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CN112304623B - Effective thermal efficiency prediction method of marine diesel engine based on fuel components - Google Patents

Effective thermal efficiency prediction method of marine diesel engine based on fuel components Download PDF

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CN112304623B
CN112304623B CN202011170193.7A CN202011170193A CN112304623B CN 112304623 B CN112304623 B CN 112304623B CN 202011170193 A CN202011170193 A CN 202011170193A CN 112304623 B CN112304623 B CN 112304623B
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刘龙
唐元亨
梅齐昊
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Harbin Engineering University
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Abstract

本发明的目的在于提供一种船用柴油机基于燃料组分的有效热效率预测方法，包括如下步骤：确定边界条件与初始条件，选择燃用的燃料种类，将缸内工作过程分为压缩、燃烧、膨胀三个阶段，对压缩过程、燃烧过程、膨胀过程进行计算，对得到的压力进行积分计算，求出工作过程的有效功，再根据有效功与总投入热量的比值求出有效热效率。本发明可实现任意定容燃烧比的有效热效率预测，使得模型应用范围不局限于特定型号柴油机。本发明可实现对柴油机燃用不同种类燃料时的有效热效率预测，适应了目前船用柴油机替代燃料的发展趋势，为更广范围的柴油机热效率优化设计提供了数值预测手段。

Figure 202011170193

The purpose of the present invention is to provide a method for predicting the effective thermal efficiency of a marine diesel engine based on fuel components, comprising the steps of: determining boundary conditions and initial conditions, selecting the type of fuel to be used, and dividing the in-cylinder working process into compression, combustion, and expansion. In three stages, the compression process, combustion process, and expansion process are calculated, and the obtained pressure is integrated to calculate the effective work of the working process, and then the effective thermal efficiency is calculated according to the ratio of the effective work to the total input heat. The invention can realize the effective thermal efficiency prediction of any constant volume combustion ratio, so that the model application range is not limited to a specific type of diesel engine. The invention can realize the effective thermal efficiency prediction when the diesel engine burns different kinds of fuel, adapts to the current development trend of marine diesel engine substitute fuel, and provides numerical prediction means for a wider range of diesel engine thermal efficiency optimization design.

Figure 202011170193

Description

一种船用柴油机基于燃料组分的有效热效率预测方法A method for predicting effective thermal efficiency of marine diesel engine based on fuel composition

技术领域technical field

本发明涉及的是一种热效率预测方法，具体地说是船用柴油机热效率预测方法。The invention relates to a thermal efficiency prediction method, in particular to a thermal efficiency prediction method of a marine diesel engine.

背景技术Background technique

随着社会上节能减排呼声日益提高，针对航运业的各种排放法规不断提出，对船用柴油机各类排放物的管控提出了要求。众多排放物中，二氧化碳作为温室气体的一种，近年来更是受到严格限制。With the increasing calls for energy conservation and emission reduction in the society, various emission regulations for the shipping industry have been continuously proposed, and requirements for the management and control of various types of emissions from marine diesel engines have been put forward. Among the many emissions, carbon dioxide, one of the greenhouse gases, has been severely restricted in recent years.

柴油机有效热效率直接影响二氧化碳排放的高低，高热效率柴油机不仅能满足二氧化碳排放法规限制要求，还能实现良好的动力性能，提高经济性。而针对有效热效率优化的实验研究往往需要高精度的测量设备与复杂的燃烧模拟装置，成本高，周期长，因此采用计算软件预测柴油机有效热效率具有重要意义。The effective thermal efficiency of a diesel engine directly affects the level of carbon dioxide emissions. High thermal efficiency diesel engines can not only meet the regulatory requirements of carbon dioxide emissions, but also achieve good power performance and improve economy. However, the experimental research on the optimization of effective thermal efficiency often requires high-precision measurement equipment and complex combustion simulation devices, which are costly and long-term. Therefore, it is of great significance to use calculation software to predict the effective thermal efficiency of diesel engines.

