A method for measuring the vaporization loss rate of a low-temperature high-pressure reciprocating pump fluid end based on a indicator diagram

Abstract

The application discloses a kind of low temperature high pressure reciprocating pump liquid force end vaporization loss rate measurement method based on indicator diagram;The method comprises: establishing the relationship between the closing lag angle of inlet valve and the measurement error, combined with the estimated error level, to determine whether the closing lag angle needs to be measured;Measure the load of piston rod and real-time phase or position, draw indicator diagram after preprocessing;According to the estimated or measured closing lag angle, and the internal relationship between the actual indicator diagram slope when the cylinder pressure of discharge stroke is equal to the critical pressure and the isothermal and adiabatic compression slope, determine the starting point of compression stage;Use low-temperature fluid saturated thermophysical property to calculate gas-liquid density;Based on mass conservation, build the vaporization loss rate calculation formula.The application solves the problem that conventional technology cannot be used for such pumps due to the significant difference in compressibility and thermophysical properties of low-temperature fluids, and has the advantages of high measurement accuracy, good engineering applicability, etc.

Description

Technical Field

[0001] This invention relates to the field of fluid machinery and testing and measurement technology, and in particular to a method for measuring the vaporization loss rate of the hydraulic end of a cryogenic high-pressure reciprocating pump based on an indicator diagram. Background Technology

[0002] Cryogenic high-pressure reciprocating pumps are core equipment for conveying and pressurizing cryogenic fluids such as liquid hydrogen, liquid helium, liquid nitrogen, liquid oxygen, and liquefied natural gas, and are widely used in hydrogen energy, aerospace, petrochemical, and nuclear power industries. In actual operation, due to the high compressibility of cryogenic fluids and the typically low subcooling at the inlet, vaporization easily occurs inside the hydraulic end of the cryogenic high-pressure reciprocating pump, leading to decreased volumetric efficiency, increased vibration, and cavitation damage to components. Therefore, accurate measurement of the vaporization loss rate is crucial.

[0003] Currently, reciprocating pumps transporting conventional fluids mostly measure vaporization loss rate based on indicator diagram characteristics (such as pressure inflection points). However, for cryogenic high-pressure reciprocating pumps, the working medium is a cryogenic fluid (such as liquid hydrogen or liquid nitrogen), which has significantly higher compressibility than conventional hydraulic and petrochemical fluids, and its thermal properties differ significantly from conventional fluids. This makes the indicator diagram characteristics during vaporization in cryogenic high-pressure reciprocating pumps drastically different from those in conventional reciprocating pumps. The pressure inflection point at the start of the compression stage disappears, and the liquefaction stage after the gas phase disappears and the subsequent compression stage transitions smoothly, making it difficult to capture the start of the compression stage. Therefore, the vaporization loss rate measurement methods for conventional reciprocating pumps cannot be directly applied to cryogenic high-pressure reciprocating pumps. Furthermore, cryogenic pumps have a complex structure, with the hydraulic end immersed in a vacuum-insulated cavity filled with cryogenic fluid, making it difficult to install and arrange conventional two-phase flow measurement instruments. To date, no mature measurement method specifically for the vaporization loss rate of the hydraulic end of cryogenic high-pressure reciprocating pumps has been found. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for measuring the vaporization loss rate of the hydraulic end of a low-temperature high-pressure reciprocating pump based on an indicator diagram, so as to solve the problems of the existing technology being unable to accurately identify the compression start point and the low accuracy of vaporization loss rate measurement under low-temperature and high-pressure conditions.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0006] This invention provides a method for measuring the vaporization loss rate at the hydraulic end of a cryogenic high-pressure reciprocating pump based on an indicator diagram, comprising the following steps:

[0007] Step 1: Establish an expression for the measurement error of vaporization loss rate with the closing hysteresis angle of the inlet valve as the independent variable;

[0008] Step 2: Based on the pump's structure and process parameters, estimate the approximate level of the closing lag angle of the inlet valve of the low-temperature high-pressure reciprocating pump using the estimation formula for the closing lag angle of the inlet valve. Substitute this into the vaporization loss rate measurement error expression established in Step 1 to estimate the level of vaporization loss rate measurement error caused by the closing lag of the inlet valve.

[0009] Step 3: When the estimated vaporization loss rate measurement error meets the measurement accuracy requirements, the estimated value of the inlet valve closing hysteresis angle can be used as its actual value, or the influence of the inlet valve closing hysteresis on the vaporization loss rate measurement result can be ignored directly. In this case, it is not necessary to measure the actual closing hysteresis angle of the inlet valve. Otherwise, a low-temperature displacement sensor is used to measure the real-time opening of the inlet valve, and a crankshaft encoder and displacement sensor are used to measure the real-time phase or position of the piston. The actual closing hysteresis angle of the inlet valve is determined by combining the real-time opening of the inlet valve and the real-time phase or position of the piston.

[0010] Step 4: Collect relevant signals of piston rod load and real-time phase or position of piston. Measure piston rod load using force measuring elements or calculate piston rod load by measuring parameters such as piston rod strain and real-time power of drive motor. Based on this, obtain real-time cylinder pressure based on piston rod load identification. Combine the real-time phase or position change of piston with piston motion equation to calculate real-time working volume, so as to draw indicator diagram.

[0011] Step 5: Determine the first working volume of the cylinder corresponding to the closing point of the inlet valve based on the estimated or measured closing hysteresis angle of the inlet valve; for the point in the discharge stroke of the indicator diagram where the cylinder pressure equals the critical pressure, determine the starting point of the compression stage on the indicator diagram based on the intrinsic relationship between the measured slope of the indicator diagram at that point and the isothermal compression slope and the adiabatic compression slope, and record the second working volume of the cylinder corresponding to the starting point of the compression stage.

