Supercritical carbon dioxide compressor isentropic work calculation method based on actual isentropic index

Abstract

The invention discloses a supercritical carbon dioxide compressor isentropic work calculation method based on an actual isentropic index, which comprises the following steps of: giving an inlet temperature, an inlet pressure, an outlet temperature and an outlet pressure of a compressor, and segmenting a temperature interval of the inlet temperature and the outlet temperature of the compressor, the pressure interval of the inlet pressure and the pressure interval of the outlet pressure are also segmented correspondingly; according to the segmentation result, the specific volume, the actual constant volume specific heat, the isothermal partial derivative item, the constant volume partial derivative item, the actual constant pressure specific heat and the actual pressure-specific volume isentropic index of the actual gas carbon dioxide are calculated; taking an average value of two end points of a sub-interval of the actual pressure-specific volume isentropic index in the ith interval as an average pressure-specific volume isentropic index of the ith interval, and calculating isentropic work of the ith interval; and for each interval, calculating all isentropic power, and summing calculation results of all the intervals to obtain an isentropic power predicted value. According to the method, the thermodynamic behavior of the supercritical carbon dioxide under the actual working condition can be reflected more accurately.

Description

Technical Field

[0001] The present invention relates to the field of mechanical technology, and particularly to a method for calculating the isentropic work of a supercritical carbon dioxide compressor based on the actual isentropic index. Background Art

[0002] The working fluid flow in a centrifugal compressor usually involves thermodynamic processes such as isothermal process, isentropic process, and polytropic process, etc., among which the isentropic flow in the impeller boosting section is the focus of research. As an important derivation parameter in this process, the isentropic index can greatly simplify the analysis of the working fluid state change and the calculation of isentropic work. The traditional method is a simplified calculation method that takes the isentropic index as a constant value according to experience. For real gases, it often brings obvious errors.

[0003] Supercritical carbon dioxide is a typical real gas with a large compression coefficient, specific heat capacity, and density, as well as a small viscosity. Its physical properties change violently with the state, and the actual isentropic index cannot be determined by empirical methods. The isentropic work of a compressor is a process quantity, and its calculation method depends heavily on the change of the isentropic index of the thermodynamic process. The traditional calculation method of compressor isentropic work has large errors and cannot meet the needs of engineering design. Therefore, it is of great significance to design a method for calculating the isentropic work of a supercritical carbon dioxide compressor based on the actual isentropic index. Summary of the Invention

[0004] To solve the above technical problems existing in the prior art, the present invention proposes a method for calculating the isentropic work of a supercritical carbon dioxide compressor based on the actual isentropic index. The actual isentropic index is derived from the real gas state equation, and then the isentropic work is obtained based on the segmented calculation method to improve the calculation accuracy of the isentropic work of the real gas compressor.

[0005] On the one hand, to achieve the above object, the present invention provides a method for calculating the isentropic work of a supercritical carbon dioxide compressor based on the actual isentropic index, including:

[0006] Given the inlet temperature, inlet pressure, outlet temperature, and outlet pressure of the compressor, segment the temperature range of the inlet temperature and outlet temperature of the compressor, and also segment the pressure range of the inlet pressure and outlet pressure accordingly;

[0007] According to the segmentation results, calculate the specific volume, actual constant-volume specific heat, isothermal partial derivative term, isochoric partial derivative term, actual constant-pressure specific heat, and actual pressure-specific volume isentropic index of the real gas carbon dioxide respectively;

[0008] Take the average value of the two endpoints of the sub-interval of the actual pressure-specific volume isentropic index within the i-th interval as the i-th average pressure-specific volume isentropic index, and calculate the isentropic work of the i-th segment;

[0009] For each interval, calculate all the isentropic work, and sum up the calculation results of all intervals to obtain the predicted value of the isentropic work.

