11th International Conference on Fast Sea Transportation FAST 2011, Honolulu, Hawaii, USA, September 2011 Comparison of Turbulence Models for Simulating Flow in Waterjets Xian Luo 1 , Brenden Epps 1 , Chryssostomos Chryssostomidis 1 and George Em Karniadakis 1,2 1 Design Laboratory, MIT Sea Grant, MIT 2 Division of Applied Mathematics, Brown University ABSTRACT We have developed a fast numerical algorithm for simulating flows in complex moving domains. The new hybrid smoothed profile/spectral element method exhibits high-order accuracy as well as great computational efficiency as it removes the tyranny of mesh generation. Here we extend this work by in- corporating a variational multiscale large eddy formulation for modeling the subgrid turbulent scales. We present veri- fication and validation studies of the combined method and compare different turbulence modeling methodologies. Sub- sequently, we apply it to study laminar, transitional and turbu- lent flows in an axial-flow waterjet propulsion system (ONR AxWJ-1). The robustness and efficiency of our methods en- able parametric studies of many cases, which may aid greatly in the early stages of design and evaluation of such propulsion systems. KEY WORDS: waterjet, CFD, high-order methods, turbu- lence modeling 1. INTRODUCTION Computational fluid dynamics (CFD) tools can now be used effectively for the design and optimization of waterjets for ship propulsion. While standard CFD approaches may be inefficient in simulating accurately the complex viscous in- teractions inside a watejet system, recent advances in immer- sive boundary methods have allowed for much faster simula- tions without the need for frequent re-meshing, hence elim- inating a large computational bottleneck in analysis. For ex- ample in [1] we developed a smooth profile method (SPM) to represent all the moving parts of a waterjet system using fixed Eulerian grids (see figure 1), which in conjunction with the high-order accuracy of spectral element discretizations re- sulted in accurate and efficient simulations. However, without the use of a turbulence model we were limited to a relatively low Reynolds number regime. For some numerical simulations of waterjets, potential flows are assumed with limited viscous corrections, e.g. based on a two-dimensional integral boundary layer analysis [2]. There have been some RANS solvers applied to waterjet sim- ulations, but numerical simulations of the interaction between rotor and stator in a fully unsteady manner are too compli- cated and computationally expensive. So many assumptions have been made, e.g. the rotor and stator problem is decou- pled and the flow is rotationally cyclic so that one can model a single blade passage only [3]. Recently, in [4] we pre- sented the first 3D simulation results by combining SPM with an unsteady RANS (URANS) approach using the Spalart- Allmaras (SA) turbulence model to account for the subgrid stresses [5, 6]. In the present work we continue on develop- ing higher fidelity turbulence models for the SPM/spectral el- ement method and focus, in particular, on formulating large- eddy simulations models for waterjet systems. Figure 1. Waterjet AxWJ-1: Geometry description for the waterjet we consider in this study; SPM models the rotor and stator subdomains. In classical LES, large- and small-scale motions are sepa- rated by applying a spatial filtering operation to the Navier- Stokes equations before discretization. Hence, there are two levels of approximation, filtering and truncation, and they both contribute to the overall modelling error. Filtering may be explicitly carried out or only implicitly assumed. The re- sult is a set of equations for the large-scale motion. The resid- ual motion, i.e., motions on scales that are smaller than the fil- ter width, appear in these equations as a residual stress term. This term is a priori unknown, and although the intention is not to describe the residual motion in itself, it must be mod- eled explicitly to incorporate the effect of the residual motion on the resolved scales. There are several technical issues in filter-based LES that have to be addressed. For instance, filter- ing and spatial differentiation do not, in general, commute on bounded domains or for non-uniform grids, so careful anal- ysis is needed to obtain the correct form of the equations. It is also not obvious how to prescribe correct boundary con- ditions for the filtered velocity at solid walls. Another issue with the filter-based LES models is that the residual stress model may adversely affect the resolved part of the energy spectrum. These questions have been the subject of a con- siderable amount of research in the last two decades. For ex- ample, Carati et al. [7] have analyzed the error contributions from filtering and truncation and found that the filtering error can be expressed in terms of the resolved velocity field and © 2011 American Society of Naval Engineers 185