Pablo M. Carrica

A model for turbulent polydisperse two-phase flow in vertical channels

A polydisperse two-phase flow model is developed and used to analyze the effect of the bubble size on the radial phase distribution in vertical upward channels. The two-fluid model is evaluated considering that the bubble size distribution can be represented with groups of constant mass. The model accounts for interfacial momentum transfer terms arising from drag, lift, turbulent dispersion and wall forces for the different bubble sizes. The turbulence is modeled with the k–e model for bubbly flow. A two-phase wall logarithmic law is developed to evaluate the boundary conditions for the k–e and the two-fluid models. The turbulence in the buffer and laminar near-wall regions is evaluated considering the asymptotic consistency of the k–e model approaching the solid surface. The model is able to predict the transition from the near-wall gas volume fraction peaking to the core peaking beyond a critical bubble size. The double gas volume fraction peak experimentally observed when both, small and big bubbles, are present can be also simulated. The model was numerically solved for fully developed flow by means of a finite difference method and the results were compared against the experimental data measured by others in air/water vertical ducts.

Computational Towing Tank Procedures for Single Run Curves of Resistance and Propulsion

A procedure is proposed to perform ship hydrodynamics computations for a wide range of velocities in a single run, herein called the computational towing tank. The method is based on solving the fluid flow equations using an inertial earth-fixed reference frame, and ramping up the ship speed slowly such that the time derivatives become negligible and the local solution corresponds to a quasi steady-state. The procedure is used for the computation of resistance and propulsion curves, in both cases allowing for dynamic calculation of the sinkage and trim. Computational tests are performed for the Athena R/V model DTMB 5365, in both bare hull with skeg and fully appended configurations, including two speed ramps and extensive comparison with experimental data. Comparison is also performed against steady-state points, demonstrating that the quasisteady solutions obtained match well the single-velocity computations. A verification study using seven systematically refined grids was performed for one Froude number, and grid convergence for resistance coefficient, sinkage, and trim were analyzed. The verification study concluded that finer grids are needed to reach the asymptotic range, though validation was achieved for resistance coefficient and sinkage but not for trim. Overall results prove that for medium and high Froude numbers the computational towing tank is an efficient and accurate tool to predict curves of resistance and propulsion for ship flows using a single run. The procedure is not possible or highly difficult using a physical towing tank suggesting a potential of using the computational towing tank to aid the design process.

A bubble number density constitutive equation

Abstract A statistical formulation is used to describe gas-liquid two-phase flows. It is shown that this kind of flow cannot be considered a dilute system as is currently done. A correction factor, the pair correlation function, is introduced to account for “dense effects”. Integrating the transport equation of the bubble volume distribution function over all possible volumes, a number density transport equation is obtained, which explicitly accounts for bubble breakup and coalescence phenomena. A complete model is constructed in conjuction with the mass and momentum conservation equations. Its predictions were compared with experimental results on bubble columns. Excellent agreement was found. The theoretical model was able to predict the void fraction axial distributions, which showed strong variations.

A multidimensional two-phase flow model for the total dissolved gas downstream of spillways

Elevated levels of dissolved gas in the spillway stilling basin, which are responsible for gas bubble disease in fish, constitute an important negative environmental effect of dams. Bubbles, entrained when a plunging jet impacts the tailwater pool, plunge beneath the surface and transfer mass to the liquid, causing an increase in the total dissolved gas (TDG) concentration. Most of the numerical studies onTDG downstream of spillways found in the literature are based on experimental correlations for the gas volume fraction.Abetter approach involves the use of a two-phase flowmodel. In this paper, a two-fluid model is used to calculate the gas volume fraction and velocity of the bubbles. A polydisperse model is used in which a Boltzmann transport equation predicts the bubble size distribution, to account for the different bubble sizes found in the flow downstream of spillways. The bubble mass is discretized considering groups of bubbles of variable mass, with the mass of the bubbles changing due to bubble/liquid mass transfer and pressure. A two-phase transport equation for the TDG is presented, whose source is the bubble/liquid mass transfer, which is a function of the gas volume fraction and bubble size distribution. Two-dimensional numerical results of TDG, gas volume fraction, bubble number density, and velocities are presented and discussed. The predictions of TDG downstream of a spillway are compared against field data in the stilling basin ofWanapum Dam, on the Columbia River.

A Note on the Numerical Treatment of the k-epsilon Turbulence Model*

Numerical solution of the equations arising from the κ mdash; ε turbulence model has difficulties inherent to nonlinear convection-reaction-diffusion equations with strong reaction terms, resulting in that numerical schemes easily become unstable. We present a formulation that stresses on the robustness of the solution method, tackling common problems that produce instability. The main contribution concerns the loss of positivity of κ and ε, which is addressed by acting on the coefficients of the reaction and diffusion terms rather than on the turbulent variables themselves. In addition, a linearized implicit, non-iterative, treatment of the wall law is proposed.