[0010] Preferably, calculate the specific volume of the actual gas carbon dioxide as:

[0011]

[0012] In the formula, p i is the pressure, with the unit of kPa; T i is the temperature, with the unit of K; v i is the specific volume, with the unit of m 3 / kmol; R is the universal gas constant; e is the natural constant; A 0 、B 0 、C 0 、D 0 、E 0 、F 0 、G 0 、H 0 、I 0 、J 0 、K 0 are all empirical parameters of the carbon dioxide equation of state.

[0013] Preferably, calculate the actual specific heat at constant volume as:

[0014]

[0015] In the formula, c v,i is the actual specific heat at constant volume, C 0 、D 0 、E 0 、H 0 、I 0 、J 0 、K 0 are all empirical parameters of the carbon dioxide equation of state, a 0 、a 1 、a 2 、a 3 、a 4 are all empirical parameters of the specific heat.

[0016] Preferably, calculate the isothermal partial derivative term and the isochoric partial derivative term as:

[0017]

[0018] In the formula, is the isothermal partial derivative term, is the isochoric partial derivative term, A 0 、B 0 、C 0 、D 0 、E 0, F 0 , G 0 , H 0 , I 0 , K 0 are all empirical parameters of the carbon dioxide equation of state, p i is the pressure, with the unit of kPa; T i is the temperature, with the unit of K; v i is the specific volume, with the unit of m 3 / kmol; R is the universal gas constant.

[0019] Preferably, the actual specific heat at constant pressure is calculated as:

[0020]

[0021] In the formula, c v,i is the actual specific heat at constant volume, c p,i is the actual specific heat at constant pressure, is the isothermal partial derivative term, is the isochoric partial derivative term.

[0022] Preferably, the actual pressure-specific volume isentropic exponent is calculated as:

[0023]

[0024] In the formula, k pv,i is the actual pressure-specific volume isentropic exponent; p i is the pressure, with the unit of kpa; v i is the specific volume, with the unit of m 3 / kmol; c p,i is the specific heat at constant pressure, with the unit of kJ / (kg·K); c v,i is the specific heat at constant volume, with the unit of kJ / (kg·K); is the isothermal partial derivative term.

[0025] Preferably, the average pressure-specific volume isentropic exponent of the i-th stage is:

[0026]

[0027] In the formula, is the average pressure-specific volume isentropic exponent of the i-th stage, k pv,i is the actual pressure-specific volume isentropic exponent.

[0028] Preferably, the isentropic work of the i-th stage is calculated as:

[0029]

[0030] In the formula, is the average pressure-specific volume isentropic exponent of the i-th stage; v iis the specific volume, with the unit of m 3 / kmol; w i is the isentropic work of the i-th stage, with the unit of kJ / kg; p i is the pressure, with the unit of kPa; ε i is the pressure ratio of the i-th stage.

[0031] On the other hand, to achieve the above object, the present invention also provides an isentropic work calculation system for a supercritical carbon dioxide compressor based on the actual isentropic index, including:

[0032] Temperature and pressure zoning module: used to specify the inlet temperature, inlet pressure, outlet temperature and outlet pressure of the compressor, segment the temperature range of the inlet temperature and outlet temperature of the compressor, and correspondingly segment the pressure range of the inlet pressure and outlet pressure;

[0033] Isentropic work calculation module: used to calculate the specific volume, actual constant volume specific heat, isothermal partial derivative term, constant volume partial derivative term, actual constant pressure specific heat, actual pressure-specific volume isentropic index of the actual gas carbon dioxide according to the segmentation result, and take the average value of the two end points of the sub-interval of the actual pressure-specific volume isentropic index within the i-th interval as the average pressure-specific volume isentropic index of the i-th stage, and calculate the isentropic work of the i-th stage;

[0034] Isentropic work prediction module: used to calculate all the isentropic work for each interval, sum up the calculation results of all intervals, and obtain the isentropic work prediction value.

