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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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... These lengths of tubing then introduce their own internal dynamics, which can severely limit the measurement bandwidth [10]. The dynamic response is typically extremely sensitive to variations in tube diameter within the range of fabrication tolerances [11], so each pressure tap must be empirically calibrated. Since a high-resolution wind tunnel model can have 500-1000 pressure tappings, the process of dynamic calibration is often too impractical if not entirely intractable. ...
... To investigate the effect of different driving functions on the spectral characterization, calibrations were carried out using the canonical test system of a 1 m long, 1 mm inner-diameter tube connecting a pressure sensor to the measurement point. This is a standard test case for which well-validated legacy data and a high-confidence analytical model are available [10,11], and is a reasonable approximation of the present experimental setup. Figure 3 shows G( f ) and ϕ(f) obtained from this test system using white noise, a chirp, and sequential sine waves as the driving function over the range 0 ⩽ f ⩽ 100 Hz. ...
... This unit-to-unit variation can be directly attributed to the very high sensitivity of the dynamic response of the system to small changes in tube diameter (the model showed that a ±0.21 m variation in tube length yielded differences in G( f ) within the overall uncertainty band). Also plotted in the figure is the theoretical envelope from the analytical model [11] yielded by the ±80 µm tolerance on the inner diameter of the silicone tubing used. For G ≲ 0.5 at these low forcing amplitudes, the uncertainty became significant (≳ 10%); this is reflected in the decreasing agreement between the signals and the tolerance envelope from the model for f ≳ 150 Hz. ...
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Measuring surface pressures in a low-speed wind tunnel which are well-resolved in both space and time can be particularly challenging. A technique has therefore been developed for the simultaneous dynamic calibration of large numbers of pressure tappings on a wind tunnel model. A portable, variable-volume plenum is used to calibrate the model in situ. A forcing function consisting of sequential sinusoids at varying frequencies is used to obtain the spectral responses, with feedback control implemented to ensure consistent amplitudes independent of the plenum’s own dynamics. This discrete calibration technique is shown to significantly reduce uncertainty propagation compared to white noise, chirp or step functions. The effectiveness of the dynamic calibration is validated against laser diagnostics in turbulent flow. As a demonstration of the capability of this technique, spatially-resolved surface pressure statistics are then presented for the five wetted faces of a cube in an atmospheric wind tunnel turbulent boundary layer.
... In the 1940s, NASA engineers [1] reported the errors caused by tubes connecting fluctuated pressure to transducers and developed models based on electromechanical analogy. Between the 1950s and 1980s, Iberall and Tijdeman [2,3] developed a model for the frequency response of pneumatic tubes, which was later improved by Wilhelm [4] and Tijdeman [5]. The works of Tijdeman became the foundation of pneumatic tube dynamics in the field of pressure measurement [6], followed by system design [7] and optimization [8] works. ...
... where p 0 is the static pressure, p is the amplitude of the pressure fluctuation, ω is the angular frequency, and i is the imaginary unit. The frequency response of the pneumatic tube system is given by [3] as in equation (5), ...
... where i= √ −1. The above equations are based on the works of Tijdeman [3], Whitmore [9], and Hurst [20], which can give the frequency response of the pneumatic tube system. A simple example is given in figure 2, where used parameters are: ...
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The pneumatic tube plays a critical role in the frequency response of the pressure measurement system, which also significantly affects the accuracy of the measurement data. This paper applied the Monte Carlo uncertainty quantification method to the pressure measurement tube system frequency response and studied the effects of four parameters, including tube length, radius, temperature, and source pressure, on uncertainty characteristics for a given tube system configuration. The reported results show the technique’s applicability, flexibility, and limitations of Guide to the Expression of Uncertainty in Measurement. It is found that the frequency response and corresponding uncertainty are not directly related to frequency but are closely related to the natural frequencies. Comparative experimental results show that the longer tube reduces the system’s natural frequencies and intensifies the phase lag. In addition, larger tube radius and source pressure result in more significant amplitude response peaks. Closed to the natural frequencies, with the increase of the parameter, the uncertainties of frequency response value and the corresponding variation range increase for tube radius and source pressure while decreasing for temperature and tube length.
... Longer samples (% 4000 shedding cycles) were taken for pitch ratios where the flow is observed to be bistable in nature. A transfer function was applied to pressure measurements based on the diameter and length of the pressure tubing according to Bergh and Tijdeman (1965). The time-varying pressure signals were transformed into the frequency domain, and this transfer function was applied before transforming the data back into time domain. ...
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This study investigates the flow behavior over roughened inline cylinders for postcritical flow, a parameter space with relatively little prior scrutiny. Two cylinders of the same relative surface roughness, ks/D=1.9×10−3, separated by a pitch (i.e., L, distance between the centers of two cylinders) between 1.175≤L/D≤10 are studied at Reynolds numbers from 3×105 to 6×105 using unsteady surface pressure measurements. As pitch ratio is increased from L/D=1.175, CD of the downstream cylinder increases sharply at (L/D)c=3.25. This critical pitch ratio (L/D)c is toward the lower end of the reported range for subcritical smooth cylinders. Asymmetric mean gap flow along with alternating reattachment is found for 1.5≤L/D<2.25 (i.e., two asymmetric modes in the gap, mode 1 and mode 2, that are the reflections of each other), and symmetric gap flow with a continuous reattachment is found for 2.25<L/D≤3. The gap flow is also symmetric for the closest pitch ratio tested of L/D=1.175. While the change in upstream cylinder drag coefficient with Reynolds number broadly follows that of an isolated cylinder, for the downstream cylinder, it is approximately independent. The critical separation is also insensitive to Reynolds number within 3×105≤Re≤6×105. Transitions between the reattachment and the co-shedding flow are predominantly continuous over the spanwise planes tested. On the other hand, alternating reattachment occurs in spanwise cells, where one sectional measurement exhibits the asymmetric mode 1 while a spanwise-adjacent section exhibits the asymmetric mode 2 or even symmetric flow. Previously reported maxima in the fluctuating lift and drag coefficients of the downstream cylinder at L/D≈2.4 at subcritical Reynolds numbers are absent in the current investigation.
