Simulation Of Viscous Flow Research Articles

Three-Dimensional Simulations of Viscous Incompressible Fluid Flows on Grids with Unmatched Grid Interfaces

The paper describes a numerical method that considers specific computational fluid dynamics (CFD) aspects of viscous incompressible flow simulations in the vicinity of interfaces between unmatched fragments of unstructured grids. The method is based on the general grid interface (GGI) principle, which involves conservative flux interpolation and does not require original grid modification at unmatched interfaces. A method is presented which combines adjacent unmatched fragments of an unstructured grid into a single domain by means of virtual interfaces considering connections between adjacent cells through virtual faces. The performance of the method is illustrated by the finite-volume discretization of the transport equation in the region of matched interfaces and its modification for the case of unmatched interfaces. The efficiency of the proposed method is demonstrated by three-dimensional CFD simulations with grid models composed of unmatched unstructured grid fragments. The simulation results are compared with equivalent simulations on matched grids. The influence of unmatched interfaces on the convergence rate and accuracy of the solution is assessed.

Study on the mechanism of the buzz flow in a supersonic intake

The flow field in a supersonic intake has been investigated computationally to understand the unsteady shock motions at an incoming Mach number of 1.95. The exit area variation is achieved by moving the flap downstream of the inlet model. Inviscid, unsteady simulations of the shock movement are compared with simulations of the viscous flow. The purpose is to understand the possibility of an inviscid mechanism as the underlying process of shock swallowing. It is observed for inviscid simulations that during the shock movement process, the system breaks the steady flow and a transient flow is initiated followed by a new steady state condition. On the contrary, this is not observed in viscous flow simulations which suggest the possibility of an unsteady mechanism that can propagate upstream of supersonic flow to make changes in the flow field. The analysis suggests that shock swallowing is related to the inviscid phenomenon and it may be associated with an unsteady chocking wave.

Gradient based reconstruction: Inviscid and viscous flux discretizations, shock capturing, and its application to single and multicomponent flows

This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier–Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative sharing between the inviscid and viscous schemes: highly accurate explicit and implicit gradients are used for the solution reconstruction expressed in terms of derivatives. The higher-order accurate gradients of the velocity components are reused to compute the viscous fluxes for efficiency and significantly improve the solution and gradient quality, as demonstrated by several viscous-flow test cases. The viscous schemes are fourth-order accurate and carefully designed with a high-frequency damping property, which has been identified as a critically important property for stable compressible-flow simulations with shock waves (Chamarthi et al., 2022). Shocks and material discontinuities are captured using a monotonicity-preserving (MP) scheme, which is also improved by reusing the gradients. For inviscid test cases, The proposed scheme is fourth-order for linear and second-order accurate for non-linear problems. Several numerical results obtained for simulations of complex viscous flows are presented to demonstrate the accuracy and robustness of the proposed methodology.

Effect of particle arrangement and density on aerodynamic interference between twin particles interacting with a plane shock wave

Unsteady drag, unsteady lift, and movement of one or two moving particles caused by the passage of a planar shock wave are investigated using particle-resolved simulations of viscous flows. The particle motion analysis is carried out based on particle-resolved simulations for one or two particles under a shock Mach number of 1.22 and a particle Reynolds number of 49, and the particle migration and fluid forces are investigated. The unsteady drag, unsteady lift, and particle behavior are investigated for different densities and particle configurations. The time evolution of the unsteady drag and lift is changed by interference by the planar shock wave, Mach stem convergence, and the shock wave reflected from the other particle. These two particles become closer after the shock wave passes than in the initial state under most conditions. Two particles placed in an in-line arrangement approach each other very closely due to the passage of a shock wave. On the other hand, two particles placed in a side-by-side arrangement are only slightly closer to each other after the shock wave passes between them. The pressure waves resulting from Mach stem convergence of the upstream particle and the reflected shock waves from the downstream particle are the main factors responsible for the force in the direction that pushes the particles apart. The wide distance between the two particles attenuates these pressure waves, and the particles reduce their motion away from each other.

