Half Angle Research Articles

Accurately predicting hypersonic transitional flow on cone via a symmetry approach

A new algebraic transition model is proposed based on a Structural Ensemble Dynamics (SED) theory of wall turbulence, for accurately predicting the hypersonic flow heat transfer on cone. The model defines the eddy viscosity in terms of a two-dimensional multi-regime distribution of a Stress Length (SL) function, and hence is named as SED-SL. This paper presents clear evidence of precise predictions of transition onset location and peak heat flux of a wide range of hypersonic Transitional Boundary Layers (TrBL) around straight cone at zero incidence, to an unprecedented accuracy as validated by over 70 measurements for varying five crucial influential factors (Mach number, temperature ratio, cone half angle, nose Reynolds number and noise level). The results demonstrate the universality of the postulated multi-regime similarity structure, in characterizing not only the spatial non-uniform distribution of the eddy viscosity in hypersonic TrBL on cone, but also the dependence of the transition onset location on the five influential factors. The latter yields a novel correlation formula for transition center Reynolds number which takes similar functional form as the SL function within the symmetry approach. It is concluded that the SED-SL model simulates TrBL around cone with uniformly high accuracy, and then points out to an optimistic alternative way to construct hypersonic transition model.

Heat transfer of MHD flow over a wedge with a surface of mutable temperature

AbstractThe objective of this study is to investigate the thermal distribution and heat transfer in the boundary layer of a wedge with a variable surface temperature in the presence of a magnetic field. To achieve this, we first used similarity solutions to transform the governing equations of magnetohydrodynamic flow for variable surface temperature conditions into ordinary differential equations. We then solved the resulting equations using the collocation method (CM) with different intensity magnetic fields and varying Hartmann (Ha) numbers and surface temperatures. The CM was further modified by incorporating boundary conditions. The results obtained from the solved equations were validated and compared with those obtained using the numerical Runge–Kutta fourth‐order method and previous literature. Finally, we investigated the impact of various parameters on the friction coefficient (Cf) and Nusselt number (Nu), including the power of variable surface temperature (n), Prandtl (Pr) number, Eckert (Ec) number, the half angle of the wedge (φ), and Ha number. We considered values for these parameters within the ranges 0.5 ≤ n ≤ 1.5, 0.5 ≤ Pr ≤ 5, 0.001 ≤ Ec ≤ 0.002, 15° ≤ φ ≤ 60°, and 0 ≤ Ha ≤ 3. Our findings indicate that the slope of the boundary layer increases with increasing Ha or φ, resulting in an increase in Cf on the surface by up to 526%. The Nu number, calculated using the energy equation, increases up to 91.7%, 39.8%, and 1.43% with increasing Ha, n, and Ec, respectively, resulting in faster growth of the thermal boundary layer, which causes the thickness to decrease and the Nu number to rise. However, as φ increases, the Nu number drops on the surface, and the heat transfer behavior remains similar to that observed previously.

Analysis of factors affecting the internal seawater flow performance of pressure-retaining drilling tool for seafloor drill during drilling process

In order to solve the low core collection rate during the natural gas hydrate pressure-retaining exploration, a pressure coring technology for seafloor drill is introduced, and the reasons for the decline in the core collection rate are analyzed. The mathematical model for predicting the water pressure change in the core barrel is established, and the design criteria of drainage path parameters of the drilling tool is formed and verified by engineering application. The results show that: when the valve spool opening x reaches 3.0 mm, the half cone angle α reaches 30°, and the equivalent annular area A1 reaches 30 mm2, the water pressure ΔP in the core barrel tends to be stable. Under the condition that the drilling speed is 20mm/s-50 mm/s and the ratio of the effective flow area of the screen is 0.2–1, the change of water pressure ΔP is little. When the valve spool opening is 4.0 mm, the velocity and pressure change of the seawater at the cone of the valve spool are stable. The engineering application in sediment formation shows that when adopting pressure coring method, the core collection rate exceeds 70% within the drilling speed of 20–30 mm/s.

