Dissertation Report

Final Report
Investigation and Analysis of the Response of a Piezoelectric
Pressure Sensor in a Shock Tube
Christopher Barrie Neill
2015
3rd Year Individual Project
I certify that all material in this thesis that is not my own work has been identified and that no
material has been included for which a degree has previously been conferred on me.
Signed..............................................................................................................
College of Engineering, Mathematics, and Physical Sciences
University of Exeter

ii
Final Report
ECM3101
Title: Investigation and Analysis of the Response of a Piezoelectric
Pressure Sensor in a Shock Tube
Word count: 6142
Number of pages: 35
Date of submission: Wednesday, 29 April 2015
Student Name: Christopher Barrie Neill
Programme: BEng Mechanical Engineering
Student number: 620014968
Candidate number: 003643
Supervisor: Dr. Matthew Baker

iii
Abstract
A shock tube generates almost instantaneous dynamic pressure changes, in a controlled
environment where the pressure step can be predicted. This system is being developed to
improve the accuracy in the calibration of piezoelectric pressure transducers. This project will
investigate the response of these sensors during an experiment, analyse in detail, patterns and
recurring frequencies with a view to develop a parameterised sensor model. Experimental
results will be supplemented with theoretical values as well as numerical analysis using
ANSYS Fluent. The results from this have identified with confidence, the sensor’s response to
a given pressure step, as well as being able to identify some of the parameters required to model
the systems response, as a combination of damped sine waves.
Keywords: shock tube, dynamic pressure, calibration, piezoelectric, sensor model,
parameterised sensor model

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Table of contents
1. Introduction and background .........................................................................................1
1.1. Background .................................................................................................................1
1.2. The Project ..................................................................................................................1
2. Literature review ..............................................................................................................2
2.1. Dynamic Metrology as a Concept...............................................................................2
2.2. Development of a Shock Tube Method.......................................................................2
2.3. Modelling the Sensor Response using Mathematical Techniques..............................3
2.4. Modelling the Sensor Response using ‘Multi-fit’ Technique.....................................4
3. Methodology and theory ..................................................................................................5
3.1. Shock Tube Theory.....................................................................................................5
3.2. Theoretical Calculations..............................................................................................6
3.3. Apparatus ....................................................................................................................8
4. Experimental work/analytical investigation/ design ...................................................10
4.1. Experimental Work ...................................................................................................10
4.2. Fluent.........................................................................................................................11
4.3. MATLAB..................................................................................................................12
5. Presentation of experimental or analytical results/descriptions of final constructed
product....................................................................................................................................13
5.1. Experimental Data.....................................................................................................13
5.2. Experimental Analysis ..............................................................................................14
5.3. Computational Analysis ............................................................................................24
5.4. Comparison of Results ..............................................................................................25
5.5. Model ........................................................................................................................28
6. Discussion and conclusions ............................................................................................29

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6.1. Sensor Response and Model .....................................................................................29
6.2. Implications...............................................................................................................29
6.3. Future Work ..............................................................................................................29
7. Project management, consideration of sustainability and health and safety............31
7.1. Project Planning ........................................................................................................31
7.2. Sustainability and Health and Safety ........................................................................32
7.3. Project Risks..............................................................................................................33
References...............................................................................................................................34

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1. Introduction and background
1.1. Background
In engineering there is a constant need to be able to measure dynamic pressure changes,
requiring accurately calibrated pressure sensors. Currently most pressure sensors are calibrated
statically, due to the complexity of producing an accurate and repeatable pressure step which
can be used. Applications include measuring the pressure changes within the cylinders of a
combustion engine, where pressure can vary between 0.1 and 10 MPa at a frequency of 30 kHz
[1, 2, 3]. This is a vital way of checking a combustion engine for knocking which can cause
catastrophic and irreparable damage to an engine if not fixed. At the National Physical
Laboratory (NPL), Middlesex physicists have been developing a method for the dynamic
calibration of piezoelectric pressure transducers, with a view to being able to provide an
accurate, dynamic pressure sensor calibration service for industry.
1.2. The Project
In this project, data collected by myself from NPL in 2014, will be analysed with a view to
identifying the sensors response to the applied pressure step. This is important because the
information found can be used to create a parameterised model of the sensors dynamic response
which can be used in calibrations. An accurately calibrated sensor will have substantial
scientific and engineering benefits, both in industry and in research. Once identified in the
experimental data the sensors dynamic response will be compared with theoretical calculations
and computational models from Fluent, this will validate what has been observed in the
experimental data. This information can then be used to predict the sensitivity of the sensor.