Design of marine propellers with prescribed and optimal spanwise circulation distributions based on genetic algorithms and neural network

Lifting-surface design methods are proposed for marine propellers based on genetic algorithms (GAs) and a two-layer back-propagation neural network (BPNN). For propellers with prescribed spanwise circulation distributions, the design problem is solved as GA-based optimization of camber surface geometry and pitch distribution which produce a circulation distribution to best fit the prescribed one. An in-house code based on the vortex lattice method (VLM) is employed to simulate circulation distribution and hydrodynamic performance of the propeller. Computer codes are developed in this research based on existing genetic algorithms, with a measure devised to accelerate convergence and improve the quality of solution. To optimize the spanwise circulation distribution, GAs are utilized again to explore the BPNN model established via the MATLAB toolbox and the in-house VLM code. Then the optimal circulation distribution is taken as the prescribed one for the GA-based design method mentioned above. Numerical tests are conducted to determine proper ranges of modeling parameters, such as the population size for GAs and the number of vortex lattices, and to assess the performance of the BPNN established. To numerically validate the proposed methods, viscous-flow simulation by solving the Reynolds-averaged Navier-Stokes equations is carried out for the propeller designed by using both methods mentioned above. The predicted pressure distributions over blade surfaces correlate consistently with the circulation distributions used to design the propeller, thus indicating that present design methods are effective and reasonably accurate.

A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations

A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations

Turbulent Eddy Generation for the CFD Analysis of Hydrokinetic Turbines

This paper presents a novel theoretical and computational methodology for the generation of an onset turbulent field with prescribed properties in the numerical simulation of an arbitrary viscous flow. The methodology is based on the definition of a suitable distribution of volume force terms in the right-hand side of the Navier–Stokes equations. The distribution is represented by harmonic functions that are randomly variable in time and space. The intensity of the distribution is controlled by a simple PID strategy in order to obtain that the generated turbulent flow matches a prescribed turbulence intensity. A further condition is that a homogeneous isotropic flow is established downstream of the region where volume force terms are imposed. Although it is general, the proposed methodology is primarily intended for the computational modelling of hydrokinetic turbines in turbulent flows representative of tidal or riverine installations. A first numerical application is presented by considering the injection of homogeneous and isotropic turbulence with 16% intensity into a uniform unbounded flow. The analysis of statistical properties as auto-correlation, power spectral density, probability density functions, demonstrates that the generated flow tends to achieve satisfactory levels of stationarity and isotropy, whereas the simple control strategy used determines underestimated turbulent intensity levels.

A systematic study of hidden errors in the bounce-back scheme and their various effects in the lattice Boltzmann simulation of viscous flows

Bounce-back schemes represent the most popular boundary treatments in the lattice Boltzmann method (LBM) when reproducing the no-slip condition at a solid boundary. While the lattice Boltzmann equation used in LBM for interior nodes is known to reproduce the Navier–Stokes (N–S) equations under the Chapman–Enskog (CE) approximation, the unknown distribution functions reconstructed from a bounce-back scheme at boundary nodes may not be consistent with the CE approximation. This problem could lead to undesirable effects such as nonphysical slip velocity, grid-scale velocity, pressure noises, the local inconsistency with the N–S equations, and sometimes even a reduction of the overall numerical-accuracy order of LBM. Here, we provide a systematic study of these undesirable effects. We first derive the explicit structure of the mesoscopic distribution function for interior nodes. Then, the bounce-back distribution function is examined to identify the hidden errors. It is shown that the relaxation parameters in the collision models play a key role in determining the magnitude of the hidden error terms, and there exists an optimal setting, which can suppress or eliminate most of these undesirable effects. While the existence of this optimal setting is derived previously for unidirectional flows, here, we show that this optimal setting can be extended to non-uniform flows under certain conditions. Finally, a systematic numerical benchmark study is carried out, including non-uniform and unsteady flows. It is shown that, in all these flows, our theoretical analyses of the hidden errors can guide us to significantly improve the quality of the simulation results.

