Abstract

The Pulsed Wire Anemometer: Review and Further Developments

L.J.S. Bradbury

Department of Mechanical Engineering, University of Plymouth, England

Introduction

In spite of the efforts of about eighty years of fairly intensive scientific effort, our understanding of turbulent flows is far from complete and our ability to predict their behaviour is still very uncertain. There are no entirely rational theories of turbulence and all the models used to predict flow development rely on experimental data in one form or another to establish various empirical constants used in the theoretical models. Thus, the history of development of turbulence modelling has been inextricably linked to progress

In the 1930's, the only significant body of data on turbulent flow development consisted of mean velocity profiles in turbulent boundary layers and this enabled various simple momentum integral models of turbulent boundary layer development to be produced which relied on only one or two constants to enable them to be used practically. However, the predictive accuracy of these models was extremely limited and confined to situations not very different from the experimental arrangements that had been used to provide the empirical constants. With the development of the hot wire anemometer, more detailed measurements of the structure of turbulent flows became possible and higher order integral methods were developed and, with the advent of computers that could be used to solve sets of simultaneous partial differential equations, point momentum and energy equation methods were developed. However, in every case, experimental data had to be used to establish an ever enlarging set of empirical constants in the models. In many ways, the theoretical models could be viewed as a sophisticated fitting procedure to the experimental data which also ensured that an increasing hierarchy of conservation relationships were also being satisfied. However, an important drawback to the experimental data was that the hot wire anemometer could only be used in turbulent flows with comparatively low levels of turbulence relative to the local mean velocity and so most of the experimental data were still confined to boundary layer flows. However, the theoretical methods based on solutions of the Reynolds equations could be applied to flows without this restriction but, without experimental data on these flows, the predictive accuracy was unknown. There was therefore a requirement for an experimental technique which could be used to study highly turbulent flows.

Without doubt, the most important development in turbulence experimental techniques was the arrival of laser light scattering methods with Doppler difference anemometry being the most important variant. With this technique and the development of laser frequency shifting techniques, measurements could be made in turbulent flows without any restriction on turbulence levels although there were and are many practical and theoretical difficulties to be overcome in producing high accuracy reliable data. It is also an expensive technique and its proper application requires that the experimenter has a good understanding of lasers, optics, light scattering theory and sampling theory.

Another but far less well known technique that can be used in highly turbulent flows is the pulsed wire anemometer and the purpose of this paper is to review work that has been done on this technique and also suggest further developments that could be made in its range of application. At the outset, it should be made clear that the potential of pulsed wire anemometry is less than that of laser Doppler anemometry but, on the other hand, it has certainly enabled measurements to be made that would not have been possible previously and there is also additional scope for further developments in the technique.

There are three types of probe that have been used in pulsed wire anemometry. They are (i) the crossed wire velocity probe, (ii) the parallel wire wall shear stress probe and (iii) the parallel wire velocity probe. These will be discussed in turn.

The Crossed Wire Velocity Probe

This is the probe configuration that has been most commonly used. The probe consists of three fine wires as shown in figure 1. The central wire is the pulsed wire and on either side of this are the sensor wires with their axes perpendicular to the pulsed wire. The principle of operation is very simple. The central wire - which is typically a 9 micron Tungsten wire of about 4 mm in length - is pulsed with a short duration voltage pulse of a few microseconds duration. The amplitude of the voltage pulsed will be discussed later but it is chosen to raise the temperature of the wire to several hundred degrees Centigrade. This causes a tracer of heated air to be released into the flow which is convected away with the velocity of the airstream passing the probe at that moment. The two sensor wires - which are usually of 2.5 micron diameter Tungsten wire - are operated as simple resistance thermometers and they are used to measure the time of arrival of the heat tracer at one or other of the two sensor wires. In an ideal situation, the time taken for the tracer to reach a sensor wire would be

where s is the spacing between the pulsed wire and the sensor wire, is the magnitude of the velocity vector and y is the angle between the direction normal to the plane of the probe and the instantaneous velocity vector (see figure 1). The plane of the probe is here defined as the plane parallel to the axes of all three wires in the probe. Thus, from the time of flight t_c the magnitude of the velocity vector resolved at right angles to the plane of the probe can be obtained. The use of two sensor wires ensures that the flow direction is unambiguously determined; the only restriction is in the length of the wires, l, since arctan(l/2s) gives the largest angular deviation of the flow that can be sensed. The most commonly used probes have a value of l/s of about 5 giving a yaw response up to about 70º. \

