Numerical Study of Propeller Slipstream Based on Unstructured Dynamic Overset Grids

Based on unstructured hybrid grid and dynamic overlapping grid technique, numerical simulations of Unsteady Reynolds Averaged Navier-Stokes equations were performed and investigation on isolated propeller aerodynamic characteristics and effects of propeller slipstream on turboprops were undertaken. The computational grid consisted of rotational subzone of propeller and stationary major-zone of aircraft, and walls criterion was used in the automatic hole-cutting procedure. Distance weight interpolation and tri-linear interpolation were developed to transfer information between the rotational and stationary subzones. The boundaries of overlapping grids were optimized for fixed axis rotation. The governing equations were solved by dual-time method and Lower Upper-Symmetric Gauss-Seidel method. The method and grid technique were verified by isolated propeller configuration and the computational results were in well agreement with the experimental data. The grid independence was studied to establish the numerical results. Finally, the flow around a turboprop case was simulated and the influence of propeller slipstream was presented by analyzing the surface pressure contours, profile pressure distribution, vorticity contours and profile streamline. It's indicated that the slipstream accelerates and rotates the free stream flow, changing the local angle of attack, enhancing the downwash effects, affecting the pressure distribution on wing and horizontal tail, as well as increasing the drag coefficient, pitching moment coefficient and the slope of lift coefficient.

Numerical Simulation Study on Propeller Slipstream Interference of High Altitude Long Endurance Unmanned Air Vehicle

[Abstract] A method of unstructured dynamic overset grids is developed for the simulation of rotor forward flight flow and unsteady rotor-fuselage interaction aerodynamics. Two overset grids are formed by dividing the initial integral grid into two parts, namely, rotational grid and static grid, and the rotational grid rotates with the rotor while the static grid keep static during the calculating process. Also the hole fringes are formed and donor elements for hole fringe points are founded at the same time when the overset grids are formed. An appropriate overlapped area can be ensured during the unsteady calculation process, and the hole fringe needn’t to be formed repeatedly in this method. A fast searching method is used to update the donor elements, which can reduce the computational effort. The linear spring analogy is used in the rotational grid to calculate the flapping and pitching movement. The unsteady Euler equations are solved using duel time stepping to simulate a two-bladed rotor forward flight flow and Georgia Tech configuration rotor-fuselage interaction flowfield and the calculation results agree well with Experimental data.

Analysis of non-conservative interpolation techniques in overset grid finite-volume methods

The capability of an unstructured hybrid grid method to compute the compressible Navier-Stokes equations is discussed for vortical flows over slender delta wings at low subsonic, high-alpha conditions as a basic study of offdesign aerodynamics of HSCT (High-Speed Civil Transport) configurations. Computations of these flows require high resolutions of the boundary layers on the wing and of the vortical flow region above the wing. The unstructured hybrid grid, which is composed of prismatic grid in boundary layers and tetrahedral and pyramidal grids for the remaining region, is used to treat such viscous flows. The compressible Navier-Stokes equations are solved on the hybrid grid by a cell-vertex, upwind finite volume method. The LU-SGS implicit time integration scheme is used for the convergence acceleration to the steady state. The numerical accuracy of the present method is discussed by comparing with the experimental data of the same configurations. It is demonstrated that the present hybrid grid method is efficient and accurate enough to predict the vortical flow fields over the delta wings. The capability of the method is also shown for a HSCT configuration at a low subsonic, high alpha condition.