Artificial compressibility approaches in flux reconstruction for incompressible viscous flow simulations

Artificial compressibility methods intend to offer divergence-free free velocity fields at the incompressible limit for compressible solvers. Three major approaches for this are compared within a high-order flux reconstruction framework: the established method (ACM) of Chorin (1967) and a new entropically damped method (EDAC) of Clausen (2013) which can keep velocity divergence sufficiently low to be run explicitly without the non-linear solver required by ACM. Furthermore, the ACM approach with hyperbolised diffusion is investigated. The accuracy and computational efficiency of these methods is investigated for a series of turbulent test cases over a range of Reynolds numbers. It is found for EDAC that velocity divergence scales linearly with the square root of compressibility, whereas for ACM a clear relation is not observed. EDAC is found to accurately resolve the low Reynolds number Taylor–Green vortex case; however, for the circular cylinder at Reynolds number 3900, earlier transition of the free shear-layer is observed due to an over-production of the turbulence kinetic energy. This over production of turbulent kinetic energy is attributed to the increased spatial pressure gradients of the EDAC method, and similar behaviour is observed for an aerofoil at Reynolds number 60 000 with an attached transitional boundary layer. These issues were not observed for the other ACM approaches. It is concluded that hyperbolic diffusion of ACM can be beneficial in terms of convergence but at the cost of case setup time, and EDAC can be a time efficient method for unsteady incompressible flows. However, care must be taken when reducing the stiffness of EDAC as the resulting pressure fluctuations can have a significant impact on transition.

Constrained least-squares based adaptive-order finite-volume WENO scheme for the simulation of viscous compressible flows on unstructured grids

We develop a novel constrained least-squares technique for fourth-order weighted essentially non-oscillatory (WENO) polynomial reconstruction on general unstructured grids composed of curved-edged quadrilateral elements. Our technique relies on a segregation of the conditions that match the spatial averages of the candidate WENO polynomial and the reconstructed state variable over stencil-forming cells into two sets. The first set consists of exactly enforced linearly independent constraints that are applied only over the central cell and its edge-sharing neighbors. The second set consists of the remaining conditions and are enforced only approximately in a least-squares sense. We develop a specialized technique that reduces the computational burden associated with the numerical solution of the constrained least-squares system for the WENO interpolation coefficients. For a comparable computational expense, our constrained reconstruction approach yields pointwise estimates that are consistently more accurate than the conventional least-squares based estimates over a wide spectrum of spatial wavenumbers. This enhanced spectral resolution yields a significant, over two-fold increase in the accuracy with which unsteady smooth flow features, such as an advecting isentropic vortex, are captured over highly distorted curvilinear unstructured grids. Our constraint based reconstruction framework is generic, facilitates implementation of high-order boundary closures, and is amenable to large scale parallelization over several thousand CPU cores. Numerical tests over a range of inviscid and viscous flow configurations are presented to demonstrate the accuracy and robustness of our technique. Our constrained least-squares based adaptive WENO discretization faithfully captures intricate features that arise in strongly shocked, and highly unsteady and separated complex geometry flows. Our results suggest exact preservation of the match between the cell averages of the interpolant and the reconstructed state variable over the nearest neighbors to be quite an effective strategy that dramatically enhances the accuracy and spectral resolution of the high-order finite-volume reconstruction operation.

Airfoil Morphed Leading-Edge Design for High-Lift Applications Using Genetic Algorithm

A genetic algorithm was developed for the optimal design of morphing airfoil leading-edge shapes to maximize airfoil , while retaining a constant leading-edge arc length. Using a candidate slotted, natural laminar flow airfoil, an inviscid–viscous flow simulation program suite was used to evaluate a randomized population of airfoils during the design process at low-speed, high-lift flight conditions of a representative single-aisle commercial transport aircraft. The use of a continuous morphing strategy to perform treatment of the leading-edge geometry in high-lift scenarios, as opposed to leading-edge flap or slat elements, is envisaged as a means to mitigate surface discontinuities and retain laminar flow qualities of future airfoil sections in cruise conditions. By using different definitions of the objective cost function, multiple morphed airfoil designs were found through the genetic algorithm to create a library of possible designs aimed to purposefully alleviate the leading-edge stall tendencies of the baseline airfoil. Three morphed designs were validated through experimentation in a low-speed, open-return wind tunnel. Resulting data were used to verify that the leading-edge separation property of the baseline airfoil during stall was effectively alleviated with use of the morphed leading-edge geometries.

