Interactive Boundary-layer Approach Research Articles

A One-Dimensional Viscous-Inviscid Strong Interaction Model for Flow in Indented Channels With Separation and Reattachment

A new one-dimensional model is presented for the calculation of steady and unsteady flow through an indented two-dimensional channel with separation and reattachment. It is based on an interactive boundary layer approach, where the equations for the boundary layer flow near the channel walls and for an inviscid core flow are solved simultaneously. This approach requires no semi-empirical inputs, such as the location of separation and reattachment, which is an advantage over other existing one-dimensional models. Because of the need of an inviscid core alongside the boundary layers, the type of inflow as well as the length of the channel and the value of the Reynolds number poses some limitations on the use of the new model. Results have been obtained for steady flow through the indented channel of Ikeda and Matsuzaki. In further perspective, it is discussed how the present model, in contrast to other one-dimensional flow models, can be extended to calculate the flow in nonsymmetrical channels, by considering different boundary layers on each of the walls.

An interactive boundary-layer method for multielement airfoils

A calculation method for the aerodynamic prediction of multielement airfoils based on an interactive boundary-layer approach using an improved Cebeci–Smith eddy viscosity formulation is described. Results are first presented for single airfoils at low and moderate Reynolds numbers in order to demonstrate the need to calculate transition for accurate drag polar prediction and the ability of the improved Cebeci–Smith turbulence model to predict flows with extensive separation, and therefore to predict maximum lift coefficient. Results, in terms of pressure distributions and lift, drag and moment coefficients, are presented for a series of multielement airfoils with flaps and slats. The importance of the compressibility effects and the turbulence model on stall, and, again, the need to calculate the onset of transition, are demonstrated. Finally, recommendations are made for the preferred approach to predicting the aerodynamic performance of multielement airfoils for use as a practical and efficient design tool.

Separation phenomenon in a hypersonic flow with strong wall cooling: Subcritical regime

This paper is concerned with a hypersonic flow past a cooled curved wall. The separation phenomenon at high Reynolds numbers is described using an interactive boundary-layer approach. For a problem of this type, a distinction must be made between two regimes subject to whether the global interaction between the boundary layer and the external flow is strong or weak. This depends on a hypersonic interaction parameter x ∼ MeRe−1/2: if x is small, the interaction is weak; if it is large, the interaction is strong. The present study is applied to a flow with a weak global interaction regime when x → 0. There are three principal motivations for the study. First, the problem of hypersonic boundary-layer separation is obviously of great practical interest. Second, the desire to demonstrate that marginal separation theory (Ruban, 1982; Stewartson et al., 1982) may be successfully applied to the description of a hypersonic flow separation. Third, the interest to verify the theoretical prediction by Smith (1988) of a local breakdown or stall occurring in any interactive boundary-layer solution at a finite value of the controlling parameter.

Steady and unsteady 3-D interactive boundary layers

The paper describes theoretical and computational research on 3-D steady and unsteady flows at medium-to-high Reynolds numbers (Re), aimed at increasing understanding of 3-D separation and boundary-layer transition. Concerning steady 3-D flows first, an interactive-boundary-layer (IBL) formulation for 3-D laminar flow of an incompressible fluid over a surface-mounted obstacle is addressed computationally and compared with other methods at various Re. The computational approach is designed deliberately to capture the extra ellipticity present due to the three-dimensionality, making use of skewed shears in linear quasi-planar sweeps of the boundary layer and local updating in the 3-D interaction law. Results including separation are presented for a range of Re and obstacle heights, together with grid-effect studies, and comparisons are made, first with triple-deck predictions for high Re and, second, with an alternative IBL approach presented in a companion work. The latter and the current work together yield a broad agreement on predictions for the 3-D flow, stretching from the triple-deck through the IBL to thin-layer Navier-Stokes predictions, over a wide range of Re. Second, the computational approach is extended to unsteady 3-D flows, for the triple-deck limit including linear and nonlinear Tollmien-Schlichting waves. Results for small and non-small disturbances and comparisons are presented, showing fairly encouraging agreement between theory, computations and experiments.

Computation of viscous transonic flow over porous airfoils

The viscous effects on transonic flow past an airfoil which contains a shallow cavity beneath a porous surface are studied numerically. The porous region occupies a small portion of the total airfoil surface, and is located near the shock. Both an interactive boundary layer (IBL) algorithm and a thin-layer Navier-Stokes (TLNS) algorithm have been modified for use in studying the outer flow, whereas a stream-function formulation has been used to model the inner flow in the small cavity. The coupling procedure at the porous surface is based on Darcy's law and on the assumption of a constant total presusre in the cavity. In addition, a modified Baldwin-Lomax turbulence model is used to consider the transpired turbulent boundary layer in the TLNS approach, and the Cebeci-Smith turbulence model is used in the IBL approach. According to the present analysis, a porous surface can reduce the wave drag appreciably, but it can also increase viscous losses. As has been observed experimentally, the numerical results indicate that the total drag is reduced at higher Mach numbers and increased at lower Mach numbers when the angles of attack are small. Furthermore, the streamline patterns of passive-shock and boundary-layer interaction are revealed in this study.

An alternative approach to linear and nonlinear stability calculations at finite Reynolds numbers

An extended version of the interactive boundary-layer approach which has been used widely in steady-flow calculations is applied here to the linear and nonlinear stability properties of channel flows and boundary layers in the moderate-to-large Reynolds-number regime. This is the regime of most practical concern. First, for linear stability the agreement found between the interactive approach and Orr-Sommerfeld results remains fairly close even at Reynolds numbers as low as about$\frac{1}{10}$of the critical value for plane Poiseuille flow, or$\frac{1}{5}$for Blasius flow. Secondly, nonlinear unsteady calculations and comparisons with full solutions obtained by enlarging the same method are also presented. Overall the work suggests that, at the finite Reynolds numbers where real interest lies, the dominant physical processes of instability in channel flow and boundary layers are of boundary-layer form, with interaction, and it suggests also an alternative numerical technique for determining those processes. This alternative technique uses the interactive boundary-layer method as the central means for obtaining full unsteady Navier-Stokes solutions.