Correction Method of Measurement Error of High Temperature Strain Gauge under Transient Heating Condition

Abstract: The plug-type transient calorimeter is one of the main means of measuring the surface cold wall heat flux in the aerodynamic heating ground simulation test model. The error analysis of the plug-type transient calorimeter test results was carried out, and the mathematical analysis model was established by using the finite difference principle. The correction calculation program of the transient calorimeter measurement results was compiled, and some typical test results were corrected and analyzed.

1 Introduction

During the high-speed flight of an aircraft in the atmosphere, especially during the re-entry of a spacecraft into the atmosphere, the airflow is affected by the shock waves around the aircraft and the resistance caused by the viscosity of the gas. The mechanical energy of the airflow along the outer wall of the aircraft is converted into thermal energy, and the airflow temperature rises sharply. The high-temperature and high-speed flow field around the aircraft surface forms a very serious aerodynamic heating for the aircraft. Therefore, the aerodynamic thermal protection problem is an issue that must be considered in the aerodynamic and structural design of the aircraft. Using ground heating equipment such as arc wind tunnels to conduct ground simulation tests on the heat-resistant materials and heat-resistant structures of the aircraft is a very important link in the aircraft design process. In the aerodynamic thermal ground simulation test research, the parameters that usually need to be simulated are airflow temperature (enthalpy), model surface heat flux, airflow pressure, heating time, etc. The model surface heat flux is an important parameter to characterize the aerodynamic heating amount and heating intensity. The accurate measurement of heat flux has an important influence on the accuracy of the aerodynamic thermal ground simulation test. The plug-type transient calorimeter is a heat flux measurement method that is convenient to process, install, and use and has a low cost. However, there is a large measurement error for high heat flux and long time measurement. This paper adopts the finite difference method to analyze and correct the measurement results, which effectively improves the measurement accuracy.

2 Measurement principle of plug-type transient calorimeter

The structure of the plug-type transient calorimeter is shown in Figure 1, which consists of a heat flux plate, a plug, an insulating sleeve, a thermocouple, etc. According to the principle of energy conservation, a plug with good thermal conductivity is used, and the side and bottom surfaces are insulated. The heat transmitted to the surface of the plug is completely absorbed by the plug itself, causing the temperature of the plug to rise. By measuring the temperature rise-time curve of the plug, the temperature gradient of the plug is calculated, and the heat flux transmitted to the surface of the plug is obtained:

3 Problems with the plug-type transient calorimeter

The measurement of the plug-type transient calorimeter is based on the following assumptions:

(1) The physical properties of the plug remain unchanged.

(2) The thermal conductivity of the plug is very good, and the temperature of each part of the plug is uniform.

(3) The increase in the surface temperature of the plug has little effect on the measurement results.

In fact, when the measured heat flux is high, the temperature gradient inside the plug must be large, and as the plug temperature increases, the thermophysical parameters of the plug material will also change with temperature. Therefore, the error between the obtained heat flux value and the actual value will be large, so the measurement results of the plug-type transient calorimeter must be corrected.

4 Analysis and correction methods of test results

If we use a cylindrical copper plug to simulate the actual plug according to the measurement principle of the plug-type transient calorimeter, and measure the temperature change at the bottom of the copper plug, we can get the heat flow from the plug surface. Here, we first establish the one-dimensional non-steady-state heat conduction analysis model of this simulated plug:

The boundary conditions of the above analysis model are different from the three traditional boundary conditions in heat transfer. Here, the heat transfer coefficient α on the surface of the plug is unknown, while the airflow temperature tg and the temperature at the bottom of the plug are known to change with time. It is required to find the temperature at each moment in the plug and the convective heat transfer coefficient. Therefore, the specific algorithm adopts an iterative solution method. First, the temperature rise of the lowest unit is used as the average temperature rise of the plug to calculate the input heat flow, calculate the temperature rise of each point, and compare it with the temperature rise of the lowest point, and then correct the heat transfer coefficient until the temperature rise of the lowest point is close to the test data. In the iterative process, the thermal conductivity, specific heat capacity and density are corrected according to the temperature rise of each point. Finally, the temperature rise and heat transfer coefficient of each point in the calorimeter are obtained, so as to obtain the cold wall heat flow required for the aerodynamic heating test. Here, the transient calorimeter of the aerodynamic heat ground simulation test of a certain aircraft is taken as an example, and the test measurement results are corrected and calculated. Figure 2 is the experimentally measured temperature rise curve of the bottom of the plug, and Figure 3 is the experimentally obtained heat flow curve and the corrected temperature rise curve.

The transient calorimeter uses oxygen-free copper material with good thermal conductivity. At a temperature of 300 K, the specific heat capacity cp=0·386 kj/(kg·k), density ρ=8930 kg/m3, and thermal conductivity λ=401 w/(m·k). The physical properties of this material change with temperature. The block has a diameter of 9 mm and a thickness of 12 mm. The block is evenly divided into 10 units along the thickness direction. The time step is 1×10-5s and the calculation time is 5 s.

The calculation results show that when the plug calorimeter is heated by a large heat flux, a temperature rise gradient will quickly appear inside, as shown in Figure 2. During a long measurement process, the surface temperature of the plug will be much greater than the initial value. Therefore, the three assumptions of using the plug calorimeter to measure the surface of the model are no longer valid. The test results must be corrected to ensure the accuracy of the aerodynamic thermal ground simulation test. Figure 3 shows the heat flow curve obtained from the test and the heat flow curve after calculation and correction. It can be seen from the figure that in the short time after the start of the test, when the temperature rise in the plug is very small, the difference between the test value and the corrected value is very small, but as the temperature in the plug increases, the gap between the test value and the corrected value becomes larger and larger. In this example, when the test time reaches 4s, the surface temperature exceeds 500k, and the difference between the test heat flow value and the corrected value reaches 25%, which will inevitably have a great impact on the aerodynamic thermal test results, so the test value must be corrected.

5 Conclusion

When using a plug-type transient calorimeter to measure a large heat flux, the plug's physical parameters have changed significantly due to the increase in temperature inside the plug, and the test value can no longer reflect the actual cold wall heat flux on the model surface, so it must be corrected. Using a one-dimensional transient heat conduction model and a finite difference discrete method to perform theoretical analysis and correction on the test data, a more realistic cold wall heat flux can be obtained, thereby improving the accuracy of the simulated heating test.