A zonal RANS-LES method to determine the flow over a high-lift configuration

High Reynolds number flows are particularly challenging problems for large-eddy simulations (LES) since small-scale structures in thin and often transitional boundary layers are to be resolved. The range of the turbulent scales is enormous, especially when high-lift configuration flows are considered. For this reason, the prediction of high Reynolds number flow over the entire airfoil using LES requires huge computer resources. To remedy this problem a zonal RANS-LES method for the flow over an airfoil in high-lift configuration at Re_c=1.0×10⁶ is presented. In a first step, a 2D RANS solution is sought, from which boundary conditions are formulated for an embedded LES domain, which comprises the flap and a sub-part of the main airfoil. The turbulent fluctuations in the boundary layers at the inflow region of the LES domain are generated by controlled forcing terms, which use the turbulent shear stress profiles obtained from the RANS solution. The comparison with an LES solution for the full domain and with experimental data shows likewise results for the velocity profiles and wall pressure distributions. The zonal RANS-LES method reduces the computational effort of a full domain LES by approx. 50%.     

Attenuating Artificial Dissipation in the Computation of Navier–Stokes Turbulent Boundary Layers

We propose a new formulation of the fourth-difference artificial dissipation coefficient needed for the Navier–Stokes solutions. This coefficient is scaled by a damping function which is expressed in terms of the Baldwin–Lomax algebraic turbulence model. The suggested scaling function damps the artificial dissipation across the boundary layer. The objective of this paper is to test the ability of the suggested damped scaling coefficient to provide (a) a given accuracy on a coarser grid; and (b) an accurate computing of turbulent boundary layers. To accomplish this, attached and separated transonic flows over the NACA 0012 airfoil, and turbulent flow over a flat plate have been considered.     

Application of triple-deck theory to the prediction of glaze ice roughness formation on an airfoil leading edge

A viscous–inviscid interaction triple-deck structure is developed to describe the thermomechanical interaction of an air boundary layer with ice sheets and liquid films. Linear stability results are compared with nonlinear triple-deck computations, and a number of nonlinear simulations of air–water–ice interactions are presented. An icing instability is encountered in regimes with simultaneous wall and air cooling that is believed to admit small scale and highly irregular surface roughness. The stabilization of the smallest scale icing disturbances is obtained through the Gibbs–Thomson relation. This local thermodynamic condition relates the freezing temperature of a pure substance to the surface tension and the mean curvature of the interface and provides a short scale stabilizing mechanism for icing instability modes. Comparison with available experimental data on glaze ice roughness diameters, accreted on NACA 0012 airfoil leading edges under glaze icing conditions, is provided. It is also found in all cases computed in this study that water beads can be formed on a wetted ice surface once the water film is locally ruptured by ice roughness elements.     

Some questions concerning the initial fields in finite difference computation of two-dimensional steady transonic flows

To study the influence of initial fields on computation results, the author, starting from a two-dimensional steady transonic small-disturbance equation, has computed the shock wave strengths and lift coefficients for the NACA0012 airfoil by the mixed finite difference relaxation iteration method. The computed results show that if (1) incident flows are supercritical, (2) a nonconservative difference scheme is used to capture shock waves, and (3) the computations are iterated with the initial fields at the lower entropy values (zero values or computed results of flow fields with smaller angles of attack or Mach numbers), then correct converged solutions can be obtained. Otherwise, erroneous converged solutions might be obtained. If incident flows are subcritical and shock waves do not appear in the flow field, then the computed results do not depend on the choice of the initial fields. This means that the converged solution is unique.     

