Aff ections of Turbine Nozzle Cross-Sectional Area to the Marine Diesel Engine Working

Summary After a long period of use, some important technical parameters of the main marine diesel engines (MDE) gradually become worse, such as the turbine speed, intake pressure, exhaust temperature, engine power, and specifi c fuel oil consumption (SFOC). This paper studies the aff ections of the turbine nozzle cross-sectional area (AT) to MDE and presents a method of AT adjustment to improve the performances of MDE. A mathematical model of an engine was built based on the existent engine construction and the theory of the diesel engine working cycle and the simulation was programmed by Matlab/Simulink. This simulation model accuracy was evaluated through the comparison of simulation results and experimental data of the MDE. The accuracy testing results were acceptable (within 5%). The infl uences of AT on the engine working parameters and the fi nding optimization point were conducted by using the simulation program to study. The predicted optimization point of the nozzle was used to improve the engine’s performances on board. The integration of the simulation and experiment studies showed its eff ectiveness in the practical application of the marine diesel engine fi eld. (AT)


INTRODUCTION / Uvod
On the commercial motor vessels, the main engines usually are high-power diesel engines (two-stroke or four-stroke), most of them turbocharged by axial turbochargers (TC) due to retaining their high effi ciency at medium and larger-size compared to the radial turbocharger [1]. Therefore, there are many studies focused on these objects. The experimental research of Rahnke [2] showed that for the same assembly of the axial and radial turbocharger, the inertia moment of the fi rst type is about half of the inertia moment of the second one. In the work [3], Pesiridis, Saccomanno, Tuccillo, and Capobianco modifi ed the design of an axial turbine and simulated by CFD theory. Their simulation results showed that the dynamic energy of the gas fl ow could be regulated by controlling the nozzle crosssectional area, such as a slide hub wall. Some methods have been used in modeling marine diesel engines. Theotokatos [4] investigated the transient response of two-stroke MDE by the cycle mean value models. The combination studies of the mean value and zero-dimensional models to enhance the accuracy of the MDE models was carried out by the following authors: Baldi, Theotokatos, and Andersson [5] for a four-stroke MDE, and Tang, Zhang, Gan, Jia, and Xia [6] for a two-stroke MDE. Sun, Wang, Yang, and Wang [7] developed and validated a sequential turbocharging MDE combustion model by the partial least squares method with acceptable accuracy.
The main marine diesel engine operates in heavy load conditions and continuity, it may operate about 6000 hours of 8760 hours per year, many of those at full design load [8], the SFOC and the emissions gradually increased. The main reason of the scavenging air amount defi ciency for the normal engine operation is the bad working of the turbocharger. Therefore, the improvements of the gas distribution system can improve the performances of the engine. In the statistical research on the ABB turbocharger [9], Schieman showed that the turbine effi ciency and charging pressure had been decreased so much due to the turbocharger dirty and found a way to clean compressor and turbine blades by water or blasting with ground nutshells.
This work focused on the MDE that has a long using time, and at the practical operation, in the load range (Load Index, LI): LI= 60% ÷ 68%. The research methodology of this paper was presented in the following procedure. Firstly, the mathematical model was built and written its code (simulating) in MatLab / Simulink program. The model was presented accurately and reliably in accordance with the diff erence between the simulation results and test records provided by the manufacturer. Secondly, the optimum nozzle cross-sectional area was predicted to receive the optimal working values of the main important parameters of the MDE by simulation way. This step is very important for practice orientation to narrow the nozzle of the turbocharger. Thirdly, the real experiment study on a turbocharged marine diesel engine was conducted and analysed the experimental results.

