How to Measure Fluctuating Pressure? | Wind Engineering

In this article we will discuss about how to measure fluctuating pressure caused my wind movements.

Pressure Transducers:

The basic requirement of a pressure transducer is a device which accurately transforms a pressure difference to an electrical voltage.

Two basic phenomena are used:

(i) The change in resistance of conducting or semiconducting element as it is strained; and

(ii) The change of capacitance as one plate of a capacitor is distorted.

A microphone is a very sensitive form of pressure transducer usually designed to measure only fluctuations at high frequencies and hence is not suitable for wind engineering applications.

Pressure transducers are available in three forms absolute (the rear of the diaphragm is exposed to a fixed reference pressure, usually a hard vacuum), gage (referenced to atmospheric pressure), and differential, for which the reference pressure is selected by the user. In wind engineering, the latter type is invariably used.

The performance of pressure transducers has improved greatly since they were first introduced in the nineteen-fifties. Modern instruments can have a response from zero to several thousand Hertz with very stable sensitivities. The desirable pressure difference range is ± 1500 Pascals (N/m²), for both wind-tunnel and full-scale measurements. This is at the low pressure end (high sensitivity) of most designs of transducer, so the choice for wind engineering purposes is fairly limited.

An older type of capacitative pressure transducer is based on the capacitance principle which was designed to fit inside a ‘Scanivalve’ pressure scanning device. These transducers had high sensitivity, but were expensive and had variable frequency response characteristics.

Modern type of solid state piezo-resistive pressure ‘sensor’ has now become the norm for wind engineering. These sensors are fabricated in high volume using silicon processing techniques from the semiconductor industry, and are hence cheap and have very repeatable properties.

Strain-sensitive resistors are ion implanted into silicon wafers on one side, and a diaphragm is created by chemically etching the silicon on the other side. Typical diaphragm thicknesses are 5 to 200 microns, with values at the lower end for wind engineering applications. Many of these devices, including that shown in Figure 2, contain built-in amplifiers.

Scanning Devices:

Scanning devices for measurement of pressures at a large number of points, were developed for, and are still mainly used, in the aerospace industry. The requirements in this industry are different to those in wind engineering. In aeronautical applications, steady pressures from many measurement positions are required to be rapidly sampled.

A reasonably short response or settling time is required to maximise the scanning speed. However, in wind engineering the requirement is to measure rapidly fluctuating pressures sequentially for a defined sample time. The physical characteristics of the scanning device form part of the measurement system and should be included in any calibration of the frequency response of the system. Two types of scanning devices are available the electro­mechanical type, and the electronic type.

In the older electro-mechanical type, a single pressure transducer is sequentially connected to many pressure tappings. The pressure transducer may be inserted in the device, or mounted externally. The internal tubing connections are complex in geometry and vary between different types. The tapered tubing and right angled bends cannot be included in theoretical models, and experimental calibration of the frequency response of measurement systems including these devices, is required.

A recent development is the electronic pressure scanner. This consists of a module containing a number (typically 16 or 32) of silicon piezo-resistive pressure sensors, one for each pressure port, which are electronically multiplexed at up to 20,000 Hertz, through an amplifier. The amplifier and multiplexing circuitry are contained inside the module, which is quite small in volume and can often be mounted within wind-tunnel models.

These devices have largely replaced the electro-mechanical scanners in the aeronautical industry, and are starting to be adopted in wind engineering. The multiplexing rate is sufficiently greater than the frequencies of interest in wind engineering, thus enabling effectively simultaneous sampling of pressures from many pressure taps on wind-tunnel models.

Prediction of Response to Fluctuating Pressures:

Determination of the response to fluctuating pressures of a proposed measurement system may be required for either of two reasons. The first reason is to determine the amplitude and phase response of a system with the intent of correcting the measurements after sampling.

Although correction circuits have been used, it is very difficult to simultaneously correct both amplitude and phase, and digital methods are more effective. The second reason is to develop a system with characteristics such that measurements can be carried out over the required bandwidth without correction. Systems of this type are the main ones of interest in this paper.