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2. Literature review
2.1. Dynamic Metrology as a Concept
Dynamic metrology is the science of measurement, and is a key area of interest in engineering
at present. “The aim on dynamic metrology is to bridge the gap between calibration as a
discipline practised by metrology institutes and scientists, engineers and designers” [4]. The
work performed in this project will contribute towards the development of a method for the
dynamic calibration of pressure sensors for use in industry. The importance of this topic has
led to the creation of a EURAMET (European Association of National Metrology Institutes)
project into the “Development of methods for the evaluation of uncertainty in dynamic
measurement” [4]. Work in this project will reduce the level of uncertainty in a model, by
making a more precise prediction of the sensor response. This is achieved by removing the
uncertainty caused by frequencies picked up by the sensor from the apparatus rather than the
shock wave.
2.2. Development of a Shock Tube Method
At NPL various shock tubes have been designed and developed, these include tubes of various
lengths and material properties, as well as the driven gas, burst pressure and diaphragm
material. This has been published in a report titled; “Towards a shock tube method for the
dynamic calibration of pressure sensors” [5]. This publication contains the majority of
preceding work to this project, and will be used as reference throughout. In this paper there is
an investigation into the effect of different sensor mount materials. The sensor itself is
manufactured to be insensitive to acceleration, but from experimental results, differences in
response with various mounting materials are significant. The work in this project will aim to
analyse the sensor response and recognise what frequencies are caused by the shock wave on
the sensor and what frequencies are generated from the mounting and surrounding apparatus.

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2.3. Modelling the Sensor Response using Mathematical
Techniques
In a paper written by NPL about work carried out by them and also SP (SP Technical Research
Institute of Sweden) there is some analysis of the sensor response. Mathematical modelling
techniques have been used to predict the response of the sensor, and its post-pressure step DC
(direct current) level. DC level represents the voltage level predicted from the sensor response.
It is identified as a “flat” line which represents the centre between each peak and trough. This
DC level can ultimately be used to calculate the sensitivity and calibrate the sensor. Figure 1
shows the mathematical model developed at NPL.
Figure 1: NPL Mathematical Model [6]
It can be seen that this mathematical model (red line) only fits a very short portion of the sensor
response (black line), in this project the aim is to develop a more accurate model. This model
should predict the DC level more accurately, thus reducing any uncertainty in a final
calibration.

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2.4. Modelling the Sensor Response using ‘Multi-fit’ Technique
Following the mathematical modelling technique a new method was devised at NPL, whereby
a series of sine waves can be combined to recreate the sensor response. By varying
characteristics such as; amplitude, frequency, phase, offset and decay in each sine wave, the
residual sum of squares can be reduced to be very small. Figure 2 shows an example of the
multi-fit performed by NPL on some of its data.
Figure 2: NPL Multi-fit Model [6]
It is clear that this model is a better fit than the one constructed mathematically, although in
this project it will be investigated further. The model developed in this project will specifically
look at the parameters required in modelling the sensor’s response, filtering out unwanted
frequencies/comparing with known natural frequencies, should enable the model to be more
accurate.

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3. Methodology and theory
3.1. Shock Tube Theory
To validate the results found using the experimental and computational data, a theoretical value
for the initial pressure step will be essential. This can be derived from ideal gas theory and is
displayed as 𝑃2 in Figure 3. Figure 3 shows how the shock wave propagates through the tube
after the diaphragm bursts.
Figure 3: Shock Wave Propagation [5]
To acquire a value for the pressure step 𝑃2 Equation 1 is used, this has been derived from ideal
gas theory.
𝑝2 = 𝑝1 (1 +
2𝛾1
𝛾1 + 1
(𝑀𝑆
2
− 1))
Equation 1: Pressure Step [5]
Where; 𝑝1 is the pressure in the driven section prior to the diaphragm bursting, and 𝛾1 is the
ratio of the specific heat at constant pressure to that of constant volume. The Mach number of
the shock wave 𝑀𝑆 can be calculated as the ratio of the speed of the shock wave to the speed
of sound in the gas used.

