# Numerical Investigation of Spray Collapse in GDI with OpenFOAM

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions. The advantages of direct injection include, but are not limited to, controlled fuel-to-air ratios during cranking and cold start, lower operating break specific fuel consumption, higher compression ratios and increased engine efficiency [1]. In recent years, liquid pressurized gas (LPG) internal combustion engines have been emerging as a suitable alternative to conventional gasoline engines and have become common in many regions of the world. While LPG offers many advantages over refinery gasoline, such as a higher compression ratio and lower specific CO

_{2}emissions, it has a significantly higher saturation pressure. Therefore, the fuel is injected in a superheated condition for several engine operating conditions that are typical for direct injection. In the superheated state, vapor bubbles nucleate within the jet and start to grow rapidly, leading to a disintegration of the jet and a fine dispersed cloud of droplets. This process is commonly referred to as flash boiling and often characterized by the superheat ratio of the saturation to ambient pressure, ${R}_{p}={p}_{\mathrm{sat}}/p$. While flash boiling can help to improve the vaporization process and reduce the droplet size, adverse effects such as spray collapse may occur [2,3,4]. Spray collapse is a result of plume-to-plume interaction [2,4,5], with a significantly increased penetration length and decreased spray angle, which negatively impacts engine performance and emissions. Even though flashing occurs in a wider range of operating conditions for LPG, higher hydrocarbons experience flashing as well and may also be subject to spray collapse.

## 2. CFD Modeling

#### Phase Change Modeling

_{0}= 3.84 × 10

^{−7}s, $\beta =-0.54$, $\lambda =-1.76$ represent the high-pressure fit to the flashing water experiments. The final expression for the phase change with $\chi $ as the liquid mass fraction is then

## 3. Single Hole Injector

^{−9}s, while keeping the exponents of the high-pressure fit of Downar-Zapolski et al. [13]. To compare the results of the OpenFOAM solver, the same settings for the HRM model were selected. For the discretization scheme, first-order temporal discretization was used together with a hybrid scheme switching between a central differencing and upwind approach depending on a shock sensor [34] for the momentum equation. The reference solution with CONVERGE used a second-order temporal discretization and a second-order upwind scheme. A second-order backwards Euler method cannot be used with the OpenFOAM solver due to the implementation of the volume fraction transport equation, which requires an explicit flux correction [18]. Therefore, for the sake of stability, all presented results used first-order Euler time discretization. The mesh was generated with the OpenFOAM tool snappyHexMesh using a mesh size of 15.625 μm in the injector and in the jet, including the shock front. The mesh size was the result of a previous mesh study [35]; in addition, the cell size was smaller than the value of 17.5 μm suggested by Saha et al. [36] and in the range of the smallest mesh size of 12.5 μm used for the reference computations by Guo et al. [21].

#### 3.1. Discussion of the Results

#### 3.2. Effects of Injection Pressure and Temperature

## 4. Simulation of Eight-Hole Spray G Configuration

#### 4.1. Mesh Generation

#### 4.2. IsoOctane Case A

^{−4}is drawn in red for the experimental data; the simulation results are represented by the blue dotted line using the original HRM model constants and by the black line for the numerical results with the HRM model using the modified constants, ${\Theta}_{0}=1\mathrm{n}\mathrm{s}$.

#### 4.3. Spray Collapse Due to Shock Interaction

#### 4.4. Shock Interaction of Neighboring Plumes

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Single-hole domain test case. The inner bore and counter bore are marked with a blue and red box, respectively.

**Figure 2.**Shock system for the case of nHexane-A visualized by the density gradient magnitude. (1) Constant pressure streamline or barrel shock, (2) intercepting shock, (3) triple point, (4) reflected shock, (5) Mach disk, (6) slip stream [37].

**Figure 3.**Velocity magnitude for the single-hole injector with n-hexane. Reference solution of Guo et al. [21] is shown in (

**a**).

**Figure 5.**Mesh used for the simulation of propane spray G cases. Cell refinement at the expected shock front by prior simulations with a coarse grid.

