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Theoretical and experimental results for the dynamic response of pressure measuring systems by H.Bergh and H.Tijdeman


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For a series-connection of N thin tubes and N volumes a general recursion formula has been derived that relates the sinusoidal pressure disturbance in volume j to the pressure disturbances in the preceding volume (j -l ) and the next volume (j+1). This forms the basis for expressions to predict the dynamic response of all types of pressure measuring systems and other pneumatic or hydraulic line systems. The theoretical predictions are validated bij experminental results.
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... However, hindering the use of pressure scanners for unsteady measurements is the connecting tubing that inherently introduces time lags and pneumatic distortion to the pressure signal received at the sensing element inside the pressure scanner. The character of the distortion varies and can be due to attenuation or resonant amplification depending on the geometry of the tubing, as well as the environmental conditions of the flow being measured [9,10]. The pneumatic distortion (lag, attenuation and resonance) due to the tubing between the sensing module and surface port limits the usefulness of such measurements to averaged, steady data only. ...
... Modeling the physics of the tubing system provides a means by which to correct the signal distortions introduced by the tubing system. Derived from the conservation of mass, momentum, and energy, the model proposed by Bergh and Tijdeman [9] demonstrates good agreement with experimental data. However, due to the nature of the system response model, the higher frequency content of the signal, including any noise, gets amplified by a more significant amount in both amplitude and phase, compared to the low-frequency content, leading to inaccurate estimates of the surface pressure. ...
... The response of a pressure transducer to an input pressure at the inlet of a length of tubing connected to the pressure transducer was first considered by Bergh and Tijdeman [9]. A typical configuration for a remotely mounted pressure transducer is depicted in Figure 1. ...
Conference Paper
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View Video Presentation: In many aerodynamic measurement applications, the ability to make time-accurate measurements with pressure scanners provides practical advantages over making the same measurements directly using flush-mounted transducers. However, the pneumatic distortion due to the tubing between the sensing module and surface port limits the usefulness of such measurements to averaged, steady data only. This issue has restricted the application of pressure scanners for unsteady pressure measurements in the wind tunnel and flight-testing applications. The Wiener-filtered inverse system response model has been proven effective in reconstructing complex unsteady pressure signals acquired remotely using pressure scanners. The unparalleled long-term thermal stability, flexibility and robustness that pressure scanners provide in wind-tunnel and flight-testing applications, combined with an ability to reconstruct the unsteady components of the measured pressure signals, could enable their use in modern applications involving dynamic flow fields and highly separated flows. This work evaluated the feasibility of using pressure scanning systems for time-resolved pressure measurements in the NASA Langley 14- by 22-Foot Subsonic Wind Tunnel. Results demonstrated good agreement between the reference transducers and reconstructed pressure scanner measurements up to frequencies of approximately 500 Hz.
... Nevertheless, due to the second-order dynamic approach, this correction method is limited to critically damped or overdamped systems. One of the most often used correction methods for acoustic attenuation in line-cavity systems and the one that is seen as the state-of-the-art solution was introduced by Bergh and Tijdeman in 1965 [113]. They analytically formulated a recursive solution for multiple line-cavity systems in a row. ...
... Moreover, the correlation of the reconstructed validation data is above 99%. Figure 4.12c shows the amplitude ratio of the discretetime identified transfer function for the LCS under investigation along with the analytic solution by Bergh and Tijdeman [113]. In contrast to the analytic solution, which shows resonance at very similar frequencies, the attenuation is more pronounced in the actual acquired and post-processed data. ...
... The following results show the post-processed data in comparison to the analytic solution, derived from the Bergh and Tijdeman approach (cf. [113] and Section 3.2.1), and also to experimentally obtained data. ...