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To calculate the speed of sound in the gas Equation 2 is used.
𝑎1 = √
𝛾1 𝑅𝑇1
𝑚1
Equation 2: Speed of Sound
Where; 𝑇1 is the initial temperature of the gas in the driven section, 𝑅 is the specific gas
constant, and 𝑚1 is the molecular weight of the driven gas. These calculations will be used to
approximate a value for the pressure step, this can then be compared to experimental data
collected from the shock tube at NPL.
3.2. Theoretical Calculations
Using the theoretical equations derived from ideal gas theory, an approximation of the pressure
step can be calculated. Table 1 shows the values necessary for the calculation.
Component Value Units
𝑝1 101000 Pa
𝛾1 1.400 -
𝑇1 293 K
𝑅 8.314 JK-1
mol-1
𝑚1 28.97 Kgmol-1
Table 1: Values for Theoretical Calculation
These values can be substituted into Equation 2 to calculate the speed of sound in the gas.
𝑎1 = 343𝑚𝑠−1
The speed of the shock wave will need to be approximated, to do this the raw experimental
data was used from three runs with plastic inserts (experimental details are explained in section
4.1). By calculating the time between the first and second peaks the time for the shock wave to
travel from the sensor end, along to the driver end and back is known. Knowing that the tube

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is 6m long gives an approximation of the velocity, making the assumption that the shock wave
does not accelerate or decelerate significantly. It is not currently known how significantly the
shock wave changes velocity during a test. Table 2 shows the time between the peaks and their
respective velocities.
Mount Material Time Gap (ms) Distance (m) Velocity (ms-1
)
Steel + Plastic 15.152 6 395.9
Aluminium + Plastic 15.134 6 396.4
Brass + Plastic 15.178 6 395.3
Table 2: Shock Wave Velocities
Using these velocities and the calculated speed of sound in the gas, the Mach number for each
shock wave can be calculated. Table 3 shows the Mach numbers for each run.
Mount Material Mach Number
Steel + Plastic 1.154
Aluminium + Plastic 1.156
Brass + Plastic 1.152
Table 3: Mach Numbers
Now using Equation 1, an approximation for the first pressure step can be calculated. Table 4
shows the value of the pressure step for each run.
Mount Material Pressure Step (bar)
Steel + Plastic 14.0
Aluminium + Plastic 14.1
Brass + Plastic 13.9
Table 4: Pressure Steps
These pressure steps can be compared the experimental results by using the bar/volt conversion
as well as the output in volts of the data.

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3.3. Apparatus
The Shock Tube
At NPL scientists have constructed a shock tube with a view to using it in the development of
a dynamic calibration method. Figure 4 shows an image of the shock tube at NPL.
Figure 4: NPL Shock Tube [5]
The shock tube itself consists of two parts. The driver section, and the driven section. These
are separated by a thin diaphragm made of brass. The pressure in the driven section remains
lower than the driver section prior to the burst. During this time the pressure in the driven
section is increased, up until the point when the diaphragm ruptures and a shock wave
propagates down the driven section of the tube. This shock wave reflects off the end wall which
houses the sensor. This sensor detects a pressure step and generates a charge in the order of a
few pC (pico-coulomb). This is converted by a charge amplifier into a voltage that can be
interpreted by the computer.

9
The Mounting
The sensor is mounted into the end wall of the driven section of the tube. Currently there are
three materials that the mounting block could viably be manufactured from; steel, aluminium
and brass. Each coming in two configurations. In configuration one, the sensor is attached
directly to the metal of the mount. In configuration two, the sensor is attached to a plastic insert
which creates a thin barrier between the sensor and the metal mount. This acts as a damper
when the shock wave hits the mount.
The Sensor
The sensors used in this study are Kistler 603B Piezoelectric Pressure Sensors. These are small,
acceleration compensated sensors which have a short rise time and are manufactured to
withstand pressures up to 200 bar. Figure 5 shows the internal structure of a sensor.
Figure 5: Internal Construction of Sensor [7]
The sensor consists of three quartz plates mounted in series behind a thin diaphragm. When the
diaphragm is distorted due to a pressure change, the crystals are deformed, this generates a very
small charge. The manufacturer estimates that the sensor sensitivity is approximately -5.0
pCbar-1
. This has a very low degree of accuracy because it has been calibrated statically. This
means that there is a significant degree of uncertainty when these sensors are used in precision
engineering, this is the reason for developing a new method for the calibration of these sensors.

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4. Experimental work/analytical investigation/ design
4.1. Experimental Work
A series of experiments were devised for this project using the shock tube at NPL. This would
include six different setups, with two runs of each to account for anomalies. It has already been
proven that this method of experimentation is extremely repeatable, therefore there is no need
to do more than two runs. In total 12 runs were performed. The experimental Details are
displayed in Table 5.
Run Mount Sample Rate Diaphragm Burst Pressure
(bar)
Sensitivity
(barV-1
)
1 Steel + Plastic 5MHz 0.1mm Brass 13.9 3
2 Steel + Plastic 5MHz 0.1mm Brass 13.7 3
3 Aluminium + Plastic 5MHz 0.1mm Brass 13.6 3
4 Aluminium + Plastic 5MHz 0.1mm Brass 14.0 3
5 Brass + Plastic 5MHz 0.1mm Brass 13.4 3
6 Brass + Plastic 5MHz 0.1mm Brass 13.9 3
7 Steel 5MHz 0.1mm Brass 13.9 3
8 Steel 5MHz 0.1mm Brass 13.8 3
9 Aluminium 5MHz 0.1mm Brass 13.8 3
10 Aluminium 5MHz 0.1mm Brass 13.8 3
11 Brass 5MHz 0.1mm Brass 13.7 3
12 Brass 5MHz 0.1mm Brass 14.3 3
Table 5: Experimental Details

