Concave Target Research Articles

A new MM algorithm for root‐finding problems

The minorization–maximization (MM) algorithm is an optimization technique for iteratively calculating the maximizer of a concave target function rather than a root–finding tool. In this paper, we in the first time develop the MM algorithm as a new method for seeking the root of a univariate nonlinear equation . The key idea is to transfer the root–finding issue to iteratively calculate the maximizer of a concave target function by designing a new MM algorithm. According to the ascent property of the MM algorithm, we know that the proposed algorithm converges to the root and does not depend on any initial values, in contrast to Newton's method. Several statistical examples are provided to demonstrate the proposed algorithm.

Experimental and numerical investigation of jet impingement cooling onto a rib roughened concave internal passage for leading edge cooling of a gas turbine blade

Considered is thermal protection of the concave surface within an internal passage, which models the leading edge cavity of vanes or blades of stationary or aero engine gas turbines. Included along the internal surface are different arrangements of V-shaped ribs to further augment surface cooling heat transfer rates. Impingement jets are employed for the cooling, which are configured so that associated cooling air exits the cavity through a crossflow outlet and an array of staggered film cooling holes. The curved part of the asymmetric, concave target plate features a constant radius and connects to straight lines on the pressure and suction sides. Addressed are H/Djet values of 2.7 and 4.0, and Reynolds number Re values of 18,000, 24,000, and 30,000. A maximum crossflow configuration is utilized wherein the coolant flow exits the cooling passage through the film cooling holes and from one end of the passage, as the opposite end is blocked. Different surface configurations are investigated, including 4 V-ribs in four different positions, 8 V-ribs in one position, and a smooth surface of the leading edge cavity. Each V-rib geometry consists of a regular V-rib pointing upstream. A transient thermochromic liquid crystal (TLC) technique is employed to obtain spatially-resolved surface heat transfer data on the internal wall of the leading edge cavity. Resulting experimental heat transfer data are used to validate and verify CFD simulations. Employed for this purpose are steady-state 3D RANS simulations obtained using the OpenFOAM Version 7 numerical code with a kω-shear-stress-transport (SST) turbulence model. Experimentally-measured surface Nusselt number results indicate significant local enhancements adjacent to rib wakes, provided local crossflow velocity values are substantial. Local surface Nusselt number enhancements thus depend upon rib position, but local surface heat transfer increases are most strongly tied to magnitudes of local crossflow velocity. In contrast to these experimental results, CFD simulation results do not show significant variations as rib position is altered. The best thermal performance is associated with 4 V-rib arrangements in two positions, and 8 V-ribs in one position.

Accurate Microwave Imaging of Concave Targets Based on High-Order Scattering Separation Using Modified Complex Exponential Model

Accurate Microwave Imaging of Concave Targets Based on High-Order Scattering Separation Using Modified Complex Exponential Model

Heat transfer in a rotating impingement cooling channel with concave target surface

Jet impingement cooling is a common technique for cooling the leading edge of turbine blades that experience high thermal loads. This study examines the effect of rotation on jet impingement cooling by conducting experiments in a rotating channel with a concave target surface. The dimensionless parameters of the jet configuration are 3 for both jet-to-jet spacing and jet-to-target surface spacing. The jet rotation number and jet buoyancy number reach a maximum of 0.26 and 0.63, respectively. The jet Reynolds number ranges between 5,000 and 15,000. The results show that a large vortex is generated in the supply channel due to the Coriolis force, which changes the mass-flowrate distribution in each jet hole. Therefore, the heat transfer in both ends increases while that in the middle region decreases, resulting in a U-shaped heat transfer distribution in the radial direction. In addition, the rotational Coriolis force is the dominant factor that affects the rotating jet impingement cooling, while the buoyancy force can affect heat transfer at high rotation numbers. The rotation-to-stationary Nusselt number ratio is defined to separate the effects of the Reynolds number, thus, the heat transfer correlations are developed between Nusselt number ratio and rotation number.

