Numerical Simulation of the Thermoelectric Model on Vehicle Turbocharged Diesel Engine Intercooler

A thermoelectric gas-solid heat transfer numerical model was established between an air-cooling tube-fin intercooler’s intake and cooling air passage channel on vehicle turbocharged diesel engine. The outlet temperature of intake air, the output power of the thermoelectric components and the thermal conversion efficiency are considered as the research objectives. When load value is constant, the outlet temperature of intake air decreases with the number of thermocouples increases and there exist maximum values for output power and thermal conversion efficiency; when the number of thermocouples is constant, there is little effect on the outlet temperature of intake air with the load value increases. When the load was been optimal designed, set the load value throughout equals to the value of thermoelectric component total internal resistance, the values of the maximum output power was increased by 20.3% and the thermal conversion efficiency was increased from 1.78 to 3.48%.


INTRODUCTION
In order to improve a diesel engine's intake air density, thereby increasing the injection quantity of the fuel to improve the mean effective pressure, it is generally need to install turbocharger in front of a diesel engine.However, due to the high temperature of the air after the turbocharger impacting the diesel combustion and emissions (Li, 2008;Lu, 2004), an intercooler should be installed at the exit of compressor outlet, in order to achieve the desired combustion standards.There is a certain temperature difference between the intake air and the cooling air, some heat is dissipated to the environment through the cooling air by convection away.Recent years, thermoelectric conversion device based on the principle of thermoelectric power generation (Thermoelectric Generator TEG), making use of the temperature difference to generate electricity, driven by the advantages of no pollution, no noise and no need for intermediate components, low-quality heat can be converted into high-quality electrical energy, is extensively researched and made utilization (Meng et al., 2010;Hoffman et al., 1997;Francis, 2009).In this study, a model of thermoelectric power generation devices between intake air passage channel and cooling air passage channel on air-cooling tube fin intercooler within a turbocharged diesel engine is researched and optimized, modeling and numerical study for future

MODELING Thermoelectric couples' arrangement:
The schematic diagram of a typical air-cooled tube-fin intercooler is shown in Fig. 1, the pressurized hot air and cooling air using the cross-flow heat exchanger arranged, can effectively exchanging heat.Since the thermoelectric appliances need to work in the temperature difference conditions, so several pairs of thermocouples are arranged between each layer of the intake air passage channel and the cooling air passage channel.The thermocouples are in array arrangement, electrically connected in series, as shown in Fig. 2.

Thermoelectric generator computing modeling:
The schematic diagram of the thermoelectric generator  3. Between the intake air passage channel and the cooling air passage channel, uniformly arranging m thermocouples, the intake air passage channel imported state temperature T 1in , mass flow q m1 and constant volume specific heat capacity c p1 , outlet temperature is T cooling air direction is perpendicular to the paper, inlet temperature, mass flow and the constant volume specific heat capacity of cooling air are T respectively, the cooling air passage outlet temperature is T 2out .The heat flow taken from intake air passage to thermoelectric generation elements is Q flow taken from thermoelectric generation elements to cooling air passage is Q 2 .External output power of the thermoelectric power generation elements is P. T are respectively the intake and the cooling air passage channels' wall temperatures.
Taking into account the general characteristics of the thermoelectric generator, make the following assumptions (Chen and Wu, 2000): • Ignoring the thermoelectric units and thermoelectric units with air convection heat transfer and radiation heat transfer • Ignoring the second stage of Thomson effect • The temperature difference between the intake air channel and the cooling air channel are ignored • The thermoelectric unit performance does not change with temperature • Ignoring the contact resistance of surfaces and the contact thermal resistanc According to the theory of non thermodynamics, thermoelectric power generation device for pumping heat from the hot end is: diagram of the array of thermoelectric Fig. 3: Diagram of thermoelectric generator model model is shown in Fig. 3. Between the intake air passage channel and the cooling air passage channel, uniformly arranging m thermocouples, the intake air respectively is and constant volume , outlet temperature is T 1out ; the cooling air direction is perpendicular to the paper, inlet w and the constant volume specific heat capacity of cooling air are T 2in , q m2 and c p2 , the cooling air passage outlet temperature .The heat flow taken from intake air passage to is Q 1 and the heat flow taken from thermoelectric generation elements to .External output power of the thermoelectric power generation elements is P. T w1 , T w2 are respectively the intake and the cooling air passage Taking into account the general characteristics of the thermoelectric generator, make the following Ignoring the thermoelectric units and thermoelectric units with air convection heat Ignoring the second stage of Thomson effect The temperature difference between the intake air channel and the cooling air channel are ignored The thermoelectric unit performance does not Ignoring the contact resistance of the contact surfaces and the contact thermal resistance According to the theory of non-equilibrium thermodynamics, thermoelectric power generation device for pumping heat from the hot end is: where α = α P -α N , α P and α N are seebeck coefficients of N-type semiconductor material I = The working current R = The total resistance K = The total thermal conductivity For the intake air and cooling air passage channel, there exists convective heat transfer.When the fluid flows through the wall, according to the theory of heat transfer, the heat exchange is: and Boelter (Cao, 2001) apply to wall temperature turbulent convective heat Re and the Prandtl are groups of parameters of the thermal diffusivity a, etc.These physical parameters are functions of temperature, so determining the Reynolds number and Prandtl number, it must give the characteristic temperature, subscript f represents the average temperature of the fluid inlet ) is the convective heat Sieder and Tate (Cao, 2001) suitable for wall temperature laminar convective represents the pipe length, µ f and µ w respectively represent the coefficient of dynamic cosity of the fluid at a characteristic temperature and represents the air density, F represents a cross-sectional area of the airflow passage, U represents the wet perimeter of the channel According to energy conservation, the thermoelectric power generation modules pumping heat from the hot end Q 1 , should be equal to the heat release from the cold end Q 2 plus the foreign output power 1 2 Thermal conversion efficiency is:

