- Email: [email protected]
An applied thermodynamic method for correction of TDC in the indicator diagram and its experimental confirmation
Applied Thermal Engineering 25 (2005) 759–768 www.elsevier.com/locate/apthermeng
An applied thermodynamic method for correction of TDC in the indicator diagram and its experimental confirmation Hanbao Chang
a,b
, Yusheng Zhang b, Lingen Chen
a,*
a
b
Faculty 306, Naval University of Engineering, Wuhan 430033, PR China College of Energy & Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Received 17 March 2004; accepted 30 July 2004 Available online 25 September 2004
Abstract A thermodynamic method of top dead center (TDC) correction in the indicator diagram of the Diesel engines is studied in this paper. The method is based on the corresponding relationship between the curve for the heat released and the computed polytropic exponent. The experiments show that this method can make the real-time correction of TDC for the Diesel engines. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Diesel engine; TDC; Heat release rate
1. Introduction Among the factors that influence the indicator diagram of work, the top dead center (TDC) position error is of great important for the calculation accuracy of the heat released rate. It can bring calculation error of the instantaneous volume V and the volumetric change dV, which remarkably influences the shape of the curve for the heat release rate, especially that around TDC. As shown in the related data [1], the deviation of 1° Crank angle (CA) of TDC position could
*
Corresponding address. Tel.: +86 27 83615046; fax: +86 27 83638709. E-mail addresses: [email protected], [email protected] (L. Chen).
1359-4311/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.07.016
760
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
Nomenclature C K N P q Qb TDC u V w Greek g U X D
a constant adiabatic exponent polytropic exponent pressure (kPa) heat quantity absorbed by working fluid in polytropic process (kJ) heat release quantity of the combustion process (kJ) top dead center internal energy (kJ) volume (m3) process work output (kJ) symbols utilization ratio crank angle (°) angular velocity (rad/s) indicates a change of value
result in the maximum errors of heat released accumulation about 10%, peak value of heat released rate from 5% to 10%, and indicated pressure from 5% to 8%. Much effort has been made on the TDC correction. There are several methods used by the data acquisition system to determine TDC position, including the TDC sensor method, microwave sensor method, and photoelectric sensor method, etc. [2–5]. As these methods all need the indicator diagram of pure compression work of the Diesel engine, it would be difficult to correct TDC when the indicator diagram is hard to be obtained. Even if the diagram is available, the existing error in experimental results would deteriorate the correction effect. Therefore, it is necessary to make study on the method of TDC correction based on the indicator diagram of work that is obtained when the Diesel engine combusts regularly.
2. Method of dynamic TDC correction under the combustion condition The correction in the case of pure compression is made based on the assumption that the whole process is adiabatic. As the fuel oil combusts, there exists bulky energy exchange throughout the process, so the above-mentioned assumption could not be met. The problems arise in TDC correction in the case of pure compression, and other methods should be studied. 2.1. Thermodynamic analysis for the working process of diesel engine It is known from the thermodynamic theory that the polytropic exponent n is dependent upon the variation of heat quantity of working medium in cylinder [6–8]. The relationship between the
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
761
Fig. 1. The change of the polytropic exponent.