A simulation method on target strength and circular SAS imaging of X-rudder UUV including multiple acoustic scattering

Target strength (TS) and circular synthetic aperture sonar (CSAS) images provide essential information for active acoustic detection and recognition of non-cooperative unmanned undersea vehicles (UUVs), which pose a significant threat to underwater preset facilities. To access them, we propose an iterative physical acoustics (IPA)-based method to simulate the multiple acoustic scattered fields on rigid surfaces in high-frequency cases. It uses the Helmholtz integral equation with an appropriate Green's function in terms of the Neumann series, and then incorporates the ideas of triangulation and iteration into a numerical implementation. Then two approximate analytic formulae with precise physical meanings are derived to predict the TS and CSAS images of concave targets, respectively. There are no restrictions on the surface's curvature and the order of multiple scattering. The method is validated against the finite element method (FEM) for acoustic scattering from a sphere segment and against an experiment involving an X-rudder UUV's stern. On this basis, we simulate and analyze the TS and CSAS images of an X-rudder UUV. In addition, the influence of the angle of adjacent rudders on the multiple scattering characteristics is discussed. Results show that this method can potentially predict accurate UUV features, especially the multiple scattered features.

On L 𝔮 convergence of the Hamiltonian Monte Carlo

Abstract We establish L 𝔮 {L^{\mathfrak{q}}} convergence for Hamiltonian Monte Carlo (HMC) algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 ≤ 𝔮 < ∞ {2\leq\mathfrak{q}<\infty} and weakly for 1 < 𝔮 < 2 {1<\mathfrak{q}<2} ) to the desired target distribution. In addition, we establish a general convergence rate for an L 𝔮 {L^{\mathfrak{q}}} convergence given a convergence rate at a specific q * {q^{*}} , and apply this result to conclude geometric convergence in the Euclidean space for HMC with uniformly strongly logarithmic concave target and auxiliary distributions. We also present the results of experiments to illustrate convergence in L 𝔮 {L^{\mathfrak{q}}} .

Predictive modeling of drop impact force on concave targets

Impacting drops are ubiquitous and the corresponding impact force is their most studied dynamic quantity. However, impact forces arising from collisions with curved surfaces are understudied. In this study, we impact small cups with falling drops across drop Reynolds number 2975–12 800, isolating five dominant parameters influencing impact force: drop height and diameter, surface curvature and wettability, and impact eccentricity. These parameters are effectively continuous in their domain and have stochastic variability. The unpredictable dynamics of the system incentivize the implementation of tools that can unearth relationships between parameters and make predictions about impact force for parameter values for which there is not explicit experimental data. We predict force due to the impacting drop in a concave target using an ensemble learning algorithm comprised of four base algorithms: a random forest regressor, k-nearest neighbor, a gradient boosting regressor, and a multi-layer perceptron. We train and test our algorithm with original experimental data comprising 387 total trials using four cup radii with two wetting conditions each. Our approach permits the determination of relative importance of the input features in producing impact force and force predictions which can be compared to scaling relations modified from those for flat targets. Algorithmic predictions indicate that deformation of the drop and surface wettability, often neglected in scaling for impact force on flat surfaces, are important for concave targets. Finally, our approach provides another opportunity for the application of machine learning to characterize complex systems' fluid mechanics for which experimental variables are numerous and vary independently.

Numerical study on flow and heat transfer characteristics of swirling jet on a dimpled surface with effusion holes at turbine blade leading edge