目前有效热效率的仿真预测主要分为有限时间热力学推导与零维模型仿真两大类。有限时间热力学推导计算方法复杂，且结果理论性太强，实际参考性较弱。而现有的零维模型主要运用韦伯公式或双韦伯公式等半经验公式对燃烧过程进行仿真，该类模型在燃烧可调性上弱，难以针对不同的柴油机型号进行普遍的有效热效率预测。此外，现有零维模型大多仅考虑柴油作为燃料进行燃烧的情况，难以适应现有的柴油机替代燃料发展趋势。At present, the simulation prediction of effective thermal efficiency is mainly divided into two categories: finite-time thermodynamic derivation and zero-dimensional model simulation. The finite-time thermodynamic derivation calculation method is complicated, and the results are too theoretical and weak in practice. However, the existing zero-dimensional models mainly use semi-empirical formulas such as Weber formula or double Weber formula to simulate the combustion process. Such models are weak in combustion adjustability, and it is difficult to predict the general effective thermal efficiency for different diesel engine models. In addition, most of the existing zero-dimensional models only consider the combustion of diesel as fuel, which is difficult to adapt to the current development trend of alternative fuels for diesel engines.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于提供用定容燃烧与定压燃烧比值替代放热率公式，通过燃料成分计算工质比热容与比热容比的一种船用柴油机基于燃料组分的有效热效率预测方法。The purpose of the present invention is to provide a fuel composition-based effective thermal efficiency prediction method for marine diesel engines, which replaces the heat release rate formula with the ratio of constant volume combustion and constant pressure combustion, and calculates the ratio of specific heat capacity and specific heat capacity of working medium by fuel composition.

本发明的目的是这样实现的：The object of the present invention is achieved in this way:

本发明一种船用柴油机基于燃料组分的有效热效率预测方法，其特征是：A method for predicting the effective thermal efficiency of a marine diesel engine based on fuel components of the present invention is characterized in that:

(1)根据柴油机几何参数与初始参数确定边界条件与初始条件，并给定燃烧过程定容燃烧比X，定容燃烧比例是定容燃烧投入热量Qcv与燃烧过程总投入热量Qtotal之比：

Figure BDA0002747064810000011
(1) Determine the boundary conditions and initial conditions according to the geometric parameters and initial parameters of the diesel engine, and give the constant volume combustion ratio X in the combustion process. The constant volume combustion ratio is the ratio of the constant volume combustion input heat Q cv to the total input heat Q total in the combustion process :
Figure BDA0002747064810000011

其中定容燃烧比是实验测得的或根据预测需求人为设定的；The constant volume combustion ratio is measured experimentally or artificially set according to the predicted demand;

(2)选择燃用的燃料种类，根据选用的燃料组分按照如下化学方程式确定燃烧后工质组分：(2) Select the type of fuel to be used, and determine the working fluid composition after combustion according to the selected fuel composition according to the following chemical equation:

Figure BDA0002747064810000021
Figure BDA0002747064810000021

根据过量空气系数a以及为燃料碳分子数n、氢分子数m、氧分子数l，得出燃烧产物中CO2分子数n1、H2O分子数n2、N2分子数n3、O2分子数n4，由道尔顿分压定理，结合上式确定工作过程中工质的比热容；According to the excess air coefficient a, the number of carbon molecules n, the number of hydrogen molecules, and the number of oxygen molecules l in the fuel, the number of CO 2 molecules n 1 , the number of H 2 O molecules n 2 , the number of N 2 molecules n 3 , and the number of N 2 molecules in the combustion products are obtained. The number of O 2 molecules n 4 is determined by Dalton's partial pressure theorem and the above formula to determine the specific heat capacity of the working medium;

(3)将缸内工作过程分为压缩、燃烧、膨胀三个阶段，每个阶段又根据0.01°曲轴转角划分步长，对每个步长采用热力学第一定律，进行迭代求解；(3) The in-cylinder working process is divided into three stages of compression, combustion and expansion, and each stage is divided into steps according to the 0.01° crankshaft rotation angle, and the first law of thermodynamics is used for each step to iteratively solve;

(4)对压缩过程进行计算，根据压缩过程一个步长内的传热量

Figure BDA0002747064810000022
体积功
Figure BDA0002747064810000023
工质质量m、工质比热容cv1，通过热力学第一定律求出一个步长内的温度变化
Figure BDA0002747064810000024
(4) Calculate the compression process, according to the heat transfer in one step of the compression process
Figure BDA0002747064810000022
volume work
Figure BDA0002747064810000023
Working fluid mass m, working fluid specific heat capacity c v1 , the temperature change within a step is obtained through the first law of thermodynamics
Figure BDA0002747064810000024

