Computational Estimation of Aerodynamic Characteristics of
Airships
ME 399 PROJECT COURSE REPORT
August-November 2013
1 November 2014
Abstract
The Aerodynamics of ZHIYUAN-1 Airship with fin and Gondola has been studied using Reynolds Averaged Navier-Stokes equations. The various aerodynamic characteristics of airship have been successfully studied using overset grids and the computed flight parameters are then compared with the experimental data and are found to be agreeing well for small angle of attacks. The static stability of the airship has also been investigated and the aerodynamic center of the airship has been located as a part of the stability analysis.
1 Introduction
Recent renewed interest in airships with varied applications in the field of advertisement, cargo transport, surveillance, communication systems, extending Internet access in remote areas is the primary motivation for this study. The estimation of aerodynamic characteristics is important for the design of control and propulsion systems of the airship. Airship analysis has traditionally been done using inviscid potential flow methods coupled with boundary layer corrections based on integral momentum methods have been used to estimate the drag coefficient of airships [1-4]. However, the application of these methods is strictly restricted to non-separating flows and flows at zero or small angles of attack. In real-life applications, the airship does encounter flow separation at large angles of attack, both of which have critical influence on the aerodynamic characteristics of the airship. Though some attempts have been made earlier to develop advanced boundary-layer methods, which can capture some flow separation effects [5], their success has been limited to merely capturing some qualitative features of the flow. Previous work carried out by Suman et al. [6] demonstrated estimation of airship aerodynamics using Reynolds Averaged Navier-Stokes (RANS) Equations for only hull case and compared computational results with experimental results of Wang et al. [7] on the ZHIYUAN-1 airship complete with empennage was used for comparison. The present study aims to develop the RANS model for the complete ZHIYUAN-1 airship with Gondola and study its Aerodynamic characteristics by varying the angle of attack from.
2 Method of Approach 2.1 Computational Modeling of the Flow
The governing equations which describe the air flow around the airship are the unsteady Navier-Stokes equations defined as follows: | (1a) | | (1b) |
Where the local velocity, is the grid velocity, p is is the pressure; is the viscous stress tensor which contains both laminar and turbulent stress components, the latter being modeled using a suitable RANS turbulence model, is the body force term and is the density of the fluid. The convective flux in the momentum equation 1(b) is discretized using the second order upwind scheme and the time integration has been carried out using global time stepping, all within the framework of the Star-CCM+ [8] CFD software. Figure 1 shows details of the hybrid mesh consisting of unstructured polyhedral mesh in the vicinity of the airship surface and wake region and unstructured polyhedral mesh in the far-field used in this study. The technique of overset mesh has been used to computationally model the problem.
(a) (b)
(c) (d)
Figure 1: (a) Airship Geometry (b) Surface mesh on the airship (c) Different meshed regions
(d) Prismatic mesh layer near the airship body
Figure 1c. Shows the overset mesh which has been used for the present study and an overlapping region is defined in the background region in which the mesh size is kept nearly the same as the overset mesh for proper interpolation to take place. The computational mesh is refined in the wake region to effectively capture the vortices and wakes emanating aft of the airship. The surface mesh is refined to capture curvature at leading and trailing edge and also at the gondola, hull and fin interfaces to resolve flow physics. A polyhedral mesh is used to mesh fluid domain with prism layer packed around the surface to capture boundary layer effectively. A mesh of 0.7 million cells has been used in this case which consists of background and overset mesh of size 0.4 million and 0.3 million cells respectively.
2.2 Computational Domain and Boundary Conditions
Figure 2 shows the computational domain defined in this problem along with the overset mesh. Since this is an external Aerodynamic flow problem, the far field has been placed at 10 mean aerodynamic chord length away from the body. For the present study a uniform free stream velocity is specified at the upstream boundary and a pressure outlet boundary where the pressure is set at downstream boundary and remaining is set as uniform free stream velocity and the airship surface is modeled as a wall with no slip boundary condition imposed on it. The inlet velocity is taken to be 60.39 m/s with Reynolds number of 2.4 x 106. The various boundary conditions given to the domain are shown in Figure 2.
Figure 2: Computational domain with boundary conditions
3 Results and Discussion
3.1 Grid Convergence Studies
As the part of the computational methodology, initial a mesh dependency study is conducted for the airship at the defined free stream velocity and at 00 angle of attack. Figure 3 shows the variation of drag coefficient (Cd) with number of mesh cells. It can be seen that a mesh consisting of 0.7 million cells is deemed adequate for the final computations reported in this work.
