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Stage cut control and simulation are the most important aspects in the optimum binary mixture or multi-component multiobjective cascades. Numerical investigation revealed that by controlling the cut of a separation cascade, defined as the ratio of the product rate to the feed rate, it is always possible to separate a multi-component mixture into two specified groups of components, a light group, and a heavy group, in just one separation run. In this paper, the equations related to the cut control are introduced and it is proposed that for controlling stage cuts, putting one valve in the product section of each stage is enough. By solving the set of non-linear equations related to the machine behavior, valve, and pressure drop in the pipelines and junctions, the valve setting for each stage can be obtained. In the end, some examples of an optimal cascade are studied and valve setting parameters are obtained.

A method has been developed for calculating the parameters of cascades with an assigned number of gas centrifuges in the stages whose separation factors depend on their feed flow and the flow cut. Based on this method, a computational experiment was conducted on separation of molybdenum hexafluoride and concentration of 92,98,100Mo isotopes with a low neutron-capture cross section in the outgoing streams of ordinary and double cascades. The author has determined the features of obtaining isotopically modified molybdenum from waste and selected products of such cascades, which is suitable for creating reactor materials with improved thermophysical characteristics. The influence of the factors associated with the feed flow of cascades and the types of stages, as far as the number of gas centrifuges is concerned, has been studied. It has been shown that the feed flows and the separation factors of the stages of gas-centrifuge cascades differ significantly from rectangular and rectangular-partitioned cascades.

It is well established from gas centrifuge (GC) development that isotope separation in a rotating, multispecies gaseous medium increases with axial circulation of the rotating gas in a long separation chamber. This article aims at the development of a commercially viable plasma centrifuge (PC) for specific, nonuranium isotopes. The proposed model PC employs crossed constant radial electric and axial magnetic fields to provide radial separation of a partially ionized gas, combined with a thermal method to establish axial circulation in the rotating medium. The proposed thermal method creates an axial temperature gradient by cooling one end of the separation chamber. By calculation, the inclusion of circulation flow is shown to create axial redistribution of the target component concentration, increasing the longitudinal separation. An analysis of the hydrodynamic and thermal problems is performed for an extended end disk PC in the framework of the boundary layer theory. Radial velocity profiles of the conducting gas in the boundary layer are calculated with respect to the temperature ratio in the external flow ( $T_{1}$ ) and the disk surface ( $T_{0}$ ) for various Prandtl (Pr) numbers. The results demonstrate that for small values of the Pr number, cooling of an end surface within the PC separation chamber results in an intensive inflow of the conducting medium to the solid surface. It is shown that in a PC with crossed fields, cooling one of its ends achieves an effective multiplication of the separation effect along the length of the column.

The dependence of the separative power of Iguassu gas centrifuges (GCs) on the rotor diameter and velocity of rotation V above 1000 m/s is investigated. The separative power is calculated exploring...

An analytical expression is obtained for the dependence of the maximum separative power of a centrifuge on the rotor length taking the feed flow into account. It is shown that the maximum separative power of a centrifuge is a nonlinear function of the rotor length.

Based on the Onsager Equation, a linearized sixth-order partial differential equation describing the flow in the volume of the rotor of a gas centrifuge is solved using a finite element algorithm e...

Gas centrifuges are widely used to isotope separation of about 154 stable isotopes. It is very important to simulate the behavior of dilute gas inside a centrifuge machine using accurate methods to increase the optimal performance of a machine. Due to the high accuracy of the molecular dynamics (MD) method in the interaction of gas molecules with the surfaces, in this paper, this method has been used for the interaction of uranium hexafluoride gas molecules with the rotor surfaces of the machine and its results have been used to simulation of the gas inside the rotor by the DSMC method. Consequently, a gas centrifuge was simulated using a new hybrid MD-DSMC method. The boundary condition used in the MD-DSMC method is the Cercignani–Lampis–Lord. In this method, the gas behavior near the scoop of the centrifuge machine was investigated using the new algorithm of the velocity reduction coefficient. The results show that for the interaction of uranium hexafluoride molecules with the composite surfaces of rotor, the accommodation coefficients take non-unit values. Also, simulation of the rarefied gas inside the rotor by the MD-DSMC method shows that for a velocity reduction coefficient equal to 0.84, the separation work value for the machine will be maximized. Finally, by comparing the separation factors obtained from MD-DSMC and DSMC methods with experimental results, it can be concluded that applying the effects of the polymeric surface of the rotor and gas conditions using the MD-DSMC method increases the accuracy of the results until 6 percent.