Figure BDA0002747064810000025
Figure BDA0002747064810000025

根据初始条件的温度t1求解出第一个步长终点的温度t2，将t2作为下一步长的初始温度迭代计算，得到压缩过程各步长的温度，已知各步长温度，由理想气体状态方程pV＝RT得到相应各步长的压力；According to the temperature t 1 of the initial condition, the temperature t 2 of the end point of the first step is solved, and t 2 is iteratively calculated as the initial temperature of the next step, and the temperature of each step of the compression process is obtained. Knowing the temperature of each step, it can be calculated by The ideal gas equation of state pV=RT obtains the pressure of each step;

(5)对燃烧过程进行计算，根据燃烧过程一个步长内的传热量

Figure BDA0002747064810000026
体积功
Figure BDA0002747064810000027
工质质量m、工质比热容cv2，燃料燃烧投入热量gf(Hu-u),通过热力学第一定律求出一个步长内的温度变化
Figure BDA0002747064810000028
(5) Calculate the combustion process, according to the heat transfer in one step of the combustion process
Figure BDA0002747064810000026
volume work
Figure BDA0002747064810000027
Working medium mass m, working medium specific heat capacity c v2 , fuel combustion input heat g f (Hu-u), the temperature change within a step is obtained by the first law of thermodynamics
Figure BDA0002747064810000028

Figure BDA0002747064810000029
Figure BDA0002747064810000029

重复步骤(4)的温度迭代步骤，求解得出各步长的温度与压力；Repeat the temperature iteration step of step (4), and solve the temperature and pressure of each step;

(6)对膨胀过程进行计算，重复步骤(4)的计算过程，代入燃烧过程后的工质比热容cv3求解得出膨胀过程各步长的温度与压力；(6) Calculating the expansion process, repeating the calculation process of step (4), and substituting the working medium specific heat capacity c v3 after the combustion process to solve the temperature and pressure of each step of the expansion process;

(7)对步骤(4)、(5)、(6)得到的压力进行积分计算，求出工作过程的有效功W，再根据有效功W与总投入热量Qtotal的比值求出有效热效率：(7) Integrate the pressure obtained in steps (4), (5) and (6) to obtain the effective work W of the working process, and then calculate the effective thermal efficiency according to the ratio of the effective work W to the total input heat Q total :

Figure BDA00027470648100000210
Figure BDA00027470648100000210

本发明的优势在于：本发明以热力学第一定律为基础，依据输入的定容燃烧比作为燃烧规律，按照压缩、燃烧、膨胀的工作顺序，对初始状态的温度与压力按步长迭代求解，可实现任意定容燃烧比的有效热效率预测，使得模型应用范围不局限于特定型号柴油机。其次本发明根据预先给定的燃料组分参数，通过不同气体成分的道尔顿分压定理，计算缸内燃烧前后的工质的比热容与比热容比参数，反映不同燃料对柴油机工作过程的影响，可实现对柴油机燃用不同种类燃料时的有效热效率预测，适应了目前船用柴油机替代燃料的发展趋势，为更广范围的柴油机热效率优化设计提供了数值预测手段。The advantage of the present invention is that: the present invention is based on the first law of thermodynamics, according to the input constant volume combustion ratio as the combustion law, and according to the working sequence of compression, combustion and expansion, iteratively solves the temperature and pressure in the initial state according to the step size, The effective thermal efficiency prediction of any constant volume combustion ratio can be realized, so that the application scope of the model is not limited to a specific type of diesel engine. Secondly, the present invention calculates the specific heat capacity and the specific heat capacity ratio parameter of the working fluid before and after combustion in the cylinder according to the predetermined fuel component parameters and the Dalton partial pressure theorem of different gas components, and reflects the influence of different fuels on the working process of the diesel engine. It can realize the effective thermal efficiency prediction of diesel engines burning different types of fuels, adapt to the current development trend of marine diesel engine alternative fuels, and provide numerical prediction methods for a wider range of diesel engine thermal efficiency optimization designs.

附图说明Description of drawings

图1为本发明的流程图；Fig. 1 is the flow chart of the present invention;

图2是针对某型号柴油机的缸压计算结果与实验结果对比；Figure 2 is a comparison between the cylinder pressure calculation results and the experimental results for a certain type of diesel engine;

图3是某型号柴油机参数；Figure 3 is the parameters of a certain type of diesel engine;

图4是不同燃料的有效热效率预测结果；Fig. 4 is the effective thermal efficiency prediction result of different fuels;

图5是各燃料的理化参数。Figure 5 shows the physical and chemical parameters of each fuel.

