Research projects are (co)financed by the Slovenian Research and Innovation Agency
- Member of the University of Ljubljana: Faculty of Mechanical Engineering
- Project code: J2-3054
- Science: Engineering sciences and technologies
- SICRIS: Advanced shock tube system for high-frequency primary dynamic pressure calibration (cobiss.net)
Project Description
The need for better accuracy and reliability of high-frequency dynamic pressure measurements is driven by a variety of industrial sectors. In the automotive industry, increasingly stringent regulations on greenhouse gas emissions require the development of internal combustion engines (ICEs) with ever better fuel efficiency. To optimize engine performance, i.e. to reduce fuel consumption and emissions, accurate measurements of the time-varying pressure due to engine misfire or knocking with amplitudes of up to a few MPa and frequencies up to 10 kHz are required. Improved dynamic pressure measurements are also necessary in many safety-critical applications, such as crash testing of cars, to reduce currently very wide safety margins and thus ensure user safety in a cost-effective way. In the development of airbag systems, it is essential to accurately measure the time evolution of pressure inside the bag with dynamic content of interest up to a few kHz. Accurate measurements of high-frequency time-varying pressure are also vital for steam and gas turbines in power plants. In recent decades, the development of the aerospace industry has brought the urgent need also for accurate measurement of rapidly changing pressures in many components, such as aero-engine, aircraft exhaust and aircraft surface. In the engineering of turbine engines and rocket propulsion systems dynamic pressure measurements with frequencies up to 30 kHz are used for feedback sensing, thrust measurement and overpressure indication.
The objective of the project was to gain a fundamental understanding of the use of shock waves for the dynamic calibration of pressure measurement systems (PMSs) in a shock tube, with the final goal of developing an advanced diaphragmless shock tube system with a fast-opening valve (FOV), which would enable high-frequency primary dynamic pressure calibration with the calibration and measurement capabilities of a primary standard. During the project, we addressed three key research questions: (1) how to manipulate shock waves to expand the pressure amplitude range of shock tubes, (2) how to decrease the uncertainty contribution caused by the incompleteness of the existing shock tube measurement model, and (3) how to provide traceable calibrations of PMSs in the range of several tens of kHz with an amplitude uncertainty of 1% and phase uncertainty of 5°.
Within four main work packages, through comprehensive numerical simulations, mathematical modelling, and experimental studies of shock waves, we designed and constructed a world-first diaphragmless shock tube with an FOV, which, with the use of a gas and a developed converging section, provides a pressure calibration range of 44 MPa, and with the use of a liquid and a newly developed double-acting actuator 230 MPa. This enabled the generation of pressure step amplitudes comparable to those generated by liquid drop-weight systems, while maintaining a significantly broader calibration frequency bandwidth. To reduce the uncertainty contribution of the generated pressure step due to the assumptions in the current shock tube model related to perfect gas behaviour and adiabatic conditions, we improved the extrapolation model used to determine the shock wave velocity and arrival time at the end-wall of the driven section. In addition, we developed an algorithm to correct systematic errors in shock wave velocity measurements along the shock tube and established an analytical correction that describes the functional dependence of the shock wave velocity on the thermodynamic and transport properties of the gas and the geometrical parameters of the shock tube. Uncertainty analyses confirmed that, as the first in the world, we successfully decreased the relative standard uncertainty of the shock tube measurement model from several percent to less than 0.4%. At the end of the project, we were the first to perform a primary dynamic calibration of pressure sensors for the automotive industry. We demonstrated that dynamic calibration of pressure sensors with the developed diaphragmless shock tube in the high-frequency range improves pressure measurement accuracy in internal combustion engines by up to 13%, and therefore the estimation of key dynamic engine parameters by up to 48%. This significantly contributes to increasing efficiency and reducing emissions of the engines which is crucial for meeting strict greenhouse gas and noise regulations during the transition towards full vehicle electrification.
Figure 1. Schematic representation of the developed diaphragmless shock tube with FOV.
The project was structured around four main work packages (WPs), each with its specific objectives and tasks, which are described in more detail below.
