A transient extrapolation method for gordon-type heat flow meters based on a physical model

Abstract

This invention relates to a method for extrapolating transient measurements from a Gordon heat flux meter, comprising two main steps: pre-test calibration and post-test data processing. The pre-test calibration process uses laser or other means to test the heat flux meter and obtain key parameters such as the output coefficient and response time. The post-test data processing mainly includes steps such as data pre-pruning, data pre-fitting, data linearization, nonlinear point removal, data fitting, and steady-state heat flux prediction. By introducing this invention, steady-state heat flux parameters can be predicted even before the heat flux meter's output parameters have stabilized. This effectively solves the problem of large heat flux measurement errors caused by the extremely short working time and limited available data in thruster tests, which result in the heat flux meter not yet being balanced. Compared to other data extrapolation methods, this application fully considers the actual physical model of the heat flux meter and combines statistical methods to efficiently and with high confidence extrapolate the range of the true heat flux.

Description

Technical Field

[0001] This invention relates to the field of spacecraft ground testing technology, and to a technique for predicting the equilibrium value of a transient heat flow meter in spacecraft testing using unbalanced data. In particular, it relates to a transient extrapolation method for a Gordon heat flow meter based on a physical model. Background Technology

[0002] In spacecraft testing, heat flow meters are one of the important sensors for measuring heat flow incident on and absorbed by the spacecraft surface. Gordon heat flow meters are widely used in high-temperature and high-heat-flow simulation tests of spacecraft, such as reentry simulation and thruster ignition tests.

[0003] In recent years, with the development of deep space exploration and other fields, planetary surface return vehicles often need to ignite and take off from the surface of extraterrestrial planets. The high-thrust engines generate a heat flux of tens of kilowatts per square meter on the surfaces of components such as landers and ascent vehicles. This special environment was not typically found in previous Earth-orbiting spacecraft. In order to measure the large heat flux generated by the engine plume on the probe surface, tests are often conducted in simulated space environments.

[0004] However, due to limitations in the experimental environment, measuring engine heat flux often presents several challenges. First, when simulating engine ignition inside a container in a ground-based space environment, pressure maintenance relies on a vacuum system. This means that the engine plume gas can only be adsorbed using multiple vacuum pumps and cryogenic cooling plates. The adsorption capacity is often insufficient to meet the gas discharge requirements under steady-state engine operation. Within a few hundred milliseconds, the pressure can rise from 0.01 Pa to around 10 Pa. Changes in back pressure often alter the engine's operating state, leading to significant differences between the experimental and actual operation in an infinitely large space. Second, for Gordon heat flux meters, the time constant is typically around tens to hundreds of milliseconds. Within one time constant, only 63% of the heat flux is usually achieved, while it is only at seven times the time constant that 99.9% of the actual heat flux value is reached. Therefore, when simulating the ignition process of a high-power engine in a vacuum and cryogenic environment, the experimental pressure often reaches the 10 Pa level by the time the heat flux meter reaches equilibrium, rendering the measured heat flux at this point meaningless. Furthermore, using the initial data introduces significant errors because the heat flux meter is not yet stable. We can only use the data from the heat flow meter, which is not yet stable, to predict its possible output when it is stable.

[0005] Therefore, designing and inventing a transient extrapolation method for Gordon heat flow meters based on a physical model has positive practical significance. Summary of the Invention

[0006] The purpose of this invention is to solve the above-mentioned problems by proposing a transient extrapolation method for Gordon heat flow meters based on a physical model.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] This invention provides a method for extrapolating transient measurements from a Gordon heat flow meter, comprising the following steps:

[0009] S1: Pre-test calibration, using laser and other means to test the heat flow meter and obtain key parameters such as the output coefficient and response time of the heat flow meter;

[0010] S2: Post-experiment data processing, using non-equilibrium data from the Gordon heat flow meter to predict data after equilibrium is reached, to address the problem of short test time and inability of the heat flow meter to reach equilibrium, including the following steps:

[0011] B1: Collect experimental data;

[0012] B2: Data pre-cropping;

[0013] B3: Data prefitting;

[0014] B4: Linearization of measurement data;

[0015] B5: Non-linear point removal;

[0016] B6: Data Fitting;

[0017] B8: Steady-state heat flow prediction.