In a turbulent flow, the probe is repetitively pulsed and an ensemble of velocity values is obtained from which both the mean velocity and the turbulent intensity can be deduced. Furthermore, the velocity and intensity in any direction can be obtained simply by aligning the probe in the appropriate direction. By making measurements at several angles, the flow direction can be obtained along with the normal and shear stresses. The ensemble of velocity values can be used to obtain probability estimates and, finally, by using a non-periodic sampling rate, it is also possible to obtain spectral information at frequencies above the normal Nyquist frequency.

Although the principle of the pulsed wire anemometer is very simple, its development into a useable technique involved overcoming a number of theoretical and practical problems. Most of these are covered in the early paper by Bradbury and Castro (1971) but these detailed problems wiII not be considered here. Castro (1992) published a comprehensive review of later developments in pulsed wire anemometry and this present paper uses some of the same examples described by Castro to illustrate the range of measurements that can be made with pulsed wire anemometry. However, the additional purpose of the present paper is to suggest some further developments in the technique.

Examples of Velocity Measurements with a Crossed Wire Probe

Before considering results of measurements with a pulsed wire anemometer, it is useful to look at typical probe calibrations. Figure 2 shows a velocity calibration. Because of the effects of thermal diffusion, the calibration of U against the reciprocal of the time of flight T is not exactly linear but a good fit to the data has been found to be given by the expression

where A and B are constants found by least squares fitting to the experimental data.

Figure 3 shows a yaw calibration which according to the simple model should be a cosine law. The data fits the cosine law quite well and a yaw response is maintained up to an angle of about 70 degrees. It is shown by Bradbury and Castro (1971) that missing tracers that Iie outside this angular range only have a small effect on the accuracy of turbulence measurements.

Some examples of measurements with a pulsed wire anemometer will now be considered.

The first example from Bradbury (1976) has been chosen simply to illustrate the use of the pulsed wire in a flow in which flow reversals occur and where, therefore, the turbulence levels are very high. The example also shows hot wire results to illustrate the errors that arise with this technique in such a flow. Figure 4 shows the mean velocity and turbulent intensity distributions in the wake of a normal flat plate, one plate width downstream within the reverse flow region.

The second example is a straightforward application of the pulsed wire anemometer to the study of the wake flow downstream of a model Ford Transit van - Watts (1982). Figure 5 shows contours of constant mean velocity in the wake of a model van. It shows the existence of a significant region of reverse flow and is an example of the sort of practical studies that can be undertaken with a pulsed wire anemometer.

The third example has been chosen to illustrate the use of the pulsed wire anemometer in a flow in which there are fluctuations in a foreign gas concentration - Hall (1979). The pulsed wire anemometer is a time-of-flight device and so, unlike the hot wire anemometer, is not sensitive to variations in foreign gas concentration provided the flow is sensibly isothermal. In figure 6, the mean velocity and turbulent intensity distributions are shown through a rough wall turbulent boundary layer into which a continuous heavy gas release has occured. The profiles are compared with the case when the gas release is absent. Although the turbulence levels are no higher than in an ordinary turbulent boundary layer, such results could not have be obtained with a hot wire because the presence of the foreign gas would have serious effects on the heat transfer rates from the hot wire.

