Integral Boundary Layer Method Research Articles

Influence of air flow field computation on an ice accretion simulation of airfoils

Ice accretion simulation is an important research technology for aircraft icing problems. Air flow field prediction of an iced aircraft is an essential step of ice accretion simulation. However, commonly used turbulence models have difficulty predicting the large flow separation of the iced aircraft, which makes air flow field calculation insufficiently accurate and further affects the ice accretion simulation. In this paper, the influence of air flow field computation on ice accretion simulation of airfoils is numerically studied. Several different turbulence models are applied to predict air flow fields of iced airfoils. Then, the Eulerian method of water droplets, integral boundary layer method and Myers model are used to simulate ice accretion. Different airfoils with several icing conditions, including glaze ice and rime ice cases, are numerically tested and compared with experimental data. The results show that the separating shear layer fixed k−ω model is more accurate than other turbulence models in predicting the pressure distribution of the iced airfoil, especially the leading-edge suction peak. Thus, a more reasonable droplet collection efficiency distribution and convective heat transfer distribution can be obtained, yielding a more consistent ice height compared with the experimental data.

Calculation and Selection of Airfoil for Flapping-Wing Aircraft Based on Integral Boundary Layer Equations

The flight of a migratory bird-like flapping-wing aircraft is characterized by a low Reynolds number and unsteadiness. The selection of airfoil profiles is critical to designing an efficient flapping-wing aircraft. To choose the suitable airfoil for various wing sections, it is necessary to calculate the aerodynamic forces of the unsteady two-dimensional airfoil with a Reynolds number in the range of 105. While accurate, calculating this by solving the Navier–Stokes equations is impractical for early design stages due to its high consumption of computing resources and time. The computational demands for extending it to 3D aerodynamic calculations are even more prohibitive. In this paper, a relatively simple method is proposed. The two-dimensional unsteady panel method is utilized to derive the inviscid flow field, the unsteady integral boundary layer method is utilized to solve the boundary layer viscous flow, and the eN transition model is adopted to predict the position of the transition. These models are coupled with the semi-inverse interaction method to solve the aerodynamics of the unsteady low-Reynolds-number two-dimensional airfoil. The unsteady aerodynamics of the symmetric and cambered airfoils at different wing sections are calculated respectively by the proposed method. Mechanism analysis of the calculation results is conducted, and a symmetrical airfoil or a slightly cambered airfoil is recommended for the wing tip, a moderately cambered airfoil is suggested for the outer-wing section, and a highly cambered airfoil is suggested for the inner-wing section.

Roughness implementation and convective heat transfer coefficient computation toward ice accretion simulation

In the simulation of icing, the calculation of the convective heat transfer coefficient for rough surfaces has significant importance. Our study investigates the extension of the γ-Reθt transition model for rough icing surfaces and aims to provide an alternative to the integral boundary layer method for facilitating the calculation of the heat transfer coefficient in three-dimensional icing simulations. Initially, the performance of the γ-Reθt transition model in predicting the transition characteristics and heat transfer for smooth surfaces is examined. Subsequently, to compensate for the deficiency of the γ-Reθt transition model in predicting the premature transition caused by roughness, an additional model equation Ar is introduced to simulate the influence of the surface roughness. Three test cases, including a clean cylinder, an iced cylinder, and a swept wing, are used to validate the applicability of the γ-Reθt-Ar transition model for heat transfer computations on rough surfaces. The results demonstrate that the γ-Reθt-Ar model is superior to other turbulence models in computing convective heat transfer for two-dimensional and three-dimensional icing rough surfaces and shows its potential for ice accretion simulation.

Extended integral boundary layer method for reactive species mass transfer in rotating films

AbstractThe present work extends the Integral Boundary Layer (IBL) Method to centrifugal force driven thin film flow with mass transfer. The proposed hybrid approach combines the IBL based solution of the flow field with a Finite Difference based solution of the mass transport equation, avoiding any concentration profile assumptions and restrictions on surface chemistry. In comparison against results from highly resolved Computational Fluid Dynamics (CFD) simulations, the proposed concept is proven as a computationally efficient and accurate method well applicable to infinitely fast surface reactions as well as finite rate kinetics.