[0018] In some embodiments, the present invention further includes the following technical features:

[0019] In step S1, an approximate step heat flow is generated by means of laser or other means, and the output millivolt signal of the Gordon heat flow meter is continuously collected until the output signal stabilizes. The data curve is then fitted according to the theoretical curve. Generally, the range of calibrated heat flow is not less than the possible heat flow range in the experiment.

[0020] In step S1, the output coefficient is obtained based on the steady-state heat flux Q0 of the sensor and the sensor output signal V; then, according to the theoretical output curve... Fitting is performed, where τ is the time constant (s). The starting point of the fitting data is generally selected at least 30ms after the calibration device starts to reduce the impact of equipment startup. The ending point of the fitting data is at least 7 times the time constant to ensure that the heat flow reaches at least 99.9% of the stable heat flow.

[0021] Step B2 is performed manually. Based on the time in the experiment, the test data of the Gordon heat flow meter is cropped so that the starting point of the cropped data at least covers the start time of the experiment and the ending point of the cropped data at least covers the end time of the experiment.

[0022] The frequency of data acquisition for the tests is generally better than 100 Hz.

[0023] Step B3 is to use the current data in a relational manner. The data is automatically fitted in the form of t, where t is the independent variable time (s) and Q is the dependent variable heat flux density (W / m³). 2 The calculation is based on the collected millivolt data and output coefficients. τ is the time constant, which is set to a fixed value according to the calibration process before the experiment. t0 and C are both constants, representing the offset of the independent variable and the dependent variable, respectively, to compensate for the measurement errors of time and heat flow. Q0 is the preliminary predicted steady-state heat flow.

[0024] Step B4 is used to linearize the results of the data prefitting, specifically, according to... All data is processed in this way.

[0025] Step B5 is used to process the linearized point set (x) n ,y n The data is processed by fitting it in the form of y = ax and calculating the Euclidean distance between all points and the line y = ax. This is a second trimming of the data to remove unusable data points due to unstable test specimen characteristics or other reasons.

[0026] Step B6 is used to fit the data after the second cropping again, and the fitting formula is: Where t is the independent variable time (s), and Q is the dependent variable heat flux density (W / m³). 2 ), calculated based on the collected millivolt data and output coefficients, τ * The time constant for linear interpolation based on the initially obtained predicted steady-state heat flux Q0 is a fixed value. The independent variable offset t0, the dependent variable offset C, and the predicted heat flux Q1 are constants obtained through fitting.

[0027] Step B8 outputs the fitted Q1 value as the average value of the predicted heat flux, and outputs the 95% confidence interval of the heat flux Q1 as a reference value based on the fitted 95% CI.

[0028] In summary, due to the adoption of the above technical solutions, the beneficial effects of this invention are as follows: Based on the actual physical model and calibration parameters of the Gordon heat flow meter, this method can quickly determine the point where the engine is operating normally based on the test data of the heat flow meter in about 100ms, and quickly and accurately fit the data points that conform to the pattern, and give the confidence interval that predicts the true heat flow. It is especially suitable for heat flow tests with extremely short durations, such as engine ignition tests. Attached Figure Description

[0029] Figure 1This is a schematic diagram of an applicable heat flow meter in an embodiment of the present invention;

[0030] Figure 2 The following are the specific working steps of the pre-test calibration process in the embodiments of the present invention;

[0031] Figure 3 The following are the specific steps for data processing after the experiment in this embodiment of the invention;

[0032] Figure 4 This is a data example of the pre-test calibration process in an embodiment of the present invention;

[0033] Figure 5 This is a schematic diagram of the data prefitting, data linearization, and nonlinear point removal processes in the post-experiment data processing of this invention.

[0034] Figure 6 This refers to the experimental data fitting and steady-state heat flow prediction process in the post-experiment data processing of this invention embodiment.

