30/11/04CEA / DEN / DM2S 1

Uranium enrichment: centrifuge process - physical principles -

F. Doneddu

30/11/04CEA / DEN / DM2S 2

Separation by pressure diffusionPredominant component in the atmosphere

Incr

easi

ngpr

essu

re

HHe

O

N2

N2+O20 -

100 -

-

-

-

-

500 -

-al

titud

e (k

m)

Ligh

t com

pone

nts d

iffus

ion:

H

e, ..

.

Hea

vy c

ompo

nent

s diff

usio

n:

N2,

...

30/11/04CEA / DEN / DM2S 3

Separation by pressure diffusionNitrogen and Helium in the atmosphere

1E-12

1E-10

1E-08

1E-06

0.0001

0.01

1

0 100 200 300 400 500

altitude (km)

pres

sion

(atm

)

p N2p Hep N2 + p He

pres

sure

(atm

)

30/11/04CEA / DEN / DM2S 4

Separation by pressure diffusion

Transposition of the atmosphere to an industrial separator

• atmosphere

– characteristic length of the separation: ~ 100 km

– acceleration of gravity: g ~ 10 m/s²

• industrial separator

– characteristic length of the separation: ~ 10 cm

⇒ 106 time weaker

– need of an acceleration 106 time stronger

⇒ centrifugal force

30/11/04CEA / DEN / DM2S 5

Outline of the gas centrifuges

• transposition

– typical radius:

r ~ 10 cm

– centrifugal acceleration:

γ = Ω2 r ~ 106 g

• orders of magnitude

– angular velocity:

Ω ~ 3 104 rad/s ~ 3 105 rpm

– peripheral velocity:

v = Ω r ~ 3000 m/s

• existing materials

v = Ω r < ~ 700 m/s

v = Ω r

Ω

γ = Ω2 r

r

30/11/04CEA / DEN / DM2S 6

Outline of the gas centrifuges

centrifuge model Iguaçu Rome Darmstadtradius r

(m) 0.06 0.25 0.25

length L (m)

0.48 5 15

aspect ratio L/2r (-)

8 20 60

peripheral velocity

V (m/s)

600 600 800

angular velocity

Ω (rad/s)

10 000 2 400 3 200

centrifugal acceleration

Ω2r/106g(-)

0.6 1.4 2.6

30/11/04CEA / DEN / DM2S 7

Outline of the gas centrifuges

molecularpump

vacuum casing

rotor

magnetic bearing

pivot

motor

30/11/04CEA / DEN / DM2S 8

Pressure gradient

• cylinder rotates at Ω

• filled with gas

• gas rotates at Ω

• suffers centrifugal force Ω2r

• and pressure force

rw

Ω

30/11/04CEA / DEN / DM2S 9

Pressure gradient• balance centrifugal force / pressure force

( )TR

rrM

w

w

epp 2

222 −Ω

=

02 =−Ωrdpdrρ

r

γ = Ω2 r

r+dr

p(r+dr)p(r) pw= wall pressure

T = temperatureM = molecular mass

30/11/04CEA / DEN / DM2S 10

Pressure gradient

UF6 rw=0.25 m V=Ω rw=600 m/s pw=1.3 104 Pa =100 torr

( ) gdvruphold 70≈=− ∫ ρ

p (Pa)

1E-07

1E-05

1E-03

1E-01

1E+01

1E+03

1E+05

0 5 10 15 20 25

r (cm)

continuousgas

rarefiedgas

30/11/04CEA / DEN / DM2S 11

Radial separation effect

increasing pressure

light species diffusion: 235 U

heavy species diffusion: 238 U

rotor wall

rrw0

30/11/04CEA / DEN / DM2S 12

Radial separation effect

UF6 rw=0.25 m V=Ω rw=600 m/s pw=1.3 104 Pa =100 torr

wallNN

NN

⎟⎠⎞

⎜⎝⎛

−−=

11α N = mole fraction of 235U

p (Pa)

1E-07

1E-05

1E-03

1E-01

1E+01

1E+03

1E+05

0 5 10 15 20 25r (cm)

rarefiedgas

continuousgasα

1,0

1,1

1,2

1,3

0 5 10 15 20 25r (cm)

