An Experimental Study of Sloshing Noise in a Partially Filled Rectangular Tank.
Liquid sloshing can be defined as the movement of liquid free-surface inside a partially filled container due to any external disturbance . Sloshing has been an important area of research in various engineering fields like transportation of liquid by all major modes of transportation [2, 3, 4, 5, 6, 7], safety of structures against seismic loading [8, 9], vehicle stability for aerospace application [10, 11], etc. More recently, slosh noise generation under sudden acceleration/deceleration condition is getting increased research attention for premium and hybrid vehicles [12, 13]. In automobiles, sloshing noise in a fuel tank can be radiated as structure borne noise and air borne noise. Structure borne noise is generated due to wall vibration (Fluid-structure interaction) and Air borne noise is radiated due to fluid-fluid interaction inside the tank. The generated vibrations propagate through mounting attachments to the passenger cabin. As a result of advancements in automotive technology, noise radiation from engine, driveline, tires, brakes, and wind sources has considerably reduced. Hence sloshing noise has become as one of the major noise source in a vehicle for particular operating conditions.
A number of experimental studies has been performed to investigate sloshing phenomenon in tanks. Ibrahim et al  have reviewed several engineering applications where liquid sloshing dynamics is an important engineering consideration. Theories based on non-linear dynamics is being extensively used to understand the complex behaviour during sloshing. However, a majority of studies are related to work towards understanding dynamic loading and stability of structures. Since this review, several other studies have been reported in open literature on sloshing dynamics. Lugni et al  performed experiments to study the behaviour of flip-through events generated upon a vertical rigid wall when subjected by impact waves. Effect of baffles on sloshing dynamics has been studied both using xperimental and numerical techniques by several groups. Akyildiz and "U" "nal  studied sloshing in a rectangular tank with varying exciting parameters to analyse the effects of baffles and fill levels on impact pressure and fluid flow inside tanks. Liu and Lin  and Cho and Lee  numerically investigated the effect of baffle height on sloshing dynamics. Rebouillat and Liksonov  reviewed different numerical techniques that are being used to study sloshing dynamics and the associated fluid-structure interaction.
As mentioned before, effect of liquid sloshing in an automotive fuel tank is gaining importance as it contributes to overall vehicle noise level. Noise generation and radiation within a vehicle due to liquid sloshing inside a tank is quite complex. Researchers till recently have typically relied on experimental measurements of such noise characterization [19, 20]. Wachowski et al  concluded on the basis of experiments that sloshing noise can be classified into three categories: Splash, Hit and Clonk noise and the three were differentiated on the basis of their dominant frequency range. Kamei et al  experimentally determined a correlation that relates fuel tank, body parts and tank mounting structure to slosh noise. The tank mounting structure, which is related to both the fuel tank and the body parts has the largest contribution to sloshing noise.
However, with the advent of powerful computational tools, researchers are now trying to develop computational based methodologies for noise estimation which can then be used in early design phase of a fuel tank. Wiesche  performed experiments and numerical simulations of sloshing in automotive fuel tanks. He reported a correlation between slosh noise and dynamic pressure fluctuations. Additionally, he used two-phase Computational Fluid Dynamics (CFD) to track liquid interface within realistic tank geometries to determine these pressure fluctuations. Park et al  have studied a vibration of automotive floor panels due to sloshing loads using Fluid - Structure Interaction (FSI) analysis. Vaishnav et al  used Eulerian based Computational Fluid Dynamics (CFD) and Arbitrary Lagrangian-Eulerian (ALE) based vibrational analysis to perform FSI studies of fuel tank sloshing. Similarly, Marriott et al  have used FSI based computational methods to study fuel tank sloshing behaviour.
As can be seen from the above literature survey, most of the research on automotive slosh noise generation is restricted to test conditions, which are very empirical in nature and therefore, do not clearly explain the mechanism of slosh noise generation and its propagation. There is a need to develop a multi-physics model to address the above lacuna. Recently, Jadon et al  performed an integrated study of liquid sloshing behaviour, its impact on structural vibration and noise radiation on the rectangular tank that was subjected to a sudden deceleration. They performed both experimental and computational study on this geometry. The current work is an extension of that study, and an in-depth analysis has been performed to understand various factors affecting noise generation and its radiation from a partially filled rectangular tank. Experiments have been performed under controlled laboratory conditions. An impulse based dynamic loading experimental rig was designed for this study. Parametric studies were conducted to understand the effect of fill level and vehicle deceleration on slosh noise generation. As this is the first step in a comprehensive study to understand the mechanism of slosh noise generation and its propagation, the authors have currently restricted themselves in reporting their experimental work. Numerical study is expected to be reported in near future.