[0035] Wherein, 101 is the direction of incident heat flow, 102 is constantan foil, 103 is copper pillar, 104 is copper wire, 201 is engine start-up section, 202 is engine stable operation section, 203 is engine data deviation section, 301 is the upper limit of predicted heat flow, 302 is the average value of predicted heat flow, 303 is the lower limit of predicted heat flow, 401 is the measured heat flow data, 402 is the linearization process, 403 is nonlinear point group 1, 404 is the available data, 405 is nonlinear point group 2, 406 is the lower limit of clipping, and 407 is the upper limit of clipping. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] Please see Figure 1This application describes a transient extrapolation method for a Gordon heat flow meter based on a physical model. The cross-sectional view of the Gordon heat flow meter is shown, where 101 represents the incident heat flow direction, i.e., the direction of the heat flow generated by the engine plume; 102 is a constantan foil, i.e., the sensing element; 103 is a copper column, typically made of pure copper, connected to the constantan foil 102; some heat flow meters also have insulating material inside the copper column; and 104 is a copper wire soldered to the center of the constantan foil 102. When the heat flow is incident along the direction 101, the constantan foil surface absorbs the external heat flow. Since the outer part connected to the copper column 103 can be considered constant temperature for a short time, the temperature at the center of the constantan foil 102 will be significantly higher than the surrounding temperature. A one-to-one correspondence can be established between the temperature difference between the center and the edge and the magnitude of the incident heat flow. Meanwhile, constantan foil 102 and copper pillar 103 form a thermocouple, and constantan foil 102 and copper wire 104 also form a thermocouple. By measuring the millivolt-level electromotive force between the two thermocouples with a measuring instrument, the temperature difference between the center and edge of the constantan foil can be measured, and the magnitude of the absorbed heat flux density can be indirectly characterized.

[0038] Please see Figure 2 This application outlines a specific pre-experiment calibration procedure for a transient extrapolation method for a Gordon heat flux meter based on a physical model, wherein:

[0039] A0: Calibration begins, preparing all test hardware and software;

[0040] A1: Start collecting millivolt signals, that is, turn on the measuring instrument, such as a digital multimeter, millivolt transmitter, etc., to collect the millivolt signals of the Gordon heat flow meter. The collection frequency is generally not lower than 100 Hz.

[0041] A2: Applying heat flux, generally by means of lasers or other means, to apply a fast and stable heat flux to the heat flux meter that is close to a step response. Multiple heat fluxes are usually required, and the coverage area is not less than the measurement range in the test.

[0042] A3: Wait for the acquired signal to stabilize. Since the Gordon heat flow meter uses the principle of temperature difference measurement to characterize the magnitude of heat flow, it often takes hundreds of milliseconds to several seconds to form a stable temperature difference. Therefore, it is necessary to continuously acquire data until the measurement data stabilizes.

[0043] A4: Determine whether all operating conditions have been completed, and continue until all heat flux curve calibration work is completed according to the test plan;

[0044] A5: The sensor coefficient is calculated based on the steady-state signal. The sensor output coefficient a = Q0 / V can be obtained by applying the steady-state heat flux Q0 to the calibration equipment and the steady-state output V of the sensor.

[0045] A6: Fitting time constant τ, based on the obtained sensor output coefficients, can be calculated according to... The transient output curve of the sensor is fitted in the form of Q, where Q is the heat flux (W / m) corresponding to the measured millivolt electromotive force at each moment. 2 , where is the dependent variable. t is time (s), and is the independent variable. After fitting using methods such as least squares, the time constant τ can be obtained.

[0046] A7: Evaluate the standard error. Since the calibration equipment can generate a heat flow that approximates a step signal, the data in the first tens of milliseconds is often different from the theoretical step and is a linear rising process. Therefore, the fitting results should be evaluated. Generally, the standard error of τ should be within 1% of the mean of τ. If the standard error exceeds the range, the data should be pruned to remove the linear rising segment and refitted until the standard error meets the requirements.

[0047] A8: End, save all calibration data.

[0048] Please see Figure 3 The specific workflow for post-experiment data processing of the transient extrapolation method for a Gordon heat flux meter based on a physical model, as described in this application, is as follows:

[0049] B0: Start, which means starting the data acquisition program of the Gordon heat flow meter, setting the test object, and collecting data;

[0050] B1: Collect experimental data, including acquiring and storing signals such as heat flow, ambient temperature, and pressure;

[0051] B2: Data pre-pruning. Based on the ambient temperature range, the usable range of the data is determined, and the data is pre-pruned. Taking a spacecraft engine test as an example, if the normal operating pressure of the engine is below 5 Pa, the starting point for data pruning is before the engine starts, and the ending point for data pruning is the time point when the pressure reaches approximately 5 Pa.