[0035] Compared with the prior art, the present invention has the following advantages and technical effects:

[0036] (1) The present invention is based on the analytical calculation model of pneumatic parameters of the real gas state equation and applies it to the prediction of the isentropic work of a supercritical carbon dioxide centrifugal compressor. The isentropic index, as an important derivation parameter in this process, can greatly simplify the analysis of the state change of the working medium and the calculation of the process work, etc. It can realize the rapid and accurate evaluation of the pneumatic performance of the compressor, help to evaluate the performance and efficiency of the supercritical carbon dioxide compressor in the design stage, and thus promote more effective design decisions. Compared with the traditional method, by using the actual pressure-specific volume isentropic index, the present invention can more accurately reflect the thermodynamic behavior of supercritical carbon dioxide under actual working conditions and reduce the error caused by idealized assumptions.

[0037] (2) The prediction method of the isentropic work of the present invention calculates the isentropic work within their respective ranges by the piecewise approximation method. Since the actual pressure-specific volume isentropic index, as a state quantity, changes violently with the state of the working medium, it can be considered that the actual pressure-specific volume isentropic index is unchanged within the interval through segmentation. The average value of the two end points of the sub-interval is used as the actual pressure-specific volume isentropic index within the interval to facilitate the accurate calculation of the isentropic work. Description of the Drawings

[0038] The accompanying drawings, which form a part of this application, are used to provide a further understanding of this application. The schematic embodiments and descriptions thereof of this application are used to explain this application and do not constitute an improper limitation of this application. In the accompanying drawings:

[0039] Figure 1 It is a flowchart of a method for calculating the isentropic work of a supercritical carbon dioxide compressor based on the actual isentropic index in an embodiment of the present invention. Specific embodiments

[0040] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the accompanying drawings and combine with the embodiments to detail this application.

[0041] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0042] This embodiment proposes a method for calculating the isentropic work of a supercritical carbon dioxide compressor based on the actual isentropic index, as Figure 1 , including:

[0043] Given the inlet temperature, inlet pressure, outlet temperature, and outlet pressure of the compressor, segment the temperature range of the inlet temperature and outlet temperature of the compressor, and correspondingly segment the pressure range of the inlet pressure and outlet pressure;

[0044] According to the segmentation results, calculate the specific volume of the actual gas carbon dioxide, the actual specific heat at constant volume, the isothermal partial derivative term, the isochoric partial derivative term, the actual specific heat at constant pressure, and the actual pressure-specific volume isentropic index respectively;

[0045] Take the average value of the two end points of the sub-interval of the actual pressure-specific volume isentropic index within the i-th interval as the average pressure-specific volume isentropic index of the i-th segment, and calculate the isentropic work of the i-th segment;

[0046] For each interval, calculate all the isentropic work, sum up the calculation results of all intervals, and obtain the predicted value of the isentropic work.

[0047] In this embodiment, for the compressor to be predicted, based on the parameters at the design point, by establishing an analytical formula or an empirical formula, the pressure range needs to be divided into several segments, the actual pressure-specific volume isentropic index takes the average value of the two end points of the sub-interval, calculate the isentropic work of each sub-interval one by one, and finally calculate the multiple sub-intervals.

[0048] Specifically, it includes:

[0049] (1) Given the compressor inlet temperature \(T\), inlet pressure \(p\), outlet temperature \(T'\), and outlet pressure \(p'\), divide the temperature range at the compressor inlet and outlet into segments, which are divided into \([T 1 ,T 2 ,[T 2 ,T 3 …[T n ,T n+1 , a total of \(n\) intervals, and divide the pressure correspondingly into \([p 1 ,p 2 ,[p 2 ,p 3 …[p n ,p n+1 .

[0050] (2) Calculate for \([T i ,p i to solve for the specific volume \(v i \) of the real gas carbon dioxide:

[0051]

[0052] In the formula, \(p i \) is the pressure, with the unit of kPa; \(T i \) is the temperature, with the unit of K; \(v i \) is the specific volume, with the unit of \(m 3 / kmol\); \(R\) is the universal gas constant (\(8.314 kJ / kmol·K\)), \(e\) is the natural constant, and its value is approximately 2.718. \(A 0 , B 0 , C 0 , D 0 , E 0 , F 0 , G 0 , H 0 , I 0 , J 0 , K 0 are all empirical parameters of the carbon dioxide state equation, and their values are respectively:

[0053]

[0054] (3) Calculate the actual specific heat at constant volume \(c v,i \):

[0055]

[0056] In the formula, \(a 1 , a 2 , a 3 , a 4 , a 5 are all empirical parameters of the specific heat, and their values are respectively:

[0057]

[0058] (4) Calculate the isothermal partial derivative term and the isochoric partial derivative term

[0059]

[0060]

[0061] where p i is the pressure, with the unit of kPa; T i is the temperature, with the unit of K; v i is the specific volume, with the unit of m 3 / kmol; R is the universal gas constant (8.314 kJ / kmol·K).

[0062] (5) Calculate the actual specific heat at constant pressure c p,i :

[0063]

[0064] (6) Calculate the actual pressure - specific volume isentropic exponent k pv,i :

[0065]

[0066] where p i is the pressure, with the unit of kPa, v i is the specific volume, with the unit of m 3 / kmol, c p,i is the specific heat at constant pressure, with the unit of kJ / (kg·K), c v,i is the specific heat at constant volume, with the unit of kJ / (kg·K), is the isothermal partial derivative term.

[0067] (7) For [T i+1 , p i+1 , repeat steps (1) - (7) to obtain k pv,i+1 .

[0068] (8) Take the average of the two endpoints of the sub - interval of the actual pressure - specific volume isentropic exponent within the i - th interval as the average pressure - specific volume isentropic exponent of the i - th segment

[0069]

[0070] (9) Calculate the isentropic work of the i - th segment:

[0071]

[0072] In the formula, is the isentropic exponent of the average pressure - specific volume for the i - th stage, v i is the specific volume, with the unit of m 3 / kmol, w i is the isentropic work, with the unit of kJ / kg, and ε i is the pressure ratio of the i - th stage.

[0073] (10) For each interval, calculate all w 1 , w 2 , …, w i , …, w n .

[0074] (11) Sum up the calculation results of multiple intervals to obtain the predicted value of the isentropic work w s , and substitute it into formula (11) for calculation.

[0075]

[0076] In the formula, w i is the isentropic work of the i - th stage, and n is the total number of intervals.

[0077] This embodiment also provides a system for calculating the isentropic work of a supercritical carbon dioxide compressor based on the actual isentropic exponent, including:

[0078] Temperature - pressure zoning module: used to specify the inlet temperature, inlet pressure, outlet temperature, and outlet pressure of the compressor, segment the temperature intervals of the inlet temperature and outlet temperature of the compressor, and also segment the pressure intervals of the inlet pressure and outlet pressure accordingly;

[0079] Isentropic work calculation module: used to calculate the specific volume, actual specific heat at constant volume, isothermal partial derivative term, isochoric partial derivative term, actual specific heat at constant pressure, and actual pressure - specific volume isentropic exponent of real - gas carbon dioxide respectively according to the segmentation results, take the average value of the two endpoints of the sub - interval of the actual pressure - specific volume isentropic exponent within the i - th interval as the average pressure - specific volume isentropic exponent of the i - th stage, and calculate the isentropic work of the i - th stage;

[0080] Isentropic work prediction module: used to calculate all the isentropic work for each interval, sum up the calculation results of all intervals, and obtain the predicted value of the isentropic work.

[0081] To more clearly express the technical solution of the present invention, specific embodiments are provided below for introducing the solution:

[0082] The method for predicting the isentropic work of the impeller component of a supercritical carbon dioxide centrifugal compressor model developed by a certain research group is as follows:

[0083] (1) Given that the inlet temperature of the compressor is \(T = 310K\), the outlet temperature is \(T' = 353.5K\), the inlet pressure is \(p = 8000kpa\), and the outlet pressure is \(p' = 16210kpa\).