SOLUTION OF THE MODEL AND OPTIMIZATION IMPROVEMENTS
Solution of the intercooler thermoelectric power generation elements model: For a particular model of diesel engine turbocharger and intercooler (Li, 2008), the size of the structure and the intake air temperature, intake mass flow, velocity and other physical parameters were chosen to be the initial conditions for numerical calculation.The inlet temperatures of the intake air and the cooling air are set for T 2in = 315K respectively, the outlet temperature of intake air and cooling air, the wall temperature, the output power and thermal conversion efficiency of thermoelectric power generation elements are output variables .There are 43 intake air passage channels 44 cooling air passage channels; each intake air passage channel's structure is the same and each cooling air passage channel's structure is also the same, as shown in Fig. 4 and 5.After calculation, the wet perimeter of the intake air passage and cooling air passage respectively are U h = 10.29 m, U c = 74.62 m, the gas flow area of the intake passage and the cooling air passage respectively are F h = 0.01 m Airflow velocity of the intake air channel is u m/s, the cool air airflow velocity u c = 3.717 m/s, the Reynolds numbers of the intake air passage and the cooling air passage can be calculated, 7948 and 3567, determined as turbulent flow state (Cao, 2001), so choose (5) as a Nusselt number calculation formula.There exist total 86 contact surfaces between the intake air passage and the cooling air passage channels and m thermocouples are uniformly arranged in each of the contact surface.
Selecting commercial thermoelectric material bismuth telluride (Bi 2 Te 3 ), having the characteristics of the lower temperature range (270-450K) (Richard and Dan, 2009), the physical parameters are shown in Table 1, thermoelectric couple leg size is 2×2 is the thermal conductivity rate, σ is the conductivity, K is the thermal conductivity, R is the internal resistance Using trusted domain dogleg MATLAB, it can solve Eq. ( 1) to sectional area of the airflow passage, represents the wet perimeter of the channel.
According to energy conservation, the thermoelectric power generation modules pumping heat should be equal to the heat release plus the foreign output power P: (9) (10)

