Impact of Ground Effect on Airplane Lateral Directional Stability during Take-Off and Landing

Computational simulations of aerodynamic characteristics of the Common Research Model (CRM), representing a typical transport airliner are conducted using CFD methods in close proximity to the ground. The obtained dependencies on bank angle for aerodynamic forces and moments are further used in stability and controllability analysis of the lateral-directional aircraft motion. Essential changes in the lateral-directional modes in close proximity to the ground have been identified. For example, with approach to the ground, the roll subsidence and spiral eigenvalues are merging creating the oscillatory Roll-Spiral mode with quite significant frequency. This transformation of the lateral-directional dynamics in piloted simulation may affect the aircraft responses to external crosswind, modify handling quality characteristics and improve realism of crosswind landing. The material of this paper was presented at the Seventh European Conference for Aeronautics and Space Sciences EUCASS-2017. Further work is carried out for evaluation of the ground effect aerodynamics for a high-lift configuration based on a hybrid geometry of DLR F11 and NASA GTM models with fully deployed flaps and slats. Some aspects of grid generation for a high lift configuration using structured blocking approach are discussed.


Introduction
According to statistics of fatal accidents worldwide for commercial Jet Fleet after the Loss-of-Control in Flight (LOC-I) [1]. Approach and landing accident reduction (ALAR) is the primary goal of the Flight Safety Foundation (FSF) [2].
It is noted that a better knowledge of flight dynamics in close proximity to the ground can provide increased understanding of the various crosswind handling techniques to increase safety during a crosswind landing [2].
Aircraft aerodynamic characteristics and dynamic behaviour are subjected to changes in proximity to the ground during landing approach and take-off flight [3]. An increase in the lift force, reduction in the amount of induced drag, onset of the pitching down moment requires control actions from the pilot for retrimming aircraft. The above mentioned aerodynamic changes due to ground effect in the aircraft longitudinal dynamics and control are well recognised. Special wind tunnel techniques are used for evaluation of the ground effect in the longitudinal aerodynamic characteristics [4]. An analytical study of the ground effect on the airplane longitudinal stability can be found, for example, in paper [5].
During crosswind landing and take-off the aircraft lateral-directional dynamics can be excited. Aircraft can be approaching and landing with sideslip and nonzero bank angle, this requires leveling aircraft in close proximity to the runway. Therefore the effect of closeness to the ground on the lateral-directional aerodynamic characteristics in such situations should be seriously evaluated. To the best knowledge of the authors, changes in the lateral-directional airplane dynamics due to ground effect have not been addressed in the aeronautical literature and not introduced in the flight simulation practice.
In this paper we approach the above problem by using CFD methods for computational prediction of airplane aerodynamic characteristics in static conditions, when the airplane is flying above the runway with nonzero bank angle. The Common Research Model (CRM) [6] [7] of a generic modern transport airplane was considered in its cruise configuration. The CFD simulations were conducted using ANSYS Fluent and OpenFOAM open source software [8]. Most of the previously reported CFD simulations of aerodynamics in ground effect have been carried out for two dimensional airfoils and low aspect ratio configurations [9] [10] [11] [12].
The ground effect in the CRM aerodynamic forces and moments dependencies has been identified in the CFD simulations and the obtained aerodynamic data were applied for stability and controllability analysis in the lateral-directional airplane motion. The performed dynamic analysis for a typical transport airliner showed transformation of the airplane lateral-directional modes of motion. For example, the roll subsidence and spiral eigenvalues in close proximity to the ground are merging creating the oscillatory Roll-Spiral mode with quite significant frequency. This transformation of the lateral-directional dynamics introduced in piloted simulation may affect the flight simulator motion-cueing and Open Journal of Fluid Dynamics handling quality characteristics. The major factor of the performed ground effect dynamic analysis was the introduction of the rolling and yawing moments dependencies on the airplane bank angle, which was equivalent to the "aerodynamic banking stiffness". The airplane responses to ailerons and rudder control inputs also change in close proximity to the ground.
The formulation of the computational framework and simulation results for CRM ground effect aerodynamics are presented in Section 2. Additionally the preliminary results in grid generation for a high-lift configuration with fully deployed flaps and slats are discussed. Section 3 presents results of dynamic analysis for the lateral-directional motion and also the 6-DOF simulations of the full scale flight simulation model in close proximity to the ground.

Grid Generation
The build topology of the CRM model has been checked and corrected to ensure air tightness on the model surfaces. After this procedure a hexahedral mesh was generated for the full model. A structured mapped blocking approach with appropriate splits and inclusion of O-grids was used to better capture the boundary layer regions on the airplane surfaces.
The blocks initially generated, were transformed through rotations and translations to generate hexahedral unstructured meshes according to flight conditions, i.e. airplane attitude and closeness to the ground. The boundary conditions on the ground were implemented as a moving wall with direction and velocity magnitude of incoming flow and were resolved with inclusion of H-grid layers with appropriate wall distance (Y+<1). The initial meshes were generated for different altitudes above the ground, i.e. The numerical simulations were carried out within reasonable accuracy of a grid between coarse to medium, i.e. about 10 million cells for a full body configuration. This seems suitable for our purpose here to evaluate ground effect.