[0084] The temperature is divided into 4 intervals (\(n = 4\)), and the obtained intervals are: the first interval (\(i = 1\)) \([310, 323.7802]\), the second interval (\(i = 2\)) \([323.7802, 335.0544]\), the third interval (\(i = 3\)) \([335.0544, 344.5412]\), and the fourth interval (\(i = 4\)) \([344.5412, 353.5]\);

[0085] The corresponding pressure intervals are: the first interval (\(i = 1\)) \([8000, 10000]\), the second interval (\(i = 2\)) \([10000, 12000]\), the third interval (\(i = 3\)) \([12000, 14000]\), and the fourth interval (\(i = 4\)) \([14000, 16210]\).

[0086] (2) For the first interval, i.e., when \(i = 1\), \(T\) i = 310K, \(p\) i = 8000kPa, solve for the specific volume \(v\) i of the real gas carbon dioxide. According to the calculation of Equation (1), the calculation result is: \(v\) 1 = 0.1275m 3 / kmol.

[0087] (3) Calculate the real isochoric specific heat \(c\) v,1 . According to the calculation of Equation (3), the calculation result is: \(c\) v,1 = 1.81kJ / (kg·K).

[0088] (4) Calculate the isochoric partial derivative term and the isothermal partial derivative term Obtained according to Equation (5) and Equation (6). The calculation result is

[0089] (5) Calculate the real isobaric specific heat \(c\) p,i : Obtained according to Equation (7). The calculation result is \(c\) p,1 = 10.158kJ / (kg·K).

[0090] (6) Calculate the real pressure - specific volume isentropic index \(k\) pv,1 . Obtained according to Equation (8). The calculation result is \(k\) pv,1 = 1.115.

[0091] (7) As known from step 1, \(T\) 2 = 323.7802K, \(p\) 2= 10000 kPa, repeat steps (1)-(5) to calculate the actual pressure-specific volume isentropic exponent k pv,2 According to formula (8), the calculation result is k pv,2 = 1.3394.

[0092] (8) Calculate the mean value of the actual pressure-specific volume isentropic exponent within the calculation interval Take the k values at both ends of the sub-interval pv,1 and k pv,2 , take the average value, obtained according to formula (9), and the calculation result is

[0093] (9) Repeat steps (1)-(8) to calculate the mean values of the actual pressure-specific volume isentropic exponents in the 2nd, 3rd, and 4th intervals, and the calculation results are Calculate the pressure ratio, ε, for each interval 1 = 1.25, ε 2 = 1.20, ε 3 = 1.17, ε 4 = 1.16. For each interval, calculate the isentropic work, obtained according to formula (10), and the results are: w 1 = 5.2796 kJ / kg, w 2 = 4.9915 kJ / kg, w 3 = 4.713 kJ / kg, w 4 = 4.9269 kJ / kg.

[0094] (10) Calculate the total isentropic work of the compressor, obtained according to formula (11), and the calculation result is: w s = 19.911 kJ / kg.

[0095] The centrifugal compressor used for prediction has detailed geometric parameters and experimental data on aerodynamic performance. Comparing with the prediction results of the present invention shows that the average error is less than 1%, the maximum error is less than 3%, and the relative error of the calculated value is reduced to 0.5%. The prediction accuracy is good and it has applicability in the aerodynamic calculation of supercritical carbon dioxide centrifugal compressors.

[0096] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for calculating the isentropic work of a supercritical carbon dioxide compressor based on an actual isentropic index, characterized in that: include: Given the compressor inlet temperature, inlet pressure, outlet temperature and outlet pressure, the temperature range of the compressor inlet temperature and outlet temperature is segmented, and the pressure range of the inlet pressure and outlet pressure is also segmented accordingly; According to the segmented results, the specific volume, actual constant volume specific heat, isothermal partial derivative, isochoric partial derivative, actual constant pressure specific heat, and actual pressure-specific volume isentropic index of the actual gas carbon dioxide are calculated respectively; Take the average of the two end points of the sub-interval of the actual pressure-specific volume isentropic index in the i-th section as the average pressure-specific volume isentropic index of the i-th section, and calculate the isentropic work of the i-th section; For each interval, all isentropic works are calculated, and the calculation results of all intervals are summed to obtain the isentropic work prediction value.