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This data will make it possible to identify the sensor’s response to individual parts of the
system. The effect of each different material and the plastic insert should be apparent, once
this is know the response of the sensor to the shock wave alone can be found.
4.2. Fluent
Fluent
It was decided that the shock wave should be analysed using ANSYS Fluent for comparison.
This will be used to validate previous analysis using theoretical and experimental calculations.
The results will show the theoretical pressure across the sensor for the duration of the
experiment.
Geometry and Mesh
The 3D experiment of a shock tube in action can be simulated as a 2D problem, therefore in
this simulation, two rectangles will be used in the place of tubes. The rectangles are of
dimensions 1x0.076m and 2x0.076m respectively. These represent the driver and driven
sections of the shock tube, with the interface between the two acting as the diaphragm. Once
the geometry is complete a mesh is applied. A 10mm mesh was chosen to accommodate the
length of the sections. The mesh generate is shown in Figure 6 below.
Figure 6: Mesh
It can be see that the mesh is uniform and regular, this means that the solution will have good
accuracy.

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Setup
The meshed geometry is taken forward into the computational setup, where the units of
pressure are changed to atm (atmospheres). This is due to the units used during the collection
of the experimental data. The solver is setup as density-based and transient, the energy model
is switched on, and the viscous model changed to inviscid [11]. The material used in the
simulation will be dry air. For consistency this will be given the properties of an ideal gas and
therefore adhere to the laws of ideal gas theory, allowing the results to be comparable with
previous analysis. In solution methods explicit formulation is chosen, meaning that the solution
will be calculated using each steps preceding time step. To simulate the diaphragm bursting an
interface is created between the two overlapping ends of the tubes. The start of the simulation
will represent a point in time immediately after the diaphragm has burst. Finally pressures of
13.9 bar and 1 bar are patched into the driver and driven sections respectively and the
simulation is calculated.
4.3. MATLAB
MATLAB is used in this project for signal analysis. The sigtool application in MATLAB
allows for the design and application of filters. A combination of high-pass, low-pass and band-
pass filters were used in an attempt to remove unwanted frequencies from the experimental
data. During the development of these filters it was decided that by removing these frequencies,
an accurate representation of the sensor response to the shock wave conditions is lost. Therefore
unfiltered, raw experimental data is used for the bulk of the analysis.

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5. Presentation of experimental or analytical
results/descriptions of final constructed product
5.1. Experimental Data
After completing the experiments the data was loaded into Excel for analysis. Figure 7 shows
the raw output data from one of the experiments.
Figure 7: Run 1, Raw Output Data
On this graph three distinct pressure steps can be seen. This represents each time the shock
wave hits the end wall of the driven section. In between steps the wave travels down to the
driver end of the tube and back again, a total of 6m. It is know that the first step is extremely
repeatable and is recorded to a high degree of accuracy. Step two is reasonably good, and will
be used to approximate shock wave velocities as well as compare the initial response of the
sensor, despite it being less repeatable. The third step will not be used as it is unrepeatable and
affected heavily by random events, one such event can be seen in Figure 7. In total 12 sets of
data like this have been attained for analysis.

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5.2. Experimental Analysis
Fast Fourier Transform
The first step in analysing the experimental data is to use a Fast Fourier Transform (FFT). The
FFT will show how often certain frequencies occur within the output signal. The aim is to use
this to identify signals that are not dependent on the mounting setup. The data from all 12 runs
is loaded into MS Excel. An average is taken for each pair of runs, leaving six sets of ‘mean’
data, one for each experimental setup. The data is then cut to a length of 4098 rows starting at
the highest point on the first pressure step. Time is not important for this analysis, therefore
t=0 is set to the first data point on the cut data. An MS Excel FFT is performed and the results
plotted. Figure 8 shows the FFT for all six different experimental setups.
Figure 8: FFT for each Experimental Setup
Most frequencies below 100 kHz will be ignored initially, as the important frequencies occur
between 100 kHz and 500 kHz. It is known from the Kistler 603B Sensor Data Sheet [8] that
the sensors natural frequency is approximately 300 kHz. It can be seen in Figure 8 that there
are a significant number of peaks on the FFT between 200 kHz and 400 kHz. To investigate
this further a comparison must be made between the use of a plastic insert and no insert. It is
expected that data collected with the plastic insert will be clearer with fewer FFT peaks due to