Multidisciplinary Design Optimization of Transonic Wings with Boundary-Layer Suction

A quasi-three-dimensional aerodynamic solver is developed for the aerodynamic analysis of wings in a transonic regime that is able to capture the effect of BLS in hybrid laminar flow control (HLFC) application or transition to turbulent flow for natural laminar flow (NLF). The tool provides accurate results, but without the high computational cost of high-fidelity tools. The solver combines the use of an Euler flow solver characterized by an integral boundary-layer method and linear stability analysis using a approximation for transition prediction. In particular, a conical transformation is adopted, including the determination of the shock-wave position. The solver is implemented in a multidisciplinary design optimization (MDO) framework, including wing weight estimation and aircraft performance analysis. The framework consists of different modules: aerodynamics, structure, suction system analysis, and performance evaluation. Using a genetic algorithm and considering HLFC technology, wing MDO has been performed to find the optimum wing planform and airfoil shape. A backward-swept wing (BSW) aircraft, developed inside the Cluster of Excellence–Sustainable and Energy Efficient Aviation (A) is studied. Novel technologies such as active flow control, limited maximum load factors due to load alleviation, and novel materials allow a fuel weight reduction of 6%.

Design Exploration of Transonic Airfoils for Natural and Hybrid Laminar Flow Control Applications

Designing transonic laminar swept wing at high Reynolds numbers is challenging due to the premature flow transition from the prominent crossflow instabilities (CFIs). Hence, natural laminar flow (NLF) wings are limited to lower sweep angles. In this study, hybrid laminar flow control (HLFC) is used to extend this limit to design low-drag transonic infinite wing. A multi-objective genetic algorithm with competing drag components as objectives is used to design NLF and HLFC airfoils. Optimal design is a tradeoff between the drag reduction from skin friction drag, pressure drag, and suction drag, and does not resemble initial airfoils. Airfoil shape and suction distribution are coupled and optimized simultaneously. Euler flow solver with integral boundary-layer method is coupled with a higher-fidelity Linear Stability Analysis using 2.5D approximation for transition prediction. At wing sweep of 22.5°, Mach number of 0.78, and Reynolds number of 30 million, optimum NLF airfoil has 27% lower drag than an optimum turbulent airfoil. The optimum HLFC airfoil showed a 25% lower total drag than the NLF airfoil. A higher optimum sweep angle was observed for low-drag HLFC airfoil (20.5°) in comparison to the NLF airfoil (16.8°) and both favored an undercut on the lower surface to dampen CFI.

A Separated-Flow Model for 2-D Viscous Flows around Bluff Bodies Using the Panel Method

Panel methods have been applied to many fields of fluid owing to their computational efficiency. However, their applications are limited in simulating highly turbulent flow with separations due to the inviscid flow assumptions, such as those associated with train aerodynamics. Some researchers employed the wake models to simulate large vortices in the wake of trains with predetermined separation locations according to experimental results. In this paper, a modified 2-D constant source/vortex panel method for modelling the separated flow around 2-D bluff bodies is presented. The proposed separated-flow model includes the prediction of separation locations based on the integral boundary-layer method and the shear layer, and large vortices in the wake of the bluff bodies are modelled by the wake model. The proposed method is validated by comparing the calculated pressure distribution on a 2-D circular cylinder with the experimental results. The method is then applied to simulate the flow around a 2-D generic train and calculate the pressure distribution on the train. Since trains run very close to the ground, the effect of the ground configuration on the pressure distribution of the 2-D train is also investigated in this paper using the proposed method. The main contribution of the work is to present a 2-D separated-flow model with wake modelling and separation prediction. The proposed model can be used in the rapid evaluation of bluff-body aerodynamics.

A new boundary layer integral method based on the universal velocity profile

A recently developed mixing length model of the turbulent shearing stress in wall bounded flows has been used to formulate a universal velocity profile (UVP) that provides an effective replacement for the widely used Coles wall-wake formulation. Comparisons with both direct numerical simulation and experimental data demonstrate the ability of the profile to approximate a wide variety of wall-bounded flows. The UVP is uniformly valid from the wall to the boundary layer edge and for all Reynolds numbers from zero to infinity. There is no presumption of logarithmic dependence of the velocity profile outside the viscous wall layer so the profile can accurately approximate low Reynolds number turbulent boundary layers. The effect of a pressure gradient is included in the UVP through the introduction of a modified Clauser parameter that correlates well with the parameters that determine the wake portion of the velocity profile. The inherent dependence of the UVP on Reynolds number, extended to include the effect of pressure gradient, enables it to be used as the basis of a new method for integrating the von Kármán boundary layer integral equation for a wide variety of attached wall bounded flows. To illustrate its application, the UVP is used to determine the zero-lift drag coefficient of the Joukowsky 0012 and NACA (National Advisory Committee for Aeronautics) 0012 airfoils over a wide range of chord Reynolds numbers.

