A time-domain calculation method for compressor piping gas flow pulsation based on actual gas properties

Abstract

The present application belongs to the field of compressor piping gas flow pulsation analysis, and particularly relates to a compressor piping gas flow pulsation time domain calculation method based on actual gas properties. The present application establishes a compressor piping gas flow pulsation model for actual gas working medium, eliminates the influence of actual gas property deviation from perfect gas on gas flow pulsation calculation, is more in line with the actual state of gas flow state parameter change of the piping system for high pressure application scenarios, and can obtain more accurate gas flow pulsation results.

Description

Technical Field

[0001] This invention belongs to the field of compressor piping airflow pulsation analysis technology, and particularly relates to a time-domain calculation method for compressor piping airflow pulsation based on actual gas properties. Background Technology

[0002] High-pressure compressors are widely used in hydrogen storage and transportation, petrochemicals, and other fields. These compressors are typically positive displacement compressors, and the intermittent intake and exhaust processes create strong airflow pulsations within the pipelines. These pulsations not only affect the compressor's performance but also induce severe vibrations in the pipeline system, significantly impacting the compressor's safe operation. Therefore, accurately calculating the airflow pulsation characteristics of the compressor pipeline system is crucial for assessing the pulsation level and developing strategies to suppress it. Typically, the physical properties of high-pressure gases deviate significantly from a fully gaseous state, but conventional methods for calculating pipeline airflow pulsations treat the gas as a fully gaseous state, affecting the accuracy of the calculations.

[0003] Under large-amplitude pulsations, the physical properties of high-pressure gas in the pipe change more significantly than under normal pressure. Conventional airflow pulsation calculation methods do not consider this factor and do not account for the changes in the equation of state caused by airflow pulsation. They still construct unsteady flow numerical models based on the case of a completely gaseous system, which makes the calculated airflow pulsation results in the pipe system far from the actual situation. This leads to misestimation of the airflow pulsation level and the location of air column resonance, and misleads the formulation of subsequent pulsation suppression schemes and pipe system acoustic design improvement schemes. Currently, two common calculation methods are used for compressor piping airflow pulsation. One is the frequency domain method based on plane wave theory, which assumes that airflow pulsation is a small disturbance superimposed on the mean flow and treats gas properties as constants of the mean flow state. This method can quickly solve for piping airflow pulsation, but the error is large when there is large pulsation. The other is the time domain method based on unsteady fluid dynamics. However, the computational cost of using full three-dimensional modeling for complex piping systems is huge. Therefore, professional analysis programs and software for piping airflow pulsation all use one-dimensional unsteady flow numerical models for calculation. However, the numerical modeling and solution of one-dimensional time domain calculation of piping airflow pulsation under actual gas properties is different from that of a complete gas. The relevant calculation methods are still lacking. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, this invention provides a time-domain calculation method for airflow pulsation in compressor piping systems based on actual gas properties. This invention can obtain more accurate airflow pulsation results.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A time-domain calculation method for airflow pulsation in compressor piping systems based on actual gas properties includes the following steps:

[0007] S1. Prepare a thermophysical property table for the physical property data involved in the solution of airflow pulsation;

[0008] S2. Based on the parameters of each pipeline component of the compressor, establish a one-dimensional unsteady flow numerical model of the compressor pipeline system of the actual gas working fluid, and set the mesh size, time step, time step number, boundary nodes, boundary type and boundary condition parameters.

[0009] The computational grid for the one-dimensional unsteady flow numerical model of a compressor piping system for a real gaseous working fluid is divided into separate grids for each piping element. After spatial and temporal discretization, the first and second characteristic equations are expressed as follows:

[0010] (1-a)

[0011] (1-b)

[0012] In the formula, ( W ± (for characteristic variables) d W + and d W - Representing feature variables respectively W + and characteristic variables W -along the feature line d X / d Z = U + A and d X / d Z = U - A The increment, Δ X、 Δ Z These represent the grid size and time step, respectively. j , n These represent the current grid point and time step number, respectively. R , P , U These represent dimensionless density, pressure, and flow velocity, respectively. X , Z Representing spatial and temporal coordinates respectively. D Indicates the inner diameter of the pipe. f This represents the coefficient of friction between the fluid and the pipe wall. F Indicates the cross-sectional area of ​​the pipe. k ref Specific heat ratio for reference conditions L ref For reference length, A Represents the speed of sound, Θ + and Θ - The left-hand term of the exponential expression (1) has no clear physical meaning;

