Incompressible Flow Solver Research Articles

LES of primary breakup of pulsed liquid jet in supersonic crossflow

The injection of a pulsed liquid jet into supersonic air flow is a promising approach to improving the fuel atomization performance in a Scramjet engine. Therefore, the primary breakup of a pulsed liquid jet in supersonic crossflow is numerically investigated in the present paper. A two-phase flow Large Eddy Simulation (LES) algorithm is developed for simulations of liquid jet atomization in supersonic gas flow. A coupled Level Set and Volume of Fluid (VOF) method is used to track the interface deformation and disintegration. The supersonic gas flow is solved using a compressible flow solver while the liquid phase is solved by an incompressible flow solver. Appropriate boundary conditions are specified at the interface for both solvers to correctly capture the interaction between the gas and liquid phases. The primary atomization of a steady liquid jet with the same average mass flow rate as the pulsed jet is also simulated as a benchmark test case. The liquid velocity pulsation produces a very different primary atomization morphology in comparison with the steady liquid jet, which significantly enhances the primary breakup process. It is observed that Rayleigh-Taylor instability dominates the development of surface waves for the steady liquid jet. For the pulsed liquid jet, the liquid column deformation induced by the liquid velocity pulsation determines the wavelength of the surface waves and thus the liquid jet breakup location. In comparison with the steady liquid jet, the penetration of the pulsed liquid jet increases by 20%, and the width of the wake zone expands by 25%, resulting in improved atomization and mixing performance.

Contact preserving Riemann solver for incompressible two-phase flows

In numerical simulation of multi-fluid flows, it is very crucial to accurately capture the interface separating the fluids, which has the properties of a contact wave. Since HLLC (Harten Lax van-Leer with contact) formulation has the ability to model contact waves exactly, a novel HLLC-type Riemann solver is proposed for calculation of convective flux in a system where the incompressible-Navier–Stokes equations are tightly coupled with the volume of fluid (VOF) equation. The efficacy of the new formulation is evaluated by solving various standard test problems involving two-fluid flows.

Interface-preserving level set method for simulating dam-break flows

An interface-preserving level set method that solves advection and re-initialization equations for simulating three-dimensional dam-break flows is developed. This method solves mass transfer problems on a uniform staggered Cartesian grid. The advection equation that is used to advect the level set function for capturing the interface is discretized by a proposed fourth-order spatial discretization scheme. This scheme is dispersion-relation-preserving and is compact-reconstruction weighted essentially non-oscillatory (DRP-CRWENO4). This scheme is compared with a previous fifth-order, weighted, essentially non-oscillatory (WENO5) scheme and can represent an interface more accurately, while exactly preserving mass conservation. This level set approach introduces a mass correction term into the re-initialization equation based on local interface-preserving conditions. An explicit Adams–Bashforth algorithm on a staggered Eulerian grid is used for the Navier–Stokes solver. The point successive over-relaxation method is then employed to solve the resulting linear system. Two one-dimensional wave propagation problems are simulated to verify the proposed DRP-CRWENO4 scheme, which is shown to be capable of effectively capturing large gradients with fourth-order accuracy. To demonstrate their resolution, the two advection schemes (WENO5 and DRP-CRWENO4) are applied in two two-dimensional benchmark cases, i.e., a vortex deforming problem and Zalesak's disk problem, where simulation results of both schemes are compared against each other. Demonstration study is then further extended to three-dimensional cases of the vortex deforming problem and Zalesak's sphere problem, and simulation results agree well with those using hybrid particle level set method. Finally, several dam-break problems with and without obstacles are investigated to validate the coupled two-phase incompressible flow and level set method solver. The results for the predicted flow structure and mass conservation properties are compared with the reported experimental data or numerical simulations.

A Hybrid Analytics Paradigm Combining Physics-Based Modeling and Data-Driven Modeling to Accelerate Incompressible Flow Solvers

Numerical solution of the incompressible Navier–Stokes equations poses a significant computational challenge due to the solenoidal velocity field constraint. In most computational modeling frameworks, this divergence-free constraint requires the solution of a Poisson equation at every step of the underlying time integration algorithm, which constitutes the major component of the computational expense. In this study, we propose a hybrid analytics procedure combining a data-driven approach with a physics-based simulation technique to accelerate the computation of incompressible flows. In our approach, proper orthogonal basis functions are generated to be used in solving the Poisson equation in a reduced order space. Since the time integration of the advection–diffusion equation part of the physics-based model is computationally inexpensive in a typical incompressible flow solver, it is retained in the full order space to represent the dynamics more accurately. Encoder and decoder interface conditions are provided by incorporating the elliptic constraint along with the data exchange between the full order and reduced order spaces. We investigate the feasibility of the proposed method by solving the Taylor–Green vortex decaying problem, and it is found that a remarkable speed-up can be achieved while retaining a similar accuracy with respect to the full order model.

