In this paper, we present two deep learning-based hybrid data-driven reduced-order models for prediction of unsteady fluid flows. These hybrid models rely on recurrent neural networks (RNNs) to evolve low-dimensional states of unsteady fluid flow. The first model projects the high-fidelity time series data from a finite element Navier–Stokes solver to a low-dimensional subspace via proper orthogonal decomposition (POD). The time-dependent coefficients in the POD subspace are propagated by the recurrent net (closed-loop encoder–decoder updates) and mapped to a high-dimensional state via the mean flow field and the POD basis vectors. This model is referred to as POD-RNN. The second model, referred to as the convolution recurrent autoencoder network (CRAN), employs convolutional neural networks (instead of POD) as layers of linear kernels with nonlinear activations, to extract low-dimensional features from flow field snapshots. The flattened features are advanced using a recurrent (closed-loop manner) net and up-sampled (transpose convoluted) gradually to high-dimensional snapshots. Two benchmark problems of the flow past a cylinder and the flow past side-by-side cylinders are selected as the unsteady flow problems to assess the efficacy of these models. For the problem of the flow past a single cylinder, the performance of both the models is satisfactory and the CRAN model is found to be overkill. However, the CRAN model completely outperforms the POD-RNN model for a more complicated problem of the flow past side-by-side cylinders involving the complex effects of vortex-to-vortex and gap flow interactions. Owing to the scalability of the CRAN model, we introduce an observer-corrector method for calculation of integrated pressure force coefficients on the fluid–solid boundary on a reference grid. This reference grid, typically a structured and uniform grid, is used to interpolate scattered high-dimensional field data as snapshot images. These input images are convenient in training the CRAN model, which motivates us to further explore the application of the CRAN-based models for prediction of fluid flows.

No abstract

In this paper, an end-to-end nonlinear model reduction methodology is presented based on the convolutional recurrent autoencoder networks. The methodology is developed in the context of overall data-driven reduced order model framework proposed in the paper. The basic idea behind the methodology is to obtain the low dimensional representations via convolutional neural networks and evolve these low dimensional features via recurrent neural networks in time domain. The high dimensional representations are constructed from the evolved low dimensional features via transpose convolutional neural networks. With an unsupervised training strategy, the model serves as an end to end tool which can evolve the flow state of the nonlinear dynamical system. The convolutional recurrent autoencoder network model is applied on the problem of flow past bluff bodies for the first time. To demonstrate the effectiveness of the methodology, two canonical problems namely the flow past plain cylinder and the flow past side-by-side cylinders are explored in this paper. Pressure and velocity fields of the unsteady flow are predicted in future via the convolutional recurrent autoencoder model. The performance of the model is satisfactory for both the problems. Specifically, the multiscale nature and the gap flow dynamics of the side-by-side cylinders are captured by the proposed data-driven model reduction methodology. The error metrics, the normalized squared error and the normalized reconstruction error are considered for the assessment of the data-driven framework.

In this paper, an end-to-end nonlinear model reduction methodology is presented based on the convolutional recurrent autoencoder networks. The methodology is developed in the context of overall data-driven reduced order model framework proposed in the paper. The basic idea behind the methodology is to obtain the low dimensional representations via convolutional neural networks and evolve these low dimensional features via recurrent neural networks in time domain. The high dimensional representations are constructed from the evolved low dimensional features via transpose convolutional neural networks. With an unsupervised training strategy, the model serves as an end to end tool which can evolve the flow state of the nonlinear dynamical system. The convolutional recurrent autoencoder network model is applied on the problem of flow past bluff bodies for the first time. To demonstrate the effectiveness of the methodology, two canonical problems namely the flow past plain cylinder and the flow past side-by-side cylinders are explored in this paper. Pressure and velocity fields of the unsteady flow are predicted in future via the convolutional recurrent autoencoder model. The performance of the model is satisfactory for both the problems. Specifically, the multiscale nature and the gap flow dynamics of the side-by-side cylinders are captured by the proposed data-driven model reduction methodology. The error metrics, the normalized squared error and the normalized reconstruction error are considered for the assessment of the data-driven framework.