Effect of blade contamination on power production of wind turbines

Wind turbines suffer from considerable power losses because of contamination on their blades, that can be due to erosion, wear, smog, insect, sand and dust particle impact. Blade contamination, its effects on the flows over the wind turbine blades and consequent power production losses form the main focus of the present study. These effects are mainly due to increased roughness on the blades leading to earlier laminar-turbulent transition and consequently, thicker boundary-layers on the blades. Early laminar-turbulent transition leads to a larger part of the flow over a blade being turbulent, thus increasing skin friction drag. Thicker boundary-layer on a blade results in blade profile being effectively modified, rendering the flow over the blade depart from ideal. In the present study, the effects of blade contamination on power output of contaminated wind turbine blades is investigated numerically using an in-house computational tool. Blade Element Momentum Method (BEM) combined with the Panel Method is used to calculate the local velocity and angle of attack at the blade sections, together with the power produced by the blade. Trajectories of particles causing contamination are calculated using Lagrangian approach, also yielding the impingement pattern of the particles on the blade surface, i.e. particle collection efficiency distribution. The effects of roughness on the boundary-layer flow are investigated by using an Integral Boundary-Layer Method, which yields the characteristics of the boundary-layer, i.e. laminar-turbulent transition location, increased skin-friction and thickening of the boundary-layer. The blade shape is modified due contamination thickness, the local height of which is assumed to be proportional to the local collection efficiency. Also, the roughness height distribution used in the boundary-layer calculations is assumed to be equal to the contamination thickness distribution on the blades. Power production and consequent losses of wind turbines with contaminated wind turbine blades are studied with respect to variations in particle size, wind speed and roughness height.

Invertible Neural Networks for Airfoil Design

The airfoil design problem, in which an engineer seeks a shape with desired performance characteristics, is fundamental to aerodynamics. Design workflows traditionally rely on iterative optimization methods using low-fidelity integral boundary-layer methods as higher-fidelity adjoint-based computational fluid dynamics methods are computationally expensive. Surrogate-based approaches can accelerate the design process but still rely on some iterative inverse design procedure. In this work, we leverage emerging invertible neural network (INN) tools to enable the rapid inverse design of airfoil shapes for wind turbines. INNs are specialized deep-learning models with well-defined inverse mappings. When trained appropriately, INN surrogate models are capable of forward prediction of aerodynamic and structural quantities for a given airfoil shape as well as inverse recovery of airfoil shapes with specified aerodynamic and structural characteristics. The INN approach offers a roughly 100 times speed-up compared to adjoint-based methods for inverse design. We demonstrate the INN tool for inverse design on three test cases of 100 airfoils each that satisfy the performance characteristics close to those of airfoils used in wind-turbine blades. All generated shapes satisfy the desired aerodynamic characteristics, demonstrating the success of the INN approach for inverse design of airfoils.

Numerical simulations of a falling film on the inner surface of a rotating cylinder.

A flow in which a thin film falls due to gravity on the inner surface of a vertical, rotating cylinder is investigated. This is performed using two-dimensional (2D) and 3D direct numerical simulations, with a volume-of-fluid approach to treat the interface. The problem is parameterized by the Reynolds, Froude, Weber, and Ekman numbers. The variation of the Ekman number (Ek), defined to be proportional to the rotational speed of the cylinder, has a strong effect on the flow characteristics. Simulations are conducted over a wide range of Ek values (0≤Ek≤484) in order to provide detailed insight into how this parameter influences the flow. Our results indicate that increasing Ek, which leads to a rise in the magnitude of centrifugal forces, produces a stabilizing effect, suppressing wave formation. Key flow features, such as the transition from a 2D to a more complex 3D wave regime, are influenced significantly by this stabilization and are investigated in detail. Furthermore, the imposed rotation results in distinct flow characteristics such as the development of angled waves, which arise due to the combination of gravitationally and centrifugally driven motion in the axial and azimuthal directions, respectively. We also use a weighted residuals integral boundary layer method to determine a boundary in the space of Reynolds and Ekman numbers that represents a threshold beyond which waves have recirculation regions.