Marine diesel engine and turbocharger relationship / Brodski dizelski stroj u odnosu na turbopuhalo
The MDE and TC relationship was based on the intake air mass fl ow rate (m  ei ) and exhaust air mass fl ow rate (m  eo ). The principle scheme of the MDE -TC relationship was shown in Fig.1.
Where, n e (rpm) -engine rotatory speed; V d (m 3 ) -total swept volume;  v (-) -volumetric effi ciency; z -diesel stroke: z=1 for two-stroke, z=2 for four-stroke engine; R a (kJ/kg.K) -gas constant; p s (kN/m 2 ) -intake air pressure; T s ( 0 K) -intake air temperature; The total intake mass fl ow rate (m  eo , kg/s) in to the cylinder is given as below: Where, m  f (kg/s) is the rate of the feed fuel oil that is calculated as equation (3) Where, m f,cycle (kg/cycle) is the amount of fuel oil per cycle (in this work, it was determined by the experiment); n cyl (-) is the number of cylinders.

Intake process / Proces unosa
The intake process quality can be evaluated by the volumetric effi ciency  v in the following expression Where, c v1 , c v2 , c v3 are adjustable parameters, and estimated by the least square regression method. In accordance with the determination coeffi cient of the model, R-squared = 0.9689, the model coeffi cients are defi ned [11]: c v1 =0.006651; c v2 =0.7429; c v3 =-0.4093.

Combustion process / Proces izgaranja
From the ideal gas, by diff erentiation of this equation: PV=mRT, the temperature model is obtained as equation (5) bellow: Where, R (J/kg.K) is the mixture gas constant; m (kg) is the amount of mixture gas. Similarly, the diff erential pressure model is [11]: Where, (-) is the specifi c heat capacity ratio of the mixed gas; The heat release equation dQ in /d is shown as bellow: Where, Q in is the total input heat in fuel combustion, Q in =m f .Q H (Q H : Low heating value of the used fuel); x f -burn fraction. Based on Wiebe's equation [13] [14], the diff erential equation dx f /dt is: Where a p , a d , m p , m d are shape factors;  p ,  d are the duration of premixed and diff usion phases;  s is the start of combustion. Combustion factors (a p , a d , m p , m d ,  p ,  d ) was estimated as [15], a p =a d =6.9;  p =70 0 ; m p =3; m d =0.5, and  d was calculated by least square regression method as [15],  d =c 1 p e 2 +c 2 p e +c 3 p e , c 1 =-0.0002931; c 2 =0.05108; c 3 =-1.313, with coeffi cient of determination R-squared=0.9956.
The heat transfer dQ w /d from the gases to the combustion surfaces is as bellow [16]: (11) Where, A w () is the area of surfaces (head, cylinder, piston); T w ( 0 K) is the average temperature of surfaces; h t () is the heat transfer coeffi cient, estimated by Woschni [17] and corrected by Heywood [12], given as below: Where, p(N/m 2 ) -gas pressure; U(m/s) -gas velocity; b(m)cylinder bore; T(K) -gas temperature.

The total mechanical losses / Ukupni mehanički gubici
The total mechanical friction pressure of the engine, p fp (kPa), includes friction losses and pumping losses which was determined through the engine speed n e (rpm), mean piston speed (m/s) and is defi ned in [12] as below: Where c fi (i=1÷3) -tuning parameters, estimated as [12], c f1 =75, c f2 =48; c f3 =0.4.

Indicated and Eff ective (Brake) powers / Navedene i efektivne konjske snage
The Powers (kW): Indicated P i , and eff ective P w of one (14) The total engine eff ective power, P Ew (kW) is defi ned as bellow:

Turbocharger Model / Model turbopuhala
In this research, the turbocharger includes a radial compressor and an axial turbine which mounted on a common shaft. The turbocharger model has two sub-models: turbine model compressor model.