• The combined effect of the jet offset ( e/d ) and dimpled target surface on heat transfer of swirling flow are investigated. • Spherical dimples (SDs) and oval-trench dimples (OTDs) in an in-line and staggered arrangement are considered. • The thermal-hydraulic performance of the target chamber demonstrates a maximum improvement of 24%. • Under the same e/d , the OTD structure is superior to the SD structure. In this paper, a numerical study has been conducted on the effect of the offset of jet holes on the flow structure and heat transfer of swirling flow in a concave target chamber with various dimple structures and effusion holes at the turbine blade leading edge. The ratio of jet holes off the centerline distance to jet hole diameter (e/d) varies from 0 to 2.0, and the ratio of jet-to-target plate spacing to jet diameter (H/d) is 4. The effusion hole diameters of 0.5d are arranged in a staggered pattern relative to the jet holes. Four types of dimple structure with a large depth ratio (δ/D) of 0.25, including spherical dimples (SDs) and oval-trench dimples (OTDs) in an in-line and staggered arrangement, are considered. The heat transfer characteristic and pressure loss of the different leading-edge are evaluated and compared at a Reynolds number of 30,000 based on the jet hole diameter. The results show that the offset of the jet holes provides 15%-higher overall heat transfer performance and more uniform heat transfer of the target surface, while having little impact on the friction factor within the e/d range of 0–2.0. The introduction of the dimple structures on the target surface decreases the overall averaged Nusselt number but enhances the total heat transfer rate from the target chamber due to the clear increase of heat transfer areas, for which a maximum of a 24% improvement of the thermal-hydraulic performance is obtained for e/d = 2.0 with OTDs in a staggered arrangement. Under the same e/d, the OTD structure, especially with the staggered arrangement, is superior to the SD structure.

Design of arbitrarily shaped acoustic cloaks through partial differential equation-constrained optimization satisfying sonic-metamaterial design requirements

We develop an optimization framework for the design of acoustic cloaks, with the aim of overcoming the limitations of usual transformation-based cloaks in terms of microstructure complexity and shape arbitrarity of the obstacle. This is achieved by recasting the acoustic cloaking design as a nonlinear optimal control problem constrained by a linear elliptic partial differential equation. In this setting, isotropic material properties’ distributions realizing the cloak take the form of control functions and a system of the first-order optimality conditions is derived accordingly. Such isotropic media can then be obtained in practice with simple hexagonal lattices of inclusions in water. For this reason, the optimization problem is directly formulated to consider suitable partitions of the control domain. Two types of inclusions are analysed, and long-wavelength homogenization is used to define the feasible set of material properties that is employed as a constraint in the optimization problem. In this manner, we link the stage of material properties optimization with that of microstructure design, aiming at finding the optimal implementable solution. The resulting cloak is numerically tested via coupled structural/acoustic simulations. As a further test benchmark, a concave target and the silhouette of a ship are considered other than the usual axisymmetric cloak.

Combined proton–photon treatment for breast cancer

Objective. Proton therapy remains a limited resource due to gantry size and its cost. Recently, a new design without a gantry has been suggested. It may enable combined proton–photon therapy (CPPT) in conventional bunkers and allow the widespread use of protons. In this work, we explore this concept for breast cancer. Methods. The treatment room consists of a LINAC for intensity modulated radiation therapy (IMRT), a fixed proton beamline (FBL) with beam scanning and a motorized couch for treatments in lying positions with accurate patient setup. Thereby, proton and photon beams are delivered in the same fraction. Treatment planning is performed by simultaneously optimizing IMRT and IMPT plans based on the cumulative dose. The concept is investigated for three breast cancers where the goal is to minimize mean dose to the heart and lung while delivering 40.05 Gy in 15 fractions to the PTV with a SIB of 48 Gy to the tumor bed. The probabilistic approach is applied to mitigate the sensitivity to range uncertainties. Results. CPPT is particularly advantageous for irradiating concave target volumes that wrap around a curved chest wall. There, protons may deliver dose to the peripheral and medial parts of the target volume including lymph nodes. Thereby, the mean dose in normal tissues is reduced compared to single-modality IMRT. However, tangential photon beams may treat parts of the target volume near the interface to the lung. To ensure target coverage for range undershoot in an IMPT plan, proton beams have to deliberately overshoot into the lung tissue—a problem that can be mitigated via the photon component which ensures plan conformity and robustness. Conclusion. CPPT using an FBL may represent a realistic approach to make protons available to more patients. In addition, CPPT may generally improve treatment quality compared to both single-modality proton and photon treatments.

