Modeling Autogenous Pressurization and Draining of a Cryogenic Storage Tank in Normal Gravity

Two-phase flow and heat transfer simulations with interfacial phase change of the Structural Heat Intercept, Insulation, and Vibration Evaluation Rig (SHIIVER) self-pressurization experiment were conducted using storage tank CFD model in the framework of the ANSYS Fluent CFD code. The simulations were performed for the 70% fill level case with MLI on domes and no vapor cooling. All the phase change calculations in these simulations were generated by in-house Schrage-based evaporation-condensation model. The calculations were performed using both the Volume of Fluid (VOF) and Sharp Interface multiphase 2D axisymmetric models. A number of parametric and sensitivity studies were performed to check the various aspects of the CFD model. These studies helped to understand the effects of varying several parameters on the tank pressure and temperature during self-pressurization. Turbulence modeling; turbulence damping at the interface; and using constant vs. temperature dependent fluid properties were shown to have the most profound influence on predicted tank pressures and temperatures. Current study indicates that including phase change at the interface into the computational model is crucial for accurate prediction of the tank self-pressurization process. The effect of accommodation coefficient was also studied. Tank pressure values predicted by the VOF, and Sharp Interface models are within 4% of the experimental ones.

Coastal areas are densely populated due to socioeconomic benefits and in turn also have a greater demand for fresh water. This ever-increasing demand for fresh water can be met by coastal aquifers, which act as large reservoirs of freshwater. Excessive and unmanaged pumping from coastal aquifer allows the salt water to flow inward encroaching on the voids created by the pumping of freshwater. This phenomenon is called saltwater intrusion. To stop the saltwater intrusion, an optimal pumping strategy needs to be adopted. Simulation models are generally linked with an optimization algorithm to develop an optimal pumping strategy for management of saltwater intrusion. Sharp interface based simulation models are often used which are computationally inexpensive but lacks in prediction accuracy, as it does not incorporate the effects of dispersion and diffusion. Density dependent simulation models include the effect of dispersion and diffusion, but have a very high computational budget in evaluating an optimal pumping strategy. To overcome above-mentioned limitation a new methodology is developed, where a density dependent model is used in conjunction with a sharp interface model to derive an optimal density ratio, such that interface obtained using this density ratio implicitly accommodated the effect of dispersion and diffusion in a sharp interface model. The performance of the developed methodology is evaluated for three hypothetical scenarios of saltwater intrusion. The performance evaluation results show the applicability of the methodology for management of saltwater intrusion while maximizing fresh water pumping in coastal aquifers.KeywordsGroundwater modellingCoastal aquifer managementPumping optimizationSaltwater intrusionDensity dependent modelSharp interface model

Managing saltwater intrusion using conjugate sharp interface and density dependent models linked with pumping optimization

Morphology: from sharp interface to phase field models

Modeling and analysis of chill and fill processes for the cryogenic storage and transfer engineering development unit tank

We present a new approach for modeling strongly anisotropic crystal and epitaxial growth using regularized, anisotropic Cahn-Hilliard-type equations as a model for the growth and coarsening of thin films. When the surface anisotropy is sufficiently strong, sharp corners form and unregularized anisotropic Cahn-Hilliard equations become ill-posed. Our models contain a high order Willmore regularization to remove the ill posedness at the corners. A key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation. In our previous work, we have provided matched asymptotic analysis to show the convergence of our diffuse interface model to the analytical sharp interface model. In previous models there was no such convergence to sharp interface model when the Willmore energy was considered. We present 2D numerical results using an adaptive, nonlinear multigrid finite-difference method. In particular, we find excellent agreement between the computed shapes using the Cahn-Hilliard approach, with a finite but small Willmore regularization, with dynamical numerical simulations of a sharp interface model. The equilibrium shapes from our diffuse model are compared with an analytical sharp-interface theory recently developed by Spencer [1] at the corners, and there is excellent match. Away from the corners there is an excellent agreement between the diffuse model and the classical Wulff shape. Finally, in order to model the misfit and displacement strains, we add the elastic energy and corresponding forces to our diffuse model. We analyze numerically the effect of elastic stress on the corner regularization in terms of two parameters: one parameter that describes the relative strength of the elastic energy to surface energy and the second that characteristics the strength of the surface energy anisotropy. Adding elastic energy modifies the equilibrium shape and in particular affects the shape of the corners. We can predict different Qdot shapes, such as pyramids and domes, based on the strength of the elastic interactions.

A number of models have been developed to simulate seawater intrusion in coastal aquifers, which differ in the accuracy level and computational demands, based on the approximation level of the application. In this paper, four seawater intrusion models are employed to calculate the optimal pumping rates in a coastal aquifer management problem. The first model considers both fluid flow and solute transport processes and assumes a variable-density transition zone between saltwater and freshwater. The implementation of the model in simulation-optimisation routines is impractical, due to the computational time required for the simulation. The second model neglects the dispersion mechanism and assumes a sharp interface between saltwater and freshwater. The sharp interface model is significantly faster than the variable density model, however, it may introduce errors in the estimation of the seawater intrusion extent. The remaining two models are modifications of the second model, which intent to correct the inaccuracies of the simplified sharp interface approximation. All four models are utilised to simulate an unconfined coastal aquifer with multiple pumping wells and an optimisation method is used to calculate the maximum allowed pumping rates. The optimisation results are then analysed, in order to examine if the three sharp interface models could provide feasible solutions in the area of the variable density optimum, which is considered as a benchmark solution.