Turbine model / Model turbine
Turbine effi ciency, t , is a function of blade speed ratio (BSR) [1] as below: Where,  t,max -maximum of the turbine effi ciency; BSR optoptimum of BSR ; c t -tunning parameters.
The turbine mass fl ow, m  t (kg/s), depends on the area of the nozzle and ratio of pressures as below [10]: Where, R e -gas constant of exhaust gas (J/kg.K); p 3 , T 3 -pressure and temperature at the inlet turbine; A T (m 2 ) -nozzle crosssectional area; f( t ) -function of the turbine pressure ratio  t , which can be modelled as following expressions below [18]: With  e (-) is the specifi c heat capacity ratio of exhaust gas. Turbine power, P t (kW), can be calculated by the isentropic enthalpy drop in the turbine stage, given as below [19] (20) Where, subscripts 3, 4 refer to the inlet and outlet of the turbine; c pe (J/kg.K) -specifi c heat value at constant pressure.

Compressor model / Model kompresora
The compressor effi ciency  c can be estimated as the quadratic function [20], given as below.
Where  c (-) -pressure ratio;  c,max ,  c,max -maximum of effi ciency and pressure ratio which are taken from the compressor map; Q c -tuning parameter. The compressor mass fl ow model was based on two dimensionless parameters: fl ow coeffi cient  c and energy transfer coeffi cient  c . The energy transfer coeffi cient  c [21] is: Where  t (rad/s) -turbine speed, r c (m) -compressor radius; c pa (J/ kg.K) -specifi c heat capacity at constant pressure;  a -specifi c heat capacity ratio of the inlet air; T 1 -inlet air temperature. The fl ow coeffi cient  c [21] is: Where, c 1 , c 2 , c 1 , c 2 -tunning parameters. From e quations  c and  c , the compressor fl ow equation is c m  given below [21]: The compressor power P c is calculated according to the expression below [1]: The balance between the turbine and the compressor / Ravnoteža između turbine i kompresora At the steady condition with a speed of turbocharger n t (rev/ min), the balancing between the turbine and the compressor powers is given in the following expression: Where, J t (kg.m 2 ) -turbocharger inertia moment;  m (-) -friction coeffi cient.

Intake manifold and exhaust manifold model / Model ulazne i izlazne mlaznice
The intake air and exhaust gas pressures are defi ned in the following equations: Where, subscripts im, em denote the intake and exhaust manifolds; R a (J/kg.K), R e (J/kg.K) -gas constant of the intake and exhaust gas.

Algorithm / Algoritam
Parameter estimation / Provjera parametara There were two types of parameters, fi xing and tuning parameters.
-Fixing parameters include MDE and TC structure parameters: cylinder bore b, stroke s, compression ratio , compressor diameter D c , turbine diameter D t , inertia moment J t ..., and ambient conditions: temperature and pressure, low heat value Q H , Cetan number CN.
-Tuning parameters include volumetric effi ciency coeffi cients c v1 ,c v2 , c v3 ; friction coeffi cients c fi ; and combustion factors a p , a d ,  p ,  d, m p , m d . -The output parameters: Eff ective power, mean pressure, and maximum pressure. -The errors: To evaluate the accuracy, the relative deviation between the simulation parameters and measured parameters from test records was calculated, and loops ensured these errors were 5% With x sim -simulation parameters; x mea -measured parameters from test records.
The algorithm chart. The algorithm was built based on the above-mentioned equations (Fig. 2).

The object for theoretical and experimental study / Predmet teoretske i eksperimentalne studije
The object for simulation is the diesel engine 8MAK43 installed on MV PhucHung of GLS company, Viet Nam. Some technical engine parameters are shown in Table 1.

Simulink model / Simulink model
The model was made in MatLab Simulink and shown in Fig. 3. In the fi gure were described the following: Input controls: u_t(u t ) was the signal of the nozzle crosssectional control; mf cyc ( m f,cycle ) was the quality of fuel per cycle; n_e(n e ) -the engine speed.
Output results: the indicated pressure (p_cyl) which was used to calculate the engine performances (brake power, specifi c fuel consumption…)

Simulation of a new engine at the rated operation mode / Simulacija novoga stroja prema prilagođenome modelu
The program simulated a new engine at the rated operation mode (100% load and 500 rpm).