Dynamic hybridization of MILES and RANS for predicting airfoil stall

Hybridization comprised of an algebraic turbulence model based on the Reynolds average Navier-Stokes (RANS) equations with a monotonically integrated large eddy simulation (MILES) is proposed to simulate transient fluid motion during separation and vortex shedding at high Reynolds numbers. The proposed hybridization utilizes the Baldwin-Lomax model with the Degani-Schiff modification as the RANS model in the near-wall region and a MILES far from the wall. Although the hybridization is assumed to be a MILES with wall modeling, the transition line between the RANS and the MILES modes is determined by the turbulent intensity that is dominated by the large eddies in the grid-scale. This hybrid model is applied to the flows past three different types of airfoils (NACA63₃-018, NACA63₁-012 and NACA64A-006) near stall, at a chord Reynolds number of Re = 5.8 × 10⁶. These airfoils are classified as trailing-edge-stall, leading-edge-stall and thin-airfoil-stall airfoils, respectively. The computed results are compared with wind tunnel experiments. The hybrid model successfully demonstrates accurate stall angle and surface pressure distribution predictions near the stall for each type of airfoil. The airfoil simulation results confirmed that the hybrid model provides a better prediction than the RANS model for unsteady turbulent flows with separation and vortex shedding simulations.     

Molecular dynamics simulations of shear-driven gas flows in nano-channels

Using the recently developed smart wall molecular dynamics algorithm, shear-driven gas flows in nano-scale channels are investigated to reveal the surface–gas interaction effects for flows in the transition and free molecular flow regimes. For the specified surface properties and gas–surface pair interactions, density and stress profiles exhibit a universal behavior inside the wall force penetration region at different flow conditions. Shear stress results are utilized to calculate the tangential momentum accommodation coefficient (TMAC) between argon gas and FCC walls. The TMAC value is shown to be independent of the flow properties and Knudsen number in all simulations. Velocity profiles show distinct deviations from the kinetic theory based solutions inside the wall force penetration depth, while they match the linearized Boltzmann equation solution outside these zones. Results indicate emergence of the wall force field penetration depth as an additional length scale for gas flows in nano-channels, breaking the dynamic similarity between rarefied and nano-scale gas flows solely based on the Knudsen and Mach numbers.     

A numerical estimate of the plankton-induced sea surface tension effects in a Langmuir circulation

Marine phytoplankton is known to produce surface-active materials as part of its metabolism. The sea surface tension gradient due to the presence of plankton produced surfactants leads to a surface shear stress, commonly known as Marangoni stress, that can be of non-negligible intensity in areas of converging (or diverging) flows, where surface-active material concentrates (or lacks). A natural set-up where this condition can be observed is the Langmuir circulation that establishes in presence of wind and waves and exhibits periodic and permanent areas of alternating convergence and divergence. In the present work we adopt a simplified Large Eddy Simulation model for describing the Langmuir circulation and, by the use of a numerical model previously published, obtain an estimate of the Marangoni stress. The computed Marangoni stress peaks in the converging flow areas to values that are two orders of magnitude higher than in the case of absence of wind burst, previously studied by the authors. Such stress, usually disregarded within the numerical simulations of sea and other basin waters, is in fact capable to modify sensibly the distribution of the ecosystem biological components and should be considered for inclusion in the mathematical modelling.     

Reduced-Order Adaptive Controllers for Fluid Flows Using POD

This article presents a reduced-order adaptive controller design for fluid flows. Frequently, reduced-order models are derived from low-order bases computed by applying proper orthogonal decomposition (POD) on an a priori ensemble of data of the Navier–Stokes model. This reduced-order model is then used to derive a reduced-order controller. The approach discussed here differ from these approaches. It uses an adaptive procedure that improves the reduced-order model by successively updating the ensemble of data. The idea is to begin with an ensemble to form a reduced-order control problem. The resulting control is then applied back to the Navier–Stokes model to generate a new ensemble. This new ensemble then replaces the previous ensemble to derive a new reduced-order model. This iteration is repeated until convergence is achieved. The adaptive reduced-order controllers effectiveness in flow control applications is shown on a recirculation control problem in channel flow using blowing (actuation) on the boundary. Optimal placement for actuators is explored. Numerical implementations and results are provided illustrating the various issues discussed.     