[0012] Step 6: Determine the inlet pressure through the inlet pipeline pressure sensor, obtain the inlet temperature directly or indirectly through the inlet pipeline temperature sensor, and calculate the saturated gas phase density and saturated liquid phase density of the cryogenic fluid under the inlet pressure using the saturated thermodynamic property relationship of the cryogenic fluid.

[0013] Step 7: Based on the clearance volume of the liquid cylinder, and using the law of conservation of mass combined with the working volume of the first liquid cylinder, the working volume of the second liquid cylinder, the saturated gas phase density, and the saturated liquid phase density, construct a formula for calculating the vaporization loss rate at the hydraulic end.

[0014] Furthermore, in step 1, the relationship model between the closing hysteresis angle of the inlet valve and the measurement error of the vaporization loss rate is as follows:

[0015] ;

[0016] In the formula, This indicates the absolute error in measuring the vaporization loss rate, ignoring the hysteresis of the inlet valve closing. This indicates the maximum working volume of the hydraulic cylinder. This is due to the volume loss caused by the delayed closing of the inlet valve. For the stroke volume, The clearance volume ratio, The hysteresis angle for closing the inlet valve.

[0017] Furthermore, in step 3, the installation method of the low-temperature displacement sensor is as follows:

[0018] A low-temperature displacement sensor mounting bracket 4 is installed on the outer surface of the inlet valve seat. The low-temperature displacement sensor is installed on the bracket. The sensor's signal lead is led out to the external environment through the return steam pipeline and the lead is extended through the branch pipe of the tee pipe. A lead sealing joint is provided at the outlet end of the branch pipe.

[0019] Furthermore, step 4 includes a signal preprocessing step before drawing the indicator diagram: using a median filtering algorithm to eliminate low-frequency spurious signals; using a five-point cubic smoothing method to smooth the filtered cylinder pressure curve; and fitting the processed indicator diagram curve to obtain a smooth indicator diagram curve.

[0020] Furthermore, the specific logic for determining the starting point of the compression stage in step 5 based on the intrinsic relationship between the measured dynamometer card slope and the isothermal compression slope and adiabatic compression slope is as follows:

[0021] If the absolute value of the slope of the measured indicator diagram at the critical pressure point is between the absolute value of the isothermal compression slope and the absolute value of the adiabatic compression slope, then for the indicator diagram segment where the cylinder pressure is less than the critical pressure during the discharge stroke, the point where the absolute value of the curve slope is greater than or equal to the absolute value of the isothermal compression slope and the working volume is the largest is selected as the starting point of the compression stage.

[0022] If the absolute value of the slope of the measured indicator diagram at the critical pressure point is greater than the absolute value of the slope of the adiabatic compression, then for the indicator diagram segment in the discharge stroke where the cylinder pressure is less than the critical pressure, the point where the absolute value of the curve slope is greater than or equal to the absolute value of the slope of the adiabatic compression and the working volume is the largest is selected as the starting point of the compression stage.

[0023] Furthermore, the isothermal compression slope and the adiabatic compression slope are calculated as follows:

[0024] Based on the pressure, temperature, and relative density at the critical pressure point, the result is calculated using the dimensionless residual Helmholtz free energy and its partial derivatives with respect to relative temperature and relative density, combined with the formula for the isothermal compressibility modulus of the liquid phase and the differential equation for entropy under adiabatic conditions.

[0025] Furthermore, in step 6, the formulas for calculating the saturated gas phase density and saturated liquid phase density using the saturated cryogenic fluid state equation are as follows:

[0026] ;

[0027] In the formula, These are the inlet pressure and the inlet temperature, respectively. It can be measured by the pressure sensor in the inlet pipeline; These are the critical pressure, critical temperature, and critical density of the cryogenic fluid, respectively. is a constant in the equation.

[0028] Furthermore, the mathematical model constructed in step 7 is as follows: When the inlet valve is completely closed, the ratio of the gas phase volume to the liquid cylinder volume is: The volumes of the gas phase and the liquid phase are respectively The saturated gas phase density and saturated liquid phase density at the inlet pressure are respectively Assuming no leakage in the pump valve, the mass conservation equations for the inlet valve closing point and the starting point of the compression stage are as follows:

[0029]

[0030] Solve the equation and combine it with the clearance volume. Calculate vaporization loss rate The formula is:

[0031]

[0032] The beneficial effects of this invention are:

[0033] 1. Highly targeted and accurate: To address the problem of the disappearance of the inflection point of the indicator diagram due to the high compressibility of cryogenic fluids, an innovative thermodynamic identification algorithm based on the comparison of critical pressure point and dual slope (isothermal / adiabatic) is proposed, which achieves sub-pixel-level accurate positioning of the compression start point.

[0034] 2. Rigorous Model: It abandons the conventional assumption of incompressible fluid, uses the equation of state of saturated cryogenic fluid to solve the density parameter in real time, and builds a calculation model based on mass conservation, which reflects the vaporization loss process from a physical perspective.

[0035] 3. High engineering application value: It provides a simplified sensor solution based on error tolerance, which reduces system cost and implementation difficulty while ensuring accuracy. Attached Figure Description

[0036] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This illustration shows an assembly diagram of the inlet valve displacement measuring device provided in an embodiment of this application.

[0038] Figure 2 This illustration shows a schematic diagram of the inlet valve measuring device provided in an embodiment of this application.

[0039] Figure 3 This illustration shows an installation diagram of the fiber optic displacement sensor provided in an embodiment of this application.