We study the stratified gas in a rapidly rotating centrifuge as a model for the Earth's atmosphere. Based on methods of perturbation theory, it is shown that in certain regimes, internal waves in the gas centrifuge have the same dispersion relation to leading order as their atmospheric siblings. Assuming an air filled centrifuge with a radius of around 50 cm, the optimal rotational frequency for realistic atmosphere-like waves is around 10 000 revolutions per minute. Using gases of lower heat capacities at constant pressure, such as xenon, the rotational frequencies can be even halved to obtain the same results. Similar to the atmosphere, it is feasible in the gas centrifuge to generate a clear scale separation of wave frequencies and therefore phase speeds between acoustic waves and internal waves. In addition to the centrifugal force, the Coriolis force acts in the same plane. However, its influence on axially homogeneous internal waves appears only as a higher-order correction. We conclude that the gas centrifuge provides an unprecedented opportunity to investigate atmospheric internal waves experimentally with a compressible working fluid.

The performance of a gas centrifuge that is used for isotopes separation is dependent on the gas flow inside it. In this study, for modeling the UF6 gas flow, an Implicit Coupled Density-Based (ICDB) solver, was developed in OpenFOAM. To validate the ICDB solver, the gas flow within the rotor in total reflux state was compared with the analytical solution obtained by Onsager model and the numerical solution obtained by the Fluent software. The results showed that the ICDB solver had acceptable accuracy and validity. Also the computational efficiency of Roe, AUSM (Advection Upstream Splitting Method) and AUSM+ up schemes were compared. The results showed AUSM+ up scheme is efficient. Then, the uranium isotopes separation in a gas centrifuge was simulated. It was revealed that all gas flow characteristics including velocity, pressure, temperature and axial mass flux, as well as uranium isotope separation parameters including separation power and separation coefficients could well be predicted.

In the fast rotating gas (with the velocity typical for Iguassu gas centrifuge), three families of linear waves exist with different polarizations and law of dispersion. The energy of the waves is basically concentrated at the axis of rotation in the rarefied region. Therefore, these waves decay on the distance comparable with the wavelength. There is only one type of waves propagating strictly along the axis of rotation with the law of dispersion similar to ordinary acoustic waves. These waves are interested for the physics of gas centrifuges. The energy density of these waves concentrates at the wall of the rotor. These waves have weak damping due to the molecular viscosity and heat conductivity. The damping coefficient is determined for this type of waves by numerical calculations. Analytical approximations for the damping coefficient are defined as well. At the parameters typical for the Iguassu centrifuge, the damping is defined by interaction of the waves with the rotor wall.

Most of the gas enters into a small portion of the rotating cylinder by increasing the rotational speed in a rotating cylinder. Navier-Stokes equations were used to evaluate gas behavior in this area. In this paper, the mass source calculated by the DSMC method at the boundary of the two regions has been used in the Onsager-Pancake equation and finite difference method was used to solve this equation. One of the assumed flow functions taking into account the effects of the scoop and thermal driving is the Olander's flow function. By combining the flow function that resulted from the Onsager-Pancake equation and the Olander's flow function, a new flow function is suggested, that in addition to applying the effect of thermal and mechanical driving, the feed driving added to it with the DSMC method. The results obtained using this new flow function in the modified diffusion equation by Onsager-Cohen, showing the resulted optimal separation power from that in comparison to the Olander's function occurs in a state where thermal driving is insignificant and scoop driving has increased. The effects of scoop drive have increased by increasing the feed value with the new flow function. Furthermore, the diffusion equations have been solved for 235UF6 and 238UF6 using the new flow function and it has been calculated the separation parameters.

Several valuable isotopes used in medicine, industry, and science cannot be separated by a gas centrifuge with a driven mechanical rotor due to the lack of a suitable working gas that has a sufficiently high vapor pressure at room temperature. Such isotopes are typically produced by more costly separation processes. An advanced plasma centrifuge (PC) has been proposed that can separate specific isotopes at a lower cost. The PC achieves increased separation performance by the excitation of an axial counterflow in the plasma medium. In this work, we consider the non-isothermal Bodewadt problem for the PC with thermally driven axial circulation created by cooling one end of the PC's separation chamber. Due to the imbalance between the centrifugal force and the radial pressure gradient, we show that a secondary flow appears, which is imposed on the medium's rotation motion. The effect is analogous to the classical Bodewadt problem, where a rotational flow decelerates over a fixed surface.

