Hessam Babaee

System-level analysis of chilled water systems aboard naval ships

A thermal management simulation tool is required to rapidly and accurately evaluate and mitigate the adverse effects of increased heat loads in the initial stages of design in all-electric ships. By reducing the dimension of Navier-Stokes and energy equations, we have developed one-dimensional partial differential equation models that simulate time-dependent hydrodynamics and heat transport in a piping network system. Besides the steady-state response, the computational model enables us to predict the transient behavior of the cooling system when the operating conditions are time-variant. As a demonstration case, we have performed a thermal analysis on a realistic naval ship.

Comprehensive system-level thermal modeling of all-electric ships: Integration of SMCS and vemESRDC

In this paper, we present the integration effort of two complementary thermal simulation tools: vemESRDC and System-level design of Marine Cooling Systems (SMCS), developed at Florida State University Center for Advanced Power Systems and Massachusetts Institute of Technology Sea Grant, respectively. We integrated these tools into a cohesive whole and expanded its overall capabilities, allowing the user to design a ship cooling system using the state-of-the-art methods and to study the impact of design decisions at the early design stages. The integration was numerically verified by solving a simple problem comprised of nine volume elements with internal heat generation and a cooling network. It was construed from the simulation results that SMCS-vemESRDC integration enhanced the design flexibility as well as reliability of the tool, in evaluating ship cooling network designs and promoting effective thermal management strategies.

Reduced-order description of transient instabilities and computation of finite-time Lyapunov exponents.

High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have a finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g., long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here, we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy-Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples.

Stochastic Domain Decomposition via Moment Minimization

Propagating uncertainty accurately across different domains in multiscale physical systems with vastly different correlation lengths is of fundamental importance in stochastic simulations. We propose a new method to address this issue, namely, the stochastic domain decomposition via moment minimization (SDD-MM). Specifically, we develop a new moment minimizing interface condition to match the stochastic solutions at the interface of the nonoverlapping domains. Unlike other stochastic domain decomposition methods, the proposed method serves as a general framework that works with heterogeneous local stochastic solvers and does not rely on accessing global random trajectories, which are typically not available in realistic multiscale simulations. We analyze the computational complexity of the method and we quantify the contributing errors. The convergence property of SDD-MM is tested in several examples that include the stochastic reaction equation, Fishers equation, as well as a two-dimensional Allen--Cahn...

A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems

Abstract We develop a new robust methodology for the stochastic Navier–Stokes equations based on the dynamically-orthogonal (DO) and bi-orthogonal (BO) methods [1] , [2] , [3] . Both approaches are variants of a generalized Karhunen–Loeve (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution. The DO and BO formulations are mathematically equivalent [3] , but they exhibit computationally complimentary properties. Specifically, the BO formulation may fail due to crossing of the eigenvalues of the covariance matrix, while both BO and DO become unstable when there is a high condition number of the covariance matrix or zero eigenvalues. To this end, we combine the two methods into a robust hybrid framework and in addition we employ a pseudo-inverse technique to invert the covariance matrix. The robustness of the proposed method stems from addressing the following issues in the DO/BO formulation: (i) eigenvalue crossing: we resolve the issue of eigenvalue crossing in the BO formulation by switching to the DO near eigenvalue crossing using the equivalence theorem and switching back to BO when the distance between eigenvalues is larger than a threshold value; (ii) ill-conditioned covariance matrix: we utilize a pseudo-inverse strategy to invert the covariance matrix; (iii) adaptivity: we utilize an adaptive strategy to add/remove modes to resolve the covariance matrix up to a threshold value. In particular, we introduce a soft-threshold criterion to allow the system to adapt to the newly added/removed mode and therefore avoid repetitive and unnecessary mode addition/removal. When the total variance approaches zero, we show that the DO/BO formulation becomes equivalent to the evolution equation of the Optimally Time-Dependent modes [4] . We demonstrate the capability of the proposed methodology with several numerical examples, namely (i) stochastic Burgers equation: we analyze the performance of the method in the presence of eigenvalue crossing and zero eigenvalues; (ii) stochastic Kovasznay flow: we examine the method in the presence of a singular covariance matrix; and (iii) we examine the adaptivity of the method for an incompressible flow over a cylinder where for large stochastic forcing thirteen DO/BO modes are active.