Figure 3: Grid Dependence study
Apart from grid dependency study, the spatial (grid) convergence using Richardson extrapolation to estimate the Grid Convergence Index (GCI) for this study is computed using the approach in Roache [9] by considering three levels of mesh density. The GCI is a measure of the percentage the computed value differs from the value of the asymptotic numerical value and indicates an error band on how far the solution is from the asymptotic value. It indicates how much the solution would change with a further refinement of the grid. A small value of GCI indicates that the computation is within the asymptotic range. The order of convergence, which is defined theoretically for a numerical algorithm, may not remain the same due to boundary conditions, quality of mesh, numerical schemes, etc. Thus an estimate of the order of convergence, p, can be obtained from the results as
| | f | 3 | f | 2 | | | | | | | | | | | | | | | | | | ln | | | | | | | | | | | | | | | | | | | | | | | f 2 f1 | | where f1 | , f2 and f3 ,are the drag coefficients computed on the finest, medium and the coarsest | | p | | | | | | | | | ln r | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | mesh respectively and | r | h1 | | is the ratio of sizing of the mesh on the wing surface. Its value for the finest grid | | | | h2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | f | f | | | | | | | | | | | | | | F | | | | | | | | can be computed using GCI fine | | | | | | where | | 2 | 1 | , and F is a factor of safety, which multiplies the | | | | r p | | 1 | | | f | | | | | | | | | | | | | | | | | | | | | | 1 | | | |
GCI for a more conservative reporting of the error. The Factor of safety (Fs), in the above expression is taken to be 1.25 for the study involving more than three mesh counts. A validation check is carried out to see if the
Solution is well within the asymptotic range of convergence by evaluating ASC = which works out to be 0.98, indicating the solution is in the range of convergence.
3.2 Computed Aerodynamic Characteristics
Figure 4 shows the computed airship aerodynamic characteristics, obtained by varying the angle of attack from 0-30°. The results show good agreement at lower angles of attack in the range of 150 compared with experimental measurements reported in Wang et al. [7]. However results deviate gradually beyond the range of 150. In comparison to experimental results the CFD study first overestimates the drag and lift coefficient and then underestimates it after 15° angle of attack whereas the opposite is true for the moment coefficient. The deviations observed in moment coefficient after 15° is rather larger than the deviations observed in lift and drag.
Considering the use of an approximate RANS turbulence model and lack of actual transition physics in forced transition flow, the deviations at small angle of attack can be deemed acceptable. The reference area and reference length of 0.4416 m2 and 1.8286 m respectively and the temperature is taken to be 25°C to compute the all the aerodynamic coefficients.
(a) (b)
(c)
Figure 4: Comparison of Aerodynamic Coefficients (a) Lift (b) Drag and (c) Pitching Moment Characteristics of the airship.
3.3 Computed Aerodynamic Flow fields
Computed results shown in Fig. 4 shows the variation of different aerodynamic parameters of the airship as the angle of attack changes from 0-30°. Figure 5 compares the computed velocity contours at mid-plane corresponding to 0°, 14° and 30° angle of attack. The wall shear stress in figure 6 shows that its value is close to zero at the stagnation point and it increases along the airship surface which can be explained by the fact that the velocity increases as the fluid flows along the airship surface and hence the free stream velocity increases which results in a higher gradient of velocity near the surface and hence a higher value of wall shear stress. The computed skin friction coefficient along the streamlines in Figure 7 shows that flow separation is taking place at the aft of the airship but the position of the separation is dependent on the angle of attack. The same flow detachment can be seen from the plot of wall shear stress on the airship surface shown in Fig. 6. In Figure 7 the vorticity contours captured on Trefftz plane shows that the vorticity increases as the angle of attack is increased which is also evident from the stream lines in Figure 9. This is theoretically supported by the fact that as the angle of attack is increased the fluid interaction with the airship increases and hence the local spinning of the fluid increases.
(a) (b)
(c)
Figure 5: Velocity contours at angles of attack (a) 0° (b) 14° (c) 30°
(a) (b) (c)
Figure 6: wall shear stress at angle of attack (a) 0° (b) 14° (c) 30°
(a) (b)
(c)
Figure 7: Front and rear view of Skin friction coefficient along the streamlines at angle of attack (b) 14°(c) 30°
(a) (b)
(c)
Figure 8: Vorticity contours on Trefftz plane at angle of attack (a) 0° (b) 14° (c) 30°
(a) (b)
(c)
Figure 9: Stream lines at angle of attack (a) 0° (b) 14° (c) 30°
(a) (b)
(c)
Figure 10: Line Integral Convolution of Velocity vector at Angle of attack (a) 0° (b) 14° (c) 30°
3.4 Longitudinal Static Stability In this section the longitudinal static stability of ZHIYUAN-1 Airship has been inspected. The moment about the center of gravity of the airship has been calculated for various angles of attack varying from 0-30 degrees. For the airship to be longitudinally statically stable it should tend to return towards the initial condition of steady motion whenever slightly disturbed from the trimmed flight[10]. Figure 11 shows the variation of Coefficient of moment about the center of gravity with varying angle of attack. It can be clearly seen from figure 9 that the slope of the graph is positive in the range of 0-25° suggesting that the airship is longitudinally statically unstable in the given range whereas after 25° the slope becomes negative indicating it is statically stable from 25-30°. All the calculations have been done by assuming the center of buoyancy to be at the center of gravity of the airship.