Solution of the intercooler thermoelectric power
For a particular model of diesel engine turbocharger and intercooler (Li, 2008), the size of the structure and the intake air temperature, intake mass flow, velocity and other physical parameters were chosen to be the initial conditions for numerical calculation.The inlet temperatures of the intake air and the cooling air are set for T 1in = 453.1K,= 315K respectively, the outlet temperature of intake air and cooling air, the wall temperature, the output power and thermal conversion efficiency of thermoelectric power generation elements are output variables .There are 43 intake air passage channels and 44 cooling air passage channels; each intake air passage channel's structure is the same and each cooling air passage channel's structure is also the same, as shown in Fig. 4 and 5.After calculation, the wet perimeter of oling air passage = 74.62 m, the gas flow area of the intake passage and the cooling air = 0.01 m 2 , F c = 0.26 m 2 .Airflow velocity of the intake air channel is u h = 18.1 = 3.717 m/s, the numbers of the intake air passage and the cooling air passage can be calculated, are respectively 7948 and 3567, determined as turbulent flow state (Cao, 2001), so choose (5) as a Nusselt number calculation There exist total 86 contact surfaces between the intake air passage and the cooling air passage channels and m thermocouples are uniformly arranged Selecting commercial thermoelectric material having the characteristics of 450K) (Richard and parameters are shown in electric couple leg size is 2×2×1 cm, λ is the thermal conductivity rate, σ is the conductivity, K thermal conductivity, R is the internal resistance.dogleg algorithm in (4), ( 5) and ( 7)  to (10).The objectives of the research are the respective outlet temperature and the wall temperature of the intake air and the cooling air passage, generator output power and the thermal conversion efficiency, with the number of thermo load R L respectively changes, using process control variable method, that is, when the number of thermo couplesm changes, set the load R L versa.
Figure 6 shows the relationships between the outlet temperatures and the wall temperatures of intake and cooling air vs. the number of thermocouples, the external load is set to be R L = 2Ω.As can be seen, as increases, the outlet temperature of the intake a and the wall temperature T w1 gradually decrease, the outlet temperature of the cooling air temperature T w2 gradually increases, the heat transfer is strengthened and the cooling effect of the intercooler is better.The temperature curve decreases rapidly before