Theoretical and experimental methods of determination of frequency response are available, and are discussed following:

1. Theoretical Model:

The response of a measurement system to fluctuating pressures depends on the characteristics of all the elements of the system, including pressure tapping, manifold if used, connecting tubing, pressure sensor and/or scanner. Although experimental calibration should always be carried out for confirmation, a theoretical model of the response of systems is extremely useful for generic studies, and for the initial design stage of proposed measurement systems.

For many years the definitive model has been that of Bergh and Tijdeman (1965). This followed a number of earlier studies, notably that of Iberall (1950). Bergh and Tijdeman derived a recursion formula for the sinusoidal pressure fluctuation in a volume j connected by lengths of tubing to a preceding volume j – 1, and to the following volume, j + 1.

It is based on a laminar viscous flow model of the fluctuating flow in the tubes, and has been shown to model well the behaviour of real measurement systems, when the tube lengths and diameters, and transducer volume and diaphragm flexibility, are accurately known and incorporated into the calculations.

The diaphragm flexibility, which can be significant for many transducers, can often be conveniently represented by an equivalent additional volume which is a constant for a given transducer. Bergh and Tijdeman (1965) and Holmes and Lewis (1987) describe methods of measuring this flexibility experimentally.

An example of the agreement between the theory and experiment is given in Figure 3. For one of the transducers, it was necessary to model the dynamic diaphragm flexibility (i.e., inertial effects on the response of the diaphragm) to obtain agreement with the measurements.

The original work of Bergh and Tijdeman was applied to series connected tubes and volumes. The theory has since been extended to parallel-tube/manifold systems by Gumley (1983), to ring-connected reference systems by Waldeck (1986), and to the leaked-tube system by Holmes and Lewis (1989).

2. Experimental Calibration:

Experimental calibration of the frequency response of measurement systems to be used in practice should always be carried out. Small changes in dimensions, especially tubing diameters can have significant effects on the response characteristics, and cannot always be measured with sufficient accuracy.

The fundamental requirements for the calibration equipment are:

(a) A source of fluctuating pressure.

(b) A reference or coupling cavity.

(c) A reference flush-mounted transducer which is used to measure the pressure in the cavity.

(d) Amplitude and phase measuring equipment for the output of the reference transducer, and that of the system under test. This could be a digital computer.

Although random pressure fluctuations, in some cases derived from a wind tunnel, have been used, sinusoidal fluctuations are recommended for more accurate calibrations. These may be obtained by use of a fluidic function generator as used by Irwin et al. (1979), and Holmes and Lewis (1987), or a loudspeaker.

3. Upper Frequency Limit:

Since wind pressure fluctuations on buildings are non-Gaussian, there is no simple relationship between the peak pressures and the standard deviation, and peak pressures or peak factors must be determined experimentally. Unfortunately the values of recorded peak pressures are highly dependent on the characteristics of the measurement system at the high frequency end. Several investigations have been carried out of the frequency response requirements for both point pressures and area-averaged pressures, e.g., Durgin (1982), Marshall and Reinhold (1982), Holmes (1984), and Letchford et al. (1992).

Irwin (1988), based on earlier work, suggested that to avoid attenuation of peaks in negative pressure regions for tall building tests in wind tunnels the measurement system should have a flat amplitude response to a frequency equal to approximately 3Ug/B, where Ug is the mean gradient wind speed and B is the building width.

This limit was supported by the work of Letchford et al. (1992), using full-scale data from the Texas Tech low-rise building. However, they converted the desirable upper frequency limit to 10U_h/B, where U_h, is the mean wind speed at the top of the building.

Although the upper frequency limit will depend on building shape, wind direction and the nature of the flow in the vicinity of the measurement position (i.e., stagnation, separation, wake), the above criteria can be used in the absence of better values.

Tubing System for Single-Point Measurements:

Examples of the theoretical amplitude and phase response characteristics of two simple measurement systems, each consisting of a length of tubing of constant diameter connecting the point of measurement to a pressure transducer, are shown in Figure 4.

The pressure transducer is represented by a volume which will comprise the actual physical volume to which the transducer diaphragm is exposed, plus the equivalent additional volume associated with the flexibility of the diaphragm. The systems shown in Figure 4 would only be suitable for measurements of static pressures, and dynamic pressures at low frequencies (less than 20 Hertz), unless analogue or digital corrections were applied to the measured pressures.