Control of separated flow past a backward facing step in a microchannel

A key concern for microdevice design is its power consumption. When such a device involves microflows, actively controlling the flow losses often reduces the power requirements. In the present study, a microsynthetic jet is proposed as a flow control device. The method used is an automated design optimization methodology coupled with computational fluid dynamics. Microflows in the Knudsen number (Kn) range of 10^–3 to 10^–1 are modeled using a Navier–Stokes solver but with slip velocity and temperature jump boundary conditions derived for microsized geometries. First, an uncontrolled flow past a backward facing step in a channel is computed. Then, a synthetic jet actuator is placed downstream of the step where the separation occurs. A large number of test cases have been analyzed. It has been observed that the reattachment point of the separated flow and the flow dissipation are quite sensitive to the location and the geometry of the synthetic jet, as well as the parameters of the oscillating membrane. The best flow control, defined as the largest decrease in dissipation, is obtained when the actuator cavity width and the membrane oscillation amplitude are increased simultaneously.     

Three-dimensional numerical simulations of viscoelastic flows – predictability and accuracy

In this paper, fully three-dimensional (3-D) numerical simulations of viscoelastic flows using an implicit finite volume method are discussed with the focus on the predictability and accuracy of the method. The viscoelastic flow problems involving the stress singularity, including plane stick–slip flow, the flow past a junction in a channel, and the 3-D edge flow, are used to test the ability of the method to predict the singularity features with accuracy. The accuracy of the numerical predictions is judged by comparing with the known asymptotic behaviour for Newtonian fluids and some viscoelastic fluids, and the investigations are extended to the viscoelastic cases with unknown singular behaviour. The Phan-Thien–Tanner (PTT) model, and in some cases, the upper-convected Maxwell (UCM) model, are used to describe viscoelastic fluids. The numerical results with mesh refinement show that the accuracy is quite satisfactory, especially for Newtonian flows. For viscoelastic flows, the asymptotic results for the flow around a re-entrant corner for the UCM as well as the PTT fluid are reproduced numerically. In the stick–slip flow, a Newtonian-like asymptotic behaviour is predicted for the UCM fluid. In edge flow, it is verified numerically that the kinematics are Newtonian for viscoelastic fluids described by models with a constant viscosity and a zero second normal stress difference. For viscoelastic fluids described by the models with a shear-thinning viscosity and zero second normal stress difference, the fluid behaves like a power-law fluid, and the difference from its Newtonian kinematics is localized in the region near the singularity, and to capture the asymptotic behaviour, a parameter-dependent mesh has to be used. With the 3-D simulations, it is confirmed that in edge flow, the flow around the edge could not be rectilinear, and some secondary flows on the plane normal to the primary flow direction are expected for viscoelastic fluids described by the models with a shear-dependent second normal stress difference, such as the full PTT model. The strength of the secondary flows will depend on the level of the departure of the second normal stress difference from a fixed constant multiple of viscosity of the fluid.     

Unstructured Grid-Based Discontinuous Galerkin Method for Broadband Electromagnetic Simulations

A parallel, unstructured, high-order discontinuous Galerkin method is developed for the time-dependent Maxwell's equations, using simple monomial polynomials for spatial discretization and a fourth-order Runge–Kutta scheme for time marching. Scattering results for a number of validation cases are computed employing polynomials of up to third order. Accurate solutions are obtained on coarse meshes and grid convergence is achieved, demonstrating the capabilities of the scheme for time-domain electromagnetic wave scattering simulations.     

Turbulence models and their applications to the prediction of internal flows: A review

The paper presents a brief account of various turbulence models employed in the computation of turbulent flows, and evaluates the application of these models to internal flows by examining the predictions of various turbulence models in selected important flow configurations. The main conclusions of this analysis are: (a) The κ-ε model is used in a majority of all the 2-D flow calculations reported in the literature. (b) Modified forms of the κ-ε model improve the performance for flows with streamline curvature and heat transfer. (c) For flows with swirl, the κ-ε model performs rather poorly; the algebraic stress model performs better in this case. (d) For flows with regions of secondary flow (noncircular duct flows), the algebraic stress model performs fairly well. Two important factors in the numerical solution of the model equations, namely false diffusion and inlet boundary conditions, are discussed. The existence of countergradient transport and its implications in turbulence modeling are examined. Finally, some recommendations for improving the model performance are made. The need for detailed experimental data in flows with strong curvature is emphasized.     