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In the aerodynamic examination of objects in wind tunnels, engineers can choose from a wide range of different measurement tools for quantifying the flow. The choice of the appropriate measurement methodology is made based on the characteristics of the possible tools. Hence, subject of the present work is the development and testing of a multi-hole probe for the measurement of unsteady aerodynamic phenomena, which tries to combine properties of the different measurement systems and is also called fast-response aerodynamic probe (FRAP). For this purpose, the characteristics of the probe and the incorporated pressure sensors are determined and unresolved concerns with respect to the associated metrological possibilities and limitations are addressed. Using miniaturized sensors in the pressure probe body, a competitive measurement solution is to be found. Therefore, the working principles of multi-hole probes and pressure sensors are briefly discussed. Special focus lies on newly developed fiber-optic pressure sensors. Various methods for the spatial calibration of the probe are presented. Furthermore, the machine learning approach, Gaussian process regression, is applied to reduce the calibration time. Additionally, a temporal calibration characterizes the acoustic system inside the probe. Various tests that determine the sensitivity of the pressure sensor with respect to external effects are explained and the sensor performance is evaluated. The multi-hole probe behavior is further analyzed in numerical investigations of the flow around the probe and of the line-cavity system inside the probe. In addition, multiple measurement campaigns are carried out in the low-speed wind tunnel facilities at the Chair of Aerodynamics and Fluid Mechanics of the Technical University of Munich (TUM-AER). The determination of the spatial and temporal resolution of the probe in grid-generated turbulence is of special interest and aspects concerning uncertainty quantification of the probe measurements are given. To demonstrate the capabilities of the fully characterized probe, the quantification of unsteady flow phenomena in different measurement scenarios are discussed, a) in the wake of a circular cylinder and b) in the wake of a dynamically actuated wind turbine. By additionally acquiring a synchronization signal, independent FRAP measurements in the wind turbine wake are synchronized in the phase-locking postprocessing procedure. The FRAP investigations unveil that the actuated cases show an earlier mixing and entrainment of high energetic fluid already near the rotor plane. Consequently, the actuated control strategy is a promising approach that can contribute to a synergistic interaction of multiple wind turbines, as found in wind farms. Measurements with the FRAP show a very robust and easy to use handling with a fast and cost-effcient setup. The incorporation of advanced (post-) processing routines, allows time-averaged, phase-locked and transient analyses of the flow field patterns.
... In a second experiment, an acoustic test rig is used to determine the probe's acoustic transfer function up to a frequency of some 5.5 kHz. This transfer function is then also compared to an analytical model for pressure measurements in thin tubes [24]. Lastly, we discuss the influence of the aforementioned interferences on the measured pressure gain. ...
... Bergh and Tijdeman [24] and Tijdeman [52] introduced an analytical model for the frequency response of an arbitrary series of circular tubes and measurement volumes to sinusoidal pressure disturbances. We can approximate the internal capillary as a series of connected tubes with a volume, housing the sensor membrane, at the end. ...
... While the prominent features in the modeled response do not strictly match the measured transfer behavior, qualitatively, their shape resembles large sections. The overall shapes of amplitude ratio and phase lag do, however, compare well with the examples given in the original publication [24]. Further, while the compression driver manufacturer specifies a more or less linear frequency response of the sound source, small variations of the output power, resulting from the imperfect calibration of the sound source, are baked into the probe's frequency response. ...
Kiel probes have the potential to be a versatile tool for determining stagnation pressure gain in rotating detonation combustors (RDCs), accompanying the commonly used equivalent available pressure method. Although average pressure gain values determined with Kiel probes are comparable to those from thrust stand experiments, one can expect several sources of measurement error from the unsteady trans- and supersonic environment. This work investigates the response of a Kiel probe in highly unsteady flow, similar to what would be encountered in an RDC. The probe is subjected to an underexpanded starting jet behind an incident shock with Mach numbers of 1.6–2.7, emanating from a shock tube with a reservoir ratio of about 394. The incidence angle of the probe is varied between 0 and 90 deg, as is the probe’s axial location with respect to the tube’s exit plane. High-speed schlieren images reveal the Mach number of the moving shock wave and the structure of the detached bow shock at the Kiel head, which is similar to that of a bluff body. It is shown that the measured stagnation pressure signal is independent of inflow angle over a range of ±45 deg, and that signal attenuation is caused by gas processing through the bow shock and viscous losses in the probe’s capillary. The frequency response of the Kiel probe to sinusoidal, small-amplitude pressure fluctuations is determined in an acoustic calibration facility up to 5500 Hz, confirming linear behavior and that no unwanted resonance is present in the probe. A Berg–Tijdeman representation delivers amplitude ratio and phase lag of comparable magnitude. An assessment of representative boundary conditions reveals that the average stagnation pressure measurement error is of the order of 1%.