Numerical study on heat transfer characteristics of swirling flow on dimpled surfaces with effusion holes at turbine blade leading edge

In this paper, we conducted a numerical study to investigate the effect of the offset of the jet holes on heat transfer of swirling flow in a concave target chamber with various dimple structures and effusion holes at the turbine blade leading edge. The distance of the jet holes off the centerline e/d varies from 0 to 2.0. Four types of dimple structure, including spherical dimples (SDs) and oval-trench dimples (OTDs) in the inline and staggered arrangement, are considered. The heat transfer performance of the different leading-edge, impingement-effusion cooling structures is evaluated and compared at a Reynolds number of 30,000 based on the jet hole diameter. Results show that the offset of the jet holes provides 15% higher overall heat transfer performance and more uniform heat transfer of the target surface within the e/d range of 0-2.0. The introduction of the dimple structures on the target surface slightly decreases the overall averaged Nusselt number but enhance the heat transfer quantity due to the clear increase of heat transfer areas. Under the same e/d, the OTD structure, especially with the staggered arrangement, is superior to SD structure.

Large-Eddy Simulation Study of Flow and Heat Transfer in Swirling and Non-Swirling Impinging Jets on a Semi-Cylinder Concave Target

Swirling impinging jet (SIJ) is considered as an effective means to achieve uniform cooling at high heat transfer rates, and the complex flow structure and its mechanism of enhancing heat transfer have attracted much attention in recent years. The large eddy simulation (LES) technique is employed to analyze the flow fields of swirling and non-swirling impinging jet emanating from a hole with four spiral and straight grooves, respectively, at a relatively high Reynolds number (Re) of 16,000 and a small jet spacing of H/D = 2 on a concave surface with uniform heat flux. Firstly, this work analyzes two different sub-grid stress models, and LES with the wall-adapting local eddy-viscosity model (WALEM) is established for accurately predicting flow and heat transfer performance of SIJ on a flat surface. The complex flow field structures, spectral characteristics, time-averaged flow characteristics and heat transfer on the target surface for the swirling and non-swirling impinging jets are compared in detail using the established method. The results show that small-scale recirculation vortices near the wall change the nearby flow into an unstable microwave state, resulting in small-scale fluctuation of the local Nusselt number (Nu) of the wall. There is a stable recirculation vortex at the stagnation point of the target surface, and the axial and radial fluctuating speeds are consistent with the fluctuating wall temperature. With the increase in the radial radius away from the stagnation point, the main frequency of the fluctuation of wall temperature coincides with the main frequency of the fluctuation of radial fluctuating velocity at x/D = 0.5. Compared with 0° straight hole, 45° spiral hole has a larger fluctuating speed because of speed deflection, resulting in a larger turbulence intensity and a stronger air transport capacity. The heat transfer intensity of the 45° spiral hole on the target surface is slightly improved within 5–10%.

Inverse ray tracing on icosahedral tetrahedron grids for non-linear laser plasma interaction coupled to 3D radiation hydrodynamics

A novel approach to efficiently model 3-D laser plasma interactions at fluid scales is presented. This method, implemented in the IFRIIT propagation code developed at CELIA, relies on inverse ray tracing to compute laser fields at arbitrary locations in a plasma. This enables to describe the fields at high order in space compared to standard forward ray tracing approaches. In addition, inverse ray tracing enables the use of etalon integral methods to reconstruct caustic fields and greatly speeds up calculations of cross-beam energy transfer by decoupling the ray amplitude and ray phase calculations. A comparison of the inverse and forward methods for 3-D calculations of fields in presence or not of cross-beam energy transfer illustrates the significant advantages of the inverse method. Conversely, while the inverse method is well suited to most spherical plasma profiles, it currently cannot treat concave profiles or target holders. The coupling of IFRIIT with the 3-D ASTER radiative hydrodynamics code developed at the Laboratory for Laser Energetics is then presented. ASTER and IFRIIT resolve their respective equations on separate grids which communicate through interpolation. As such, IFRIIT uses a dedicated laser grid adapted to the computations at play, which also allows to use different parallelization methods for both codes: block decomposition for the hydrodynamics versus domain duplication for the laser. Applications to direct-drive implosions for inertial confinement fusion are presented, for which a geodesic icosahedron grid is implemented in IFRIIT. The performances of the ASTER/IFRIIT coupling are demonstrated by conducting simulations of cryogenic implosions performed on the OMEGA laser system, in presence of various sources of 3-D effects; laser port geometry, cross-beam energy transfer, beam imbalance and target mis-alignment. Comparison with neutron data, measured through bang-time, for a cryogenic implosion experiment shows an excellent agreement for the laser-plasma coupling.