Figure 1 shows the schematic diagram of the sloshing noise test rig, which simulates the sloshing phenomenon under controlled braking load to measure dynamic force and dynamic acceleration on the tank wall. It also measures sloshing noise radiated from the tank. The system consists of four major subsystems: (i) carriage and track, (ii) rectangular tank with provision for sensor mounting, (iii) loading mechanism and (iv) braking mechanism. The carriage consists of a wooden platform mounted on four polymer wheels designed for low rolling noise in order to minimize background noise. An aluminium track of approximately 1.5 m was prepared on which the vehicle would travel. Special care was taken to minimize lateral movement of the vehicle. The track was maintained at a horizontal position with respect to the ground with the help of a spirit level. A transparent rectangular tank made of Acrylic with the dimensions of 0.238 (L) x 0.220 (W) x 0.238 (H) [m.sup.3] was fabricated to perform the experiments in this study. The tank wall was 6 mm thick and it was rigidly placed on the platform to avoid any relative motion. The tank and carriage together is referred as vehicle in rest of this paper.
A three-axis linear inertia acceleration sensor (3g-ADXL335) and a line triggering sensor were mounted on the wooden platform. The line sensor was used to trigger the dynamic sensors, which include the dynamic pressure, force, acceleration and microphones. Additionally, a high speed camera, which was used to record the liquid motion inside the tank was also triggered using this line sensor.
The vehicle was accelerated when a dead weight falls under gravity. The vehicle was tethered to this dead weight by a string and pulley mechanism. A band brake was used to apply the brake when the vehicle approached the end of its traverse. The liquid inside the tank sloshes due to the sudden application of this brake. Different sensors are mounted on the vehicle to record the effect of this sloshing activity. Sensor specifications are given in Table 1. Data from dynamic pressure sensors was acquired using HBM DAQ Quantum MX410. Data from all other sensors were acquired using a NI cDAQ-9178 data acquisition system. The line sensor was activated by a change in the colour of a strip mounted along the vehicle track, which in turn triggers other sensors. Phantom V12.1 high speed camera was used to capture the liquid sloshing behaviour, which was also triggered by the line sensor. Various camera settings were used to acquire the video. The present work reports the images that were obtained with a camera frame rate of 1000 fps. This frame recording setting was chosen based on test duration and memory required for online recording. Noise radiated due to liquid sloshing from the tank was monitored using four microphones that were placed in front, left, right and top direction of the tank at a distance of 1 m from the final resting position of the tank wall.
The acceleration and deceleration of vehicle due to the loading mechanism and the band brake arrangement as described above is estimated from Eq. 1a) and 1(b) respectively
[a = [[m.sup.2]g - [mu][m.sub.1]g/[m.sub.1] +[m.sup.2]]] (1a)
[mathematical expression not reproducible] (1b)
where, [m.sub.1] is the mass of the tank with water, [m.sup.2] is the mass of the dead weight, a is the acceleration of the tank, d is the deceleration of the tank, [t.sub.1] is the time required to reach the required acceleration, [t.sub.2] is required time for deceleration, and [mu] is coefficient of friction.
Figure 2 shows the mounting arrangement of the various sensors on the
vehicle. The dynamic force and dynamic acceleration sensors were attached on the external wall surface of the tank. The dynamic pressure sensors were mounted such that they were in direct contact with the liquid inside the tank. The sensor mounting were so designed to avoid liquid leakage from the tank.
Three dynamic pressure sensors were mounted at a height of 10% below the liquid free surface. These sensors were mounted on the front, back and right walls of the tank as shown in Figure 2. Another sensor was placed at 0.1 times of the tank height and was mounted on the tank front wall. The acceleration and forces were placed on the front and back walls of the tank and are adjacent to the dynamic pressure sensor that was placed 10% below the liquid free surface. The high speed camera was placed normal to the track. The camera field of view could capture the complete tank at the time of braking.
RESULTS AND DISCUSSION
The current test setup was used to perform several parametric studies to understand the effect of tank fill level and deceleration magnitude on slosh noise generation. The effects of these parameters on fluid structure interaction of the tank was recorded using the dynamic sensors; liquid slosh visualization using the high speed video camera; and radiated sloshing noise using the microphones. A minimum of three trials on at least two different days were performed to establish the repeatability of the current test methodology.
Background Noise Measurement
Before measuring the liquid sloshing noise, a separate test was performed to estimate the background noise due to vehicle motion on the track. This background noise incorporates tyre noise, noise due to loading and braking mechanisms. Two different tests were performed to estimate the background noise: (a) tank filled with water and (b) tank filled with sand of equivalent mass. Both these tests were performed under the same loading conditions.
