Multiparametric optimization of a medium-speed marine diesel at increase its capacity

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   The program DIESEL - 2/4t has the built-in function of multiparametric optimization which allows to solve the problem of optimum choice of several parameters of a working process of an engine and its turbocharger.

    At development or boosting of the engine it is very important to choose several parameters of a working process which will provide minimum specific fuel consumption and minimum emission of harmful materials at necessary capacity both admissible levels of thermal and mechanical tension.

     An example of simulation to increase of power of a medium speed marine diesel is represented below. Beforehand the program was customized on this engine and the calculation of its performance in a basic configuration was carried out.
   In the basic configuration, the diesel is equipped with the system of 2 stage free turbocharging with cooling of air after each of stages. At the initial configuration, the engine capacity is characterized by BMEP = 16 bar at operation with exhaust back pressure of 1.52 bar. The task of boosting is directed to increase BMEP up to 20 bar (by a factor 25%), thus the diesel parameters should not fall outside the limits indicated in the table 1.

Table 1.  Limits parameters.

Engine parameters Base level Limit level
Max. cylinder pressure [Pz], bar 140 Pz < 145
Max. injection pressure [P_inj], bar 1100 P_inj < 1300
Temperature in the turbine inlet [Tr], K 933 Tr < 953
Air fuel equivalence ratio, A/F_eq 1.7 A/F_eq> 1.7
Compression ratio 13.2 CR > 11.5

     Whet the fuel portion "mf" increases by 25 % (from 2.8 to 3.5 g. per cycle) the diesel  power increases only by 20 %, the specific fuel consumption "SFC" increases by 7 g/(kW h), the main limitations are disturbed (see tab. 2, combination: "mf=3.5 g"):
- The level of maximum cylinder pressure Pz  increases  to 153 bar;
- The level of temperature of gases in front of the turbine Tr  increases to 996 K;
- The level of A/F_eq  decreases to  1.57.

    The boost pressure increases from 3.22   to 3.78 bar. (the calculation is carried out at condition of share simulation of a diesel working process and of gas-dynamic calculation of flow in blading sections of turbines and compressors.)

      As follows from the results of additional simulation of the piston engine it is necessary to increase a boost pressure up to 4.1 bar. (see tab. 2, combination: " Increase. ذي ") for preservation of the A/F_eq =1.7 in the initial configuration.
   To reach of this purpose the wheels of both compressors were updated. As a result, the air fuel equivalence ratio was increased to 1.7, however the level of specific fuel consumption had exceeded its initial value on 6 g / (kW h), and the maximum cylinder pressure has grown even more: to Pz=162 bar., temperature of gas in front of the turbine was decreased from 996 K to 966 K, but its value had exceeded the limits value: Tr = 953 K.

   To decrease the specific fuel consumption and satisfy limitations it is necessary to carry out the complex optimization of several diesel parameters and supercharging units.

Optimization  of the gas exchange

    Before to perfect the processes of compression and combustion in the cylinder, and  perfect a blading section of units of a supercharge, it is necessary to provide conditions of maximum charging of the cylinder with a fresh charge. It is necessary to select phases of a valve timing.
   The choice of phases of the valve timing on the first stage of investigation will allow to except these parameters from a vector of independent variables at following stages. It will decrease essentially a size of calculations of all research, and will also decrease probability of determination of a local optimum.

   The choice of a goal function at optimization of a valve timing phases is caused by a main purpose of gas exchange system. In most cases, it has been done to provide clearing and charging of the cylinder. A goal function is a volumetric efficiency.

The following is included in a vector of explanatory variables:
- Angle of closing of exhaust valves;
- Angle of opening of inlet valves;
- Angle of closing of inlet valves.
     The value of angle of exhaust valve opening influences faintly on value of a volumetric efficiency. But this angle influences strongly on cylinder diagram power and pumping loop losses, therefore the angle of exhaust valve opening is expedient to include him in a vector of explanatory variables on further investigation stages when the specific fuel consumption will be entered in a goal function.

     The optimum search was carried out without of gas dynamic calculation of a gas flow in blading sections of turbines and compressors. The boost pressure was set as a stationary value of 4.1 bar, the fuel portion is 3.5 g., and the boundary conditions in the input of a high-pressure turbine were calculated from condition of a balance of turbines and compressors capacities.
     The search of optimum combination of phases of a valve timing was carried out by the "heavy ball" method, and then the solution was improved by the "deformable polyhedron" method. As a result, the solution was obtained: (see tab. 2, combination: "Optimum phases of valve timing"):
- Close exhaust valves earlier by 20 deg. of crank angle;
- Open inlet valves earlier by 5 deg. of crank angle;
- Close inlet valves earlier by 13 deg. of crank angle.