Bench to batch: Linking pharmaceutical powder flow characterisation, intermediate bulk container discharge and video observations

Five well known excipients and a model drug substance with varied particle properties and bulk behaviour were chosen for the study. Based on the results APAP, NaCMC-XL, mannitol and DCPA were selected for a design to understand the impact of different blends. Two pilot scale unvented IBCs were used in the study. The IBC discharge rates were measured using a catch balance and the mode of flow and powder behaviour inside the IBC was recorded using a camera. The videos inside the IBC showed that regardless of flow mode, for powder to flow from the IBC an air burst was necessary. This was similar to observations when emptying water from a bottle. The extent of the air flow inside the IBC was strong and could possibly result in fluidisation segregation. The discharge curves of 15° and 30° hopper half angles were very similar, which was explained by the vertical air movement in the steeper hopper, which reduces the particle acceleration. Several good indicators of flow/no flow in the IBCs were found. However, for predicting the discharge rate there was a linear correlation between flow through an orifice and IBC discharge rate.

Investigation of drag and heat flux reduction induced by a novel combinational spike-aerodisk and channel concept for hypersonic blunt body

For the drag and heat flux reduction of hypersonic blunt body, a novel combinational spike-aerodisk and channel concept has been proposed. The high pressure air behind the bow shock flows into the channel at the head of the aerodisk, and then sprays out through the lateral jet in the middle of the spike. The Reynolds-averaged Navier-Stokes (RANS) equations coupled with the shear stress transport (SST) k - ω turbulence model have been employed to simulate the flow field. The numerical results reveal that compared with the spike-aerodisk, with the application of the channel, the lateral jet pushes the separated shock wave away from the spike. The range of the recirculation zone between the shear layer and the spike is increased, and the intensity of the reattached shock wave is significantly weakened, so the drag and heat flux reduction properties of the combinational configuration are significantly improved. The influences of the channel convergent half angle and lateral jet location on the flow field, drag and heat flux reduction properties are investigated thoroughly. When the channel convergent half angle is appropriate and the location of the lateral jet is close to the middle of the spike, the drag and heat flux reduction effect becomes better. Besides, with the increase of the Mach number and the decrease of the flying height, the drag and heat flux reduction performance become more significant. In the research range, the combinational configuration in which the convergent half angle is 60° and the lateral jet is located in the middle of the spike has a better overall effect of drag and heat flux reduction, and the effect reaches the best when the Mach number is 6 and the flying height is 20 km. Compared with the spike-aerodisk, the total drag coefficient of the configuration is reduced by 12.95%, and the peak value of Stanton number along the blunt body surface is reduced by 35.19%.

Three-Dimensional Division of Visible Light Communication Irradiation Area

In this article, we divide the irradiated area of visible light communication (VLC) into three parts, according to the influence of diffuse reflection, the irradiance half angle at the source and the communication distance on VLC. We present a volume ratio method to quantitatively analyze each divided part. In this work, based on the Lambertian reflection model of the VLC system in line-of-sight channels, five factors affecting the VLC performance are compared and discussed. A VLC system of a single white-light-emitting diode in a 10 m line-of-sight channel indoors is designed by using the intensity modulation and direct detection technique, and a three-dimensional model of the irradiated area is established.By comparing the distribution of the bit error rate (BER) of the optical signal at different lampshade heights, the volume ratio method is used to calculate the volume percentage of the three irradiated areas. The experimental results show that area II with a volume ratio greater than 50% is the best signal receiving area when compared with areas I and III, having a volume ratio in the range 20∼30%.

Impact of combustion chamber wall heat loss on the energy, exergy, ecology, NOx emission based performance and multiobjective optimization of the precooled scimitar engine

In this paper, the impact of the combustion chamber wall heat loss on the performance of the hydrogen-fueled precooled combined cycle Scimitar engine is investigated. Overall and exergy efficiencies, coefficient of ecological performance and coefficient of emission based ecological performance (CEEP) are considered as the performance indicators to analyze the effects of wall heat loss flux, chamber length, chamber contraction area ratio, throat area and nozzle convergent half angle. A multiobjective optimization is carried out to find the optimum values of hydrogen and air mass flow rates, cruise speed and altitude and core nozzle outlet area. It is found that a wall heat loss flux of 10 MW/m2 decreases the overall efficiency by 1.1% and causes an increase of 2 kJ/gNOx in CEEP. Multiobjective optimization revealed that increasing the hydrogen mass flow rate, decreasing the cruise speed and air mass flow rate improve the overall performance while the optimum values of cruise altitude and core nozzle outlet area are 23 km and 4.94 m2, respectively. The optimized design has a 20.35% better emission performance than the base design with a compromise of a 3.38% reduction in the overall efficiency.

