to build a mathematical model with the fuel consumption rate as the target to optimize the operating parameters and achieve the goal of reducing fuel consumption and improving economy [6] .

Constructing and validating the simulation model
parameters are as follows: the compression ratio is 14:1; the firing order is 1-3-4-2; the cylinder bore×stroke is 190 mm×210 mm; and the power is 220 kW per 1,000 r/min.CAD to draw two-dimensional combustion chamber graphics to obtain a longitudinal section 1/2 cross-section (see Figure .1).The ESE module in AVL-FIRE was then used to generate the 3D mesh automatically and to divide and check the mesh [7] .As the diesel engine combustion chamber model is a centrosymmetric circular structure, the nozzle is located in the middle of the cylinder and has eight symmetrically distributed nozzles.To simplify the calculation process, 1/8 of the combustion chamber is selected for the simulation (see Figure 2).Under the rated working condition, the blending ratio of butanol was set to 0. The cylinder pressure curve and exothermic rate curve of the simulation model and the original machine's underrated working condition were compared, as shown in Figure 3.The curves showed the same trend, and the overall fit was more than 95%, which proved that the simulation model was constructed accurately and could be used for the simulation of the in-cylinder combustion process [8] .

Optimum blending ratio of butanol
Figure 4 shows the variation of indicated power and fuel consumption rate for different butanol blending ratios.As can be seen from the graph, with the increase in the butanol blending ratio, the indicated power decreases, and the fuel consumption rate increases.The main reason for this is that butanol has a lower calorific value, and a higher latent heat of evaporation value, which means that the fuel needs to absorb more heat in the process of atomization injection and exerts less heat at the same injection volume.At the same time, the lower cetane number of butanol leads to a longer stalling period, which delays the ignition of the fuel and reduces the maximum burst pressure in the cylinder, decreasing the indicated power and an increase in the fuel consumption rate.
In summary, the blending of different proportions of butanol on diesel combustion characteristics, combined with the results of simulation tests, ensure the powerfulness of the diesel engine, and this paper studies the practical significance of dual-fuel blending with careful consideration: 4190ZLC-2 type medium-speed diesel engine blending butanol the best proportion of 20%.In the following article, the optimizing fuel consumption rates on this basis.

Matching optimization of one-off regression orthogonal test designs
One-time regression orthogonal test design is an experimental method that uses a combination of orthogonal methods and regression analysis [9] .The advantage of this method is that a mathematical model with higher accuracy can be established with a smaller number of tests.In this paper, five factors, namely EGR rate, inlet pressure, inlet air temperature, injection advance angle, and diameter of oil injection hole, will be selected as the factors for the orthogonal test, where each factor contains four levels, and one regression orthogonal test will be conducted.The fuel consumption rate (y1) was used as the evaluation index to pursue the lowest fuel consumption rate, and the factor level table is shown in Table 1.
The five test factors take values in the range [Xj1, Xj2] (j=1,2,3,4,5), where Xj1, Xj2 is called factor Xj upper and lower levels, while the arithmetic mean of the upper and lower levels is calculated and called the zero level of the factor, expressed as Xj0.The difference between the upper or lower level and the zero level is called the spacing of variation and is denoted as  j.The expressions are: The coding is a linear transformation of the levels of the factors, denoted by Zj.The time specification variable Zj varies between [-1,1] and is not affected by the size of the natural variable taken.The expressions are: Where Zj and Xj0 correspond, the corresponding codes for Xj1, Xj0, and Xj2 are Zj1=-1, Zj0=0, and Zj2=1.The factor-level coding table is shown in Table 2.The actual working process of a dual-fuel engine is more complex, and the interaction between different factors needs to be considered.Since the EGR rate and inlet conditions significantly impact the combustion and emission characteristics of the engine, a two-by-two interaction between three factors EGR rate, inlet pressure, and inlet temperature was chosen.Based on a one-time regression orthogonal test design scheme, the orthogonal table L8(2 7 ) was selected for the test, as shown in Table 3 [10] .Three zero-level test groups were also added to ensure the accuracy of the test [11] .Based on the principle of least squares and the characteristics of the orthogonal table for the one-time regression equation, the formula for calculating the coefficients of the one-time regression equation is as follows: The natural variable one-time regression prediction equation for the fuel consumption rate can be obtained by simplifying zj (j=1-5) by substituting it into (8) from the coding equation (3): y1=107.267+1.8628x1-296.25x2+0.39x3-0.529x4+145.43x5-10.664x1x2+0.0057x1x3(9) By the magnitude of the absolute value of the partial regression coefficient in the regression equation, the importance of the influence of each factor on the fuel consumption rate can be obtained as z2>z1>z3>z5>z1z2>z4>z1z3, that is, inlet pressure>EGR rate>inlet temperature>diameter of oil injection hole>injection advance angle.Using the [Planning Solution] module in the Excel sheet, the equation was solved according to the constraints of y1≥0, -1≤z1≤1, -1≤z2≤1, -1≤z3≤1, -1≤z4≤1 and -1≤z5≤1 to obtain: when z1=-1, z2=1, z3=-1, z4=1 and z5=-1, the minimum value of the equation predicted fuel consumption rate was 181.93 (g/ kW•h).

