Chapter 7 Results and Discussion: Particle Impact and Impact Energy
7.2 Understanding Particle Impact Detection and Interpretation
In this study, optimisation of the detection threshold was achieved at a 40 dB setting (see Chapter 5, section 5.5), sampling rate of 2.5 MHz, and filter applied between 90- 850 kHz so as to capture adequate emissions due to sand impacts while excluding noise from background interference. The event count rate and energy analysis were chosen because each sand particle impact generates a discrete AE signal with a clear beginning and end that is recorded by the counter and the energy analysis can give a continuous measurement of the amplitude of the emission which can be standardised and used for comparative experiments.
The beginning of the AE signal from each sand impact called a ‗hit‘ is defined by its first threshold crossing, the end, by the absence of threshold crossing for a defined period of time known as the Duration Discrimination Time (DDT) [192, 194] which was set at 100 às for all tests. This is illustrated in Figure 7.1. The energy analysis also provides data that may be readily relatable to the mechanisms and processes of the impacts
and erosion occurring on the material. Just as stated in previous chapters, AE energy is the integral of squared or absolute amplitude ( ) over time of signal duration (t) [154, 168, 183, 192, 194, 200]. The energy measurement is realised in AE tests by sensing the signal, converting the signal to a electrical signal, filtering, amplifying and squaring the resulting signal to obtain a curve. The area under the resulting curve within the specific time gives a measure of the AE signal energy expressed in energy unit ( ) [192, 194].
Figure 7.1: Schematic illustration of duration discrimination time (DDT) [192].
If a single sand particle with mass, , impinges the specimen as shown in the illustration of generation of AE signal from single sand impact (Figure 7.2), the particle has a velocity, , that forms an incident angle with the specimen‘s surface. The change of the particle‘s momentum due to impact and the impulse imparted onto the specimen is given by , where is the coefficient of restitution (the ratio of the velocities after and before an impact, taken along the line of impact) and is less than unity. The corresponding AE signal that can be measured on the back of the specimen can be approximated as follows [201]:
(7.1)
where, is a factor representing the transfer function for the impulse imparted onto the specimen to form the voltage from the AE sensor. This factor accounts for energy dispersion and damping due to the transmission of acoustic energy from one material to another [201].
In order to determine the contribution of the AE signal from multiple sand particles impinging on the specimen with associated signals measured by the AE sensor in a given period of time, , then the particles‘ flux ( in the solid-liquid mixture impinging the specimen per time which depends mainly on the kinematic viscosity, , and the average particle velocity, ̅, can be expressed as, ̅ [201]. The particles exiting the nozzle and impinging the specimen per second will have a total mass, M (g/sec) and will impinge the specimen with vertical velocity component, ̅ .
Hence, the total AE signal due to the solid-liquid mixture impingement per second, measured by the sensor will be given by [201]:
̅ ̅ (7.2)
where, ; is a fraction of the particles hitting the surface per time which depends on the kinematic viscosity of the fluid, , and the average velocity of the particles, ̅; and is signal due to background noise and flow.
The technique and validity of measuring rely on the increase in the integrated AE signals with increasing sand loading when compared with the stable value of the integrated signal without any sand in the flow. The AE signal without sand is given by ̅ , and is equal to . To determine the amount of sand impinging the specimen per second, equation (4) becomes [201]:
̅ (7.3)
Figure 7.2: Illustration of generation of AE signal from single sand impact [201].
In theory and practice, the AE signals without sand given by ̅ , can be subtracted from the AE signal with sand, ̅ , to determine the amount of sand, M or the number of sand impacts per second using the measured AE count rate.
The subtraction technique relies on the hypothesis that the measured AE signal is stable if sand is not present in the flow. The presence of sand can be deduced from the observation of changes in the residual of the subtraction.
This signal interpretation technique has been successfully applied by the Cawley group [202, 203] at Imperial College London in the application of guided acoustic waves in health monitoring of structures. In their approach, the component under test is interrogated with guided acoustic waves from an exciting transducer (sensor) and the scattering of the waves by a defect in the structure captured by a receiving transducer gives an indication of the integrity of the structure. The part under test plays a passive role, and the only contribution it makes to the test is its ability to absorb or scatter energy in unique ways.
In this study, the AE technique eliminates the passive nature of the structure and makes it an active participating member of the test. This is accomplished by using the transducing action of the sand impingement with associated deformation in an elastic stress field as a secondary source of energy in the test, and the primary energy being
supplied by the solid-liquid mixture impingement onto the specimen. The technique is applied to quantify the number of sand impacts per second using AE event count rate.
A baseline signal measurement (zero sand) was established for all the flow velocities studied and measurements with sand were taken for each sand loading and flow velocity.
The baseline AE event count rate for each velocity was then subtracted from AE event count rate of each sand loading measurement to obtain the particle impacts at the specific velocity and sand loading. The measured signal showing the sensor‘s response to multiple sand impacts is shown in Figure 7.3. The validity of this technique was verified by comparing the results with theoretical prediction from volumetric flow rate calculations with the assumption that all sand particles passing the nozzle strike the target.
Figure 7.3: Measured AE signal waveform due to multiple sand impacts at 7m/s flow velocity, 90o impingement angle and 50oC temperature with tap-water saturated with N2 (pH ≈ 7.0).