LUO Qing-guo(駱清國(guó))，F(xiàn)ENG Jian-tao(馮建濤)，LIU Guo-fu(劉國(guó)夫)，GUI Yong(桂勇)

(1.Department of Mechanical Engineering，Academy of Armored Force Engineering，Beijing 100072，China;2.Department of Vehicular Engineering，Armored Force Technology Institute，Changchun 130117，Jilin，China)

Introduction

Diesel engine cooling system has been developed to intelligent cooling system with the engine power increase［1］.The military vehicle engines are high power，and their operating conditions are complex.The cooling water temperature can not be controlled easily.Its control is a closed loop with nonlinear，time-varying and large time lag［2］，etc.Therefore，the coolant temperature overshoot and the slow adjustment process arise easily，if its time-varying and large delay characteristics are not considered accurately in the cooling control strategies［3］.It has been a difficult problem for development of control strategy.To master the influences of the system parameters on the coolant temperature is significance to develop wonderful control systems and ensure the engine run always in the best temperature range.

In this paper，a simulation model for the diesel engine cooling system is established by using GTCOOL，and the cooling water temperatures in different operation conditions are simulated numerically to provide a basis for intelligent control.

1 Simulation Modeling for Diesel Engine Cooling System

1.1 Principle of Cooling System

The engine cooling system uses high and low temperature dual-circulation loop technology.Major components include diesel body，water pump，oil exchanger，high temperature exchanger，low temperature exchanger，air cooler，expansion tank and corresponding pipes，as shown in Fig.1.The high and low temperature loops share the water pump［4］.

Fig.1 Principle of cooling system

The pump forces the cooling water to enter the oil heat exchanger，and the cooling water passed the ex-changer is divided in two parts.One of them enters into the body，head and then high temperature exchanger;another into the air cooler through the low temperature exchanger，and mixes with the high temperature circulating cooling water after cooling the charged air，and finally enters into the water pump to circulate［4］.

1.2 Mathematical Model of Pipeline Flow

The flow model involves the simultaneous solution of the continuity，momentum and energy equations［5］.These equations can be solved in one dimension.It means that all quantities are averages across the flow direction.The primary solution variables are mass flow，density and total internal energy.The whole pipeline system is divided into many control volumes，and each pipe is divided into one or more volumes.These volumes are connected by boundaries.The scalar variables，such as the density，total internal energy，pressure，temperature and total enthalpy，are assumed to be uniform in each volume and are calculated at the center of the volume.The vector variables，such as the mass flux，velocity and mass fraction fluxes，are calculated in each boundary.The basic equations include the continuity，enthalpy and momentum equations［5］.

Continuity equation:

Enthalpy equation:

Momentum equation:

wheremis the volume mass in kg;is the boundary mass flux in kg/s;ρis the density in kg/m3;His the total enthalpy in J/kg andH=e+;eis the total internal energy per unit mass in J/kg;Vis the volume in m3;pis the pressure in Pa;his the heat transfer coefficient in W/(m2·K);Asis the heat transfer area in m2;Tfluidis the fluid temperature in K;Twallis the wall temperature in K;Ais the flow cross-sectional area in m2;uis the boundary flow velocity in m/s;Cfis the surface friction coefficient;Cpis the pressure loss coefficient;Dis the pipe's equivalent diameter in m.

1.3 Simulation Model of Cooling System

According to the principle of cooling system，a simulation model can be set up by using GT-COOL，as shown in Fig.2.

Fig.2 Simulation model of cooling system

The high and low temperature exchangers heat transfer coefficients can be calculated by using Nusselt number［6］.

and

whereLis the reference length in m;kis the fluid's thermal conductivity in W/(m·K);μis the fluid's dynamic viscosity in Pa·s;vis the fluid velocity in m/s;cpis the fluid's heat capacity in J/(kg·K).

The constantaandbcan be determined by the heat exchanger experiments.The high and low temperature heat exchangers are plate types.Their main parameters are listed in Tab.1 and Tab.2，respectively.a=1.7，b=0.85 for the high temperature heat exchanger;a=3.78，b=0.96 for the low temperature heat exchanger.

Tab.1 Parameters of high temperature radiator

Tab.2 Parameters of low temperature radiator

2 Analyses for Simulation Results

2.1 Verification for Simulation Model

The thermal balance for the engine cooling system is tested in a test bench，as shown in Fig.3.The experiment ambient parameters are 89.1 kPa in pressure，25℃ in temperature，40%in humidity，and external circulating cooling water is used instead of cooling fan.In the experiment，the steady state engine parameters are measured only，and the transient state parameters are not measured for limited experiment conditions.

Fig.3 Test bench

The simulation and experiment results are compared，as shown in Fig.4 －6.It can be seen that they coincide with each other，and the simulation model is verified.

2.2 Analyses for Response of Cooling System

Fig.4 Cooling water temperature

Fig.5 Thermal loss in low temperature radiator

Fig.6 Pump flow rate

This paper only analyzes the water outlet temperature change when the diesel engine runs from a stable condition to another.In order to ensure the previous operation is steady，the simulation time is set longer when the simulation under variable operation conditions.Changed the operation conditions and the cooling system parameters at 3 000 s，the effects of the engine speed，torque and external circulating water flow rate on the outlet water temperature are all analyzed.Now，the transient responses of the cooling system are discussed in four different cases.

1)The engine speed is 2 200 r/min.Change engine torque from 458.1 N·m to 1726.7 N·m at 3000 s，as shown in Fig.7.