Three common practical systems for single-point measurements, that require no correction will be discussed:

(a) “Short” tube systems;

(b) “Restricted” tube systems; and

(c) “Leaked” tube systems.

A comparison of the relative merits of each system for typical measurement situations will be given:

(a) Short-Tube Systems:

This system uses a relatively short length of tubing to connect the measurement point to the sensor. Typically, for wind-tunnel application, this may consist of tubing 20-100 millimetres long, and 1-2 mm internal diameter. The short tube lengths will result in resonant frequencies that are high, hopefully well above the range of interest for the measurements.

However, the short tube also results in low dissipation of energy, and the amplitude response rises to a high value at the peak. The amplitude ratio may exceed 1.1 at frequencies as low as 20% of the resonant frequency. The transducer volume may also be of the same order of magnitude as the tubing volume; in this case, the frequency response will be quite dependent on this variable. Normally, an electronic low-pass filter will be required for this system.

Figure 5 shows the computed responses for two systems of this type with typical tube lengths and diameters. A transducer volume of 100 mm³ has been assumed. The usable frequency range for both the systems shown is 0 Hertz to about 120 Hertz. This may be adequate for many applications, but in many cases a much higher upper frequency limit is required. Then restricted-tube systems or leaked-tube systems are more appropriate.

(b) Restricted-Tube Systems:

Restricted-tube systems may be defined as those involving one or more changes in internal diameter along the tube length. Such systems often allow location of pressure sensors at distances of 150-500 mm from the measurement point, with good amplitude and phase characteristics up to 200 Hertz, or more.

The simplest system of this type is the two-stage type, in which a section of narrower tube is inserted between the main tube section and the transducer. Figure 6 shows the computed response characteristics for a two-stage system with a second stage tube diameter equal to one-third of that of the first stage.

Keeping the overall tube length constant, the length of the second stage tube has been chosen to give the least departure from unity of the amplitude response. The figure also shows the contributions of each stage to the amplitude and phase response. The resonance in the first stage tube is damped by the second stage, consisting of the narrow tube with transducer volume, to give a nearly flat combined amplitude response, and near-linear phase response.

Figure 7 shows the response for three systems, including that shown in Figure 6, giving similar response characteristics. They each have the same overall tubing length (500 mm), but have the small diameter tubing arranged differently with respect to the main tube. The three systems shown have two-, three- and four- stage tubing arrangements, and have acceptable frequency response characteristics to frequencies approaching 300 Hertz.

Systems which are most popular in wind engineering studies, i.e. model studies of wind loads on structures, consist of one or more short lengths of very small diameter capillary tubing or “restrictors”, usually made from metal, inserted in the flexible main tube line, thus forming a three-stage system. Restrictors were originally used by Surry and Isyumov (1975), and their effects first investigated in detail by Irwin et.al. (1979).

Holmes and Lewis (1987) describe an optimisation process for systems of this type. Figure 8, derived from results in that paper, shows the response characteristics for three-stage systems with restrictors of three different internal diameters; in each case, the amplitude response has been optimised by moving the restrictor to the position to produce a flat (within ±5%) amplitude response to the highest frequency, whilst keeping the overall tube length constant. The three-stage system from Figure 7 is included in Figure 8.

There is an optimum length of restrictor, of a given internal diameter, to give the best response. This tends to be one whose optimum position is close to the transducer, rather than close to the tube inlet, even though the latter position produces a larger damping effect.

Figure 9 shows an example of the relationship between the optimum position of a restrictor and its length for a fixed internal diameter (0.5 mm). As the length of the restrictor increases, its optimum position becomes independent of its length. For a given main tube length and diameter, there is an optimum restrictor internal diameter.

Comparing Figures 7 and 8 with Figure 4, which includes the response of a system with the same overall tube length, main tube diameter and transducer volume, it can be seen that restricted-tube systems are very effective in removing resonant peaks and giving linear phase response characteristics. Comparison with Figure 5 shows that an effective frequency range can be obtained which is better than that for a constant diameter tubing with a fraction of the length.

