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At least 235 records · Page 13

Fundamental Aerodynamic Investigations for Development of Arrow-Stabilized Projectiles

The numerous patent applications on arrow-stabilized projectiles indicate that the idea of projectiles without spin is not new, but has appeared in various proposals throughout the last decades. As far as projectiles for subsonic speeds are concerned, suitable shapes have been developed for sometime, for example, numerous grenades. Most of the patent applications, though, are not practicable particularly for projectiles with supersonic speed. This is because the inventor usually does not have any knowledge of aerodynamic flow around the projectile nor any particular understanding of the practical solution. The lack of wind tunnels for the development of projectiles made it necessary to use firing tests for development. These are obviously extremely tedious or expensive and lead almost always to failures. The often expressed opinion that arrow-stabilized projectiles cannot fly supersonically can be traced to this condition. That this is not the case has been shown for the first time by Roechling on long projectiles with foldable fins. Since no aerodynamic investigations were made for the development of these projectiles, only tedious series of firing tests with systematic variation of the fins could lead to satisfactory results. These particular projectiles though have a disadvantage which lies in the nature cf foldable fins. They occasionally do not open uniformly in flight, thus causing unsymmetry in flow and greater scatter. The junctions of fins and body are very bad aerodynamically and increase the drag. It must be possible to develop high-performance arrow-stabilized projectiles based on the aerodynamic research conducted during the last few years at Peenemuende and new construction ideas. Thus the final shape, ready for operational use, could be developed in the wind tunnel without loss of expensive time in firing tests. The principle of arrow-stabilized performance has been applied to a large number of caliburs which were stabilized by various means Most promising was the development of a subcaliber wing-stabilized projectile with driving disc (Treibspiegel) where rigid control surfaces extend beyond the caliber of the projectile into the free stream. The stabilized projectiles of full-caliber, wing-stabilized projectiles with fins within the caliber is considerably more difficult. A completely satisfactory solution for the latter has not been found yet.

Kurzweg, Hermann↗

Validation study of RWM stability in DIII-D high- β N plasmas

The n = 1 (n is the toroidal mode number) resistive wall mode (RWM) stability is numerically investigated for two DIII-D high-β N discharges 176440 and 172461, utilizing the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) and MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) codes. Systematic validation efforts are attempted, for the first time, for discharges with very slow or vanishing toroidal flow for a large fraction of the plasma volume. While gaining physics insights in accessing stable operation regime at β N exceeding the Troyon no-wall limit in these slow-rotation experiments, the predictive capability of fluid and non-perturbative magnetohydrodynamic-kinetic hybrid models for the RWM is further confirmed. The MARS-F fluid model, with a strong but numerically tunable viscosity mimicking ion Landau damping of parallel sound waves, finds complete stabilization of the n = 1 RWM in the considered DIII-D plasmas under the experimental flow conditions. Similarly, either full stabilization (for discharge 176440) or marginal stability (for discharge 172461) of the mode is computed by the MARS-K hybrid model, which is first-principle based without free model parameters. In particular, all drift kinetic resonances, including those of thermal and energetic particles, are found to synergistically act to marginally stabilize the RWM in discharge 172461. These MARS-F/K modeling results explain the experimentally observed stable operational regime in DIII-D, as far as the RWM stability is concerned. Extensive numerical sensitivity studies, with respect to the plasma toroidal flow speed as well as the radial location of the resistive wall, are also carried out to further support the validation study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A new concept of stability in orbit propagation, useful for quantifying numerical errors

We present the concept of topological stability in the numerical propagation of orbits, and show how it results in a useful new method for measuring the global numerical error of an orbit propagation. The concept applies to any problem in orbital dynamics. Moreover, it can be extended to any three-dimensional system of di erential equations of second order. In order to assess the topological stability of a given integration a special metric is introduced, which can be used to estimate the numerical errors robustly. The method is particularly well suited for dealing with strongly perturbed and chaotic systems. The construction is based on the constraint imposed by the Hopf map that supports the Kustaanheimo-Stiefel transformation. Generic concepts of stability are translated to KS space.

Pelaez, Jesus↗

Numerical experiments in climate stability.

