A thin-film platinum resistance dynamic total temperature probe for measuring two-dimensional flow field in narrow interstage

Abstract

The present application belongs to the technical field of dynamic temperature test, and particularly relates to a thin-film platinum resistance dynamic total temperature probe for measuring a two-dimensional flow field between narrow stages, comprising a probe head, a positioning block, a thin-film platinum resistance, a probe support rod, a lead hole and a circular pipeline. The probe head and the probe support rod are both cylindrical, the probe support rod is internally provided with a circular pipeline, the tail of the probe support rod is additionally provided with a positioning block, the cylindrical surface of the probe head is provided with three lead holes, the thin-film platinum resistance is mounted on the lead holes, and the leads of the thin-film platinum resistance are connected with external collection equipment through the lead holes and the circular pipeline. Compared with the existing temperature probe, the present application can measure the total temperature, static temperature, deflection angle and Mach number of the flow field between narrow stages of turbomachinery varying with time after calibration in a wind tunnel, and provides a high-efficiency and accurate means for measuring two-dimensional unsteady flow field parameters in the experiment of turbomachinery between narrow stages.

Description

Technical Field

[0001] This invention belongs to the field of dynamic temperature testing technology, specifically relating to a thin-film platinum resistance dynamic total temperature probe for measuring two-dimensional flow fields between narrow stages. It is suitable for measuring transient information of two-dimensional unsteady flow fields between narrow stages of turbomachinery. Its core lies in rapidly and accurately measuring and monitoring the transient total temperature, static temperature, deflection angle, and Mach number changes of two-dimensional unsteady flow fields between narrow stages of turbomachinery. Background Technology

[0002] The interstage space in turbomachinery is narrow, especially the interstage clearance in later stages, which is even smaller. Due to the sweeping effects of blade wakes, leakage vortices, angular vortices, and other secondary flows, the interstage flow field exhibits strong unsteadiness and vorticity. This makes it extremely difficult to rapidly and accurately obtain the time-varying temperature field changes between turbomachinery stages. Researchers in turbomachinery prefer to obtain the dynamic temperature distribution and airflow direction angles between stages to validate designs and conduct flow field diagnostics, thereby improving machine performance. Therefore, to rapidly and accurately obtain the transient temperature field between turbomachinery stages, more targeted testing methods must be developed.

[0003] Currently, dynamic pressure probes are commonly used to obtain the deflection angle information of the incoming flow. However, due to the influence of the test incoming flow temperature, the maximum test incoming flow temperature for dynamic pressure probes, while ensuring accuracy, does not exceed 200℃, which greatly limits their application range. In contrast, thin-film platinum resistance temperature sensors can be used in environments up to 800℃. For the total flow temperature, thermocouple temperature sensors are often used to obtain the dynamic temperature signal of the flow field. However, due to the limited frequency, even the fine-wire thermocouple temperature sensor with the highest frequency response cannot fully meet the testing requirements of the transient temperature field at the inlet, outlet, and interstage of the impeller under special operating conditions. Moreover, compared with thin-film platinum resistance temperature sensors, thermocouples have lower accuracy. During long-term use, thermocouples may experience increased measurement errors due to material aging and thermoelectric drift, and are easily affected by environmental factors. Hot-wire temperature probes offer extremely fast thermal response times, enabling rapid capture of transient changes in temperature and flow. While typically very small and possessing high spatial resolution, their construction and maintenance are costly due to their fine wire construction. They are also prone to breakage and damage, resulting in poor durability and increased testing costs and unreliability. Furthermore, thermocouple temperature sensors and hot-wire temperature probes can only measure the total temperature, failing to capture changes in deflection and pitch angles within the high-subsonic three-dimensional unsteady flow field of turbomachinery.

