Effect of the Dynamic Response of a Side-Wall Pressure Measurement System on Determining the Pressure Step Signal in a Shock Tube Using a Time-of-Flight Method

Abstract

Technological progress demands accurate measurements of rapidly changing pressures. This, in turn, requires the use of dynamically calibrated pressure meters. The shock tube enables the dynamic characterization by applying an almost ideal pressure step change to the pressure sensor under calibration. This paper evaluates the effect of the dynamic response of a side-wall pressure measurement system on the detection of shock wave passage times over the side-wall pressure sensors installed along the shock tube. Furthermore, it evaluates this effect on the reference pressure step signal determined at the end-wall of the driven section using a time-of-flight method. To determine the errors in the detection of the shock front passage times over the centers of the side-wall sensors, a physical model for simulating the dynamic response of the complete measurement chain to the passage of the shock wave was developed. Due to the fact that the use of the physical model requires information about the effective diameter of the pressure sensor, special attention was paid to determining the effective diameter of the side-wall pressure sensors installed along the shock tube. The results show that the relative systematic errors in the pressure step amplitude at the end-wall of the shock tube due to the errors in the detection of the shock front passage times over the side-wall pressure sensors are less than 0.0003%. On the other hand, the systematic errors in the phase lag of the end-wall pressure signal in the calibration frequency range appropriate for high-frequency dynamic pressure applications are up to a few tens of degrees. Since the target phase measurement uncertainty of the pressure sensors used in high-frequency dynamic pressure applications is only a few degrees, the corrections for the systematic errors in the detection of the shock front passage times over the side-wall pressure sensors with the use of the developed physical dynamic model are, therefore, necessary when performing dynamic calibrations of pressure sensors with a shock tube.

Dynamic Calibration of Pressure Sensors With the Use of Different Gases in the Shock Tube

“…A diaphragmless shock tube, which was developed in the Laboratory of Measurements in Process Engineering at the Faculty of Mechanical Engineering in Ljubljana, consists of two straight gas-filled tubes with the same circular cross-section that are initially separated with the fast-opening valve (FOV): a high pressure driver section and a lower pressure driven section, see Figure 1 [2]- [4]. An instantaneous opening of the FOV generates a shock wave that propagates through the driven gas.…”

“…where 𝑡 last and 𝑥 last are the passage time of the shock wave over the last side-wall pressure sensor installed downstream of the driven section and its location, respectively, 𝑥 wall is the location of the end-wall of the driven section and 𝑉(𝑥) is shock wave velocity distribution along the driven section determined using a time-of-flight (TOF) method [2]- [4].…”

Method for Correction of the Systematic Errors in Detected Shock Wave Passage Times in the Shock Tube

“…The dynamic response of the side-wall pressure measurement system (PMS) used for determining the shock wave passages depends on its frequency response function (FRF), the velocity of the shock wave at the locations of the side-wall pressure sensors Vi and the effective diameter of the side-wall pressure sensors D. In the recent work [6], we have developed the physical mathematical model that simulates the side-wall PMS input and output signals. The developed model considers the integral effect of the shock wave pressure on the pressure sensor to be proportional to the size of the pressure sensor diaphragm's effective area covered by the shock wave and determines the response of the PMS to the input pressure by considering the FRF of the complete side-wall PMS chain.…”

“…The developed model considers the integral effect of the shock wave pressure on the pressure sensor to be proportional to the size of the pressure sensor diaphragm's effective area covered by the shock wave and determines the response of the PMS to the input pressure by considering the FRF of the complete side-wall PMS chain. The use of the physical model requires the information about Vi and D. The effective diameter of four identical sidewall pressure sensors installed along the developed diaphragmless shock tube was determined based on the best fit between the normalised measured output signals of the side-wall PMS and the theoretical output signals obtained with the physical model [6].…”

Pressure Sensors: Working Principles of Static and Dynamic Calibration

“…On the other hand, in other application areas, such as military engineering, chemical explosion tests [ 4 ], petroleum exploration and well testing [ 5 ], gas turbine testing and combustion engine testing [ 6 , 7 ], and biomedical applications [ 8 ], among others, dynamic calibration of pressure sensors is essential. A typical example that can be referred to in the automotive area is related to air flow control in combustion engines [ 9 ]. Pollution of the combustion air can result in a reduction in the oxygen available for combustion and can alter the chemistry of exhaust emissions, with a negative impact on environmental air quality.…”