The least square-based finite difference-finite volume (LSFD-FV) method has been developed and successfully applied to solve various two-dimensional flow problems with a high-order of accuracy. In this paper, the extension of the LSFD-FV method to the three-dimensional (3D) case on unstructured grids is presented. Different from other existing high-order methods, the LSFD-FV method combines the good features of the least square-based finite difference (LSFD) scheme for derivative approximation and the finite volume (FV) discretization for conservation of physical laws. Within each control cell, a high-order polynomial resultant from a Taylor series expansion is used to approximate the solution in the FV discretization of governing equations, where the derivatives are approximated by the LSFD scheme. As a result, the mesh-free nature of the LSFD scheme endows the LSFD-FV method with the flexibility on unstructured grids. Additionally, the straightforward algorithm of the LSFD scheme and the direct utilization of the Taylor series polynomial make the LSFD-FV method user-friendly and easy to implement. Furthermore, the inviscid and viscous fluxes are simultaneously evaluated by lattice Boltzmann and gas kinetic flux solvers in this work, which avoids additional and complicated treatment for the viscous discretization. Accuracy studies on unstructured hexahedral and tetrahedral grids validate the third-order of accuracy of the 3D LSFD-FV method. Various 3D incompressible and compressible numerical experiments are also presented. The results show that the proposed method enjoys the higher accuracy than the conventional second-order method on the same mesh. When the same accuracy is achieved, the present high-order method has superior computational efficiency to the second-order counterpart.

The standard approach to applying IRK methods in the solution of two-point boundary value problems involves the solution of a non-linear system ofn×s equations in order to calculate the stages of the method, wheren is the number of differential equations ands is the number of stages of the implicit Runge-Kutta method. For two-point boundary value problems, we can select a subset of the implicit Runge-Kutta methods that do not require us to solve a non-linear system; the calculation of the stages can be done explicitly, as is the case for explicit Runge-Kutta methods. However, these methods have better stability properties than the explicit Runge-Kutta methods. We have called these new formulas two-point explicit Runge-Kutta (TPERK) methods. Their most important property is that, because their stages can be computed explicity, the solution of a two-point boundary value problem can be computed more efficiently than is possible using an implicit Runge-Kutta method. We have also developed a symmetric subclass of the TPERK methods, called ATPERK methods, which exhibit a number of useful properties.

The implementation of two different types of turbulence models for a flow solver using the Chimera overset grid method is examined. Various turbulence model characteristics, such as length scale determination and transition modeling, are found to have a significant impact on the computed pressure distribution for a multielement airfoil case. No inherent problem is found with using either algebraic or one-equation turbulence models with an overset grid scheme, but simulation of turbulence for multiple-body or complex geometry flows is very difficult regardless of the gridding method. For complex geometry flowfields, modification of the Baldwin-Lomax turbulence model is necessary to select the appropriate length scale in wall-bounded regions. The overset grid approach presents no obstacle to use of a one- or two-equation turbulence model. Both Baldwin-Lomax and Baldwin-Barth models have problems providing accurate eddy viscosity levels for complex multiple-body flowfields such as those involving the Space Shuttle.

SummaryA robust and efficient dynamic grid strategy based on an overset grid coupled with mesh deformation technique is proposed for simulating unsteady flow of flapping wings undergoing large geometrical displacement. The dynamic grid method was implemented using a hierarchical unstructured overset grid locally coupled with a fast radial basis function (RBF)‐based mapping approach. The hierarchically organized overset grid allows transferring the grid resolution for multiple blocks and overlapping/embedding the meshes. The RBF‐based mapping approach is particularly highlighted in this paper in view of its considerable computational efficiency compared with conventional RBF evaluation. The performance of the proposed dynamic mesh strategy is demonstrated by three typical unsteady cases, including a rotating rectangular block in a fixed domain, a relative movement between self‐propelled fishes and the X‐wing type flapping‐wing micro air vehicle DelFly, which displays the clap‐and‐fling wing‐interaction phenomenon on both sides of the fuselage. Results show that the proposed method can be applied to the simulation of flapping wings with satisfactory efficiency and robustness. Copyright © 2016 John Wiley & Sons, Ltd.

The small disturbance potential flow theory is applied to determine the lift of an airfoil in a nonuniform parallel stream. The given stream is replaced by an equivalent stream with a certain number of velocity discontinuities, and the influence of these discontinuities is obtained by the method of images. Next, this method is extended to the problem of an airfoil in a nonuniform stream of smooth velocity profile. This model allows perturbation velocity potential in a rotational undisturbed stream. A comparison of these results with numerical solutions of Euler equations indicates that, although approximate, the present method provides useful information about the interaction problem while avoiding the need to solve the Euler equations. The assumptions of the classical lifting line theory applied to the wing-slipstream interaction problem are scrutinized. One of the assumptions (uniform velocity in the slipstream) of the classical theory is dropped, and the governing equations are derived for the spanwise lift distribution on a wing in a single axisymmetric slipstream. Spanwise lift and induced drag distributions are obtained for two typical cases, and the effects of nonuniformity in the slipstream velocity profile are examined.