An implicit Cartesian cut-cell method for incompressible viscous flows with complex geometries

A versatile conservative three-dimensional Cartesian cut-cell method for simulation of incompressible viscous flows over complex geometries is presented in this paper. The present method is based on the finite volume method on a non-uniform staggered grid together with a consistent mass and momentum flux computation. Contrary to the commonly cut-cell methods, an implicit time integration scheme is employed in the present method, which avoids numerical instability without any additional small cut-cell treatment. Strict conservation of the mass and momentum for both fluid and cut cells is enforced through the PISO algorithm for the pressure–velocity coupling. The versatility and robustness of the present cut-cell method are demonstrated by simulating various two- and three-dimensional canonical benchmarks (flow over a circular cylinder, airfoil, sphere, pipe, and heart sculpture) and the computed results agree well with previous experimental measurements and various numerical results obtained from the boundary-fitted, immersed boundary/interface, and other cut-cell methods, verifying the accuracy of the proposed method.

A fast unsmoothed aggregation algebraic multigrid framework for the large-scale simulation of incompressible flow

Multigrid methods are quite efficient for solving the pressure Poisson equation in simulations of incompressible flow. However, for viscous liquids, geometric multigrid turned out to be less efficient for solving the variational viscosity equation. In this contribution, we present an Unsmoothed Aggregation Algebraic MultiGrid (UAAMG) method with a multi-color Gauss-Seidel smoother, which consistently solves the variational viscosity equation in a few iterations for various material parameters. Moreover, we augment the OpenVDB data structure with Intel SIMD intrinsic functions to perform sparse matrix-vector multiplications efficiently on all multigrid levels. Our framework is 2.0 to 14.6 times faster compared to the state-of-the-art adaptive octree solver in commercial software for the large-scale simulation of both non-viscous and viscous flow. The code is available at http://computationalsciences.org/publications/shao-2022-multigrid.html.

Numerical investigation of wave-induced loads on an offshore monopile using a viscous and a potential-flow solver

Wave-induced loads on an offshore monopile were investigated using a viscous-flow solver and a potential-flow solver. Considered were only two steep regular wave trains, with the same height but different periods. The potential-flow approach relied on a weakly nonlinear time-domain solver (i.e., Green function). The viscous-flow solver used three solution schemes, namely, an Euler scheme that neglected the flow viscosity, a Laminar scheme that numerically integrated the full Navier–Stokes equations without a model accounting for the fluctuating portion of the velocity field, and a Reynolds-averaged Navier–Stokes scheme that modeled turbulent flow via a two-equation eddy-viscosity model. Numerical uncertainties of viscous-flow simulations were quantified, and computed results were validated against model test measurements. Overall, the main characteristics of wave-induced forces and bending moments were well predicted by all adopted numerical schemes. In terms of higher harmonic components, predictions only from the viscous-flow solver compared favorably to the experimental measurements, including the local free surface elevations, higher harmonic forces/moments, and the secondary wave load cycles. The effect of strong nonlinear motion of free surface on the wave-induced total loading was secondary, and the contribution from the associated viscous and turbulent effects was also very limited. Nevertheless, they attribute to the generation of higher harmonic forces/moments as well as the secondary load cycle. In addition, the effects of wave steepness on the global, first- and higher harmonic forces were addressed.

Numerical simulation of time-dependent two-dimensional viscous fluid flow with thermal radiation

Numerical simulation of time-dependent two-dimensional viscous fluid flow with thermal radiation

Pore-scale modelling of fluid flow in porous media using the projection method for incompressible Navier-Stokes equations in irregular domains

This paper presents the results of numerical simulation of incompressible viscous flow in porous media, which comprise periodically arranged cylinders. This simulation is based on the numerical solution of the incompressible Navier-Stokes equations in irregular domains using the projection method on staggered grids, where the irregular boundary is represented by its level-set function at the pore-scale level. The main problem in numerical calculation of fluid flow through porous media occurs when the value of the porosity is close to 1 or is close to the threshold value since it is necessary to take a very fine numerical mesh, which requires additional computing power and increases the calculation time. There are exact analytical solutions for simple types of porous media which consist of periodically arranged cylinders. In this paper, the permeabilities of these porous media were numerically calculated and compared with the previous works based on the numerical solution of the Lattice-Boltzmann equation in irregular domains, when the fluid flow obeys Darcy’s law. The comparison of numerical and theoretical values of porosity shows that this method is sufficiently accurate for porosity values φ=0.2–0.8.