[0004] Therefore, to quickly and accurately obtain the transient temperature deflection angle between compressor stages, there is an urgent need to develop a fast, high-precision testing technology that is resistant to airflow erosion, has low spatial resolution, and causes minimal interference to the flow field. This technology will enable the accurate measurement of dynamic temperature and deflection angle in unsteady flow fields, providing reliable measurement methods and technical support for the high-performance design and optimization of turbomachinery. Summary of the Invention

[0005] This invention discloses a dynamic total temperature probe for measuring a two-dimensional flow field in a narrow interstage space using a thin-film platinum resistance thermometer. The probe comprises a probe head, a positioning block, a left thin-film platinum resistance thermometer, a middle thin-film platinum resistance thermometer, a right thin-film platinum resistance thermometer, a probe support rod, a circular tube, and lead holes. Both the probe head and the probe support rod are cylindrical structures. The left, middle, and right thin-film platinum resistance thermometers are mounted on the probe head. Three non-interconnected lead holes are opened on the cylindrical surface. The left, middle, and right thin-film platinum resistance thermometers are respectively mounted on the lead holes. A circular tube is opened axially inside the probe support rod. The wires of the thin-film resistance thermometers are connected to an external data acquisition device through the lead holes and the circular tube.

[0006] During use, the resistance value of the thin-film platinum resistance thermometer changes with temperature, as shown in the following formula:

[0007] R t =R0[1+AT+BT] 2 ]

[0008] Where R0 is the resistance value at 0℃, and A and B are the graduation constants. The probe is placed in the measured flow field. Before the formal test, static calibration is performed on three thin-film platinum resistance thermometers as the temperature of the flow field changes. To achieve higher precision measurements, a standard temperature device and a standard ohmmeter are needed to calibrate the specific platinum resistance thermometer to obtain its characteristic curve, i.e., to obtain the coefficients of each term in the characteristic curve, which are used for resistance-temperature conversion during measurement. The static calibration steps are as follows: connect the thin-film platinum resistance sensor to be calibrated to a high-precision resistance meter and place it in the constant temperature bath of a dry metrology furnace, ensuring that the sensor is centered in the furnace and avoiding contact with the furnace wall. After completing the above installation preparations, turn on the dry metrology furnace, adjust to the calibration point temperature, and wait for at least 30 minutes until the sensor reaches thermal equilibrium (the sensor reading remains unchanged). The calibration temperature point should include 0℃, and temperature calibration should be performed according to the actual temperature measurement range, calibrating every 10℃.

[0009] Measuring the resistance of a thin-film platinum resistance sensor at 0°C and two other temperatures within the measurement range is called the "three-point calibration" method, which yields the following set of equations:

[0010]

[0011] Solving the system of equations simultaneously yields:

[0012]

[0013] Finally, the temperature measurement formula for platinum resistance thermometers within the calibration range is obtained:

[0014]

[0015] After the above static calibration, the calibration constants A and B, as well as the formula for calculating the measured temperature, are obtained through data processing methods.

[0016] After static calibration, a wide-range calibration was performed in the calibration wind tunnel, with a calibration speed range of Mach 0.1 to Mach 1.4 and a deflection angle range of -80° to 80°. A data processing method for a thin-film platinum resistance thermometer dynamic total temperature probe for measuring a two-dimensional flow field in narrow interstages was used to obtain calibration curves for different deflection angles and deflection coefficients, deflection angles and total temperature coefficients, and deflection angles and static temperature coefficients at each Mach number. The data processing method for this method is as follows:

[0017] Define the deflection angle coefficient:

[0018]

[0019] Define the total temperature coefficient:

[0020]

[0021] Define the static temperature coefficient:

[0022]

[0023] Where yaw is the probe rotation deflection angle, T1, T2, and T3 are the calibration temperature data of the middle, left, and right thin-film platinum resistance thermometers under different airflow deflection angles α, Tt is the total temperature of the incoming flow to the calibration wind tunnel, and Ts is the static temperature of the incoming flow to the calibration wind tunnel.

[0024] This invention provides a thin-film platinum resistance dynamic total temperature probe for measuring two-dimensional flow fields in narrow interstages. The technical problems it addresses are: first, the insufficient accuracy of existing dynamic temperature probes; second, the low frequency response of existing dynamic temperature probes due to limitations imposed by traditional dynamic temperature sensors; and third, the inability of existing dynamic temperature probes to measure deflection angle, static temperature, and Mach number.