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the damping effect of the plastic. Figure 9 shows a comparison of the FFT plots for steel and
steel with plastic insert.
Figure 9: FFT for Steel
As expected many of the frequencies that occur in the “no insert” tests are removed by the
damping effect of the plastic, therefore during further analysis only the runs with inserts will
be used initially, although in the final analysis all tests will be considered. The final comparison
from the FFT is between the various metal mounts.

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Figure 10 shows the FFT for each of the metal mounts with plastic insert.
Figure 10: FFT of Metal Mounts with Plastic Insert
Figure 10 shows the best representation of the frequencies detected by the sensor in the
moments just after the shock wave hits. As expected there are frequencies at approximately
300 kHz. More specifically the frequencies of; 115 kHz, 250 kHz and 350 kHz have been
identified as consistent throughout all the materials and of significant amplitude. These
frequencies will be overlaid onto the data to identify them within the sensor output.
Frequency of the Tube
Having performed the FFT analysis, the next stage is to identify each of the key frequencies.
250 kHz and 350 kHz are in the region of the sensors natural frequency. 115 kHz is not,
therefore it was considered that this could be caused by the u-PVC tube’s natural frequency as
the shock wave passes through it. Therefore the natural frequency of the tube was calculated.
The equation for the natural frequency of a hollow cylinder is shown in Equation 3.
𝑓 =
𝜋
2
(
𝜋
𝐿
)
2
(
𝐸𝐼
𝑚𝑎𝑠𝑠 𝑝𝑒𝑟 𝑙𝑒𝑛𝑔𝑡ℎ 𝑖𝑛 𝑚𝑒𝑡𝑟𝑒𝑠
)
1
2
Equation 3: Natural Frequency of a Hollow Cylinder

17
Where 𝐼 is the second moment of area. Which can be calculated from Equation 4.
𝐼 =
𝜋
4
(𝑟2
4
− 𝑟1
4)
Equation 4: Second Moment of Area
Where 𝑟1 and 𝑟2 are the inner and outer diameters of the tube respectively. Substituting in the
known values and solving gives a second moment of area 𝐼.
𝐼 = 1.312 × 105
Using this and the known properties of the tube a theoretical value for the natural frequency of
the tub can be calculated.
𝑓 = 181 𝐻𝑧
Having solved this and found the natural frequency of the tube it has been decided that the 115
kHz frequency is not related. 181 Hz represents a frequency that is very low relative to the
majority of frequencies in the output data. Therefore any frequencies contributed by the tube
at approximately 181 Hz will be ignored.
Frequency Comparison
The three frequencies identified from the FFT analysis are now used to identify similar
characteristics within the output data. For simplicity, only run one from the steel with plastic
insert will be used in the analysis of this section, all the sets of data showed extremely similar
FFT’s therefore analysing all the runs is not necessary.

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Figure 11 shows a simple sine wave of frequency 115 kHz plotted onto the output data from
the sensor.
Figure 11: 115 kHz Comparison
On Figure 11 arrows have been drawn at points where the data appears to match the frequency
plot. This shows that there may be an underlying frequency of 115 kHz, although it is not as
dominant as would be expected from then sensors natural frequency. Also 115 kHz is not
relatively close to the approximate 300 kHz natural frequency given by the manufacturer.

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Figure 12 shows the same data, but with a 250 kHz sine wave applied.
On Figure 12 an arrow has been drawn which identifies the region in which this frequency can
be identified. The frequency matches the majority of peaks well, although there is some
deviation. These small deviations are of a higher frequency than 250 kHz, therefore they should
be more prominent on the 350 kHz comparison.

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Figure 13 shows a comparison of the data with a 350 kHz sine wave overlaid.
The arrow on Figure 3 shows the region which corresponds with the 350 kHz frequency. This
suggests that between the times of 0.005ms and 0.02ms the frequencies of 250 kHz and 350
kHz are dominant. This analysis agrees with the manufacturer’s approximation of a natural
frequency of 300 kHz. From analysing the experimental data it is reasonable to suggest that
this is the response of the sensor to the initial shock wave impact, and not the effect of
surrounding apparatus/outside effects.
Pressure Step Comparison
Having identified the first 0.02ms after the peak as the most significant section, it was decided
that a comparison between these sections for various mounts would be useful. As well as
comparing the mount materials a comparison will be made between the first pressure step and
the second for each run.