Schematic diagram of intercooler intake air passage of intercooler cooling air passage
The relationships between the outlet-temperatures and of intake and cooling air vs. the earch are the respective the wall temperature of the nd the cooling air passage, thermoelectric power and the thermal conversion efficiency, with the number of thermo couplesm and the respectively changes, using process control variable method, that is, when the number of thermo L a constant and vice re 6 shows the relationships between the outlet temperatures and the wall temperatures of intake and cooling air vs. the number of thermocouples, the As can be seen, as m increases, the outlet temperature of the intake air T 1out gradually decrease, the outlet temperature of the cooling air T 2out and the wall gradually increases, the heat transfer is strengthened and the cooling effect of the intercooler is curve decreases rapidly before Fig. 7: The relationships between the output power and the thermal convection efficiency vs. the number of thermocouples Fig. 8: The relationships between the temperatures of intake air vs. the number of thermocouples at different fixed load values Fig. 9: The relationships between the outlet temperature and the wall temperature vs. the value of external load m equals 500, because the temperature difference between the intake air and cooling air passage channel is bigger, the performance of thermoelectric generator is working on an ideal condition; the curve becomes f after m equals 1000 because the intake and cooling air passage channel wall temperature difference is relatively small, continuing to increase m has little effect on the heat exchanger.
Figure 7 shows the relationships between the output power and the thermal convection efficiency vs.
The relationships between the output power and the efficiency vs. the number of temperatures of intake air vs. the number of thermocouples at different fixed The relationships between the outlet temperature and temperature vs. the value of external load m equals 500, because the temperature difference between the intake air and cooling air passage channel is bigger, the performance of thermoelectric generator curve becomes flat after m equals 1000 because the intake and cooling air passage channel wall temperature difference is relatively small, continuing to increase m has little Figure 7 shows the relationships between the l convection efficiency vs.
Fig. 10: The relationships between the output power and the thermal convection efficiency vs. the value of external load the number of thermocouples, setting the external load R L = 2Ω.As can be seen, the output power and the thermal conversion efficiency curves increase rapidly as m increases, reach the maximum value, respectively 497W and 1.78%; after the maximum points, as increases, the cooling effect is enhanced and the intake and cooling air passage channels' difference is reduced, the output power and the thermal conversion efficiency are decreasing Figure 8 shows the relationships between the temperatures of intake air vs. the number of thermocouples at different fixed load values.With the number of the thermocouples increases, outlet temperatures of intake air for three different fixed load values decrease.Larger the load, smaller the power consumption and smaller the heat exchange from the intake air to the cooling air, the worse effect of heat transfer, the outlet temperature is relatively higher As shown in Fig. 7, in the case of thermoelectric generator load unchanged, there respectively exist corresponding numbers of thermocouples, so that the output power and the thermal conversion efficiency reach maximum values.Meanwhile, the outlet temperature of intake air is too high to meet the cooling requirements of the diesel engine cooler, it should choose a slightly bigger number of thermocouples than the output power and thermal conversion efficiency's optimal points, in order to take the energy recycling and intercooler cooling effect of the turbocharger airflow into account.
Figure 9 and 10 respectively gives when 500, the relationships between the four temperatures shown in Fig. 6 and the corresponding output power and the thermal conversion efficiency vs. the value of external load.As can be seen from Fig. 9, increases, the outlet temperature of increases, while the outlet temperature of the cooling air decreases, load values increase reduces the output power of the load, but each of the temperature changing width is only 2~3K, indicating very limited impact, so the size of the load can be chosen more flexibility The relationships between the output power and the thermal convection efficiency vs. the value of setting the external load As can be seen, the output power and the thermal conversion efficiency curves increase rapidly as m increases, reach the maximum value, respectively and 1.78%; after the maximum points, as m increases, the cooling effect is enhanced and the intake d cooling air passage channels' temperature difference is reduced, the output power and the thermal conversion efficiency are decreasing.
Figure 8 shows the relationships between the temperatures of intake air vs. the number of ixed load values.With the number of the thermocouples increases, outlet temperatures of intake air for three different fixed load values decrease.Larger the load, smaller the power consumption and smaller the heat exchange from the ing air, the worse effect of heat transfer, the outlet temperature is relatively higher.
As shown in Fig. 7, in the case of thermoelectric generator load unchanged, there respectively exist corresponding numbers of thermocouples, so that the nd the thermal conversion efficiency reach maximum values.Meanwhile, the outlet temperature of intake air is too high to meet the cooling requirements of the diesel engine cooler, it should choose a slightly bigger number of thermocouples than power and thermal conversion efficiency's optimal points, in order to take the energy recycling and intercooler cooling effect of the turbocharger airflow Figure 9 and 10 respectively gives when m equals 500, the relationships between the four temperatures shown in Fig. 6 and the corresponding output power and the thermal conversion efficiency vs. the value of external load.As can be seen from Fig. 9, when load , the outlet temperature of the intake air increases, while the outlet temperature of the cooling increase reduces the output power of the load, but each of the temperature changing indicating very limited impact, so can be chosen more flexibility Fig. 11: The relationships between the output power vs. the number of thermocouples at different load values and the optimal load value Fig. 12: The relationships between the thermal convection efficiency vs. the number of thermocouples at different load values and the optimal load value according to the actual situation.Figure 10 shows the output power and thermal convection efficiency similar with Fig. 7, there are still respectively optimal the value of the load has a great impact on the output power and the thermal conversion efficiency Optimization of intercooler thermoelectric generation elements model: According to the thermoelectric theory (Gao and Rowe, power obtained by the external load is: When the total internal resistance R equals to the external load R L , that is, R L /R = 1, the load can obtain the maximum output power from the elements, its value is: In some practical applications, achieving maximum output power in order to get the best The relationships between the output power vs. the number of thermocouples at different load values and The relationships between the thermal convection vs. the number of thermocouples at different load values and the optimal load value according to the actual situation.Figure 10 shows the output power and thermal convection efficiency similar with Fig. 7, there are still respectively optimal R L value, the value of the load has a great impact on the output power and the thermal conversion efficiency.

Optimization of intercooler thermoelectric power
According to the 1996), the output (11) When the total internal resistance R equals to the /R = 1, the load can obtain the maximum output power from the thermoelectric (12) In some practical applications, achieving the in order to get the best performance of electrical appliances is often With the number of thermocouples changes in the analysis of Fig. 7, the single thermocouple has the same electrical properties and the internal resistance is also unchanged, but due to total internal resistance of the thermoelectric element is equal to a single thermocouple internal resistance multiplied by the number of thermocouples, thermoelectric elements total internal resistance R will also changes.Thermoelectric generators can't always guarantee operating at its maximum output power regardless of any constant load value.So in numerical simulation, optimize the load value for the thermoelectric generation elements model.With the change of m, setting load R L is always equal to the thermoelectric elements' total internal resistance R, it can reach the maximum output power P corresponding m. Figure 11 shows comparison between the output power respectively corresponds to load 0.2Ω, 2Ω, 20Ω and the output power after optimization of the load, P B , As can be seen, P B curve entirely locat above the curve of the output power on three different fixed load values and the adaptation range is wider.The peak of output power curve researches 598W, increased by 20.3% compared with the peak of the power curve in Fig. 7.
Figure 12 shows comparisons between the thermal conversion efficiency respectively corresponds to load 0.2Ω, 2Ω, 20Ω and the thermal conversion efficiency after optimization of the load, η B .As can be seen, η curve also entirely locates above the curve of the thermal conversion efficiency on three different fixed load values, η B curve peak rises from 1.78 compares with Fig. 7.

CONCLUSION
• When thermoelectric generator' doesn't change, the outlet temperature of the intake air decreases with the number of thermocouples increases, indicating that the heat exchanger between the intake air passage channels cooling air passage channels is strengthening • When the number thermocouples i value of thermoelectric generator external load's change has little effect on the outlet temperature of cooling air, changing width is only about 2~3K • After thermoelectric generator load optimization, thermoelectric power generation elemen the best working conditions, the output power increases by 20.3% compared with previous simulations, thermal conversion increases from 1.78 to 3.48%.

ACKNOWLEDGMENT
This study was supported in part by the Aviation Fund of China (2011ZA51). of electrical appliances is often required.With the number of thermocouples changes in the analysis of Fig. 7, the single thermocouple has the same electrical properties and the internal resistance is also unchanged, but due to total internal resistance of the ual to a single thermocouple internal resistance multiplied by the number of thermocouples, thermoelectric elements total internal resistance R will also changes.Thermoelectric generators can't always guarantee operating at its less of any constant load So in numerical simulation, optimize the load value for the thermoelectric generation elements model.With is always equal to the thermoelectric elements' total internal resistance R, it reach the maximum output power P max on any corresponding m. Figure 11 shows comparison between the output power respectively corresponds to load 0.2Ω, 20Ω and the output power after optimization of the curve entirely locates above the curve of the output power on three different and the adaptation range is wider.The peak of output power curve researches 598W, increased by 20.3% compared with the peak of the power curve in sons between the thermal conversion efficiency respectively corresponds to load 20Ω and the thermal conversion efficiency .As can be seen, η B curve also entirely locates above the curve of the thermal conversion efficiency on three different fixed curve peak rises from 1.78 to 3.48%

CONCLUSION
When thermoelectric generator's external load outlet temperature of the intake air decreases with the number of thermocouples increases, indicating that the heat exchanger between the intake air passage channels and the is strengthening.When the number thermocouples is constant, the value of thermoelectric generator external load's change has little effect on the outlet temperature of cooling air, changing width is only about 2~3K.After thermoelectric generator load optimization, thermoelectric power generation elements achieve the best working conditions, the output power increases by 20.3% compared with previous simulations, thermal conversion efficiency

ACKNOWLEDGMENT
This study was supported in part by the Aviation

Fig. 1 :
Fig. 1: Schematic diagram of tube-fin intercooler design applications provide a scientific basis for the new thermoelectric generator based on the intercooler.

Fig. 2 :
Fig. 2: Schematic diagram of the array of thermoelectric couples in , T out ) : The convective heat transfer coefficient, if the airflow passage size and mass flow are fixed, it depends on the inlet and outlet temperature of air T bm : The average temperature of the gas stream T bm = (T out -T in ) /2, T w : The wall temperature A : The effective area of the heat exchanger Convective heat transfer coefficient can be calculated as follows (Chen and Wu, 2000Nusselt number of the gas stream λ = The airflow rate of the thermal conductivity D = The equivalent diameter of the airflow channe is proposed by Dittus and apply to wall temperature turbulent convective heat transfer, the Reynolds number Re number Pr are groups of parameters of the thermal conductivity λ, thermal diffusivity physical parameters are functions of temperature, so determining the Reynolds number and Prandtl number, it must give the characteristic temperature, subscript represents the average temperature of the fluid inlet characteristic temperature; (6) is the convective heat transfer formula proposed by Sieder 2001) suitable for wall temperature laminar convective heat transfer, L represents the pipe length, respectively represent the coefficient of dynamic viscosity of the fluid at a characteristic temperature and the wall temperature; ρ C represents the air density, are seebeck coefficients of P and semiconductor material cooling air passage channel, there exists convective heat transfer.When the fluid flows through the wall, according to the theory of heat coefficient, if the airflow passage size and mass flow are fixed, and outlet temperature e temperature of the gas stream wall temperature tive area of the heat exchanger Convective heat transfer coefficient can be calculated