... Die akustischen Spektren der Sensoren in den Verteilervolumen können durch die Röhrchenanbindung verfälscht werden. Diese Übertragungsfunktionen können durch Modelle aus der Fachliteratur abgeschätzt werden [8,33,359,360]. Eine Abschätzung der Übertragungsfunktion für den H 2 -Injektor befindet sich in Anhang B.2 und kommt zu dem Ergebnis, dass die Anbindung der Sensoren zu Unsicherheiten von maximal 10 dB führen kann. Abbildung 6.19(a) zeigt den Vergleich der PSDs der Druckschwankungen in Brennkammer und Injektorkopf für den exemplarischen LH-Versuch, berechnet für den Zeitpunkt kurz vor dem erstmaligen Auftreten der Instabilität. ...
... Die Anbindung führt aufgrund von Resonanzmoden im Röhrchen zu einer Verfälschung des aufgenommenen Spektrums. Der Einfluss der Röhrchen auf das Signal lässt sich über Übertragungsfunktionen abschätzen[8,33,359,360]. Der Einfluss der Anbindung auf das Spektrum wird in Anhang B.2 abgeschätzt. ...
Der Fokus dieser Arbeit liegt auf der Untersuchung der Flammen-Akustik-Interaktion der Injektorkopplung in einer LOX/H2-Forschungsbrennkammer durch 2D-Flammenvisualisierungen im injektornahen Bereich. Die Flammendynamik wurde mittels Dynamic Mode Decomposition untersucht. Dabei ergaben sich symmetrische, longitudinale Intensitätsverteilungen als Antwort auf die Injektormoden. Eine Rekombination der DMDModen mit dem zeitlich gemittelten Bild der blauen Strahlung zeigt, dass symmetrische, wellenartige Strukturen auf dem Sauerstoff-Strahl vorliegen. Dies lässt sich durch periodische Sauerstoff-Massenstromfluktuationen erklären und ist somit im Einklang mit dem Anregungsmechanismus nach Gröning. Die Analyse der Phasenlage zwischen der OH*- Strahlung und der 1T-Mode ergab, dass berechnete Rayleigh-Indizes konsistent zum Stabilitätsverhalten sind. In der OH*-Strahlung wurde außerdem ein weiteres dynamisches System identifiziert, dessen Frequenzen mit den Sauerstoff-Strömungsgeschwindigkeiten korrelieren. Ein hydrodynamischer Effekt am Einlauf der Injektoren erzeugt dabei periodische Wirbel, welche die Injektorakustik verstärken können. Somit besteht nun ein umfassendes Verständnis des Anregungsmechanismus in BKD. Basierend auf den gewonnenen Erkenntnissen konnten Konstruktionsvorschläge der Injektoreinlaufblende zur Reduktion des Risikos injektorgekoppelter, hochfrequenter Verbrennungsinstabilitäten abgeleitet werden.
... È quindi necessario verificare la risposta dinamica del sistema di trasmissione comprensivo di guida d'onda previsto e realizzato in fase progettuale del TVC. Una serie di modelli teorici sono stati proposti negli anni per capire le caratteristiche di un sistema di trasmissione complesso della pressione alcuni di questi sono riportati in bibliografia [11,12,13]. Solo recentemente alcuni modelli avanzati hanno incluso dei termini dissipativi viscosi ed hanno preso in considerazione l'effetto della temperatura [14,15]. ...
... Both pressure 79 scanners, rated up to 7000 Pa, have static errors within ± 0.0« %. As the 1 meter length 80 tubing can introduce resonance and damping effects, signal corrections were performed 81 using a theoretical transfer function based on the work of Bergh and Tijdeman (1965). 82 Four-hole Cobra probes were used to measure the wake characteristics. ...