... Space constraints and machinability of the model require tubing as transmission lines to connect the transducer with the pressure tap. The tubing affects the system's dynamic response, leading to signal distortion (i.e., frequencydependent signal amplification and attenuation as well as phase lag) (Bergh and Tijdeman 1965). Additionally, often the membrane of piezoresistive pressure transducers is embedded within a housing cavity. ...
Article
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Dynamic pressure measurements are indispensable in the field of fluid mechanics. Attaching tubing as a transmission line to the pressure transducer is often unavoidable but significantly reduces the usable bandwidth of the measurement system. Complex fluid-wall interactions and potential outgassing of air are present within systems with water-filled tubes. Comprehensive studies aiding researchers in selecting suitable transmission line parameters (i.e., material, length, and diameter) are not available. A simple calibration apparatus is designed for the frequency response characterization of multiple pressure transducers simultaneously applying a pressure step. The setup is thoroughly characterized and a detailed description is provided to optimize the bandwidth. A piezoresistive pressure transducer attached to water-filled tubes, as commonly used in hydrodynamic experiments, is characterized in the low-frequency range (i.e., f≤300f300f \le {300} Hz). Tube-related effects, such as length, diameter, and material are investigated. The impact of entrapped air within the tubing is analyzed. The feasibility of substituting water with silicone oil to fill the tubes is explored. To optimize the usable bandwidth of the pressure measurement system for dynamic applications, it is essential to maintain short tubing that is as rigid as possible and free from entrapped air. Pressure wave propagation speed is reduced by two orders of magnitude in elastic transmission lines made of silicone. Pressure corrections through dynamic calibration are challenging due to the system’s sensitivity to various parameters affecting the dynamic response.
... The pressure taps on the model surface were connected to two scanners with 128 measurement channels by 750 mm-long PVC tubes. Bergh and Tiedeman (1965) utilized the basic differential equations of fluid dynamics. Based on the transmission characteristics of the pipe, the theoretical formulas for the frequency-response function were derived. ...
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Biomimetic flow control is being widely applied. In the present study, a biomimetic flow control method, i.e., Kirigami scales, was applied on a 1:2 rectangular cylinder. The effects of scales' shapes and pasting surfaces on the aerodynamics and circumferential flow patterns of a 1:2 rectangular cylinder were studied. Three scale shapes were investigated with different pasting methods, i.e., elliptical, circular, and triangular scales. The Reynolds number (Re) was set at 1.3–3.1 × 10⁴. The surface pressure distributions and the integrated aerodynamic forces were further analyzed at Re = 1.3 × 10⁴. Results show that pasting the elliptical scales on all surfaces performs best, reaching a 2.4% drag reduction and a 76.4% lift reduction. Moreover, the elliptical and triangular scales on the windward and leeward surfaces can significantly reduce the Re effect. To reveal the control mechanism, the particle image velocimetry technique was employed to obtain the circumferential and wake flow fields. The time-averaged and phase-averaged results indicate that the Kirigami scales can push the interactions of shear layers and the shedding vortices further downstream. The Proper orthogonal decomposition analysis and time-averaged turbulent kinetic energy (TKE) results indicate that the wake vortex shedding is significantly suppressed. The spanwise wake flow field was also investigated. Results show that the spanwise TKE values are significantly reduced. This study further deepened the application of Kirigami scales on the common blunt bodies.
Article
Resonant oscillations of gas in a closed tube with a heat source are studied. The amplitude–frequency characteristics and spatial distributions of pressure and velocity amplitudes in a tube with a radial temperature gradient are calculated. It is shown that a radial temperature gradient leads to the radial dependence of the oscillation velocity in the flow core and reduces the average value of the momentum source due to viscosity. Together with the temperature dependence of the viscosity, this leads to the amplification of resonant gas oscillations in a tube with a heat source. The influence of the heat source on the resonant gas oscillations is determined by the radial temperature gradient and the square of the reduced oscillation frequency.
Article
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Surface pressure measurement via pressure taps is an integral part of wind tunnel testing. Commonly, the pressure signal is transferred from the taps to a pressure measurement device through an appropriate system of tubing and possibly other components. Depending on its characteristics, the system distorts the dynamics of the signal and, when these dynamics are of interest, appropriate correction/calibration is necessary, taking into account its frequency response. In this context, a novel approach of tubing dynamic calibration is proposed here, using a single pressure measurement device instead of two or more, as is commonly done. The approach accounts for both the amplitude distortion and the phase shift of a selectable range of computer-generated dynamic signals, produced through a speaker. Apart from the innovative use of a single pressure sensor, e.g. in situations where a suitable multi-port pressure scanner is unavailable, the principal merits of the proposed procedure include its straightforward implementation whenever a component of the tubing system is altered (e.g. tube length, different pressure scanner) and the elimination of uncertainty stemming from differences between pressure sensors due to malfunction, inappropriate calibration and inattentive maintenance. The procedure is successfully validated by applying it to two different types of input signal.
Article
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.