A consistent balanced force refined moment-of-fluid method for surface tension dominant two-phase flows

Inconsistent implementation of surface tension in an interfacial solver for incompressible two-phase flow results in spurious currents near the interface. The balanced force algorithm (BFA) enforces consistent implementation of surface tension force and pressure gradient at the cell faces thereby generating conservative face center velocity field, even though the cell center velocity may not be divergence free and spurious current free. The implication of this inconsistency is directly reflected in interface smoothness while using a Lagrangian–Eulerian interface evolution in contrary to Eulerian advection where divergence free face velocities are used. This paper describes a consistent balanced force algorithm (CBFA) in collocated grid for consistent implementation of surface tension force. The interface evolution is tracked by refined moment-of-fluid (RMOF) method using Lagrangian–Eulerian advection scheme. In CBFA, additional Poisson equation is solved to obtain cell face corrections for conservative cell center velocity computation. The effectiveness of the proposed method is demonstrated in this article for several test cases.

A high-order cross-platform incompressible Navier–Stokes solver via artificial compressibility with application to a turbulent jet

Modern hardware architectures such as GPUs and manycore processors are characterised by an abundance of compute capability relative to memory bandwidth. This makes them well-suited to solving temporally explicit and spatially compact discretisations of hyperbolic conservation laws. However, classical pressure-projection-based incompressible Navier–Stokes formulations do not fall into this category. One attractive formulation for solving incompressible problems on modern hardware is the method of artificial compressibility. When combined with explicit dual time stepping and a high-order Flux Reconstruction discretisation, the majority of operations can be cast as compute bound matrix–matrix multiplications that are well-suited for GPU acceleration and manycore processing. In this work, we develop a high-order cross-platform incompressible Navier–Stokes solver, via artificial compressibility and dual time stepping, in the PyFR framework. The solver runs on a range of computer architectures, from laptops to the largest supercomputers, via a platform-unified templating approach that can generate/compile CUDA, OpenCL and C/OpenMP code at runtime. The extensibility of the cross-platform templating framework defined within PyFR is clearly demonstrated, as is the utility of P-multigrid for convergence acceleration. The platform independence of the solver is verified on Nvidia Tesla P100 GPUs and Intel Xeon Phi 7210 KNL manycore processors with a 3D Taylor–Green vortex test case. Additionally, the solver is applied to a 3D turbulent jet test case at Re=10,000, and strong scaling is reported up to 144 GPUs. The new software constitutes the first high-order accurate cross-platform implementation of an incompressible Navier–Stokes solver via artificial compressibility and P-multigrid accelerated dual time stepping to be published in the literature. The technology has applications in a range of sectors, including the maritime and automotive industries. Moreover, due to its cross-platform nature, the technology is well placed to remain relevant in an era of rapidly evolving hardware architectures. Program summaryProgram Title: PyFR v1.7.5Program Files doi:http://dx.doi.org/10.17632/65m665nt9c.1Licensing provisions: BSD 3-clauseProgramming language: Python, CUDA, OpenCL and CSupplementary material: Configuration and mesh files for the Taylor–Green Vortex and Turbulent jet test casesJournal reference of previous version: Comput. Phys. Commun. 185 (2014) 3028–3040Does the new version supersede the previous version?: YesReasons for the new version: Adding support for incompressible flowsSummary of revisions: Introducing a new high-order cross-platform incompressible flow solver via artificial compressibility and P-multigrid accelerated dual time stepping.Nature of problem: Incompressible Euler and Navier–Stokes equations for solving unsteady turbulent flows.Solution method: Artificial compressibility formulation discretised with a high-order Flux Reconstruction approach in space and P-multigrid accelerated dual time stepping in time.Additional comments including restrictions and unusual features: The algorithm targets modern massively parallel hardware platforms. Cross-platform capability is achieved via runtime code generation.

Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows

In the present work, a highly efficient incompressible flow solver with a semi-implicit time advancement on a fully staggered grid using a high-order compact difference scheme is developed firstly in the framework of approximate factorization. The fourth-order compact difference scheme is adopted for approximations of derivatives and interpolations in the incompressible Navier–Stokes equations. The pressure Poisson equation is efficiently solved by the fast Fourier transform (FFT). The framework of approximate factorization significantly simplifies the implementation of the semi-implicit time advancing with a high-order compact scheme. Benchmark tests demonstrate the high accuracy of the proposed numerical method. Secondly, by applying the proposed numerical method, we compute turbulent channel flows at low and moderate Reynolds numbers by direct numerical simulation (DNS) and large eddy simulation (LES). It is found that the predictions of turbulence statistics and especially energy spectra can be obviously improved by adopting the high-order scheme rather than the traditional second-order central difference scheme.

Multiphase computational method for thermal interactions between compressible fluid and arbitrarily shaped solids

SummaryA numerical method was investigated for multiphase fields consisting of compressible gas and arbitrarily shaped solids. Since the proposed model is based on a one‐fluid model in which variables are averaged according to the phase fractions in the computational cells; it enables us to estimate gas‐solid momentum and thermal interactions without setting up adapting grids even if the solids have extremely complicated shapes. The governing equations are derived with the characteristics of an ideal gas assuming the specific heat to be uniform in the multiphase field. The derived equations in conservative form are discretized with a finite volume method. In addition, the pressure is calculated implicitly in a similar way to incompressible flow solvers. Because of these improvements, the proposed method allows us to calculate low Mach number compressible flows free from the Courant‐Friedrichs‐Lewy condition based on the speed of sound and to conserve the mass more accurately. To confirm the validity of the proposed method, it was applied to natural convection around an isothermal cylinder and a heat‐conducting pipe. In comparison with previous studies, it was confirmed that the gas flows and temperature distributions are predicted reasonably. In addition, a numerical experiment was conducted under more complicated conditions, namely, gas leaking from a container including heat sources. As a result, it was demonstrated that the proposed method enables us to predict unsteady variations of pressure and temperature distributions in the container due to the leakage while still conserving mass accurately.

Numerical investigation of wake induced vibrations of cylinders in tandem arrangement at subcritical Reynolds numbers

Wake-induced vibrations are considered distinctively different from well-known vortex induced vibrations where bluff body structures vibrate under vortex shedding in the wake of flows passing through them. Understanding characteristics of wake-induced vibrations plays an important role in design of marine-offshore structures such as platform columns, risers operating at high Reynolds number currents. This work presents an extensive study of wake-induced vibrations using a computational fluid dynamics approach. The numerical model is based on an incompressible Navier-Stokes flow solver with a hybrid detached eddy simulation (DES) approach for turbulence modelling of high Reynold number flows. The hybrid DES approach is first validated for wake-induced vibrations at subcritical Reynolds number ranging from 103−105. Comparison between numerical results and experiment shows very good agreement in prediction of downstream cylinder responses including amplitudes, frequency and phase angle. Data from numerical simulations is then used to characterize and study mechanisms of wake-induced vibrations by looking at detailed force components and their frequencies in relation to cylinder responses. The effect of different Reynolds number flow conditions in tandem cylinder responses are also analysed in the present work. It is found that Reynolds number has strong influence in changing response amplitude and frequency of cylinders in wake-induced vibrations.

A variational projection scheme for nonmatching surface-to-line coupling between 3D flexible multibody system and incompressible turbulent flow

This paper is concerned with the partitioned iterative formulation to simulate the fluid-structure interaction of a nonlinear multibody system in an incompressible turbulent flow. The proposed formulation relies on a three-dimensional (3D) incompressible turbulent flow solver, a nonlinear monolithic elastic structural solver for constrained flexible multibody system and the nonlinear iterative force correction scheme for coupling of the turbulent fluid-flexible multibody system with nonmatching interface meshes. While the fluid equations are discretized using a stabilized Petrov–Galerkin formulation in space and the generalized-α updates in time, the multibody system utilizes a discontinuous space-time Galerkin finite element method. We address two key challenges in the present formulation. Firstly, the coupling of the incompressible turbulent flow with a system of nonlinear elastic bodies described in a co-rotated frame. Secondly, the projection of the tractions and displacements across the nonmatching 3D fluid surface elements and the one-dimensional line elements for the flexible multibody system in a conservative manner. Through the nonlinear iterative correction and the conservative projection, the developed fluid-flexible multibody interaction solver is stable for problems involving strong inertial effects between the fluid-flexible multibody system and the coupled interactions among each multibody component. The accuracy of the proposed coupled finite element framework is validated against the available experimental data for a long flexible cylinder undergoing vortex-induced vibration in a uniform current flow condition. Finally, a practical application of the proposed framework is demonstrated by simulating the flow-induced vibration of a realistic offshore floating platform connected to a long riser and an elastic mooring system.