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Vibrations due to the alternating shedding of vortexes (vortex-induced vibrations) are a great concern when designing industrial chimneys. These vibrations are complex and can give large amplitudes of motion at low speeds. There are many methods for predicting these vibrations (e.g. wind tunnels or predictive models) but they need improvements.An experiment in a large wind tunnel revealed important, new knowledge on the vortex-shedding frequency which will help predict vortex-induced vibrations using wind tunnels. Instead of a finding a single vortex-shedding frequency, either in the range 0.25-0.27 or near 0.2 as in previous studies, two distinct Strouhal numbers were found at around 0.2 and 0.25.In addition, the spatial unsteady pressure distributions and forcing results at large-scale helped validate an experimental method for simulating the high Reynolds number flow in smaller wind tunnels. These tests showed that surface roughness can trigger high Reynolds number flow and mostly reproduce the spatial pressure distributions. While promising, the vortex-shedding frequencies and forces were different at small-scale than at large-scale.Turbulent atmospheric boundary layers were found to affect the response more than the surface roughness in 3D aeroelastic tests. When testing a rough and a smooth cylinder with a turbulent boundary layer, the responses were similar but the vibration amplitudes and differences increased when testing without the boundary layer. The importance of the turbulent boundary layer on the response was corroborated in a field experiment on a chimney exposed to naturally varying turbulence profiles.Lastly, ways to improve analytic modeling of predicting vortex-induced vibrations were found by finding the best model for a given situation. This was done using two classical design models and a newly approximated model and the best predictive model was found to depend on the product of mass and damping. When this product was low, the newly approximated model worked best while one of the design models was better when the mass-damping product was high.
... Indeed, the unsteady phenomena involved here have a characteristic frequency of the order of 2.5 Hz, which is of course below the cutoff frequency of both systems. This cutoff frequency is estimated to be about 100 Hz for the ESP-64HD (Bergh and Tijdeman, 1965) system and 2000 Hz for the HCLA 12X5DB scanners (Haffner, 2020). Nevertheless, a small time delay of about 5 ms is found in the measurements carried out by the ESP-64HD system ( Fig. 3.11b). ...
The flow around a NACA 0015 airfoil is experimentally controlled using pulsed vortex generator jets (PVGJs) at a chord-based Reynolds number of 4.6 × 105. A special focus is given to the transient effects occurring after the actuation onset. The main objective is the improvement of the performance and maneuverability of the airfoil and more generally of aircrafts. In order to take into account all the phases of the flight envelope, the control has been tested on "baseline" configurations where the flow is attached to (e.g. cruise) or partially separated (e.g. take-off, landing) from the airfoil surface. In all these phases, unsteady loads fluctuations might arise from continuously changing flow conditions such as gusts or rapid maneuvers. The fluidic actuation might help to alleviate these unsteady loads, but to increase the control effectiveness we need to optimize the variation rate of the forces and moment coefficients induced by actuation. For this reason, a detailed study of the transient phenomena occurring after the actuation onset in response to a single-pulse actuation, of duration smaller than the convective time over the airfoil, is carried out. The results of the single-pulse actuation are compared with those obtained from a steady actuation, both operated with the same maximum jet exit velocity.It is observed that a fine-tuned single-pulse actuation, over a partially separated airfoil, can improve the initial rate of variation of the aerodynamic loads by up to 50 % compared to the case of the steady blowing.The analysis of unsteady pressure fields on the airfoil surface and of the velocity fields, obtained using particle image velocimetry (PIV), around the airfoil, showed the preponderant role of the duration of the actuation on the gains obtained. The use of Lagrangian tools (finite-time Lyapunov exponent -FTLE) for the detection of unsteady flow detachments/reattachments showed that the optimal duration of actuation (in terms of loads variation) is associated with transient reattachment/detachment of the flow over the suction surface of the airfoil. Therefore, the transient effects on naturally attached configurations are much less important and the evolution of the loads is not strongly affected by the duration of the actuation. Parametric studies have been carried out to investigate the influence of the location of the actuation over the suction surface of the airfoil compared to the mean baseline separation point. We show that the rates of variation obtained are considerably decreased if the actuation is operated from inside the naturally separated zone. The optimal pulse duration is therefore obtained by a fine-tuned control of the formation and evolution of an unsteady separation region over the suction surface of the airfoil. The understanding of the transient physical mechanisms induced by single-pulse control has finally allowed us to develop energy-efficient control strategies (in terms of the trade-off between the aerodynamic gain and energy expenditure). In particular, we found that a fine-tuned control strategy,consisting of periodic repetition of the single-pulse, can improve the energy efficiency of the control compared to steady blowing. This periodic control strategy is, also, able to increase the initial rate of loads variation compared to the steady control because it exploits the beneficial effects associated with the formation of a separation bubble between successive pulses. The transient improvement of the rate of loads variation obtained in this work might be effective in situations where a fast time response is needed to compensate unsteady aerodynamic effects, such as in gusting flows or during rapid maneuvers.