[0040] Figure 4 This illustrates the testing principle of the indicator diagram of the cryogenic high-pressure reciprocating pump provided in the embodiments of this application;

[0041] Figure 5 The diagram shows the measured dynamometer diagram of the cryogenic high-pressure reciprocating pump provided in the embodiments of this application under liquid nitrogen medium.

[0042] Figure 6 The illustration shows a PV diagram at an inlet pressure of 70 MPa provided in an embodiment of this application.

[0043] Figure 7 This illustration shows a schematic diagram of the selection of vaporization test points on the indicator diagram provided in this application embodiment;

[0044] Figure 8 This illustration shows a comparison of vaporization loss rate measurement results under different discharge pressures provided in this application, with and without considering the hysteresis of the inlet valve closing.

[0045] Figure 9 This illustrates the variation of the vaporization loss rate measurement error as a function of the inlet valve closing hysteresis angle provided in the embodiments of this application.

[0046] Figure 10 This document illustrates a flowchart of a method for measuring the vaporization loss rate at the hydraulic end of a cryogenic high-pressure reciprocating pump based on an indicator diagram, provided in an embodiment of this application.

[0047] In the attached diagram: 1. Inlet valve seat; 2. Low-temperature displacement sensor; 3. Low-temperature displacement sensor mounting bracket; 4. T-connector for lead wire extension; 5. Lead wire sealing connector; 6. Crankshaft; 7. Encoder; 8. Connecting rod; 9. Piston rod. Detailed Implementation

[0048] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0049] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0050] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0051] Reference Figures 1-10 This is one embodiment of the present invention, which provides a method for measuring the vaporization loss rate of the hydraulic end of a cryogenic high-pressure reciprocating pump based on an indicator diagram, comprising the following steps:

[0052] Step 1: Establish an expression relating the closing hysteresis angle of the inlet valve to the measurement error of the vaporization loss rate.

[0053] This step is specifically as follows:

[0054] By combining the law of conservation of mass with the equation of state for cryogenic fluids, a mathematical model is constructed to calculate the vaporization loss rate, specifically:

[0055] When the inlet valve is fully closed, the ratio of the gas phase volume to the liquid cylinder volume can be approximated as: At this time, the volumes of the gas and liquid phases are respectively The corresponding gas and liquid phase masses are respectively ,

[0056] in, These are the saturated gas phase density and saturated liquid phase density at the inlet pressure, respectively. Assuming no pump or valve leakage... At point [point], the mass of the low-temperature saturated liquid in the cylinder Should equal to The sum of the masses of the gas and liquid phases at the point:

[0057] (1)

[0058] Solving equation (1) yields:

[0059] (2)

[0060] Further, engineering criteria are provided to allow the omission of the inlet valve displacement sensor. Specifically:

[0061] To quantify the impact of the inlet valve closing hysteresis on the vaporization loss rate measurement results, the relationship between the inlet valve closing hysteresis angle and the vaporization loss rate measurement error was derived based on expression (2):

[0062] (3)

[0063] Step 2: Based on the pump's structure and process parameters, estimate the approximate level of the closing lag angle of the inlet valve of the low-temperature high-pressure reciprocating pump using the estimation formula for the closing lag angle of the inlet valve. Substitute this into the vaporization loss rate measurement error expression established in Step 1 to estimate the level of vaporization loss rate measurement error caused by the closing lag of the inlet valve.

[0064] This step is specifically as follows:

[0065] By combining the fluid continuity equation with the valve plate motion dynamics equilibrium equation, a mathematical model is constructed to estimate the closing hysteresis angle of the inlet valve, specifically:

[0066] (4);

[0067] In equation (4), The equivalent diameter of the inlet valve seat bore is... This represents the maximum lift of the inlet valve disc. Crankshaft-connecting rod ratio correction factor For piston lift, The diameter of the cylinder piston is [value missing].

[0068] Step 3: When the estimated vaporization loss rate measurement error meets the measurement accuracy requirements, the estimated value of the liquid inlet valve closing hysteresis angle can be used as its actual value, or the influence of the liquid inlet valve closing hysteresis on the vaporization loss rate measurement result can be ignored directly. In this case, there is no need to measure the actual closing hysteresis angle of the liquid inlet valve.

[0069] Otherwise, a low-temperature displacement sensor 2 is used to measure the real-time opening of the inlet valve, and a crankshaft 6 encoder 7 and a displacement sensor are used to measure the real-time phase or position of the piston. By combining the real-time opening of the inlet valve and the real-time phase or position of the piston, the closing hysteresis angle of the inlet valve of the low-temperature high-pressure reciprocating pump is determined.

[0070] Specifically, in step 1, the relationship model between the liquid inlet valve closing hysteresis angle and the vaporization loss rate measurement error is as follows:

[0071] ;

[0072] In the formula, This indicates the absolute error in measuring the vaporization loss rate, ignoring the hysteresis of the inlet valve closing. This indicates the maximum working volume of the hydraulic cylinder. This is due to the volume loss caused by the delayed closing of the inlet valve. For the stroke volume, The clearance volume ratio, The hysteresis angle for closing the inlet valve. When the vaporization loss rate measurement error... Less than the allowable error in engineering At that time, it was assumed that the displacement sensor of the inlet valve could be omitted.

[0073] Using equation (3), the curve of the vaporization loss rate measurement error under a discharge pressure of 98 MPa as a function of the inlet valve closing hysteresis angle can be obtained, as shown below. Figure 9 As shown. From Figure 9 It can be seen that the measurement error of the vaporization loss rate increases slightly with the increase of the inlet valve closing hysteresis angle, and is typically < for low-temperature high-pressure reciprocating pumps. Regarding the closing hysteresis angle of the inlet valve, the absolute error is <1.23%, which can be approximately ignored.