According to Dirac’s equation the upper limit of the separative power of a gas centrifuge grows with rotation velocity V of the rotor as V 4 . This equation has two significant drawbacks. First, it was obtained assuming zero axial fluxes. Secondly, it does not take into account formation of a vacuum core near the axis of rotation. Its volume grows with the speed of rotation. Separation of isotopes does not occur in the vacuum core. In our work, we propose a new formulation of the problem of finding the upper limit of separative power without assumptions about zero axial flows and taking into account the limitation of the volume involved in the separation processes. According to our results, the upper limit of separative power increases with increasing speed much slower than the Dirac estimate, in proportion to V 2 .

We have developed and realized on software a mathematical model of the nonstationary separation processes proceeding in the cascades of gas centrifuges in the process of separation of multicomponent isotope mixtures. With the use of this model the parameters of the separation process of germanium isotopes have been calculated. It has been shown that the model adequately describes the nonstationary processes in the cascade and is suitable for calculating their parameters in the process of separation of multicomponent isotope mixtures.

UF6 gas flow in the total regions of a rotor with the radius of 0.1 m and the length of 1 m in axisymmetric and steady states was simulated using a new hybrid CFD-DSMC method in the OpenFOAM framework. Implicit coupled density-based scheme was performed for CFD method, and Variable Hard Sphere (VHS) and diffuse model were employed in DSMC method. Also, as an initial estimation, the local Knudsen number was applied to determine the interface location between the continuum-rarefied regions (r = 0.0855 m). Then it was modified (r = 0.084 m) to reduce the computational cost. The comparison results of pure CFD and CFD-DSMC methods illustrated that there were large differences between the flow properties in the rarefied regions. Finally, the results showed that the separation factor of 6.5% and the separation power of 9.5% were different.

Modeling of a nonstationary process caused by changing the cascade feed flow value using germanium isotope separation as an example. During a nonstationary process, the concentrations of isotopes with intermediary mass number in light and heavy fraction flows may cross the range limits restricted by the initial and final stationary values and exceed the maximum reachable values for a three-flow cascade. Time for stationary isotope concentrations to settle is different for isotopes and depends on the final values of cascade flow.

Rapid development of technologies for production of new materials may provide design of gas centrifuges (hereafter GC) with rotor speed above 1000 m/s. The question about efficiency of such GCs remains open. At present no experimental or theoretical studies regarding the separation effciency of such GCs exist. We present the results of calculations of the optimized separative power of the hyper-speed Iguassu GCs with a length of 1 to 5 meters and rotational speeds from 1000 to 1500 m/s. The calculations were performed in axisymmetric approximation in frameworks of the source-sink model. It is shown that for the hyper-speed GCs the optimized separative power, pressure at the rotor wall, feed flux and gas friction power linearly grow with the rotor length, while the temperature drop along the rotor does not depend on the rotor length.

Impact of the pulsed braking force on the axial gas circulation in centrifuges for a uranium isotope separation was investigated by the method of numerical simulation. Two camera model has been explored. The pulsed braking of the rotating gas results into generation of waves which propagate along all length of the rotor of the centrifuge. The wavelength appears in accordance with predictions of our analytic theory. Pulsations almost doubles the axial circulation flux in the working camera in comparison with the case of the steady state breaking force with the same average power.

This article presents the results of research filling of gas centrifuge cascade for separation of the multicomponent isotope mixture with process gas by various feed flow rate. It has been used mathematical model of the nonstationary hydraulic and separation processes occurring in the gas centrifuge cascade. The research object is definition of the regularity transient of nickel isotopes into cascade during filling of the cascade. It is shown that isotope concentrations into cascade stages after its filling depend on variable parameters and are not equal to its concentration on initial isotope mixture (or feed flow of cascade). This assumption is used earlier any researchers for modeling such nonstationary process as set of steady-state concentration of isotopes into cascade. Article shows physical laws of isotope distribution into cascade stage after its filling. It’s shown that varying each parameters of cascade (feed flow rate, feed stage number or cascade stage number) it is possible to change isotope concentration on output cascade flows (light or heavy fraction) for reduction of duration of further process to set of steady-state concentration of isotopes into cascade.