... The tubing connected to the base-pressure taps had a 1.2 mm inner diameter in 600 mm lengths. The fluctuating pressure measurements were corrected using the methodology described in Bergh & Tijdeman (1965). An appropriate transfer function was applied based on ambient conditions, sampling frequency and the pressure-tap tubing dimensions. ...
The discovery of wake bistability has generated an upsurge in experimental investigations into the wakes of simplified vehicle geometries. Particular focus has centred on the probabilistic switching between two asymmetrical bistable wake states of a square-back Ahmed body; however, the majority of this research has been undertaken in wind tunnels with turbulence intensities of less than $1\,\%$ , considerably lower than typical atmospheric levels. To better simulate bistability under on-road conditions, in which turbulence intensities can easily reach levels of $10\,\%$ or more, this experimental study investigates the effects of free-stream turbulence on the bistability characteristics of the square-back Ahmed body. Through passive generation and quantification of the free-stream turbulent conditions, a monotonic correlation was found between the switching rate and free-stream turbulence intensity.
Small uncrewed aerial vehicles (UAVs) capable of stable, controlled stalled descent offer the possibility for a wider operating envelope and for precise, steep approaches and landings. However, the aerodynamics of stalled flight are inherently complex and underexplored compared to flight regimes with attached flow. This paper presents a number of advancements in these areas—particularly focusing on pressure sensors for estimating flow states. This paper presents a modular, open-source design for in-wing, flow-based differential pressure sensor arrays for estimating flow states without the requirement of fragile pitot tubes or airflow vanes. An extensive, publicly available set of wind tunnel and flight test results from a small UAV with 24 in-wing pressure sensors is provided. The data contain a wide range of incidence angles, including deep stalled states. This paper also presents data-driven regression models for predicting airflow angles and airspeed using only pressure information. Our results demonstrate predictions for airspeed, angle of attack (AoA), and angle of slip (AoS) with root mean square error (RMSE) of 0.07 m⋅s−1, 0.20°, and 2.83°, respectively, using wind tunnel data and all 24 sensors. Finally, this paper provides a placement analysis to determine the optimal sensor locations for estimating airflow data with fewer pressure sensors. Models trained and validated with real flight data show airspeed, AoA, and AoS predictions with RMSE of 0.44 m⋅s−1, 1.54°, and 4.07°, respectively, using data from only three pressure sensors each.
The results of measurements of the three-dimensional flowfield in a low-speed single-stage compressor operating in deep rotating stall are presented in this paper. The measurement technique includes a specially designed omnidirectional five-hole pressure probe, a specially designed near-wall hot-wire probe, high-frequency pressure transducers, and oil flow visualization. The test results provide a detailed description of the flow in and around the stall cell. The flow pattern of the cell is described by velocity vectors, streamlines, and pressure contours. A definition of the stall cell is proposed by using the streamlines in the frame of reference of the stall cell. Upstream of the rotor, the stall cell is characterized by a reversed jet flow at the rotor’s tip and downstream flow at the midspan and hub. Downstream of the stator, the stall cell is composed of low-speed wake flow with circumferential flow near the shroud from the trailing edge to the leading edge of the stall cell.
Practical solutions to the problem of accurately measuring unsteady pressures in wind tunnels are described, with emphasis on the response of pressure systems, calibration techniques and equipment, and wind-tunnel instrumentation. Basic guides for the selection of a pressuregage-volume-connecting-tubing system are given. A cam-type pulsator calibrator with a sinusoidal pressure variation up to !3 psi and a frequency range up to 5000 c is described. The minimum number of pressure gages required for lift and moment measurements is discussed. A brief comment on the interpretation of pressure fluctuations in terms of velocity fluctuations is given. (Author)
A new method Ïor'measuring the pressure distribution on harmonically oscillating wings
  • H Bergh
Bergh, H., A new method Ïor'measuring the pressure distribution on harmonically oscillating wings. Proceedings of the 4th ICAS-congress, Paris 1964 (also NLR-MP.224).
The response of pressure measuring systems to oscillating pÍessures
  • I Taback
Taback, I., The response of pressure measuring systems to oscillating pÍessures. NACA TN 1819; 1949.