[0074] Setup of the inlet valve displacement measuring device:

[0075] When the calculated vaporization loss rate measurement error does not meet the measurement accuracy requirements, the sensor installation and measurement method is as follows: a low-temperature displacement sensor mounting bracket 3 is set on the outer surface of the inlet valve seat 1, and the low-temperature displacement sensor 2 is fixedly installed on the bracket to ensure that the sensor probe can be accurately aligned with the moving parts of the inlet valve. Considering that the hydraulic end of the low-temperature high-pressure reciprocating pump is usually immersed in a low-temperature medium and the external environment is a high-vacuum insulation environment, the sensor signal lead needs to be specially sealed before being led out: the signal lead is led out through the return steam pipeline, specifically by extending the lead out through the branch pipe of the tee pipe 4 installed on the return steam pipeline to lead the lead to the external environment, and a lead sealing joint 5 is set at the outlet end of the branch pipe of the tee pipe to achieve a high-vacuum seal at the lead extension point, preventing external air from entering and causing insulation failure or freezing. Based on this, the displacement data of the inlet valve is measured and output in real time using the low-temperature displacement sensor 2, thereby obtaining the real-time opening degree of the inlet valve. When the calculated vaporization loss rate measurement error meets the measurement accuracy requirements, the influence of the liquid inlet valve closing lag on the vaporization loss rate measurement result can be ignored, and the liquid inlet valve displacement sensor can be directly omitted.

[0076] Obtaining the real-time phase or position of the piston:

[0077] A linear displacement sensor is installed on the extended section of the piston rod 9, or a rotary encoder 7 is installed on the drive crankshaft 6. By indirectly measuring the rotation angle of the crankshaft 6 or directly measuring the linear displacement of the piston rod 9, the real-time phase or position of the piston relative to the top dead center (TDC) or bottom dead center (BDC) can be obtained and calculated.

[0078] Logic for determining the closing hysteresis angle of the inlet valve:

[0079] The real-time opening signal of the synchronously acquired inlet valve is aligned with the real-time phase or position signal of the piston measured by a crankshaft encoder or displacement sensor. The discharge stroke phase is locked in the data stream, and the change in the real-time opening value of the inlet valve during this phase is monitored. When the real-time opening value of the inlet valve decreases from a value greater than 0 to 0, the corresponding real-time phase or position of the piston is recorded. This specific phase or position is defined as the inlet valve closing hysteresis angle of the cryogenic high-pressure reciprocating pump, and this serves as the time reference for subsequently calculating the working volume of the cylinder at the inlet valve closing point.

[0080] Step 4: Collect the load-related signals of piston rod 9 and the real-time phase or position of the piston (or crankshaft 6 rotation angle). Measure the piston rod load using a force measuring element or calculate the piston rod load by measuring parameters such as piston rod strain and real-time power of the drive motor. Based on this, obtain the real-time cylinder pressure by identifying the piston rod 9 load. Combine the real-time phase or position change of the piston (or crankshaft 6 rotation angle change) and the piston motion equation to calculate the real-time working volume, and then draw the indicator diagram.

[0081] This step specifically involves: establishing a reasonable indicator diagram test scheme, and using a combination of hardware acquisition and mathematical calculation to obtain the real-time pressure and volume inside the cylinder. Specific implementation details are as follows:

[0082] Sensor layout and installation:

[0083] Strain gauges are attached to the surface of the piston rod 9 of the low-temperature high-pressure reciprocating pump to form a pressure sensing unit; an encoder 7 is installed on the transmission crankshaft 6 as a position sensing unit.

[0084] Data acquisition and transmission:

[0085] The strain signal output by the full-bridge circuit composed of strain gauges is acquired by a data acquisition instrument and communicated with an industrial computer via a network cable. The industrial computer runs the test software, receives and outputs the acquired piston rod 9 strain data directly on the interface in real time, and saves the acquired data to the hard drive of the industrial computer in real time for subsequent processing.

[0086] Real-time cylinder pressure identification and calibration:

[0087] Based on the collected strain data of piston rod 9, the industrial control computer identifies the real-time cylinder pressure through a preset mechanical model. To ensure measurement accuracy, a high-precision pressure sensor is installed at the pump's discharge outlet during the test. The standard pressure data measured by this sensor is compared in real time with the cylinder pressure calculated from the strain of piston rod 9, thereby verifying and correcting the accuracy of the strain identification model.

[0088] Real-time working volume conversion:

[0089] The industrial control computer uses the crankshaft 6 rotation angle change data collected by encoder 7 and the piston motion equation (i.e. the motion law of crank connecting rod 8 mechanism) to calculate the position of the piston in the hydraulic cylinder in real time, and then obtains the corresponding real-time working volume of the hydraulic cylinder.

[0090] Indicator diagram generation:

[0091] Using the real-time identified cylinder pressure as the ordinate and the real-time calculated working volume as the abscissa, a pressure-volume (PV) relationship curve is constructed in the industrial control computer testing software to draw a complete indicator diagram.

[0092] Step 5: Determine the first working volume of the cylinder corresponding to the closing point of the inlet valve based on the estimated or measured closing hysteresis angle of the inlet valve; for the point in the discharge stroke of the indicator diagram where the cylinder pressure equals the critical pressure, determine the starting point of the compression stage on the indicator diagram based on the intrinsic relationship between the measured slope of the indicator diagram at that point and the isothermal compression slope and the adiabatic compression slope, and record the second working volume of the cylinder corresponding to the starting point of the compression stage.