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Figure 14 shows the first 0.02ms after the pressure step for each mount material.
Figure 14: 0.02ms after Pressure Step
It is clear from Figure 14 that there is little difference in the response of the sensor between
the three mounts over this section of the output. It can also be seen that between the times of
0.0075ms and 0.015ms there is a decaying signal. This matches with the frequencies of the
sensor. To check that this does not just occur a given time after the diaphragm bursting, the
first and second pressure steps from each of the runs have been compared.

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Figure 15 shows this comparison for a steel mount with plastic insert.
Figure 15: Comparison of 1st and 2nd Pressure Steps
Figure 15 shows that the signal being produced is more than likely to be caused by the shock
wave hitting the sensor, as it repeats with the same frequency at the next pressure step. The
repeatability of the second pressure step is not as good as the first, therefore some differences
will occur.
Now that this section of the output data has been identified as the response of the sensor to the
shock wave it can be analysed to find the decay and DC voltage level.
Pink Noise
Some low frequency signals were noticed in the output data. It was thought that these could be
due to certain components of the apparatus oscillating.

23
Figure 16 shows an example where this low frequency was noticed.
Figure 16: Low Frequency Signal
These signals were most noticeable in setups where the plastic insert was not used. Therefore
it is likely that the plastic insert damps out these frequencies. The lines on Figure 16 show a
very rudimentary outline of the suspected frequency signal. Having already ruled out the
possibility of this being due to the tube, it was suspected that the frequency is due to a
phenomenon known as pink noise [9](also known as
1
𝑓
noise [10]). This is similar to white
noise, which effects electrical systems in that it causes fluctuations within the signal. Pink noise
does not have a lower bound, therefore can be attributed to this frequency and many other low
frequencies within the data. Examples of pink noise include; fluctuations in tide heights, heart
beats and quasar light emissions.

24
5.3. Computational Analysis
Figure 17 shows the pressure at the diaphragm against time (iterations) and Figure 18 shows
the pressure at the sensor wall against time (iterations).
Figure 17: Pressure at the Diaphragm
Figure 18: Pressure at the Sensor Wall

25
As expected immediately after the diaphragm bursts there is a sudden drop in pressure at the
driver end. This is shown in the first 250 iterations of Figure 17, from 250 to 500 iterations
represents a decrease in pressure change due to the shock wave travelling along the tube
features on Figure 18 can be attributed to features on Figure 3: Shock Wave Propagation [5].
The first pressure step occurs at approximately 1500 iterations on Figure 16, prior to this the
end of the tube remains at atmospheric pressure. This reiterates the fact that the shock wave is
the first thing to reach the sensor after the diaphragm burst. The first pressure step represents
an instantaneous pressure increase of approximately 8 bar, which can be compared to the value
from the equivalent experimental results. After the initial pressure step there is a period of
constant pressure before the shock front catches up and causes a further pressure increase which
peaks at just below 14 bar as expected. On Figure 18 in the final 250 iterations a rise can be
seen. This is the shock wave returning back down the tube and passing the interface in the
opposite direction, verifying that the shock wave has been reflected correctly.
5.4. Comparison of Results
The results from the three analysis sections will now be compared to verify the experimental
results. For this the experimental data will be compared with both the theoretical approximation
of the pressure step, and the numerical model generated in Fluent.

26
Comparison of Experimental and Computational Results
Figure 19 shows the first pressure step from the experimental data next to the equivalent
section from the computational results.
Figure 19: Comparison of Experimental and Computational
It is clear that both the experimental and computational results share similar characteristics.
Both show a steep, instantaneous rise of approximately 8 bar, although the experimental data
shows some “overshoot” which is likely to be due to the sensors response. This is followed by
a period of no pressure change and then a rise to a peak, where the pressure begins to decrease
again. Obviously in the experimental data there is a lot more “noise” from the apparatus,
whereas in the Fluent analysis everything is considered ideal and therefore the data is cleaner.
Comparison of Experimental and Theoretical Pressure Steps
The approximation calculated using the shock tube and ideal gas theories can be compared
with the peak of the pressure step generated during the experiment.

