Discrete Transfer Method Research Articles

Study on transferring the refrigeration power in the temperature-distributed regenerative refrigeration cycle

The temperature-distributed regenerative refrigeration cycle utilizes the real-gas properties to generate the temperature-distributed refrigeration power and improves the cooling performance and liquefaction rate of cryogenic gases. The temperature-distributed refrigeration power is distributed in the volume of the regenerator. It is challenging to transfer this distributed refrigeration power, and the regenerative heat loss is usually inevitable. The transfer process of the temperature-distributed refrigeration power is studied in this paper. A comprehensive investigation into associated influencing factors is presented in this paper. Furthermore, a parameter of the temperature-distributed transfer coefficient (TTC) is proposed to evaluate the transfer process. This study extends into a broader range of the discrete transfer method from liquid-helium temperatures to ambient temperatures and further analyzes the rules from scattered points to multiple points. The internal DC flow method is adopted to eliminate the radial thermal resistance and improve the TTC, recognizing the constraints of the traditional distributed transfer method (coiling heat exchange tubes outside the regenerator). The TTC of the distributed method with the DC flow is improved around 1–2 times by optimizing the mass flux of multi-strand DC flow and temperature range. It is also improved 1.5–2 times by combining the DC flow and discrete method. Additionally, the TTC is improved about 1–1.5 times with the DC flow when using the refrigeration power for gas liquefaction.

Multi-objective optimization design of aerodynamic and infrared characteristics of multi-stream serpentine nozzle

A multi-objective optimization design of multi-stream serpentine nozzle was carried out to improve the aerodynamic performance and reduce the infrared radiation signal. A numerical simulation was carried out to investigate the effects of nozzle pressure ratio (NPR), Aspect ratio (AR) and Ratio of length and diameter (L/D). Computational fluid dynamics (CFD) simulation was employed to study the aerodynamic performance of the multi-stream serpentine nozzle, and the narrow-band method with discrete transfer method were used to calculate its infrared radiation intensity distribution characteristics. A 3-factor, 21-level orthogonal table was designed based on the orthogonal experimental method, and multi-stream serpentine nozzle with different geometrical parameter and operating conditions were designed to obtain the aerodynamic performance and infrared radiation intensity data of each experimental sample point. Radial Basis Function (RBF) neural network and Multi-Objective Particle Swarm Optimization algorithm were used to optimize the geometry and operating conditions with better aerodynamic performance and weaker infrared signal. The result shows that the Pareto solutions obtained by the optimization have good accuracy compared with the numerical simulation results, with an aerodynamic performance error of 0.02% and an infrared radiation intensity error of 0.24%.

Rapid freezing of ground meat: Discrete heat transfer

The paper deals with the optimum conditions for quick freezing of ground meat by continuous and discrete heat transfer. We constructed curves of temperature changes and heat flux during quick freezing of semi-processed meats (ground beef). It was revealed that an increase in the heat flux and a reduction of freezing period by about 1.4 times occurs when the temperature of the cooling medium decreases from -20 С to -40С at air speed of 6 m/s. Comparative characteristics of the change in the freezing duration and the speed of the process by continuous and discrete heat transfer methods are shown. It is proved that with discrete heat transfer, the freezing period lasts 20 minutes, with continuous heat transfer it takes 26 minutes. The paper presents a thermograph and the kinetics of heat transfer during freezing under discrete mode conditions. The quality indicators of ground meat are considered depending on the conditions of heat transfer, as well as the change in the physical and chemical properties of the food after freezing and during storage.

Vectorial discrete ray tracing approach for solving radiative transfer in irregular variable index media via discrete transfer method

A novel vectorial discrete ray tracing approach is applied for tracking the curve paths of radiative beams through the variable index media with complex geometries. In this approach, the irregular solution domain is discretized by a boundary-fitted grid, where the radiative properties, including the refractive index, are considered to be constant for each control volume and control surface. Radiative beams travel along straight lines through each volume element until they hit the interfaces between adjacent volume elements, where the direction of rays changes according to the Snell's law of refraction. The radiation heat transfer in absorbing, emitting, and isotropically scattering media is solved by the discrete transfer method. The problem is solved for one-, two-, and three-dimensional media. Axisymmetric media are simulated by detaching a sector with specular sidewalls. Verification is done by comparing the results with available benchmark solutions in literature. For the cases where the data is not available, the accuracy is proved by satisfaction the energy conservation criterion.