Figure 11: Coefficient of moment about center of gravity vs. Angle of attack 3.5 Aerodynamic center Aerodynamic center plays an important role in the study of stability and control. The force and moment system on a body can be fully specified by the lift, drag and moment acting on the aerodynamic center of the body. In the present study the aerodynamic center has been calculated by an iterative process in which the moment is first calculated at the center of volume and at points before and aft of that point. The general trend of moment is then observed where the slope of the curve, Moment coefficient vs angle of attack, is changing its sign. The same procedure is simultaneously done by taking points above and below the center of volume. The point where the moment coefficient does not change with angle of attack is then obtained by iteratively converging to a point where the slope is nearly zero. Figure 12 shows the moment about the aerodynamic center with the varying angle of attack.
Figure 12: Coefficient of moment vs Angle of attack 4 Conclusion and Future Work
The Reynolds-averaged Navier–Stokes computation has been evaluated for ZHIYUAN-1 airship for hull with fin and Gondola configuration and the results have been compared with available experimental data for varying angle of attack. The computed value of aerodynamic coefficients agree well with experimental data at lower angle of attack but seems to show significant deviation from the experimental date at higher angles of attack. Further, investigation will be carried out to assess the reasons for this deviation and its mitigation. Considering the limitation of RANS turbulence models, improved turbulence models such as LES (large eddy simulation) will be used to predict the aerodynamic behavior at higher angles of attack. Also the longitudinal static stability of the airship has been inspected and it has been found out that the airship is longitudinally statically unstable in the range of 0-25° and becomes stable after 25°. Also further study will be carried out to study the dynamics of the airship by giving 6 Degrees of Freedom to the airship.
References
[1] Shanebrook, J. R., and Sumner, W. J., “Entrainment Theory for Axisymmetric, Turbulent, Incompressible Boundary Layers,” Journal of Hydronautics, Vol. 4, No. 4, 1970, pp. 159–161.
[2] Parsons, J. S., and Goodson, R. E., “Shaping of Axisymmetric Bodies for Minimum Drag in
Incompressible Flow”, Journal of Hydronautics, Vol. 8, No. 3, 1974, pp. 100–107.
[3] Pinebrook, E., and Dalton, C., “Drag Minimization on a body of Revolution Through Evolution”,
Computer Methods in Applied Mechanics and Engineering, Vol. 39, No. 2, 1983, pp. 179–197.
[4] Lutz, T., and Wagner, S., “Drag Reduction and Shape Optimization of Airship Bodies”, AIAA Journal of Aircraft, Vol. 35, No. 3, 1998, pp. 345–351.
[5] Lutz, T., Funk, P., Jakobi, A., and Wagner, S., “Aerodynamic Investigations on Inclined Airship Bodies”,
2nd International Airship Convention and Exhibition, Bedford, U.K., 26–28 July 1998.
[6] Suman, S., Lakshmipathy, S., & Pant, R. S., “Evaluation of Assumed-Transition-Point Criterion in Context
of Reynolds-Averaged Simulations Around Lighter-Than-Air Vehicles”, AIAA Journal of Aircraft, Vol.50. No.2, 2013, pp. 450-456.
[7] Wang, X., Fu, G., Duan, D., and Shan, X., “Experimental Investigations on Aerodynamic Characteristics of the ZHIYUAN-1 Airship”, AIAA Journal of Aircraft, Vol. 47, No. 4, 2010, pp. 1463–1468.
[8] Computational Fluid Dynamics and Multi-physics Engineering Software-STAR-CCM+ Version:8.04.2013 User Manual, CD-Adapco, Lebanon, NH, USA. url: (http://www.cd- adapco.com/products/star-ccm)
[9] Roache, P. J., “Verification and Validation in Computational Science and Engineering”, pp. 107-136. Hermosa Publishers, Albuquerque, NM, USA, 1998.
[10] John D. Anderson, Jr. “INTRODUCTION TO FLIGHT”. pp. 369-374. McGraw-Hill, Third edition.
