In this study, the first objective is to investigate the flow pattern of the fluid passing through the corrugated pipe and the effect of pipe geometries on whistle amplitude and peak whistle Strouhal number (𝑆𝑟𝑝−𝑤). The flow pattern of the fluid passing through the corrugated tube and the effect of tube geometries including cavity height (𝐻), downstream edge radius (𝑟𝑑𝑜𝑤𝑛), upstream edge radius (𝑟𝑢𝑝), cavity width (𝑊) and plateau (𝑝) 𝑆𝑟𝑝−𝑤 and wing amplitude are investigated using the proposed software.
Comparison of Experimental Results and
Equipment and Material Needed for Experiment 59
Geometric Characteristics of the Corrugated
Helmholtz Number and Dimensionless Sound Amplitude v. Mach Number for a Typical
Helmholtz Number and Dimensionless Sound Amplitude v. Mach Number for a Multiple Side
Two Different Corrugated Pipe Configurations
Dimensionless Sound Amplitude v. Strouhal
Quasi Stationary Flow Field Solution Controls 27
Sound Pressure Level as a Function of Strouhal
Sound Pressure Level as a Function of Strouhal
Boundary Layer and Velocity Magnitude of
Small Recirculation Flow in Counter-clockwise
Vorticity Magnitude of Vortex for Geo 4 37
Graph of Whistling Amplitude and
Boundary Layer and Velocity Magnitude of
Boundary Layer and Velocity Magnitude of
Boundary Layer and Velocity Magnitude of
Boundary Layer and Velocity Magnitude of
Experimental Setup 59
Device Configuration in imc Devices 2.6 61
Srp-w peak whistle Strouhal number U average flow velocity in the pipe, m/s Ucr critical flow velocity in the pipe, m/s W width of the corrugated pipe cavity, m Weff effective width of the side branch cavity, m ρ0 air density, kg/m3.
Background
It is important to note that although the lateral branches are non-axisymmetric, it exhibits similar whistling characteristics as the corrugated tube (Nakiboğlu et al., 2011). As shown in Figure 1.4 (Nakiboğlu et al., 2010), the pipe inner diameter (𝐷𝑝) varies periodically along the pipe length (𝐿𝑝) in both systems.
Aims and Objectives
However, the effect of flow-induced vibration on the whistle phenomenon is neglected in this project. In addition, the possible damping effect of the water outside the corrugated pipe is also assumed to be negligible.
Strouhal Number and Whistling Amplitude
Strouhal Number
The Strouhal number in the acoustic amplitude of the sound in a particular acoustic mode is known as the peak whistle Strouhal number (𝑆𝑟𝑝−𝑤). 2010) explained that 𝑆𝑟𝑝−𝑤 is obtained through a global gradient plot of successive modes. 2010) claimed that the sum of the cavity width and the upstream edge radius, 𝑊 + 𝑟𝑢𝑝, which is also known as the modified gap width is the best representation of the characteristic dimension. The modified gap width is thus the optimum characteristic dimension as the Strouhal number range is smaller.
Whistling Amplitude
Then, the increase in the average flow rate increases the sound amplitude until it reaches a maximum value. In the study by Nakiboğlu et al. 2010) with 14 different configurations of corrugated tubes, the optimal characteristic dimension was determined among pitch (𝑃𝑡 = 𝑟𝑢𝑝+ 𝑊 + 𝑟𝑑𝑜𝑤𝑛 + 𝑙 𝑙 ), slot width𝑟+ (𝑟𝑟+ 𝑑𝑜𝑤𝑛) and changed slot width (𝑊 + 𝑟𝑢𝑝).
Similarities and Differences between Corrugated Pipe and Multiple Side Branch System
The first whistling or singing mode is therefore the 2nd acoustic mode for corrugated pipes and multi-branch system. One of the main differences between both systems is that corrugated pipes have slit-shaped cavities, while the side branches of multiple side branches are circular in cross-section. For system with multiple side branches, the total effective cavity width and upstream edge radius (𝑊𝑒𝑓𝑓+ 𝑟𝑢𝑝) are used as the characteristic dimension.
Moreover, the corrugated pipes used in the experiment have 2 x 102 corrugations, but the multiple side branching system has only 19 side branches. Corrugated pipes are normally found to have higher whistle frequencies compared to multiple branch systems. However, the wave quantity per wavelength in corrugated pipe at high frequencies (Helmholtz number) is closed to that of multiple side branching systems at low frequencies.