The problem of non-identity in characteristics of the GCs for uranium isotope separation grows up with increase of a rotor speed of rotation. It may lead to noticeable decrease of the separative power of the centrifugal machines. The carried out assessments allowed to get the dependence of the relative separation performance losses on the non-identity in the hydraulic characteristics of the GCs connected in parallel. The results of calculation are compared with that of obtained in experiments.

2D axisymmetric transient flow induced by a pulsed braking force in the Iguasu gas centrifuge was simulated numerically. The computational domain consists of three cameras: top, working and bottom. The feed flow injected to the working camera, product and waste fluxes removed in the bottom and top cameras, respectively. The transient case is compared with the stationary case where the flow is excited by the stationery braking force. The braking forces averaged over the period of the rotation are equal each other in both cases. In the transient case the gas flux through the gap in the bottom baffle 15% exceeds the flux in the stationary case for the same pressure and temperature. We argued that the waves reduce the pressure in the GC on the same 15%.

An analytical equation defining separative power of an optimized concurrent gas centrifuge is obtained for an arbitrary binary mixture of isotopes. In the case of the uranium isotopes the equation gives δU= 12.7(V/700 m/s)2(300 K/T)L, kg SWU/yr, where L and V are the length and linear velocity of the rotor of the gas centrifuge, T is the temperature. This formula well agrees with an empirical separative power of counter current gas centrifuges.

Analyzing behavior inside a gas centrifuge machine can be divided into two parts: modeling and simulating spaces inside and outside of a rotor. Examining the mass percentage of the gas used in the Holweck-type pump is essential in approaching the desired compression ratio. Due to the contact between outside and inside spaces of a rotor with each other, after flow equilibrium, it is possible to predict the gas components outside the rotor by examining the concentration of gas components at the axis of the rotor. For this purpose, Multi Component Concentration-Direct Simulation Monte Carlo (MCC-DSMC) solver has been developed in this paper. By this solver, variations in concentration inside a rotor for a different combination of light gas with heavy gases were examined. Based on the mass percentages of the components formed in the rotor axis, the gas was selected to simulate the Holweck-type molecular pump by the modified Sickafus method in different geometries. The results show that the compression ratios of the modified Sickafus method are in good agreement with the experimental results. Also, the presence of small percentages of a light gas inside the rotor has a significant influence on the compression ratio made by a molecular pump.

No Feed and Single Withdrawal (NFSW) cascades are of non-conventional gas centrifuge cascades. The present study has been conducted to investigate the effect of holdup of pipes and stages as well as the shape of cascade in separating the multi-component isotopes in NFSW cascades. These cascades are optimized by the Particle Swarm Optimization (PSO) algorithm with an advanced objective function to evaluate the effect of the cascade shape. Moreover, we take into account the holdup term in the equations to study the effect of the holdup of pipes and stages. By investigating the effect of the Holdup of pipes and stages, we found that as the holdup increases, the amount of flow concentration changes. We also compare the optimal tapered structure with the square shape of the NFSW cascade. The results showed that the optimal tapered shape is superior over the square shape in separating the middle component of Xenon.

The effect of bellows in a supercritical gas centrifuge on the separative power is studied experimentally. It is found that the separative power of a gas centrifuge with bellows placed in the rotor is lower than that of a centrifuge with a smooth rotor and the difference increases with increasing number of bellows in the rotor. It is shown that the reduction of the separative power can be compensated to a large extent by increasing the temperature component of the circulation flow.

A 3D numerical simulation of pressure distribution in the helicoid multi-groove Holweck pump as the compression of a gas centrifuge is carried out. It was shown that the combination of the free molecular regime and clearance between the compression rotor and stator leads to an appreciable effect of collisionless jumping, which essentially influences the pressure in a high vacuum chamber. When neglecting the jumping effect, the limit compression ratio is very large. The jumping considerably reduces the compression ratio to approximately the same moderate value for different gases. As a result of the simulation, the limit compression ratio can be obtained as an optimizable function of variable parameters such as the groove depth, width and angle of inclination. The numerical results can be interpreted within the framework of a simple phenomenological model.

Of all mass, momentum, and energy sources and sinks in simulating the feed, withdrawals, and scoops in the flow field of a gas centrifuge by using Onsager’s pancake equation, the most complicated ones are mass sources/sinks, which impose very different boundary conditions from those by other sources/sinks. Therefore, so far an analytical solution has not been found for the flow field with a mass source/sink. Here a solution procedure is described in detail for solving the flow field in the presence of a mass source/sink, and an analytical solution is given. Numerical examples are also presented and analyzed.