Figure 3 shows the recorded sound pressure levels as recorded by the front microphone. As can be seen from this figure, multiple peaks were observed for the case where the tank is filled with water. However, only one peak is observed when the tank is filled with sand. In both cases, the first peak happens at the same time and occurs before or at the time of braking. Hence, it can be concluded that the first peak is due to the background noise. Subsequent events corresponds to liquid sloshing and the effect of background noise is insignificant during these instances. High speed camera recordings were not made during noise measurements due to significant background noise contribution from its cooling fan.
Table 2. Set of Experiments shows the set of experiments that was performed to understand the effect of fill level and deceleration magnitude on slosh noise radiation. As mentioned previously, one dynamic pressure sensor was placed at 0.1 times of the tank height in all the cases and all remaining dynamic sensors were placed at 10% below the liquid free surface. Major events that were recorded in inertial acceleration sensor and dynamic pressure sensors were analysed using high speed camera images of that instant.
Figure 4 shows results from the base case, which is defined as fill level of 40% and deceleration of 0.25 g. In this case the sensors were placed at 30% of tank height. Figure 4 (a) shows the inertial acceleration data in three directions. It was observed that the vertical component of inertial acceleration sensor is within the range 9.8 [+ or -]0.2 m/[s.sup.2] (1g) and therefore captures the acceleration due to gravity with sufficient accuracy. Lateral acceleration is significantly lower compared to the axial acceleration and therefore it can be assumed that vehicle lateral movement is negligible.
Based on the high speed video images, it was observed that the liquid inside the tank impacts the front wall immediately after braking and the corresponding image is shown in Figure 5. This impact event was recorded by all dynamic sensors. Dynamic sensors includes dynamic pressure, dynamic force, dynamic acceleration sensors and microphones. Subsequently, the liquid moves towards the rear wall and it attains its maximum height along the rear wall at t=0.74 sec after sensor triggering. Part of the liquid hits the tank roof and a corresponding peak in the recorded sound pressure level of top microphone is observed. Figure 5 shows the liquid position at this moment of time. The fluid then again returns back towards the front wall and it becomes progressively more bubbly as observed in Figure 5 at t= 1.113 sec. These major events were well captured by the dynamic sensors. After two set of events, the sloshing phenomenon inside the tank transitions towards linear sloshing regime and is well supported by high speed camera images. Therefore, active duration of the dynamic activities is typically restricted to two or three sloshing periods after application of brake. This is defined as the active slosh duration. However, the dynamic signals were captured for longer duration of time. The previous experiment was repeated for the same fill level of 40% and deceleration of 0.25g. However, in this case the dynamic sensors were placed at 10% of the tank height. The corresponding dynamic sensor plots are shown in Figure 6. As can be seen by comparing the dynamic plots from Figure 4 it is clearly observed that the dynamic response is lower when the sensors are mounted away from the liquid free surface. This is because most of the dynamic events are restricted to a region close to the liquid free surface. The dynamically active region varies significantly with fill level and deceleration. More rigorous studies are required to identify the dynamically active region.
Spectrogram analysis has attracted attention for its ability to analyse rapidly changing transient signals and it provides localized temporal and frequency information in the signal. Figure 7 shows the Spectrogram analysis for 40% fill level and 0.25g deceleration. Sound Pressure Level (SPL) variation with respect to time acquired from the top microphone is considered for Spectrogram analysis as shown in Figure 7(b). Based on the sound wave form, the total measurement duration is divided into three zones: (a) pre-braking zone, (b) impact zone and (c) linear zone. Impact zone starts at the instance of start of braking which is identified based on the sudden decrease in the inertial acceleration data. Pre-braking zone is identified as the zone before this instance. Linear zone starts when the SPL values reduces by approximately 10 dB with respect to the peak SPL value in the Impact zone. It can be observed from the figures that the impact zone is confined to 2-3 sloshing periods. Spectrogram analysis is suitable to classify different sloshing noise i.e. hitting noise, clonk noise and splash noise . It is observed that hitting noise is low frequency noise and is significant till 800 Hz. First peak in impact zone as shown Figure 7(b) is associated with hit event on the back wall at 1.2 sec for 40% fill level and 0.25g deceleration. Subsequent hit event on the front wall occurs at 1.5 sec. As can be seen from the same figure, higher noise levels are confined to the active slosh duration and in the remaining time only background noise is recorded. Hence, acoustic analysis should be performed for the active slosh duration. The SPL spectrogram shown in the Figure 7(c) is also divided into the three zones as described above. Zone 3 does not show any major noise generation activity. Though zone 1 shows significant amount of noise generation activity, however as mentioned previously, these noise generation is due to vehicle background noise. Hence, zone 2 has been analyzed thoroughly and therefore an exploded view is given in Figure 7(d).