[0025] The technical solution of this invention is:

[0026] 1. A dynamic total temperature probe for measuring a two-dimensional flow field in a narrow interstage, comprising a probe head (1), a positioning block (2), a left thin-film platinum resistor (3), a middle thin-film platinum resistor (4), a right thin-film platinum resistor (5), a probe support rod (6), a circular pipe (7), and lead holes (8), characterized in that: the probe head (1) and the probe support rod (6) are both cylindrical structures, the left thin-film platinum resistor (3), the middle thin-film platinum resistor (4) and the right thin-film platinum resistor (5) are installed on the probe head (1), and three non-interconnected lead holes (8) are opened on the cylindrical surface, the left thin-film platinum resistor (3), the middle thin-film platinum resistor (4) and the right thin-film platinum resistor (5) are respectively installed on the lead holes (8), and the probe support rod (6) has a circular pipe (7) opened inside along the axial direction, and the wires of the thin-film thermal resistor are connected to the external acquisition equipment through the lead holes (8) and the circular pipe (7).

[0027] 2. Probe head (1) The diameter D of the cylinder, the value of D is 2 mm ≤ D ≤ 10 mm. The probe head is made of heat insulation material to reduce the heat conduction between the sensing part and the substrate during the measurement of thin film platinum resistance, and improve the dynamic response of the total temperature probe of thin film platinum resistance.

[0028] 3. The probe support rod (6) is a cylinder with a diameter d. The value of d is 2 mm ≤ d ≤ 10 mm. The probe support rod (6) has a circular pipe (7) inside along the axial direction. The diameter of the circular pipe is a. The value of a is 1 mm ≤ a ≤ 8 mm. The thin film platinum resistance wire passes through the lead hole (8) and then connects to the external acquisition equipment through the circular pipe (7).

[0029] 4. The cross-section of the positioning block (2) is a regular quadrilateral. The cross-section shape can be a regular pentagon, a regular hexagon, or a regular heptagon. The center line of the cross-section and the center line of the thin film platinum resistance (4) are on the same plane as the axis of the probe support rod (6). The thickness of the positioning block is a, and the value of a is 2 mm ≤ d ≤ 10 mm. The distance between the positioning block (2) and the bottom of the probe support rod (6) is b, and the value of b is 5 mm ≤ b ≤ 20 mm.

[0030] 5. Install the left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), and the right thin-film platinum resistance (5) on the three lead holes (8), respectively. The plane where the center of the lead hole (8) is located is parallel to the bottom surface of the probe support (6) and the distance is 1 to 5 mm. The positions of the left thin-film platinum resistance (3) and the right thin-film platinum resistance (5) are symmetrically distributed with respect to the center line of the middle thin-film platinum resistance (4) and the center line of the cylindrical surface. The angle between the center lines of the left thin-film platinum resistance (3) and the right thin-film platinum resistance (5) is 60° to 100°.

[0031] 6. The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), and the right thin-film platinum resistance (5) are respectively installed on the corresponding lead holes (8). The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), and the right thin-film platinum resistance (5) are made of the same material and size. The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), the right thin-film platinum resistance (5), and the upper thin-film platinum resistance (6) are all miniature four-wire thin-film platinum resistances with a length of 0.5 mm to 3 mm, a width of 0.1 mm to 1.5 mm, and a thickness of 0.01 mm to 0.2 mm. The four-wire measurement can effectively eliminate the influence of lead resistance on the measurement results, improve the measurement accuracy, and ensure the stability and accuracy of the data.

[0032] This invention provides a thin-film platinum resistance dynamic total temperature probe for measuring two-dimensional flow fields in narrow interstages, which has the following advantages:

[0033] Beneficial effect 1: After calibration in a wind tunnel, this invention can obtain information on the transient total temperature, static temperature, deflection angle, and Mach number of the incoming flow using a unique data processing method.

[0034] Second beneficial effect: After calibration in a calibrated wind tunnel and constant temperature furnace calibration box, this invention can improve measurement accuracy and obtain deflection angle information; it provides an efficient and accurate means for testing unsteady flow fields between compressor stages.

[0035] Benefit 3: The probe of this invention has a built-in positioning function, the positioning block forms a positioning reference, the probe is easy and simple to install, no rotation is required during measurement, there is no periodic requirement for the flow field being measured, and it has a wide range of applications.

[0036] Benefit 4: The probe head structure of this invention is simple and compact, in the shape of an "I", with a small size. The three thin-film platinum resistance thermometers are arranged vertically, which improves the spatial resolution of the probe and makes it suitable for measurements between compressor stages.