[0052] B3: Data prefitting, based on the cropped data, using correlation... The data is automatically fitted in the form of t, where t is the independent variable time (s) and Q is the dependent variable heat flux density (W / m³). 2 The calculation is based on the collected millivolt data and output coefficients. τ is the time constant, which is set to a fixed value according to the calibration process before the experiment. t0 and C are both constants, representing the offset of the independent variable and the dependent variable, respectively, to compensate for the measurement errors of time and heat flow. Q0 is the preliminary predicted steady-state heat flow. The variation law of the measurement data can be preliminarily established through data prefitting.

[0053] B4: Measurement data linearization, which involves linearizing the results of data prefitting, i.e., according to... All data is processed in a linearized manner, making it easier to remove points that deviate from the pattern, thereby reducing the impact of points where the engine starts and then stabilizes, and points where pressure exceeds limits, which lead to unreliable data.

[0054] B5: Nonlinear point elimination. Based on the linearization result of the linearization process B4, the linearized point set (x) is eliminated. n ,y n The data is processed and fitted in the form of y = ax, and the Euclidean distance between all points and the line y = ax is calculated to perform a second cropping of the data. The nonlinear points at the beginning are mainly due to the unstable characteristics of the test piece, while the nonlinear points at the end are mainly due to the change in engine working state caused by excessive pressure. After the nonlinear points are extracted, the existing data points represent the performance of the engine in a stable working state in a vacuum environment.

[0055] B6: Data Fitting, used to fit the data again after the second cropping. The fitting formula is: Where t is the independent variable time (s), and Q is the dependent variable heat flux density (W / m³). 2 ), calculated based on the collected millivolt data and output coefficients, τ * The time constant τ is a fixed value, representing the linear interpolation based on the initially obtained predicted steady-state heat flux Q0. The independent variable offset t0, dependent variable offset C, and predicted heat flux Q1 are constants obtained through fitting. The interpolated time constant τ is used... * This can reduce the impact of heat flux on the temperature of constantan-sensitive tablets, thus compensating for the differences in time constants caused by changes in the physical properties of constantan tablets.

[0056] B7: Linearity judgment, fitting results, determine whether all nonlinear points have been deleted. If the linearity of the remaining points does not meet the requirements, return to the nonlinear point removal step B5 to continue removing nonlinear points.

[0057] B8: Obtain the predicted steady-state heat flux and 95% CI. Based on the data fitting results in B6, output the fitted Q1 value as the average value of the predicted heat flux, and based on the fitted 95% CI, output the 95% confidence interval of the heat flux Q1 as a reference value.

[0058] B9: Output the parameters.

[0059] Please see Figure 4 This is a data example of the pre-experiment calibration process for a transient extrapolation method for a Gordon heat flux meter based on a physical model, as described in the present invention. The figure shows data for a 300kW / m² heat flux meter. 2 ~1000kW / m 2The heat flux was tested to fully cover the possible heat flux measurement range in the experiment, so as to reduce the temperature difference of constantan plate caused by different heat flux in the experiment, which in turn affects the sensor time constant.

[0060] Please see Figure 5 This diagram illustrates the data prefitting, data linearization, and nonlinear point removal processes in the post-experiment data processing of a Gordon heat flux meter transient extrapolation method based on a physical model, according to the present invention. 401 represents the measured heat flux data, typically a set of points close to an exponential curve; 402 represents the linearized data, i.e., the measured heat flux data processed according to… The transformation produces an approximately linear set of points; 403 represents nonlinear point group 1, which is the nonlinear data selected from the linearized data 402 through the linearization process. In engine testing, this is generally caused by unstable states during engine startup and needs to be removed in the preliminary data; 405 represents nonlinear point group 2, which is the nonlinear data selected from the linearized data 402 through the linearization process. In engine testing, this is generally caused by excessive back pressure after the engine has been running for a period of time, leading to changes in the engine's operating state and needs to be removed from the preliminary data; 404 represents usable data, which is the result of removing nonlinear point group 1 at the beginning and nonlinear point group 2 at the end of the existing data; 406 and 407 are the lower and upper limits for clipping, respectively, used to remove nonlinear point group 1 and nonlinear point group 2. Figure 5 After the aforementioned processing, invalid experimental data can be eliminated, and the data can then be fitted to obtain the true heat flux value.