The Effect of Adhesion on Indentation Behavior of Various Smart Materials

The nanoindentation technique plays a significant role in characterizing the mechanical properties of materials at nanoscale, where the adhesion effect becomes very prominent due to the high surface-to-volume ratio. For this paper, the classical adhesion theories were generalized to study the contact behaviors of various piezoelectric materials indented by conical punches with different electric properties. With the use of the Hankel integral transform, dual integral equations, and superposing principle, the closed-form solutions of the physical fields for the Johnson-Kendall-Roberts (JKR) and Maugis-Dugdale (M-D) models were obtained, respectively. The contribution of the electrical energy to the energy release rate under the conducting punch was taken into consideration. The relationships between the contact radius, the indentation load, and the indentation depth were set up using the total energy method for the JKR model and the Griffith energy balance for the M-D model, respectively. Numerical results indicate that increasing the half cone angle of the conical punch enhances the adhesion effect, which can significantly affect the accuracy of the results of characterization in nanoindentation tests. It was found that the effect of electric potential on adhesion behaviors is sensitive to different material properties, which are not revealed in the existing studies of axisymmetric adhesive contact of piezoelectric materials and multiferroic composite materials. The load-displacement curves under conical punches with different half cone angles have very different slopes. These results indicate that the half cone angle has a prominent effect on the characterization of mechanical properties of piezoelectric solids in nanoindentation tests.

Computation of eigenvalues of a real, symmetric 3 × 3 matrix with particular reference to the pernicious case of two nearly equal eigenvalues

AbstractStandard, closed‐form solutions for eigenvalues of symmetric, real‐valued matrices are susceptible to loss of significance in floating point computation in the case of two nearly equal eigenvalues. The non‐negative discriminant of the cubic characteristic polynomial vanishes as these two eigenvalues merge. Turning points of the cubic curve reveal two non‐negative invariant factors of the discriminant. These factors are defined in the favorable form of sums of squares by the Cayley–Hamilton theorem, to be used as numerically stable invariants instead of the determinant. Full numerical stability of the procedure is attained by expressing the angular coordinate in terms of the tangent function rather than the cosine, enhanced by range reduction obtained by considering the half angle. This approach combines robust performance in floating point computation with run times that are on par with conventional schemes.

Flow characteristic evaluation of iron ore for design of bunkers and chutes with different liner materials

Powders and bulk solids have to be handled and stored in all industries, ranging from powders, food, and pharmaceutical substances to raw materials such as cement, coal, and iron ore, as well as dry materials such as fly ash and moist bulk solids such as filter cake and clay. All these materials must be transported, conveyed, or otherwise handled. Thus, the characterization of powders and bulk solids in terms of flow properties is critical. The objective of this paper is to establish the flow characteristics of typical Indian iron ore for the design of test rig bunkers and chutes at different moisture levels.In this paper, the effect of moisture content on the iron ore's flow properties and its interaction with various liner materials is studied. Experimental tests were carried out for various moisture levels to determine the critical levels of moisture which adversely affecting the flow properties of bulk solids. A Jenike ring shear tester (RST) is used to find flow properties like bulk density, wall yield locus, internal friction angle, and wall friction angle of iron ore when it is interacting with different liner materials, i.e. SS 304 2B, Hardox400, Sailhard, and Chromium carbide. The results shows that 11.9% is the critical moisture level. Further, based on this, conical hopper half angle and critical opening size are evaluated for the design of mass flow bunkers and chutes.

Development of an analytical uncertainty model for ship-based lidar measurements

Ship-based lidar systems are a cost-efficient alternative for retrieving highly-reliable offshore wind data. However, the non-stationary nature of ship-mounted lidars hinders the comparison against reference datasets and, therefore, a straightforward characterization of the uncertainty levels associated with these sorts of measurements. For this reason, in this paper we have set up and report an analytical model for estimating the uncertainties of ship-based lidar measurements. The model follows the standard uncertainty propagation method considering the relevant parameters for assessing the wind speed from pulsed Doppler-lidar observations, such as the half cone opening angle, the radial velocity estimation, or the lidar beams’ orientations. Additionally, the derivation of the presented uncertainty model contemplates the technology-specific variables and considerations like the ship linear velocity or tilting, as well as the implementation of a motion correction algorithm.