polytropic exponent n, the heat transfer quantity q, the pressure P and volume V is shown in Fig. 1. The polytropic exponent can be used to reflect the adiabatic process, isothermal process, and the isochoric process in practice. From the first law of thermodynamics, one has q Du w ¼ 0;
ð1Þ
where q is the heat quantity absorbed by working fluid in the polytropic process, Du is the variation of internal energy, and w is the process work output. Substituting Du and w into Eq. (1) yields w k1 ¼ ; q kn
ð2Þ
where k is the ratio of specific heats, and k > 1. So, k 1 > 0 and the plus or minus sign of the ratio w/q depends on the exponent n. Four p–V curves denoting different processes are illustrated in Fig. 1. Theoretically, the polytropic exponent n ranges from 1 to +1. Eq. (2) shows that pressure would rise in the expansion process and drop in the compression process when exponent n ranges from 1 to 0, which is scare in reality. Yet, that kind of process really exists during the combustion process of Diesel engine (between the TDC and the maximum pressure position). Thus, the polytropic exponent can effectively reflect the characteristics of the process. The compression process is complex, and it relates to a series of factors. In the compression stroke, w < 0 holds [9]. In the initial stage of the compression, the medium temperature is less than that of the cylinder wall and the top of the piston, and the medium is heated. Eq. (2) shows n > k. The medium temperature rises with the pressure increase, and the medium get relatively less heat compared with the initial stage of the compression. When the medium temperature is equal to that of the cylinder wall, there is no energy exchange between the medium and the cylinder wall (point r in Fig. 2). The instantaneous adiabatic process appears, and n = k holds. The compression goes on, and the medium temperature would be higher than that of the cylinder wall. At that time, heat is transferred from the medium to the cylinder wall, and q < 0 holds. Eq. (2) shows n < k. This stage would continue until the combustion begins.
762
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
Fig. 2. Polytropic exponent versus the volume of cylinder in compression condition.
The expansion of combustion outcome exists in the process that piston moves from TDC to BDC. Because there exists the varying temperature contrast at any time between the gas with high temperature and the cylinder wall, bulky heat exchanges between them. It is different from the compression process that heat transfers from the gas to cylinder throughout the expansion process, then q < 0. It is also an expansion process, hence w > 0 holds. The expansion process begins from the TDC. Around the TDC, the process can be regarded as isochoric, and the heat exchange rate is less than zero. So, the polytropic exponent trends to 1 (i.e. n ! 1). When the combustion continues violently and the heat exchange rate increases, the absolute value of the polytropic exponent would be lower (see Fig. 3). The maximum pressure point is called instantaneous constant pressure point, and here n = 0. The heat release continues
Fig. 3. Polytropic exponent versus the volume of cylinder in expansion condition.
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
763
and the temperature approaches its maximum, which can be taken as a constant temperature process, and here n = 1. The afterward compression accompanies with the heat release and heat transfer. The quantity of the released heat is more than that of the absorbed heat before the thermal equilibrium point, and here n < k. As the blast gate is open at that time, it is no need to analyze further. It can be seen from the above analysis that the curve for the heat release rate, which is important to evaluate the combustion process, can illustrate the real process. And the curve for the heat release rate can be drawn with simplified methods. For the polytropic process pvn ¼ C;
ð3Þ
where C is a constant. From Eq. (2), one has n¼k
k 1 dq : p dV
ð4Þ
According to Eq. (3) the polytropic exponent (n) can be expressed as n¼
dp=p : dV =V
ð5Þ
Rewriting Eq. (4) yields dQb p dV x ðk nÞ ; ¼ k1 d/ g d/
ð6Þ
where Qb is the heat release quantity of the combustion process; g is the utilization ratio of the heat quantity; x is the angular velocity of the crank; and k is the adiabatic exponent. Substituting Eq. (5) into Eq. (6) yields dQb 1 dV dp x kp þV : ð7Þ ¼ k1 d/ d/ g d/ For the characteristic points in the indicator diagram of work (see Fig. 4), equation (6) or (7) can be rewritten. c is the initial point of actual heat release, and here n = k. Then, Eq. (6) becomes dQb ¼ 0: d/ c is the TDC, and here
ð8Þ dV d/
¼ 0. Then, Eq. (7) becomes
dQb x dp V : ¼ gðk 1Þ d/ d/ z is the maximum pressure point, and here n = 0 or dQb pk x dV : ¼ k 1 g d/ d/
ð9Þ dp d/
¼ 0. Then, Eq. (7) becomes ð10Þ
764
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
Fig. 4. The relationship between the indicator diagram of work and the curve for heat release rate.
