Aug 8, 2007 - high speed transom ship flows, Athena R/V. Resistance predictions for ... URANS/DES for the Athena barehull at model-scale. Seakeeping ...
9th International Conference on Numerical Ship Hydrodynamics Ann Arbor, Michigan, 5-8 August 2007
Model- and Full-Scale URANS/DES Simulations for Athena R/V Resistance, Powering, and Motions Shanti Bhushan, Tao Xing, Pablo Carrica, Frederick Stern IIHR-Hydroscience and Engineering The University of Iowa Iowa City, IA 52242-1585 ABSTRACT This study develops and implements a two-layer, twopoint wall-function model in the general-purpose URANS/DES solver CFDSHIP-IOWA-V.4 to routinely simulate model- and full-scale ship flows for resistance, propulsion, seakeeping, and maneuvering. The wall-function is validated for smooth flat-plate flows for high Reynolds numbers, and applied to study high speed transom ship flows, Athena R/V. Resistance predictions for Athena barehull with skeg at modelscale compare well with the near-wall turbulence model results and EFD data. For full-scale simulations frictional resistance predictions are in good agreement with the IITC line. No significant Reynolds number effect is found for free surface wave elevation and sinkage and trim (smooth wall). Full-scale boundary layer is thinner than that of the model-scale. Rough wall simulations show higher frictional and total resistances and relative large and unexpected changes are observed for sinkage and trim, which may be due to the coarse grid used and needs to be confirmed by further study. Resistance and powering computations are performed at full-scale for self-propelled fully appended Athena free to sink and trim with smoothand rough-walls, and results are compared with fullscale data extrapolated from model scale measurements using ITTC ship-model correlation line including a correlation allowance. Rough wall conditions predict higher frictional and total resistances leading to better Froude number and resistance without significant effects on sinkage and trim. Sinkage and trim are not significantly affected by Reynolds number. Full-scale computations are performed for the towed fully appended Athena free to sink and trim and the boundary layer and wake profiles are compared with full-scale EFD data. Rough-wall results are found to be in better agreement with the EFD data than the smoothwall results. Transom flow instability is studied for the
fully appended Athena free to sink and trim at fullscale using DES with the wall-function. Karman-like vortex shedding and associated instabilities are analyzed and compared with the previous URANS/DES for the Athena barehull at model-scale. Seakeeping capability of the wall-function is also demonstrated at both model- and full-scale. Finally, limitations of the current wall-function approach and future work are discussed. INTRODUCTION In the past few years, tremendous advances have been made in the development and validation of computational fluid dynamics (CFD) for ship hydrodynamics, thereby assisting in ship design (Larsson, 1997; Gorski, 2002; Stern, 2006a). As documented in the previous symposiums on naval hydrodynamics, most of the CFD studies have focused on model-scale ship flows, i.e., Reynolds number (Re~107), including resistance, propulsion, seakeeping, and maneuvering (Miller et al, 2006; Carrica et al, 2006b). In contrast, full-scale ship flow computations (Re~109) are very limited such that, in spite of its importance, routine capability is lacking due to the challenging issues with regard to both CFD (turbulence modeling and numerical methods) and EFD (procurement of full-scale validation data). Numerical issues for full-scale simulations include several aspects. First, near-wall turbulence models require a very expensive grid density near the wall, which is usually unaffordable for ship geometries. Secondly, the extremely small grid spacing in the wall normal direction near the wall causes huge aspect ratio of grid cells, which significantly increases the errors of computing mass and momentum fluxes through the interfaces of grid cells. Turbulence modeling issues for