Atomistic Modeling of Jet Formation in Charged Droplets.

The first atomistic simulations that reveal the mechanism of Rayleigh fission are presented. It is demonstrated that simple ion or macroion ejection takes place through droplet deformation from a spherical into a distinct "tear" shape that contains a conical protrusion. We assert that the latter state is a free-energy minimum along an order parameter that measures the degree of droplet asphericity. The charged droplet's long-time evolution proceeds by alternating between the two minima above and below the critical value that are reached through solvent evaporation and ion ejection, respectively. For the first time, this mechanism allows one to explain the nature of the progeny droplets and the percentage of charge lost during fission. The cone half angle is estimated and found to be in good agreement with the value predicted from the solution of the electrostatic equation for the dielectric liquid. It is found that the conical deformation is independent of the effect of electrohydrodynamic forces reported in experiments. Contrary to the experimental observations of two diametrically opposite jets for droplets suspended in the electric field, we find that a single jet is formed at the Rayleigh limit. The study provides insight into the mechanism of capture of a macroion in jets appearing in electrospray ionization mass spectrometry (ESI-MS) experiments and may explain the tolerance of the ESI-MS spectrum to salt contamination of the sample.

Competing roughness effects on the non-stationary crossflow instability of the boundary-layer over a rotating broad cone

There are two primary aims of this paper: the first aim is to investigate the effects of the roughness types of the Miklavčič and Wang model on stationary disturbances of the boundary-layer flow over a broad rotating cone in still fluid. The second aim is to examine similar effects of surface roughness, but on non-stationary modes of crossflow instability. This study begins with the formulations of the mean-flow system based on the cone geometry. These equations are solved using a spectral numerical method based on Chebyshev polynomials and then used to formulate the linear stability system, which are computed for obtaining neutral curves of the unsteady flows. For the stationary modes, our results indicate that the inviscid instability (type I mode) is more stable, while the viscous instability (type II mode) entirely eliminates, as concentric grooves or isotropic roughness and the cone half-angle increase. In contrast, streamwise grooves have a slight stabilizing effect on the type I mode and a significant destabilizing effect on the viscous instability. Another finding indicates that decreasing the half-angle leads to a greater stabilizing effect of isotropic roughness on the type I modes. Our outcomes are also confirmed by the growth rate and the energy analysis, which shows a large reduction of the total energy balance as a result of increasing concentric grooves or isotropic roughness for the crossflow mode. For non-stationary modes, similar effects are observed in that increasing all levels of roughness stabilizes the type I branch (with concentric grooves and isotropic roughness having a much stronger effect than streamwise grooves), and although increasing concentric grooves and isotropic roughness stabilizes the type II branch, increasing streamwise grooves destabilizes this branch. For modes traveling slower than the rotation of the cone, concentric grooves generally have a stronger stabilization effect for the type I branch, whereas for modes traveling faster than the cone, isotropic grooves have a stronger stabilization effect on the type I branch for all broad half angles. Importantly, increasing concentric grooves and isotropic roughness increases the frequency at which the most dangerous modes occur, whereas increasing the streamwise grooves reduces the frequency at which the most dangerous modes occur.

Performance enhancement of visible light communication (VLC) system incorporating WMZCC‐OCDMA codes and PDM‐QPSK‐DSP data encoding

