Linearized potential solution for an airfoil in nonuniform parallel streams

A small perturbation potential flow theory is applied to the problem of determining the chordwise pressure distribution, lift and pitching moment of a thin airfoil in the middle of five parallel streams. This theory is then extended to the case of an undisturbed stream having a given smooth velocity profile. Two typical examples are considered and the results obtained are compared with available solutions of Euler's equations. The agreement between these two results is not quite satisfactory. Possible reasons for the differences are indicated

Studies on the interference of wings and propeller slipstreams

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

A modified lifting line theory for wing-propeller interference

An inviscid incompressible model for the interaction of a wing with a single propeller slipstream is presented. The model allows the perturbation quantities to be potential even though the undisturbed flow is rotational. The governing equations for the spanwise lift distribution are derived and a simple method of solving these is indicated. Spanwise lift and induced drag distribution for two cases are computed

Effect of Out-Gassing on the Onset of Hypersonic Boundary Layer Transition

Prediction and control of the onset of transition and the associated variation in aerothermodynamic parameters in high-speed flows is key to optimize the performance and design of Thermal Protection Systems (TPS) of next-generation aerospace vehicles [1]. Boundary Layer Transition (BLT) characteristics can influence the surface heating budget determining the TPS thickness and consequently its weight penalty. Ablative heatshields are designed to alleviate the high heat flux at the surface through pyrolysis of their polymeric matrix and subsequent fiber ablation [2]. Pyrolysis leads to out-gassing and non-uniform ablation lead to surface roughness, both of which are known to influence the transition process. An ablator impacts BLT through three main routes: gas injecting into the boundary layer from the wall, changing the surface heat transfer due to wall-flow chemical reactions, and modifying surface roughness [3]. In preparation to Mars 2020 mission post-flight analysis, the predictive transition capability has been initiated toward hard-coupling porous material response analysis and aerothermal environment calculation

Extremal primes for elliptic curves without complex multiplication

Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to the Hasse bound. Assuming that all the symmetric power L-functions associated to E are automorphic and satisfy the Generalized Riemann Hypothesis, we give the first non-trivial upper bounds for the number of such primes when E is a curve without complex multiplication. In order to obtain this bound, we use explicit equidistribution for the Sato-Tate measure as in the work of Rouse and Thorner (arXiv:1305.5283) and refine certain intermediate estimates taking advantage of the fact that extremal primes have a very small Sato-Tate measure

The AGN and Gas Disk in the Low Surface Brightness Galaxy PGC045080

We present radio observations and optical spectroscopy of the giant low surface brightness (LSB) galaxy PGC 045080 (or 1300+0144). PGC 045080 is a moderately distant galaxy having a highly inclined optical disk and massive HI gas content. Radio continuum observations of the galaxy were carried out at 320 MHz, 610 MHz and 1.4 GHz. Continuum emission was detected and mapped in the galaxy. The emission appears extended over the inner disk at all three frequencies. At 1.4 GHz and 610 MHz it appears to have two distinct lobes. We also did optical spectroscopy of the galaxy nucleus; the spectrum did not show any strong emission lines associated with AGN activity but the presence of a weak AGN cannot be ruled out. Furthermore, comparison of the H$\alpha$ flux and radio continuum at 1.4 GHz suggests that a significant fraction of the emission is non-thermal in nature. Hence we conclude that a weak or hidden AGN may be present in PGC 045080. The extended radio emission represents lobes/jets from the AGN. These observations show that although LSB galaxies are metal poor and have very little star formation, their centers can host significant AGN activity. We also mapped the HI gas disk and velocity field in PGC 045080. The HI disk extends well beyond the optical disk and appears warped. In the HI intensity maps, the disk appears distinctly lopsided. The velocity field is disturbed on the lopsided side of the disk but is fairly uniform in the other half. We derived the HI rotation curve for the galaxy from the velocity field. The rotation curve has a flat rotation speed of ~ 190 km/s.Comment: Paper contains 14 figures and 4 tables. Figures 8, 10 (color) and 13 supplied separately. Accepted for publication in MNRA

Optical dosimetry tools and Monte Carlo based methods for applications in image guided optical therapy in the brain

Purpose: The long-term goal of this research is to determine the feasibility of using near infra-red light to stimulate drug release in metastatic lesions within the brain. In this work, we focused on developing the tools needed to quantify and verify photon fluence distribution in biological tissue. To accomplish this task, an optical dosimetry probe and Monte Carlo based simulation code were fabricated, calibrated and developed to predict light transport in heterogeneous tissue phantoms of the skull and brain. Empirical model (EM) of photon transport using CT images as input were devised to provide real-time calculations capable of being translated to preclinical and clinical applications. Methods and Materials: A GPU based 3D Monte Carlo code was customized to simulate the photon transport within head phantoms consisting of skull bone, white and gray matter with differing laser beam properties, including flat, Gaussian, and super-Gaussian profiles that are converging, parallel, or diverging. From these simulations, the local photon fluence and tissue dosimetric distribution was simulated and validated through the implementation of a novel titanium-based optical dosimetry probe with an isotropic acceptance and 1.5mm diameter. Empirical models (EM) of photon transport were devised and calibrated to MC simulated data to provide 3D fluence and optical dosimetric maps in real-time developed around on a voxel-based convolution technique. Optical transmission studies were performed using human skull bone samples to determine the optical transmission characteristics of heterogeneous bone structures and the effectiveness of the Monte Carlo in simulating this heterogeneity. These tools provide the capability to develop and optimize treatment plans for optimal release of pharmaceuticals to metastatic breast cancer in the brain. Results: At the time of these experiments, the voxel-based CUDA MC code implemented and further developed in this study had not been validated by measurement. A novel optical dosimetry probe was fabricated and calibrated to measure the absolute photon fluence (mW/mm2) in phantoms resembling white matter, gray matter and skull bone and compared to 3D Monte Carlo simulated data. The TiO2-based dosimetry probe was shown to have superior linearity and isotropicity of response to previous Nylon based probes, and was better suited to validate the Monte Carlo using localized 3D measurement (\u3c 25% systematic error for white matter, gray matter and skull bone phantoms along illumination beam axis up to a depth of 2cm in homogeneous tissue and 3.8cm in heterogeneous head phantom). Next, the transport parameters of the empirical algorithm was calibrated using the 3D Monte Carlo and EMs and validated by optical dosimetry probe measurements (with error of 10.1% for White Matter, 45.1% for Gray Matter and 22.1% for Skull Bone phantoms) along illumination beam axis. Conclusions: The design and validation of the Monte Carlo, the optical dosimetry probe and the Empirical algorithm increases the clinical feasibility of optical therapeutic planning to narrow down the complex possibilities of illumination conditions, further compounded by the heterogeneous structure of the brain, such as varying skull thicknesses and densities. Our ultimate goal is to design a fast Monte Carlo based optical therapeutic protocol to treat brain metastasis. The voxelated nature of the MC and EM provides the necessary 3D photon distribution to within 25% error to guide future clinical studies involving optically triggered drug release