full-scale calculations include insufficient validations at full-scale even for canonical flows and ability to account for wall roughness effects (Patel, 1998). One typical approach to avoid the numerical limitations discussed above is to use “wall-functions.” It is well established that for equilibrium flows the near-wall region is governed by either the turbulent stresses (log-layer) or viscous stresses (sub-layer). Under this assumption universal profiles for velocity and turbulent quantities can be obtained analytically. Several studies have used the wall-function approach to investigate the Reynolds number effects, by comparing with model-scale (Choi et al, 2003) or full-scale (Bull et al, 2002) experimental data. The study conducted for a HSVA ship model (Oh and Kang, 1992: Re=109 and 5×106) showed that the pressure coefficient is not influenced by Reynolds number in the thin boundary layer region, but results in much reduced skin friction. In the thick boundary layer around the stern and near the wake, the pressure coefficients for full-scale are noticeably changed by the reduction of viscous-inviscid interaction and have the trend of approaching the values of the inviscid region. Similar conclusions were also drawn by Tahara, et al (2002) from the full-scale simulations of Series 60 ship model. Another study using URANS (unsteady Reynolds averaged Navier-Stokes) for a low-speed TDW VLCC (Choi et al, 2003) showed that full-scale has weaker strength of bilge vortices that cause a smaller vortex and turbulence region, and a smaller value of nominal wake fraction on the propeller plane. However, there is little scale effect on the limiting streamline and hull pressure except on the stern region. Effects of full-scale on the propeller inflow were investigated by Gorski, et al (2004) for two naval surface combatants, an aircraft carrier and a destroyer for both model- and full-scale, with the former comparing well with experimental data. It was found that the measured model-scale inflow to the propeller planes has a larger wake deficit than seen at full-scale. Bull, et al (2002) studied full-scale effects on two hull forms: the Dutch frigate the “DeRuyter” and the NATO research vessel “Alliance.” They concluded that the results compare accurately with EFD data for the bare hull geometry, and capture the main flow features for the appended ships. The European Union project EFFORT has focused on the full-scale calculations for several hull forms and report significant scale effect on wave and wake profiles (Hanninen and Mikkola, 2006). The most commonly used wall-function is the standard wall-function (Launder and Spalding, 1974). This approach is based on the stringent criteria that the first grid point away from the wall lies in the log-layer. However, it is not always possible to place the first grid point in the log-layer for flows with considerable variation of the wall stresses, e.g., laminar-turbulent
transition zone, variation of the boundary layer thickness along the ship hull or when the ship is slowly accelerated from a static condition. This limitation is addressed by using a two-layer wall-function model, which assumes that near-wall region consists of suband log-layers only (Esch and Menter, 2003). In this approach, boundary conditions for the velocity and turbulent quantities are switched between the sub- or log-layer analytic profiles, depending upon the local y+ value of the first grid point away from the wall. Threelayer wall-function model includes an additional buffer-layer (Temmerman et al, 2003), but still suffers from the deficiency that the near-wall representation is not continuous. Recently, Shih, et al (2003) proposed a multi-layer (generalized) wall-function model using curve-fitting to provide a continuous function to bridge the sub- and log-layers. The multi-layer wall-function model thus provides the most flexibility in the choice of the grid spacing for the first grid point away from the wall. In the non-equilibirium flows involving mild pressure gradients, wall-functions can be sensitized to the pressure gradient effect for better prediction of separation, recirculation and reattachment regions (Kim and Chaudhury, 1995; Wilcox, 1993). However, wall-functions have limitations in predicting massively separated and reattaching flows due to strong pressure gradients (Patel, 1988). Further, log-layer assumption is not adequate for describing the cross-flow features in three-dimensional boundary layer (Bradshaw and Huang, 1995). Implementation of a wall-function requires evaluation of friction velocity to provide the boundary conditions for velocity and turbulence variables. The two-point approach discussed by Tahara, et al (2002) uses the velocity at the second grid point away from the wall to obtain its value. An alternate one-point approach has been introduced by Kim and Chaudhary, (1995) which uses the flow variables at the wall neighboring cells only. In full-scale computations, surface roughness is important as it leads to significant increase in frictional coefficient. Modeling of surface roughness involves two important parameters, non-dimensional roughness length (k+) and the roughness type (Jimenez, 2004). Several studies have been performed to study the roughness effect of the painted surface at model-scale (Schultz, 2002 and the reference therein). However, for full-scale this would lead to higher k+ value, as roughness parameter is directly proportional to Reynolds number. A simplified approach involves Clauser’s hypotheses according to which surface roughness affects only the inner boundary layer leading to a downward shift in the log-layer profile (White, 2003). Although this hypothesis seems to breakdown for the fully rough regime, for ship flows surface roughness lies mostly in the transitional regime (Patel,