SummaryMulti‐user optical code division multiplexing (OCDMA) in visible light communication (VLC) is an imminent domain for providing an even distribution of available bandwidth and improved security. Q4R1Zero cross‐correlation (ZCC) codes are widely reported, and improved performance is offered by them due to insignificant multiple access interference (MAI). However, practically, MAI exists in ZCC codes due to adjacent weights (W) in the code matrix rows for each user. Therefore, a novel ZCC code with a nonadjacent W is designed in this work to eradicate MAI limitations and is named weight managed ZCC codes (WMZCC). An indoor 100 Gbps/User OCDMA‐VLC system is realised using polarisation division multiplexed quadrature phase shift keying (PDM‐QPSK) and digital signal processing (DSP). Incorporation of DSP in the coherent receiver compensates the effects of dispersion and nonlinear effects and also performs phase estimation. Further, a state‐of‐the‐art comparison of WMZCC codes with diagonal identity matrix (DIM) and zero cross‐correlation resultant weight (ZCCRW) codes has been performed in terms of log symbol error rate (SER), Q factor, error vector magnitude percentage (EVM%) and log bit error rate (BER) log at different VLC lengths, Q4R1Transmitter half angles (THA), incidence half angles (IHA) and optical concentrators (cm2). Constellations are analysed with and without DSP, and according to the author's best knowledge, a 100 Gbps VLC system for five users covering 6 m at −3.42 log BER is demonstrated for the first time. Results revealed that weight management in WMZCC codes makes its performance improve as compared with ZCCRW and DIM codes.

Effect of Local Momentum Ratio on Spray Windward Distribution of a Gas–Liquid Pintle Injector Element

The variable-area pintle injector has unique geometry and spray characteristics compared to traditional coaxial injectors, and is advantageous for weight lightening and deep throttling of liquid rocket engines. To obtain an accurate prediction of the spray windward distribution of a gas–liquid pintle injector with discrete radial orifices, a pintle injector element using air and water as simulants was designed for spray experiments in the atmospheric environment. The air-film injection pressure drop and water-jet injection orifice diameter were both adjusted for a wide variance range from 0.19 to 2.85 for the local momentum ratio. Backlight imaging was adopted for shooting the frozen spray pattern from one side, and a new dimensionless parameter, i.e., the spray fraction, was defined to quantitatively analyze the time-averaged windward boundary band. The dimensionless spray windward boundary band model for a circular-orifice jet and the corresponding derivative formula of the spray half angle were summarized through parameter study. The predicted results of empirical models were in good agreement with the experimental results. It was found that when the local momentum ratio was about 1, the spray distribution range basically overlapped with the coverage scope of gas film with uniform liquid mist.

Boundary-Layer Instabilities over a Cone–Cylinder–Flare Model at Mach 6

Computations are performed to investigate the convective and global boundary-layer instabilities over a sharp cone–cylinder–flare model at zero-degree angle of attack. The model geometry and the flow conditions are selected to match the experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel at Purdue University. The geometry consists of a nominally sharp 5 deg half-angle cone, followed by a cylindrical segment, and then a 10 deg flare. Additionally, flare half angles equal to 8 and 12 deg and nosetip radii equal to 0.1, 1, and 5 mm are studied. An axisymmetric separation bubble is generated as a result of the laminar shock–boundary-layer interaction in the cylinder–flare region. The comparison of the laminar flow solution and the schlieren images shows a remarkable agreement between the respective locations of both the boundary-layer edge and the reattachment shock. The linear amplification of first and second Mack mode instabilities that begin to amplify in the cone region are computed with a combination of the parabolized stability equations and the harmonic linearized Navier–Stokes equations. The predicted frequency spectra of the surface pressure fluctuations associated with both planar and oblique instability waves capture the distinct lobes within the disturbance amplification spectra measured with PCB® and Kulite sensors. To our knowledge, this represents the first successful comparison between convective instability analysis and measured surface pressure fluctuations for a hypersonic configuration with a separation bubble. Finally, the global instability analysis shows that the laminar flow becomes supercritical for flare half angles larger than 8 deg.

Numerical simulation and experimental evaluation of flow ripple characteristics of Truninger pump

