# A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

## Abstract

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for themore »

- Authors:

- Department of Aerospace Engineering, Iowa State University, Ames, IA (United States)
- Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT (United States)

- Publication Date:

- OSTI Identifier:
- 22622296

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 339; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACOUSTICS; APPROXIMATIONS; ATOMIZATION; CAPILLARIES; CAPTURE; COMBUSTORS; COMPRESSION; COMPUTERIZED SIMULATION; DIFFUSION; DROPLETS; INTERFACES; LIQUIDS; MODIFICATIONS; MULTIPHASE FLOW; RUNGE-KUTTA METHOD; SHOCK WAVES; SURFACE FORCES; SURFACE TENSION; SURFACES

### Citation Formats

```
Garrick, Daniel P., Owkes, Mark, and Regele, Jonathan D., E-mail: jregele@iastate.edu.
```*A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension*. United States: N. p., 2017.
Web. doi:10.1016/J.JCP.2017.03.007.

```
Garrick, Daniel P., Owkes, Mark, & Regele, Jonathan D., E-mail: jregele@iastate.edu.
```*A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension*. United States. doi:10.1016/J.JCP.2017.03.007.

```
Garrick, Daniel P., Owkes, Mark, and Regele, Jonathan D., E-mail: jregele@iastate.edu. Thu .
"A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension". United States.
doi:10.1016/J.JCP.2017.03.007.
```

```
@article{osti_22622296,
```

title = {A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension},

author = {Garrick, Daniel P. and Owkes, Mark and Regele, Jonathan D., E-mail: jregele@iastate.edu},

abstractNote = {Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.},

doi = {10.1016/J.JCP.2017.03.007},

journal = {Journal of Computational Physics},

number = ,

volume = 339,

place = {United States},

year = {Thu Jun 15 00:00:00 EDT 2017},

month = {Thu Jun 15 00:00:00 EDT 2017}

}