Table. 3 One-time regression orthogonal test protocol table
The above optimization parameters were substituted into the simulation model, and the simulation results were compared with the prediction model, as shown in Table 5.The results show that the difference between the prediction model and the simulation model is 0.37%, which is a more accurate prediction.The fuel consumption rate was 9.96% lower than when the original engine was burning pure diesel fuel without optimization.The combination of parameters with the lowest fuel consumption rate was: EGR rate of 0, the inlet pressure of 0.233 MPa, the inlet temperature of 325.15 K, injection advance angle of 22.6 °CA, and the diameter of the oil injection hole of 0.26 mm.The AVL-FIRE software was used to select a suitable combustion and emission model and to establish a simulation model concerning the actual dimensions of the combustion chamber of the 4190ZLC-2 diesel engine for the one-eighth high-pressure cycle calculation.The numerical curves of cylinder pressure and heat release rate calculated by the simulation were compared with the data obtained from the original engine bench test, and the results showed that the curve fit was more than 95%, and the simulation model established was accurate and could be used for simulation research.
2) With the increase of the butanol blending ratio, NO emission increases, the indicated power decreases, and the fuel consumption rate increases.Under the premise of ensuring diesel engine dynamics, combined with the significance of this paper's research: 4190ZLC-2 marine medium-speed diesel engine blending butanol, the best proportion of 20%.
3) Five parameters of the combustion system were selected for a regression orthogonal design to construct a mathematical model with fuel consumption rate as the objective function.The magnitude of the absolute value of the partial regression coefficients in the regression equation can be obtained: inlet pressure has the greatest influence on the fuel consumption rate, followed by EGR, inlet temperature, etc.The lowest fuel consumption rate is achieved by the following combinations (EGR rate 0, inlet pressure 0.233 MPa, inlet temperature 325.15 K, injection advance angle 22.6 °CA, the diameter of oil injection hole 0.26 mm); after optimization, the fuel consumption rate is reduced by 9.96% compared to the original machine.

Figure. 1
Figure. 1 Schematic diagram of the central section 1/2 of the combustion chamber

Figure. 3 Figure. 4
Figure. 3 Comparison of simulated and experimental values of Mean pressure/Rate of heat curves

Table . 1
Factor level table The one-time regression equation between the test indicator (y) and the factor (xm) is as follows: 4

Table . 2
Factor-Level Coding Table Combined with the regression orthogonal test design table in Table 3, the fuel consumption rate design calculation table is shown in Table 4.The coefficients of the regression equation can be obtained from Table 4 and collated to obtain the regression equation between the canonical variables and the fuel

Table . 4
One-time regression orthogonal test results calculation table

Table . 5
Comparison table of fuel consumption rates for different options