Governing Equations and Boundary Conditions
The Navier-Stokes equations governing incompressible fluid flow are: For the Reynolds numbers typical for industrial applications, the computa- tum. For closure, in this study the turbulence k-ω-SST formulation is used [13].
where turbulent viscosity is defined as: Far field is assumed at least 100 chord lengths away from the aircraft in x and y direction and +z direction. The -z distance was measured in terms of distance h as it was normal to the ground. A free stream turbulence intensity 0.1% was assumed at the inlet and pressure was discretized to be zero gradient in normal direction at inlet, outlet and the airplane surfaces.

Solver and Numerical Settings
The ground effect aerodynamics was simulated using the steady-state and un- about 5% and is subject to many differences such as grid and numerical setup.

Simulation Results
In close proximity to the ground the airplane wing tip vortices are modified giving a reduced downwash contribution. This leads to increase in the lift force, reduction in the amount of induced drag, onset of the pitching down moment.
For illustration purposes, Figure 4 shows

High-Lift Configuration
The ground effect in aerodynamic characteristics is proportional to the lift force.
For CRM configuration we considered high angle of attack runway approach.
The airplanes are normally approach landing with deployed leading and trailing edge flaps, which produce a high lift at low angles of attack. Hereafter, we present preliminary set up for a high-lift configuration.

Grid Generation
The grid for this particular configuration is structured using Hexa-8 and quad-4 elements. The hexa elements are ideally 8 node elements in 3D space, and 2D quads are 4 node elements. Such a grid is made using blocking and mapping the blocks to the model under consideration. The current mesh contains more than 1500 blocks and hence for complex full flight configurations such as DLR F11 it is difficult to maintain mesh quality in terms of orthogonality, skewness and aspect ratio for such a mesh. This becomes even more difficult when specially applied to the small gaps in between the flaps, slats and the main wing as we need to resolve the boundary layer for each of them separately, but also maintain connectivity in mesh such that they are resolved as a single structure.
However, as seen in Figure 6 and Figure 7 the special blocking allows us to control the boundary layer from flaps, slats and wing without having them collapse each other. This is one of the main advantages of using a structured blocking approach for such configurations along with other benefits such as reduction in cell count, higher quality meshes and more flexible and solvable by matrix solvers as the nodes are in a much regular order.

Airplane Lateral-Directional Dynamics in Close Proximity to the Ground
The obtained in CFD simulations dependencies for the aerodynamic coeffi-

Lateral-Directional Equations
For evaluation of the airplane lateral-directional dynamics in close proximity to the ground the stability-axis lateral-directional equations are considered in the following vector-matrix form (see notations in [16]): The new terms in the state matrix of Equation

Oscillatory Roll-Spiral Mode in Lateral-Directional Dynamics
The lateral-directional characteristic equation with account of ground effect can be represented in the following form: The eigenvalues of the linearised equations of motion are presented in Figure   8 with variation of parameter h . The eigenvalues root-loci shows significant transformation of the lateral-directional modes of motion.
The roll subsidence and spiral eigenvalues in close proximity to the ground Open Journal of Fluid Dynamics There are very little changes in the short-period longitudinal eigenvalues, SP λ and practically no changes in the longitudinal phugoid mode, Ph λ . In Table 1 the eigenvalues for the lateral-directional motion modes for flight at h = ∞ and 1 h c = , are presented for clarity showing a substantial transformation of the lateral-directional dynamics.
The new factor introduced in the performed eigenvalues analysis was the rolling and yawing moments depending on the airplane bank angle, which was equivalent to the "aerodynamic banking stiffness". This "aerodynamic stiffness" is strongly affecting the airplane controllability in close proximity to the ground. The airplane responses to aileron and rudder control inputs obtained in the 6-DOF flight simulation are shown in Figure 9 and      angles. Figure 11 shows the required control pilot inputs in trim flight with steady sideslip 8 α =  , 4 φ =  and 10 β =  . The control inputs are normalised with respect to maximum deflections. One can see that during landing significant retrimming is required in the longitudinal and lateral control channels and thrust control, and less sensitivity is shown in the directional channel.

Concluding Remarks
CFD simulation results for evaluation of the ground effect aerodynamics have been obtained for CRM model [17] in its cruise configuration using Fluent software. The k-ω SST turbulence model and the "moving wall" boundary conditions were utilised to realistically simulate runway boundary layer. The future plans include evaluation of the ground effect aerodynamics for a high-lift configuration F11/GTM using the OpenFOAM software with objective to additionally evaluate unsteady and rotary aerodynamic derivatives in close proximity to the ground and their effect on the lateral-directional stability.
The presented dynamic analysis of the lateral-directional motion modes and controllability during approach-and-landing shows the importance of the ground effect for the improved realism of piloted simulation and estimation of critical crosswinds. The introduced aerodynamic modelling allows improved pilot training on various types of flight simulators.