具体实施方式Detailed ways

下面结合附图举例对本发明做更详细地描述：The present invention will be described in more detail below in conjunction with the accompanying drawings:

结合图1-5，针对现有的柴油机有效热效率预测方法过于复杂、不适用于不同型号柴油机燃烧、无法推广于多种类燃料燃烧等问题，本发明提出了基于任意燃料组分的有效热效率预测方法。1-5, in view of the problems that the existing diesel engine effective thermal efficiency prediction method is too complicated, not suitable for different types of diesel engine combustion, and cannot be extended to various types of fuel combustion, the present invention proposes an effective thermal efficiency prediction method based on arbitrary fuel components. .

本发明的目的通过以下步骤实现：The object of the present invention is achieved through the following steps:

步骤1，根据柴油机几何参数与初始参数确定边界条件与初始条件，并给定燃烧过程定容燃烧比X。定容燃烧比例是定容燃烧投入热量Qcv与燃烧过程总投入热量Qtotal之比：

Figure BDA0002747064810000031
Step 1: Determine the boundary conditions and initial conditions according to the geometric parameters and initial parameters of the diesel engine, and specify the constant volume combustion ratio X in the combustion process. The constant volume combustion ratio is the ratio of the constant volume combustion input heat Q cv to the total input heat Q total in the combustion process:
Figure BDA0002747064810000031

其中定容燃烧比可以是实验测得的，也可以根据预测需求人为设定。The constant volume combustion ratio can be measured experimentally, or can be set artificially according to the predicted demand.

步骤2，选择燃用的燃料种类，根据选用的燃料组分按照如下化学方程式确定燃烧后工质组分。Step 2, select the type of fuel to be used, and determine the working fluid composition after combustion according to the selected fuel composition according to the following chemical equation.

Figure BDA0002747064810000032
Figure BDA0002747064810000032

根据过量空气系数a以及为燃料碳分子数n、氢分子数m、氧分子数l，可以得出燃烧产物中CO2分子数n1、H2O分子数n2、N2分子数n3、O2分子数n4。由道尔顿分压定理，结合上式可以确定工作过程中工质的比热容。According to the excess air coefficient a, the number of carbon molecules n, the number of hydrogen molecules, and the number of oxygen molecules l, the number of CO 2 molecules n 1 , the number of H 2 O molecules n 2 , and the number of N 2 molecules n 3 in the combustion product can be obtained. , the number of O 2 molecules n 4 . According to Dalton's theorem of partial pressure, combined with the above formula, the specific heat capacity of the working fluid can be determined in the working process.

步骤3，将缸内工作过程分为压缩、燃烧、膨胀三个阶段，每个阶段又根据0.01°曲轴转角划分为更小步长，对每个步长采用热力学第一定律，进行迭代求解。Step 3: Divide the in-cylinder working process into three stages: compression, combustion, and expansion. Each stage is divided into smaller steps according to the 0.01° crankshaft angle, and the first law of thermodynamics is used for each step to iteratively solve.

步骤4，对压缩过程进行计算，根据压缩过程一个步长内的传热量

Figure BDA0002747064810000041
体积功
Figure BDA0002747064810000042
工质质量m,工质比热容cv1，通过热力学第一定律求出一个步长内的温度变化
Figure BDA0002747064810000043
Step 4: Calculate the compression process, according to the heat transfer in one step of the compression process
Figure BDA0002747064810000041
volume work
Figure BDA0002747064810000042
Working fluid mass m, working fluid specific heat capacity c v1 , the temperature change within a step is obtained through the first law of thermodynamics
Figure BDA0002747064810000043

Figure BDA0002747064810000044
Figure BDA0002747064810000044

根据初始条件的温度t1求解出第一个步长终点的温度t2，将t2作为下一步长的初始温度迭代计算，得到压缩过程各步长的温度。已知各步长温度，由理想气体状态方程pV＝RT可以得到相应各步长的压力。According to the temperature t 1 of the initial condition, the temperature t 2 of the end point of the first step is calculated, and t 2 is iteratively calculated as the initial temperature of the next step, and the temperature of each step of the compression process is obtained. Knowing the temperature of each step, the pressure of each step can be obtained from the ideal gas state equation pV=RT.