Use of a Two-Dimensional Finite Volume Integral Boundary-Layer Method for Ice-Accretion Calculations

In this paper, a two-dimensional integral boundary-layer method developed in a recent work is applied to ice-accretion computations. The method has already been validated in terms of boundary-layer dynamic effects in another paper. It is here validated for its ability to capture ice shapes, once the method is included in an icing suite. To be more specific, the results in using the new boundary-layer method are compared to experimental ice shapes and simulated ones with the widely used simplified integral method. The validation is carried out at an aggregated level because icing databases generally provide access to final ice shapes only. However, because the simplified integral method is used in many icing numerical tools, this comparison makes it possible to investigate the benefits of introducing the new method for calculating the boundary layer. The main outcome of the new method is an improvement of the prediction of the boundary-layer prediction under a smooth-wall assumption, which in turn improves ice-shape prediction. It is shown that, overall, the ice shapes are indeed either better predicted with the new method than with the baseline approach, or equally predicted with both methods. In addition, because the heat transfer coefficient tends to be underestimated by simplified integral methods, the new approach tends to predict lower horn angles than the baseline approach. Finally, the consequences of these results on current and future developments of ice-accretion solvers are discussed. In particular, the new method is better suited to a three-dimensional extension than the simplified integral method.

A Comparative Study of Program FloSim Results Against SYRF Wide Light Project Data

In November, 2015, the Sailing Yacht Research Foundation (SYRF) published the tank test data from their "Wide Light Yacht Project" for the hydrodynamics of a modern, high performance, semi-planing yacht. This comprehensive data set, comprising canoe body with and without appendages in upright, heeled and yawed conditions, provides an important validation base for Computational Fluid Dynamics (CFD) codes. The SYRF report includes a number of comparative results from commercial CFD codes. In this paper, we present results computed using an advanced Boundary Element Method (BEM), FloSim, these calculations being compared against the test matrix of "Wide Light" measured data and also STAR-CCM+ RANS calculated results. Computer model preparation is discussed and FloSim and RANS case execution times and computer requirements are compared. FloSim is an unsteady, time-stepping BEM with a non-linear vortex wake rollup procedure and a coupled integral boundary layer method for viscous effects. The free surface wave development is treated with a non-linear procedure that includes a breaking-wave model to deal with excess wave energy issues. The program was developed specifically to bridge the gap between basic potential flow panel methods and RANS codes, with the objective of providing accurate, practical solutions on a laptop computer within a reasonable turnaround time and cost. In essence, the results presented in this paper demonstrate the development objectives have been achieved. The comparisons of FloSim's essentially "low-order" results against test data and STARCCM+ RANS calculations, provide a measure of tradeoff between calculation accuracy versus cost and turnaround time for a case.

Modelling gravity-driven film flow on inclined corrugated substrate using a high fidelity weighted residual integral boundary-layer method

A computational investigation is conducted concerning the stability of free-surface gravity-driven liquid film flow over periodic corrugated substrate. The underpinning mathematical formulation constitutes an extension of the weighted residual integral boundary-layer (WIBL) method proposed by Ruyer-Quil and Manneville [“Improved modeling of flows down inclined planes,” Eur. Phys. J. B 15(2), 357–369 (2000)] and D’Alessio et al. [“Instability in gravity-driven flow over uneven surfaces,” Phys. Fluids 21(6), 062105 (2009)] to include third- and fourth-order terms in the long-wavelength expansion. Steady-state solutions for the free-surface and corresponding curves of neutral disturbances are obtained using Floquet theory and validated against corresponding experimental data and full Navier-Stokes (N-S) solutions. Sinusoidal and smoothed rectangular corrugations with variable steepness are considered. It is shown that the model is capable of predicting characteristic patterns of stability, including short-wave nose and isles of stability/instability as reported experimentally for viscous film flow over inclined topography, providing an attractive trade-off between the accuracy of a full N-S computation and the efficiency of an integral method. The range of parameter values for which the WIBL model remains valid is established; in particular, it is shown that its accuracy decreases with the Reynolds number and corrugation amplitude, but increases with the steepness parameter and ratio of wavelength to capillary length.