**Figure 6.**Liquid volume fraction distribution for the case IsoOctane-A as measured in the experiment. Experimental data are taken from Hwang et al. [39], and the iso-contour for volume fraction α = 5 × 10

^{−4}is shown in black for the homogeneous relaxation model (HRM) model with modified constants, with a blue dotted line for the original HRM model and red for the experimental results.

**Figure 7.**Mie-scattering images at 500 μs after injection start: (

**a**) shows a slightly evaporating case (${R}_{p}=9.38$), (

**b**) the case of Propane-A and (

**c**) the case of Propane-B. The liquid penetration length ${L}_{p}$ is marked in the images (

**a**,

**b**). Reprinted from Lacey et al. [4] with permission from Elsevier.

**Figure 8.**A simplified view of the injector with a pitch circle diameter ${d}_{cc}$ and the fuel expansion ${d}_{c,\mathrm{fuel}}$ [4].

**Figure 9.**Velocity magnitude for different times for the case of Propane-A in the left column (subfigures (

**a**)–(

**d**)) and Propane-B in the right column (subfigures (

**e**)–(

**h**)).

**Figure 10.**Logarithmic pressure contour for the case of Propane-B for different time steps: (

**a**) 0.020 ms, (

**b**) 0.035 ms, (

**c**) 0.040 ms and (

**d**) 0.150 ms. The formed pressure cells are marked in (

**c**) with Roman numerals I and II.

**Figure 11.**(

**a**) Three-dimensional iso-contour of the density gradient for the case of Propane-B at 150 μs. The left side shows a cut through an injector and the right side shows a cut between two injector bores. (

**b**) Density gradient contour for the case of Propane-B; the first pressure cell is colored in light blue.

**Figure 12.**(

**a**) Pressure distribution at a plane 0.65 mm above the injector and 2D velocity vector. (

**b**) Schematic drawing of the shock system for the marked area in (

**a**) showing the velocity vector through the incident shock wave AB. The reflective shock is marked with R and the Mach disk with M.

**Figure 13.**Liquid mass fraction contour at x–y plane at 0.65 mm (

**a**) and 1.5 mm (

**b**) above the injector.

Case | ${\mathit{P}}_{\mathbf{inj}}$ [MPa] | ${\mathit{T}}_{\mathbf{inj}}$ [K] | ${\mathit{P}}_{\mathbf{amb}}$ [kPa] | ${\mathit{T}}_{\mathbf{amb}}$ [K] | ${\mathit{R}}_{\mathit{p}}$ |
---|---|---|---|---|---|

nHexane-A | 7.5 | 403 | 101 | 300 | 4.49 |

nHexane-B | 7.5 | 403 | 60 | 300 | 8.31 |

nHexane-C | 7.5 | 403 | 20 | 300 | 24.9 |

Case | Fluid | ${\mathit{P}}_{\mathbf{inj}}$ [MPa] | ${\mathit{T}}_{\mathbf{inj}}$ [K] | ${\mathit{P}}_{\mathbf{amb}}$ [kPa] | ${\mathit{T}}_{\mathbf{amb}}$ [K] | ${\mathit{R}}_{\mathit{p}}$ |
---|---|---|---|---|---|---|

IsoOctane-A (G2) | Iso-octane | 20 | 363.0 | 50 | 293 | 1.5 |

Propane-A | Propane | 20 | 363.0 | 100 | 293 | 26.3 |

Propane-B | Propane | 20 | 363.0 | 53 | 293 | 70.8 |

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**MDPI and ACS Style**

Gärtner, J.W.; Feng, Y.; Kronenburg, A.; Stein, O.T.
Numerical Investigation of Spray Collapse in GDI with OpenFOAM. *Fluids* **2021**, *6*, 104.
https://doi.org/10.3390/fluids6030104

**AMA Style**

Gärtner JW, Feng Y, Kronenburg A, Stein OT.
Numerical Investigation of Spray Collapse in GDI with OpenFOAM. *Fluids*. 2021; 6(3):104.
https://doi.org/10.3390/fluids6030104

**Chicago/Turabian Style**

Gärtner, Jan Wilhelm, Ye Feng, Andreas Kronenburg, and Oliver T. Stein.
2021. "Numerical Investigation of Spray Collapse in GDI with OpenFOAM" *Fluids* 6, no. 3: 104.
https://doi.org/10.3390/fluids6030104