[0013] S3. Set the initial field of the pipeline airflow pulsation, and solve the one-dimensional unsteady flow equation of the actual gas working medium in the pipeline system in the time domain (i.e., time domain) (specifically including the aerodynamic equation described by equation (2) and the characteristic equations described by equations (4-a) and (4-b)). Obtain the airflow parameters (including pressure, density, sound speed, flow velocity, etc.) of each grid point at each time step, that is, obtain the flow field result of the output airflow pulsation (the so-called flow field result refers to the airflow parameters of each grid point at each time step).

[0014] Preferably, in step S1, data tables are created with pressure and density as independent variables and entropy, internal energy, and sound speed as dependent variables, respectively; data tables are created with pressure and entropy as independent variables and density as dependent variables; and data tables are created with density and internal energy as independent variables and pressure as dependent variables.

[0015] Preferably, in step S1, the range of the independent variable in the thermal property table covers the range of airflow state parameter changes caused by airflow pulsation in the pipeline. The values ​​of the independent variables are taken at non-equal intervals, and the intervals of the independent variables are adjusted according to the gradient of the change of the dependent variable at the value of the independent variable.

[0016] Preferably, in step S2, the aerodynamic equations of the one-dimensional unsteady flow numerical model of the compressor pipeline system of the actual gaseous working fluid are:

[0017] (2)

[0018] In equation (2) above, the pressure, density, sound velocity, and length of the reference state have been dimensionlessly processed, where R , P , U , E Let these represent the dimensionless density, pressure, flow velocity, and internal energy, respectively. X , Z Representing spatial and temporal coordinates respectively. D Indicates the inner diameter of the pipe. f This represents the coefficient of friction between the fluid and the pipe wall. F Indicates the cross-sectional area of ​​the pipe. k ref Specific heat ratio for reference conditions L ref For reference length, q It represents the amount of heat exchanged by a unit mass of fluid to the outside per unit time; A ref The speed of sound is for reference.

[0019] Preferably, in step S2, the aerodynamic equations of the one-dimensional unsteady flow numerical model of the compressor pipeline system for the actual gaseous working fluid, for valve components, are expressed by the following equation:

[0020] (3)

[0021] In the above formula (3), z ( θ () represents the valve loss coefficient. θ Indicates the valve opening degree. L v Indicates the length of the valve component.

[0022] Preferably, in step S2, the first and second characteristic equations of the one-dimensional unsteady flow numerical model of the compressor pipeline system of the actual gaseous working fluid are as follows:

[0023] (4-a)

[0024] (4-b)

[0025] In the above formula, the pressure, density, sound velocity, and length under the reference state have been dimensionless, where R , P , U These represent dimensionless density, pressure, and flow velocity, respectively. X , Z Representing spatial and temporal coordinates respectively. D Indicates the inner diameter of the pipe. f This represents the coefficient of friction between the fluid and the pipe wall. F Indicates the cross-sectional area of ​​the pipe. k ref Specific heat ratio for reference conditions L ref For reference length, A It indicates the speed of sound.

[0026] Preferably, in step S3, the one-dimensional unsteady flow equation of the actual gas working fluid in the pipeline system is solved in the time domain. During the solution process, other gas state variables are obtained by interpolation using a property table based on two known gas state variables. At the grid points of pipes, diameter changes, and valve components, the aerodynamic equations are solved using conventional flow field methods to calculate the airflow parameters. At the tee junctions, open ends, closed ends, and compressor ends, the characteristic equations are used to solve for the airflow parameters at the boundary grid points.