d is the maximum temperature point, and here n = 1. Then, Eq. (6) becomes dQb x dV : ¼p g d/ d/
ð11Þ
g is the final point of heat release, and here n = k. Then, Eq. (6) becomes dQb ¼ 0: d/
ð12Þ
Fig. 4 reflects the corresponding relationship between the indicator diagram of work and the curve for heat release rate. 2.2. Dynamic TDC correction using the heat release rate The polytropic exponent and the heat release rate could clearly illustrate the working process of the Diesel engine, and there is a corresponding relationship between them. Eq. (6) shows that the heat release rate is zero in the c point and here n = k. From the above analysis, one also can know that there must be an adiabatic point where n = k as the polytropic exponent varies from the value less than k to one greater than k. Some assumptions are made as following based on the characteristics of the polytropic process and the working process in cylinder. (a) The whole combustion process is made up of several polytropic processes. Though the polytropic exponent n is constant in every polytropic process, it varies continuously in the whole combustion process. (b) The point where the heat release rate varies from negative value to positive value before TDC is the initial point of actual heat release.
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
765
Begin
Input the measured TDC position Φ0 and the indicator diagram of work
Compute the value of n by Eq. (6)
Compute the heat release rate by the established model
Define Φ 1 while n=k
Define Φ 2 while dQb=0
Φ 1=Φ2
No
Regulate Φ 0 using the step size
Yes Φ 1= Φ 2 = Φ0, define the TDC position
End
Fig. 5. The flow diagram of calculation for determining the TDC position.
According to the assumptions, the conditions for TDC correction in the regular combustion process are dQb ¼ 0; ð13Þ n¼k The TDC correction can be computed by using Eq. (13), and the flow diagram for calculation is shown in Fig. 5.
3. Experimental apparatus and results Using the methodology outlined above, the correction is computed for the type of 6-135ZC Diesel engine with different load and speed. The correction results are listed in Table 1. The value of polytropic exponent before and after correction is shown in Fig. 6. The heat release rate before and after correction is shown in Fig. 7. It can be seen from the figures that the polytropic exponent is just the adiabatic coefficient after TDC correction, assuming the heat release rate of the initial point of actual combustion is zero. To confirm this methodology, an experiment of fuel cut-off of single cylinder is performed at the speed of 1500 r/min. An experimental system has been set up to measure the indicator diagrams at different load and speed. A schematic view of the system is shown in Fig. 8. The TDC, rotational
766
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
Table 1 The TDC correction of different speed Load (kW) n (r/min)
30
40
50
60
70
80
100
1500 1400 1300 1200 1100 1000
2.7 0.5 2.08 2.88 4.4 4.8
2.5 0 2.08 2.88 0 4.8
2.7 0 2.34 3.12 4.4 4.8
2.25 0.5 2.08 2.88 4.8 4.6
2.9 0 2.34 2.88 4.4 4.6
2.7 0 2.08 3.12 4.4 4.8
2.7 0.5 2.34 2.88 4.4 4.2
Fig. 6. Comparison of n before and after TDC correction.
Fig. 7. Comparison of dQb before and after TDC correction.
speed and cylinder pressure signal were acquired by CRAS data acquisition processing system, a random and vibration signal processing system, via magnetic-electric sensor and piezoelectric
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
1
3 7
8
767
2
4 9
10 5
6
Fig. 8. Schematic of experimental system, 1—6-135ZC-type Diesel engine; 2—YS-1900 hydraulic dynamometer; 3— magnetic-electric sensor; 4—piezoelectric pressure sensor; 5—CRAS data acquisition processing system; 6—computer; 7—TDC signal; 8—rotational speed signal; 9—cylinder pressure signal; 10—torque signal.