An extensive parametric studies was performed for various fill levels, deceleration magnitudes and sensor locations as given in Table 2. Set of Experiments. Similar to the base case, measurements were recorded for dynamic sensors along with high speed video. Two different sloshing regimes were observed during this parametric study:
1. Linear flow Regime
2. Non-linear Flow Regime
Linear Flow Regime
This regime is associated with small oscillations of fluid free surface in which the surface remains planar without rotation. This regime is recorded in the form of smooth waves as seen in the high speed video image in Figure 8.
Non-Linear Flow Regime
This flow regime can be further classified into impact zone also termed as strongly non-linear zone and transition zone or weakly non-linear zone.
This non linearity is mainly due to rapid velocity changes associated with hydrodynamic pressure impacts of the liquid motion close to the free surface. This zone is characterized by highly bubbly liquid free-surface and rotational flow Illustrative example of this flow regime is given in Figure 8. This zone dominates for first few cycles of sloshing phenomenon and the number of cycles depend upon fill level and deceleration value.
This type of nonlinearity arises due to oscillations of large amplitude in which the free liquid surface experiences non-planar motion. In dynamic pressure sensor data this region can be identified as region where the pressure value decays gradually from peak towards the linear regime. The high speed video images show a clear liquid free surface as seen in Figure 8. Similarly, the same figure shows the three flow regimes as identified from a typical dynamic pressure data. The following parameter effects are discussed below:
Effects of Fill Level & Deceleration Magnitude
Figure 9 and Figure 10 shows the effect of fill level on peak values of dynamic pressure and force at different deceleration level. The relative magnitude of the peak values at the front and rear walls show a strong dependency on the fill level. The magnitude of peak dynamic pressure and force at the front and rear walls is almost same for 20% fill level at 0.2g deceleration. However, when the fill level is 40%, the front wall value is higher than the rear wall value. In contrast, the rear wall value is higher than the front wall value in case of 60% fill level. In case of 0.25g deceleration, the relative magnitude trends are similar to the previous case, but the difference between the front and rear wall values are subdued. Dynamic force plot also show the same behaviour for different fill levels. However, for 0.3 g, the relative trends are significantly different than the previous two cases. Based on this observation, fill level and deceleration magnitude have non-linear relationship with dynamic pressure and force.
This non-linear behaviour between deceleration magnitude and dynamic parameters is due to the non-linearity of the fluid motion. As can be seen from the high speed video images of Figure 11. at 20% fill level, wave front impact takes place on both the walls. However, in case of 40% fill level, liquid surges smoothly over the back wall but it makes an impact on the front wall. The available ullage space over the liquid surface is limited in case of 60% fill level. As can be seen from the figure, the amount of liquid interacting with back wall is higher than the front wall. Therefore, the impact force on the back wall is higher. Similarly, as can be observed from the Figure 9. the dynamic pressure on the rear wall is higher than the front wall for 20% and 60% fill level and deceleration of 0.25g and 0.3g. However, the dynamic pressure at front wall dominates over the dynamic pressure at back wall for 40% fill level. It must be noted that 80% fill level was only tested for 0.25g deceleration. In this case, it was noted that the dynamic activities are less compared to 60%. This is because, the rigid mass, which is defined as the volume of fluid whose centre of gravity does not change significantly relative to the vehicle centre of gravity, is higher in case of 80% fill level and therefore correspondingly has lower dynamic mass and this results in lower dynamic activity. Hence, dynamic peak values of 80% is lower than 60% fill level. Hence it can be concluded from the above observations that the fluid interaction with tank walls may be smooth or impact dominated depending on the vehicle deceleration and fill level in a non-linear fashion.
Effect of Sensor Location
Table 2. Set of Experiments summarizes the location of the sensors for the different experiments performed in the current study. This arrangement was done to determine the effective liquid height for dynamic events. Figure 12 shows the dynamic pressure data from these two sets of sensors for different fill levels at 0.25 g deceleration. The following observations can be made from this study:
* Other than the 20% fill case, the dynamic pressure observations were significantly muted for the first set of sensors.
* Significant dynamic events can be observed for the second set of sensors as they are closer to the free surface.
Fluid mass within the tank can be divided into two zone: (a) rigid mass and (b) dynamic mass as given in ref . The rigid mass is expected to have very low relative velocity with respect to the tank and because of this the dynamic activities observed by the first set of sensors are muted. On the contrary, dynamic mass will have a high relative velocity with respect to the tank and therefore the dynamic pressure sensor shows elevated dynamic activities. However, further investigations are required to quantify these two regions within a tank.
Sloshing Time Period
Time period of sloshing is different for impact and linear regime due to the difference in the fluid flow characteristics in these two regimes. Theoretical sloshing time period can be determined using the following equation :
[mathematical expression not reproducible] (2)
[k.sub.m] = (2m - 1 )[pi]/L for asymmetric modes
[k.sub.m] = 2m[pi]/L for symmetric modes
[f.sub.s] = sloshing natural frequency (Hz),
L = maximum dimension of base of the tank (m),
h =height of fluid filled in the tank (m),
g=acceleration due to gravity (m/[s.sup.2])
Figure 13 show the comparison of experimentally determined time period in the impact and the linear flow regimes along with theoretical values as calculated from Eq. (2) for different fill levels at a deceleration of 0.25g.The time period in impact regime is higher than the linear regime for all fill levels. However, the time period in linear regime is close to theoretical time period. Hence, Eq. (2) is valid only for linear sloshing regime.
Figure 14 shows the SPL waveform and Spectrogram in the impact zone for different fill levels at 0.25 g deceleration. It can be observed that the SPL values in the pre-braking zone is associated with the background noise due to the vehicle movement. The values of background noise increases with increase in fill level due to increased inertial effects. The peak SPL values in the impact zone decreases with increase in fill level. At 20% fill level, two distinct peaks in the SPL data is observed. However, the values of the second peak relative of the first one decreases with increase in fill level and at 60% and 80% fill level it becomes marginal. These peaks are associated with the fluid impact on the tank walls. As can be observed from Figure 14, the decrease in SPL values corresponds to a similar decrease in the dynamic force values at 0.25g. The major noise generation due to impact is restricted to low frequency region. As can be observed from the figure, higher noise level is confined between 200-600 Hz. These observations are consistent with observations made by  and they termed it as hit noise.
An experimental setup was developed to study liquid sloshing noise generation and its propagation from a rectangular tank. Proper instrumentation was done to record dynamic pressure, acceleration, force and sound pressure level along with high speed images. The current experimental setup has the capability to simulate hit and splash noise for various fill levels and acceleration/deceleration conditions. Extensive parametric studies were conducted for understanding sloshing noise generation mechanisms. All dynamic sensors synchronously showed large peaks during major events in sloshing. High speed image analysis with integrated sensor data shows that major events in sloshing noise is restricted to active duration time period and effective liquid height.
The sloshing phenomenon inside the tank was classified as non-linear and linear flow regime. Dynamic activities in the non-linear regime are the source of sloshing noise generation. Sloshing noise is a non-linear function of fill level and acceleration/deceleration. Spectrogram analysis of microphone data shows that hit noise is dominant in a low-frequency region. Sloshing period for non-linear and linear regime was measured from dynamic response data and compared with analytical results. There is a good match between analytical and experimental results in the linear regime. However, further studies will be required to develop the validated sloshing noise prediction model.
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Department of Mechanical & Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, Telangana, India 502285
The authors would like to acknowledge the financial support of Mercedes Benz India Pvt. Ltd. for this work.
G Agawane, Varun Jadon, Venkatesham Balide, and R Banerjee
Indian Institute of Technology Hyderabad
Table 1. Sensors Specifications Sensor Type Make and Model Range Inertial Accelerometer 3g-ADXL335 [+ or -]3.6g Dynamic Pressure Dytran 2300 V3 500 psi Sensor Dynamic Force Sensor Dytran 1053 V3 and [+ or -] 100 lbf 1051 V4 Dynamic Acceleration Dytran 3055 B1 Sensor Microphone MPA 401 Sensor Type Sensitivity Inertial Accelerometer 300 mV/g Dynamic Pressure 10 mV/psi Sensor Dynamic Force Sensor 50 mV/lbf Dynamic Acceleration Sensor Microphone Table 2. Set of Experiments S. No. Fill Level Deceleration Sensor Height (% of tank height) (g) (% of tank height) 1 20 0.20, 0.25, 0.30 10 2 40 0.20, 0.25, 0.30 10, 30 3 60 0.20, 0.25, 0.30 10, 50 4 80 0.25 10, 70
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|Author:||Agawane, G.; Jadon, Varun; Balide, Venkatesham; Banerjee, R.|
|Publication:||SAE International Journal of Passenger Cars - Mechanical Systems|
|Article Type:||Technical report|
|Date:||Jul 1, 2017|
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