Curvature and entropy based wall boundary condition for the high order spectral volume Euler solver

A curvature and entropy based wall boundary condition is implemented in the high order spectral volume (SV) context. This method borrows ideas from the “curvature-corrected symmetry technique” developed by (Dadone A, Grossman B. Surface Boundary Conditions for Compressible Flows. AIAA J 1994; 32(2): 285–93), for a low order structured grid Euler solver. After numerically obtaining the curvature, the right state (by convention, the left state is inside the computational domain and the right state lies outside of the computational domain) face pressure values are obtained by solving a linearised system of equations. This is unlike that of the lower order finite volume and difference simulations, wherein the right state face values are trivial to obtain. The right state face density values are then obtained by enforcing entropy conservation. Accuracy studies show that simulations performed by employing the new boundary conditions deliver much more accurate results than the ones which employ traditional boundary conditions, while at the same time asymptotically reaching the desired order of accuracy. Numerical results for two-dimensional inviscid flows around the NACA0012 airfoil and over a bump with the new boundary condition showed dramatic improvements over those with the conventional approach. In all cases and orders, spurious entropy productions with the new boundary treatment are significantly reduced. In general, the numerical results are very promising and indicate that the approach has a great potential for 3D high order simulations.     

A 3D finite element model for free-surface flows

The present work deals with the validation of 3D finite element model for free-surface flows. The model uses the non-hydrostatic pressure and the eddy viscosities from the conventional linear turbulence model are modified to account for the secondary effects generated by strong channel curvature in the natural rivers with meandering open channels. The unsteady Reynolds-averaged Navier–Stokes equations are solved on the unstructured grid using the Raviart–Thomas finite element for the horizontal velocity components, and the common P1 linear finite element in the vertical direction. To provide the accurate resolution at the bed and the free-surface, the governing equations are solved in the multi-layers system (the vertical plane of the domain is subdivided into fixed thickness layers). The up-to-date k–ε turbulence solver is implemented for computing eddy coefficients, the Eulerian–Lagrangian–Galerkin (ELG) temporal scheme is performed for enhancing numerical time integration to guarantee high degree of mass conservation while the CFL restriction is eliminated. The present paper reports on successful validation of the numerical model through available benchmark tests with increasing complexity, using the high quality and high spatial resolution three-dimensional data set collected from experiments.     

A generalized continuous surface tension force formulation for phase-field models for multi-component immiscible fluid flows

We present a new phase-field method for modeling surface tension effects on multi-component immiscible fluid flows. Interfaces between fluids having different properties are represented as transition regions of finite thickness across which the phase-field varies continuously. At each point in the transition region, we define a force density which is proportional to the curvature of the interface times a smoothed Dirac delta function. We consider a vector valued phase-field, the velocity, and pressure fields which are governed by multi-component advective Cahn–Hilliard and modified Navier–Stokes equations. The new formulation makes it possible to model any combination of interfaces without any additional decision criteria. It is general, therefore it can be applied to any number of fluid components. We give computational results for the four component fluid flows to illustrate the properties of the method. The capabilities of the method are computationally demonstrated with phase separations via a spinodal decomposition in a four-component mixture, pressure field distribution for three stationary drops, and the dynamics of two droplets inside another drop embedded in the ambient liquid.     

A higher order numerical scheme for scalar transport

The computational principles of a numerical scheme for the solution of the two-dimensional scalar transport equation are presented. The scheme is designed for use in transient flow situations where accurate simulation of the advective process is important. Advective transport is computed by the method of characteristics in which the scalar field is represented by a Hermitian polynomial complete through the third degree in both coordinate directions, while diffusion is computed by central differencing. The superior accuracy of the new method is demonstrated by analysing its propagation characteristics and by comparing its performance on standard test problems with that of some well-known lower order methods. Finally, the method's applicability is demonstrated in several examples involving tracer releases into channel flows. Where possible the results of these simulations are compared with analytical solutions.     