Role of Compressibility on Tsunami Propagation

AbstractIn the present paper, we aim to reduce the discrepancies between tsunami arrival times evaluated from tsunami models and real measurements considering the role of ocean compressibility. We perform qualitative studies to reveal the phase speed reduction rate via a modified version of the Mild Slope Equation for Weakly Compressible fluid (MSEWC) proposed by Sammarco et al. (2013). The model is validated against a 3‐D computational model. Physical properties of surface gravity waves are studied and compared with those for waves evaluated from an incompressible flow solver over realistic geometry for 2011 Tohoku‐oki event, revealing reduction in phase speed.

Validation and scalability of an open source parallel flow solver

SummaryThis article concerns validation and verification (V&V) of the open source OpenFOAM incompressible flow solver that is widely used in both research and industry for the simulation of turbulent flows. Its numerical discretization scheme relies on classical finite volumes that are second order in space on regular grids. The solver is benchmarked using a challenging test case for which direct numerical simulation (DNS) reference data exist. The geometrical configuration of this flow is very simple, yet the behavior of the flow is 3D, complex, and unsteady, requiring an accurate flow solver to capture the associated physics. The physical problem addressed here requires huge computational grids. Computations are thus carried using parallel domain decomposition methods on a fairly large number of cores. The validation study performed here is particularly severe as it consists in comparing OpenFOAM results with DNS data obtained using high‐order codes. As simulations of turbulent flows require great computational resources, results concerning strong and weak scalability of the OpenFOAM flow solver are also presented. The performances of the code are assessed on two different HPC infrastructures. The experiences carried here show that OpenFOAM scales fairly up to 1000 cores on a Tier‐1cluster. The influences of the processor hardware and network topology are also highlighted. This study also provides profiling diagnostics thanks to the Integrated Performance Monitor (IPM).

A 3-D numerical study of solitary wave interaction with vertical cylinders using a parallelised particle-in-cell solver

This paper aims to provide a better understanding of the interaction between solitary waves and vertical circular cylinders. This is achieved via process based numerical modelling using the parallel particle-in-cell based incompressible flow solver PICIN. The numerical model solves the Navier-Stokes equations for free-surface flows and incorporates a Cartesian cut cell method for fluid-structure interaction. Solitary waves are generated using a piston-type wave paddle. The PICIN model is first validated using a test case that involves solitary wave scattering by a single vertical cylinder. Comparisons between the present results and experimental data show good agreement for the free surface elevations around the cylinder and the horizontal wave force on the cylinder. The model is then employed to investigate solitary wave interaction with a group of eleven vertical cylinders. The wave run-up and wave forces on the cylinders are discussed.

Solution of lid-driven cavity problems with an improved SIMPLE algorithm at high Reynolds numbers

The SIMPLE algorithm and its variants have been successfully employed to solve the driven-cavity problem at Re<10,000. However, converged steady solutions cannot be achieved at higher Re (15,000–30,000) by SIMPLE-family algorithms owing to its inherent drawbacks. In this work, a new segregated solver, ISTEC-N (incompressible flow solver with two explicit N correction loops), for determining the solution of incompressible flow on structured collocated grid systems is proposed. A pressure equation is deduced from the discretized continuity equation to overcome the “Semi-Implicit” characteristic of the SIMPLE algorithm. An explicit velocity update loop is introduced to improve the consistency between the pressure field and the velocity field in each outer iteration. The performance of the ISTEC-N algorithm is evaluated by solving the driven-cavity problem at high Re number of (15,000<Re<30,000). It is shown that the ISTEC-N algorithm manifests a strong robustness feature under these high convection conditions. The computational results given by the ISTEC-N algorithm are in excellent agreement with the benchmarking data.

A Discrete Adjoint Formulation for Inviscid Flow Nozzle Optimization

A discrete adjoint formulation with an ad hoc flow solver has been recently developed and tested on transonic inviscid flow optimization problems. In the present paper the formulation is extended to compressible as well as incompressible flow solvers. First, the adjoint equations are coupled with an accurate in-house flow solver to test the approach on some inverse design problems involving two- and three-dimensional transonic and subsonic flows. Then, the previous design test cases are re-computed coupling the extended adjoint formulation with commercial and open source flow solvers, without noticing any relevant difference in the optimization convergence histories. Finally, incompressible design test cases are successfully computed by means of commercial solver for incompressible flows. The extended compressible adjoint formulation appears to have a wide application, insofar as it allows to perform accurate and efficient design optimization using different flow conditions, different flow solvers and even a solver for incompressible flows.