步骤5，对燃烧过程进行计算，根据燃烧过程一个步长内的传热量

Figure BDA0002747064810000045
体积功
Figure BDA0002747064810000046
工质质量m,工质比热容cv2，燃料燃烧投入热量gf(Hu-u),通过热力学第一定律求出一个步长内的温度变化
Figure BDA0002747064810000047
Step 5, calculate the combustion process, according to the heat transfer in one step of the combustion process
Figure BDA0002747064810000045
volume work
Figure BDA0002747064810000046
Working medium mass m, working medium specific heat capacity c v2 , fuel combustion input heat g f (Hu-u), the temperature change within a step is obtained by the first law of thermodynamics
Figure BDA0002747064810000047

Figure BDA0002747064810000048
Figure BDA0002747064810000048

重复步骤四的温度迭代步骤，求解得出各步长的温度与压力。Repeat the temperature iteration step of step 4, and solve the temperature and pressure of each step.

步骤6，对膨胀过程进行计算，重复步骤4的计算过程，代入燃烧过程后的工质比热容cv3求解得出膨胀过程各步长的温度与压力。Step 6: Calculate the expansion process, repeat the calculation process of Step 4, and substitute the specific heat capacity of the working fluid cv3 after the combustion process to obtain the temperature and pressure of each step of the expansion process.

步骤7，对步骤4、步骤5、步骤6得到的压力进行积分计算，求出工作过程的有效功W，再根据有效功W与总投入热量Qtotal的比值求出有效热效率。Step 7: Integrate the pressures obtained in steps 4, 5 and 6 to obtain the effective work W of the working process, and then calculate the effective thermal efficiency according to the ratio of the effective work W to the total input heat Q total .

Figure BDA0002747064810000049
Figure BDA0002747064810000049

本发明以热力学第一定律为基础，依据输入的定容燃烧比作为燃烧规律，按照压缩、燃烧、膨胀的工作顺序，对初始状态的温度与压力按步长迭代求解，可实现任意定容燃烧比的有效热效率预测，使得模型应用范围不局限于特定型号柴油机。其次本发明根据预先给定的燃料组分参数，通过不同气体成分的道尔顿分压定理，计算缸内燃烧前后的工质的比热容与比热容比参数，反映不同燃料对柴油机工作过程的影响，可实现对柴油机燃用不同种类燃料时的有效热效率预测，适应了目前船用柴油机替代燃料的发展趋势，为更广范围的柴油机热效率优化设计提供了数值预测手段。The invention is based on the first law of thermodynamics, according to the input constant volume combustion ratio as the combustion law, according to the working sequence of compression, combustion and expansion, iteratively solves the temperature and pressure in the initial state according to the step size, and can realize any constant volume combustion The effective thermal efficiency prediction of the ratio makes the application of the model not limited to a specific model of diesel engine. Secondly, the present invention calculates the specific heat capacity and the specific heat capacity ratio parameter of the working fluid before and after combustion in the cylinder according to the predetermined fuel component parameters and the Dalton partial pressure theorem of different gas components, and reflects the influence of different fuels on the working process of the diesel engine. It can realize the effective thermal efficiency prediction of diesel engines burning different types of fuels, adapt to the current development trend of marine diesel engine alternative fuels, and provide numerical prediction methods for a wider range of diesel engine thermal efficiency optimization designs.

Claims (1)