Two semiempirical climate models are formulated as time-dependent problems in order to study the stability of their asymptotic steady state equilibrium solutions to perturbations in internal (in this case, initial) conditions. For fixed external conditions the time-dependent versions of these models exhibit fully transitive behavior to positive perturbations in initial conditions, slight intransivity to negative perturbations up to -18 K, and an ice-covered earth regime is obtained for extremely large negative perturbations in initial temperatures (below -18 K). The parametrization found to be most critical in these models is the albedo-temperature coupling, especially in tropical regions. The temperature albedo parametrization from an intransitive climate model used in a time-dependent form of one of the preceding models is found to be highly sensitive to negative perturbations in both internal and external conditions. Numerical experimentation with these semiempirical models shows the important role of the tropics in maintaining the equilibrium climate and suggests that the radiation balance in equatorial latitudes might have a controlling influence on the equatorward extent of the polar ice cap.

Schneider, S. H.↗

Solution of the minimum time-to-climb problem by matched asymptotic expansions

Application of singular perturbation techniques to trajectory optimization problems of flight mechanics is discussed. The method of matched asymptotic expansions is used to obtain an approximate solution to the aircraft minimum time-to-climb problem. Outer, boundary-layer, and composite solutions are obtained to zeroth and first orders. A stability criterion is derived for the zeroth-order boundary-layer solutions (the theory requires a form of boundary-layer stability). A numerical example is considered for which it is shown that the stability criterion is satisfied and a useful numerical solution is obtained. The zeroth-order solution proves to be a poor approximation, but the first-order solution gives a good approximation for both the trajectory and the minimum time-to-climb. The computational cost of the singular perturbation solution is considerably less than that of a steepest descent solution. Thus singular perturbation methods appear to be promising for the solution of optimal control problems.

Ardema, M. D.↗

A numerical study of capillary stability in a circular cylindrical container with a concave spheroidal bottom

The paper describes a theoretical investigation of the stability under gravitational and surface forces of a liquid in a circular cylindrical container with a concave spheroidal bottom for the case in which the volume of the liquid is sufficiently small so that the bottom is not covered completely. The gravitational field is assumed to be directed along the symmetry axis of the container, and for a specific container shape the critical Bond number is calculated as a function of liquid volume for contact angles of gamma = 0, 1, 2, and 4 deg. For gamma = 0 deg, some critical equilibrium configurations and corresponding perturbation modes are presented.

Concus, P.↗

Numerical experiments on the stability of controlled shear flows

Three-dimensional, nonlinear simulations are presented for the parallel water boundary layer subjected to pressure gradient, suction, or heating control. The focus is on the secondary instability responsible for the K-type transition. Heating control is found to be the least effective in delaying the secondary instability. Flow-field details (including temperature profiles) are presented for both the uncontrolled boundary layer and the heated boundary layer.

Zang, T. A.↗

A numerical study of flare stabilized projectiles at Mach 7.0

The effect of nose shape on two flare stabilized projectiles was studied using a Parabolized Navier-Stokes code. Pressure coefficients, forces and moments, skin friction coefficients, and Stanton number calculations are presented for the hemisphere-cylinder-flare and the cone-cylinder-flare configurations. Pitching moment and static margin plots versus flare angles and flare lengths are presented in a parametric study to show aerodynamic stability effects. Distinctly different flow field values of pressure, local Mach number, and dynamic pressure were generated by the two different nose configurations. These flow field values just upstream of the flare will be examined. The code demonstrated its value as a design tool by making a clear distinction between aerodynamically stable characteristics for this variety of nose shapes, flare angles, and flare lengths.

Hughson, Montgomery C.↗

CONDIF - A modified central-difference scheme with unconditional stability and very low numerical diffusion

This paper describes a method, called CONDIF, which retains the essential nature of the central difference scheme (CDS) but eliminates the over- and under-shoots. It modifies the CDS by introducing a controlled amount of numerical diffusion based on local gradients. The results obtained for a number of test problems show that the CONDIF is significantly more accurate than the hybrid scheme when the Peclet number is very high and the flow is at large angles to the grid. In the worst case, it yields results similar to those of the hybrid scheme. Though the CONDIF is unconditionally stable, under some conditions the rate of convergence deteriorates as the grid Peclet number is increased. Efforts are currently underway to develop a faster converging variation of CONDIF.