Fig. 9. The value of n before and after correction under the condition of pure compression.
pressure sensor. The CRAS data acquisition processing system has the capability of simultaneously acquiring 16 channels of data, and itÕs sampling frequency is up to 51,200 Hz for every channel. The curves under the condition of pure compression are drawn, and the TDC is corrected by the method of polytropic exponent. The results are 6 samples (i.e. 2.7° crank angle for the sampling frequency of 20 KHz). Fig. 9 shows the rules of change for exponent n before and after the correction under the condition of pure compression. Obviously, two methods have the same correction results, which confirms the validity of the method studied in this paper.
4. Conclusions The method of TDC correction in this paper is based on the corresponding relationship between the curve for the heat release and the computed polytropic exponent at the adiabatic point
768
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
where the instantaneous heat release rate is zero before combustion begins. As only the pressure signal in cylinder and the speed are required and there is no need of the curve relative to pure compression, the method has the dynamic property.
References [1] J. Zhou, D. Qiu, M. Xie, Numerical Computation of the Working Process of the Diesel Engine, Dalian University of Technology Press, 1990 (in Chinese). [2] M.J. Stas, Thermodynamic determination of TDC in piston combustion engines, 1996, SAE 960610. [3] S. Shi, W. Shu, The thermodynamic methodology of error correction for the indicator diagram of work, Chinese J. Eng. Thermophy. 10 (1) (1989) 104–108 (in Chinese). [4] M. Morishita, T. Kushiyama, An improved method for determining the TDC position in a PV-diagram, 1997, SAE 970062. [5] M.J. Stas, A universally applicable thermodynamic model for TDC determination, 2000 SAE 2000-01-0561. [6] A. Bejan, Advanced Engineering Thermodynamics, second ed., Wiley, New York, 1997. [7] M.J. Moran, H.N. Shapiro, Fundamentals of Engineering Thermodynamics, fourth ed., Wiley, New York, 2000. [8] M. Feidt, Thermodynamique et Optimisation Energetique des Systems et Procedes, second ed., Technique et Documentation, Lavoisier, Paris, 1996 (in French). [9] Z. Li, The Computation and Working Process of Diesel Engine, Jilin PeopleÕs Publishing House, 1984 (in Chinese).
An applied thermodynamic method for correction of TDC in the indicator diagram and its experimental confirmation Hanbao Chang
a,b
, Yusheng Zhang b, Lingen Chen
a,*
a
b
Faculty 306, Naval University of Engineering, Wuhan 430033, PR China College of Energy & Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Received 17 March 2004; accepted 30 July 2004 Available online 25 September 2004
Abstract A thermodynamic method of top dead center (TDC) correction in the indicator diagram of the Diesel engines is studied in this paper. The method is based on the corresponding relationship between the curve for the heat released and the computed polytropic exponent. The experiments show that this method can make the real-time correction of TDC for the Diesel engines. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Diesel engine; TDC; Heat release rate
1. Introduction Among the factors that influence the indicator diagram of work, the top dead center (TDC) position error is of great important for the calculation accuracy of the heat released rate. It can bring calculation error of the instantaneous volume V and the volumetric change dV, which remarkably influences the shape of the curve for the heat release rate, especially that around TDC. As shown in the related data [1], the deviation of 1° Crank angle (CA) of TDC position could
*
Corresponding address. Tel.: +86 27 83615046; fax: +86 27 83638709. E-mail addresses: [email protected], [email protected] (L. Chen).
1359-4311/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.07.016
760
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
Nomenclature C K N P q Qb TDC u V w Greek g U X D
a constant adiabatic exponent polytropic exponent pressure (kPa) heat quantity absorbed by working fluid in polytropic process (kJ) heat release quantity of the combustion process (kJ) top dead center internal energy (kJ) volume (m3) process work output (kJ) symbols utilization ratio crank angle (°) angular velocity (rad/s) indicates a change of value
result in the maximum errors of heat released accumulation about 10%, peak value of heat released rate from 5% to 10%, and indicated pressure from 5% to 8%. Much effort has been made on the TDC correction. There are several methods used by the data acquisition system to determine TDC position, including the TDC sensor method, microwave sensor method, and photoelectric sensor method, etc. [2–5]. As these methods all need the indicator diagram of pure compression work of the Diesel engine, it would be difficult to correct TDC when the indicator diagram is hard to be obtained. Even if the diagram is available, the existing error in experimental results would deteriorate the correction effect. Therefore, it is necessary to make study on the method of TDC correction based on the indicator diagram of work that is obtained when the Diesel engine combusts regularly.