Effect of Different Pipe Geometries
- Effect of Pipe Termination
- Effect of Edge Shape
- Effect of Cavity Depth
- Effect of Pitch Length
- Effect of Confinement Ratio
- Effect of Pipe Length
- Effect of Plateau Length
- Source Localisation
In a study conducted by Nakiboğlu et al. 2011), this result was found to be due to the different velocity profile found in the two systems due to the different ratio of the tube diameter to the sum of the cavity width and upstream edge radius (closure ratio). Therefore, the lowest modes in a system with multiple side branches are of most concern. 2010) studied the effect of pipe closure on whistle amplitude. As shown in Figure 2.3, two different types of pipe terminations were used in the experiment, namely sharp terminations and whistle terminations (Nakiboğlu et al., 2010).
From the experiment of Nakiboğlu et al. 2011), it is observed that 𝑆𝑟𝑝−𝑤 decreases as the confinement ratio increases. According to Nakiboğlu et al. 2011), the change in 𝑆𝑟𝑝−𝑤 is caused by the variation in the flow profile when there is a change of confinement conditions. Furthermore, the saturation in dimensionless sound amplitude was observed in multiple side branch system with 19 side branches at.
Effect of Different Velocity Profiles
Eventually, the secondary peak replaces the primary peak at the same Strouhal number and similar pressure amplitude as at 𝐿𝑝⁄𝑊=0, when 𝐿𝑝⁄ reaches it is found that the noise originates mainly in the pressure nodes of the longitudinal standing waves along the pipe, where the grazing acoustic velocity is the highest. First, there is only one range of Strouhal numbers, with singing or whistling observed for the configuration. However, there are two different ranges of Strouhal numbers where the whistling phenomenon is observed in configuration B. 2012) stated that this is because configuration A has weaker hydrodynamic amplification at the higher range of Strouhal numbers due to the thicker initial thickness of the shear layer moment.
Second, configuration B is also observed to have higher 𝑆𝑟𝑝−𝑤 than configuration A in the lower range of whistling Strouhal numbers. According to Nakı̇boğlu et al. 2012), this is due to the difference in the thickness of the shear layer moment for the two different configurations.
Numerical Method Involving Incompressible Flow Simulations and Vortex Sound Theory
In the numerical method, the hydrodynamic interference between the cavities is assumed to be negligible. However, according to Nakı̇boğlu and Hirschberg (2012), the hydrodynamic interaction affects both the 𝑆𝑟𝑝−𝑤 and dimensionless sound amplitude. In addition, the presented numerical method does not include turbulence modeling, which is important for shallow cavities (𝐻 𝑊⁄ ≤ 0.5).
A similar numerical method is also applied in a study of the aeroacoustic flow behavior inside T-joints by Martinez-Lera, Golliard, and Schram (2010). According to them, CFD simulations are very computationally efficient as it is possible to obtain a wide range of valuable information at a low computational cost. They have also verified that this method can produce results that are consistent with the experimental method.
Gantt Chart and Flow Chart
Numerical Method .1 Assumptions
Simulation Steps
As shown in Figure 3.3, the important steps involved in the simulation work. As shown in Figure 3.4, quadrilateral cells are used instead of triangular cells because they generate less numerical diffusion in Large Eddy Simulation (LES). It is also necessary to set the reference values as shown in Figure 3.9 which are necessary in the calculation of drag coefficient, lift coefficient and Strouhal number.
Before defining the acoustic model, iteration is started to ensure that the drag and lift forces are periodic and oscillatory in nature as shown in Figure 3.10 and Figure 3.11 respectively. Additionally, the acoustic source is defined as shown in Figure 3.13 before the simulation is run again. After that, the recipients are added to the File XY chart as shown in Figure 3.16.
Benchmarking and Flow Patterns of Fluid
Benchmarking
Flow Patterns of Fluid
The main flow has uniform velocity from inlet to outlet and is not affected by the eddy in the cavity. When this happens, there will be a backflow along the pipe wall in the opposite direction to the main flow. The flow in the boundary layer is distorted and strongly affected by the eddy in the cavity.
As shown in Figure 4.5, several vortices can be observed in the cavity of corrugated pipes. The main vortex rotates clockwise at a much higher speed than the small recirculation current which rotates counterclockwise, as shown in Figure 4-6. Therefore, it is concluded that the 𝑆𝑟𝑝−𝑤 and whistle amplitude are mainly influenced by the main vortex flowing clockwise.