Theory and Validation of a 2D Finite-Volume Integral Boundary-Layer Method for Icing Applications

A two-dimensional integral boundary-layer method is developed to enable fast and economical computations of boundary-layer flows. The ultimate goal is to provide some experience for the extension of this method in three dimensions. In this study, the unsteady momentum and kinetic energy integral equations are solved numerically, together with a set of closure relations based on assumed velocity profiles for laminar and turbulent flows. The robustness of the method is ensured by a finite-volume formulation based on an upwind scheme and a semi-implicit time discretization. Moreover a control method has been developed in order to avoid the Goldstein singularity. The accuracy of the numerical method in the vicinity of the stagnation point is strongly improved by introducing a consistent corrective source term in the right-hand side of the equation system. The chosen closure relations are validated with test cases of self-similar flows. Numerical results are also compared with those of a full Prandtl equations code for NACA0012, GLC305, and MS317 airfoils test cases to demonstrate the capabilities of the method. Finally, preliminary results are shown proving the ability of the method to deal with iced airfoils even for complex glaze ice shapes.

Interfacial dynamics of a confined liquid–vapour bilayer undergoing evaporation

The dynamics of an interface between a thin liquid–vapour bilayer undergoing evaporation is studied. Both phases are considered to be hydrodynamically and thermally active, with momentum and thermal inertia taken into account. A reduced-order model based on the weighted-residual integral boundary layer method is used to investigate the dynamical behaviour for two cases,viz., phase change in the absence of gravity and then phase change in the presence of gravity. In the first case, it is shown that evaporative instability may cause rupture of either liquid or vapour layer depending on system parameters. Close to interfacial rupture, the disjoining pressure due to intermolecular forces results in the formation of drops (bubbles) separated by a thin film for low liquid (vapour) hold-up. Momentum inertia is shown to have a stabilizing effect, while thermal inertia has a destabilizing effect. In the second case, evaporative suppression of Rayleigh–Taylor (R–T) instability shows emergence of up to two neutral wavenumbers. Weak nonlinear analysis of these neutral wavenumbers suggests that the instability may be either supercritical or subcritical depending on the rate of evaporation. At high rates of evaporation, both neutral wavenumbers are supercritical and computations on the interface evolution lead to nonlinear saturated steady states. Momentum inertia slows down the rate of interface deformation and results in an oscillatory approach to saturation. Thermal inertia results in larger interface deformation and the saturated steady state is shifted closer to the wall. At very low evaporation rates, only one neutral wavenumber of subcritical nature exists. The nonlinear evolution of the interface in this case is then similar to pure R–T instability, exhibiting spontaneous lateral sliding as it approaches the wall.

Robust fluid-structure interaction analysis of an adaptive airfoil using shape memory alloy actuators

In the present paper, an aero-structure interaction model for the rapid simulation of morphing structures realized through shape memory alloy (SMA) actuators is presented. The aerodynamic simulation method implements a potential flow method strongly coupled with an integral boundary layer method in the context of a viscous-inviscid interaction approach, which includes a transition prediction model and a simplified shear stress-transport equation for the turbulence closure. The structural analysis model of the airfoil integrates a well-established SMA constitutive model for the prediction of the actuator behavior into finite element software. The two numerical models are loosely interconnected by exchanging geometrical and loading data at each iteration. An articulated 2-link adaptive mechanism for load alleviation purposes in horizontal axis wind turbine blades is investigated considering two different morphing scenarios: (1) operation of a single hinged flap; (2) combined movement of two sequential airfoil segments is attempted to achieve a smoother camber variation. The present fluid-structure interaction (FSI) model is employed with the aim to quantify its effect and benefits on the active shape control of the morphing airfoil, the actuator response, and the aerodynamic performance including lift and drag coefficients. The presented results demonstrate the robustness and numerical performance of the developed FSI method.

Assessment of d’Alembert’s paradox in panel methods by tangency correction

The aim of this study is to introduce a correction for panel methods in order to obtain correct viscous pressure drag of a steadily moving body in a viscous fluid. The boundary tangency correction implemented through a surface normal deflection term was added into a panel method implementation. A quadratic programming algorithm was used to solve inverse problems in order to prove the correction well-posedness and to obtain accurate surface pressure distribution, based on the experimental data. The experimental surface pressure distributions were collected from the literature for circular cylinders in steady uniform flow. The solutions of normal deflections were validated and the direct connection of the introduced correction to the boundary layer displacement thickness was found, which can simplify the process of viscous–inviscid coupling between integral boundary layer and panel methods.

Exact and approximate solutions for transient squeezing flow

In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity of the analytical approaches. The study presented herein fills the gap in the literature and will have a broad impact on industrial and biomedical applications.

Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver

An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver (Euler/BL) in a “semi-inverse” manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the computational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics (HIRENASD) Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are significant for these cases and the further data analysis confirms the validity and practicability of the coupled method.