Boundary Layer Method Research Articles

An inverse integral 3D compressible boundary layer method and coupling with transonic inviscid solution

A new velocity profile, which has a simple expression and agrees well with experimental data in a wide range, is proposed in the present paper. Based on this profile, the governing equations of the 3D compressible inverse boundary layer method are deduced. The steady transonic viscous flow around a 3D wing can be calculated as follows: the inviscid flow is calculated by using nonisentropic full potential equation; the viscous flow is calculated by using present boundary layer method; the viscous and inviscid solutions are coupled by using semi-inverse method. Numerical results agree well with the experimental data and required computer resources are less, so that it has broad prospects in the engineering application.

Three-dimensional application of the Johnson-King turbulence model for a boundary-layer direct method

Abstract The Johnson-King turbulence model[1; AIAA Paper 84-0175 (1984)] as extended to three-dimensional flows was evaluated using a finite-difference boundary-layer direct method. Calculations were compared against the experimental data of the well-known van den Berg-Elsenaar[2; Report NLR-TR-72092U (1972)] incompressible flow over an infinite swept-wing, as well as with some other boundary-layer methods. The Johnson-King turbulence model, which includes the non-equilibrium effects in a developing turbulent boundary layer, was found to significantly improve the predictive quality of a direct boundary-layer method. The improvement was especially visible in the computations with increased three-dimensionality of the mean flow, larger integral parameters and decreasing eddy-viscosity and shear-stress magnitudes in the streamwise direction; all in better agreement with the experiment than simple mixing-length-based methods.

Transonic computational method for an aft-mounted nacelle/pylon withpower effect

A computational method has been developed for computing transonic flows about an aft-fuselage mounted capped-nacelle/pylon configuration with/without propeller power. A hybrid conformal-mapping/transfinite-interpolation scheme is developed to generate body conforming grid systems; a multigrid line-relaxation scheme is applied to solve the potential flowfield; an Euler correction method based on the Clebsch transformation is employed to simulate the power effect; and an inverse boundary-layer method is incorporated to calculate the viscous flows over the pylon and fuselage surfaces. Included are comparisons of the solutions with available test data and the solutions of a panel method. The importance of the fuselage boundary-layer effect on the pylon pressure distribution is studied. The present method has been shown to be reliable, efficient, and general and has been successfully applied to compute a wide range of flow conditions, including those of high angles of attack.

On the application of boundary layer method in the large deflection plastic buckling of a cylindrical shell

Using a cylindrical shell under axial loading as an example, we discuss the possibility of applying the membrane theory together with the boundary layer correction to analyze the large deflection plastic buckling problem. In the cases of fixed ends and simply-supported ends, the conditions to be satisfied for using the boundary layer method (also called the composite-expansion method) are given and discussed.

Defect stream function, law of the wall/wake method for compressibleturbulent boundary layers

The application of the defect stream function to the solution of the two-dimensional, compressible boundary layer is examined. A law of the wall/law of the wake formulation for the inner part of the boundary layer is presented which greatly simplifies the computational task near the wall and eliminates the need for an eddy viscosity model in this region. The eddy viscosity model in the outer region is arbitrary. The modified Crocco temperature-velocity relationship is used as a simplification of the differential energy equation. Formulations for both equilibrium and nonequilibrium boundary layers are presented including a constrained zero-order form which significantly reduces the computational workload while retaining the significant physics of the flow. A formulation for primitive variables is also presented. Results are given for the constrained zero-order and second-order equilibrium formulations and are compared with experimental data. A compressible wake function valid near the wall has been developed from the present results.

Interactive boundary-layer method for unsteady airfoil flows - Quasisteady model

An interactive boundary-layer method previously developed and tested for steady flows is used here in a quasisteady manner to examine the evolution of the flow behavior of airfoils subject to harmonic oscillation and ramp-type motions. The calculations encompass the airfoil and wake flows at angles of attack that lead to separation. The results quantify the effects of the viscous boundary layer and wake on the variation of lift coefficient with angle of attack and reduced frequency. These effects are shown to be large at angles of attack that involve boundary-layer separation.

Calculation of transonic flows with separation past arbitrary inletsat incidence

A method of calculating transonic separated flows past arbitrary inlets at incidence and yaw is presented. The inviscid flow solver is based on the transonic potential equation, which is approximated and solved numerically on a boundary-conforming coordinate system. The multrigrid finite-volume method is used to solve the flow equation. The inviscid flow technique is coupled with an interactive boundary-layer method that uses an inverse formulation to calculate shock-induced separated flows

Motion of two viscous immiscible incompressible liquids in a rotating cylinder

The shape of the interface is determined using the boundary layer method and the position of the center of mass of the liquid and the value of the braking torque exerted by the liquid on the walls of the rotating cylinder are calculated.