27
Figure 20 shows a comparison plot of these two sets of data.
Figure 20: Comparison of Experimental and Theoretical Pressure Steps
The calculated theoretical value for the pressure step is a lot greater than the experimental value
gained from the data. There could be many reasons for this including the fact that in the
theoretical calculation air is treated as an ideal gas, which it is not. This is unlikely to be the
reason, due to how well the computational results match the experimental data, given that
Fluent considers air to be an ideal gas. Therefore this theoretical value is likely to be incorrect
due to the velocity values used. By taking the velocity as the time between the first and second
pressure steps there is a lot of error in the calculation. To make this theoretical value more
accurate a precise measurement of the shock velocity would be required. This experiment is in
process at NPL and will enable more accurate and reliable theoretical pressure steps to be
calculated.
The experimental, theoretical and computational results and analysis can now be used in an
attempt to model the sensor response.

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5.5. Model
The first thing required to create the model is the damping of the system. This can be found
using the equation for a damped sine wave shown in Equation 5 below.
𝑥(𝑡) = 𝑋0 𝑒−𝜀𝜔 𝑛 𝑡
∙ sin(𝜔 𝑑 𝑡 + 𝜙)
Equation 5: Damped Sine Wave
Where 𝑋0 𝑒−𝜀𝜔 𝑛 𝑡 represents the damping of the system.
Using this equation to plot upper and lower bounds on the experimental data shows the systems
damping. This is performed by using a least squares differencing method to ensure that the
damped curve is as close to the peaks of the data as possible. Figure 21 shows the plot.
Figure 21: Damping Model
This model now gives values for the parameters shown in Equation 5 and in Table 6 below.
𝑿 𝟎 𝝎 𝒅 𝝓 𝜺 𝝎 𝒏
4.280810563 298.3814482 0 0.103736384 300
Table 6: Parameters

29
These can be used to create a complete sensor model in the future, by substituting them into
Equation 5 and solving.
6. Discussion and conclusions
In this project, analysis has been performed on experimental data with a view to generating a
model of the sensor response. The experimental data has also been compared with theoretical
and computational results. Key concepts covered by this project include; identifying the sensors
response to the shock wave within the experimental data, applying numerical/computational
methods to the experiment and attempting to identify parameters to allow a rudimentary model
of the sensor response to be calculated.
6.1. Sensor Response and Model
From the analysis of the experimental data it can be suggested with relative confidence that the
section of the data identified in Figure 12: 0.02ms after Pressure Step, is the sensors immediate
response to the shock wave. This is very important as any model produced will need to fit this
response. The confidence in this theory is high due to the comparison with various other
experimental results, such as multiple peaks and different runs. But also comparison with
numerical/computational results which back up this theory. However, this does not mean that
the response shown in the raw data is wrong. In reality, this is the data that will be used for a
calibration and a future model should take this into account. The model itself can be designed
using the parameters found using the equation for a damped sine wave.
6.2. Implications
The research performed in this project will be useful in further developing more accurate
models for the sensors dynamic response. With every improved model, calibration error
decreases, thus making a shock tube method for the dynamic calibration of pressure sensors
more viable. Once error has been significantly reduced, calibrated sensors will be available in
industry to provide precision measurements of high frequency dynamic changes in pressure.
6.3. Future Work
The next steps for this line of work are to design and build apparatus to investigate how the

30
velocity of the shock wave behaves during a test. At NPL the construction of a steel shock tube
is already underway. This will enable more accurate theoretical calculations to be made, as
these calculations will be the basis of a dynamic calibration, reducing the error here will signify
the greatest benefit in accuracy of a final calibration service. A steel tube will decrease the
amount of “noise” in the sensor response, reducing error in the analysis.
In conclusion this project has provided crucial parameters in the development of a shock tube
method for the dynamic calibration of pressure sensors. By producing an accurate model, a
better prediction of the sensors sensitivity can be made. This reduces the error in a calibration
and provides industry with a valuable tool for making dynamic pressure measurements.

31
7. Project management, consideration of
sustainability and health and safety
7.1. Project Planning
At the beginning of the project a gantt chart was produced. This would enable tasks to be carried
out on time. Due to the research nature of this project, task were added and removed as time
went on to allow for the changing purpose of the project.
Figure 22 shows the project Gantt chart as set out at the beginning of the project.