30/11/04CEA / DEN / DM2S 13

Axial counter-current

downwards convection flow

upwards convection flow

30/11/04CEA / DEN / DM2S 14

Axial counter-current

increasing pressure

upwards flow

downwards flow

238 U diffusion

235 U diffusionradial separation

effect

axial separation effect

30/11/04CEA / DEN / DM2S 15

Counter-current drives• Thermal: temperature difference between rotor ends

hot

cold

increasing density

resultingconvective flowlocal effect

30/11/04CEA / DEN / DM2S 16

Counter-current drives• mechanical : drag of a stationary object

drag

resulting convective flowlocal effect

30/11/04CEA / DEN / DM2S 17

Internal components of the rotor

• feed F:

injected in the vacuum core

• enriched product P and

depleted product W:

extracted by scoops F

P

W

30/11/04CEA / DEN / DM2S 18

Internal components of the rotor

scoop

baffle

scoop

baffle

internalflow

P chamber

W chamber

separationzone

30/11/04CEA / DEN / DM2S 1919

Operating conditions

P

W

F

R

∆T

• gas pressure, working temperature

• optimised counter-current drives

– temperature difference ∆T

– feed F

– products P, W

– recirculation flow R

or

– ∆T

– F

– geometry of scoops and chambers

30/11/04CEA / DEN / DM2S 20

Separation performances modelling• internal flow

• Navier-Stokes equations for the gaseous mixture• axial symmetry

– code “Tryphon”• Onsager’s approximation of NS equations (no pancake approx.)• finite element method• structured rectangular grids• separation zone only

– code “Molina”• full NS equations• finite volume• Marker and Cell discretization• 2D model of scoop chambers

• diffusion equations• use convective flow resulting from fluid dynamics of the mixture• provide composition field and product composition

– finite volume method

30/11/04CEA / DEN / DM2S 21

Separation performances modellingRome machine:

rw = 0.25 m L = 5.0 mV = 600 m/s

pw=1.3 104 PaT0 = 320 K

F = 100 mg/sθ = 1/2R = 360 mg/s∆T= 2.7 K

∆U=59 UTS/an

0.0085

0.008

0.0075

0.0065

0.006

0.007

r (cm)

z(c

m)

19 21 23 250

100

200

300

400

500

30/11/04CEA / DEN / DM2S 22

Centrifuge cascade

• typical plant (separation capacity: ~600 000 SWU/yr)

– feed: NF=0.71%

– product: NP=3-5% , ~100 t U/yr

– waste: NW=0.2-0.3%

• typical centrifuge (Rome machine)

– feed NF=0.71% product NP=0.87%, waste NW=0.55%

⇒ centrifuges connected in series

– product flow rate ~1 t U/yr

⇒ centrifuges connected in parallel

30/11/04CEA / DEN / DM2S 23

Centrifuge cascade

6711202

16221955

18791048

732482

283126

F

P

W

NF=0.71%

NP=3.6%

NW=0.28%

F=915 t U/yr

P=119 t U/yr

W=796 t U/yr

∆U=5.7 105

SWU/yr

cascade design: number of centrifuges per stage(Rome centrifuges - α=1/β=1.6061/2)

1

Uranium enrichment: centrifuge process International Seminar on Nuclear Fuel Cycle

29/11/04 – 10/12/04 F. DONEDDU – CEA/DEN/DM2S

The gas centrifuge process is very commonly used for separating uranium isotopes, and also for

separating some stable isotopes. The design of centrifuges raises problems in various technological and engineering domains such as material selection, mechanical stability, economics, etc …, which will not be addressed here. Only few physical principles of the gas centrifuge separation are presented: the main components of a centrifuge, the mechanism of diffusion in a centrifugal field, the internal aerodynamics and the counter-current flows, and the centrifuge cascades. Numerical tools used in the French CEA to model the internal aerodynamics and the separation performance are very briefly described, and numerical results are presented in order to illustrate these physical principles and the optimisation of the operating conditions. The only type of centrifuge dealt with is Zippe’s [1],[2].

Separation by pressure diffusion In a mixture, the various species may move at different velocities. This leads to diffusion fluxes:

for each species, the diffusion flux is the difference between the partial flux and the average flux of the mixture. According to the thermodynamics of irreversible processes, the mass diffusion fluxes result from four “driving forces”: the concentration gradients (ordinary diffusion), the pressure gradient (pressure diffusion), the external forces acting unequally on the various species (forced diffusion), and the temperature gradient (thermal diffusion). As far as the gas centrifuge process is concerned, there is no forced diffusion, as the centrifugal force acts equally on the various species; moreover, the thermal diffusion is negligible. The separation is due to the pressure diffusion resulting from the pressure gradient due to the action of the centrifugal force on the gaseous mixture. This separation effect leads to concentration gradients which induce ordinary diffusion tending to balance the separation effect.