The boundary-layer method in the fracture mechanics of composites of periodic structure

The problem of a rectilinear crack in a composite material of doubly — periodic structure is considered. It is assumed that the dimensions of the crack are considerably greater than the cell of material periodicity. A boundary-layer method based on the use of the asymptotic method of averaging periodic structures, taking additional solutions of boundary-layer type /1/ into account to allow the edge effect that occurs near the boundary of the crack outline to be considered, is proposed for analysing the stress field in the neighbourhood of a macrocrack. Analysis of the stress field in highly inhomogeneous (composite) materials with an idealized smooth macrocrack is usually performed by replacing the inhomogeneous composite medium by a certain homogeneous anisotropic medium that is equivalent to the composite material with respect to the average reaction. Such an approach enables the computation of the average stress field in the composite with a macrocrack to be reduced to solving elasticity theory problems for an anisotropic homogeneous material with a mathematical slit. If the material has a periodic structure (as is true of many composites), the average (effective) characteristics of the equivalent should be determined by the method of averaging periodic structures /1–3/ which yields an asymptotically correct approximation to the exact solution of the problem for the initial inhomogeneous medium. The averaging method here allows the local structure of the fields being investigated to be determined with a high degree of accuracy. This approach was used in /4/ to analyse the stress field near a macrocrack in laminar composites of periodic structure. In a number of cases formulas were obtained for the stress intensity factors that express them in terms of the characeristics of the individual composite components and parameters which fix the crack location in the laminar material. A more rigorous approach to the estimation of the state of stress of a composite material with a crack is proposed.

Calculation in the unsymmetrical bending problem of thin plates by spline boundary layer method

The weighted-residual and perturbation methods are usually used to solve the unsymmetrical bending problem of thin plates. Here a mixed method of the weighted-residual and singular perturbation is considered. It is known that there are many ways from which a combination of the two methods can be chosen to obtain numerical solutions which are uniformly valid throughout the region, but they are very different in theory. In this article the main purpose is to give a description of a mixed method for calculation in the unsymmetrical bending problem of plates, so only the singular perturbation problem for the differential equation involving a small parameter in higher derivatives will be discussed. Called the spline boundary layer method for short, boundary layer solutions are constituted with the spline function in order to overcome the difficulties of obtaining the boundary layer solution. An example is given. Not only is the method simple and convenient for computations with a computer, but also the expression for the outer solution is offered simultaneously, and if necessary the expression of the boundary layer solution can also be given without using any complicated matching principle. Therefore the applications of the singular perturbation method in engineering calculations can be expanded.

Defect stream function, law-of-the-wall/wake method for turbulent boundary layers

The application of the defect stream function to the solution of the two-dimensional, incompressible boundary layer problem is reexamined. A law-of-the-wall/law-of-the-wake formulation for the inner part of the boundary layer is presented which greatly simplifies the computational task near the wall and eliminates the need for an eddy viscosity model in this region. The eddy viscosity model in the outer part of the boundary layer is arbitrary. Formulations for both equilibrium and nonequilibrium boundary layers are presented, and results are compared with previous methods for equilibrium boundary layers. A formulation for primitive variables is presented. The present treatments eliminate the need for resolving the flow in the inner part of the boundary layer computationally, thereby improving computational efficiency.

Calculation of laminar separation bubbles in the wake inflation/deflation regime

A new interacting boundary-layer method is developed for calculating two-dimensional incompressible laminar separation bubbles. The method relies on a completely consistent mixed boundary value treatment of the outer inviscid flow. For attached flows, the new method is found to converge as fast as the classical Cauchy-Hilbert method and to yield the same solutions. For separated flows, the new method is found to converge two to three times faster than a comparable Cauchy-Hilbert method. The physical asymptotic theories that underlie this new numerical method will be discussed, in so far as they motivate the method.

A numerical method for treating time-periodic boundary layers

Etude du developpement d'une couche limite laminaire incompressible, pulsatoire sur une plaque plane semi-infinie

Calculation of Flow Over Iced Airfoils

Progress toward the development of a method for predicting the flowfield of an iced airfoil is described and shown to offer the prospect of a priori calculations of the effects of ice accretion and roughness on airfoil performance. The approach is based on interaction of inviscid flow solutions obtained by a panel method and improved upon by a finite-difference boundary-layer method which, operating in an inverse mode, incorporates viscous effects including those associated with separated flows. Results are presented for smooth, rough and iced airfoils as a function of angle of attack. Those for smooth and rough airfoils confirm the accuracy of the method and its applicability to surfaces with roughness similar to that associated with insect deposition and some forms of ice. Two procedures have been developed to deal with large ice accretion and their performance is examined and shown to be appropriate to the engineering requirements.