Optical Tomography in Variable Index Media Using the Transient Discrete Transfer Method

This paper presents the optical tomography based on the reconstruction of optical properties in one- and two-dimensional variable index media. A transient discrete transfer method is used to solve the forward problem of transient radiative transfer. A multistart conjugate gradient method is applied to solve the inverse problem, and a straightforward approach is used to obtain the sensitivity coefficients. Different numerical examples are presented to show the efficiency of this method. The results show that the proposed algorithm can effectively estimate the distribution of absorption and scattering coefficients, even with noisy measured data.

Using a flamelet generated manifold method in transported probability density function modeling of soot formation and thermal radiation

The simple semi-empirical precursor soot model of Brookes and Moss based on the soot number density and soot mass concentration is adopted in a transported probability density function (PDF) method for turbulent diffusion flames. The gas phase chemistry is described by a flamelet generated manifold (FGM) based on the mixture fraction, progress variable and enthalpy loss. The accuracy of the FGM method is validated by using flamelet solutions that are not included in the generating set of the FGM. To account for the radiative heat transfer in the flames, we use a non-gray weighted sum of gray gases model for the gas radiation and a gray soot radiation model. Turbulence–radiation interaction is closed at the level of the optically thin fluctuation approximation and the Reynolds averaged radiative transfer equation is solved by means of a discrete transfer method. The proposed modeling approach is applied in simulations of two turbulent non-premixed methane–air flames at one bar and three bar pressure, respectively. Predictions of the mean temperature and mean soot volume fraction are in good agreement with the measurements in the one bar flame. In the higher pressure flame the mean soot volume fraction is over predicted. For this flame, simulation results using the semi-empirical model of Lindstedt provided better agreement with the measurements. The main difference between the Brookes and Moss model and the Lindstedt model is the nine-times increased soot particle agglomeration rate of the latter. When using the same increased agglomeration rate parameter in the Brookes and Moss model the results become virtually identical. The negligible molecular diffusion of the soot was accounted for by neglecting mean molecular diffusion of the soot variables and by greatly reducing their micro-mixing. The effect of this differential soot diffusion on the mean soot volume fraction is found to be small, but it is significant for the variance of the soot volume fraction.

A dynamic two‐level artificial neural network for estimation of parameters in combined mode conduction‐radiation heat transfer in porous medium: An application to handle huge dataset with noise

AbstractA dynamic two‐level artificial neural network (DTLANN) approach is used for the estimation of parameters in combined mode conduction–radiation heat transfer in a porous medium. Four commonly used neural networks: feed forward, cascade forward, fitnet, and radial basis are used in mapping artificial neural network (ANN), and their performance is compared under noisy big data (10,302 × 1300 matrix size). Governing equations for heat transfer in the porous medium through conduction and radiation modes are solved by finite volume method and discrete transfer method. This numerical model is called a direct model. A large amount of data is generated by using the direct model for different values of extinction coefficient β and convective coupling P2. These data were divided into different groups (class) based on the temperature difference between the gas and solid phase. In the inverse analysis, a new pair of temperature profiles for the solid and gas phase is taken as input and classified with the help of a pattern net artificial neural network model. On the basis of classification, data from that particular class and its neighbor class are used for training the mapping ANN model. After the training of the mapping ANN model, corresponding values of β and P2 are obtained as output for any new input. This DTLANN model has a high regression coefficient (R) of .99131 and can predict highly accurate values of parameters under a huge dataset with noise, within much less CPU time.