[0037] Benefit 5: The thin-film platinum resistance thermometer of the present invention is small in size and is a four-wire platinum resistance thermometer, which has high measurement accuracy. The sensing part is not affected by the structure of the probe itself, and it senses the pulsation of the incoming flow first. The flow field information is not distorted, and the measurement accuracy is high. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the structure of a thin-film platinum resistance dynamic total temperature probe for measuring a narrow interstage two-dimensional flow field in an embodiment of the present invention.

[0039] Figure 2 yes Figure 1 Top view.

[0040] Figure 3 yes Figure 1 Side view.

[0041] Figure 4yes Figure 1 Sectional view along direction A.

[0042] Figure 5 yes Figure 1 Sectional view along direction B.

[0043] Figure 6 yes Figure 5 A magnified view of a portion of the image.

[0044] Figure 7 Figure 1 The C-direction sectional view.

[0045] The components are: 1-probe head, 2-positioning block, 3-left thin-film platinum resistance, 4-middle thin-film platinum resistance, 5-right thin-film platinum resistance, 6-probe support rod, 7-circular tube, and 8-lead hole. Detailed Implementation

[0046] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more explicit definition of the scope of protection of the present invention.

[0047] like Figures 1-7 The image shows a dynamic total temperature probe for measuring a two-dimensional flow field in a narrow interstage, consisting of a probe head (1), a positioning block (2), a left thin-film platinum resistor (3), a middle thin-film platinum resistor (4), a right thin-film platinum resistor (5), a probe support rod (6), a circular pipe (7), and lead holes (8). The probe head (1) and probe support rod (6) are both cylindrical structures. The left thin-film platinum resistor (3), the middle thin-film platinum resistor (4), and the right thin-film platinum resistor (5) are mounted on the probe head (1). Three non-interconnected lead holes (8) are opened on the cylindrical surface. The left thin-film platinum resistor (3), the middle thin-film platinum resistor (4), and the right thin-film platinum resistor (5) are respectively mounted on the lead holes (8). The probe support rod (6) has a circular pipe (7) opened axially inside. The wires of the thin-film thermal resistors are connected to external data acquisition equipment through the lead holes (8) and the circular pipe (7).

[0048] The diameter D of the cylinder of the probe head (1) is 10 mm.

[0049] The probe support rod (6) is a cylinder with a diameter d of 10 mm. The probe support rod (6) has a circular pipe (7) with a diameter a of 6 mm. The thin film platinum resistance wire passes through the lead hole (8) and then through the circular pipe (7) to connect to the external acquisition equipment.

[0050] The positioning block (2) has a regular quadrilateral cross section. The center line of the cross section and the center line of the thin film platinum resistance (4) are in the same plane as the axis of the probe support rod (6). The thickness of the positioning block (2) is a, and the value of a is 5 mm. The distance between the bottom of the positioning block (2) and the bottom of the probe support rod (6) is b, and the value of b is 15 mm.

[0051] The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), and the right thin-film platinum resistance (5) are respectively installed on the three lead holes (8). The plane where the center of the lead hole (8) is located is parallel to the bottom surface of the probe support (6) and the distance is 3 mm. The positions of the left thin-film platinum resistance (3) and the right thin-film platinum resistance (5) are symmetrically distributed with respect to the center line of the middle thin-film platinum resistance (4) and the center line of the cylinder. The angle between the center lines of the left thin-film platinum resistance (3) and the right thin-film platinum resistance (5) is 60°.

[0052] The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), and the right thin-film platinum resistance (5) are respectively installed on the corresponding lead holes (8). The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), and the right thin-film platinum resistance (5) are made of the same material and are the same size. The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), the right thin-film platinum resistance (5), and the upper thin-film platinum resistance (6) are all miniature four-wire thin-film platinum resistances with a length of 1 mm, a width of 0.5 mm, and a thickness of 0.1 mm. The four-wire measurement can effectively eliminate the influence of lead resistance on the measurement results, improve the measurement accuracy, and ensure the stability and accuracy of the data.

