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2005-01-1913

Simulation of Sloshing in Fuel Tanks andParametric Study on Noise Reduction by

Decreasing Impact Pressure

Won-Joo Roh, Sok-Hyun Cho and Jae In ParkHyundai-Kia Motor Company

Reprinted From: Computational Fluid Dynamics(SP-1925)

2005 SAE World CongressDetroit, MichiganApril 11-14, 2005

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2005-01-1913

Simulation of Sloshing in Fuel Tanks and Parametric Study on Noise Reduction by Decreasing Impact Pressure

Won-Joo Roh, Sok-Hyun Cho and Jae In Park Hyundai-Kia Motor Company

Copyright © 2005 SAE International

ABSTRACT

Noise from automotive fuel tanks is generated by sloshing flow of fuel. Flow inside fuel tanks is incompressible, turbulent and free surface problem which is analyzed by Marker and Cell (MAC) algorithm. The simulation result of gross sloshing flow pattern is compared and verified by experiments with transparent fuel tanks. Characteristics of impact pressure on the tank wall are analyzed to find noise source on the wall. It is influenced by both the inertia of fuel mass and the dynamic motion of sloshing flow. In addition, a parametric study has been done to decrease impact pressure by changing its dimensions and shape.

INTRODUCTION

Noise from fuel tanks by sloshing is generally classified by structure-borne noise and flow-induced noise. Structure-borne noise is generated by either impulsive pressure or convective pressure. The first is impact pressure on the fuel tanks by fuel sloshing during acceleration or deceleration. The latter is produced by external force during rough driving condition and is not closely related to customer complaints. The sloshing noise which passengers can hear is produced in a quiet driving condition such as parking their cars in an underground parking lot. Flow-induced noise is defined by turbulent mixing of fluid and bubble burst of trapped air or fuel vapor. It is still difficult to find the exact relations between the noise and the fuel sloshing even if many different experiments and simulations have been conducted for a few years [1, 2, 5]. In the computational analysis, deformation and vibration of fuel tanks caused by fuel sloshing is needed to analyze. Also, vibro-acoustic phenomenon should be included to find the noise generation mechanism exactly. This technique is still under development. However, the simulation cost will be high if all coupled analysis is included. In this paper, the gross pattern of the sloshing flow and its impact pressure on fuel tanks are focused on because impact pressure on fuel tanks by sloshing has been known as one of the main cause of the noise [1]. Marker and Cell (MAC) algorithm is applied to obtain the

sloshing flow pattern which is limited to the gross flow motion. The simulation is verified by rig experiments with transparent fuel tanks. In addition, we focus on reducing impact pressure by changing the dimensions of fuel tanks and the degree of inclination of the front tank wall in a parametric study.

SLOSHING IN FUEL TANKS

SIMULATION OF SLOSHING FLOW

Analysis modeling and experiment set up

Sloshing is a free surface problem of fuel flow inside fuel tank. Computational algorithms such as Volume of Fluid (VOF) and Marker and Cell (MAC) have been mainly applied to solve the free surface problem by many researchers. Recently, level set method has been developed to track the free surface by applying a level set function, which represents the distance from the free surface boundary but it has not been reported to solve fuel sloshing problem yet. In this research, SCRYU/Tetra, which is a general purpose computational fluid dynamics program with fast solving algorithm using a node-based finite volume method, is applied to solve the fuel sloshing. It analyzes the sloshing problem using MAC algorithm, which is relevant to observe the gross pattern of sloshing flow. Both fuel liquid drops from free surface and air entrapment are not described in detail. It is assumed that these drops may not affect impact pressure on the wall significantly. The grid for the sloshing simulation of a fuel tank is generated by the built-in preprocessor in SCRYU/Tetra and it has a total number of 610000 elements including both tetrahedral and prism elements as shown in Figure 1. In the simulation, the time step for the transient analysis is set to 0.002 initially and it is adjusted by keeping CFL number below 0.3 for stability of computation.

The rig experiment is performed using fuel tanks made of transparent plastic and blue-colored water, which volume is 34L (75% of fuel tank capacity), to verify the simulation results (see Figure 2). Many different types of boundary conditions such as deceleration, acceleration,

and tip in-out (decelerate and accelerate repeatedly) in creeping driving condition are applied in both the experiments and the simulations. Figure 3 shows the simplified tip in-out boundary condition and the range of the deceleration and acceleration is between -2.5 and 2.7 m/s2. The comparison between the simulation and experiment for the tip in-out boundary condition is presented in the following section.

Figure 1. Fuel tank geometry and grid for sloshing analysis

Figure 2. Experimental setup of transparent fuel tank

Comparison of gross pattern of sloshing flow

The gross patterns of sloshing flow by the simulations are compared with the experiment results. Figure 4 and Figure 5 show the sloshing flow pattern in deceleration and acceleration while applying tip in-out boundary condition, respectively. The sloshing pattern can be predicted well by SCRYU/Tetra but fluid drops and small air bubble entrapments cannot be described in detail because of the limitation of MAC algorithm. However, it is enough to predict pressure gradient with respect to time in the fuel tank wall, which is one of the main source to generate sloshing noise [1].

Figure 3. Simplified tip in-out boundary condition of fuel tank experiment

Figure 4. Comparison of sloshing flow at deceleration under tip in-out condition (time = 0.4605 sec)

Figure 5. Comparison of sloshing flow at acceleration under tip in-out condition (time = 1.0401 sec)

IMPACT PRESSURE OF SLOSHING FLOW

Sloshing noise comes from many different mechanisms such as impact pressure on the tank wall resulting in vibration of fuel tank and propagation of acoustic sound into surroundings, air trapped bubble burst and turbulent mixing of fuel flow itself. Correlations between the magnitude of pressure on the fuel tank wall and the level of sloshing noise have not been proved clearly and it has been assumed they have a close relation [1]. Although the impact pressure is not the only reason to generate sloshing noise, we focus on the characteristics of impact pressure on the wall based on the assumption.

time (sec)

Acceleration

(m/s

2)

The characteristic of impulsive pressure on the tank wall is different for the first impact and the others followed. At the first impact, inertia of fluid mass is the main reason

to generate a peak pressure on the wall while the others happen by turbulent sloshing flow. It can be verified that the magnitude of the impact pressure at first is not significantly reduced by just adding baffles. After the first impact, the sloshing fluid pattern is different and free surface problem is important. Initially it is relevant to measure total pressure to account for hydrostatic pressure because the pressure along the wall varies hydrostatically. After the first impact, it is better to measure the dynamic pressure to avoid the risk to ignore the dynamic effects of sloshing flow because the magnitude of the hydrostatic pressure is greater than the dynamic pressure. And noise generation is related not by the magnitude of the peak pressure but by the pressure gradient with respect to time.

The locations of the pressure measurement in analysis at each time steps are shown in Figure 6. Three analysis results of the total pressure distribution on the front wall near the time step when the maximum pressure gradient occurs (t=4.0 s) are shown in Figure 7. It is analyzed under deceleration in creeping driving condition (refer to Figure 11). This condition is different from the tip in-out condition used for the flow comparison with experiment as shown on Figure 4, 5. It represents the driving condition under parking process as the automobile decelerates slowly and stops finally. The applied deceleration condition is -0.2g (0 ≤ t < 0.4 s) describing slow deceleration and -0.6g (0.4 ≤ t < 0.5 s) describing final stop of automobile where g is the acceleration of gravity. The measured pressure data in analysis on the lower, middle and upper part of both the front and the rear wall of the fuel tank are shown in Figure 8. Total amount of fuel is 75% of the official capacity of the fuel tank. The reason for the lower side pressure is the greatest is hydrostatic pressure, i.e. mass of fluid. Similar pressure distribution on the rear wall is shown in Figure 9.

Figure 6. Locations of pressure measurement in analysis on the front and the rear wall of fuel tank

For the dynamic impact, the magnitude of the pressure on the rear wall is greater than on the front wall because the turbulent sloshing flow and its wave motion is more important than the inertia effects in dynamic impact as shown in Figure 9. The maximum pressure on the front wall is less than 150 Pa but the pressure on the rear wall is near 1000 Pa. From the observation of the impact

pressure on the front and the real wall, it is important to check both total pressure and dynamic pressure to locate the noise source on the fuel tank wall.

Figure 7. Contour of total pressure on the front wall under deceleration in creeping driving condition

upper middle

lower

Front wall

Rear wall

right center

left

Forward direction of automobile movement

t=0.2 sec

t=0.4 sec

t=0.6 sec

Figure 8. Total pressure time history on the front and the rear wall of fuel tank

Front wall lower middle

upper

Total Pressure (Pa)

upper

middle

lower

time (sec)

Rear wall

Total Pressure (Pa)

upper

middle

lower

time (sec)

lower middle

upper

Figure 9. Dynamic pressure time history on the top part (left, right, center sides) of the front and the rear wall of fuel tank

PARAMETRIC STUDY

Dynamic equivalent model

While the sloshing phenomenon and its impact pressure on the wall has been analyzed by applying both continuity, and Navier-Stokes equations, a simplified model called dynamic equivalent model has been used in aerospace to design baffles to control the dynamic behavior of both airplanes and liquid propellant missiles. One of the reason is that it is complicated to solve the free surface problem and then, to apply the result to build up the dynamic model to control their flight motion. Figure 10 shows the dynamic equivalent model and only the concept is used and is a helpful hint for the following parametric study. In this model, the dynamic wave motion of sloshing flow happens mainly in an upper portion of fuel and a lower portion of fuel is considered as a semi-rigid body.

Figure 10. Flow model of sloshing in fuel tanks (1) Dynamic equivalent model (2) Impact force (3) Flow distribution at inclined wall

Impact force

Impact force by sloshing flow on the wall consists of normal and tangential force as shown in Figure 10. The magnitude of impact pressure on the wall, which is one of main sources for noise in fuel tanks, depends only on the normal force Fn. It suggests that an inclined wall can reduce impact pressure.

θθ cos,sin FFFF tn ==

where F is the total force on the wall by sloshing flow, θ is the incline angle of the wall, Fn is the normal impact force directly related to the sloshing noise and Ft is the tangential force.

Flow distribution at wall

By applying control volume analysis, the flow distribution on the wall is

2/)cos1(,2/)cos1( 21 θθ +=−= QQQQ

where Q is the total flow, Q1 and Q2 are the flow directed to the upper and lower portion of the fuel flow, respectively. Therefore, by decreasing the angle of wall inclination θ, the amount of flow headed into the semi-rigid body model (Q2) is increased and it is directly beneficial to reduce noise by decreasing dynamic impact

Rear top wall

Dynam

ic Pressure (Pa) D

ynamic Pressure (Pa)

time (sec)

time (sec)

left right

center

left right

center

Front top wall

Q1

Q2 Q

F

Fn

Ft

θ

upper

lower m, I fuel

air Dynamic equivalent model

Impact force

Flow distribution (1)

(2)

(3)

pressure and reducing the entire duration time of sloshing flow.

H/L ratio

The effects of height (H) and length (L) of overall dimension of fuel tanks on impact pressure by sloshing flow is investigated. The volume of fuel used for the parametric study is 560 mL, which is 70% of the entire volume of semi-three dimensional fuel tank, which has

a unit depth. A total of five cases of H/L ratio, which ranges between 0.5 and 2.0, in deceleration boundary condition is conducted (See Figure 11).

Figure 11. (1) Two dimensional fuel tanks by H/L ratio (unit depth of fuel tanks is 1 cm) (2) Deceleration in creeping driving condition

0.4 0.5

a= -0.2g a= -0.6g

time (sec)

Velocity (m/s)

a : acceleration (m/s2) g : acceleration of gravity (9.81 m/s2)

Forward direction

H/L=0.5

H/L=2.0

H/L=0.75 H/L=1.0

H/L=1.5

Fuel tank

(1) (2)

Figure 12. Impact pressure on the front and rear wall with H/L ratio

H/L ratio Front wall Rear wall 0.5 743 Pa 843 1.0 167 50 1.5 94 36 2.0 81 36

Table 1. Impact pressure on the wall of fuel tanks varying H/L ratio between 0.5 and 2.0

The maximum impact pressure on the front and the rear wall is 743 and 843 Pa with 0.5 H/L ratio while it is reduced to 81 and 36 Pa with 2.0 H/L ratio. While the impact pressure reduces by increasing the H/L ratio, this tendency continues until the H/L ratio is up to 1.0 as shown in Figure 12. The variation of the maximum pressure with respect to the H/L ratio is listed on Table 1.

Effects of inclined walls of fuel tank

Shape modification of tanks is limited to the front wall assuming that (1) impact pressure on side walls is negligible in acceleration or deceleration condition (2) similar effects on both front and rear walls by modifying their shapes. Figure 13 shows six different fuel tanks prepared to measure impact pressure by sloshing flow during the same deceleration boundary condition used for the effects of H/L ratio analysis.

