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At least 577 records · Page 32

The linearized characteristics method and its application to practical nonlinear supersonic problems

The methods of characteristics has been linearized by assuming that the flow field can be represented as a basic flow field determined by nonlinearized methods and a linearized superposed flow field that accounts for small changes of boundary conditions. The method has been applied to two-dimensional rotational flow where the basic flow is potential flow and to axially symmetric problems where conical flows have been used as the basic flows. In both cases the method allows the determination of the flow field to be simplified and the numerical work to be reduced to a few calculations. The calculations of axially symmetric flow can be simplified if tabulated values of some coefficients of the conical flow are obtained. The method has also been applied to slender bodies without symmetry and to some three-dimensional wing problems where two-dimensional flow can be used as the basic flow. Both problems were unsolved before in the approximation of nonlinear flow.

Ferri, Antonio↗

Two-dimensional laminar incompressible separated flow past airfoils

A method is proposed to treat the problem of steady, two-dimensional, laminar, incompressible high Reynolds number separated flow past thin airfoils. An integral form of the boundary layer equations with interaction is used and the interaction between the inviscid and viscous flow fields is provided for by use of a thin-airfoil integral. Documentation of the attempts at obtaining a solution is presented. A survey of the current state-of-the-art of problems involving viscous-inviscid interactions in flow fields with separation is given.

Plotkin, A.↗

Two-dimensional subsonic compressible flow past elliptic cylinders

The method of Poggi is used to calculate, for perfect fluids, the effect of compressibility upon the flow on the surface of an elliptic cylinder at zero angle of attack and with no circulation. The result is expressed in a closed form and represents a rigorous determination of the velocity of the fluid at the surface of the obstacle insofar as the second approximation is concerned. Comparison is made with Hooker's treatment of the same problem according to the method of Janzen and Rayleight and it is found that, for thick elliptic cylinders, the two methods agree very well. The labor of computation is considerably reduced by the present solution.

Kaplan, Carl↗

Plane and Three-Dimensional Flow at High Subsonic Speeds

For two- and three-dimensional flow in a compressible medium, a simple relation is given by which, to a first approximation, the quantitative influence of compressibility upon the velocities and pressures can be understood in a clear manner. In the application of this relation the distinct behaviors of two-dimensional and axially symmetric three-dimensional flow with increasing Mach number are brought out. For slender elliptic cylinders and ellipsoids of revolution, calculations are made of the critical Mach number; that is, the Mach number at which local sonic velocity is achieved on the body. As a further example, the lifting wing of finite span is considered, and it is shown that the increase of wing lift with Mach number at a given angle of attack is greatly dependent upon the aspect ratio b(exp 2)/F.

Gothert, B.↗

Numerical solution of two-dimensional turbulent blunt body flows with an impinging shock

An implicit finite-difference method has been developed to compute two-dimensional, turbulent, blunt body flows with an impinging shock wave. The full time-averaged Navier-Stokes equations are solved with algebraic eddy viscosity and turbulent Prandtl number models employed for shear stress and heat flux. The irregular-shaped bow shock is treated as a discontinuity across which the Rankine-Hugoniot equations are applied. A Type III turbulent shock interference flow field has been computed and the numerical results compare favorably with existing experimental data. In addition, comparisons are made between the present implicit code and a previous explicit code.

Tannehill, J. C.↗

A low speed two-dimensional study of flow separation on the GA(W)-1 airfoil with 30-percent chord Fowler flap

Measurements of flow fields with low speed turbulent boundary layers were made for the GA(W)-1 airfoil with a 0.30 c Fowler flap deflected 40 deg at angles of attack of 2.7 deg, 7.7 deg, and 12.8 deg, at a Reynolds number of 2.2 million, and a Mach number of 0.13. Details of velocity and pressure fields associated with the airfoil flap combination are presented for cases of narrow, optimum and wide slot gaps. Extensive flow field turbulence surveys were also conducted employing hot-film anemometry. For the optimum gap setting, the boundaries of the regions of flow reversal within the wake were determined by this technique for two angles of attack. Local skin friction distributions for the basic airfoil and the airfoil with flap (optimum gap) were obtained using the razor blade technique.

Seetharam, H. C.↗

Acoustic effects on profile drag of a laminar flow airfoil

A two-dimensional laminar flow airfoil (NLF-0414) was subjected to high-intensity sound (pure tones and white noise) over a frequency range of 2 to 5 kHz, while immersed in a flow of 240 ft/sec (Rn of 3 million) in a quiet flow facility. Using a wake-rake, wake dynamic pressures were determined and the deficit in momentum was used to calculate a two dimensional drag coefficient. Significant increases in drag were observed when the airfoil was subjected to the high intensity sound at critical sound frequencies. However, the increased drag was not accompanied by movement of the transition location.

Shearin, John G.↗

Numerical experiments with flows of elongated granules

Theory and numerical results are given for a program simulating two dimensional granular flow (1) between two infinite, counter-moving, parallel, roughened walls, and (2) for an infinitely wide slider. Each granule is simulated by a central repulsive force field ratcheted with force restitution factor to introduce dissipation. Transmission of angular momentum between particles occurs via Coulomb friction. The effect of granular hardness is explored. Gaps from 7 to 28 particle diameters are investigated, with solid fractions ranging from 0.2 to 0.9. Among features observed are: slip flow at boundaries, coagulation at high densities, and gross fluctuation in surface stress. A videotape has been prepared to demonstrate the foregoing effects.