From Reeds and Shepp's to continuous-curvature paths

This paper presents Continuous Curvature (CC) Steer, a steering method for car-like vehicles, i.e., an algorithm planning paths in the absence of obstacles. CC Steer is the first to compute paths with: 1) continuous curvature; 2) upper-bounded curvature; and 3) upper-bounded curvature derivative. CC Steer also verifies a topological property that ensures that when it is used within a general motion-planning scheme, it yields a complete collision-free path planner. The coupling of CC Steer with a general planning scheme yields a path planner that computes collision-free paths verifying the properties mentioned above. Accordingly, a car-like vehicle can follow such paths without ever having to stop in order to reorient its front wheels. Besides, such paths can be followed with a nominal speed which is proportional to the curvature derivative limit. The paths computed by CC Steer are made up of line segments, circular arcs, and clothoid arcs. They are not optimal in length. However, it is shown that they converge toward the optimal "Reeds and Shepp" paths when the curvature derivative upper bound tends to infinity. The capabilities of CC Steer to serve as an efficient steering method within two general planning schemes are also demonstrated.     

Nonlinear model predictive control scheme for stabilizing annulus pressure during oil well drilling

This paper presents a nonlinear model predictive control scheme for stabilizing the well pressure during oil well drilling. While drilling, a fluid is pumped through the drill string and the drill bit, and is returning through the annulus between the drilled well and the drill string. Varying reservoir conditions and fluctuation in circulation flow rates cause sudden variations in the pressure conditions along the well. To compensate for these pressure fluctuations, the annulus choke valve opening can be adjusted. The proposed control scheme is based on a first-principles two-phase flow model using spatial discretization of the complete well. The optimal future choke settings are found using the Levenberg–Marquardt optimization algorithm. This control scheme is evaluated against two other control methods, a manual control scheme and a standard feed-back PI-control scheme of the choke valve with feed-forward control of the pump rates. The PI-control parameters are found using the Ziegler–Nichols closed-loop method based on simulations from a low-order model. The results show that both the PI-control scheme and the model predictive control scheme are superior to manual control. However, the PI-control scheme requires that the control parameters are re-designed when the operating conditions are deviating from the original design conditions. The model predictive control scheme will perform within the operating limits as long as the detailed model is able to describe the actual conditions of the well.     

A numerical method for the simulation of free surface flows with surface tension

A numerical model for the simulation of three-dimensional liquid–gas flows with free surfaces and surface tension is presented. The incompressible Navier–Stokes equations are assumed to hold in the liquid domain, while the gas pressure is assumed to be constant in each connected component of the gas domain and to follow the ideal gas law. The surface tension effects are imposed as a normal force on the interface.

An implicit splitting scheme is used to decouple the physical phenomena. Given the curvature of the liquid–gas interface, the method described in [Caboussat A, Picasso M, Rappaz J. Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas. J Comput Phys 2005;203(2):626–49] is used to track the liquid domain and compute the velocity and pressure in the liquid and the pressure in the gas domain. Then the surface tension effects are added. A variational method for the computation of the curvature is presented by smoothing the characteristic function of the liquid domain and using a finite element unstructured mesh.

The model is validated and numerical results in two and three space dimensions are presented for bubbles and/or droplets flows.     

Optimization of the motion of a flapping airfoil using sensitivity functions

The motion of a flapping NACA0012 airfoil is optimized by means of numerical simulations for a Reynolds number equal to 1100. The control parameters are the amplitudes and the phase angles of the flapping motion in addition to the mean angle of attack. Sensitivity functions are used to compute the gradient of a cost functional related to the propulsive efficiency of the airfoil and a quasi-Newton method is adopted to drive the control parameters towards their optimal values. The ability of a flapping airfoil to produce sufficient lift and thrust forces for appropriate kinematics is demonstrated. Furthermore, a linear dependence between heaving and pitching amplitudes is found for optimal configurations leading to a constant value of the maximum effective angle of attack roughly equal to 11°. This value corresponds to the angle yielding the maximal lift-to-drag ratio for this Reynolds number when the NACA0012 airfoil does not flap. Previous results such as the high propulsive efficiency when a 90° phase angle exists between heaving and pitching, or the reversal of the von Karman street for a Strouhal number close to 0.2, are confirmed here with a new methodology. Finally, optimal kinematics for various types of missions are given and the corresponding flows are described.