Fig.7 Torque vs.time

The effect of torque on water temperature is shown in Fig.8.At 1 306 s，the engine reaches a stable condition of 2 200 r/min in speed and 458.1 N·m in torque.After increase of torque，the coolant takes more heat quantity from the engine body.The water temperature gradually increases from 337.2 K at 3 000 s to 375.8 K at 4 057 s.That is，the process lasts 1 057 s，and the cooling system can reach a new steady state of 2 200 r/min in speed and 1 726.7 N·m in torque.

Fig.8 Effects of torque on water temperature

2)The engine speed is 2 200 r/min，and its torque 1 726.7 N·m.Change the low temperature external circulating water flow from 1 L/s to 1.28 L/s at 3 000 s.

As the flow increases，the flow rates of the internal and external circulating water in the low temperature exchanger increase and heat transfer coefficient changes.Fig.9 showsh·A，i.e.heat transfer coefficient multiplied by heat transfer area，of the external circulating water in the low temperature exchanger.When the water flow increases，h·Aincreases first，and then decreases，from 5 247.0 W/K at 3 000 s to 6 331.8 W/K at 3 008 s and then to 6 240.0 W/K at 3 865 s.The reason is the increases of water flow rate and heat transfer coefficient and the decrease of the water's dynamic viscosity with temperature［7］.The heat dissipation capacity of the low temperature exchanger is enhanced after the external circulating water flow increases，and it makes the engine outlet water temperature gradually decrease the low temperature exchanger's water temperature also fall，and the dynamic viscosity of water increase.According to Eq.(4)，the transfer coefficient decreases.Fig.10 shows that the outlet water temperature changes from 375.8 K at 3 000 s to 369.9 K at 3 865 s，and it lasts 865 s.

Fig.9 Effects of flow rate of external circulating water on h·A of low temperature exchanger's external circulating water

Fig.10 Effects of low temperature external circulating water flow on cooling water temperature

3)The engine torque is 1 718 N·m.Change the engine speed from 1800 r/min to 2200 r/min at 3000 s.

The water pump is a mechanical pump connected with the diesel engine crankshaft.The pump speed changes in a certain gear ratio，and in turn the pump flow rate changes，when the engine speed changes.Fig.11 shows that the pump flow rate changes from 9.051 L/s at 3 000 s to 11.262 L/s at 3 865 s.Fig.12 shows thath·Aof the internal circulating water in the low temperature exchanger changes with the pump flow from 10310 W/K at 3000 s to 12964.7 W/K at 4211 s.It make the heat capacity of the exchanger enhance.In addition，due to the engine speed increases，the heat coolant removed by the coolant from engine increases.By these two effects，the outlet water temperature changes，as shown in Fig.13，from 360.2 K at 3 000 s to 371.4 K at 4 211 s，and it lasts 1 211 s.

Fig.11 Effects of engine speed on pump flow rate

Fig.12 Effects of engine speed on h·A of internal circulating water in low temperature exchanger

4)Change the engine speed from 1 800 rpm to 2 200 rpm，the engine torque from 1 717.9 N·m to 1 726.8 N·m，and the external circulating water flow from 0.722 L/s to 1 L/s，at 3 000 s.

Fig.13 Effects of engine speed on cooling water temperature

Fig.14 shows thath·Aof the external circulating water in the low temperature exchanger changes from 3 971.4 W/K at 3 000 s to 5 247.0 W/K at 4 340 s.h·Aof the internal circulating water in the low temperature exchanger changes from 11105.8 W/K at 3 000 s to 13 335.0 W/K at 4 340 s，as shown in Fig.15.Fig.16 shows that the outlet water temperature changes from 370.5 K at 3 000 s to 375.8 K at 4 340 s，and it lasts 1 340 s.

Fig.14 Effects of multiple parameters on h·A of external circulating water in low temperature exchanger

Fig.15 Effects of multiple parameters on h·A of internal circulating water in low temperature exchanger

Fig.16 Effects of multiple parameters on cooling water temperature

It can be seen that，if the external circulating water flow rate changes only，the system takes the shortest time to reach a steady state.The reason is，in this case，the affected main parameter is the external cooling water flow rate in the low temperature exchanger.It makes the heat transfer coefficient of low temperature exchanger change.And，the other parameters of the cooling system are less affected;the outlet water temperature reaches a steady state quickly.While the engine speed changes，the cooling water flow rate changes because the water pump is connected with the diesel engine crankshaft.The outlet water temperature reaches a steady state slowly.If the engine operation conditions and the external water flow all change，the system will reach a steady state，taking longer time than in single parameter change.The reason is that，in this case，not only the heat transfer coefficient of the low temperature radiator changes，but also the flow of the cooling system，the coolant flow rate in each exchanger and the cooling system parameters are all changed.

3 Conclusions

1)A simulation model for a certain diesel engine cooling system is established.Referred to the thermal balance test，it is verified.

2)If the external circulating water flow changes only，the engine cooling system will take the shortest time，865 s，to reach a steady state.If the engine torque changes only，it will take 1 057 s to reach a steady state.If the engine speed changes only，it will take 1 211 s to reach a steady state.And，if the conditions and the water flow all change，the cooling system will need 1 340 s to reach a steady state.It is the longest time to reach a steady state

3)In study on intelligent control systems，the mechanical water pump can be replaced with an electronically controlled pump which can not be affected by the engine speed.In development of control strategies，to make the outlet water temperature reach a steady state quickly，the external circulating water flow should be adjusted first according to engine operation conditions，then the water pump speed should be controlled according to the water temperature.

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