The circulation efficiency of gas centrifuges for uranium enrichment is compared for domestically produced gas centrifuges, the TC-12 and TC-21 models from the European concern Urenco, the American AC-100 model, and the Iguasu model centrifuge in order to search for general physical mechanisms. It is found that for the domestic centrifuges the optimal gas pressure P a near the wall of the rotor is a linear function of the optimal temperature difference ΔT along the rotor. It is shown that the degree of optimality of the circulation flow in a gas centrifuge ha a maximum as a function of the dimensionless rotational speed of the rotor, which is associated with the difficulties of organizing the optimal circulation flow in a thin layer of viscous gas at the rotor wall at high rotational speeds.

It is demonstrated that the total flow in the optimum cascade composed of three different types of gas centrifuges with varied separative performance levels and overall separation factors varying over the cascade stages is less than that in the corresponding ideal (non-mixing) cascade. The data obtained make it possible to use the parameters of the optimum cascade to find the operational mode for the cascade stages that provides the minimum total flow in a separation cascade.

Based on an analysis of the results of a series of numerical experiments, the principles of isotope-selective mass transfer have been analyzed in ordinary square cascade from gas centrifuges to separate multi-component mixtures depending on the relationship between external flows. It has been shown that the ratio of product and feed flows considerably affects the mass transfer of the components of separated mixture along the square cascade primarily on the components with intermediate mass number (in a series of mass numbers of all components of separated mixture). With change in the given ratio, the transfer of intermediate components may undergo qualitative changes and shift the direction of enrichment, e.g., from the light end of the cascade to the heavy end. The determined principles rationalize the opportunities to control mass transfer of intermediate components due to the change in the ratios between external flows of cascade.

We discuss the possibility of applying the semi-empirical formula derived for evaluating the separative power of the Russian-type optimized gas centrifuge, with a rotor length about 1 m, to centrifugal machines of arbitrary length. It is demonstrated that the formula can adequately describe the dependence of a single gas centrifuge's performance on rotor peripheral rotation, length, and diameter for machines with lengths of up to 5 m. The comparison of the calculated values for separative power, obtained by numerical simulations of flow and diffusion in gas centrifuges with that of the URENCO machines, demonstrates satisfactory agreement.

A new method for verification of numerical codes for modeling of gas flow and isotope separation in gas centrifuges (GC) is proposed. The method is based on a semi-analytical solution of the problem of gas circulation in the rotating cylinder (rotor) with an infinite length. The problem is solved for a small amplitude perturbation of the rigid rotation of the gas. It is assumed that the circulation drives, thermal or mechanical origin, vary with the coordinate along the rotation axis harmonically. Solution of the system of equations in partial derivatives is reduced to the solution of the system of ordinary differential equations which can be solved with any accuracy by well known methods. The gas circulation in the solution consists of the system of vortexes periodically located along the rotation axis. The comparison of the semi-analytical solution with the numerical one is possible provided that periodical boundary conditions are specified at the end caps of the rotor of GC. Special attention is paid to the case when the conventional rigid wall boundary conditions are specified at the end caps of the rotor. It is shown that the developed semi-analytical solution can be applied for the verification of the numerical codes in this case as well.

A simple semi-analytical solution is proposed for the problem of an unsteady gas flow in a gas centrifuge. The circulation in the centrifuge is driven by a source/sink of energy and by an external force (deceleration/acceleration of the gas rotation) acting on the gas at a given frequency. In the semi-analytical solution, the rotor is infinite, while the given forces vary harmonically with a given wave-length along the axial coordinate. As a result, the unsteady flow problem is reduced to a system of ordinary differential equations, which can be quickly solved to any prescribed accuracy. This problem is proposed for verifying numerical codes designed for the simulation of unsteady processes in gas centrifuges. A similar unsteady problem is solved numerically, in which case the cylinder is finite with the rotor length equal to the wavelength of the external force along the axis of rotation. The periodicity of the solution is set at end faces of the cylinder. As an example, the semi-analytical solution is compared with the numerical one obtained with these boundary conditions. The comparison confirms that the problem formulations are equivalent in both cases.