2. The method for calculating isentropic work of a supercritical carbon dioxide compressor based on actual isentropic index according to claim 1, characterized in that: Calculate the specific volume of real gas carbon dioxide as: In the formula, p i is the pressure, in kPa; T i is the temperature, in K; v i is the specific volume, in m 3 / kmol; R is the universal gas constant; e is the natural constant; A0, B0, C0, D0, E0, F0, G0, H0, I0, J0, K0 are all empirical parameters of the carbon dioxide state equation.

3. The method for calculating the isentropic work of a supercritical carbon dioxide compressor based on the actual isentropic index according to claim 2, characterized in that: The actual specific heat at constant volume is calculated as: In the formula, c v,i is the actual specific heat at constant volume, C0, D0, E0, H0, I0, J0, K0 are all empirical parameters of the carbon dioxide state equation, a0, a1, a2, a3, a4 are all empirical parameters of specific heat.

4. The method for calculating isentropic work of a supercritical carbon dioxide compressor based on actual isentropic index according to claim 1, characterized in that: The isothermal partial derivative and the isochoric partial derivative are calculated as: In the formula, is the isothermal partial derivative, is the isochoric partial derivative, A0, B0, C0, D0, E0, F0, G0, H0, I0, K0 are all empirical parameters of the carbon dioxide state equation, p i is the pressure, in kPa; T i is the temperature, in K; v i is the specific volume, in m 3 / kmol; R is the universal gas constant.

5. The method for calculating isentropic work of a supercritical carbon dioxide compressor based on actual isentropic index according to claim 4, characterized in that: The actual constant pressure specific heat is calculated as: In the formula, c v,i is the actual specific heat at constant volume, c p,i is the actual specific heat at constant pressure, is the isothermal partial derivative, is the isochoric partial derivative.

6. The method for calculating isentropic work of a supercritical carbon dioxide compressor based on actual isentropic index according to claim 1, characterized in that: The actual pressure-specific volume isentropic index is calculated as: In the formula, k pv,i is the actual pressure-specific volume isentropic index; p i is the pressure, the unit is kpa; v i is the specific volume, in m 3 / kmol;c p,i is the specific heat capacity at constant pressure, in kJ / (kg·K); c v,i is the specific heat at constant volume, in kJ / (kg·K); is the isothermal partial derivative.

7. The method for calculating isentropic work of a supercritical carbon dioxide compressor based on actual isentropic index according to claim 1, characterized in that: The average pressure-specific volume isentropic index of the i-th segment is: In the formula, is the average pressure-volume isentropic index of the i-th segment, k pv,i is the actual pressure-specific volume isentropic index.

8. The method for calculating the isentropic work of a supercritical carbon dioxide compressor based on the actual isentropic index according to claim 1, characterized in that: Calculate the isentropic work of the i-th segment as: In the formula, is the average pressure-volume isentropic index of the ith segment; v i is the specific volume, in m 3 / kmol;w i is the isentropic work of the ith segment, in kJ / kg; p i is the pressure, in kpa; ε i is the pressure ratio of the i-th section.

9. A supercritical carbon dioxide compressor isentropic work calculation system based on actual isentropic index, characterized in that: include: Temperature and pressure partitioning module: for given compressor inlet temperature, inlet pressure, outlet temperature and outlet pressure, dividing the temperature range of the compressor inlet temperature and outlet temperature into segments, and also dividing the pressure range of the inlet pressure and outlet pressure into segments accordingly; Isentropic work calculation module: used to calculate the specific volume, actual constant volume specific heat, isothermal partial derivative, isochoric partial derivative, actual constant pressure specific heat, and actual pressure-specific volume isentropic index of the actual gas carbon dioxide according to the segmented results, and take the average value of the two end points of the sub-interval of the actual pressure-specific volume isentropic index in the i-th segment as the average pressure-specific volume isentropic index of the i-th segment, and calculate the isentropic work of the i-th segment; Isentropic work prediction module: used to calculate all isentropic works for each interval, sum up the calculation results of all intervals, and obtain the isentropic work prediction value.

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