Modeling and Analysis of Temperature Compensation for Multi-temperature Zone Sintering Furnace Temperature Sensing

The surface temperature of workpieces in a multi-temperature zone sintering furnace is an important parameter to characterize the performances of a multi-temperature zone system. Due to the practical structural properties of the sintering furnace, however, the conventional way of temperature measurement cannot detect the exact surface temperature of the workpieces directly, making it difficult to control the multi-temperature zone system performances precisely. To address such an issue, this paper proposes, for the first time to the best of our knowledge, a temperature compensation algorithm based soft-measurement technique to compensate for the temperature of the measuring points. Specifically, we analyze the heat-transfer mechanism within the electric heating surface and the workpiece surface and establish a mathematical model for it first, and then calculate the radiative heat transfer coefficient between the diffuse gray surface within sintering furnace using the discrete radiation heat transfer method. Finally, the heat transfer mechanism based soft measurement technique is proposed and applied to compensate for the temperature. Both simulations and experiments with a practical sintering furnace are conducted to verify the correctness and effectiveness of the proposed temperature compensation algorithm in different cases. Results show that the proposed algorithm could help maintain the temperature difference within a range limit of ±5°, which is much better as compared with the conventional temperature measurement methods.

Radiation effects in confined spherically expanding flames: Application to C5[sbnd]C10 flames at engine-relevant conditions

Radiation heat loss introduces one of the main uncertainties associated with the determination of laminar flame speeds from experiments using the spherically expanding flame constant volume method. In this study, a radiation model was developed to solve for the volumetric radiative power in spherical geometry using discrete transfer method accounting for spectrally dependent emission and absorption. The model was validated against the results obtained from the discrete ordinate method. Subsequently, the newly developed radiation model was integrated into a hybrid thermodynamic-radiation model used to derive laminar flame speeds from experimental pressure-time history data. Laminar flame speeds were measured for flames of C5C10n-alkanes and isooctane for pressure and unburned mixture temperature ranges of 13–25 atm and 540 – 670 K respectively, and the data are reported with properly derived uncertainties. Additionally, the data are free from measurable instability-induced effects and to assure that a systematic analysis of cell formation was undertaken. Comparison of the experimental data with predicted laminar flame speeds showed consistency and reasonable agreement with two kinetic models. The development of new modeling tools over the last few years, allows for the derivation of accurate laminar flame speeds using the spherically expanding flame constant volume method for engine-relevant fuels and thermodynamic conditions, which other methods cannot accommodate.

Transient radiative transfer in variable index media using the discrete transfer method

The discrete transfer method is adopted to solve the transient radiative transfer with collimated or diffuse irradiation in variable index media with arbitrary distribution of refractive index. The advantage of this approach is its ability to simulate the transient radiation in semi-transparent media with non-continuous refractive index distributions. The solution method is verified by comparison the results with those reported in literature for one, two and three-dimensional cases. The reflectance and transmittance for some locations over the boundaries are obtained, and the effects of optical thickness, scattering albedo, and scattering phase function are examined.

Global heat transfer model and dynamic ray tracing algorithm for complex multiple turbine blades of Ni-based superalloys in directional solidification process

High-quality solidification microstructure during directional solidification relies on precise temperature gradient control, so accurate calculation of the temperature field is critical. In this study, a 3D transient global heat transfer model of directional solidification by the Bridgman method based on the finite difference method is developed. The radiation heat in this model is calculated by the discrete transfer method, and a modified method of external surface area for irregular geometric models is proposed to reduce the zigzag shape caused by finite difference grids. Considering the radiative heat transfer between any surface elements of all materials in the directional solidification furnace, a dynamic ray tracing algorithm is developed to simulate the entire process of directional solidification. Then, the simulated results are compared with the theoretical results and experimental results, respectively. Finally, based on the present model and method, the simulation program developed is applied to the directional solidification of actual castings. The simulated results are in good agreement with the experimental results, which indicate that the model and method developed in this study is effective and practical.