2. Method of dynamic TDC correction under the combustion condition The correction in the case of pure compression is made based on the assumption that the whole process is adiabatic. As the fuel oil combusts, there exists bulky energy exchange throughout the process, so the above-mentioned assumption could not be met. The problems arise in TDC correction in the case of pure compression, and other methods should be studied. 2.1. Thermodynamic analysis for the working process of diesel engine It is known from the thermodynamic theory that the polytropic exponent n is dependent upon the variation of heat quantity of working medium in cylinder [6–8]. The relationship between the
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
761
Fig. 1. The change of the polytropic exponent.
polytropic exponent n, the heat transfer quantity q, the pressure P and volume V is shown in Fig. 1. The polytropic exponent can be used to reflect the adiabatic process, isothermal process, and the isochoric process in practice. From the first law of thermodynamics, one has q Du w ¼ 0;
ð1Þ
where q is the heat quantity absorbed by working fluid in the polytropic process, Du is the variation of internal energy, and w is the process work output. Substituting Du and w into Eq. (1) yields w k1 ¼ ; q kn
ð2Þ
where k is the ratio of specific heats, and k > 1. So, k 1 > 0 and the plus or minus sign of the ratio w/q depends on the exponent n. Four p–V curves denoting different processes are illustrated in Fig. 1. Theoretically, the polytropic exponent n ranges from 1 to +1. Eq. (2) shows that pressure would rise in the expansion process and drop in the compression process when exponent n ranges from 1 to 0, which is scare in reality. Yet, that kind of process really exists during the combustion process of Diesel engine (between the TDC and the maximum pressure position). Thus, the polytropic exponent can effectively reflect the characteristics of the process. The compression process is complex, and it relates to a series of factors. In the compression stroke, w < 0 holds [9]. In the initial stage of the compression, the medium temperature is less than that of the cylinder wall and the top of the piston, and the medium is heated. Eq. (2) shows n > k. The medium temperature rises with the pressure increase, and the medium get relatively less heat compared with the initial stage of the compression. When the medium temperature is equal to that of the cylinder wall, there is no energy exchange between the medium and the cylinder wall (point r in Fig. 2). The instantaneous adiabatic process appears, and n = k holds. The compression goes on, and the medium temperature would be higher than that of the cylinder wall. At that time, heat is transferred from the medium to the cylinder wall, and q < 0 holds. Eq. (2) shows n < k. This stage would continue until the combustion begins.
762
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
Fig. 2. Polytropic exponent versus the volume of cylinder in compression condition.
The expansion of combustion outcome exists in the process that piston moves from TDC to BDC. Because there exists the varying temperature contrast at any time between the gas with high temperature and the cylinder wall, bulky heat exchanges between them. It is different from the compression process that heat transfers from the gas to cylinder throughout the expansion process, then q < 0. It is also an expansion process, hence w > 0 holds. The expansion process begins from the TDC. Around the TDC, the process can be regarded as isochoric, and the heat exchange rate is less than zero. So, the polytropic exponent trends to 1 (i.e. n ! 1). When the combustion continues violently and the heat exchange rate increases, the absolute value of the polytropic exponent would be lower (see Fig. 3). The maximum pressure point is called instantaneous constant pressure point, and here n = 0. The heat release continues
Fig. 3. Polytropic exponent versus the volume of cylinder in expansion condition.