Before considering other types of pulsed wire technique, it should also be mentioned that near wall measurements with a crossed wire pulsed wire probe can be made if a through wall probe is constructed. Figure 7 shows a photograph of such a probe used by Castro and Dianat (1990). In this probe, the two sensor wires are welded to electrodes flush in the wall and are mounted at right angles to the wall by being welded to an outer electrode as shown. The pulsed wire is mounted on a micrometer traversing gear and can be traversed up and down between the two sensor wires. The geometry is thus the same as that of a normal crossed wire probe but it enables measurements to be made in the very near wall region. Figure 8 shows a comparison between pulsed wire measurements and hot wire measurements in a conventional turbulent boundary layer. The hot wire measurement were confined to the outer region of the boundary but the agreement with the pulsed wire results is very good. However, very close to the wall in the sub-layer, the pulsed wire results deviate from the viscous sub-layer profile. Castro and Dianat (1990) showed that this was due the effect of thermal diffusion on the transport of the tracer and they developed a simple method for correcting for this effect. Figure 9 shows the velocity profile in the sub-layer before and after their correction has been applied. With the correction, the agreement with the viscous sub-layer profile is now very good. Of course, the advantage of the pulsed wire probe is that it can be used in separating boundary layer flows. In addition to Castro and Dianat (1990), wall region measurements of this sort have also been made by Devenport, Evans and Sutton (1990).

It is important to stress the limitations of pulsed wire anemometry. The really significant limitations are as follows:

(i) In order to achieve satisfactory sensor wire signals, it is generally necessary to use sensor wires of 2.5 micron diameter Tungsten. These wires are usually in the range from 3-5 mm in length and can easily be broken by mechanical shock. The probes are much more fragile than hot wire probes and an experimental environment free of significant mechanical shocks is necessary. On the other hand, this problem should not be over-exaggerated because, with experience, it is possible to use probes for a considerable period without breaking them. As an example, a probe that the author uses for checking the electronic processing circuitry has been in use for five years without breaking a wire.

The fragility of the pulsed wire probes would be greatly reduced if, instead of the 2.5 micron Tungsten wires, thin films on Quartz fibres were used for the sensor elements. The technology for doing this is certainly now available but it would no doubt require some development work in order to construct such a probe.

(ii) The velocity range over which the probe can be used is limited to a range from about 0.1-0.2 metres/sec up to about 8-10 metres/sec. The lower limit comes from the need for the transport of the heat tracer to be dominated by convection rather than thermal diffusion. The upper limit arises from some restrictions in the signal processing circuitry and also that the single/noise ratio decreases with increasing velocity.

(iii) The flows must be isothermal. Clearly, if temperature fluctuations are present in the flow which are of the same order as the temperatures of the heat tracers then the individual heat tracer times-of-flight cannot be discerned.

The pulsed wire wall shear stress probe.

In the early period of developing the pulsed wire anemometer, Gaster (1969) suggested to the author that the technique might be used to develop a means of measuring wall shear stress that could be used in flows with large fluctuations in wall shear stress including reversals of stress direction. In the original idea, it was proposed to surface mount three parallel thin films with a geometry similar to that shown in the sketch in figure 10. The principle of operation is very similar to the pulsed wire velocity probe in that the central film is pulsed with a short duration voltage pulse and the time for the resultant heat tracer to reach one or other of the two sensor films is measured. On the basis of simple dimensional analysis, the time of flight, t, is related to the instantaneous velocity gradient, ¶u/¶y, the thermal diffusivity coefficient, k , and the space between the pulsed and sensor films, h, by the simple functional relationship

In the case of the wall probe, the transport of the heat tracer is through a combination of diffusion and convection. On the basis of a very simple argument, Bradbury and Ginder (1973) obtained a form for this relationship namely

Experiments carried out with surface mounted thin film gauges in a laminar flow channel resulted in the calibration results shown in figure 10. Considering the simplicity of the argument behind equation (4), the agreement with its general form is very good. However, a major drawback with these surface mounted thin film results was that the signal levels were very low (typical sensor film amplitudes were of the order of a few microvolts) with a poor signal to noise ratio. In spite of various efforts to improve the situation, it proved impossible to use surface mounted thin films in a turbulent flow. In order to produce a useable wall shear stress probe, it was necessary to resort to the use of thin wires mounted close to but not touching the surface. The small air gap (typically 50 micron) avoided heat loss to the substrate and improved the signal to noise ratio dramatically. It should be added that a whole series of numerical solutions to the heat convection/conduction equation were carried out by Ginder (1971) and these confirmed the findings of the experimental observations about the effect of the substrate on reducing the signal levels.