Modeling of High Density Polyethylene Regression Rate in the Simulation of Hybrid Rocket Flowfields

Numerical analysis of hybrid rocket internal ballistics is carried out with a Reynolds-averaged Navier–Stokes solver integrated with a customized gas–surface interaction wall boundary condition and coupled with a radiation code based on the discrete transfer method. The fuel grain wall boundary condition is based on species, mass, and energy conservation equations coupled with thermal radiation exchange and finite-rate kinetics for fuel pyrolysis modeling. Fuel pyrolysis is governed by the convective and radiative heat flux reaching the surface and by the energy required for the propellant grain to heat up and pyrolyze. Attention is focused here on a set of static firings performed with a lab-scale GOX/HDPE motor working at relatively low oxidizer mass fluxes. A sensitivity analysis was carried out on the literature pyrolysis models for HDPE, to evaluate the possible role of the uncertainty of such models on the actual prediction of the regression rate. A reasonable agreement between the measured and computed averaged regression rate and chamber pressure was obtained, with a noticeable improvement with respect to solutions without including radiative energy exchange.

Dimensionally adaptive techniques for computationally efficient discrete transfer radiation calculations

The use of long slender cylindrical pressure vessels and rotationally periodic burners in Pressurized Oxy-Coal (POC) furnaces leads to physical behavior that is 3D periodic near the burner, but which transition to axisymmetric towards the outlet. A fully 3D model would consume unneeded resources, and an axisymmetric model would fail to capture periodic features of the near burner region, such as recirculation zones. The present work therefore seeks to demonstrate the ability of a dimensionally adaptive mesh (i.e. one that transitions from 3D to axisymmetric and, when applicable, 1D) to improve computational speed while still accurately calculating heat flux. The Discrete Transfer Method (DTM) was used to solve the Radiative Transfer Equation (RTE) on both a fully 3D mesh and a dimensionally adaptive mesh. Three techniques were tested for calculating heat transfer across the boundary between 3D and axisymmetric regions. The Single Unweighted Ray (SUR) method uses a single ray to represent the radiative exchange between 3D bounding faces and axisymmetric ring elements. The Multiple Unweighted Ray (MUR) method subdivides the axisymmetric face into a number of sub-faces, with a ray connecting each sub-face with the 3D face, and tracks radiative intensity along each ray. Finally, the Single Weighted Ray (SWR) method tracks intensity along a single ray, with radiative properties averaged from multiple points along several paths. Flux results were compared between the four approaches. The SUR, MUR, and SWR methods agreed with the fully 3D calculations within median percent differences of less than 1%.

Study of an Annular Photoreactor with Tangential Inlet and Outlet. II. The UV/H2O2 Reactive Flow

AbstractThe concentration profiles of species involved in the degradation of phenol by an advanced oxidation process (AOP) are modeled by a computational fluid dynamics tool in an annular reactor whose fluid dynamics was the object of a previous study. The reactive flow was fully described together with the radiation field and the kinetic model, which encompasses large kinetic constants such as 1010 L mol−1s−1. Phenol degradation can be simulated by using relaxation factors of at least 1012 kg m−3s−1. The hydroxyl radical concentration profile depends on the radiation field, assessed by the discrete ordinate and the discrete transfer methods. Phenol can be completely degraded along the reactor. A centrifugal effect was observed, with higher concentrations of degradation products along the inner wall at the reactor outlet.

Experimental and numerical methods for radiative wall heat flux predictions in paraffin–based hybrid rocket engines

The paper is intended to present both experimental and numerical approaches for estimating the heat exchange through thermal radiation towards the walls of lab–scale paraffin–based thrust chambers. Two firing tests of a lab–scale gaseous–oxygen/paraffin–wax hybrid rocket engine have been performed to apply such methods. In particular, the radiative wall heat flux has been evaluated by both spectroscopic measurements and discrete transfer method computations. Details of such approaches are given together with results achieved. The significant gap between experimental and numerical estimations suggested further investigations of influencing processes, whose main outcomes and lessons learned are critically discussed.