Scalability studies and large grid computations for surface combatant using CFDShip-Iowa

Scalability studies and computations using the largest grids to date for free-surface flows are performed using message-passing interface (MPI)-based CFDShip-Iowa toolbox curvilinear (V4) and Cartesian (V6) grid solvers on Navy high-performance computing systems. Both solvers show good strong scalability up to 2048 processors, with V6 showing somewhat better performance than V4. V6 also outperforms V4 in terms of the memory requirements and central processing unit (CPU) time per time-step per grid point. The explicit solvers show better scalability than the implicit solvers, but the latter allows larger time-step sizes, resulting in a lower total CPU time. The multi-grid HYPRE solver shows better scalability than the portable, extensible toolkit for scientific computation solver. The main scalability bottleneck is identified to be the pressure Poisson solver. The memory bandwidth test suggests that further scalability improvements could be obtained by using hybrid MPI/open multi-processing (OpenMP) parallelization. V4-detached eddy simulation (DES) on a 300 M grid for the surface combatant model DTMB 5415 in the straight-ahead condition provides a plausible description of the vortical structures and mean flow patterns observed in the experiments. However, the vortex strengths are over predicted and the turbulence is not resolved. V4-DESs on up to 250 M grids for DTMB 5415 at 20° static drift angle significantly improve the forces and moment predictions compared to the coarse grid unsteady Reynolds averaged Navier–Stokes, due to the improved resolved turbulence predictions. The simulations provide detailed resolution of the free-surface and breaking pattern and vortical and turbulent structures, which will guide planned experiments. V6 simulations on up to 276 M grids for DTMB 5415 in the straight-ahead condition predict diffused vortical structures due to poor wall-layer predictions. This could be due to the limitations of the wall-function implementation for the immersed boundary method.

Water entrainment due to spillway surface jets

Strong flow entrainment has been observed downstream of spillways constructed with flow deflectors. This water entrainment has important environmental and ecological impacts because it improves the mixing of powerhouse and spillway flows, but may negatively impact fish migration or create adverse flow conditions. Most studies found in the literature attempt to explain this entrainment with turbulent mixing. Both reduced-scale hydraulic models and single-phase, isotropic RANS models grossly under-predict the degree of entrainment observed in prototypes. In this paper, an anisotropic model that accounts for the bubble volume fraction and attenuation of the normal velocity fluctuations at the free surface is presented. The model adequately predicts the main mechanisms causing water entrainment and compares well against experimental data for a round surface jet and for Brownlee Dam at model scale. It is shown that appropriate entrainment can only be captured if the turbulence anisotropy and the two-phase nature of the flow are modelled.

URANS simulations for a high-speed transom stern ship with breaking waves

An exploratory study of high-speed surface ship flows is performed to identify modelling and numerical issues, to test the predictive capability of an unsteady RANS method for such flows, to explain flow features observed experimentally, and to document results obtained in conjunction with the 2005 ONR Wave Breaking Workshop. Simulations are performed for a high-speed transom stern ship (R/V Athena I) at three speeds Froude number (Fr) = 0.25, 0.43 and 0.62 with the URANS code CFDSHIP-IOWA, which utilizes a single-phase level set method for free surface modelling. The two largest Fr are considered to be high-speed cases and exhibit strong breaking plunging bow waves. Structured overset grids are used for local refinement of the unsteady transom flow at medium speed and for small scale breaking bow and transom waves at high-speeds. All simulations are performed in a time accurate manner and an examination of time histories of resistance and free surface contours is used to assess the degree to which the solutions reach a steady state. The medium speed simulation shows a classical steady Kelvin wave pattern without breaking and a wetted naturally unsteady transom flow with shedding of vortices from the transom corner. At higher speeds, the solutions reach an essentially steady state and display intense bow wave breaking with repeated reconnection of the plunging breaker with the free surface, resulting in multiple free surface scars. The high-speed simulations also show a dry transom and an inboard breaking wave, followed by outboard breaking waves downstream. In comparison to an earlier dataset, resistance is well predicted over the three speeds. The free surface predictions are compared with recent measurements at the two lowest speeds and show good agreement for both non-breaking and breaking waves.

Integral Force/Moment Waterjet Model for CFD Simulations

An integral force/moment waterjet model for computational fluid dynamics (CFD) is derived for ship local flow/powering predictions, including sinkage and trim. The waterjet induced reaction forces and moment and waterjet/hull interaction stern force replicate the effects of the waterjet without requiring detailed simulations of the waterjet system. The model extends the International Towing Tank Conference (IITC) waterjet model for sinkage and trim by using an alternative control volume also appropriate for CFD and by including vertical forces and pitching moment in the waterjet/hull force/moment balance. The same grid is used for both without and with waterjet simulations. The CFD waterjet model requires limited waterjet geometry (inlet and outlet areas and locations, and weight of working fluid) and several waterjet flow (mass flow rate, inlet pressure force, inlet and outlet momentum correction factors and flow angles, and stern force and location) input variables. The CFD waterjet model can be used for local flow predictions by using waterjet flow input variables provided by ITTC waterjet model test data, including additional data for waterjet induced inlet pressure and stern forces. It can also be used for powering predictions once waterjet flow input variable correlations are available based on CFD for the waterjet system and/or experimental data. The CFD waterjet model is demonstrated for local flow predictions for the DTMB 5594 high-speed sealift ship model for which ITTC waterjet model test data, including additional data for waterjet induced stern forces, are available. Correlations for the waterjet flow input variables are shown to be feasible using a combination of CFD and experimental data for the waterjet system for three different hulls.

A boiling heat transfer paradox

An instructive experiment for observing the Leidenfrost phenomenon is presented. The experiment, suitable for an undergraduate experimental course, consists of introducing a copper body at room temperature into liquid nitrogen and observing its temperature history. The experiment is then repeated with the body covered by a thermal insulating material, observing that the body reaches thermal equilibrium much more rapidly in the second case. This apparent paradox greatly motivates the students, who need to understand the different regimes of boiling heat transfer to resolve it. The paper also contains an approximate method to determine the insulator thickness that gives the minimum cooling period.