The full procedure of the numerical calculation of the optimized parameters of the Iguassu gas centrifuge (GC) is under discussion. The procedure consists of a few steps. On the first step the problem of a hydrodynamical flow of the gas in the rotating rotor of the GC is solved numerically. On the second step the problem of diffusion of the binary mixture of isotopes is solved. The separation power of the gas centrifuge is calculated after that. On the last step the time consuming procedure of optimization of the GC is performed providing us the maximum of the separation power. The optimization is based on the BOBYQA method exploring the results of numerical simulations of the hydrodynamics and diffusion of the mixture of isotopes. Fast convergence of calculations is achieved due to exploring of a direct solver at the solution of the hydrodynamical and diffusion parts of the problem. Optimized separative power and optimal internal parameters of the Iguassu GC with 1 m rotor were calculated using the developed approach. Optimization procedure converges in 45 iterations taking 811 minutes.

We have made comparative calculations of the heat exchange in the subpersonic flow of gaseous UF6 around the stationary cylindrical body inside the rotating rotor of the gas centrifuge. It has been revealed that the integral heat flux from the gas to the body calculated with the use of the ANSYS-CFX program complex from the viewpoint of the continuum model is much smaller than the heat flow calculated by the Monte Carlo method of direct statistical simulation. Estimates show that under the conditions being considered the boundary layer on the surface of the body has no time to be formed and has a thickness of the order of the mean free path of the gas molecules and, therefore, the use of the methods of continuum mechanics in this region is incorrect. On the contrary, the method of direct statistical simulation permits taking into account the interaction of gas molecules directly with the surface of the streamline body and obtaining more correct results. © 2012 Springer Science+Business Media New York.

A finite difference method for numerical simulation of a high speed rotating flow is improved by applying a homotopy algorithm. As a result a large-scale convergence algorithm is constructed to make numerical simulation of a rotating flow in the 2D axisymmetric model of a gas centrifuge for uranium enrichment. The computing code is verified and then applied for calculation of the flow field in a 2D GC operating in a total reflux mode. The peculiarities of an axial circulation flow in a working chamber of a GC are studied. The conclusion about the rate of attenuation of an axial circulation flow is made on the basis of the results obtained.

In gaseous diffusion and gas centrifuge uranium enrichment plants, separating units are connected in cascades. The stage separation factor in gaseous diffusion is close to unity, while in a gas centrifuge it is much larger. Ideal cascades for separating binary mixtures have been designed with no mixing of the species. A new concept, particularly applicable to cascades with large stage separation factors, is called the “optimum” cascade. These cascades allow mixing, but the value of the total flow as found in some cases is less than in corresponding ideal cascades. In this paper, ideal and optimum cascades are discussed and compared.

Numerical modelling and optimization of the gas flow and isotope separation in the Iguasu gas centrifuge (GC) for uranium enrichment have been performed for different lengths of the rotor. The calculations show that the specific separative power of the GC reduces with the length of the rotor. We show that the reduction of the specific separative power is connected with the growth of the pressure in the optimal regime and corresponding growth of temperature to prevent the working gas sublimation. The specific separative power remains constant with the growth of the rotor length provided that the temperature of the gas is taken to be constant.

2D axisymmetric transient flow induced by a pulsed braking force in the Iguasu gas centrifuge is simulated numerically. The simulation is performed for two cases: transient and stationary. The braking forces averaged over the period of rotation are equal to each other in both cases. The transient case is compared with the stationary case where the flow is excited by the stationary braking force. In the transient case the gas flux through the gap in the bottom baffle exceeds on 15 % the same flux in the stationary case for the same gas content and temperature at the walls of the rotor. We argue that the waves can reduce the gas content in the GC on the same 15 %.

We compare two models used to compute the internal hydrodynamics of a gas centrifuge. The scoop action is taken into account through boundary conditions on the flow entering the bowl of the centrifuge in the first model, and through sinks and drag forces in the chambers of the centrifuge in the second. The numerical approximations of the models are based on a finite volume scheme on staggered rectangular grids and on a fixed-point iterative method. Convergence of the approximations is studied numerically on a family of refined grids and comparisons of the two models are discussed for the Iguacu centrifuge. It appears that linear computations on rough grids are sufficient in the first model to correctly predict the separative power of the centrifuge, while other parameters like the return flow or the drag forces require finer meshes and non-linear computations in the second model.