Modeling of Anisotropic Scattering of Thermal Radiation in Pulverized Coal Combustion

In this work, the effect of applying different approximations for the scattering phase function on radiative heat transfer in pulverized coal combustion is investigated. Isotropic scattering, purely forward scattering, and a δ-Eddington approximation are compared with anisotropic scattering based on Mie theory calculations. To obtain suitable forward scattering factors for the δ-Eddington approximation, a calculation procedure based on Mie theory is introduced to obtain the forward scattering factors as a function of temperature, particle size, and size of the scattering angle. Also, an analytical expression for forward scattering factors is presented. The influence of the approximations on wall heat flux and radiative source term in a heat transfer calculation is compared for combustion chambers of varying size. Two numerical models are applied: A model based on the discrete transfer method (DTRM) representing the reference solution and a model based on the finite volume method (FVM) to also investigate the validity of the obtained results with a method often applied in commercial CFD programs. The results show that modeling scattering as purely forward or isotropic is not sufficient in coal combustion simulations. The influence of anisotropic scattering on heat transfer can be well described with a δ-Eddington approximation and properly calculated forward scattering factors. Results obtained with both numerical methods show good agreement and give the same tendencies for the applied scattering approximations.

Inverse Estimation of Main Parameters of Spectral Line-Based Weighted Sum of Gray Gases Model With Few Gray Gases to Simulate the Radiation in Nongray Media

The aim of this study is to present a reduced spectral line-based weighted sum of gray gases (SLW) model to simulate the radiation heat transfer in nongray media at high temperatures. Inverse approach is used to divide the absorption cross section band into a clear gas with one gray gas and two gray gases, which are called the S-1 and S-2 approaches, respectively. The unknown absorption cross sections are determined from the knowledge of measured total incident intensities received by wall surfaces. In order to simulate the exact solution of radiation heat transfer in nongray gaseous media, the discrete transfer method (DTM) in combination with S-20 model is used, where the nongray medium is replaced with a set of a clear gas and 20 gray gases. The inverse problem is formulated as an optimization problem to minimize a least square objective function, which is solved by the conjugate gradient method (CGM). The accuracy of the present method is verified by comparing with previous researches and the S-20 approach with a large number of gray gases. The effects of noisy data on the inverse solution are investigated by considering an extreme case with large measurement error. The results show that the unknown absorption cross sections are retrieved well, even for noisy data.

Convective and Radiative Wall Heat Transfer in Liquid Rocket Thrust Chambers

The relative weight of convective and radiative wall heat transfer in liquid rocket engine thrust chambers is estimated by means of dedicated computational fluid dynamics tools. In particular, although the convective wall heat flux is directly evaluated from the solution of the flowfield, an appropriate computational tool, based on the discrete transfer method, is developed to evaluate the radiative wall heat flux. Numerical results are compared against experimental data from the literature, concerning sub-scale thrust chambers fed with either oxygen/methane or oxygen/hydrogen. Then, the effect of varying the chamber pressure or the wall temperature is investigated via a parametric analysis. Results indicate a contribution of radiation up to 15% of the total wall heat flux for oxygen/methane and up to 11% for oxygen/hydrogen propellants.

Solution of multi-dimensional radiative heat transfer in graded index media using the discrete transfer method

The discrete transfer method is extended to solve the radiative transfer equation in two- and three-dimensional semi-transparent media with variable refractive index. The radiative transfer equation and other related equations are organized based on the refracted quantities. A cell-based ray tracing approach is used to track the curve paths of radiative rays in the medium. The complex geometries in multi-dimensional media are simulated by a simple blocked-off strategy. The present method is verified by comparing its results with benchmark solutions, and the performance of the method is examined by some numerical experiments.

Simultaneous estimation of parameters in analyzing porous medium combustion—assessment of seven optimization tools

ABSTRACTSimultaneous estimation of the gas velocity, scattering albedo, and downstream pore diameter in a two-layer planar porous matrix involving combined mode conduction, convection, and radiation heat transfer with combustion is reported. Non-local thermal equilibrium between the gas and the solid phase is accounted by separate energy equations for the two phases. Performances of the genetic algorithm, genetic algorithm parallel, simulated annealing, multiple starting point algorithm parallel, pattern search algorithm, pattern search algorithm parallel, and global search algorithm in the simultaneous estimation of three parameters are analyzed. All the algorithms utilize a priori knowledge of the axial gas temperature distribution, and the magnitudes of the convective and the radiative heat fluxes at the outer surface of the porous matrix. With volumetric radiative information needed in the solid phase energy equation computed using the discrete transfer method, the two energy equations are simultaneously solved using the finite volume method. Pattern search algorithm provides better estimation, and computationally it is also the fastest.