32
Figure 22: Project Gantt
The Gantt chart shows all the key stages in the project. This is shown from a perspective before
the project start date. Therefore some stages were started slightly earlier/later, some work was
performed during holidays and some tasks were considered not relevant, such as the later
MATLAB tasks. Tasks shown in red represents sections that require predecessors. These tasks
must be completed on time for the project to run smoothly. There is no critical path as such,
this is because all the main tasks are independent and only come together when the report is
written.
7.2. Sustainability and Health and Safety
Table 7 shows the risk assessment for the project.
Table 7: Risk Assessment
There are very few risks during this project due to the amount of computer work involved.
There are risks associated with acquiring the experimental data, although this was performed
prior to the start of the project. Therefore the only risk to personal health is the overuse of
computers. There are risks associated with delaying the project itself and preventing its
objectives being reached as explained below.
Sustainability and environmental implications have been considered in this project as this is an
important aspect of an engineer’s role.
Obviously during the analysis section of this project there is very little to discuss in terms of
sustainability. The use of a computer and paper for printing are obvious negatives, but not
significant enough to warrant discussion. However, the experimental apparatus itself has

33
sustainability issues. The use of large sections of u-PVC pipe is cheap and easy to manufacture
making it sustainable from a user’s point of view. The u-PVC pipe is not sustainable in terms
of its environmental sustainability. Large amounts of energy go into manufacturing the pipe
and its required fixtures and fittings. These components have poor recyclable properties and
therefore will likely end up in landfill.
The diaphragms used in each test are manufactured from brass which is rolled to a thickness
of 0.1mm, this requires large amounts of energy. With a section of area 225cm2
being used in
each test, a vast amount of this material can be used in a short space of time.
The gas used to pressurise the system comes from a cylinder of high pressure dry air. High
energy compressors are used to fill these canisters which uses a lot of energy. Unfortunately
this is the most viable method of providing high pressure gas to the system.
7.3. Project Risks
This section discusses risk to the project, these include tasks that, if not completed could
jeopardise the final objectives from being completed.
Due to the nature of the research in this project, each section of analysis is independent and
does not require previous tasks to be completed. The contact with NPL and the initial research
are the only sections that must be completed on time to allow the analysis sections to
commence. Once each section of analysis is underway the tasks must be completed in
chronological order as each sub-task leads on to the next. Upon completion of each section the
experimental, computational and theoretical work can be compiled into a comparison. This,
and the report write up are the only sections that are dependent on all the predecessors.

34
References
[1] C. Hudson, X. Gao and R. Stone, Knock measurement for fuel evaluation in spark ignition
engines, 2001.
[2] M. Syrimis and D. Assanis, Knocking cylinder pressure data charactersitics is a spark-ignition
engine, 2003.
[3] M. Brunt, C. Pond and J. Biundo, Gasoline Engine Knock Analysis Using Cylinder Pressure Data,
1998.
[4] T. Esward, J. P. Elster and J. P. Hessling, Analysis of the dynamic measurements: new challenges
require new solutions, 2009.
[5] S. Downes, A. Knott and I. Robinson, "Towards a shock tube method for the dynamic
calibration of pressure sensors," The Royal Society, July 2014.
[6] S. Downes, A. Knott and I. Robinson, "Comparison of NPL and SP shock tubes," National
Physical Laboratory, UK, London, September 2014.
[7] PCB Piezotronics, "Sensor Construction," PCB Piezotronics, 2015. [Online]. Available:
http://www.pcb.com/TechSupport/Tech_Pres.aspx.
[8] Kistler, "Piezoelectric Pressure Sensor," 2013. [Online]. Available: www.Kistler.com.
[9] Live Science, "What is Pink Noise?," livescience.com, 2015. [Online]. Available:
http://www.livescience.com/38464-what-is-pink-noise.html.
[10] P. Bak and C. Tang, Self-Organized Critically: An Explanation of 1/f Noise, 1987.
[11] CADFEM-CIS Tutorial #VL1216-Shockwaves numerical simulation using ANSYS Fluent. [Film].
Youtube, 2012.
[12] J. McCall, "Genetic Algorithms for Modelling and Optimisation," Journal of Computational and
Applied Maths, 2005.

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[13] C. D. Johnson, Process Control Instrumentation Technology.
[14] S. Eichstadt, Deconvolution filters for the analysis of dynamic measurement processes: a
tutorial, 2010.
[15] C. Bartoli, Traceable Dynamic measurement of Mechanical quantities: Objectives and first
results of this European project, 2012.
[16] H. J. Pain and E. Rogers, Shock Waves in gases, 1962.
[17] D. Holder and D. Schultz, On the flow in a reflected shock tunnel, 1962.
[18] J. Teichter, Design of a shock tube, 2005.
[19] R. McMillan, shock tube investigation of pressure and ion sensors used in pulse detonation
engine research, 2004.
[20] E. Petersen and R. Hanson, Nonideal effects behind reflected shock waves in a high pressure
shock tube, 2001.
[21] S. Li, W. Ren and D. Davidson, Boundary layer effects behind incident and reflected shock waves
in a shock tube, 2012.
[22] S. Downes, A. Knott and I. Robinson, Determination of pressure transducer sensitivity to high
frequency vibration, 2014.

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