[0093] This step specifically involves selecting the area between the inlet valve closing point and the compression stage starting point as the measurement range, based on the characteristics of the indicator diagram.

[0094] Vaporization loss rate is an important indicator reflecting the degree of vaporization inside the liquid cylinder. It is defined as the ratio of the gas phase volume to the total gas and liquid phase volume inside the cylinder at the end of liquid feeding. To measure the vaporization loss rate, this study establishes a measurement method based on the lag in the compression stage in the indicator diagram.

[0095] The working volume of the liquid cylinder corresponding to the liquid inlet valve closing point is This can be determined by combining the inlet valve displacement curve measured by the inlet valve rod displacement sensor. The working volume of the cylinder corresponding to the starting point of the compression stage is... The accurate selection of this point is crucial for the precision of vaporization loss rate measurement. Because a slight increase in cylinder temperature during liquefaction can lead to a slight increase in cylinder pressure, while... After that point, the cylinder pressure will rise rapidly again as the piston moves upward. Therefore, to ensure... The accuracy of point selection requires identification using objective mathematical features. Before plotting the dynamometer card using cylinder pressure data from a cryogenic high-pressure reciprocating pump, signal preprocessing is performed using cylinder pressure noise signal filtering and cylinder pressure curve smoothing algorithms; a median filtering algorithm is used to eliminate low-frequency stray signals; and then a five-point cubic smoothing method is used to obtain the cylinder pressure curve of one cycle of the dynamometer card. Since the dynamometer card still has burrs, the curve is first fitted to obtain a smooth dynamometer card curve. The dynamometer card shows a variable process curve from the inlet valve closing point to the starting point of the compression stage. Figure 6 A comparison is given between the isotherm, adiabatic curve and the actual indicator curve at an inlet pressure of 0.4854 MPa and an inlet temperature of 93.14 K. The curve lies between the isotherm and the adiabatic curve.

[0096] In practical engineering, the starting point of the compression stage can be determined by taking different values ​​based on the adiabatic compression efficiency of different products within the allowable error range of the project. That is, a slope between the isothermal slope and the adiabatic slope can be selected as the starting criterion.

[0097] For example, when the slope at the critical pressure point lies between the isothermal compression slope and the adiabatic compression slope, the point on the indicator curve where the slope is equal to that in the isothermal case is selected as the starting point of the compression stage. At this point, since the system is in thermodynamic equilibrium and the pressures of the gas and liquid phases are equal, the expression for the slope in the isothermal case of the liquid phase can be obtained:

[0098] (5)

[0099] In the formula, is the liquid phase pressure; This refers to the working volume inside the cylinder; It is the isothermal compression modulus; The density of the liquid phase of the cryogenic fluid; The molar gas constant; The thermodynamic temperature of the cryogenic fluid inside the cylinder; The dimensionless residual Helmholtz free energy; For density comparison,

[0100] The critical density of the cryogenic fluid; It is the molar mass.

[0101] When the absolute value of the slope at the critical pressure point is greater than the absolute value of the adiabatic compression slope, the point on the indicator curve where the slope is equal to the adiabatic curve is selected as the starting point of the compression stage. This is combined with the differential equation of entropy under adiabatic conditions:

[0102]

[0103] The slope expression under the adiabatic shape of the liquid phase can be obtained:

[0104] (7);

[0105] In the formula, This refers to the total mass of the liquid phase. This refers to the specific isochoric heat capacity of a cryogenic fluid. For temperature comparison, This is the critical temperature of the cryogenic fluid.

[0106] Since the total mass remains constant during compression, based on the pressure at the starting point... volume temperature The initial density of the liquid phase can be determined. and total mass Further demonstration through practical application

[0107] Points in the diagram The coordinates can determine the density at that point. Combining the state equations modified for cryogenic fluids and high pressure, we obtain the point... temperature Based on its thermodynamic state, the slope at that point can be calculated using equations (1) and (3). For example, for liquid nitrogen, one could consider... The state equation, due to its nonlinear characteristics, requires the use of Newton's iteration method to iteratively solve for the temperature at the measured point. Until the error To achieve the required working accuracy, the slope at a given point is calculated after the thermodynamic state is determined. This formula compares the slope of the isothermal liquid phase calculated using the formula with the slopes at various points obtained by differentiating the actual indicator curve. This allows the location of the point on the indicator curve with the same slope, which is then used as the starting point of the compression stage.

[0108] Step 6: Determine the inlet pressure using the inlet pipeline pressure sensor, and obtain the inlet temperature directly or indirectly using the inlet pipeline temperature sensor. Calculate the saturated gas phase density and saturated liquid phase density of the cryogenic fluid under the inlet pressure using the saturated thermodynamic property relationship of the cryogenic fluid.

[0109] This step specifically involves: based on the inlet pressure and inlet temperature, calling the physical property database for table lookup and interpolation, or calculating using the saturated cryogenic fluid state equation.

[0110] For example, by combining the law of conservation of mass with the equation of state for saturated cryogenic fluids, a mathematical model can be constructed to calculate the vaporization loss rate, specifically:

[0111] ;

[0112] Assume the clearance volume of the hydraulic cylinder is vaporization loss rate The ratio of the gas phase volume to the liquid phase volume within the cylinder. The relationship between them is:

[0113] (8);

[0114] In the formula, the saturated gas phase density of the cryogenic fluid is... With saturated liquid density It can be calculated using the equation of state for saturated cryogenic fluids. The equation of state is shown in equations (9) to (11):

[0115]

[0116] In equations (9) to (11), These are the inlet pressure and the inlet temperature, respectively. It can be measured by the pressure sensor in the inlet pipeline; These are the critical pressure, critical temperature, and critical density of the cryogenic fluid, respectively. Let be a constant in the equation. We can obtain the result by solving equation (9). Further calculate Substituting into equations (10) and (11), the vaporization loss rate can be calculated. Required The obtained And the measured Substituting into equation (8), the vaporization loss rate at the hydraulic end of the cryogenic high-pressure reciprocating pump can be calculated. .

