Method of designing airfoils with prescribed velocity distributions in compressible potential flows
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THEORIES - AIRFOILS↗
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On the circulatory subsonic flow of a compressible fluid past a circular cylinder
The circulatory subsonic flow around an infinite circular cylinder is computed using the linearized pressure-volume relation, by a method developed in a previous report. Formulas and graphs are given for the velocity and pressure distributions, the circulation, the lift, and the dependence of the critical Mach number upon the position of the stagnation point.
FLOW, COMPRESSIBLE-MEASUREMENT↗
On a method of constructing two-dimensional subsonic compressible flows around closed profiles
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FLOW-CONFORMAL TRANSFORMATION↗
Multiplicity of Solutions in Aerodynamics
One of the most striking phenomena which accompany the flow of fluids such as air and water about bodies, is that of changes in character. This phenomena is still very little understood. We will first discuss the nature of these changes and then show that pure theory leads to a multiplicity of characters of flow, among which we will endeavor to indicate those bearing some analogy to experimental results.
AERODYNAMICS↗
On the plane potential flow past a symmetrical lattice of arbitrary airfoils
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FLOW - AIRFOILS↗
A Solution of the Direct and Inverse Potential Problems for Arbitrary Cascades of Airfoils
Methods are given of determining the potential flow plast an arbitrary cascade of airfoils and the inverse problem of determining an airfoil having a prescribed velocity distribution in cascade. Results indicated that Cartesian mapping function method may be satisfactorily extended to include cascades. Numerical calculation for computing cascades by Cartesian mapping function method is considerably greater than for single airfoils but much less than hitherto required for cascades. Detailed results are presented graphically.
PRESSURE DISTRIBUTION - AIRFOILS↗
On rotational conical flow
Some general properties of isoenergetic rotational conical fields are determined. For such fields, provided the physical parameters of the fluid flow are known on a conical reference surface, it being understood that they satisfy certain imposed conditions, it is shown how to construct the hodographs in the various meridional semiplanes, as the envelope of either the tangents to the hodographs or of the osculatory circles.
BODIES - AERODYNAMIC THEORY↗
Extending the Mott–Gurney law to one-dimensional nonplanar diodes using point transformations
Recent studies have applied variational calculus, conformal mapping, and point transformations to generalize the one-dimensional (1D) space-charge limited current density (SCLCD) and electron emission mechanisms to nonplanar geometries; however, these assessments have focused on extending the Child–Langmuir law (CLL) for SCLCD in vacuum. Since the charge in the diode is independent of the coordinate system (i.e., covariant), we apply bijective point transformations to extend the Mott–Gurney law (MGL) for the SCLCD in a collisional or semiconductor gap to nonplanar 1D geometries. This yields a modified MGL that replaces the Cartesian gap distance with a canonical gap distance that may be written generally in terms of geometric scale factors that are known for multiple geometries. We tabulate results for common geometries. Such an approach may be applied to any current density, including non-space-charge limited gaps and SCLCD that may fall between the CLL and MGL.
Garner, Allen L. [Purdue Univ., West Lafayette, IN↗
Inter-image matching
Interimage matching is the process of determining the geometric transformation required to conform spatially one image to another. In principle, the parameters of that transformation are varied until some measure of some difference between the two images is minimized or some measure of sameness (e.g., cross-correlation) is maximized. The number of such parameters to vary is faily large (six for merely an affine transformation), and it is customary to attempt an a priori transformation reducing the complexity of the residual transformation or subdivide the image into small enough match zones (control points or patches) that a simple transformation (e.g., pure translation) is applicable, yet large enough to facilitate matching. In the latter case, a complex mapping function is fit to the results (e.g., translation offsets) in all the patches. The methods reviewed have all chosen one or both of the above options, ranging from a priori along-line correction for line-dependent effects (the high-frequency correction) to a full sensor-to-geobase transformation with subsequent subdivision into a grid of match points.
Wolfe, R. H., Jr.↗
Regularizations of the plane restricted three- body problem.
Simultaneous removal of singularities of plane circular restricted three-body problem by coordinate transformation defined by conformal mapping
CONFORMAL MAPPING↗
Analytical determination of propeller performance degradation due to ice accretion
A computer code has been developed which is capable of computing propeller performance for clean, glaze, or rime iced propeller configurations, thereby providing a mechanism for determining the degree of performance degradation which results from a given icing encounter. The inviscid, incompressible flow field at each specified propeller radial location is first computed using the Theodorsen transformation method of conformal mapping. A droplet trajectory computation then calculates droplet impingement points and airfoil collection efficiency for each radial location, at which point several user-selectable empirical correlations are available for determining the aerodynamic penalities which arise due to the ice accretion. Propeller performance is finally computed using strip analysis for either the clean or iced propeller. In the iced mode, the differential thrust and torque coefficient equations are modified by the drag and lift coefficient increments due to ice to obtain the appropriate iced values. Comparison with available experimental propeller icing data shows good agreement in several cases. The code's capability to properly predict iced thrust coefficient, power coefficient, and propeller efficiency is shown to be dependent on the choice of empirical correlation employed as well as proper specification of radial icing extent.