[0027] Preferably, in step S2, the compressor's piping components at the boundary of the tee junction are aligned based on the equal pressure at the junction point. And the isentropic assumption yields that the density and sound speed are equal at the convergence point, i.e. and According to the continuous flow condition at the confluence point, i.e. Combining equations (4-a) and (4-b), we obtain

[0028] (5)

[0029] In the above formula (5), P Indicates pressure, F Indicates the cross-sectional area of ​​the pipe. k ref Specific heat ratio for reference conditions A Indicates the speed of sound. n Indicates the current time step number.

[0030] The advantages of this invention are:

[0031] (1) This invention establishes a compressor piping system airflow pulsation model for actual gas working fluid, eliminating the influence of the actual gas properties deviating from the complete gas on the airflow pulsation calculation. Especially for high pressure application scenarios, it is more in line with the actual state of the airflow state parameters of the pipeline system, and can obtain more accurate airflow pulsation results.

[0032] (2) This invention is particularly applicable to the case of large airflow pulsation in compressor piping systems. During the solution process, the gas property parameters are calculated by interpolation of property tables. The property data in the tables can be obtained by experimental testing. The range of independent variables can be adjusted, which can avoid the situation where the actual gas properties deviate significantly from the applicable range of the gas state equation when the airflow pulsates significantly, thereby improving the accuracy of airflow pulsation calculation.

[0033] (3) The present invention takes into account the change of cross-sectional area of ​​pipeline components and introduces a valve loss coefficient to account for valve momentum loss. It can directly solve the airflow pulsation of the variable diameter and valve components numerically, which improves the accuracy of the calculation of airflow pulsation of the variable diameter and valve components. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the calculation process for airflow pulsation in the piping system according to the present invention.

[0035] Figure 2 This is a schematic diagram illustrating the solution of the characteristic equation of this invention.

[0036] Figure 3 This is a schematic diagram of a pipe tee.

[0037] Figure 4 This is the time-domain curve of mass flow rate fluctuation at a point in the piping system calculated according to the method of this invention and the plane wave theory method. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0039] like Figures 1-4As shown, a time-domain calculation method for airflow pulsation in compressor piping systems based on actual gas properties includes the following steps:

[0040] S1. Prepare thermal property tables. Obtain property data by consulting property calculation software or through experiments. Using pressure and density as independent variables, prepare separate tables with entropy, internal energy, and sound speed as dependent variables. Prepare tables with pressure and entropy as independent variables and density as dependent variables. Prepare tables with density and internal energy as independent variables and pressure as dependent variables. When preparing property tables, the range of independent variable variation should cover the range of airflow state parameter variation caused by airflow pulsation in the pipeline. The independent variable values ​​should be non-equally spaced, and the spacing of the independent variables should be adjusted according to the gradient of the dependent variable variation at the independent variable value.

[0041] S2. Establish one-dimensional unsteady aerodynamic equations and characteristic equations for the flow in a pipeline system for real gases. The aerodynamic equations for the one-dimensional unsteady flow numerical model of a compressor pipeline system for a real gas working fluid are expressed by the following equations:

[0042] (2)

[0043] Equation (2) above has been dimensionless using the pressure, density, sound velocity, and length of the reference state, where R , P , U , E Let these represent the dimensionless density, pressure, flow velocity, and internal energy, respectively. X , Z Representing spatial and temporal coordinates respectively. D Indicates the inner diameter of the pipe. f This represents the coefficient of friction between the fluid and the pipe wall. F Indicates the cross-sectional area of ​​the pipe. k ref Specific heat ratio for reference conditions L ref This is a reference length.

[0044] For valve components, the momentum equation is now expressed as follows:

[0045] (3)

[0046] In the above formula (3), z ( θ () represents the valve loss coefficient. θ Indicates the valve opening degree. L v This indicates the length of the valve component; the meanings of other physical quantities are the same as in the previous formula.

[0047] The first and second characteristic equations of the one-dimensional unsteady flow numerical model of a compressor piping system for a real gaseous working fluid are expressed by the following two equations:

[0048] (4-a)

[0049] (4-b)

[0050] in A Let represent the speed of sound. The first equation of each equation represents the equations of the first and second characteristic lines, respectively, and the second equation of each equation represents the compatibility equations corresponding to the first and second characteristic lines, respectively.

[0051] The aerodynamic equations and characteristic equations take into account the changes in the pipe cross-sectional area, enabling the simulation of flow inside variable-diameter pipes.

[0052] Discretization methods and boundary condition handling methods for various piping system components are determined, and spatiotemporal discretization schemes for aerodynamic equations and characteristic equations are established. After spatial and temporal discretization, the characteristic lines are as follows: Figure 2 As shown, the first and second characteristic equations are expressed as follows:

[0053] (1-a)

[0054] (1-b)

[0055] Where Δ X、 Δ Z These represent the grid size and time step, respectively. j , n These represent the current grid point and time step number, respectively.

[0056] For the boundary of pipe components at the tee junction, such as Figure 3 As shown, Figure 3 The pipe numbers in the formula correspond to subscripts 1, 2, and 3 in the following formula, and the plus or minus signs of the flow rates at each point in the denominator of the formula are... Figure 3 The flow direction is corresponding, that is, inflow to the confluence point is positive, and outflow to the confluence point is negative; according to the fact that the pressure is equal at the confluence point, that is... And the isentropic assumption yields that the density and sound speed are equal at the convergence point, i.e. and According to the continuous flow condition at the confluence point, i.e. Combining equations (1-a) and (1-b) above, we get:

[0057] (5)

[0058] Therefore, according to equation (1), we can obtain , and .

[0059] For the initial boundary, according to And the isentropic assumption yields If the starting point is the right end of the piping element, then the result can be obtained according to equation (1-a). If the starting point is the left endpoint, then the answer can be obtained according to equation (1-b). .

[0060] For closed-end boundaries or compressor-end boundaries, closed end compressor end and The excitation function of the compressor cylinder is used to determine the result. If the closed end or the compressor end is the right end of the pipeline component, then it can be calculated according to equation (1-a). If the closed end or compressor end is the left end, then the result can be obtained according to equation (1-b). .

[0061] The numerical calculation method for the aerodynamic equations is the same as the conventional method for treating it as a completely gaseous system, and will not be repeated here.

[0062] The calculation parameters are set, including the length, inner diameter, and volume of each pipeline component such as pipes, reducers, and containers, as well as the mesh size, time step, number of time steps, boundary nodes, boundary type, and boundary condition parameters. This completes the establishment of a one-dimensional unsteady flow numerical model of a compressor pipeline system for a real gaseous working fluid.

[0063] S3. Set the initial field of the pipeline airflow pulsation, solve the one-dimensional unsteady flow equation of the actual gas working medium in the pipeline system in the time domain. During the solution process, other gas state variables are obtained by interpolation using property tables based on two known gas state variables. At the grid points of pipes, diameter changes, and valve components, the aerodynamic equations are solved using conventional flow field methods to calculate the airflow parameters. At the tee junction, open end, closed end, and compressor end, the characteristic equations are used to solve the airflow parameters at the boundary grid points. The gas pressure, density, sound velocity, and flow velocity at each grid point of the pipeline components at each time step are calculated, and the flow field results of the airflow pulsation are output.

[0064] Example 1

[0065] The compressor has a rated speed of 450 rpm, uses hydrogen as the working fluid, and has a rated flow rate of 450 Nm³. 3 / h, initial boundary pressure 10.3MPa, density 8 kg / m³ 3 The airflow pulsation of the compressor intake system was solved using the calculation method provided in this invention, and the results were compared with those obtained by calculation based on a complete gas model. Figure 4The figure shows the mass flow rate curve at the inlet of the piping system for one pulsation cycle. The average flow rate calculated using the method provided in this invention has a relative error of 3% compared to the compressor's rated flow rate, and a relative error of 6% compared to the calculation using plane wave theory. These errors are significantly smaller than those calculated using safe gas modeling, indicating that the time-domain calculation method for compressor piping system airflow pulsation based on actual gas properties proposed in this invention is beneficial for accurately calculating the airflow pulsation level of the compressor piping system. Figure 4 It can be seen that the airflow pulsation results obtained by using actual gas in this embodiment differ significantly from the results obtained by using complete gas in the conventional method.