[0053] A dynamic total temperature probe for measuring two-dimensional flow fields in narrow interstages using a thin-film platinum resistance thermometer is first calibrated. The resistance value of the thin-film platinum resistance thermometer changes with temperature, as shown in the following equation:

[0054] R t =R0[1+AT+BT] 2 ]

[0055] Where R0 is the resistance value at 0℃, and A and B are the graduation constants. The probe is placed in the measured flow field. Before the formal test, static calibration is performed on four thin-film platinum resistance thermometers as the temperature of the flow field changes. To achieve higher precision measurements, a standard temperature device and a standard ohmmeter are needed to calibrate the specific platinum resistance thermometer to obtain its characteristic curve, i.e., to obtain the coefficients of each term in the characteristic curve, which are used for resistance-temperature conversion during measurement. The static calibration steps are as follows: connect the thin-film platinum resistance sensor to be calibrated to a high-precision resistance meter and place it in the constant temperature bath of a dry metrology furnace, ensuring that the sensor is centered in the furnace and avoiding contact with the furnace wall. After completing the above installation preparations, turn on the dry metrology furnace, adjust to the calibration point temperature, and wait for at least 30 minutes until the sensor reaches thermal equilibrium (the sensor reading remains unchanged). The calibration temperature point should include 0℃, and temperature calibration should be performed according to the actual temperature measurement range, calibrating every 10℃.

[0056] Measuring the resistance of a thin-film platinum resistance sensor at 0°C and two other temperatures within the measurement range is called the "three-point calibration" method, which yields the following set of equations:

[0057]

[0058] Solving the system of equations simultaneously yields:

[0059]

[0060]

[0061] Finally, the temperature measurement formula for platinum resistance thermometers within the calibration range is obtained:

[0062]

[0063] After the above static calibration, the calibration constants A and B, as well as the formula for calculating the measured temperature, are obtained through data processing methods.

[0064] After static calibration, a wide-range calibration was performed in the calibration wind tunnel. The calibration speed range was Mach 0.1 to Mach 1.4, with an interval of Mach 0.1; the deflection angle range was -80° to 80°, with an interval of 5°. A data processing method for a thin-film platinum resistance thermometer dynamic total temperature probe for measuring a two-dimensional flow field in narrow interstages was used to obtain calibration curves for different deflection angles and deflection angle coefficients, deflection angles and total temperature coefficients, and deflection angles and static temperature coefficients at each Mach number. The data processing method for a thin-film platinum resistance thermometer dynamic total temperature probe for measuring a two-dimensional flow field in narrow interstages is as follows:

[0065] Define the deflection angle coefficient:

[0066]

[0067] Define the total temperature coefficient:

[0068]

[0069] Define the static temperature coefficient:

[0070]

[0071] Where yaw is the probe rotation deflection angle, T1, T2, and T3 are the calibration temperature data of the middle, left, and right thin-film platinum resistance thermometers under different airflow deflection angles α, Tt is the total temperature of the incoming flow to the calibration wind tunnel, and Ts is the static temperature of the incoming flow to the calibration wind tunnel.

[0072] According to the above definition, the calibration curves of deflection angle-deflection angle coefficient, deflection angle-total temperature coefficient and deflection angle-static temperature coefficient at different deflection angles for each incoming Mach number are calculated;

[0073] During real-time measurement, the deflection angle coefficient is calculated from the incoming flow temperature sensed by the thin-film platinum resistance thermometer. The deflection angle is calculated using the calibration grid. Then, the total temperature coefficient is obtained by interpolation on the deflection angle-total temperature coefficient calibration curve, and the total temperature is obtained. The static temperature coefficient is obtained by interpolation on the deflection angle-static temperature coefficient calibration curve, and the static temperature is obtained. Finally, the incoming flow Mach number is calculated based on the total temperature and static temperature.