In pumping optimization of coastal aquifers, the evaluation of the objective function and constraints using density-dependent models is overwhelmed by complex and time-consuming numerical simulations. To address those cases where the available density-dependent model runs are very limited, due to excessive computational burden, an efficient optimization strategy is developed. The proposed methodology uses an efficient sharp interface model jointly with a complex density-dependent model in an evolutionary optimization algorithm. While most evaluations are based on the sharp interface model, the density-dependent model is selectively called to evaluate promising solutions and to improve the predictions of the sharp interface model through the adaptive modification of the saltwater-freshwater density ratio. The method is tested for pumping optimization problems in confined and unconfined coastal aquifers with multiple pumping wells. The optimal solutions are compared to those obtained by density-dependent as well as by sharp interface optimization alone. Under a very restrictive computational budget, the best feasible solution is attained in less than 25 density-dependent model runs for two optimization problems of 10 and 20 decision variables. The results indicate that this optimization method leads to good feasible solutions and that an improved estimation of optimal pumping rates can be achieved within a limited computational budget. The method could also stand as an efficient preliminary exploration of the optimal search space, to provide good feasible starting points for the implementation of more comprehensive methods of coastal aquifer management.

<p>In coastal areas, seawater intrusion is a main driver of groundwater salinization and numerical models are widely used to support sustainable groundwater management. Sharp interface models, in which mixing between freshwater and seawater is not explicitly simulated, have fast run times which enable the implementation of parameter estimation and uncertainty analysis. These are essential steps for decision-support modeling, however their implementation in sharp interface models has remained limited. Few guidelines exist regarding which observations to use, and what processing and weighting strategies to employ. We developed a data assimilation framework for a regional, sharp interface model designed for management purposes. We built a sharp interface model for an island aquifer using the SWI2 package for MODFLOW. We then extracted freshwater head observations from shallow wells, pumping wells and deep open wells, and observations of the seawater-freshwater interface from deep open wells, time-domain electromagnetic (TDEM) and electrical resistivity tomography (ERT) surveys. After quantification of measurement uncertainties, parameter estimation was conducted with PEST and a data worth analysis was carried out using a linear approach. Model residuals provided insight on the potential of different observation groups to constrain parameter estimation. The data worth analysis provided insight on these groups’ importance in reducing the uncertainty of model forecasts. Overall a satisfying fit was obtained between simulated and observed data, but observations from deep open wells were biased. While observations from deep open wells and geophysical surveys had a low signal-to-noise ratio, parameter estimation effectively reduced predictive uncertainty. Interface observations, especially from geophysical surveys, were essential to reduce the uncertainty of model forecasts. The use of different types of observations is discussed and recommendations are provided for future data collection strategies in coastal aquifers. This framework was developed in the Magdalen Islands (Quebec, Canada) and could be carried out more systematically for sharp interface seawater intrusion modeling.</p>

Pumping well management in coastal aquifers required to account for the saltwater intrusion problem. The prevention saltwater contamination of pumping wells should be considered along with the objective of maximum groundwater withdrawal. Saltwater intrusion constraint can be based on (1) sharp interface model (2) density-dependent transport model. Sharp interface models are preferable in the case of limited computation cost available and density-dependent transport models are preferable for accuracy. The correction factor introduced to account for the density-dependent dispersion by Pool and Carrera (Water Resour Res 47(5):W05506, 2011) vastly improves the sharp interface solution. In this present study, the application of the modified sharp interface solution based on the density-dependent correction factor for the pumping optimization is demonstrated for a regional scale aquifer in Nellore, Andhra Pradesh, India. The proposed optimization model sought to maximize the total pumping and minimize the landward toe intrusion from the sea.

On a relation between the volume of fluid, level-set and phase field interface models

Modeling and simulation of cryogenic propellant tank pressurization in normal gravity

Solute trapping in non-equilibrium solidification: A comparative model study

We study vesicles formed by lipid bilayers that are governed by an elastic bending energy and on which the lipids laterally separate forming two different phases. The energy laden phase interfaces may be modeled as curves on the hypersurface representing the membrane (sharp interface model). The phase field methodology is another powerful tool to model such phase separation phenomena where thin layers describe the interfaces (diffuse interface model). For both approaches we characterize equilibrium shapes in terms of the Euler–Lagrange equations of the total membrane energy subject to constraints on the area of the two phases and the volume. We further show by matching appropriate formal asymptotic expansions that the sharp interface model is obtained from the diffuse interface model as the thickness of the phase interface tends to zero. The essential challenge lies in the fact that also the geometry of the membrane is unknown and depends on a small parameter representing the interface thickness.

We discuss the sharp interface limit of a diffuse interface model for a coupled Cahn–Hilliard–Darcy system that models tumor growth when a certain parameter \epsilon > 0 , related to the interface thickness, tends to zero. In particular, we prove that weak solutions to the related initial boundary value problem tend to varifold solutions of a corresponding sharp interface model when \epsilon goes to zero.