# L1T2 3 element airfoil

## Introduction

The UK National High Lift Programme (NHLP) was a collaborative project carried out in the 1970s between DERA and BAE SYSTEMS (RAE and BAC at the time). A range of models was tested including a 3-D half model, a swept panel wing, a quasi-2-D (end plate) model and a truly 2-D model. A comprehensive set of well analysed and understood data exist for the last of these. Measurements carried out by Moir [1] at low subsonic conditions are available for a 2D wing of supercritical aerofoil section for three different high lift device configurations. Surface pressures together with lift, drag and pitching moment (obtained by integrating surface pressures) are available. The momentum deficit in the wake was measured by a pitot-static traverse. In addition, information on boundary layer and wake development and their interactions was provided by pitot-static traverses normal to the wing at various chordwise locations. All measurements are available in the form of an AGARD dataset.

This application challenge is focussed on one of the 2D high lift configurations (The L1T2 test case). The L1T2 case is a 3 element aerofoil consisting of a main element, a slat forward of the main element (deflection angle ${\displaystyle 25^{0}}$), and a Fowler flap aft of the main element (deflection angle ${\displaystyle 20^{0}}$). See Figure 1. Measurements were made at two incidences, one at a low angle of attack and one close to maximum lift.

QinetiQ has provided computations for the L1T2 test case on a multi-block mesh using the BAE SYSTEMS RANSMB flow solver with a ${\displaystyle k-g}$ turbulence model.

## Relevance to Industrial Sector

The optimal design of high lift devices for take-off and landing conditions is an important and challenging problem for the aircraft industry. Difficulties are caused by the geometrical complexity and the flow physics modelling. The flow field around a multi element aerofoil is dominated by viscous flow phenomena such as strong interactions between wakes from upstream elements with boundary layers on elements downstream, flow separation, streamline curvature effects and adverse pressure gradients. It is a challenging task for a turbulence model to predict correctly the turbulent boundary layer development, flow in the wake, and in regions where wake and boundary layer interact. Poor modelling of these regions of the flow can lead to inaccurate prediction of wing loads and inaccurate prediction of flow separation. It is crucial for a CFD method to be able to accurately model these effects and flow features in order to give useful estimates of aerodynamically relevant quantities such as maximum lift.

## Design or Assessment Parameters

The DOAPs for this test case are lift/incidence and lift/drag polars, boundary layer and wake profiles, and pressures on the surface and in the wake. However, only surface pressures and total pressure profiles normal to the wing surface at four chordwise locations are compared in this document. The four chordwise locations are defined in section 2.1. The surface pressure coefficients and total pressure coefficients are defined as follows:-

${\displaystyle C_{p}={{P-P_{\infty }} \over {{1 \over 2}\rho _{\infty }Q_{\infty }^{2}}}}$

${\displaystyle C_{p_{tot}}={{P_{tot}-P_{\infty }} \over {{1 \over 2}\rho _{\infty }Q_{\infty }^{2}}}}$

where ${\displaystyle \rho _{\infty }}$, ${\displaystyle P_{\infty }}$ and ${\displaystyle Q_{\infty }}$ are the free-stream density, pressure and speed respectively.

The total pressure is defined as:

${\displaystyle P_{tot}=P{\left(1+{1 \over 2}(\gamma -1)M^{2}\right)}^{\gamma \over {\gamma -1}}}$

Where M is the Mach number and ${\displaystyle \gamma }$ is the ratio of specific heat capacities (1.4 for air).

## Flow Domain Geometry

Figure 1 shows a picture of the L1T2 profile. It consists of a main element, slat and flap. The main element comprises a BAC 3-11/RES/30/21 section and the overall chord of the assembly with all elements retracted is 0.7635m. The thickness/chord ratio is 11% and the leading edge radius is r/c=0.0137. The AGARD reported measurements were taken with slat and flap deployed at deflection angles of ${\displaystyle 25^{0}}$ and ${\displaystyle 20^{0}}$ respectively. The geometry is available in electronic form on a disk supplied by AGARD. However, a better resolution of the geometry is available here (slat.dat, main.dat and flap.dat). The model was mounted between turntables on the floor and the roof of the BAC 3.96m x 2.74m low-speed wind tunnel. The length of the test section is 6.35m and the corner fillets measure approximately 0.762m x 0.762m. Local suction was applied at the wing roots to ensure that the flow was essentially two-dimensional. For the purposes of CFD computations presented here, the flow was assumed to be two-dimensional and the domain unbounded. The x-coordinate is in the stream wise direction.

## Flow Physics and Fluid Dynamics Data

The L1T2 configuration was tested at a Mach number of 0.197, and a Reynolds number of 3.52x106 (based on retracted chord). The model was tested at angles of incidence (corrected) of 4.01° and 20.18°. Transition was fixed on the main element upper and lower surface at 12.5% of the retracted chord. However, at high lift, transition on the upper surface is forward of the transition fix due to a short laminar bubble close to the leading edge.

The main flow physics is characterised by strong interactions between the turbulent boundary layers and wakes of the slat/wing/flap elements. The interaction between a wake and a downstream boundary layer can lead to boundary layer thickening and separated flow. The flow is considered to be two-dimensional.

Figure 1 Geometry of the L1T2 Multi Element Aerofoil.