[0117] Step 7: Based on the clearance volume of the liquid cylinder, and using the law of conservation of mass combined with the working volume of the first liquid cylinder, the working volume of the second liquid cylinder, the saturated gas phase density, and the saturated liquid phase density, construct a formula for calculating the vaporization loss rate at the hydraulic end.

[0118] This step specifically involves: Based on the law of conservation of mass, this step constructs a mathematical model to solve for the degree of vaporization by combining the thermodynamic parameters of the inlet valve closed state and the compression initiation state. Specific implementation details are as follows:

[0119] 1. Parameter Acquisition:

[0120] Obtain the working volume of the first liquid cylinder corresponding to the liquid inlet valve closing point determined in step 5, and denot it as... The working volume of the second hydraulic cylinder corresponding to the starting point of the compression stage is denoted as... Simultaneously, obtain the saturated gas phase density at the inlet pressure calculated in step 6. and saturated liquid phase density and the known clearance volume of the hydraulic cylinder. .

[0121] 2. Establish the mass conservation equation:

[0122] Assuming the pump valve operates without leakage, according to the law of conservation of mass, the moment the inlet valve is fully closed (corresponding to the volume) The total mass of the fluid in the cylinder should be equal to the mass at the start of the compression phase (corresponding to the volume). The total mass of the fluid inside the cylinder. At the moment the inlet valve is closed, the cylinder is in a gas-liquid two-phase mixture state. Assume that the ratio of the gas phase volume to the liquid cylinder volume at this moment is... The gas phase volume is The liquid phase volume is The corresponding masses are the gas phase masses. and liquid phase mass Therefore, the total mass equation at the inlet valve closing point is established, and an equal relationship is established with the fluid mass state at the compression starting point (as shown in formula (1)).

[0123] 3. Solve for the gas phase volume ratio:

[0124] Solving the above equations simultaneously, we can find the known parameters. Substituting the values ​​and solving the equation yields the ratio of the gas phase volume to the liquid cylinder volume at the moment the inlet valve closes. (As shown in formula (2)).

[0125] 4. Calculate the vaporization loss rate:

[0126] Based on the obtained gas phase volume ratio and the clearance volume of the liquid cylinder Using the definition and calculation formula of vaporization loss rate (as shown in formula (8)), the vaporization loss rate of the hydraulic end of the low-temperature high-pressure reciprocating pump is finally calculated. This loss rate reflects the degree of effective volume loss caused by vaporization inside the cylinder at the end of the liquid inlet process.

[0127] Furthermore, comparative experiments were conducted to verify the feasibility of omitting the displacement sensor of the inlet valve, specifically:

[0128] The vaporization test method based on the dynamometer card includes the measurement of the inlet valve displacement, which requires an additional low-temperature displacement sensor 2 mounting bracket outside the inlet valve seat. Furthermore, the low-temperature displacement sensor 2 is typically quite expensive. However, in engineering applications, it is often desirable to minimize the machining of the test fixture and reduce testing costs. Therefore, this paper explores the possibility of omitting the inlet valve displacement sensor. For the tests conducted in this paper, the vaporization loss rate measurement results under different discharge pressures, ignoring and considering the inlet valve closing hysteresis, are compared... Figure 8 As shown. From Figure 8As can be seen, the two exhibit good consistency, with a maximum absolute error of 1.22%, which meets engineering accuracy requirements. Therefore, this method can save costs by omitting the inlet valve displacement sensor, making it more competitive.

[0129] Furthermore, the specific logic for determining the starting point of the compression stage in step 5 based on the intrinsic relationship between the measured dynamometer card slope and the isothermal compression slope and adiabatic compression slope is as follows:

[0130] If the absolute value of the slope of the measured indicator diagram at the critical pressure point is between the absolute value of the isothermal compression slope and the absolute value of the adiabatic compression slope, then for the indicator diagram segment where the cylinder pressure is less than the critical pressure during the discharge stroke, the point where the absolute value of the curve slope is greater than or equal to the absolute value of the isothermal compression slope and the working volume is the largest is selected as the starting point of the compression stage.

[0131] If the absolute value of the slope of the measured indicator diagram at the critical pressure point is greater than the absolute value of the slope of the adiabatic compression, then for the indicator diagram segment in the discharge stroke where the cylinder pressure is less than the critical pressure, the point where the absolute value of the curve slope is greater than or equal to the absolute value of the slope of the adiabatic compression and the working volume is the largest is selected as the starting point of the compression stage.

[0132] Furthermore, in step 6, the specific method for obtaining the saturated gas phase density and saturated liquid phase density is as follows:

[0133] Based on the inlet pressure and inlet temperature, the values ​​are obtained by calling the physical property database for table lookup and interpolation, or by using the saturated cryogenic fluid state equation.

[0134] Furthermore, in step 6, the formulas for calculating the saturated gas phase density and saturated liquid phase density using the saturated cryogenic fluid state equation are as follows:

[0135] ;

[0136] In the formula, These are the inlet pressure and the inlet temperature, respectively. It can be measured by the pressure sensor in the inlet pipeline; These are the critical pressure, critical temperature, and critical density of the cryogenic fluid, respectively. is a constant in the equation.