A hybrid Cartesian grid and gridless method for compressible flows

A parallel implicit hole-cutting method based on background mesh for unstructured Chimera grid

Ships sailing in harbour environments will experience four-quadrant manoeuvres, based on the direction of ship velocity and propeller rate. A better understanding of ship hydrodynamics in such manoeuvres will contribute to the navigation safety. Aimed at ships equipped with a conventional single propeller and single rudder, the hydrodynamic performance of a rudder with the engine ahead and astern is studied. The KP505 propeller and NACA 0018 semi-balanced rudder (from the KCS benchmark ship) are selected for numerical studies for extended experimental data published. After validating numerical methods with open-water test data for the single propeller and the single rudder, CFD simulations based on RANS methods are conducted for different advance ratios ahead and astern, with rudder deflections ranging from 0 to 15 degrees. To understand propeller impact on lift and drag forces of the rudder in different working conditions, inflow to the rudder in propeller slipstreams are analysed by extracting the flow field data in different profiles along the rudder span. Streamlines around the rudder and pressure distributions on the rudder surfaces, along with the turbulent kinematic energy distributions and the vortex structures visualised by Q-criterion, are compared to reveal propeller-rudder interaction mechanisms in ahead and astern conditions. The study shows that the propeller rotation mode has a significant impact on rudder inflow patterns, and induced rudder forces change in different trends with propeller loading variations.

and back portion of the airfoil is shown in Figs. 2b and 2c, respectively. The smooth transition of the grid from one type to another and the decency of the grid at sharp corners and between close surfaces are clearly shown, which indicate excellent compatibility and communication between the two grid strategies as controlled by a common background grid. The grid was generated using a Silicon Graphics IRIS 4D/210 VOX workstation. The code's performance is about 360 triangles/s on that workstation and 2350 triangles/s on a Cray Y-MP. The total turnaround time required for generating a grid around a complex geometry, including the setup time, is about 1 h. To examine the fidelity of the grids generated with the present method, a turbulent viscous-flow computation was performed on the grid shown in Fig. 2. The flow solution was obtained with an available node-based, upwind flow solver8 using the BaldwinEarth turbulence model at a Mach number of 0.2, an angle of attack of 16.2 deg, and a Reynolds number of 9 X 106. Comparisons for surface pressure distributions and velocity profiles are shown in Figs. 3a and 3b, respectively. Excellent agreement with experimental data confirms the viability of the generated grid. Concluding Remarks A new method of unstructured viscous grid generation has been introduced. The approach is conceptually simple but powerful, and capable of producing high-quality viscous unstructured grids for complex configurations with ease. Being based on a totally unstructured grid strategy, the method is fully automatic and flexible and, thus, alleviates the difficulties stemming from the structural limitations of the existing structured or semi-unstruct ured techniques. Because of an efficient grid-marching strategy and a simple front-detection algorithm, the method is highly efficient and operational on small workstations. The method is also self-sufficient for insertion of grid points in the boundary layer and beyond. The method has been applied to two-dimensional problems with satisfactory results. The basic elements of the technique, however, have been primarily designed for its subsequent extension for generating three-dimensional highly stretched tetrahedral grids which is currently in progress. The full benefit of the method will be realized for generation of three-dimensi onal viscous grids where the complexity of the problem becomes excessive.

An adaptive finite volume method for the simulation of time-dependent, viscous flow is presented. The Navier–Stokes equations are discretized by central schemes on unstructured grids and solved by an explicit Runge–Kutta method. The essential topics of the present study are a new concept for a local Runge–Kutta time-stepping scheme, called multisequence Runge–Kutta, which reduces the severe stability restriction in unsteady problems, a common grid generation and adaptation procedure and the application of dynamic grids for capturing moving flow structures. Results are presented for laminar, separated flow around an aerofoil with a flap.