- Effect of Cavity Depth, 𝑯
- Effect of Downstream Edge Radius, 𝒓 𝒅𝒐𝒘𝒏
- Effect of Upstream Edge Radius, 𝒓 𝒖𝒑
- Effect of Cavity Width, 𝑾
- Effect of Plateau, 𝑰
From the results obtained from simulation (Table 4.2 and Figure 4.8), it is found that the change of cavity depth, 𝐻 from 4mm to 10mm, has only a minor effect on the 𝑆𝑟𝑊+𝑟𝑢𝑝. Moreover, it also has a negligible effect on the whistle amplitude which only varies between 100dB to 102.5dB. This can be deduced from the eddy velocity profile in which all the four types of geometries have similar clockwise eddy velocity magnitude around 1.5m/s, although the 𝐻 varies from 4mm to 10mm as demonstrated in Figure 4.9 and 4.10. As demonstrated in Figure 4.12 and Figure 4.13, the eddy velocity in two geometries is similar, even though their 𝑟𝑑𝑜𝑤𝑛 differs significantly.
On the other hand, although thicker boundary layers and stronger clockwise vorticity are observed, the whistle amplitude is significantly reduced as 𝑊 increases. The secondary whorl can be observed in Figure 4.19 and both secondary and tertiary whorls can be observed in Figure 4.20. From table 4.6 and figure 4.21 it can be seen that the whistle amplitude does not show an explicit trend as the plateau, 𝐼 changes.
Optimal Characteristic Dimension
Determination of Optimal Characteristic Dimension
The value of 𝑆𝑟𝑝−𝑤 can be obtained from data obtained through simulations when a certain value of the characteristic dimension (𝑊+𝑟𝐼2 . 𝑢𝑝) is chosen. Once the critical flow rate 𝑈𝑐𝑟 is determined, it can be easily avoided by manipulating the fluid flow rate. It is also possible to select or design the parameters of the corrugated pipe if the flow rate cannot be varied.
It should also be noted that the simulation method proposed in this project is able to effectively contribute to the research of induced flow acoustics in corrugated pipes. Various models of corrugated pipes can be easily drawn in a few minutes, and simulation results can be easily obtained with high accuracy. This can also reduce material wastage as different configurations of corrugated pipes are not required.
Conclusion
We can conclude that when 𝐼 < 𝑊 + 𝑟𝑢𝑝, 𝑊 and 𝑟𝑢𝑝 have a dominant effect over 𝐼 in influencing the flow over the corrugated pipe, so the value of 𝑆𝑟𝑊+𝑟𝑢𝑝 fluctuates. The change in 𝑆𝑟𝑊+𝑟𝑢𝑝 in this range is insignificant, which means that 𝐼 does not contribute much to the change in 𝑆𝑟𝑊+𝑟𝑢𝑝 compared to 𝑊 and 𝑟𝑢𝑝 as mentioned earlier. In addition, it was found that using 𝑊 + 𝑟𝑢𝑝 as a characteristic dimension results in a Strouhal number variation of 0.30 ≤ 𝑆𝑟𝑊+𝑟𝑢𝑝≤ 0.43.
Using W as the characteristic dimension resulted in greater variation of Strouhal number in the range of 0.09 ≤ 𝑆𝑟𝑊≤ 0.29. It is also possible to design the pipe parameters if the flow condition cannot be manipulated in certain conditions. Finally, the simulation method proposed in this project can effectively contribute to the research of flow-induced acoustics in corrugated pipe.
Recommendations
Multiple Cavities and 3D Simulation
This is because the simulation method is able to save cost, time and space compared to the experimental method, without jeopardizing the accuracy of the results obtained.
Experimental Method
The experimental setup is shown in Figure 5.1 (Nakiboğlu et al., 2011) which is exactly the same as the experimental setup produced by Nakiboğlu et al. On the other hand, two straight measuring sections are used upstream and downstream of the corrugated tube respectively to facilitate the installation of microphones. The microphones are connected to the four analog channels of the dynamic signal analyzer (as shown in Figure 5.2) which is then connected to the computer.
The steps to use imc Devices 2.6 to obtain data such as sound level (dB), frequency and Strouhal number are very simple. After the dynamic signal analyzer is connected, the device is configured for active status as shown in Figure 5.3. Aeroacoustic force generated by a compact axisymmetric cavity: prediction of self-sustained oscillation and influence of depth.