A unit molar weight mass difference diffusion equation was derived and solved by the radial averaging approximation method for binary component isotopes. There was no limit to the range of concentration value. The expression of γ0 was given for arbitrary concentrations. In addition, the analytical solution of a purely axial flow in a gas centrifuge was obtained by a linearized motion equation for a centrifuge. The solution was not under the condition that the speed parameter A 2≫1. Calculation examples show the distributions of different magnitudes of A 2. The parameters that influence the value of γ0, such as the feed flow rate, F, the product, ρD, the speed parameter, A 2 and the wall pressure, p w , are discussed.

The goal of this study is to determine the order of magnitude of the maximum achievable separation for decontaminating a natural gas well using a gas centrifuge. Previously established analytical approximations are not applicable for natural gas decontamination. Numerical simulations based on the batch case show that although the separative strength of the centrifuge is quite good, its throughput is very limited. Both enrichment and throughput are only a function of length and peripheral velocity. A centrifuge with a length of 5 m and a peripheral velocity of approximately 800 m/s would have a throughput of 0.57 mol/s and a product flow of 0.17 mol/s. These numbers are calculated with the assumption that the centrifuge is refilled and spun up instantaneously. The results for the countercurrent centrifuge show how the production rate varies as a function of internal circulation, product–feed ratio, peripheral velocity and centrifuge length and radius. Under conditions similar to those of the batch case the production is approximately half compared to the batch case, i.e., 0.08 mol/s. Optimization can yield a higher production at the cost of lower enrichment. Considering the current natural gas prices and the low production rate of the centrifuge, it is certain that the gas centrifuge will not generate enough revenue to make upfor the high investment costs. 2005 Elsevier Ltd. All rights reserved.

A nonconventional gas centrifuge cascade, called the NFSW (no feed and single withdrawal) cascade, is studied in the separation of middle components by means of numerical simulation. The cascade has no feed and only a single withdrawal at either end of the cascade, different from conventional cascades, which usually have two withdrawals at the two ends of the cascade and one feed in between. The material to be separated is loaded in a reservoir at either end, and the desired component is enriched in either the reservoir or the withdrawal at the other end. The effects of the unit separation factor (equivalently, the cascade length) and the ratio of the upstreaming flow rate to the withdrawal rate are investigated on separation. The separation performance is evaluated in terms of the material recovery and the operation time efficiency, and is compared with those of the corresponding conventional cascades and another type of nonconventional cascade, the SW (single withdrawal) cascade. It is found th...

The theory of separation, based on radial averaging, in a Zippe centrifuge is developed. Certain aspects of the theory of the rotational potential and the errors in understanding the essence of the Helmholtz decomposition as it applies to a gas centrifuge are elucidated. It is shown that the Helmholtz decomposition method does not have cetain drawbacks of the classical theory of the radial averaging method and makes it possible to take account of the rotational flows due to the feed, find expicitly the transit flow distribution, take account of the radial nonuniformity, and take account of the radial convective transport of an isotope by the circulation and transit flows, and the method is not limited by the assumption that the feed flow is small.

A theory of separation in a Zippe gas centrifuge is developed on the basis of the radial averaging method. Certain aspects of the theory of the rotational potential, which recent publications have shown to be inadequately understood, are clarified. It is demonstrated that the rotational potential plays a fundamental role in the description of convective diffusion in a closed vloume. An equation is derived for the transit flow in the separation chamber of the rotor in the centrifuge.

The hydrodynamic equations for a long-bowl gas centrifuge can be simplified to obtain a one-dimensional differential equation for the variation of the non-dimensional axial velocity in the radial direction. In this study the solution of the one-dimensional differential equation was revisited and an approximate finite element solution of the differential equation was developed. The primary analytical solution was found to be consistent with the finite element solution, but the associated simplified solutions were found not always to be consistent with the finite element solution. Improved values for the originally published centrifuge flow function parameters are also presented.

The theory of separation in a Zippe centrifuge is developed. The physical meaning of the concept “separation power” is examined in application to a gas centrifuge. Ideas concerning the separation power in certain publications and the associated incorrect arguments concerning the optimization of a gas centrifuge are analyzed. The errors are clarified, and the correct way to optimize a centrifuge from the standpoint of the separation power is shown.

A generalized isotope transport equation that is valid for arbitrary convective flows in a rotor is constructed by the radial averaging method on the basis of the isotopic approximation. A more accurate equation, differing from the classical equation by the presence of additional terms, for a countercurrent centrifuge is obtained for small radial flows and weak dependence of the axial gradient of the concentration on the radial coordinate.