In this paper, we introduce a reduced order model (ROM) for the propagation of nonlinear multi-directional ocean wave-fields. The ROM relies on Galerkin projection of Zakharov equations embedded in the high-order spectral (HOS) method, which describes the evolution of nonlinear waves. The dominant flow features of wave evolution are computed from proper orthogonal decomposition (POD) and these modes are used for the projection. The HOS scheme to compute the vertical velocity is treated in a novel way for an efficient implementation of POD-based ROM. We refer to this alternative formalism of HOS as HOS-simple. The final reduced order model (ROM) is derived from the Galerkin projection of HOS-simple. For the case of irregular waves, where the number of modes required are in the range of 200, the ROM has no significant advantage since both HOS and HOS-simple are much faster than real-time. The real advantage is demonstrated in multi-directional (or short-crested) irregular waves, where the ROM is the only model capable of achieving real-time computation, a major improvement to the standard HOS method. The potential use of the ROM in propagating short-crested waves from far-field to near-field for real-world applications involving wave probes in a wave tank/controlled environment as well as X-band radar in open ocean is also demonstrated.

No abstract

No abstract

A flotel is often used to house personnel and equipment for on-site maintenance of ageing FPSOs. Although tankers are designed to be dry-docked, operating FPSOs (which may be reconverted tankers) must be maintained in the field. The advantage to industry of on-site maintenance and inspection rather than dry-docking of FPSOs is crucial to cost-effectiveness. For multibody systems like FPSO and flotel in a side-by-side configuration, one of the primary questions is the time for which the gangway can remain safely connected between the two bodies. Operators always seek for a maximum possible uptime to operate the gangway, so that FPSO maintenance works are not halted for long durations during the harsh environments. The main factors limiting the operation of a gangway are its extension and rotation due to the relative motions between FPSO and flotel. Therefore, it is firstly important to accurately predict the hydrodynamic interaction between the two bodies for estimating their motions. In the present work, the variation of current drag on the flotel due to the presence of a turret-moored FPSO is investigated. The current drag variation on the flotel is studied by modelling the multibody system in OpenFOAM. Steady state simulations are performed using simpleFoam algorithm to compute the hydrodynamic coefficients of pontoons and columns. SimpleFoam is a steady-state solver for incompressible, turbulent flow, using the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The meshes for FPSO, flotel and fluid domain are created in ICEM-CFD and imported into OpenFOAM. A mesh convergence study is conducted. The simulations are performed for various current velocities and directions in combination with different drafts of FSPO. Finally, a lookup table comprising of current drag coefficients for several cases is prepared for future reference in designing the flotel. A non-collinear environment is the worst scenario for turret-moored FPSO. In most cases, the wind-driven current direction is within ±45° relative to the wave heading. The drag load experienced by the flotel on the columns and pontoons varies as a function of the current direction, the draft and the heading of FPSO relative to the flotel and the location of the flotel (upstream or downstream of FPSO). As FPSO changes yaw angle, the flotel experiences current loads which sometimes vary abruptly due to the shielding effects. The paper presents novel results and explains how the hydrodynamic interactions affect the important current loads experienced by the flotel under various scenarios. The choice of orientation of the flotel relative to FPSO (pontoons parallel or perpendicular to FPSO) is influenced by and must be decided by considering the effect on the current loads. The effects of varying shielding need to be considered by the dynamic positioning system in order to develop robust control methods to maximize uptime for a given installed thruster power. Several studies have been performed to investigate the hydrodynamic interaction between two bodies like cylinders, square columns, rectangular structures, etc. However, very little work has been on the hydrodynamic interaction between FPSO and flotel (semi-submersible platform), especially when this multibody system is subjected to current forces. The present study aims to fill this gap and aid the industry in the preliminary design and configuration of the flotel.