Compared with involute internal gear pumps and gerotor pumps, lower flow ripple is the main advantage of Truninger pumps. Understanding the flow ripple mechanism and characteristics is of great significance to guide the design and manufacture of this type of pump. In this paper, the theoretical flow ripple and flow ripple rate expressions of the pump are derived based on the vector ray method, and the effects of variations of the design parameters of the pump on the theoretical flow ripple characteristics are studied. A three-dimensional numerical simulation model was established in Simerics-MP+ that accounted for the fluid properties and cavitation. All the geometric features, including unloading grooves, the oil distribution areas, the shapes of the suction and delivery passageways, and the axial and radial leakage gaps, were considered to achieve the highest accuracy in the prediction of flow ripple. Finally, a flow ripple test platform was built based on the secondary source method. The validity and accuracy of the model were verified by test results. The flow ripple characteristics under different working conditions were compared and analyzed. The following conclusions were obtained: (1) The smaller module, the larger addendum coefficient and the half angle of the tooth profile in the design process, the lower the pump speed during operation is beneficial to reduce the vibration and noise of this pump; (2) Flow ripple is the comprehensive result of the oil characteristics, internal leakage, and geometric characteristics through the comparisons of theoretical, simulation and experimental results; (3) The flow ripple amplitude and the ripple rate increased with the increase in the outlet pressure and the influence of the pump speed variations on the flow ripple characteristics is less than that of outlet pressure variations. The conclusions obtained in this paper will help designers understand the flow ripple mechanism, achieve low-noise pump designs, and optimize Truninger pumps.

Direct measurement system of water-leaving albedo in the field by the skylight-blocked approach: Monte Carlo simulations.

Water-leaving albedo (αw(λ)) is an important component of the ocean surface albedo. Direct measurement of αw(λ) in the field is not yet available due to difficulties in removing the contribution of surface-reflected solar radiation. Following the concept of the skylight-blocked approach (SBA), a novel system, termed αwSBA, is proposed in this study to directly measure Ew(λ), where a wide-angle black cone is used to block the surface-reflected radiance. The shading errors associated with the cone and the measuring system are examined via Monte-Carlo (MC) simulations for a wide range of water inherent optical properties (IOPs), solar zenith angle, and different configurations of the αwSBA system (i.e., half cone angle, and the length of supporting arm). Based on sensitive analysis using MC simulations, an optimal configuration of αwSBA is recommended. We further propose a mathematical expression to parameterize the shading error (ɛ), along with an error correction scheme (αwOPT). It is found that, with the optimal configuration and αwOPT, the uncertainties of obtained αw(λ) by αwSBA are generally less than 7% for a wide range of waters with different IOPs and particulate scattering phase functions.

Investigation on anti-penetration capability of water filled aluminum alloy cell structure to the shaped charge jet

Passive protective armor is reliable and cheap, and is favored by many armored weapons and equipment. However, reports on metal-liquid composite armor are not sufficient and systematic. Based on the shaped charge jet (SCJ), the anti-penetration capabilities of water filled aluminum alloy cell structure were studied. The hourglass cell structure (HCS) was designed according to the shock wave propagation characteristics in liquid, and the expansion-convergence cell structure (E-CCS) was derived. Based on the virtual origin theory, the residual tip velocity of jet after SCJ penetrated the cell structure was calculated. According to the theory of supersonic disturbance propagation, the Mach cone half angle of SCJ shock wave propagation in liquid was defined and corrected. The propagation and reflection behavior of shock wave were discussed to analysis the radial convergence of liquid. Via the Van Leer Arbitrary Lagrangian Euler finite element simulation model verified by experiments, the simulation studies of SCJ penetrated the circular cell structure (CCS), HCS, E-CCS and convergence/expansion multi-cell structure were performed. The results show that HCS has better effect of interfering with SCJ than that of CCS and E-CCS. An important discovery is that when the liquid composite multi-cell structure is penetrated by SCJ, the attacked cell will not affect other cells due to the shock wave has been trapped in a single cell.

Non-axisymmetric die-less spinning using ball-crown-shape roller

The non-axisymmetric cone has broad application prospects. However, the severe wall thickness thinning has been the bottleneck problem restricting the application of non-axisymmetric parts which are manufactured via die-less shear spinning. In order to control the spun wall thickness distribution, the ball-crown-shape roller is adopted to carry out the non-axisymmetric spinning. The spun workpiece with the non-axisymmetric cone shape is obtained, and the deviation of the maximum and minimum half cone angles α and β between the experimental results and the theoretical values is no more than 4.11%. The wall thicknesses are much greater than that of the shear spinning value with the corresponding half cone angles, and basically maintain at (even locally exceed) the initial blank thickness. At the same time, the half cone angle is considered to have small effect on the wall thickness distribution. The finite element model for this spinning process is established and verified to reveal the wall thickness distribution mechanism which is illustrated as that the BCSR causes the complementary relationship between the metal outflow and circumferential replenishment in the each half cone angle direction.