WP 1. Study of shock waves in the shock tube – completion level: 100%
In WP 1, we developed a comprehensive numerical model in the open-source CFD library OpenFOAM to analyse the effects of operating conditions on the distribution of the supersonic shock wave velocity in the shock tube. The model includes the moving geometry of the fast-opening valve (FOV). The results of numerical analyses of the effect of the FOV dimensions and opening speed on the development of shock wave velocity along the shock tube were presented in an open-access scientific paper [1]. Due to the high computational demand and the long runtime required to achieve satisfactory accuracy in simulations, we also investigated the effects of thermodynamic and transport properties of gases in individual sections of the shock tube, as well as geometrical parameters, through experimental work. For this purpose, we built three shock tubes with different dimensions. The results of both the numerical analyses and experiments showed that the Mach number of the generated shock waves, and consequently the pressure and temperature step changes generated at the end-wall of the shock tube and thus the excited frequencies of the generated pressure increase with increasing pressure ratio of the initial driver and driven pressures, decreasing diameter of the driven section and increasing ratio of the speed of sound of the gases in both sections of the shock tube. The results of the experimental analysis were presented in an open-access scientific paper [2]. To further increase the pressure range of the shock tube, which is limited by the use of a constant cross-section, we successfully designed an optimally dimensioned converging section of the tube using shock dynamics theory and the developed numerical model. In this section, by converging and transforming the initial planar shock front into an ideal spherical shape without diffraction losses caused by shock wave reflections, we significantly increased the energy density of the generated shock wave per unit length. This part was key to the design of the diaphragmless shock tube with extended pressure capability in WP 3.
WP 2. Evaluation of the uncertainty of the shock tube measurement model – completion level: 100%
In WP 2, uncertainty analyses of the pressure step at the end wall of the driven section of the shock tube predicted by the measurement model of the shock tube showed that the largest contribution to uncertainty arises from determining the shock wave velocity at the end wall and the time of its arrival. To reduce the contribution of measurement uncertainty of the generated pressure step in the shock tube, we improved the extrapolation model for determining the shock wave velocity and its arrival time. In addition, based on the developed physical model, we developed an algorithm for correcting systematic errors in measuring the velocity along the shock tube. At the same time, we established an analytical correction that describes the functional dependence of the velocity of the generated shock waves along the tube on various thermodynamic and transport properties of the gas and the geometrical parameters of the shock tube. The results will be presented in an open-access scientific paper, which is currently in the final stages of preparation for publication. We experimentally validated the correction by comparing pressure steps predicted by the improved shock tube model with pressure steps measured in the developed diaphragmless shock tube using a quasi-statically calibrated piezoelectric PMS with suitable dynamic properties. Uncertainty analyses confirmed that, with this, we successfully reduced the relative standard uncertainty of the shock tube measurement model under various initial conditions from several percent to less than 0.4%. The results were presented in an open-access scientific article [3] and a scientific conference contribution [4].
WP 3. Design and construction of the upgraded diaphragmless shock tube – completion level: 100%
In WP 3, based on the results obtained in WP 1, we first used a combination of helium as the driver gas and nitrogen as the driven gas to achieve pressure steps of up to 4.8 MPa in the constant-diameter shock tube [5]. Then, by implementing an optimally designed converging section, we were the first to extend the calibration pressure range of the shock tube when using gas to 44 MPa and broaden the frequency range from 0 Hz to several hundred kHz [6]. At the end of WP 3, in collaboration with the research team from the company SPEKTRA in Germany, we developed a double-acting actuator at the end wall of the driven section of the shock tube, based on the developed physical-mathematical model, for performing dynamic calibration of pressure sensors using liquid. This approach represents an entirely new principle in the field of liquid-based dynamic pressure generators. With it, we were the first to extend the range of pressure amplitudes generated in the shock tube to approximately 230 MPa. This allowed us to achieve pressure step amplitudes comparable to those generated by drop-weight liquid systems, while maintaining a wider calibration frequency bandwidth. The advantages of the newly developed liquid-based dynamic calibrator using a shock tube were confirmed through comparison with results obtained using a commercially available dynamic pressure exciter (SPEKTRA, DPE-03) [7].
