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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.

According to statistics of fatal accidents worldwide for commercial Jet Fleet during the period 2006-2015 presented by Boeing Company Ltd the number of fatalities during landing due to Abnormal Runway Contact (ARC) and Runway Excursion (RE) holds the second place with controlled flight into terrain (CFIT) after the Loss-of-Control in Flight (LOC-I) [

Aircraft aerodynamic characteristics and dynamic behaviour are subjected to changes in proximity to the ground during landing approach and take-off flight [

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) [

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 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.

For evaluation of the ground effect aerodynamics in this study the Common Research Model (CRM) geometry of a generic airliner was selected. The CRM geometry in wing-body-horizontal tail configuration is available on NASA repository for Drag Prediction Workshop [_{ref} = 383.7 m^{2} and C_{ref} = 7 m, the wing has an aspect ratio of AR = 9.0.

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. h = 4 c ¯ , h = 2 c ¯ , h = 1 c ¯ , and h = 0.5 c ¯ . At each altitude h, the grid was adapted for a number of different angles of attack settings α = 4 ∘ , 8 ∘ , 12 ∘ . At altitude h = 0.5 c ¯ additionally a number of bank angle settings was considered ϕ = 4 ∘ , 8 ∘ , 12 ∘ with additional adaptation of the grid.

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.

The Navier-Stokes equations governing incompressible fluid flow are:

∇ ⋅ u = 0 (1)

∂ u ∂ t + ( u ⋅ ∇ ) u − ν ∇ 2 u = − ∇ p / ρ (2)

For the Reynolds numbers typical for industrial applications, the computational resources required for a Direct Numerical Simulation (DNS) of Equations (1) (2) are exceeding the currently available technical capabilities. The effect of turbulence is normally simplified by solving the Reynolds-Averaged Navier-Stokes (RANS) equations, which are the time averaged approximation of Equations (1) (2). The averaging of fluctuating velocities generates additional terms, known as the Reynolds stresses. To describe these stresses the additional empirical equations, generally in the form of partial differential equations are required to close the computational model. The majority of RANS models are based on the concept of an eddy viscosity, equivalent to the kinematic viscosity of the fluid, which describes the turbulent mixing or the diffusion of momentum. For closure, in this study the turbulence k-ω-SST formulation is used [

∂ k ∂ t + ∂ ( u j k ) ∂ x j = P k − β * k ω + ∂ ∂ x j ( μ + σ k μ t ) ∂ ω ∂ t (3)

∂ ω ∂ t + ∂ ( u j ω ) ∂ x j = γ μ t P k − β ω 2 + ∂ ∂ x j ( μ + σ ω μ t ) + D (4)

where turbulent viscosity is defined as:

μ t = a 1 k max ( a 1 ω , Ω F 2 ) (5)

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.

The ground effect aerodynamics was simulated using the steady-state and unsteady solver (U/RANS), closed by the k-ω-SST model for turbulence. Under relaxation is applied for solution of U/RANS equations to increase convergence stability. Second order discretization schemes were used to solve momentum and continuity equations. All scalar variables are solved with the first order accuracy. The residuals for all the equations are allowed to reach a satisfactory convergence of 1/10,000th of the initial values (see

In the case of unsteady simulations at moderately high angle of attack and bank angle, the steady state solution is computed first, which is then used to initialize the unsteady solution to improve the convergence and stability for the unsteady solution.

The simulations were run on a University cluster with 24 processors and the time for convergence for a single point in steady state simulations took an average of 1 - 2 days, while for unsteady simulations it took 4 - 5 days to reach convergence. The average CPU time was about 1.05 min/iteration. Most of the simulations ran from at least 5000 iterations to a maximum of 15,000 iterations.

The results for M = 0.4, Re = 24 million at zero angle of attack is validated against available data obtained at the Netherlands Aerospace Center (NLR)

using their in-house CFD code ENFLOW. The lift coefficient at the above mentioned flight conditions is C_{L} = 0.188 for our simulations and C_{L} = 0.197 for ENFLOW simulations. The variation in the lift coefficient between two codes is about 5% and is subject to many differences such as grid and numerical setup.

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,

Transformations of the wing tip vortices in ground effect produce changes in the aerodynamic forces and moments acting on the aircraft.

The aerodynamic moments are also affected by the bank angle in close proximity to the ground. There is a significant pitching down effect at ϕ = 12 ∘ , i.e. Δ C m = − 0.198 (see _{l} proportionally

decreases with increase of bank angle ϕ , which is acting in a way as a stiff spring. The yawing moment coefficient increases with increase of bank angle until ϕ = 8 ∘ , but decreases with the change of sign at ϕ = 12 ∘ (see

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.

A hybrid model is constructed by combining the wing-body configuration (DLR F11) provided in the 2nd AIAA High Lift Prediction workshop [^{th} of the fuselage length from the nose. The geometry is then also simplified for CFD by cleaning up in terms of topology. Surfaces are further simplified and merged together to automate the ease of blocking with caution such that the authenticity of the model is not lost and the geometry is not violated.

The reference area for this model is 419,130 mm^{2} for the half model and the mean aerodynamic chord length of 347.09 mm is at quarter chord along wing span. The flaps are deflected down at 32 degrees and the slats are deflected down at 26.5 degrees.

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

The gridding also follows the guide lines given by the High Lift Prediction Workshop [_{ref} away from the body in every direction. The grids are intended for the landing conditions of Re = 15.1 million and the same grids are recommended to be used for lower Reynolds tests as well.