   In this case (at reduction of overlap of valves and approaching of it to TDC), the volumetric efficiency is increased by 0.042 and reaches value of 0.782, temperature of gas is decreased by 26 K. The last circumstance is a reason of increment of a gas pressure in front of the turbine and of increase of losses of pumping loop. The additional increase of pumping losses takes place for the reason of reduction of valve overlap and approaching of it to TDC, in a zone of minimum volume: "peak" of the curve of pressure in the cylinder at the end of exhaust is increased. The considerable increase of pumping losses is a reason of increase of value of a specific fuel consumption by 9 g. (compared to initial one).
   The increase of a mass of a charge causes further breaking the limitation of a value of a maximum firing pressure (Pz = 167 bar).


Table 2. Sequence of optimization of engine parameters

Color notations The broken limitations which are not take part in operating search
Explanatory variables Goal function Limits
Engine parameters Combinations of engine parameters  (mf=3.5 g)
Base configuration
mf=2.8 g
Base configuration
mf=3.5 g.
Increase of boosting pressure Pk Optimum of phases of a valve timing Optimum of engine parameters
Compression ratio 13.2       11.55
Injection lead, deg. up TDC 17       18
Injection timing, deg. 38       35
Number of nozzles 8       8
Nozzles diameter, mm 0.5       0.5
Exhaust valves opening, deg. Initial       1 deg. before init.
Exhaust valves closing, deg. Initial     20 deg. before init. 20 deg. before init.
Inlet valves opening, deg. Initial     5 deg. before init. 5 deg. before init.
Inlet valves closing, deg. Initial     13 deg. before init. 13 deg. before init.
Designed angle of turbine nozzles outlet, deg. High pres. 13.6       12.8
Low pres. 13.6       15.3
Boost pressure, bar 3.22 3.78 4.1 4.1 3.88
BMEP, bar 1.6 1.92 1.93 1.91 2.0
D SFC,  g / kW h 0 - initial +7 +6 +9 0
Max. cylinder pressure [Pz], bar 140 153 162 167 145
Temperature in the turbine inlet, [Tr], K 933 996 966 940 948
Air fuel equivalence ratio, A/F_eq 1.7 1.57 1.7 1.79 1.7
Max. injection pressure [P_inj], bar 1100 1120 1120 1120 1300
Volumetric efficiency 0.73 0.731 0.74 0.782 0.78

     It would seem that the engine parameters have worsened and the optimization of phases of a valve timing has negative results, however it is not so. The increase of a volumetric efficiency and of air fuel equivalence ratio and caused by them lowering of temperature of gas in front of turbines opens possibilities for reduction of boost pressure and consequently pumping losses. The elaboration of value of a boost pressure should be carried out already on the next stage at the search of optimum combination of other parameters of the engine.

Optimization of parameters of combined engine at its boosting

   Except phases of a valve timing, there are other parameters of an engine which influence strongly on its performance. They are:
-  compression ratio;
-  injection lead;
-  injection timing and injection characteristic form;
-  number and diameter of nozzles, direction of nozzles;
-  piston bowl design;
-  design of turbines and compressor blading, etc.

     At a choice of parameters forming a vector of explanatory variables it is necessary if possible to limit their number and to prefer those of them which effect is most strong and not connected with technological problems. There are many geometrical quantities to describe a flow part of double-stage turbine and compressors. To optimal search two of them were chosen: angles of flow outlet from high and low pressure turbine nozzles. These parameters allow to regulate both summary boost pressure and distribution of pressure ratio between stages of compression. Besides, such the change of a blading sections of turbines causes minimum technological efforts.

    8 controlling factors are included in vector of explanatory variables:
-  compression ratio ;
-  injection lead;
-  injection timing;
-  injector nozzles bore;
-  number of injector nozzles;
-  angle of exhaust valves opening;
designed angle of turbine nozzles outlet (high pressure stage);
designed angle of turbine nozzles outlet (low pressure stage).
    The limits parameters are shown in the table 1.
    The goal function is specific fuel consumption "SFC".

     The "start point" of optimization is the combination of parameters obtained as a result of optimization of valve timing phases. At first, the search of optimum was carried out by method of the "quickest descent", and then the solution was improved by a method of the "deformable polyhedron". The goal function and the limitations was calculated 124 times (in view of calculation of derivatives by the numerical method). Usage of other optimization procedures and other start points results to the same solution too. It shows that the obtained optimum is not local.

   The results of the optimization  problem solution are presented in the table 2 (combination: "Optimum of engine parameters"). The results have shown that the atomizer applied in the initial configuration ( 8 x 0.5) is optimum. The initial value of the angle of the exhaust valves opening is optimum too. Other optimized parameters require changes which will allow to boost this engine up to BMEP = 20 bar without increase of a specific fuel consumption and at admissible levels of thermal and mechanical tension.

     Thus it is possible to reach the best engine performances by the optimization with all the limitations and view of behavior of different phenomena.

     It is necessary to note that the problem of the soot and NOx emission reducing is not stated. Otherwise the solution will be substantially differ.


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