ShyyLab :: Research

Multiphase Flows

An adaptive Cartesian grid based multiphase flow solver with marker based interface tracking is developed. The underlying interfacial dynamics is modeled using immersed boundary method. The time-dependent interface shapes are tracked using triangulated surface grids in 3D, and line-segments in 2D or axisymmetric computational domains. The implementation is capable of handling arbitrary topological changes often seen in bubble dynamics computations during a merger or a break-up. The flow solver is also capable of handling arbitrary shaped solid boundaries within the flow field.

The flow computations are performed on a Cartesian grid that adapts based on the interface location and solution features. Parallel computations via additive Schwarz domain decomposition is implemented using a partitioning strategy based on Hilbert space filling curves. Details can be found in this link.


Fuel delivery	Off-axis collision

Following list highlights the components of the current implementation:

Immersed boundary method
Marker-based interface tracking
Adaptive grid
Solid boundary treatment
Parallel computing

Even though the code is able to handle large variety of flow problems ranging from bubble-droplet dynamics to drug delivery problems, our present effort focuses mainly on fuel delivery problem under micro-gravity conditions which is motivated by spacecraft applications. Some of our recent results can be found in this link.


Flow over a cylinder	Binary Collision

People: Eray Uzgoren, Jaeheon Sim

References:

Cavitation

In liquid flows, cavitation generally occurs if the pressure drops below the vapor pressure and consequently the negative pressures are relieved by means of forming gas filled or gas and vapor filled cavities. Cavitation can be observed in a wide variety of hydrodynamic systems like pumps, nozzles, injectors, marine propellers, hydrofoils and underwater bodies. Cavitating flows in most engineering systems are turbulent, and the dynamics of the interface formed involves complex interactions between vapor and liquid phases. Undesirable features of cavitation are structural damage, noise and power loss. On the other hand, drag reduction can be observed on bodies surrounded fully or partially with a natural or gas ventilated cavity. For liquid rocket propulsion, the cryogenic operating condition makes the thermal effect important in the cavitation dynamics. This further complicates the simulations and deserves further investigations.

Cavitation Model

We have been developing transport equation-based models (TEM) along with suitable turbulence closures and numerical techniques to advance the capability of simulating turbulent cavitating flows. In TEM, a transport equation of the liquid/vapor phase fraction is established, the transport equation for either mass or volume fraction, with appropriate source terms to regulate the mass transfer between vapor and liquid phases (volume fraction or vapor mass fraction with pressure source terms), is adopted. Different modeling concepts embodying qualitatively similar source terms with alternate numerical techniques have been proposed by various researchers. Generally speaking, only the constants in the cavitation source terms need to be modified so that it can be applied to both isothermal and cryogenic cavitation.

1. Cavitation in Non-cryogenic Fluids


Figure 1 Illustration of the computational domain for hemispherical projectile [4]	Figure 2 Impact of cavitation models [4]

The flow configuration discussed here is cavitating flow over a hemispherical projectile (figure 1) under the isothermal assumption with Re=1.36E5. Figure 2 shows the performance of the Mushy interfacial dynamic model (Mushy IDM) with the Merkle’s TEM and Sharp interfacial dynamic model (Sharp IDM) at cavitation number=0.4. (Cavitation is stronger when the cavitation number is lower).

The impact of the choice of cavitation model is revealed by the pressure coefficient predicted along the hemispherical projectile surface in the figure 2. The three models illustrate noticeable variations in the condensation region (near the closure region). The Mushy IDM produces a small pressure dip below the vapor pressure value at the beginning of the cavity due to the lower evaporation rate and higher condensation rate.

These features are reflected by the cavity sizes described in figure 3. The Mushy IDM will decrease the cavity length compared to the Sharp IDM. Also, the flow structure in the recirculation zone of the cavity closure region doesn’t exist when using Mushy IDM.

Figure 3. Cavity shapes and flow structures for different cavitation models on hemispherical projectile (cavitation number=0.4). (a) Sharp IDM (b) Mushy IDM [3].

2. Cavitation in Cryogenic Fluids

Figure 4 Illustration of the computational domains for the hydrofoil geometry [4].

Instead of isothermal cavitation, we investigate the cryogenic cavitation for the given geometry above. Again, we can see the flow structure impact similar to that of the previous case. Additionally, the cavity length in figure 5 (a), under the isothermal assumption, is larger than that of the cavity in the figure 5 (b) using the Sharpy IDM with thermal effects. This means under the same conditions, thermal effects will lower the strength of cavitation.

The ideas to compare and contrast the Sharpy IDM and Mushy IDM are:(1) the gradual density variation and less extent of the vapor phase inside the cavity is shown in Mushy IDM, and (2) the streamlines don’t deflect sharply or have a backflow region after the closure region when using Mushy IDM. The weaker intensity and mushy nature of the Mushy IDM are also the natures of the cryogenic cavitation. Actually, the flow structure of cryogenic cavitation doesn’t seem to be largely different than the single phase structure. As the result, the instability caused by the re-entrant jet is not shown here, which makes the cryogenic cavitation weaker and more stable.

Figure 5.Cavity shape indicated by liquid phase fraction α. Arrow lines are streamlines(a) Sharpy IDM without isothermal effects. (b) Sharpy IDM with themal effect (c) Mushy IDM with thermal effect.

References:

Researchers: Chien-Chou Tseng

U of M \| CoE \| Aerospace
Computational Thermo-Fluids @ U of M, Aerospace Engineering