1.一种船用柴油机基于燃料组分的有效热效率预测方法，其特征是：1. a method for predicting the effective thermal efficiency of a marine diesel engine based on fuel components, is characterized in that: (1)根据柴油机几何参数与初始参数确定边界条件与初始条件，并给定燃烧过程定容燃烧比X，定容燃烧比例是定容燃烧投入热量Qcv与燃烧过程总投入热量Qtotal之比：
Figure FDA0002747064800000011
(1) Determine the boundary conditions and initial conditions according to the geometric parameters and initial parameters of the diesel engine, and give the constant volume combustion ratio X in the combustion process. The constant volume combustion ratio is the ratio of the constant volume combustion input heat Q cv to the total input heat Q total in the combustion process :
Figure FDA0002747064800000011
 其中定容燃烧比是实验测得的或根据预测需求人为设定的；The constant volume combustion ratio is measured experimentally or artificially set according to the predicted demand; (2)选择燃用的燃料种类，根据选用的燃料组分按照如下化学方程式确定燃烧后工质组分：(2) Select the type of fuel to be used, and determine the working fluid composition after combustion according to the selected fuel composition according to the following chemical equation:
Figure FDA0002747064800000012
Figure FDA0002747064800000012
 根据过量空气系数a以及为燃料碳分子数n、氢分子数m、氧分子数l，得出燃烧产物中CO2分子数n1、H2O分子数n2、N2分子数n3、O2分子数n4，由道尔顿分压定理，结合上式确定工作过程中工质的比热容；According to the excess air coefficient a, the number of carbon molecules n, the number of hydrogen molecules, and the number of oxygen molecules l in the fuel, the number of CO 2 molecules n 1 , the number of H 2 O molecules n 2 , the number of N 2 molecules n 3 , and the number of N 2 molecules in the combustion products are obtained. The number of O 2 molecules n 4 is determined by Dalton's partial pressure theorem and the above formula to determine the specific heat capacity of the working medium; (3)将缸内工作过程分为压缩、燃烧、膨胀三个阶段，每个阶段又根据0.01°曲轴转角划分步长，对每个步长采用热力学第一定律，进行迭代求解；(3) The in-cylinder working process is divided into three stages of compression, combustion and expansion, and each stage is divided into steps according to the 0.01° crankshaft rotation angle, and the first law of thermodynamics is used for each step to iteratively solve; (4)对压缩过程进行计算，根据压缩过程一个步长内的传热量
Figure FDA0002747064800000013
体积功
Figure FDA0002747064800000014
工质质量m、工质比热容cv1，通过热力学第一定律求出一个步长内的温度变化
Figure FDA0002747064800000015
(4) Calculate the compression process, according to the heat transfer in one step of the compression process
Figure FDA0002747064800000013
volume work
Figure FDA0002747064800000014
Working fluid mass m, working fluid specific heat capacity c v1 , the temperature change within a step is obtained through the first law of thermodynamics
Figure FDA0002747064800000015
Figure FDA0002747064800000016
Figure FDA0002747064800000016
 根据初始条件的温度t1求解出第一个步长终点的温度t2，将t2作为下一步长的初始温度迭代计算，得到压缩过程各步长的温度，已知各步长温度，由理想气体状态方程pV＝RT得到相应各步长的压力；According to the temperature t 1 of the initial condition, the temperature t 2 of the end point of the first step is solved, and t 2 is iteratively calculated as the initial temperature of the next step, and the temperature of each step of the compression process is obtained. Knowing the temperature of each step, it can be calculated by The ideal gas equation of state pV=RT obtains the pressure of each step; (5)对燃烧过程进行计算，根据燃烧过程一个步长内的传热量
Figure FDA0002747064800000017
体积功
Figure FDA0002747064800000018
工质质量m、工质比热容cv2，燃料燃烧投入热量gf(Hu-u),通过热力学第一定律求出一个步长内的温度变化
Figure FDA0002747064800000019
(5) Calculate the combustion process, according to the heat transfer in one step of the combustion process
Figure FDA0002747064800000017
volume work
Figure FDA0002747064800000018
Working medium mass m, working medium specific heat capacity c v2 , fuel combustion input heat g f (Hu-u), the temperature change within a step is obtained by the first law of thermodynamics
Figure FDA0002747064800000019
Figure FDA00027470648000000110
Figure FDA00027470648000000110
 重复步骤(4)的温度迭代步骤，求解得出各步长的温度与压力；Repeat the temperature iteration step of step (4), and solve the temperature and pressure of each step; (6)对膨胀过程进行计算，重复步骤(4)的计算过程，代入燃烧过程后的工质比热容cv3求解得出膨胀过程各步长的温度与压力；(6) Calculating the expansion process, repeating the calculation process of step (4), and substituting the working medium specific heat capacity c v3 after the combustion process to solve the temperature and pressure of each step of the expansion process; (7)对步骤(4)、(5)、(6)得到的压力进行积分计算，求出工作过程的有效功W，再根据有效功W与总投入热量Qtotal的比值求出有效热效率：(7) Integrate the pressure obtained in steps (4), (5) and (6) to obtain the effective work W of the working process, and then calculate the effective thermal efficiency according to the ratio of the effective work W to the total input heat Q total :
Figure FDA0002747064800000021
Figure FDA0002747064800000021
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