WP 4. Experimental determination of the frequency response function (FRF) of the tested PMS using a shock tube – completion level: 100%
In WP 4, we developed a computational algorithm for calculating the discrete complex FRF from the time responses of high-frequency PMSs to pressure step changes in the shock tube. From the complex frequency response, amplitude and phase frequency characteristics of the tested PMSs were determined in the frequency range from 0 Hz to several hundred kHz. Uncertainty analysis confirmed that the proposed method, in combination with the developed diaphragmless shock tube, enables the determination of the amplitude frequency characteristic of the PMS with a relative expanded uncertainty of less than 4%, and the phase frequency characteristic with an expanded uncertainty of less than 8° in the range of 10 kHz. Subsequently, in collaboration with researchers from the Swedish National Metrology Institute (RISE), we developed and validated a method for correcting acceleration-induced errors caused by vibration influences during the determination of the frequency response of pressure measurement systems using a shock tube. The study was published in the journal Mechanical Systems and Signal Processing, which ranks among the top 5% of journals in the field of mechanical engineering [8]. Because in many industrial applications pressure sensors must often be installed at a certain distance from the measured object, where the connecting tube between the object and the pressure sensor affects the dynamic properties of the PMS, we, in collaboration with researchers from the Laboratory for Process Measurement at the Faculty of Mechanical Engineering and Naval Architecture of the University of Zagreb, mathematically modelled the dynamic behaviour of pressure transmission lines in order to develop guidelines for the optimal design of such systems in both the frequency and time domains [9]. In the final phase of the project, in collaboration with researchers from the Laboratory for Internal Combustion Engines and Electromobility at the Faculty of Mechanical Engineering, University of Ljubljana, and researchers from the company Hidria Advancetec, we were the first to perform a primary dynamic calibration of pressure sensors for the automotive industry. The results showed that, compared to quasi-statically calibrated sensors, pressure sensors calibrated with the finally developed advanced diaphragmless shock tube system in the frequency range from 0 Hz to 50 kHz improve pressure measurement accuracy in internal combustion engines by up to 13%. This also significantly improves the accuracy of determining dynamic engine parameters, which are crucial for improving the efficiency and reducing emissions of internal combustion engines in their further development, namely, rate of pressure rise by up to 38%, average temperature of the cylinder gas by up to 4.8%, and rate of heat release by up to 48%.
[1] Francisco Javier Hernández Castro, Jože Kutin, Andrej Svete. Effects of the opening speed of the valve in a diaphragmless shock tube for metrological purposes. IEEE sensors journal. Jan. 2024, vol. 24, no. 1, p. 158-168 [COBISS.SI-ID 179395587].
[2] Benjamin Novak, Andrej Svete, Jože Kutin. Effects of the shock tube diameter on shock wave propagation in a diaphragmless shock tube. Measurement: Sensors. 2025, vol. , no. , 101687, p. 1-4 [COBISS.SI-ID 230247939].
[3] Andrej Svete, Francisco Javier Hernández Castro, Jože Kutin. 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. Sensors. Mar. 2022, vol. 22, iss. 6, no. 2103, p. 1-15 [COBISS.SI-ID 100476931].
[4] Francisco Javier Hernández Castro, Andrej Svete, Jože Kutin. Method for correction of the systematic errors in detected shock wave passage times in the shock tube. V: IMEKO [joint] 24th TC3, 14th TC5, 6th TC16 and 5th TC22 International Conference, 11 – 13 october 2022, Cavtat-Dubrovnik, Croatia: IMEKO conference proceedings. 2022, p. 1-5 [COBISS.SI-ID 140261379].
[5] Urh Planko, Andrej Svete, Jože Kutin. Dynamic calibration of pressure sensors with the use of different gases in the shock tube. In: IMEKO [joint] 24th TC3, 14th TC5, 6th TC16 and 5th TC22 International Conference, 11 – 13 october 2022, Cavtat-Dubrovnik, Croatia: IMEKO conference proceedings. 2022, p. 1-5 [COBISS.SI-ID 140263427].
[6] Benjamin Novak, Andrej Svete, Jože Kutin. Nadgradnja etalona z udarno cevjo za časovno spreminjajoče tlake z zožitvenim elementom. In: Akademija strojništva 2023: inženirstvo – povezovanje za trajnostni preboj, 22. november 2023, Ljubljana, Slovenia: zbornik prispevkov 12. Mednarodne konference Zveze strojnih inženirjev Slovenije, 2023, p. 64-65 [COBISS.SI-ID 180673539].
[7] Urh Planko, Andrej Svete, Jože Kutin. Characterization of Spektra DPE-02 dynamic pressure exciter for the dynamic calibrations of pressure sensors. Measurement: Sensors. 2025, vol. , art. no. , 101689, p. 1-5 [COBISS.SI-ID 230248707].
[8] Andrej Svete, Eynas Amer, Gustav Jönsson, Jože Kutin, Fredrik Arrhén. A method for correcting the high-frequency mechanical vibration effects in the dynamic calibration of pressure measurement systems using a shock tube. Mechanical systems and signal processing. Jun. 2023, vol. 193, no. 110246, p. 1-13 [COBISS.SI-ID 144267011].
[9] Jože Kutin, Andrej Svete, Lovorka Grgec Bermanec. Towards an optimal frequency and time response of singe-tube pressure measurement systems under continuum-flow conditions. Sensors and actuators. A, Physical. Feb. 2024, vol. 366, no. 114943, p. 1-11 [COBISS.SI-ID 179378179].