Miller, T. L.↗
Calculation of transonic potential flowfields about complex, three-dimensional configurations
Methods for extending iterative, finite-difference calculations of transonic potential flowfields to complex three-dimensional configurations are discussed. One particularly attractive approach is to use relatively simple conformal mappings in combination with shearing transformations to generate computational domains that are nearly-conformally mapped from the physical space in one family of coordinate surfaces, and which map the complex boundaries to grid surfaces. The application of such a method to a general wing-body combination or to a multi-bladed fan is discussed. A transformation to map the wing-fuselage or fan-hub combination to a convenient computational domain is proposed. The transformation is useful in its own right for treating the two-dimensional problems of flow past a profile in a wind tunnel or through a cascade. Some results of preliminary calculations are presented.
Caughey, D. A.↗
Conformal mapping for potential flow about airfoils with attached flap.
The conformal mapping sequence presented transforms the potential flow about a circle into that about an airfoil with an attached flap or spoiler. It is found that adequate versatility of the flap shape for a given airfoil can usually be obtained with the indicated functions, although other transformations would expand the variety of possible flap shapes.
Rossow, V. J.↗
On a new method for calculating the potential flow past a body of revolution
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THEORIES-FLOW-KARMAN↗
Logarithmic spiral grids for image processing
A picture digitization grid based on logarithmic spirals rather than Cartesian coordinates is presented. Expressing this curvilinear grid as a conformal exponential mapping reveals useful image processing properties. The mapping induces a computational simplification that suggests parallel architectures in which most geometric transformations are effected by data shifting in memory rather than arithmetic on coordinates. These include fast, parallel noise-free rotation, scaling, and some projective transformations of pixel defined images. Conformality of the mapping preserves local picture-processing operations such as edge detection.
Weiman, C. F. R.↗
Non-Covalent Interactions and Helical Packing in Thiophene-Phenylene Copolymers: Tuning Solid-State Ordering and Charge Transport for Organic Field-Effect Transistors
In this study, we introduce two thiophene-phenylene-thiophene (TPT) polymers designed to leverage noncovalent intramolecular interactions to regulate main-chain conformation and enhance solid-state ordering. By incorporating unsubstituted thiophene (T) or bithiophene (2T) units, we reveal striking divergence in the thermal, morphological, and optoelectronic properties of the resulting films, facilitated by these noncovalent interactions. Using a combination of computational and experimental approaches, we show that annealing yields remarkably different polymer conformations and, consequently, charge transport properties. TPT-T undergoes a significant structural transformation, adopting a more planar backbone conformation and a highly crystalline, edge-on molecular orientation. In contrast, the introduction of a single additional thiophene unit in TPT-2T leads to a more isotropic molecular orientation with a slight preference for face-on alignment, resulting in a heterogeneous film structure that hinders charge transport despite achieving tighter molecular packing. Remarkably, despite being composed of achiral components, TPT-2T develops chirality upon annealing, indicating the formation of a helical conformation. Organic field-effect transistor measurements reveal that the well-ordered alignment in annealed TPT-T films results in higher charge carrier mobility and a narrower distribution of mobility values than in TPT-2T. These findings provide critical insights into the structure−property relationships of conjugated polymers, offering guidance for optimizing molecular design and processing strategies for highperformance organic electronic materials.
36 MATERIALS SCIENCE↗
Analysis of heat transfer for a normally impinging liquid-metal slot jet
A two-dimensional liquid-metal slot jet that is impinging normally against a uniformly heated flat plate is analyzed. The distributions of wall temperature and heat-transfer coefficient are obtained as functions of position along the plate. The liquid-metal assumptions are made that the jet is inviscid and that molecular condition is dominating heat diffusion. The solution is obtained by mapping the jet flow region into a potential plane where it occupies a strip of uniform width. The energy equation is transformed into potential coordinates, and an exact solution obtained in the strip region. Conformal mapping is then used to transform the solution into the physical plane.
Siegel, R.↗
Analysis of impingement heat transfer for two parallel liquid-metal slot jets
An analytical method is developed for determining heat transfer by impinging liquid-metal slot jets. The method involves mapping the jet flow region, which is bounded by free streamlines, into a potential plane where it becomes a uniform flow in a channel of constant width. The energy equation is transformed into potential plane coordinates and is solved in the channel flow region. Conformal mapping is then used to transform the solution back into the physical plane and obtain the desired heat-transfer characteristics. The analysis given here determines the heat-transfer characteristics for two parallel liquid-metal slot jets impinging normally against a uniformly heated flat plate. The liquid-metal assumptions are made that the jets are inviscid and that molecular conduction is dominating heat diffusion. Wall temperature distributions along the heated plate are obtained as a function of spacing between the jets and the jet Peclet number.
Siegel, R.↗