[0137] Furthermore, the mathematical model constructed in step 7 is as follows: When the inlet valve is completely closed, the ratio of the gas phase volume to the liquid cylinder volume is: The volumes of the gas phase and the liquid phase are respectively The saturated gas phase density and saturated liquid phase density at the inlet pressure are respectively Assuming no leakage in the pump valve, the mass conservation equations for the inlet valve closing point and the compression stage starting point are:

[0138]

[0139] Solve the equation and combine it with the clearance volume. Calculate vaporization loss rate .

[0140] Furthermore, step 4 includes a signal preprocessing step before drawing the indicator diagram:

[0141] For example, a median filtering algorithm is used to eliminate low-frequency spurious signals; a five-point cubic smoothing method is used to smooth and reduce noise in the filtered cylinder pressure curve; and the processed indicator curve is fitted to obtain a smooth indicator curve.

[0142] Furthermore, in step 1, the relationship model between the closing hysteresis angle of the inlet valve and the measurement error of the vaporization loss rate is as follows:

[0143] ;

[0144] In the formula, This indicates the absolute error in measuring the vaporization loss rate, ignoring the hysteresis of the inlet valve closing. This indicates the maximum working volume of the hydraulic cylinder. This is due to the volume loss caused by the delayed closing of the inlet valve. For the stroke volume, The clearance volume ratio, The hysteresis angle for closing the inlet valve.

[0145] Furthermore, the isothermal compression slope and the adiabatic compression slope are calculated as follows:

[0146] Based on the pressure, temperature, and relative density at the critical pressure point, the result is calculated using the dimensionless residual Helmholtz free energy and its partial derivatives with respect to relative temperature and relative density, combined with the formula for the isothermal compressibility modulus of the liquid phase and the differential equation for entropy under adiabatic conditions.

[0147] Furthermore, in step 3, the installation method of the low-temperature displacement sensor 2 is as follows:

[0148] A low-temperature displacement sensor mounting bracket 3 is provided on the outer surface of the inlet valve seat 1. The low-temperature displacement sensor 2 is mounted on the bracket. The sensor's signal lead is led out to the external environment through a branch pipe of a three-way pipe 4 via the return steam pipeline. A lead sealing joint 5 is provided at the outlet end of the branch pipe.

[0149]

[0150]

[0151] In summary, this method overcomes the limitations of conventional methods under low temperature and high pressure conditions, and achieves high measurement accuracy.

[0152] Existing technologies rely on the pressure abrupt change inflection point under the assumption of incompressibility of fluids at room temperature to identify the compression initiation point. This invention, however, creatively proposes a backtracking identification algorithm based on "critical pressure point" and "slope comparison logic (isothermal / adiabatic)" to address the challenge of inflection point disappearance and curve smoothing caused by the strong compressibility of cryogenic fluids. This method can accurately pinpoint the starting point of the compression stage, eliminating identification errors caused by nonlinear thermophysical properties, thereby achieving accurate measurement of the vaporization loss rate.

[0153] It has excellent anti-interference ability and the measurement results are reliable.

[0154] This invention abandons the simplified ideal gas assumption and uses the saturated cryogenic fluid state equation based on the dimensionless residual Helmholtz free energy to solve for the saturated gas-liquid phase density. This high-precision thermodynamic model fully considers the complex nonlinear characteristics near the critical point of cryogenic fluids, making this method applicable not only to liquid nitrogen but also to various cryogenic media such as liquid hydrogen, liquid oxygen, and LNG, thus possessing broad engineering applicability.

[0155] Optimized signal processing techniques have improved the accuracy of feature extraction.

[0156] Before plotting the dynamometer card, the original strain signal was preprocessed using median filtering and a five-point cubic smoothing method. This effectively eliminated the influence of high-frequency noise and low-frequency stray signals, and a smooth dynamometer card was obtained through curve fitting. This provided a high-quality data foundation for subsequent slope calculation and feature point extraction, further ensuring the stability of the measurement results.

[0157] It provides a low-cost, low-barrier engineering implementation plan.

[0158] This invention not only provides a standard measurement scheme based on high-precision sensors, but also derives a mathematical model of the relationship between the closing hysteresis angle of the inlet valve and the measurement error. Based on this model, engineers can, while meeting accuracy requirements (typically with an error of <1.5%), justifiably omit the expensive cryogenic displacement sensor 2 and its complex installation fixtures, and directly use the crankshaft 6 rotation angle for calculation. This feature greatly reduces the hardware cost and implementation difficulty of the system, and has strong industrial application value.