An even better frequency range can be obtained with a leaked-tube system, as described following:

(c) Leaked-Tube Systems:

The leaked-tube system was proposed by Gerstoft and Hansen (1987). A relatively flat amplitude frequency response to frequencies of 500 Hertz, with 1 metre of connecting tubing, is possible with a system of this type.

This is achieved by inserting a controlled side leak part-way along the main connecting tube, usually close to the transducer. It has the effect of attenuating the amplitude response to low frequency fluctuations, and to steady pressures, to the level of a conventional closed system at higher frequencies. Thus, the leak effectively introduces a high- pass filter into the system. The amplitude ratio at frequencies approaching zero, is simply a function of the resistance to steady laminar flow of the main tube and leak tube.

Figure 10 shows the amplitude response of a leaked tube system computed using a modified version of the Bergh and Tijdeman theory. The response of the closed system with the same tube length and diameter is also shown in this Figure. The low-frequency attenuation effect of the leak, as described above, is clearly shown.

The response characteristics of several practical realisations of this system, with and without a ‘Scanivalve’ scanning device, have been described by Holmes and Lewis (1989). A requirement when using these systems in practice, is to ensure that the outlet of the leak tube is exposed to an environment with a negligible level of pressure fluctuations, otherwise the system will try to average any pressure fluctuations there with those being measured at the inlet to the main tube.

Parallel Tube or Manifold Systems:

Systems which attempt to average the pressure fluctuations from a number of measurement points have become popular recently, after being first used in wind engineering by Surry and Stathopoulos (1977).

Figure 11 shows the type of parallel tube and manifold arrangement that has been commonly used in wind engineering work. Provided that the inlet tubes are identical in length and diameter, such a system should provide a true average in the manifold, of the fluctuating pressures at the entry to the m input tubes, assuming that laminar flow exists in the tubes. Gumley (1983) extended the Bergh and Tijdeman theory to cover the manifolds for pressure averaging. Holmes and Lewis (1987) also used the theory to optimize the design of systems of this type.

Figure 12 shows the amplitude and phase response for optimized systems of this type with ten input tubes supplying a manifold of 100 mm³ volume. The response of a single input system of the same overall length, and using the same restrictor tube, is shown for comparison purposes.

Usually, flatter amplitude response curves out to higher frequencies, can be obtained with the multi-tube-manifold systems, due to the reinforcement of the higher frequencies in the input tubes. However, once the number of input tubes exceeds about five, there is little change to the response characteristics. The response is also not greatly sensitive to the volume of the averaging manifold.

Gumley (1981) and Letchford (1987) investigated systems with more than one manifold, both theoretically and experimentally. However, it is difficult to see any advantage of such systems over the single manifold system, except for the convenience of making tube connections.

The assumption that the average of discrete fluctuating point pressures, sampled within a finite area of a surface, adequately approximates the continuous average aerodynamic load on the surface requires consideration. This has been carried out by Surry and Stathopoulos (1977) and Holmes and Lewis (1987).

Figure 13, reproduced from Holmes and Lewis (1987), shows the ratio of the variance of the averaged panel force to the variance of the point pressure, using firstly, the correct continuous averaging over the panel denoted by R_c, and secondly, the discrete averaging approximation performed using the pneumatic averaging system with the ten pressure tappings within a panel, denoted by R_d.

Calculations of these ratios were made, assuming a correlation coefficient for the fluctuating pressures of the form, exp(-Cr), where r is a separation distance, and C is a constant. The variance of the local pressure fluctuations across the panel of dimensions B by B/2, were assumed constant.

It can be seen that R_d exceeds R_c for all values of CB. This is due to the implied assumption, in the discrete averaging, that the pressure fluctuations are fully correlated in the tributary area around each pressure tap. Clearly, the error increases with increasing C due to the lower correlation of the pressure fluctuations, and with increasing panel size, B.

However, the errors can be decreased by increasing the number of pressure tappings within a panel of a certain size. However, it should be noted that the errors are larger at higher frequencies than at lower frequencies; a more detailed analysis of the errors requires knowledge of the coherence of the pressure fluctuations.