[0066] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A time-domain calculation method for airflow pulsation in compressor piping systems based on actual gas properties, characterized in that, Includes the following steps: S1. Prepare a thermophysical property table for the physical property data involved in the solution of airflow pulsation; S2. Based on the parameters of each pipeline component of the compressor, establish a one-dimensional unsteady flow numerical model of the compressor pipeline system of the actual gas working fluid, and set the mesh size, time step, time step number, boundary nodes, boundary type and boundary condition parameters. The computational grid for the one-dimensional unsteady flow numerical model of a compressor piping system for a real gaseous working fluid is divided into separate grids for each piping element. After spatial and temporal discretization, the first and second characteristic equations are expressed as follows: (1-a) (1-b) S3. Set the initial field of the pipeline airflow pulsation, solve the one-dimensional unsteady flow equation of the actual gas working fluid in the pipeline system in the time domain, obtain the airflow parameters of each grid point at each time step, and output the flow field results of the airflow pulsation. In step S1, data tables are created with pressure and density as independent variables and entropy, internal energy, and sound speed as dependent variables, respectively; data tables are created with pressure and entropy as independent variables and density as dependent variables; and data tables are created with density and internal energy as independent variables and pressure as dependent variables. In step S2, the aerodynamic equations of the one-dimensional unsteady flow numerical model of the compressor pipeline system of the actual gaseous working fluid are: (2) in R , P , U , E Let d represent the dimensionless density, pressure, flow velocity, and internal energy, respectively. W + and d W - Representing feature variables respectively W + and characteristic variables W -along the feature line d X / d Z = U + A and d X / d Z = U - A The increment, Δ X、 Δ Z These represent the grid size and time step, respectively. j , n These represent the current grid point and time step number, respectively. X , Z Representing spatial and temporal coordinates respectively. D Indicates the inner diameter of the pipe. f This represents the coefficient of friction between the fluid and the pipe wall. F Indicates the cross-sectional area of ​​the pipe. k ref Specific heat ratio under reference conditions L ref For reference length, A Indicates the speed of sound; q It represents the amount of heat exchanged by a unit mass of fluid to the outside per unit time; A ref The speed of sound is for reference only. In step S3, the one-dimensional unsteady flow equation of the actual gas working fluid in the pipeline system is solved in the time domain. During the solution process, other gas state variables are obtained by interpolation using a property table based on two known gas state variables. At the grid points of pipes, diameter changes, and valve components, the aerodynamic equations are solved using conventional flow field methods to calculate the airflow parameters. At the tee junction, open end, closed end, and compressor end, the airflow parameters at the boundary grid points are solved using characteristic equations.

2. The method for time-domain calculation of airflow pulsation in compressor piping systems based on actual gas properties according to claim 1, characterized in that: In step S1, the range of the independent variable in the thermal property table covers the range of airflow state parameter changes caused by airflow pulsation in the covering pipeline, and the values ​​of the independent variable are taken at non-equal intervals.

3. The method for time-domain calculation of airflow pulsation in compressor piping systems based on actual gas properties according to claim 1, characterized in that: In step S2, the aerodynamic equations of the one-dimensional unsteady flow numerical model of the compressor pipeline system for the actual gaseous working fluid, for valve components, are expressed by the following equation: (3) In the above formula (3), ζ ( θ () represents the valve loss coefficient. θ Indicates the valve opening degree. L v Indicates the length of the valve component.

4. The method for time-domain calculation of airflow pulsation in compressor piping systems based on actual gas properties according to claim 1, characterized in that: In step S2, the first and second characteristic equations of the one-dimensional unsteady flow numerical model of the compressor pipeline system of the actual gaseous working fluid are as follows: (4-a) (4-b)。 5. The method for time-domain calculation of airflow pulsation in compressor piping systems based on actual gas properties according to claim 4, characterized in that: In step S2, the compressor's piping components are located at the boundary of the tee junction. Based on the equal pressure at the junction, that is... And the isentropic assumption yields that the density and sound speed are equal at the convergence point, i.e. and ; Based on the continuity condition of the flow at the confluence point, i.e. Combining equations (4-a) and (4-b), we obtain (5)。

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