[0159] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for measuring the vaporization loss rate at the hydraulic end of a cryogenic high-pressure reciprocating pump based on an indicator diagram, characterized in that, Includes the following steps: Step 1: Establish an expression for the measurement error of vaporization loss rate with the closing hysteresis angle of the inlet valve as the independent variable; Step 2: Based on the pump's structure and process parameters, estimate the approximate level of the closing lag angle of the inlet valve of the low-temperature high-pressure reciprocating pump using the estimation formula for the closing lag angle of the inlet valve. Substitute this into the vaporization loss rate measurement error expression established in Step 1 to estimate the level of vaporization loss rate measurement error caused by the closing lag of the inlet valve. Step 3: When the estimated vaporization loss rate measurement error meets the measurement accuracy requirements, The estimated value of the closing hysteresis angle of the inlet valve can be used as its actual value, or the influence of the closing hysteresis of the inlet valve on the vaporization loss rate measurement result can be ignored directly. In this case, it is not necessary to measure the actual closing hysteresis angle of the inlet valve. Otherwise, a low-temperature displacement sensor is used to measure the real-time opening of the inlet valve, and a crankshaft encoder and displacement sensor are used to measure the real-time phase or position of the piston. The actual closing hysteresis angle of the inlet valve is determined by combining the real-time opening of the inlet valve and the real-time phase or position of the piston. Step 4: Collect relevant signals of piston rod load and real-time phase or position of piston. Measure piston rod load using force measuring elements or calculate piston rod load by measuring parameters such as piston rod strain and real-time power of drive motor. Based on this, obtain real-time cylinder pressure based on piston rod load identification. Combine the real-time phase or position change of piston with piston motion equation to calculate real-time working volume, so as to draw indicator diagram. Step 5: Determine the first working volume of the cylinder corresponding to the closing point of the inlet valve based on the estimated or measured closing hysteresis angle of the inlet valve; for the point in the discharge stroke of the indicator diagram where the cylinder pressure equals the critical pressure, determine the starting point of the compression stage on the indicator diagram based on the intrinsic relationship between the measured slope of the indicator diagram at that point and the isothermal compression slope and the adiabatic compression slope, and record the second working volume of the cylinder corresponding to the starting point of the compression stage. Step 6: Determine the inlet pressure through the inlet pipeline pressure sensor, obtain the inlet temperature directly or indirectly through the inlet pipeline temperature sensor, and calculate the saturated gas phase density and saturated liquid phase density of the cryogenic fluid under the inlet pressure using the saturated thermodynamic property relationship of the cryogenic fluid. Step 7: Based on the clearance volume of the liquid cylinder, and using the law of conservation of mass combined with the working volume of the first liquid cylinder, the working volume of the second liquid cylinder, the saturated gas phase density, and the saturated liquid phase density, construct a formula for calculating the vaporization loss rate at the hydraulic end.

2. The method according to claim 1, characterized in that, In step 1, the relationship model between the closing hysteresis angle of the inlet valve and the measurement error of the vaporization loss rate is as follows: ； In the formula, This indicates the absolute error in measuring the vaporization loss rate, ignoring the hysteresis of the inlet valve closing. For the stroke volume, The clearance volume ratio, The hysteresis angle for closing the inlet valve.

3. The method according to claim 1, characterized in that, In step 3, the installation method of the low-temperature displacement sensor is as follows: A low-temperature displacement sensor mounting bracket 4 is installed on the outer surface of the inlet valve seat. The low-temperature displacement sensor is installed on the bracket. The sensor's signal lead is led out to the external environment through the return steam pipeline and the lead is extended through the branch pipe of the tee pipe. A lead sealing joint is provided at the outlet end of the branch pipe.

4. The method according to claim 1, characterized in that, Step 4, before drawing the indicator diagram, also includes a signal preprocessing step: Spurious noise in the cylinder pressure signal is eliminated, and the cylinder pressure curve is smoothed and denoised to obtain a smooth indicator curve for subsequent slope calculation.

5. The method according to claim 1, characterized in that, The specific logic for determining the starting point of the compression stage in step 5, based on the intrinsic relationship between the measured dynamometer card slope and the isothermal compression slope and adiabatic compression slope, is as follows: If the absolute value of the slope of the measured indicator diagram at the critical pressure point is between the absolute value of the isothermal compression slope and the absolute value of the adiabatic compression slope, then for the indicator diagram segment where the cylinder pressure is less than the critical pressure during the discharge stroke, the point where the absolute value of the curve slope is greater than or equal to the absolute value of the isothermal compression slope and the working volume is the largest is selected as the starting point of the compression stage. If the absolute value of the slope of the measured indicator diagram at the critical pressure point is greater than the absolute value of the slope of the adiabatic compression, then for the indicator diagram segment in the discharge stroke where the cylinder pressure is less than the critical pressure, the point with the absolute value of the curve slope greater than or equal to the absolute value of the slope of the adiabatic compression and the largest working volume is selected as the starting point of the compression stage.

6. The method according to claim 5, characterized in that, The isothermal compression slope and adiabatic compression slope are calculated in the following way: Based on the pressure, temperature, and relative density at the critical pressure point, the result is calculated using the dimensionless residual Helmholtz free energy and its partial derivatives with respect to relative temperature and relative density, combined with the formula for the isothermal compressibility modulus of the liquid phase and the differential equation for entropy under adiabatic conditions.

7. The method according to claim 1, characterized in that, The specific method for obtaining the saturated gas phase density and saturated liquid phase density in step 6 is as follows: Based on the inlet pressure and inlet temperature, the values ​​are obtained by calling the saturated property database for table lookup and interpolation, or by using the saturated cryogenic fluid state equation.

8. The method according to claim 7, characterized in that, In step 6, the formulas for calculating the saturated gas phase density and saturated liquid phase density using the saturated cryogenic fluid state equation are as follows: ; In the formula, and These are the inlet pressure and the inlet temperature, respectively. It can be measured by the pressure sensor in the inlet pipeline; These are the critical pressure, critical temperature, and critical density of the cryogenic fluid, respectively. is a constant in the equation.

9. The method according to claim 1, characterized in that, The vaporization loss rate calculation formula constructed in step 7 is: when the inlet valve is completely closed, the ratio of the gas phase volume in the cylinder to the liquid cylinder volume is: The volumes of the gas phase and the liquid phase are respectively The saturated gas phase density and saturated liquid phase density at the inlet pressure are respectively The mass conservation equations for the inlet valve closing point and the compression stage starting point are: Solve the equation and combine it with the clearance volume. Calculate vaporization loss rate The formula for calculation is: 。

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