1998), thus such modeling can be used with relative confidence (Tahara et al, 2002). The overall objective of this study is to extend the general-purpose URANS/DES solver, CFDSHIPIOWA-V.4 to routinely simulate full-scale ship flows using wall functions for applications that will meet the naval architect needs for resistance, propulsion, seakeeping, and maneuvering. Also of interest is application of wall-function at model-scale to reduce the number of grids points near the wall. This study extends previous URANS and DES at model-scale simulations (Wilson et al, 2006; Xing et al, 2007b) to full-scale with the ability to account for the wallroughness. To achieve this overall objective, a twolayer wall-function model (Esch and Menter, 2003) is developed and implemented using a two-point approach (Tahara et al., 2002) for future work involving multi-layer wall-function models. The wallroughness effects are included following White (2003). The wall-function model is validated for smooth flat-plate flows using analytical log-law profiles and experimental data at high Reynolds numbers (equivalent to full-scale ship Reynolds numbers). The wall-function model is then applied to high speed transom ship flows, Athena R/V. The resistance calculations are performed for the Athena barehull with skeg at model-scale for both fixed and predicted sinkage and trim, and results are compared with near wall turbulence model results and experimental data. Full-scale calculations are performed for Athena barehull free to sink and trim using smooth- and roughwalls. Verification study is performed for resistance, sinkage and trim at full-scale for Athena barehull with skeg for smooth-walls. Self propelled simulations are performed for the fully appended Athena free to sink and trim at full-scale using smooth- and rough-walls. The results are compared with full-scale data extrapolated from model scale measurements using ITTC ship-model correlation line including a correlation allowance. Towed fully appended Athena free to sink and trim are simulated using smooth- and rough-wall conditions and boundary layer and wake profiles are compared with the full-scale EFD data. Next, transom flow instability is studied at full-scale for towed fully appended Athena free to sink and trim. Finally, seakeeping capability is demonstrated at model- and full-scale using both barehull with skeg and fully appended Athena. COMPUTATIONAL METHOD The general-purpose URANS/DES solver, CFDSHIPIOWA-V.4 (Carrica et al, 2007a,b) uses a single-phase level set method, advanced iterative solvers, conservative formulations, and extension of the dynamic overset grid approach for free surface flows.
The DES capability was implemented by Xing, et al (2007a). Equations of Motion CFDSHIP-IOWA-V.4 solves only the water phase. The underlining assumptions involved in this approach are described in Carrica, et al (2007a,b) and Wilson, et al (2006). The governing equations for the water phase in dimensionless form are:
∂U i =0 ∂xi
(1)
∂U i ∂U i ∂pˆ ∂ 1 ∂ 2U i +U j =− + − ui u j ∂t ∂x j ∂x j Re ∂x j ∂x j ∂x j
(2)
where, Ui=(U,V,W) are the Reynolds-averaged velocity components, xi=(x,y,z) are the independent coordinate 2 2 directions, lp = pabs / ρU 0 + z / Fr + 2k / 3 is the dimensionless piezometric pressure where pabs is the
absolute pressure, ui u j are the Reynolds stresses,
Fr = U 0 / gL is the Froude number, and k is the turbulent kinetic energy (TKE). U0 is the free stream velocity, L is the ship length Turbulence Modeling Blended k-ω/k-ε and DES model Two-equation closure is used for the Reynolds stresses, where they are modeled as a linear function of the mean rate-of-strain tensor through an isotropic eddy viscosity (νt),
⎛ ∂U ∂U j −ui u j = ν t ⎜ i + ⎜ ∂x ∂xi ⎝ j
⎞ 2 ⎟⎟ − δ ij k ⎠ 3
(3)
where δ ij is the Kronecker delta. The unknown eddy viscosity is evaluated from the TKE and the specific dissipation rate (ω). Additional transport equations, presented below, are solved following Menter’s (1994) blended k-ω/k-ε (BKW) approach.