Claims

1. A dynamic total temperature probe for measuring a two-dimensional flow field in a narrow interstage platinum resistance thermometer, comprising a probe head (1), a positioning block (2), a left thin-film platinum resistance thermometer (3), a middle thin-film platinum resistance thermometer (4), a right thin-film platinum resistance thermometer (5), a probe support rod (6), a circular tube (7), and a lead hole (8), characterized in that: The probe head (1) and probe support rod (6) are both cylindrical structures. The probe head (1) is equipped with a left thin film platinum resistance (3), a middle thin film platinum resistance (4) and a right thin film platinum resistance (5). Three non-interconnected lead holes (8) are opened on the cylindrical surface. The left thin film platinum resistance (3), the middle thin film platinum resistance (4) and the right thin film platinum resistance (5) are respectively installed on the lead holes (8). The probe support rod (6) has a circular pipe (7) opened inside along the axial direction. The wires of the thin film thermal resistor are connected to the external acquisition equipment through the lead holes (8) and the circular pipe (7). The diameter D of the cylinder of the probe head (1) is 2 mm ≤ D ≤ 10 mm. The probe head is made of heat-insulating material to reduce the heat conduction between the sensing part and the substrate during the measurement of the thin film platinum resistance and improve the dynamic response of the total temperature probe of the thin film platinum resistance. The probe support rod (6) is a cylinder with a diameter d. The value of d is 2 mm ≤ d ≤ 10 mm. The probe support rod (6) has a circular pipe (7) inside along the axial direction. The diameter of the circular pipe is a. The value of a is 1 mm ≤ a ≤ 8 mm. The thin film platinum resistance wire passes through the lead hole (8) and then connects to the external acquisition equipment through the circular pipe (7). The positioning block (2) has a cross-section of a regular quadrilateral, a regular pentagon, a regular hexagon, or a regular heptagon. The center line of the cross-section and the center line of the thin-film platinum resistance (4) are in the same plane as the axis of the probe support rod (6). The thickness of the positioning block is a, and the value of a is 2 mm ≤ d ≤ 10 mm. The distance between the positioning block (2) and the bottom of the probe support rod (6) is b, and the value of b is 5 mm ≤ b ≤ 20 mm. The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), and the right thin-film platinum resistance (5) are respectively installed on the three lead holes (8). The plane where the center of the lead hole (8) is located is parallel to the bottom surface of the probe support (6) and the distance is 1 to 5 mm. The positions of the left thin-film platinum resistance (3) and the right thin-film platinum resistance (5) are symmetrically distributed with respect to the center line of the middle thin-film platinum resistance (4) and the center line of the cylindrical surface. The angle between the center lines of the left thin-film platinum resistance (3) and the right thin-film platinum resistance (5) is 60° to 100°. The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), and the right thin-film platinum resistance (5) are respectively installed on the corresponding lead holes (8). The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), and the right thin-film platinum resistance (5) are made of the same material and are the same size. The left thin-film platinum resistance (3), the middle thin-film platinum resistance (4), and the right thin-film platinum resistance (5) are all miniature four-wire thin-film platinum resistances with a length of 0.5 mm to 3 mm, a width of 0.1 mm to 1.5 mm, and a thickness of 0.01 mm to 0.2 mm. The four-wire measurement can effectively eliminate the influence of lead resistance on the measurement results, improve the measurement accuracy, and ensure the stability and accuracy of the data. A data processing method is proposed based on a thin-film platinum resistance thermometer dynamic total temperature probe for measuring two-dimensional flow fields in narrow interstages. The probe is calibrated over a wide range in a calibration wind tunnel, with calibration speeds ranging from Mach 0.1 to Mach 1.4 and deflection angles ranging from -80° to 80°. Using this data processing method, calibration curves for different deflection angles and their coefficients (deflection angle-total temperature coefficient, and deflection angle-static temperature coefficient) are obtained at each Mach number. The method is as follows: Define the deflection angle coefficient: Define the total temperature coefficient: Define the static temperature coefficient: Among them, T1, T2, and T3 are the calibration temperature data of the middle thin-film platinum resistance, the left thin-film platinum resistance, and the right thin-film platinum resistance under different airflow deflection angles α, Tt is the total temperature of the incoming flow to the calibration wind tunnel, and Ts is the static temperature of the incoming flow to the calibration wind tunnel. According to the above definition, the calibration curves of deflection angle-deflection angle coefficient, deflection angle-total temperature coefficient and deflection angle-static temperature coefficient at different deflection angles for each incoming Mach number are calculated; In actual measurement, the deflection angle coefficient is calculated from the temperature data measured by each thin-film platinum resistance thermometer, and the deflection angle is calculated using the calibration curve. Then, the total temperature coefficient is obtained by interpolation on the deflection angle-total temperature coefficient calibration curve, and the total temperature is calculated by back-calculation using the definition of the total temperature coefficient. Similarly, the static temperature coefficient is obtained by interpolation on the deflection angle-static temperature coefficient calibration curve, and the static temperature is calculated by back-calculation using the definition of the static temperature coefficient. Finally, the incoming flow Mach number is calculated from the obtained total airflow temperature and static temperature.

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