Runchal, Akshai K.↗

Numerical experiments on the stability of controlled boundary layers

Nonlinear simulations are presented for instability and transition in parallel water boundary layers subjected to pressure gradient, suction, or heating control. In the nonlinear regime, finite amplitude, 2-D Tollmein-Schlichting waves grow faster than is predicted by linear theory. Moreover, this discrepancy is greatest in the case of heating control. Likewise, heating control is found to be the least effective in delaying secondary instabilities of both the fundamental and subharmonic type. Flow field details (including temperature profiles) are presented for both the uncontrolled boundary layer and the heated boundary layer.

Zang, Thomas A.↗

A numerical study of the nonlinear thermal stability of solar loops

A time-dependent numerical model is used to investigate the nonlinear thermal stability of static loops of various heights. Simulations show that the instability of a hot state with loop heights of less than about 1000 km is physically significant, with an initially hot atmosphere in low-lying compact loops evolving to an extended atmosphere with temperatures far below 100,000 K. Results also show that high-lying loops are stable to all reasonable perturbations, including those of large initial amplitude and long wavelength. The simulation results suggest that low-lying compact loops should not be common to the sun, and that cool loops with temperatures near 100,000 K must be formed in the cool state initially and cannot evolve from preexisiting loops.

Klimchuk, J. A.↗

Thermal stability during rotation in space - A scaling and numerical analysis

An analysis of thermal stability in a fluid during rotation is presented. The conditions resulting in thermal stability are examined and numerically verified. It is shown that at least one thermal field exists for any rotating fluid, with or without a gravitational background field, where convection does not occur. The numerical model used is fully nonlinear and 3D. Results are presented on the basis of both steady-state and fully transient models. The thermally stable condition is further investigated in the context of the average net acceleration and the inhomogeneous part of the acceleration field (gradient of acceleration). It is shown that in the thermally stable condition the flow that would result from the average net acceleration is equal and opposite to the flow that would result from the inhomogeneous part of the acceleration field. It is concluded that the thermally stable condition is actually a flow mode transition at Ad = 1.

Arnold, William A.↗

Numerical solution of wave equations for the stability of the inner cometo-sheath

Numerical solution of the MHD wave equations for stability of the cometary sheath determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is obtained by using a two-point boundary value method. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary inner sheath as a layer of finite thickness, bounded by the contact surface, i.e., the diamagnetic cavity boundary. The magnetic field structure discovered in the ionosphere of Comets Halley and Giacobini-Zinner is found to be unstable. The effects of finite plasma pressure, dissociative recombination, and mass loading due to photoionization are found to be stabilizing but are unable to quench the instability completely. It is also found that the higher the neutral production rate the lesser is the growth rate for the instability.

Srivastava, Krishna M.↗

Impact of turbulence modeling on numerical accuracy and efficiency of compressible flow simulations

Discussed is the numerical implementation of turbulence models used in viscous compressible flow simulations and their performance described with respect to numerical accuracy, efficiency and stability. The basic approach utilizes the Reynolds-averaged compressible Navier-Stokes equations in which the Reynolds stresses and heat fluxes are mathematically modeled by suitable turbulence models. The turbulence models investigated include zero-, one-, and two-equation eddy viscosity models. The flow fields investigated include theoretical and supersonic flows about two-dimensional and axisymmetric bodies. Discussions concerning the numerical implementation of models include differencing procedures and boundary conditions used to assume numerical stability and accuracy. Numerical performance is also evaluated by comparing computations with experimental results.

Coakley, Thomas J.↗

A numerical study of a marine subtropical stratus cloud layer and its stability

A model for numerical simulation of stratus cloud layers is constructed by combining a second-order closure, turbulent transfer model with a thermal radiative transfer model. The turbulent transfer model allows water vapor saturation. The combined turbulence-radiation model is applied to both a horizontally uniform one-dimensional case and a horizontally nonuniform two-dimensional case. In the latter, the dynamics of mesoscale circulations are also incorporated. Results of the two-dimensional simulation show that the layer cloud instability occurs where the sea surface temperature is high and the large-scale subsidence is weak. The simulated instability is analyzed in view of an instability criterion, the eddy kinetic energy budget, and evaporative cooling near the cloud top.

Moeng, C.-H.↗

Numerical Modeling of a Vortex Stabilized Arcjet

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.

Pawlas, Gary E.↗