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
763
and the temperature approaches its maximum, which can be taken as a constant temperature process, and here n = 1. The afterward compression accompanies with the heat release and heat transfer. The quantity of the released heat is more than that of the absorbed heat before the thermal equilibrium point, and here n < k. As the blast gate is open at that time, it is no need to analyze further. It can be seen from the above analysis that the curve for the heat release rate, which is important to evaluate the combustion process, can illustrate the real process. And the curve for the heat release rate can be drawn with simplified methods. For the polytropic process pvn ¼ C;
ð3Þ
where C is a constant. From Eq. (2), one has n¼k
k 1 dq : p dV
ð4Þ
According to Eq. (3) the polytropic exponent (n) can be expressed as n¼
dp=p : dV =V
ð5Þ
Rewriting Eq. (4) yields dQb p dV x ðk nÞ ; ¼ k1 d/ g d/
ð6Þ
where Qb is the heat release quantity of the combustion process; g is the utilization ratio of the heat quantity; x is the angular velocity of the crank; and k is the adiabatic exponent. Substituting Eq. (5) into Eq. (6) yields dQb 1 dV dp x kp þV : ð7Þ ¼ k1 d/ d/ g d/ For the characteristic points in the indicator diagram of work (see Fig. 4), equation (6) or (7) can be rewritten. c is the initial point of actual heat release, and here n = k. Then, Eq. (6) becomes dQb ¼ 0: d/ c is the TDC, and here
ð8Þ dV d/
¼ 0. Then, Eq. (7) becomes
dQb x dp V : ¼ gðk 1Þ d/ d/ z is the maximum pressure point, and here n = 0 or dQb pk x dV : ¼ k 1 g d/ d/
ð9Þ dp d/
¼ 0. Then, Eq. (7) becomes ð10Þ
764
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
Fig. 4. The relationship between the indicator diagram of work and the curve for heat release rate.
d is the maximum temperature point, and here n = 1. Then, Eq. (6) becomes dQb x dV : ¼p g d/ d/
ð11Þ
g is the final point of heat release, and here n = k. Then, Eq. (6) becomes dQb ¼ 0: d/
ð12Þ
Fig. 4 reflects the corresponding relationship between the indicator diagram of work and the curve for heat release rate. 2.2. Dynamic TDC correction using the heat release rate The polytropic exponent and the heat release rate could clearly illustrate the working process of the Diesel engine, and there is a corresponding relationship between them. Eq. (6) shows that the heat release rate is zero in the c point and here n = k. From the above analysis, one also can know that there must be an adiabatic point where n = k as the polytropic exponent varies from the value less than k to one greater than k. Some assumptions are made as following based on the characteristics of the polytropic process and the working process in cylinder. (a) The whole combustion process is made up of several polytropic processes. Though the polytropic exponent n is constant in every polytropic process, it varies continuously in the whole combustion process. (b) The point where the heat release rate varies from negative value to positive value before TDC is the initial point of actual heat release.
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
765
Begin
Input the measured TDC position Φ0 and the indicator diagram of work
Compute the value of n by Eq. (6)
Compute the heat release rate by the established model
Define Φ 1 while n=k
Define Φ 2 while dQb=0
Φ 1=Φ2
No
Regulate Φ 0 using the step size
Yes Φ 1= Φ 2 = Φ0, define the TDC position
End
Fig. 5. The flow diagram of calculation for determining the TDC position.
According to the assumptions, the conditions for TDC correction in the regular combustion process are dQb ¼ 0; ð13Þ n¼k The TDC correction can be computed by using Eq. (13), and the flow diagram for calculation is shown in Fig. 5.