Experimental and Numerical Heat Transfer Investigation of Impingement Jet Nozzle Position in Concave Double-Wall Cooling Structures

In this paper, experimental and numerical study has been carried out to investigate impingement cooling with a row of five circular jets, varied between target positions on a realistic leading edge region of gas turbine blade geometry. Experimental data is collected from a transient thermochromic liquid crystal measurement technique at the target surface. Numerical study was conducted with the geometry using commercial computational fluid dynamics software to analyze the fluid flow. The unique aims of the study are to observe the effects of variation in jet location, and those specific to realistic target and nozzle geometries. Distributions of local and average Nusselt number show that a location targeting the concave surface at 90° demonstrates an overall higher heat transfer coefficient, especially in the stagnation region, and toward the airfoil sides, with significantly fewer swirls. The experiment was performed with the following parameters: distance from nozzle to target of 1.7 to 2.1 jet diameters, pitch between jets of 4.4 jet diameters, and concave target diameter of 8.0 jet diameters. The jet Reynolds number range during this test was 20,000 − 40,000. A standard flat target plate impingement test is also experimentally conducted and compared against existing literature for method validation.

Production of copper-64 using a hospital cyclotron: targetry, purification and quality analysis.

To construct and evaluate a 64Cu production system that minimises the amount of costly 64Ni, radionuclidic impurities and nonradioactive metal contamination and maximises radiochemical and radionuclidic purity and molar activity; and to report analytical and quality control methods that can be used within typical PET radiochemistry production facilities to measure metal ion concentrations and radiometal molar activities. Low volume was ensured by dissolving the irradiated nickel in a low volume of hydrochloric acid (<1 mL) using the concave gold target backing as a reaction vessel in a custom-built target holder. Removal of contaminating 55Co and nonradioactive trace metals was ensured by adding an intermediate hydrochloric acid concentration step during the conventional ion-exchange elution process. The radionuclidic purity of the product was determined by half-life measurements, gamma spectroscopy and ion radiochromatography. Trace metal contamination and molar activity were determined by ion chromatography. On a small scale, suitable for preclinical research, the process produced typically 3.2 GBq 64Cu in 2 mL solution from 9.4 ± 2.1 mg nickel-64 electroplated onto a gold target backing. The product had high molar activity (121.5 GBq/µmol), was free of trace metal contamination detectable by ion chromatography and has been used for many preclinical and clinical PET imaging applications.

On heat transfer and flow characteristics of jets impinging onto concave surface with varying bleeding arrangements

Purpose The purpose of this study is to investigate the effects of film holes’ arrangements and jet Reynolds number on flow structure and heat transfer characteristics of jet impingement conjugated with film cooling in a semicylinder double wall channel. Design/methodology/approach Numerical simulations are used in this research. Streamlines on different sections, skin-friction lines, velocity, wall shear stress and turbulent kinetic energy contours near the concave target wall and vortices in the double channel are presented. Local Nusselt number contours and surface averaged Nusselt numbers are also obtained. Topology analysis is applied to further understand the fluid flow and is used in analyzing the heat transfer characteristics. Findings It is found that the arrangement of side films positioned far from the center jets helps to enhance the flow disturbance and heat transfer behind the film holes. The heat transfer uniformity for the case of 55° films arrangement angle is most improved and the thermal performance is the highest in this study. Originality/value The film holes’ arrangements effects on fluid flow and heat transfer in an impingement cooled concave channel are conducted. The flow structures in the channel and flow characteristics near target by topology pictures are first obtained for the confined film cooled impingement cases. The heat transfer distributions are analyzed with the flow characteristics. The highest heat transfer uniformity and thermal performance situation is obtained in present work.