Figure 13. Two dimensional fuel tanks for inclined wall effects on impact pressure (unit depth of fuel tanks is 1 cm)

Impact pressure is measured on the upper side of the front and the rear wall to minimize the effects of hydrostatic pressure. On the front wall, two peaks of impact pressure are observed for each model and only one peak on the rear wall is found. It is assumed that the major contribution is done by inertia effect at the first peak on the front wall and the second peak is done by dynamic effects of sloshing flow. There is only dynamic impact pressure peak on the rear wall under deceleration boundary condition.

For the models with wall inclined acute angle to the bottom (m1, m2, m3), peak pressure is decreased from 743 Pa to 480 Pa compared to the base model with wall orthogonal to the bottom (m0). The pressure time history of the front and the real wall is given in Figure 14. For the models with wall inclined obtuse angle to the bottom (m4, m5, m6), the peak pressure is increased compared to the base model as shown in Figure 15. The difference between the two different angle models is that the impact pressure by dynamic effects of sloshing flow is not reduced both on the front and the rear wall for the obtuse angle models compared to the acute angle models. Two reasons are (1) normal force on the inclined wall is reduced by sinθ (2) by decreasing angle θ of the wall, flow into the lower portion of fuel flow increases rather than into the upper portion. For example, the first peak pressure in m1, m2, m3 is

45o

m1 m2 m3m0

m4 m5

m6

135o

Inclined wall (acute angle) Inclined wall (obtuse angle)

H/L ratio

843 Pa

743

Total Pressure (Pa)

Front wall Rear wall

the greater the dynamic effects of sloshing flow by increasing the amount of flow into the upper portion of fuel flow in the dynamic equivalent model.

Figure 14. Pressure on the front and the rear wall for the acute inclined angle wall models (m1, m2, m3)

Figure 15. Pressure on the front and the rear wall for the obtuse inclined angle wall models (m4, m5, m6)

CONCLUSION

The gross flow pattern of sloshing phenomenon in fuel tanks can be predicted by computational analysis with comparing rig experiments. No correlation is made between impact pressure in simulation and noise level measurement in experiments at this time. This procedure should be setup to support the assumptions and the attempt to measure the pressure and noise level in experiments is under development. From the findings of the research, the behavior of the fuel flow and its impact pressure on fuel tanks by simulation can be used to design baffles to control the sloshing flow in the future. The effects of the dimensions and the degree of the front and the rear wall angle of fuel tanks are helpful hint to design shapes of fuel tanks to reduce the impulsive pressure within a limited space available in automobile layout.

ACKNOWLEDGMENTS

The authors would like to thank to ECIM Ltd. for their cooperation in the development of technology for predicting the sloshing flow.

Rear wall

time (sec) Total Pressure (Pa)

time (sec)

Total Pressure (Pa)

Front wall

m4 m5

m6

m4 m5

m6

Rear wall

time (sec)

Total Pressure (Pa)

time (sec)

Total Pressure (Pa)

m1 m2

m3

m1 m2

m3

480 Pa

Front wall

REFERENCES

1. Kamiya, K., Yamaguchi, Y. and de Vries, E.: “Simulation Studies of Sloshing in a Fuel Tank”, SAE paper 2002-01-0574.

2. IU, H.S, Cleghorn, W.L. and Mills, J.K.: “Design and Analysis of Fuel Tank Baffles to Reduce the Noise Generated from Fuel Sloshing”, SAE paper 2004-01-0403.

3. Dutta, S. and Laha, M.K.: “Analysis of the small amplitude sloshing of a liquid in a rigid container of arbitrary shape using a low-order boundary element method”, Int. J. Numer. Mech. Engng., 47:1633-1648, 2004.

4. Kang, X, Rakheja, S. and Stiharu, I. : ”Directional Dynamics of a Partly-Filled Tank Vehicle under Braking and Steering”, SAE paper 2000-01-3477

5. Song, J.S. : “Analysis and reduction of sloshing vibration and noise of automobile fuel tank”, Ph.D. Thesis, Korea University, Korea, 1998

CONTACT

Won-Joo Roh, Sok-Hyun Cho, Jae In Park

Hyundai-Kia Motor Company, 772-1, Jangduk-Dong, Whasung-Si, Gyunggi-Do, KOREA

Email : rohwj@hyundai-motor.com