3. Experimental apparatus and results Using the methodology outlined above, the correction is computed for the type of 6-135ZC Diesel engine with different load and speed. The correction results are listed in Table 1. The value of polytropic exponent before and after correction is shown in Fig. 6. The heat release rate before and after correction is shown in Fig. 7. It can be seen from the figures that the polytropic exponent is just the adiabatic coefficient after TDC correction, assuming the heat release rate of the initial point of actual combustion is zero. To confirm this methodology, an experiment of fuel cut-off of single cylinder is performed at the speed of 1500 r/min. An experimental system has been set up to measure the indicator diagrams at different load and speed. A schematic view of the system is shown in Fig. 8. The TDC, rotational
766
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
Table 1 The TDC correction of different speed Load (kW) n (r/min)
30
40
50
60
70
80
100
1500 1400 1300 1200 1100 1000
2.7 0.5 2.08 2.88 4.4 4.8
2.5 0 2.08 2.88 0 4.8
2.7 0 2.34 3.12 4.4 4.8
2.25 0.5 2.08 2.88 4.8 4.6
2.9 0 2.34 2.88 4.4 4.6
2.7 0 2.08 3.12 4.4 4.8
2.7 0.5 2.34 2.88 4.4 4.2
Fig. 6. Comparison of n before and after TDC correction.
Fig. 7. Comparison of dQb before and after TDC correction.
speed and cylinder pressure signal were acquired by CRAS data acquisition processing system, a random and vibration signal processing system, via magnetic-electric sensor and piezoelectric
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
1
3 7
8
767
2
4 9
10 5
6
Fig. 8. Schematic of experimental system, 1—6-135ZC-type Diesel engine; 2—YS-1900 hydraulic dynamometer; 3— magnetic-electric sensor; 4—piezoelectric pressure sensor; 5—CRAS data acquisition processing system; 6—computer; 7—TDC signal; 8—rotational speed signal; 9—cylinder pressure signal; 10—torque signal.
Fig. 9. The value of n before and after correction under the condition of pure compression.
pressure sensor. The CRAS data acquisition processing system has the capability of simultaneously acquiring 16 channels of data, and itÕs sampling frequency is up to 51,200 Hz for every channel. The curves under the condition of pure compression are drawn, and the TDC is corrected by the method of polytropic exponent. The results are 6 samples (i.e. 2.7° crank angle for the sampling frequency of 20 KHz). Fig. 9 shows the rules of change for exponent n before and after the correction under the condition of pure compression. Obviously, two methods have the same correction results, which confirms the validity of the method studied in this paper.
4. Conclusions The method of TDC correction in this paper is based on the corresponding relationship between the curve for the heat release and the computed polytropic exponent at the adiabatic point
768
H. Chang et al. / Applied Thermal Engineering 25 (2005) 759–768
where the instantaneous heat release rate is zero before combustion begins. As only the pressure signal in cylinder and the speed are required and there is no need of the curve relative to pure compression, the method has the dynamic property.
References [1] J. Zhou, D. Qiu, M. Xie, Numerical Computation of the Working Process of the Diesel Engine, Dalian University of Technology Press, 1990 (in Chinese). [2] M.J. Stas, Thermodynamic determination of TDC in piston combustion engines, 1996, SAE 960610. [3] S. Shi, W. Shu, The thermodynamic methodology of error correction for the indicator diagram of work, Chinese J. Eng. Thermophy. 10 (1) (1989) 104–108 (in Chinese). [4] M. Morishita, T. Kushiyama, An improved method for determining the TDC position in a PV-diagram, 1997, SAE 970062. [5] M.J. Stas, A universally applicable thermodynamic model for TDC determination, 2000 SAE 2000-01-0561. [6] A. Bejan, Advanced Engineering Thermodynamics, second ed., Wiley, New York, 1997. [7] M.J. Moran, H.N. Shapiro, Fundamentals of Engineering Thermodynamics, fourth ed., Wiley, New York, 2000. [8] M. Feidt, Thermodynamique et Optimisation Energetique des Systems et Procedes, second ed., Technique et Documentation, Lavoisier, Paris, 1996 (in French). [9] Z. Li, The Computation and Working Process of Diesel Engine, Jilin PeopleÕs Publishing House, 1984 (in Chinese).