The parallel wire wall shear stress probe (shown schematically in figure 11) has been used by several authors to study both mean and fluctuating wall shear stress in a variety of flows. Figure 12 shows some results of Ruderich and Fernholz (1986) of the mean and fluctuating wall shear stress on the splitter plate behind a normal fence.

Another example of the use of the wall shear stress probe was in the study of the flow beneath a simplified model of a tricone drilling bit. Tricone drilling bits are widely used in drilling oil wells and there is some interest in the distribution of wall shear stress produced by the three jets of drilling mud used to remove rock particles from the drill face. White, Escudier and Gavignet (1987) carried out a study of the shear stress distributions in a simplified model of the drilling situation - see figure 13 - using air rather than mud for the jet flows. The flow around the drill bit is complex and three-dimensional and, in addition, to wall shear stress measurements with the pulsed wire probe, they also made a number of surface flow visualisation studies. Figure 14 shows an example of one of their flow visualisation results with vectors of the wall shear stress obtained from the pulsed wire probe superimposed on the flow pattern. The qualitative agreement is very good and, with the quantitative results given in the original report, is a good demonstration of the complex flows that can be studied with the pulsed wire wall shear stress probe.

The potential of the pulsed wire wall shear stress gauge seems to the author to be very significant and it has been therefore rather surprising that it has not found more widespread use - particularly in areas like the three dimensional flows over aircraft wings.

It is not possible in a short review article to cover all the facets of the pulsed wire wall shear stress probe but a more complete discussion of the technique is given by Castro, Dianat and Bradbury (1987).

Possible Developments with Wall Shear Stress Measurements

It was mentioned in section 3 that the initial idea for wall shear stress measurements was to use surface mounted thin films. The original work on these thin film gauges was included in this paper because this remains an attractive proposition. As has already been mentioned, the idea had to be abandoned originally because of the low signal to noise ratio of the surface sensor gauges. However, the signal to noise ratio would be significantly improved if, instead of using thin film gauges as resistance thermometers, thermoelectric gauges could be laid down by standard thin film vacuum deposition techniques. In principle, multi-junction thermocouples could be produced in a thin film form and would result in a very robust probe that could be manufactured with a high degree of repeatability. In this way, individual probe calibrations might not be necessary.

Parallel Wire Velocity Probe

The first paper on pulsed wire anemometry was by Bauer (1965). In this paper, Bauer used a pulsed wire probe consisting of two parallel wires as shown in figure 15. The drawback with this arrangement is that, in a turbulent flow, most of the tracer signals miss the sensor wires - which is the reason for developing the crossed wire probe discussed in section 2. On a number of occasions, this restricted angular response has been exploited by using a parallel wire probe as a yaw meter and, in particular, Almeida (1986) used such a probe in the study of a circular jet issuing into a cross flow. However, there is potential for such probes in highly turbulent flows as well.

Let us suppose that we have a parallel wire probe in a turbulent flow as shown in figure 16. It is assumed that the probe is pulsed a large number of times N and that sensor wire signals are obtained on n occasions. On each occasion that a trace is detected, we will have a velocity estimate q and, if we define an angle, dj , as the angular range over which this estimate can be sensed, we may define an estimate of joint probability density function as

where the true value is approached as N® ¥ and dq and dj both tend to zero. p(q,j) is the probability of finding a velocity estimate in the velocity range from q to q+dq and in the angular range from j to j + dj . If this function can be measured, it enables any cross-products of the velocity fluctuations to be calculated since

and this includes, of course, the normal and shear stresses and the turbulent diffusion term that appear in the turbulent energy equation.

