Transonic Navier-Stokes wing solution using a zonal approach. Part 1: Solution methodology and code validation
Abstract : A fast diagonalized Beam Warming algorithm is coupled with a zonal approach to solve the three dimensional Euler/Navier Stokes equations. The computer code, called Transonic Navier Stokes (TNS), uses a total of four zones for wing configurations (or can be extended to complete aircraft configurations by adding zones). In the inner blocks near the wing surface, the thin layer Navier Stokes equations are solved, while in the outer two blocks the Euler equations are solved. The diagonal algorithm yields a speedup of as much as a factor of 40 over the original algorithm/zonal method coded. The TNS code, in addition, has the capability to model wind tunnel walls. Transonic viscous solutions are obtained on a 150,000 point mesh for a NACA 0012 wing. A three order of magnitude drop in the L2 norm of the residual requires approximately 500 iterations, which takes about 45 min of CPU time on a Cray-XMP processor. Simulations are also conducted for a different geometrical wing called WING C. All cases show good agreement with experimental data.
Strake-generated vortex interactions for a fighter-like configuration
A combination of the Euler and thin-layer Navier-Stokes equations were solved for the flowfield around a wing- strake-fuselage configuration similar to the General Dynamics F-16A aircraft. Steady-state solutions were obtained at angles-of-attack ranging from 6 to 10 deg at My = 0.3, 0.6, and 0.9, and Reynolds numbers matching those of wind-tunnel and water-tunnel experiments. The flowfield was divided into multiple blocks using a zoning program and the transonic Navier-Stokes wing-fuselage (TNSWF) solution program, based on an implicit solution algorithm, which updates each subregion of the flowfield sequentially. The total grid contained approximately 300,000 grid points, and clustering was affected normal to all aircraft surfaces. The computed solutions agreed well quantitatively with wind-tunnel pressure distribution data, and they agreed well qualitatively with flow visualization from wind- and water-tunnel tests. OR many years, a goal of computational aerodynamicists has been to compute accurately the fluid flow around highly maneuverable aircraft configurations at transonic speeds. The attainment of this goal requires solving the proper equation set within an adequately fine grid to capture correctly the significant physical flow phenomena. This paper describes the computation of subsonic and transonic flow around a wind-strake-fuselage body, derived from the General Dynam- ics F-16A aircraft. This approach utilizes a combination of the Euler and the thin layer form of the Navier-Stokes equations, for both laminar and turbulent cases. These solutions portray the strake-vortex interaction with the wing flow, and other appropriate flow features at moderate angles of attack. Questions regarding the proper design and employment of strakes and canards were summarized by Peake and Tobak1 and concern the concepts of properly understanding the struc- ture and mechanisms of three-dimensional separations and the resulting vortical development. How these vortical mechanisms react with each other and with boundary layers, especially un- der the influence of shock waves, is critical to both their control and eventual breakdown in transonic flight. There is a need for employing the Navier-Stokes equations, which are computationally expensive and complicated to ap- ply, to complete aircraft configurations. It is required by the design effort to improve maneuvering performance using the nonlinear-type lift generated by a strake (also called leading- edge extension (LEX)) or canard. This inducement of an in- board vortex allows maintainable and controllable lift high above the angles of attack at which a wing, conventionally designed for attached flow, would have stalled. In the recent past, the application of linear and nonlinear panel-type meth- ods has become adequate and cost-effective to solve the neces- sary flowfields for the design of commercial transports over their limited performance range.2-3 Solutions for more exotic geometries have been computed using the nonlinear, full-po- tential equations.4 However, the underlying assumptions of
Effect of superficial gas velocity on the particle temperature distribution in a fluidized bed with heat production
The heat transfer behavior of particles and gas in an olefin polymerization fluidized bed was numerically analyzed using an in-house developed 3-D computational fluid dynamics discrete element model (CFD-DEM). First the implementation of the model was verified by comparing simulation results with analytical results. A constant volumetric heat production rate was implemented in the particle energy equation to mimic the heat production due to the polymerization reaction. It was found that the probability density function (PDF) of the particle temperature becomes more homogeneous with increasing superficial gas velocity. Furthermore, instantaneous snapshots of the thermal driving force (the difference between the single particle temperature and bed-average gas temperature, Tp− ) for different heat production rates provide detailed insight in the particle temperature distribution inside the fluidized bed. The time- and bed-averaged particle convective heat transfer coefficient, which was calculated by Gunn׳s correlation, was found to be independent of the superficial gas velocity. This is explained by the fact that the relative velocity of gas and particles in the emulsion phase, where most of the particles and gas interact, is hardly influenced when increasing the gas superficial velocity. From the spatial distribution of Nusselt number, it becomes apparent that the high heat transfer regions are found in the wake of rising bubbles, whereas low heat transfer rates are found in the clouds of the bubbles.