∂k 1 + ( v − σ k ∇ ν t ) ⋅ ∇ k − ∇ 2 k + sk = 0 ∂t Pk
(4a)
∂ω 1 + ( v − σ ω ∇ν t ) ⋅∇ω − ∇ 2ω + sω = 0 ∂t Pω
(4b)
The turbulent viscosity and the effective Peclet numbers are
ν t = k / ω , Pk / ω =
1 1/ Re + σ k / ων t
(5)
and the source terms in k and ω equations constitute the production and dissipation terms (refer to Carrica et al, 2006a for details). The model constants, say α, are calculated from the standard k-ω (α1), and k-ε (α2) values using a blending function (refer to Menter, 1994 for the model constants values):
α = F1α1 + (1 − F1 ) α 2
(6)
The blending function F1 is designed to be unity in the near-wall regions of boundary layers and gradually switches to zero in the wake region to tak`e advantage of the strengths of the k-ω and k-ε models respectively. The detached eddy simulation (DES) model modifies the dissipative term of the k-transport equation as (refer to Xing et al, 2007a for details): k DRANS = ρβ * kω = ρ k 3 2 / lk −ω D k = ρ k 3 2 / l
DES
(7a)
(8a) (8b)
The constant CDES is set at 0.65, the typical value for homogeneous turbulence, and Δ is computed using the local grid spacing. Wall-Function Implementation In the two-layer wall-function (WF) model, the velocities in the sub- and log-layer regions are: + ⎧⎪ y + ≤ 11.67 : sub − layer ; y2,3 = ⎨ −1 + + uτ ⎪⎩κ ln( y2,3 ) + B − ΔB ; y2,3 > 11.67 : log− layer
u2,3
For the log-layer, the friction velocity is obtained by iteratively solving the log-layer equation using the Newton-Rapshon method; B. The computed friction velocity is then used in Equation (9) to obtain the magnitude of tangential velocity at j=2, with the same direction of the tangential velocity at j=3. The normal velocity at j=2 is approximated using linear interpolation, based on the normal velocities and wall distances at j=2 (Δy2) and j=3 (Δy3). Coordinate transformation is needed to give velocity boundary conditions in the physical coordinate system. C. The boundary conditions for the turbulence quantities k, ω are specified at j=2 using (Wilcox, 1993):
(7b)
where length scales are defined as:
lk −ω = k 1 2 /( β *ω ) l = min(lk −ω , CDES Δ )
where, k+ is the non-dimensional roughness parameter. For naval applications, the wall roughness lies in the transitional roughness regime (Patel, 1998), i.e., 5≤ k+ 11.67 : y2+ ≤ 11.67
(12) : y2+ > 11.67
Figure 1 shows the implementation procedure.
(9)
where, superscript + quantities are non-dimensionalized by friction velocity (uτ= τ w / ρ , where τw is the wall shear stress) and Re. Constants κ and B are chosen to be 0.4 and 5.1, respectively (Knobloch and Fernholz, 2002). The factor ΔB in Equation (9) accounts for the effect of wall roughness, resulting in the downshift of the log-layer region, which is computed as (White, 2003): ΔB = κ −1 ln(1 + k + ) − 3.5
(10)
Figure 1: Flow chart of the wall-function implementation considering j=1 as the wall point.
The near wall region has three flow regimes: sublayer (y+≤5), buffer layer (530). Since the buffer layer is neglected in the current wall function model, the implementation of the two-point would result in the following possibilities: (y2+: sub-layer, y3+: sub-layer; y2+: sub-layer, y3+: loglayer; or y2+: log-layer, y3+: log-layer). In the current study, Reynolds number is at the order of 107~109, for which the sub-layer is thin and log-layer extent is large. Thus, both j=2 and j=3 can be conveniently placed in the log-layer region, e.g., Tahara, et al (2002) used y2+ to be 103 in Series 60 ship model calculations. To resolve the boundary layer as best as we can and still save sufficient grid points near the wall, y2+≈30 is applied for most simulations in the current study. However, if either y2+ or y3+ is placed in the buffer layer (5