Elrod, Harold G.↗

Comparison of turbine annulus mass flow computed by one- and two-dimensional analysis

Variations in specific heat ratio, flow angle, critical velocity ratio, swirl distribution exponent, and radius ratio were considered in computing the mass flow. Variations in specific heat ratio had no significant effect and variations in critical velocity ratio had only small effect on computed mass flow between a one- and two-dimensional analysis. All non-free-vortex cases considered showed larger differences in computed mass flow between one- and two-dimensional analysis than for free vortex flow. For the non-free-vortex cases, decreasing radius ratio and increasing flow angle resulted in larger differences in mass flow as computed by the two methods.

Wasserbauer, C. A.↗

A general theory of two- and three-dimensional rotational flow in subsonic and transonic turbomachines

This report represents a general theory applicable to axial, radial, and mixed flow turbomachines operating at subsonic and supersonic speeds with a finite number of blades of finite thickness. References reflect the evolution of computational methods used, from the inception of the theory in the 50's to the high-speed computer era of the 90's. Two kinds of relative stream surfaces, S(sub 1) and S(sub 2), are introduced for the purpose of obtaining a three-dimensional flow solution through the combination of two-dimensional flow solutions. Nonorthogonal curvilinear coordinates are used for the governing equations. Methods of computing transonic flow along S(sub 1) and S(sub 2) stream surfaces are given for special cases as well as for fully three-dimensional transonic flows. Procedures pertaining to the direct solutions and inverse solutions are presented. Information on shock wave locations and shapes needed for computations are discussed. Experimental data from a Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt e.V. (DFVLR) rotor and from a Chinese Academy of Sciences (CAS) transonic compressor rotor are compared with the computed flow properties.

Wu, Chung-Hua↗

A viscous-inviscid interactive procedure for rotational flow in cascades of two dimensional airfoils of arbitrary shape

A viscous-inviscid interactive calculation procedure is developed for application to flow in cascades of two-dimensional airfoils. This procedure has essentially three components. First, a numerical solution of the Eulers equations which can accommodate an arbitrarily specified cascade geometry of the cascade. A method of grid generation has been used which relics in part on a succession of conformal mappings. Second, a viscous solution for use in boundary layers and wake regions was programmed. Finally, an interactive scheme which takes the form of a source-sink distribution along the blade surface and wake centerline is employed. Results were obtained with this procedure for several cascade flow situations, and some comparisons with experiment are presented.

Johnston, W. A.↗

Spatiotemporal periodicity of dislocation dynamics in a two-dimensional microfluidic crystal flowing in a tapered channel

Collective interactions in many-body systems can give rise to unexpected order. Such interactions underlie a wide range of complex phenomena such as swarming in animals and traffic patterns. This work reports an unexpected order in the flow of highly confined and highly concentrated water-in-oil drops, which can be explained and modeled as a soft crystal being extruded in the nanoscale. The findings are important to the understanding of out-of-equilibrium many-body systems, and the flow control of these drops used as microreactors in droplet microfluidics. Furthermore, contrary to the unpredictable microscale crystal deformation process, the discoveries here indicate that nanoscale crystal deformation can be highly ordered and predictable, and imply that the manufacturing of nanocrystalline materials may be easier than perceived.

42 ENGINEERING↗

Non-Diffusive Volume Advection with A High Order Interface Reconstruction Method

We show that non-diffusive volume advection in two-dimensions is achieved with several benchmark problems using a newly developed high-order volume of fluids (VOF) interface reconstruction method. (1) A new VOF interface reconstruction method using circular/corner facets (linear facets are a degenerate case of arcs). We create a circular interface facet in each mixed zone by matching neighbor volume with a hybrid Newton’s-bisection method and the local solution is final. In the general case, the new VOF interface reconstruction has 3rd order accuracy and can be easily made seamless. The new method addresses intrinsic issues with Young’s method such as gaps between interface facets in the case of a curved interface, and inability to define curvature nor identify corners. (2) A non-diffusive volume advection scheme. In an ALE advection step, a well-defined interface can be carried over through a Lagrange step and used to compute volume distribution into a relaxed mesh. Then, an interface reconstruction step is performed to redefine the interface in the relaxed mesh. We must point out that the interface carried over is also a solution of interface reconstruction because all the volume fractions in the relaxed mesh are naturally matched. We provide an interface tracking method compatible with our reconstruction scheme, where it is granted to use the prior info as an initial guess to capture sub-mesh resolution features. As a result, we are able to treat multiple facets inside a single mixed cell and obtain highly accurate, non-diffusive solution for advection problems with rather coarse meshes. We show our solutions for two-dimensional incompressible flows with two materials with a) the X + O diagonal translation; b) the Zalesak rotational test; and c) the single vortex spiral test.

97 MATHEMATICS AND COMPUTING↗