Desktop version

Home arrow Engineering

  • Increase font
  • Decrease font


<<   CONTENTS   >>
Table of Contents:

Results

The AMAZON-CW code has been verified through a series of benchmark test cases including ID gravity-induced liquid piston, water-air shock tube, free drop of a water column in a closed 2D tank, slamming of a 2D flat plate into pure water and plunging wave impact at a vertical wall (Ma et al., 2014). It has also been applied to study intensive underwater explosions in close proximity to structures (Ma et al., 2015) and to investigate aeration effects on the slamming of blunt bodies (Ma et al., 2016). A few representative benchmark test cases are selected here to demonstrate the hydro-code’s capability properly to handle the compressibility of air and water-air mixture as well as liquid cavitation in both and high pressure regimes.

D problems

In order to verify the capability of the developed code in dealing with fluid compressibility and cavitation, we firstly exam it with ID water-air shock tube and water cavitation problems.

4.1.1 Water-air shock tubes

Here, we consider two shock tube problems involving water-air mixtures. The shock tube initially has an imaginary membrane in the middle of the tube, which separates it into left and right parts filled with fluids at different thermodynamic states as shown in Figure 3. The initial conditions, stopping times and number of mesh cells used for the two shock tubes are listed in Table 1 (cases 1 and 2). Gravitational effects are not included for these problems.

Computed results for these two cases are shown in Figure 4 and 5. Computations of water-air shock tube problems are known to be challenging for numerical methods, particularly around the material interface where spurious nonphysical oscillations may occur. A

Setup of the water-air shock tube

Figure 3: Setup of the water-air shock tube.

Table 1: Initial conditions for water-air shock tubes (cases 1 and 2) and ID cavitation test (case 3). p: density (units in kg/m3); 7: polytropic constant; Pc: pressure constant (units in MPa); p: pressure (units in bar); u: velocity (units in m/s); T: stop time (units in fis): N: number of mesh cells.

Case

T

N

<*,(%)

Pi

7i

Pc 1

P2

72

Pc2

U

p

Side

1

200

1000

  • 0.5
  • 0.5
  • 50
  • 50
  • 1.4
  • 1.4
  • 0
  • 0
  • 1000
  • 1000
  • 4.4
  • 4.4
  • 600
  • 600
  • 0
  • 0
  • 10000
  • 1

Left

Right

2

551.37

800

  • 0.00195
  • 0.01
  • 0.908
  • 1.33
  • 1.4
  • 1.4
  • 0
  • 0
  • 1027
  • 1027
  • 4.4
  • 4.4
  • 600
  • 600
  • 0
  • 0
  • 10
  • 1

Left

Right

3

1850

1000

  • 0.01
  • 0.01
  • 1
  • 1
  • 1.4
  • 1.4
  • 0
  • 0
  • 1000
  • 1000
  • 4.4
  • 4.4
  • 600
  • 600
  • -100
  • 100
  • 1
  • 1

Left

Right

Comparison of the present computation (red curve) and Murrone and Guillard’s results (Murrone and Guillard, 2005) (black line) for water-air shock tube 1

Figure 4: Comparison of the present computation (red curve) and Murrone and Guillard’s results (Murrone and Guillard, 2005) (black line) for water-air shock tube 1.

Comparison of the present computation (red curve), exact solution (black curve) and Plumerault et al. ’s results (Plumerault et ah, 2012) (blue dots) for water-air shock tube 2

Figure 5: Comparison of the present computation (red curve), exact solution (black curve) and Plumerault et al. ’s results (Plumerault et ah, 2012) (blue dots) for water-air shock tube 2.

close examination of these results shows generally good agreement with exact solutions and published independent numerical predictions with other flow codes. This verifies that the present method resolves wave speeds correctly and does not produce spurious nonphysical oscillations near shocks or at material interfaces.

In particular in Figure 5, it can be seen, in contrast, that the solution produced by Plumerault et al. exhibits strong nonphysical numerical oscillations around the shock and material interface and the present method has superior performance. Agreement with the exact solution is good apart from a slight underprediction of the discontinuity in density in the present results at the material interface in the region around x = 0.5.

4.1.2 Cavitation test

This case is used to test the capability of a numerical method to deal with liquid flow cavitation. Figure 6 shows the setup of the water expansion tube. The imaginary membrane is placed at the middle of the tube at t = 0. The initial conditions for this case are listed in Table 1 (case 3). The obtained solution is depicted in Figure 7. Rarefaction waves are observed to propagate outwards from the centre of the tube and the pressure decreases symmetrically from the middle in both left and right directions. Responding to the reduction of pressure, air entrained in the water begins to expand and its volume fraction increases. Accordingly, the volume fraction of the liquid phase falls. This creates a cavitation pocket in the middle of the tube and results in the dynamic appearance of two interfaces that were not present initially (Saurel et al., 2009). These results indicate that the present method can deal with low pressures quite well neither violating the physics nor producing a nonphysical negative value of absolute pressure that would cause the solver to diverge numerically. The model can also handle the creation, during the computation, of interfaces not present initially. Excellent agreement with the exact solution and Saurel et al. ’s calculated results is observed in Figure 7.

Setup of the water cavitation tube

Figure 6: Setup of the water cavitation tube.

Liquid expansion tube with a cavitation pocket

Figure 7: Liquid expansion tube with a cavitation pocket. The present results (dashed line) are compared to the exact solution (black line) and Saurel et al. ’s independent computation (Saurel et al., 2009) (blue dots).

 
<<   CONTENTS   >>

Related topics