An immersed boundary method with implicit body force for compressible viscous flow

We present a new immersed boundary method for the simulation of compressible viscous flow. The method is based on the singular source approach where the immersed boundary adds surface singularities to the governing equations. The strengths of the surface singularities are treated as algebraic variables under the framework of differential-algebraic equations and are implicitly calculated to enforce the corresponding boundary conditions. Discrete delta functions are used to approximate the surface singularities in the Eulerian grid and interpolate variables back to the surface mesh. A half-explicit Runge-Kutta method is used to achieve desired temporal accuracy. The method has been generalized from the well-known no-slip and isothermal condition to stress and heat flux conditions. The latter necessitates the introduction of further singularities in the stresses and heat flux, which is a new feature of the formulation. Furthermore, the approach has been extended to porous surfaces. The method is also applicable to flow-structure interaction problems. Two- and three-dimensional numerical tests are carried out to demonstrate accuracy. The results are compared with previous numerical and experimental studies or analytical solutions. Finally, a fully three-dimensional fluid-structure interaction simulation of a subsonic parachute is showcased to demonstrate applicability to a real problem.

Boundary conditions for fluid-dynamic parameters of a single-component gas flow with vibrational deactivation on a solid wall

Boundary conditions for fluid-dynamic parameters of a strongly non-equilibrium singlecomponent rarefied gas flow in the slip regime are obtained using kinetic-theory methods. The gas flow is described in the frame of the state-to-state approach assuming vibrational energy exchange as the slow relaxation process. The set of governing equations including conservation equations coupled with additional relaxation equations for vibrational state populations is presented. The gas-solid surface interaction is considered on the basis of the specular-diffusive model, and possible vibrational deactivation/excitation processes on the wall are taken into account. The obtained boundary conditions depend on the accommodation and deactivation coefficients along with the transport coefficients such as the multi-component vibrational energy diffusion and thermal diffusion coefficients; the thermal conductivity; the bulk and shear viscosity coefficients and the relaxation pressure. The dependence of boundary conditions on the normal mean stress has been obtained for the first time. In the particular case of the gas without internal degrees of freedom, the slip velocity and the temperature jump can be reduced to the well-known in the literature expressions. Implementation of the state-specific boundary conditions should not cause additional computational costs in numerical simulations of viscous flows in the state-to-state approach, since the slip/jump equations depend on the transport coefficients which have to be evaluated regardless of the boundary conditions used in the code.

HYDRODYNAMIC HULL FORM DESIGN SPACE EXPLORATION OF LARGE MEDIUM-SPEED CATAMARANS USING FULL-SCALE CFD

Large medium-speed catamarans are a new class of vessel currently under development as fuel-efficient ferries for sustainable fast sea transportation. Appropriate data to derive design guidelines for such vessels are not available and therefore a wide range of demihull slenderness ratios were studied to investigate the design space for fuel-efficient operation. Computational fluid dynamics for viscous free-surface flow simulations were utilised to investigate resistance properties of different catamaran configurations having a similar deadweight at light displacement, but with lengths ranging from 110 m to 190 m. The simulations were conducted at full-scale Reynolds numbers (log(Re) = 8.9 – 9.6) and Froude numbers ranged from Fr = 0.25 to 0.49. Hulls of 130 m and below had high transport efficiency below 26 knots and in light loading conditions while hulls of 150 m and 170 m showed benefits for heavier displacement cases and speeds up to 35 knots. Furthermore, the study concluded that the lowest drag was achieved with demihull slenderness ratios between 11 and 13.

A mixed u\u2013p edge-based smoothed particle finite element formulation for viscous flow simulations

A mixed u–p edge-based smoothed particle finite element formulation is proposed for computational simulations of viscous flow. In order to improve the accuracy of the standard particle finite element method, edge-based and face-based smoothing operations on the displacement gradient are proposed for 2D and 3D analyses, respectively. Consequently, spatial integration involving the smoothing operator is performed on smoothing domains. The constitutive model is based on an elasto-viscoplastic formulation allowing for simulations of viscous fluid or fluid-like solid materials. The viscous response is modeled using an overstress function. The performance of the proposed edge-based smoothed particle finite element method (ES-PFEM) is demonstrated by several numerical benchmark studies, showing an excellent agreement with analytical and reference solutions and an improved accuracy and computational efficiency in comparison with results from the standard PFEM model. Finally, a numerical application of the ES-PFEM to the computational simulation of the extrusion process during 3D-concrete-printing is discussed.