Interface of simulation / Sučelje simulacije
The interface of this simulation was shown in Fig. 4. There were described: the input controls; Indicated cylinder pressure and key results.

The comparison of the simulation results with the MDE data in accordance with the technical documents / Usporedba rezultata simulacije s podacima o brodskome stroju u skladu s tehničkom dokumentacijom
At the LI={25; 50;75;100;110}%, the simulation results and the reference data that are given in the engine technical documents [22] were compared and shown in Fig. 5 ÷ Fig. 8.

Simulation at the practical operation mode / Simulacija pri praktičnome modelu djelovanja
In accordance with the MDE book log, the engine 8MAK43 operated at the speed 412 rpm and LI range of (60% ÷68%). The regime with the LI 65% and speed 412 rpm was regularly used. Therefore, this mode was simulated to fi nd the optimization point of the nozzle cross-sectional area for improving the engine's performances. The interface and main results of the simulation was presented in Fig. 9. Prediction of the infl uence of the nozzle cross-sectional area / Predviđanje utjecaja prostora presjeka mlaznice The variation of engine performance parameters (turbine speed n t , SFOC, exhaust temperature T e , brake power P w ) via the nozzle cross-sectional area (%A T ) were modelled by regressive models (equations) (30), (31), (32), and (33) with t he confi dence testing in accordance with the statistic F criterion: F(=0.99;n 1 ;n 2 ), where, =0.99 is confi dence; n 1 and n 2 are freedom degrees [24].
Regressive model of the turbine speed n t (A T ) was received with the 99%-confi dence:  Figure 13 Regressive analysis of the simulated results of the relation between P Ew -A T Slika13. Regresivna analiza simuliranih rezultata odnosa P EW -A T From the simulation, the optimization point of the nozzle crosssectional area (%A T ) was found out at the practical operation mode (LI 65% and n= 412 rpm). With the A T =91%, the turbine speed n t and brake power P w reached the maximum (n t =13545 rpm, P Ew =2982 kW); at the same time, the exhaust temperature and specifi c fuel consumption g e were minimum (T w =579 0 K, g e =229 g/kW.h).

EXPERIMENTAL STUDYING / Eksperimentalno proučavanje
According to the above simulation results the experiment was carried out. The nozzle of the TC was removed and then changed it sizes as Fig.14  The comparison results / Rezultati usporedbe The MDE with improved nozzle has well operated. At the same regime operation (LI 60%÷68%, n= 412 rpm), the main output parameters before and after improving were shown in Fig.15 ÷ Fig.17 Table 2 co mpares the measured output parameters at the most regularly mode (load 65% and speed 412 rpm), with before and after narrowed the nozzle to evaluate the eff ectiveness of improvement. The engine's performances have signifi cantly improved, the maximum combustion pressure increased by 13 bar (+11.3%), turbine speed increased by 2176 rpm (+19.5%), the intake pressure increased by 0.46 bar (+25.5%), and the exhaust temperature decreased by 35,5 0 C (-9.4%).

CONCLUSION / Zaključak
In this research, there were synthesized the mathematical fundaments and made the simulation software in MatLab / Simulink for studying the working cycles of the turbocharged MDE. By using the made simulation software, the aff ections of nozzle cross-sectional area to the engine, were evaluated and an optimum point was determined to improve the engine brake power, SFOC, and exhaust temperature.
The experimental study was carried out on a marine diesel engine on board. At the practical operation with the LI=65% and speed n = 412 rpm, the nozzle cross-sectional area was narrowed with 91% of maximum area, same as in the simulation study, the results were positive. The turbine speed improved by 19.5%, at the same time, the intake pressure increases by 25.1%, and exhaust temperature reduced by 9,4%. Therefore, this method may be useful for improving old turbocharged engines with a fi xed nozzle. However, it depends on the kinds of engine and the time of use, the nozzle cross-sectional area would be adjusted suitably.