Future plans include to run CFD simulations for the ground effect aerodynamics considering the described high-lift configuration with additional objective to evaluate unsteady and rotary aerodynamic derivatives in proximity to the ground and their effect on the lateral-directional stability.

The obtained in CFD simulations dependencies for the aerodynamic coefficients, presented in the previous section, have been used for modification of the full flight simulation model of a typical transport aircraft for conducting 6-DOF simulations in a level trimmed flight in close proximity to the ground. Trim and linearisation procedures have been applied to evaluate aircraft stability conditions and small amplitude modes of motion in the longitudinal and lateral-directional motion. Additionally, the impact of ground proximity on stability of the lateral-direction dynamics is addressed in this section complemented by the eigenvalues analysis for the linearised 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 [

| r ˙ β ˙ p ˙ ϕ ˙ | = [ N r N β N p N ϕ − 1 Y ¯ β 0 g / V L r L β L p L ϕ 0 0 1 0 ] | r β p ϕ | + [ N δ a N δ r 0 0 L δ a L δ r 0 0 ] | δ a δ r | (6)

The new terms in the state matrix of Equation (6) are N ϕ = C n ϕ ( h ¯ ) ρ V 2 S b 2 I z z and L ϕ = C l ϕ ( h ¯ ) ρ V 2 S b 2 I x x . They represent the rolling and yawing accelerations

induced by bank angle ϕ. The ground effect in this case is equivalent to a kind of “aerodynamic roll stiffness”, which will tend to level the airplane above the runway.

In flight away from the ground, when N ϕ = L ϕ = 0 , the lateral-directional modes are defined by the Roll-Dutch complex-conjugate eigenvalues λ D R = − ξ ± ω n 1 − ξ 2 , the roll subsidence eigenvalue λ R and the spiral mode eigenvalue λ S . It is reasonable to represent the ground effect in the form of a root-loci with a parameter indicating variation of the reduced flight altitude h ¯ = h / c ¯ .

The lateral-directional characteristic equation with account of ground effect can be represented in the following form:

( s − λ S ) ( s − λ R ) ( s 2 + 2 ξ ω n + ω n 2 ) D R − L ϕ ( s 2 + a 1 s + a 0 ) G E = 0 (7)

where

a 1 = N ϕ L ϕ L r − N r − Y ¯ β

a 0 = N β − N ϕ L ϕ L β + ( N r − N ϕ L ϕ L r ) Y ¯ β (8)

Parameter L ϕ varies from zero value in flight with no ground effect ( h ¯ = ∞ ) to its maximum value in close proximity to the ground ( h ¯ = 0.5 - 1.0 ). The N ϕ / L ϕ ratio in expressions a_{1} and a_{2} (8) has a weak dependence on reduced altitude h ¯ . So, with increase of parameter L ϕ the eigenvalues will move on the complex plane from their initial values λ D R = − ξ ± ω n 1 − ξ 2 , λ R and λ S toward s the values defined by zeros z_{1}, z_{2} of the second order polynomial equation s 2 + a 1 s + a 0 = 0 and one pair of eigenvalues will migrate to infinity. The location of zeros z_{1} and z_{2} depends on lateral directional coefficients in the expressions for a_{1} and a_{0} (8). These zeros can be located in the left half of the complex plane, being a complex-conjugate pair, or move to the right unstable half of the complex plane creating an opportunity for onset of oscillatory instability due to ground effect, when a_{1} < 0. There is also a possibility for onset of aperiodical instability due to ground effect if a_{0} < 0.

A full flight simulation model of a typical transport aircraft has been modified taking into account the aerodynamic dependencies presented in the previous section for the 6-DOF flight simulations in a level trimmed flight in close proximity to the ground. The ground effect is strong in close proximity to the ground and at the altitude exceeding four mean aerodynamic chords practically vanishes.

The eigenvalues of the linearised equations of motion are presented in

The roll subsidence and spiral eigenvalues in close proximity to the ground

are merging creating the oscillatory Roll-Spiral mode with quite significant frequency ω R S = 0.538 rad / s (see

There are very little changes in the short-period longitudinal eigenvalues, λ S P and practically no changes in the longitudinal phugoid mode, λ P h . In

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

Ground Effect | Short Period (SP) | Phugiod (Ph) | Roll® | Spiral (S) | Dutch Roll (DR) |
---|---|---|---|---|---|

h ( ∞ ) | 0.549 ± 0.742i | 0.012 ± 0.17i | −0.8 | −0.008 | −0.133 ± 1.048i |

h = 0.5 c ¯ | −0.554 ± 0.8i | −0.012 ± 0.17i | −0.344 + 0.538i | −0.344 - 0.538i | −0.2 ± 1.335i |

In crosswind approach-and-landing the aircraft should fly with some nonzero sideslip angle to compensate side-wind. To fly a straight line along the runway the aircraft at the same time should have some non-zero sideslip and bank

angles.

CFD simulation results for evaluation of the ground effect aerodynamics have been obtained for CRM model [

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.

The authors appreciate discussions with test pilot Vladimir Biryukov and are grateful for his comments on crosswind approach-and-landing. His participation in preliminary piloted simulations helped to tune the aerodynamic model to produce realistic results.

Sereez, M., Abramov, N. and Goman, M.G. (2018) Impact of Ground Effect on Airplane Lateral Directional Stability during Take-Off and Landing. Open Journal of Fluid Dynamics, 8, 1-14. https://doi.org/10.4236/ojfd.2018.81001