A solution method for the three-dimensional compressible turbulent boundary-layer equations

SummaryThe development of a new calculation method for compressible 3D boundary layers is described. The method involves a finite-difference discretisation of the governing mean-flow equations. In particular, the differencing scheme used to discretise spanwise derivatives adapts automatically to the sign of the local crossflow within the boundary layer. A plane-by-plane solution procedure in the spanwise direction enables second-order accuracy to be maintained throughout the whole flowfield. A normal coordinate scaling with the local total momentum thickness removes most of the boundary layer growth in computational space. The Cebeci-Smith algebraic turbulence model is used for the initial validation of the calculation method. A simple modification to this model is tested, involving an explicit dependence of the outer eddy viscosity on the crossflow within the boundary layer. There results a significantly improved prediction of the NLR infinite swept wing flow experiment.

A direct viscid-inviscid interaction scheme for the prediction of two-dimensional aerofoil lift and pitching moment in incompressible flow

SummaryThis paper presents a method for assessing two-dimensional aerofoil lift and pitching moment characteristics including trailing edge and gross laminar separation. The model used is a direct viscid-inviscid interaction scheme based on a vortex panel method with boundary-layer corrections and an inviscidly modelled wake. The integral boundary-layer methods adopted behave well in the region of separation and thus, good comparisons with measured separation characteristics are obtained. Generally the predictions of lift and pitching moment may be considered to be within the experimental error, but where this is not the case, the applicability of the modelling technique is discussed.

Analysis of wings with flow separation

An interactive viscous/inviscid procedure has been developed combining a three-dimensional panel method with an inverse finite-difference boundary-layer method. The scheme incorporates both a two-dimensional and a quasi-three-dimensional boundary-layer scheme. The resulting method has been applied to the calculation of the flow over three-dimensional wings and wing/body configurations and it has been shown that the procedure can compute flows with significant regions of boundary-layer separation.

Electrokinetics of concentrated suspensions and porous media: I. Thin electrical double layers

This is a theoretical analysis of electrophoresis and electroosmosis of highly charged unconsolidated porous media (packed beds) or concentrated suspensions, taking into account particle-particle interactions by means of a unit cell model. A boundary layer method is used to derive an analytical expression for electrophoretic or electroosmotic mobility that is valid for thin electrical double layers. The effect of porosity on mobility is shown to be a zeroth order correction to the term that accounts for the relaxation effect. Even moderately concentrated suspensions are affected by this correction. The analysis reduces to the single sphere analysis of O'Brien and Hunter ( Canad. J. Chem., 59, 1878 (1981)) when the porosity tends to unity and to the classical result of Smoluchowski ( Z. Phys. Chem., 93, 129 (1913)) in the limit of very thin double layers for any porosity. In the second paper of this pair the restriction of a thin double layer is relaxed, and an alternate solution is developed.

Finite-difference outer-layer, analytic inner-layer method for turbulent boundary layers

A new turbulent boundary-layer method is developed which models the inner region with the law of the wall, whereas the outer region uses Clauser's eddy viscosity in Matsuno's finite-difference method. The match point between the inner and outer regions, as well as the wall shear stress, is determined at each marching step during the computation. Results obtained for incompressible, two-dimensional flow over flat plates and ellipses are compared with solutions from a baseline method that uses a finite-difference method for the entire boundary layer. Since the present method used the finite-difference method in the outer region only, the number of grid points required was about half that needed for the baseline method. Accurate displacement and momentum thicknesses were predicted for all cases. Skin Friction was predicted well for the flat plate but the accuracy decreased significantly for the ellipses. Adding a wake function to the law of the wall allows some of the pressure gradient effect to be taken into account, thereby increasing the accuracy of the method.

Experimental Investigation of the Three-Dimensional Flow in an Annular Compressor Cascade

A detailed experimental investigation was carried out to examine the influence of blade loading on the three-dimensional flow in an annular compressor cascade. Data were acquired over a range of incidence angles. Included are airfoil and endwall flow visualization, measurement of the static pressure distribution on the flow passage surfaces, and radial-circumferential traverse measurements. The data indicate the formation of a strong vortex near the rear of the blade passage. This vortex transports low-momentum fluid close to the hub toward the blade suction side and seems to be partly responsible for the occurrence of a hub corner stall. The effect of increased loading on the growth of the hub corner stall and its impact on the passage blockage are discussed. Detailed mapping of the blade boundary layer was done to determine the loci of boundary layer transition and flow separation. The data have been compared with results from an integral boundary layer method.