Wall modeling via function enrichment within a high‐order DG method for RANS simulations of incompressible flow

SummaryWe present a novel approach to wall modeling for the Reynolds‐averaged Navier‐Stokes equations within the discontinuous Galerkin method. Wall functions are not used to prescribe boundary conditions as usual, but they are built into the function space of the numerical method as a local enrichment, in addition to the standard polynomial component. The Galerkin method then automatically finds the optimal solution among all shape functions available. This idea is fully consistent and gives the wall model vast flexibility in separated boundary layers or high adverse pressure gradients. The wall model is implemented in a high‐order discontinuous Galerkin solver for incompressible flow complemented by the Spalart‐Allmaras closure model. As benchmark examples, we present turbulent channel flow starting from Reτ=180 and up to Reτ=100000 as well as flow past periodic hills at Reynolds numbers based on the hill height of ReH=10595 and ReH=19000.

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier–Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad–div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ=180 as well as 590.

Application of a preconditioned high‐order accurate artificial compressibility‐based incompressible flow solver in wide range of Reynolds numbers

SummaryIn the present study, the preconditioned incompressible Navier‐Stokes equations with the artificial compressibility method formulated in the generalized curvilinear coordinates are numerically solved by using a high‐order compact finite‐difference scheme for accurately and efficiently computing the incompressible flows in a wide range of Reynolds numbers. A fourth‐order compact finite‐difference scheme is utilized to accurately discretize the spatial derivative terms of the governing equations, and the time integration is carried out based on the dual time‐stepping method. The capability of the proposed solution methodology for the computations of the steady and unsteady incompressible viscous flows from very low to high Reynolds numbers is investigated through the simulation of different 2‐dimensional benchmark problems, and the results obtained are compared with the existing analytical, numerical, and experimental data. A sensitivity analysis is also performed to evaluate the effects of the size of the computational domain and other numerical parameters on the accuracy and performance of the solution algorithm. The present solution procedure is also extended to 3 dimensions and applied for computing the incompressible flow over a sphere. Indications are that the application of the preconditioning in the solution algorithm together with the high‐order discretization method in the generalized curvilinear coordinates provides an accurate and robust solution method for simulating the incompressible flows over practical geometries in a wide range of Reynolds numbers including the creeping flows.

A High-Order Local Projection Stabilization Method for Natural Convection Problems

In this paper, we propose a local projection stabilization (LPS) finite element method applied to numerically solve natural convection problems. This method replaces the projection-stabilized structure of standard LPS methods by an interpolation-stabilized structure, which only acts on the high frequencies components of the flow. This approach gives rise to a method which may be cast in the variational multi-scale framework, and constitutes a low-cost, accurate solver (of optimal error order) for incompressible flows, despite being only weakly consistent. Numerical simulations and results for the buoyancy-driven airflow in a square cavity with differentially heated side walls at high Rayleigh numbers (up to $$Ra=10^7$$ ) are given and compared with benchmark solutions. Good accuracy is obtained with relatively coarse grids.

Investigation of the NREL phase VI experiment with the incompressible CFD solver THETA

AbstractDLR's incompressible flow solver THETA is introduced for wind turbine applications on the isolated NREL phase VI Unsteady Aerodynamic Experiment rotor. The optimization of parameter settings for the prediction of attached and separated flows on the rotor is performed, including time step size, spatial discretization scheme, turbulence models and Chimera overset grid technique. Afterwards, a systematic study on the pressure distributions, rotor thrust and rotor torque for experimental series S, I and J is performed. The accuracy of results for wind velocities between 7 and 25 m s[[EQUATION1]], covering attached, partly separated and deep stalled flow conditions, is discussed. While good to excellent agreement between THETA sectional pressure distributions and the experimental reference data is achieved in attached flow and deep stall configurations, more efforts are needed to predict partly separated flow cases with comparable accuracy. A code‐to‐code comparison with DLR's compressible flow solver TAU enabled the quantification of differences in pressure prediction because of the use of incompressible and compressible flow solvers. Copyright © 2017 John Wiley &amp; Sons, Ltd.