[0061] Please see Figure 6 This invention relates to the experimental data fitting and steady-state heat flow prediction process in the post-experiment data processing of a transient extrapolation method for a Gordon heat flow meter based on a physical model. The data used is based on… Figure 5 The data is processed through the pre-fitting, linearization, and nonlinear point removal processes. 201 represents the engine start-up phase, which has been removed in the previous steps because its operation is not yet stable. 202 represents the stable engine operating phase, which is the data used for fitting; by fitting this part of the data, the mean of Q1 and 95% CI can be obtained. 203 represents the engine data deviation phase, i.e., data where changes in back pressure cause differences in the engine's operating state, which has been removed from the previous data.

[0062] 301 represents the upper limit of the predicted heat flux, i.e., the upper limit of the 95% CI obtained from the fitted data; 302 represents the average predicted heat flux, i.e., Q1; and 303 represents the lower limit of the predicted heat flux, i.e., the lower limit of the 95% CI obtained from the fitted data. Through this process, the actual heat flux range with a 95% confidence level can be obtained, thus predicting the steady-state heat flux in the experiment.

[0063] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for extrapolating transient measurements from a Gordon heat flow meter, comprising the following steps: S1: Pre-test calibration, using laser to test the heat flow meter to obtain key parameters such as the output coefficient and response time of the heat flow meter; S2: Post-experiment data processing, using non-equilibrium data from the Gordon heat flow meter to predict data after equilibrium is reached, to address the problem of short test time and inability of the heat flow meter to reach equilibrium, including the following steps: B1: Collect experimental data; B2: Data pre-cropping; B3: Data prefitting, based on the current data, using correlation... The data is automatically fitted in the form of [formula], where t Let time be the independent variable. Q The dependent variable is heat flux density (W / m³). 2 Calculations are performed based on the collected millivolt data and output coefficients. The time constant is set to a fixed value according to the calibration process before the experiment. t 0、 C All are constants, representing the offsets of the independent and dependent variables, respectively, to compensate for measurement errors in time and heat flow. Q 0 represents the initially obtained predictive steady-state heat flux; B4: Measurement data linearization, used to linearize the results of data prefitting, specifically, according to... All data is processed in this way; B5: Nonlinear point removal, used for linearized point sets ( x n ,y n Process it according to y=ax Fit the line in the form of a given line and calculate the relationship between all points and the line. y=ax The Euclidean distance is used to perform a second cropping of the data, filtering out unusable data points due to unstable test specimen characteristics; B6: Data Fitting; used to fit the data again after the second cropping, the fitting formula is: ,in t Let time be the independent variable. Q is Dependent variable: heat flux density (W / m³) 2 Calculations are performed based on the collected millivolt data and output coefficients. Based on the preliminary obtained predictive steady-state heat flow Q The time constant of the linear interpolation is a fixed value, and the independent variable is offset. t 0 dependent variable offset C、 Predicting heat flow Q 1 represents a constant obtained through fitting; B7: Linearity judgment. Determine whether all nonlinear points have been deleted. If the linearity of the remaining points does not meet the requirements, return to the nonlinear point elimination step B5 and continue to eliminate nonlinear points. B8: Steady-state heat flow prediction, output obtained through fitting. Q The value of 1 is used as the average value of the predicted heat flux, and the heat flux is output based on the 95% CI obtained from the fitting. Q The 95% confidence interval of 1 is used as a reference value.

2. The method according to claim 1, characterized in that, In step S1, an approximately step-like heat flow is generated by laser, and the output millivolt signal of the Gordon heat flow meter is continuously acquired until the output signal stabilizes, and the data curve is fitted according to the theoretical curve.

3. The method according to claim 1, characterized in that, In step S1, based on the initially obtained predicted steady-state heat flow... Q 0 and sensor output signal V The output coefficients are obtained; then, according to the theoretical output curve... Fit, where Let be the time constant in seconds.

4. The method according to claim 1, characterized in that, Step B2 is performed manually. Based on the time in the experiment, the test data of the Gordon heat flow meter is cropped so that the starting point of the cropped data at least covers the start time of the experiment and the ending point of the cropped data at least covers the end time of the experiment.

5. The method according to claim 4, characterized in that, The frequency of the test data acquisition is greater than 100 Hz.

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