Experimental validation of a viscous-inviscid interaction model Mikaela Lokatt and David Eller Aeronautical and Vehicle Engineering Royal Institute of Technology SE-100 44 Stockholm, Sweden Abstract A combined numerical and experimental study aimed at eval- uating the performance of a relatively recently developed three- dimensional viscous-inviscid interaction model is presented. Nu- merical predictions are compared to experimental data and aspects such as accuracy and computational cost are discussed. An exper- imental study of the flow over a constant chord wing model with a natural laminar flow airfoil profile is performed in order to pro- vide suitable validation data. The experimental wing model is equipped with a trailing edge flap and a significant variation in boundary layer characteristics is observed when the flap deflection and the angle of attack is varied. The experimental results, to which the numerical predictions are compared, include chordwise pressure distributions and oil flow photographs for a range of an- gles of attack and flap deflections. Numerical predictions are also compared to experimental data for a three-dimensional wing-body configuration. A comparison of the chordwise pressure distribu- tions at a number of spanwise locations as well as of integrated force coefficients is made. The numerically predicted skin friction field is also studied, with particular focus on the area near the wing-fuselage junction where a notable interaction between the flow over the wing and the flow over the fuselage is observed. It is found that the flow model can provide relatively accurate predic- tions of boundary layer characteristics and pressure distribution in attached flow fields as well as in flow fields including small to moderate separated flow regions. The computational cost is found to be sufficiently low for the model to be considered to be useful for aircraft design. 1 1 Introduction Prediction of aerodynamic loads is an important part of aerodynamic design and aircraft performance analysis. As such, mathematical models which can provide accurate flow field predictions at a low computational cost are desirable. Because of their relatively high accuracy and rela- tively low computational cost, viscous-inviscid interaction (VII) models have long received interest in aeronautical research [1]. Significant ef- forts aimed at developing two-dimensional, three-dimensional as well as combined two and three-dimensional VII models have been made, see for example [2, 3, 4, 5, 6, 7, 8, 9]. In a relatively recent paper by the present authors [10] the develop- ment of a fully three-dimensional VII model aimed at application to aircraft configurations was described. The model is applicable to three- dimensional geometries discretized by unstructured meshes. In a set of validation cases focusing on the flow over different wing models the VII model has been found to robustly provide relatively accurate predictions of flow field properties in attached as well as mildly separated flow fields including transitional flow [10]. As such, it appears to be promising for use in aeronautical engineering applications. A main purpose of the present study is to perform a thorough evaluation of the performance of the above described flow model [10]. Applications to flow cases with relatively complex boundary layer characteristics as well as to a more complex aircraft-related geometry are considered and comparisons are made to experimental data as well as to predictions of another, two-dimensional, VII model. In particular, an experimental study of the flow over a wing model which has a natural laminar flow airfoil and is equipped with a trailing edge flap has been conducted and is described in some detail. The experimental wing model has interesting boundary layer characteristics. A laminar separation bubble and a trailing edge flow separation are present in some of the flow cases and the transition location varies significantly depending on the angle of attack and flap deflection. The experimental data is considered to be suitable for validation of flow models aimed at prediction of aerodynamic characteristics of laminar flow airfoils, the study of which has received renewed attention in recent years [11]. As such, a main contribution of the present work is that it not only evaluates the accuracy of the present flow model but also presents data which can be useful for 2 validation of other flow models aimed at aeronautical applications. In a second validation study numerical predictions of the present flow model are compared to experimental data for the DLR-F4 model pre- sented by Redeker [12]. The DLR-F4 model is a three-dimensional wing body configuration which was designed to resemble a transport aircraft. As such, this test case allows to evaluate the performance of the VII model when applied to a more complex aircraft-related geometry. The focus is not only on the accuracy of the predictions of the flow model but computational efficiency is also discussed. 2 Flow model The flow model employed in the present study is based on a fully three- dimensional VII model previously developed by the present authors [13, 14, 10]. The inviscid part of the VII model, known as PHI [13], is based on an equation governing potential flow which is discretized by a Galerkin finite-element scheme with linear or quadratic Lagrange elements. It is applicable to subsonic flow cases which may include small pockets of supersonic flow [13]. The viscous part of the VII model is based on a set of three-dimensional integral boundary layer (IBL) equations consisting of the momentum loss equations in two wall tangential directions and an equation for the kinetic energy loss [14, 10]. These are combined with a transition model based on a transport equation for the Tollmien-Schlichting amplification factor [15] as well as with a transport equation for the turbulent shear stress lag [15] intended to account for turbulent non-equilibrium effects. The viscous model is discretized by a finite-volume scheme which is ro- tationally invariant and stabilized by an upwind scheme applicable to hyperbolic and mixed hyperbolic systems [14, 10]. The viscous and inviscid flow models are coupled by velocity and ve- locity gradient terms, defined as first and second order differentials of the potential field variable, as well as with wall transpiration boundary conditions [10]. The coupled VII system is solved by a Newton-based algorithm using a direct coupling scheme [10]. To enable application also to flow cases including separated flow regions the viscous model has been modified to avoid the boundary layer singularity [16, 17], com- 3 monly known as the Goldstein singularity [17]. The numerical stability of the, modified, direct coupling scheme has been illustrated in test cases including both quasi two-dimensional and three-dimensional separated flow [10]. A detailed description of the flow model and its discretization can be found in the papers [13, 14, 10]. In the present study a few updates have been made in order to improve the accuracy, robustness and computa- tional efficiency. These are described in the appendix. 3 Natural laminar flow experiment This section provides a description of an experimental study of a wing model with a natural laminar flow airfoil. In the experimental study both steady and unsteady flow cases have been investigated. The present study presents results from the steady measurements whereas the un- steady part will be discussed in a follow up paper. Also, numerical predictions of the VII model are compared to experimental data as well as to predictions of a two-dimensional VII model. It may be noted that results from an earlier experimental campaign con- cerning measurements performed with the same wing model but with a different experimental setup have been presented in a previous paper [10], where they were used for validation of an earlier version of the three-dimensional VII model. While these experimental results resem- ble the ones presented in this paper, they result from a different set of measurements and, as such, are not the same as the ones presented here. 3.1 Experimental setup The experiment was performed in the low-speed wind tunnel L2000 at the Royal Institute of Technology KTH. The experimental model, shown in Figures 1, 2, consists of a straight, constant chord wing model with the natural laminar flow airfoil profile ED36F128. The model has a span of 2 m and a chord of 0.5 m and is equipped with a trailing edge flap spanning 15 percent of the chord. When deflecting the flap a gap appears along the hinge axis. The gap is covered by a polyester strip, seen as a white line in the figures. On the lower side of the wing model a 4 transition trip is placed at 93 percent of the chord. Regarding the upper side of the wing model, the transition was free in one set of experiments whereas a transition trip was placed at 19% of the chord in another set of experiments. The wing model is mounted vertically on a turntable which can be ro- tated to adjust the angle of attack. Since the same experimental set up was used for both steady and unsteady measurements, the wing model is connected to a mechanism which can be rotated to set the model into a periodic motion. For the steady measurements the mechanism is kept in a constant position. To cover the mechanism, a boundary layer splitter plate is placed 15 cm above the wind tunnel floor. The flap setting is adjusted manually by moving the flap to a desired position where it is clamped by a set of aluminum plates. The wing model and its attachment can deform elastically when sub- jected to aerodynamic loading. As such, both the angle of attack and the flap deflection can vary depending on the flow conditions.