The measurement of this joint probability is in principle possible with a parallel wire probe with the slight complication that the angular response of the probe is a function of the velocity q. In ^{appendix A} APPENDIX A. , the form of this function is discussed and it is shown that the angular window decreases with increase in velocity due to the smaller diffusive spread of the wake.

In practice, it might be rather difficult to make such measurements but it is certainly worthy of investigation. In practice, a parallel wire probe would have to be calibrated in a steady stream so that a conventional velocity calibration could first be obtained. Then a series of yaw calibrations would have to be carried out at different velocities in order to determine the variation of the angular window as a function of velocity. The analysis in ^{appendix A} APPENDIX A. should prove useful in establishing the form of this variation from a small number of yaw calibrations.

The main practical difficulty in a highly turbulent flow might be the very large number of samples that may be involved in obtaining reasonable estimates of the complete joint probability distribution. Due to the time constants of the wires, samples cannot be obtained at a rate greater than about 100 samples per second and, without doing any calculations, the author's intuition is that something like a 100,000 samples might be needed at twenty or thirty angles in order to obtain a reasonable estimate of the probability distribution. This would take something of the order of an hour of sampling for each spatial point in the flow. However, this is not entirely unreasonable and it would provide for the first time important information about the higher order cross-products in a highly turbulent flow. Such information would no doubt provide useful data for turbulence modellers!

Concluding Remarks.

This paper has reviewed briefly the various forms of pulsed wire technique that have so far been developed. It has been shown that the crossed wire technique can be used to make velocity and turbulence measurements in highly turbulent flows without any upper restriction on turbulence level and that these measurements can be extended to near wall regions as well. In addition, the parallel wire wall shear stress probe has been discussed and it has again been shown that wall shear stress measurements can be made without any upper restriction on the turbulence levels. The limitations of both the crossed wire probe and the wall shear stress probe have been discussed and a number of suggestions for improving both of them have been made.

Finally, some comments have been made on the potential of a parallel wire probe for use in highly turbulent flows that would enable higher order velocity cross-product terms to be measured. However, a programme of experiments is required to establish if this potential can be realised or not.

The Response of a Pulsed Parallel Wire Probe.

Ignoring the effects of longitudinal diffusion, the temperature distribution in the wake of a pulsed wire is given by

where q(x,y,t) is the temperature in the wake of the pulsed wire, q_pi, is the temperature of the pulsed after the voltage impulse. N_p is the Nusselt number for heat transfer from the pulsed wire. T_pis the pulsed wire time constant. P=Ux/k is the Peciet number and H(x/U) is a Heaviside step function at time t=x/U.

If a sensor wire is placed in this wake at position x, y, its temperature q_s(t) is given by

where T_s is the sensor wire time constant. Using equation (1A) in (2A) gives

In the practical circuit, the sensor vare is differentiated with respect to time and it is this differential signal that is used to trigger the time-of-flight counter. This differential signal has a step-like behaviour at t=U/x with an amplitude given by

If we assume for simplicity that Nusselt number varies like the square root of the Reynolds number, we find that

using the expression for the time constants given by Bradbury and Castro (1971). The angular window of the probe is defined by that value of y/x at which the amplitude of the differentiated signal falls below the trigger level. It can be shown from equation (5A) that this window narrows with increasing velocity. This is simply due to the narrowing of the wake as lateral diffusion diminishes with increasing velocity. There is a counter effect from the other terms in the equation for the differentiated signal but the overall effect is still to produce a narrowing of the ’ window’.

Article presented at the 1st Brazilian School on Transition and Turbulence, Rio de Janeiro, September 21-25, 1998.

Technical Editor: Atila P. Silva Freire.

APPENDIX A. 

Publication Dates