Experimental and numerical investigation of jet impingement cooling onto a concave leading edge of a generic gas turbine blade

This study focuses on an experimental and numerical heat transfer investigation of an impingement jet array with a concave target plate that resembles a turbine blade's leading edge. The array consists of nine circular jets with a diameter of Djet and the target plate has a curvature radius of R=Djet. The target plate also features film cooling holes in a staggered configuration so that each jet is surrounded by three film cooling holes. A Reynolds number of 30,000 is tested, while the separation distance H is altered between H/Djet=2.7 and H/Djet=4. In addition the jets are exposed to a crossflow (cf). The experimental heat transfer data are obtained by using the transient Thermochromic Liquid Crystal (TLC) method. In the Computational Fluid Dynamics (CFD) study 3D steady state Reynolds-Averaged Navier-Stokes (RANS) simulations with the software package OpenFOAM and the kω−shear−stress−transport (SST) turbulence model are performed. The numerical results from OpenFOAM agree well with the experimental data and local flow phenomena are captured correctly. The crossflow decreases the stagnation point heat transfer as well as the overall heat transfer but homogenizes the local heat transfer distribution. A smaller separation distance enhances the crossflow effects and generally increases the heat transfer level.

Impingement heat transfer on flat and concave surfaces by piston-driven synthetic jet from planar lobed orifice

The heat transfer characteristics of a single synthetic jet (SJ) issuing from planar lobed orifice are investigated experimentally in current study. Two specific planar-lobed orifices (petal-shaped orifice and arch-shaped orifice) and two typical targets (flat target and semi-cylindrical concave target) are taken into consideration. For each lobed orifice, three configurations are included. In the petal-shaped orifices, the lobe numbers are chosen as N=4, 6 and 8 in turns. While in the arch-shaped orifices, the lobe number is fixed as N=6 but the lobe aspect ratios are altered as AR=1, 2 and 3 respectively. All lobed orifices have the same exit area with the baseline round orifice. The experimental tests are performed under a series of operational frequencies (ranging from 10Hz to 25Hz) and dimensionless jet-to-target distances (ranging from 2 to 14 for flat target, and from 6 to 14 for concave target). Under the present conditions, SJ impingement heat transfer enhancement is mostly achieved by the planar lobed orifices when compared to the baseline round orifice, which depends tightly on the lobe shape and target shape. Among current petal-shaped orifices, the N=6 petal-shaped orifice is demonstrated to be a most promising orifice configuration. With regard to current arch-shaped orifices, a moderate lobe aspect ratio is demonstrated to be the superior. When compared to the flat target, SJ impingement heat transfer on the concave target is seriously reduced, regardless of orifice shapes. Interestingly, the relationship of SJ impingement heat transfer on the concave target, between the N=6 petal-shaped orifice and AR=2 arch-shaped orifice, is found contrary to that on the flat target. On the concave target, the N=6 petal-shaped orifice does not show its advantages on SJ heat transfer enhancement as appeared on the flat target. However, the AR=2 arch-shaped orifice still shows its positive role on SJ heat transfer enhancement obviously in comparison to the baseline round orifice.

Dense high-energy γ -rays emission by ultra-intense laser interacting with a concave target

We propose to use a 10 petawatt (PW) laser irradiating onto a target with a concave surface, which can focus the laser beam and attain a more intense laser field, so as to increase both the yield and mean energy of emitted γ-rays. 2D particle-in-cell simulation results show that the peak electric field after the reflection of the laser from the target in this new scheme can reach ∼1.8 times as high as that in the plane target case. Such an enhanced laser field enables an increase in the number of hot electrons in front of the incident plane and raises the probability rate of generating high-energy γ-rays significantly by non-linear Compton scattering. As a result, 1.5×1013 γ photons with a mean energy of 9.2 MeV are obtained. These photons mainly point toward two directions and distribute in pulses with the duration of each pulse of ∼400 as. A brightness as high as 3.6×1025 photons/(mm2mrad2s0.1%BW) is obtained in one pulse. Compared to no positron observed for a plane target, a positron yield of 3.0×108 can be achieved in this new scheme.

Cosine Error Elimination Method for One-Dimensional Convex and Concave Surface Profile Measurements

AbstractThis paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed.