Specular Walls Research Articles

A New Approach to Solve Inverse Boundary Design of a Radiative Enclosure With Specular–Diffuse Surfaces

Abstract The maintenance of uniform temperature distribution affects the efficiency in most industrial applications. In this study, a novel strategy has been developed for inverse radiative boundary design problems in radiant enclosures with participating medium. This study presents the Backward Monte Carlo method to investigate the inverse boundary design of an enclosure composed of specular and diffuse surfaces. A new optimized Monte Carlo method is proposed to determine the temperature distribution of heaters to achieve desirable prescribed uniform heat flux on the design surfaces. The proposed approach is highly efficient and simple to implement with appropriate results. The evaluated heat fluxes on design surfaces and temperature distribution of heaters are compared with the case where the reradiating walls are assumed to be perfectly diffuse. In the proposed approach, for a specific range of specularity, the absorptivity of the reradiating surfaces does not affect the temperature distribution of heaters. Compared to the diffuse walls, the specular walls have a more uniform temperature distribution and heat flux of heaters. This finding will provide insight into solar furnaces design to enhance temperature uniformity, making specular surfaces suitable in many industrial applications.

Rarefied reactive gas flow in T-shape microreactors

The present study investigates the reactive gas flows in T-shape microreactors by means of a 3D direct simulation Monte-Carlo method (DSMC). The reactive process is modeled by incorporating a single step irreversible exothermic reaction of gas species A and B. The energy released in each reaction is added to the system by increasing the kinetic energy of the product gas specie C. The reactive collisions are modeled by means of a momentum preserving hard sphere collision model in 3D DSMC. We analyzed several process and gas parameters to observe their extent of influence on the characteristics of the reactive flow. The T-microreactor with thermal walls showed much higher mass carrying capacity as compared to the specular walls. The reaction front, which initially for maximum reaction rate was close to the inlet of gas specie of higher mass density, moved towards the center of the inlet part of the T-channel and eventually dissolved with decreasing reaction rates. This transition was smooth in the T-channel with thermal walls, whereas, quite abrupt in case of specular walls. Moreover, in T-microreactors with thermal walls, the amount of A and B converted to C follows an exponential decrease especially in moderate to low reaction rates. Further, with a clear separation between high and low reactive regimes, a piece-wise exponential decay in concentration of C with respect to decreasing reaction rates was also observed in the T-channel with specular walls.

Geometric phases in electric dipole searches with trapped spin-1/2 particles in general fields and measurement cells of arbitrary shape with smooth or rough walls

The important role of geometric phases in searches for a permanent electric dipole moment of the neutron, using Ramsey separated oscillatory field nuclear magnetic resonance, was first noted by Commins and investigated in detail by Pendlebury et al. Their analysis was based on the Bloch equations. In subsequent work using the spin density matrix Lamoreaux and Golub showed the relation between the frequency shifts and the correlation functions of the fields seen by trapped particles in general fields (Redfield theory). More recently we presented a solution of the Schr\"odinger equation for spin-$1/2$ particles in circular cylindrical traps with smooth walls and exposed to arbitrary fields [Steyerl et al.] Here we extend this work to show how the Redfield theory follows directly from the Schr\"odinger equation solution. This serves to highlight the conditions of validity of the Redfield theory, a subject of considerable discussion in the literature [e.g., Nicholas et al.] Our results can be applied where the Redfield result no longer holds, such as observation times on the order of or shorter than the correlation time and non-stochastic systems and thus we can illustrate the transient spin dynamics, i.e. the gradual development of the shift with increasing time subsequent to the start of the free precession. We consider systems with rough, diffuse reflecting walls, cylindrical trap geometry with arbitrary cross section, and field perturbations that do not, in the frame of the moving particles, average to zero in time. We show by direct, detailed, calculation the agreement of the results from the Schr\"odinger equation with the Redfield theory for the cases of a rectangular cell with specular walls and of a circular cell with diffuse reflecting walls.

Design of the Secondary Optical Elements for Concentrated Photovoltaic Units with Fresnel Lenses

The goal of this presented study was to determine the optimum parameters of secondary optical elements (SOEs) for concentrated photovoltaic (CPV) units with flat Fresnel lenses. Three types of SOEs are under consideration in the design process, including kaleidoscope with equal optical path design (KOD), kaleidoscope with flat top surface (KFTS), and open-truncated tetrahedral pyramid with specular walls (SP). The function of using a SOE with a Fresnel lens in a CPV unit is to achieve high optical efficiency, low sensitivity to the sun tracking error, and improved uniformity of irradiance distribution on the solar cell. Ray tracing technique was developed to simulate the optical characteristics of the CPV unit with various design parameters of each type of SOE. Finally, an optimum KOD-type SOE was determined by parametric design process. The resulting optical performance of the CPV unit with the optimum SOE was evaluated in both single-wavelength and broadband simulation of solar spectrum.

Effect of directional dependency of wall reflectivity and incident concentrated solar flux on the efficiency of a cavity solar receiver

Managing the optical properties of a cavity solar receiver to create spectral and directional selectivities is a solution to improve receiver efficiencies. A reduction in the incident solar power lost by reflection and by emission in a solar receiver allows the absorption of the solar flux to be maximized. This report investigates the influence of the cavity walls directional reflectivity on the thermal radiative efficiency of a cubic cavity solar receiver. A Monte Carlo ray-tracing method is used to calculate the power lost by reflections and by emission with respect to the incident radiation angular distribution and the bidirectional reflectance distribution function of the cavity walls. To study the influence of the directional dependency of the incident flux on the radiative efficiency, four patterns are considered: collimated, diffuse, focused, and Themis incidences. The directional-hemispherical reflectivity for the bottom wall (face to aperture) and lateral walls are distinguished. For diffuse walls, the absorption efficiency is primarily affected by the lateral walls reflectivity because of the back reflection losses. For specular walls, the driving parameter is the bottom wall reflectivity. In addition, the radiative efficiency with thermal emission was studied for the Themis configuration and a slightly weakest dependency of the efficiency on the lateral walls reflectivity was found.

Alternative Designs of a High Efficiency, North-facing, Solid Particle Receiver

Falling solid particle receivers can enable increased working-fluid temperatures for central receiver power plants, but will need to have high thermal efficiencies. This can increase power-cycle efficiencies and reduce thermal storage costs. A previous north- facing solid particle receiver (SPR) design was estimated to have a thermal efficiency of 72.3%. This design included a large aperture (17 m x 17 m), a slight downward facing nod (20°), a high-sloping ceiling to accommodate the beam angles from the closest heliostats, and particles released near the back wall of the receiver. Receiver design modifications have been introduced to achieve a thermal efficiency of >90% as stated in the SunShot initiative. Design changes including a reduced aperture size, bottom lip on aperture, increased nod angle, deeper cavity, reduced ceiling slope angles, and more specular walls resulted in higher thermal efficiency designs.DELSOL was used to determine viable receiver dimensions, aperture sizes, and nod angles for a desired power output. The optimum receiver parameters were 10.63 m x 10.63 m aperture size, 50° nod angle, and a tower height of 194.7 m. The new aperture size had a higher concentration ratio and provided maximum incident power on the particles with minimum radiative loss. An aperture with a lip, nod angle of 50°, and extended back wall prevented buoyant hot air from leaving the receiver. A ceiling with higher reflectivity allowed more incident radiation to be reflected onto the particles rather than absorbed and thermally re-emitted.

New shape of blackbody cavity: conical generatrix with an inclined bottom

A new shape of blackbody cavity composed of a conical generatrix and a flat inclined bottom is developed for absolute optical radiation measurement in space. For the new-shape cavity with specular isothermal cavity walls, the Monte Carlo method was used to obtain the optimal cavity geometrical parameters, such as the conical angle and inclination angle of the bottom. Distribution maps of the number of reflections over the aperture for traced rays were depicted for demonstrating the performance of the new cavity. Finally, the new-shape cavity was simulated as a blackbody absorber in cryogenic solar absolute radiometer (CSAR). Calculation results reflect that the new-shape cavity can get high absorptivity and achieve high accuracy measurements in CSAR from space.

A theoretical framework for quantitatively characterizing sound field diffusion and sound energy decay curves based on the scattering coefficients and absorption coefficients of walls.

A theoretical framework for characterizing sound field diffusion based on the scattering coefficients and absorption coefficients of walls was developed. The concepts of the equivalent scattering area, equivalent scatter reflection area, average scattering coefficient, and average scatter reflection coefficient are introduced in order to express each room’s capability of scattering. Using these concepts and the mean free path, the scatter‐to‐absorption ratio, mean scatter time, and the diffusion time are defined in order to evaluate the degree of diffusion of a space. Furthermore a theoretical model for characterizing sound energy decay curves in a non‐diffused sound field based on the above mentioned concepts was also developed. First a reverberation model for a room which consists of perfect specular reflective walls was examined. Second the scattering coefficient was introduced to the above reverberation model in order to consider the effects of the sound scattering from the walls on the energy decay c...

Analysis of the slip coefficient and defect velocity in the Knudsen layer of a rarefied gas using the linearized moment equations

The linearized R13 and R26 moment equations are used to study Kramers' problem. Analytical solutions for the defect velocity and slip coefficient are derived and compared with numerical results from the kinetic theory. It is found that the linearized R26 equations can capture the Knudsen layer fairly accurately in terms of the defect velocity and slip coefficient, while the linearized R13 equations underpredict the kinetic data. At the wall, however, the kinetic models predict a slightly higher value for the defect velocity than the linearized R26 equations. In general, the linearized R26 equations perform well for both specular and diffusive walls.

Hybrid atomistic–continuum method for the simulation of dense fluid flows

We present a hybrid atomistic–continuum method for multiscale simulations of dense fluids. In this method, the atomistic part is described using a molecular dynamics description, while the continuum flow is described by a finite volume discretization of the incompressible Navier–Stokes equations. The two descriptions are combined in a domain decomposition formulation using the Schwarz alternating method. A novel method has been proposed in order to impose non-periodic velocity boundary conditions from the continuum to the atomistic domain, based on an effective boundary potential, consistent body forces, a particle insertion algorithm and specular walls. The extraction of velocity boundary conditions for the continuum from the atomistic domain is formulated by taking into account the associated statistical errors. The advantages and drawbacks of the proposed Schwarz decomposition method as compared to related flux-based schemes are discussed. The efficiency and applicability of the method is demonstrated by considering hybrid and full molecular dynamics simulations of the flow of a Lennard–Jones fluid past a carbon nanotube.

Experimental modelling of time-of-flight sonar

This paper describes empirical models of sonar time-of-flight, derived from a large quantity of data collected with a single Polaroid ultrasonic rangefinder. We give a closed form model for the mean and standard deviation of range readings from a rough brick wall as a function of normal distance and beam incidence angle. For specular walls, we give the probability of direct (as opposed to multiple specular) return, and the mean and standard deviation of direct return range readings, as a function of incidence angle in tabular form. The models presented in this paper extend and correct those currently used in many robot sonar systems, particularly in the case of oblique incidence angles.

A method of acoustic landmark extraction for mobile robot navigation

Describes a method to extract multiple acoustic landmarks for the indoor navigation of a mobile robot. The environment is modeled by specular vertical walls. An ultrasonic sensor mounted on the mobile robot scans around the surrounding walls and detects multiple echo pulses. On the horizontal plane at the height of the ultrasonic sensor from the floor, the two-dimensional environment is described by the distance as a function of angle in the scan. Due to the specularity of the walls, the distance function has a manageable number of retroreflective parts that can be used as landmarks. By virtue of the constancy of the relative positions between the ultrasonic sensor and the walls in scanning, the echo pulses reflected from a certain reflection points (RP) have the same time-of-flight in the ultrasonic scan data. The authors determine the position of an RP from the collection of the echo pulses that have the same time-of-flight. The direction to an RP is estimated from the orientation of the ultrasonic sensor at which the maximum magnitude is obtained for the group of echo pulses that correspond to the RP. The mean time-of-flight of the group of echo pulses provides the distance to the RP. Some experimental results are provided to show the validity and the performance of the proposed method.

Development of advanced mathematical models for numerical calculations of radiative heat transfer in metalorganic chemical vapour deposition reactors

The effect of radiative heat transfer in a horizontal chemical vapour deposition (CVD) reactor on the upper wall temperature is studied in detail. A three-band model for the quartz absorption coefficient is introduced and the wall emittance, reflectance, and transmittance are calculated for the cases of specular and diffuse walls, and also for walls covered by a film. Numerical simulation of the heat transfer in the horizontal reactor has shown that the upper wall temperature varies about up to 40–70 K depending on the type of the wall and the emissivity of the susceptor.

Quasiclassical Green's function in slab geometry: Application to A-B transition of superfluid3He in a slab

We show that the quasiclassical Green's function method can be used in slab geometries when the separation is much longer than the Fermi wavelength; consequently, quantum interference effects due to the double walls can be averaged out. We apply the quasiclassical method to the A-B transition of superfluid3He in a slab with specular walls at arbitrary temperature. We consider the phase transition between the planar state and the BW state within the weak coupling theory. The phase transition is shown to be of second kind at all temperatures. We obtain the critical size at which the B phase becomes unstable as a function of temperature. AtT=0 K and at SVP, the critical size is estimated to be 0.78 µm.

Monte Carlo method for radiative heat transfer analysis of general gas‐particle enclosures

AbstractA new Monte Carlo method is developed to analyse multi‐dimensional radiative heat transfer in an enclosure containing grey gas with anisotropically scattering grey particles. One set of variables, called READ (Radiative Energy Absorption Distribution), is introduced to represent radiative transfer, thus appreciably reducing repeated computations required by the conventional Monte Carlo technique. A 1 m × 1 m square duct is used as the enclosure with the upper and lower walls at different temperatures in the one‐dimensional case and with adiabatic specular or diffuse side walls in the two‐dimensional case. Results agree well with the existing analytical solutions for one‐dimensional, non‐scattering cases. It is concluded that, with anisotropic scattering, an increase in the absorption coefficient and/or single scattering albedo produces adverse effects on radiative heat transfer. Anisotropic scattering effects cannot be simulated by the use of the effective absorption coefficient.

BW State of the Superfluid 3He in Restricted Geometry

The BW state of the superfluid 3He in a slab with specular reflection walls is investigated by the method of quasiclassical Green function. The separation of the slab is still much larger than the Fermi wave length, but not necessarily larger than the coherence length. The second order phase transition between the BW state and the Planar state due to the size effects is studied in detail. The phase diagram shows a reentrant behavior.

Monte Carlo study of light transmission through a cylindrical tube

The transmission of light in vacuum through a cylindrical tube with specular walls has been evaluated using the Monte Carlo method. Uniform as well as cosine angular distributions have been assumed as the initial conditions at the entrance aperture; both cases were treated separately for a light cource of uniform density. From the results, which are given as a function of the tube's length-to-diameter ratio L / D and the reflectivity of the inner wall R (0 ≤ R ≤ 0.99), a simple expression has been derived that holds for long tubes L ≥ 4D/ln(1/R) and R ≤ 0.6. The relation T(L,D,R) also yields the molecular transmissivity if specular reflection applies with a sticking coefficient S = 1 − R.

Performance characteristics of rectangular honeycomb solar-thermal converters

An array of rectangular cells, properly shaped with highly reflecting specular walls absorbing to infrared radiation, is shown to be an effective device to limit heat losses when placed over a solar absorber. Theoretical relationships are presented which permit the prediction of the performance of closed-cell and air transpiration systems. The theory rests on analytical and experimental studies of radiant transmission through cells with specularly reflecting, polarizing walls coated with an absorbing film and studies of the suppression of natural convection in cells heated from below. Good agreement was obtained between theory and experiments for the air transpiration system. Three experimental honeycombs of different geometries were tested over a 1-sq ft blackened fiberglass porous absorber, assembled in a well-insulated and glazed housing mounted on a tilting platform to permit any desired orientation. Experiments over a 1-yr period, and theoretical predictions, indicated that the thermal efficiency could be given as a linear function of the ratio of temperature difference between the average temperature of the working fluid and ambient air to the incident solar power, virtually independent of flow, angle of tilt and time of collection. For the best honeycomb tested, the thermal efficiency ranged from 82 to 63 per cent for values (T av − T a) G s equal to 0·10 and 0·30°F/ (B.t.u./hr ft 20, respectively. The honeycomb-porous bed solar-air heater is shown to perform as well as the best previously reported solar-air heater at moderate temperatures. At higher temperatures, of the order of 200°F, it is greatly superior.