A simple example of such a separation phenomenon is the variation of the composition of the atmosphere with the altitude above the surface of the Earth. Basically, this separation is due to gravity, but not because of a forced diffusion, as it acts equally on each component of the gaseous mixture. In fact, gravity makes the pressure decrease with the altitude, and this pressure gradient induces mass diffusion fluxes, the heavier species tending to migrate to the higher pressure zone (downwards), and the lighter ones to the lower pressure zone (upwards). As the ordinary diffusion tends to balance this separation effect, the equilibrium composition of the atmosphere varies continuously with the altitude, with a predominance of molecular nitrogen and oxygen near ground level, and a predominance of helium and atomic hydrogen above 500 km. So, the separation of the atmosphere components is basically induced by the gravitational acceleration and takes place over a characteristic scale length of the order of 100 km. To carry out a similar separation in an industrial separator, the acceleration field has to be much stronger, as the separator is smaller. Consider a device whose typical dimension is of the order of 10 cm (this means more than 1 cm, but less than 1 m); the characteristic scale length of the separation is then 106 times less than in the atmosphere (10 cm versus 100 km), and the acceleration field must be 106 times stronger than the gravitational field to obtain a similar separation: typically, γ~106 g. Such acceleration can be reached only by use of a centrifugal force field created by a very high rotational speed.

Outline of the gas centrifuges Let rw denote the radius of the centrifuge and Ω its angular velocity; the centrifugal acceleration is

then γ=Ω2rw. With the above typical orders of magnitude (rw~0.1 m, γ~106 g~107 m/s2), the angular velocity is Ω~3 104 rad/s (~3 105 rpm) and the peripheral velocity V=Ωrw~3000 m/s. In practice, the

2

rotational speed is lower because no existing material can rotate at such a high velocity without breaking: the maximum permissible velocity is of the order of 700 m/s [1].

Table 1 indicates dimensions and speeds of typical centrifuges; the rotor radius varies from 6 cm to few tenths of centimetres, the rotor length from half a meter to few meters, the rotor aspect ratio from 8 to few tenths (this parameter is important from the point of view of mechanics: vibrations, critical frequencies,…). Note that these centrifuges are not real ones, but are hypothetical machines used to compare the results of models [3].

centrifuge model Iguaçu [3] Rome [4] Darmstadt [5] radius rw (m) 0.06 0.25 0.25 length L (m) 0.48 5 15 aspect ratio L/2rw 8 20 60 peripheral veloc. V (m/s) 600 600 800 angular velocity Ω (rad/s) 10 000 2 400 3 200 centrifugal accel. Ω2rw / 106g 0.6 1.4 2.6

Table 1: characteristics of model centrifuges

molecularpump

vacuum casing

rotor

magnetic bearing

pivot

motor

molecularpump

vacuum casing

rotor

magnetic bearing

pivot

motor

Figure 1: main mechanical components of a centrifuge

As the rotor has to spin at very high speed, the centrifuge is designed in order to minimise the

frictions; its main mechanical components are (fig. 1): - a rotor with cylindrical symmetry; - an electric motor to drive the rotor; - a pivot at the bottom of the rotor, constituted by a needle rotating in a hard cup, which supports

the weight of the rotor while minimising friction; - a magnetic bearing at top of the rotor which holds the axis of rotation (together with the pivot) and

which provides damping; - a vacuum casing to minimise the drag of the surrounding gas on the rotating components; - a molecular pump, spirally grooved, which avoids the leaking of gas from the rotor to the vacuum

casing.

Pressure gradient Let us consider the case of a spinning cylinder filled with a certain amount of an ideal gas. The

mass density ρ, the pressure p, the temperature T and the molecular mass M of the gas are related by p=ρRT/M. In the steady state, the gas rotates at the same angular velocity as the rotor, and it is in thermal

3

equilibrium with the rotor. Moreover, the equilibrium of the gas results from the balance of the two forces acting on it: the centrifugal force and the pressure force. Applying this balance to an elementary volume

of the gas leads to ρΩ2r-dp/dr=0, then, by integrating and using the ideal gas law, to ( )

TRrrM

w

w

epp 2

222 −Ω

= where pw is the gas pressure at the peripheral wall of the rotor and rw is the radius of the rotor. Thus, the gas pressure varies exponentially with the radius; and, as the angular velocity Ω is very high, this variation is very sharp.

This is illustrated on fig. 2 in the case of the Rome model centrifuge where pw=1.33 104 Pa [4]. Near the wall, the pressure decreases by a factor 104 over a length of 5 cm: the centrifugal force compresses the gas onto the wall and confines it on a few centimetres thickness in the periphery of the rotor, while a vacuum exists in the central region.

p (Pa)

1E-07

1E-05

1E-03

1E-01

1E+01

1E+03

1E+05

0 5 10 15 20 25r (cm)

rarefiedgas

continuousgasα

1,0

1,1

1,2

1,3

0 5 10 15 20 25r (cm)

Figure 2: radial profiles of pressure p and of separation factor α (Rome model centrifuge)

As most of the centrifuge is empty, its hold-up is very little (70 g of UF6 in this example).

Elementary radial separation The sharp pressure gradient induces pressure diffusion fluxes in the radial direction: the heavier

species migrate towards the periphery where the pressure is higher, the lighter ones towards the axis where the pressure is lower. At equilibrium, the mixture is depleted in 235U near the peripheral wall, and enriched near the axis; the mole fraction N of 235U increases from the wall to the axis, and so does the

equilibrium separation factor wallN

NN

N⎟⎠⎞

⎜⎝⎛

−−=

11α . This is the elementary separation effect which

occurs in the radial direction. The maximum enrichment takes place when the depleted fraction is extracted from the rotor

periphery and the enriched one on the axis. But no material can be produced with that maximum enrichment, as there is no gas near the axis (on fig. 2, p=10-6 Pa at r=0). An enriched product can be extracted only where the gas is in continuous regime, so that the radial separation factor is, in practise, less than its maximum value. For example, on fig. 2, α reaches 1.22 in the centrifuge centre while it is less than 1.08 when the gas extraction is restricted to the continuous zone.

Axial separation in a counter-current centrifuge In order to multiply the elementary radial separation effect, a convective motion is superimposed

on the gas rotation (fig. 3): the gas moves downwards along the peripheral wall of the rotor and upwards

4

inside of the rotor (in the continuous zone, thus not too far from the wall); these two axial counter-current flows are linked by two radial flows which close the vortex, one at the bottom of the rotor and the other at the top.

increasing pressure

upwards flow

downwards flow

238 U diffusion

235 U diffusionradial separation

effect

axial separation effect

increasing pressure

upwards flow

downwards flow

238 U diffusion

235 U diffusion

increasing pressure

upwards flow

downwards flow

238 U diffusion

235 U diffusionradial separation

effect

axial separation effect

Figure 3: axial counter-current

Because of the radial separation effect, the light species migrate from the periphery towards the

centre, the heavier ones in the opposite direction. Thus, the peripheral axial flow loses little light species while it moves downwards, and gains little heavy species: it is depleted in light species (235U) from the top to the bottom of the rotor, thus richer at the top than at the bottom. On the contrary, the internal axial flow gains little light species while it moves upwards, and loses little heavy species: it is enriched in light species from the bottom to the top of the rotor, thus richer at the top than at the bottom. As a result, both of the axial flows are enriched in light species at the top, and depleted at the bottom. So, the axial counter-current uses the radial separation effect to produce an axial separation.

When the counter-current flow rate is naught, the axial enrichment doesn’t takes place and the radial separation is not multiplied. On the other hand, when the counter-current flow rate is intense, the convective vortex mixes the internal enriched gas with the peripheral depleted one; the gas mixture is then homogenised in the whole rotor, and no separation occurs. Thus, the intensity of the counter-current flow rate must be optimised in order to maximise the overall separation of the centrifuge.

Counter-current drives In a centrifuge, two different ways are used to generate an axial counter-current, the thermal and the mechanical ones, in addition to the vortices created by the incoming and outgoing flows.

The thermal counter-current is driven by a temperature difference imposed between the top and the bottom ends of the rotor (fig. 4-a). Near the hot end, the gas is heated, its density decreases, then it tends to go towards the low density zone (as heated air goes up in the atmosphere); in a centrifuge, the low density zone is at the centre: an inwards radial flow is induced near the hot end. By the same way, an outwards radial flow is induced near the cold end, and both of them result in a convective vortex in the whole centrifuge (in fact, near the peripheral wall).

The mechanical counter-current is driven by the drag due to a stationary object interacting with the rotating gas (fig. 4-b). Locally, the drag slows down the gas rotation, which decreases the centrifugal force; the equilibrium between the centrifugal and the pressure forces is perturbed, and the pressure force pushes the gas towards the rotor centre. This results in a local inwards flow which generates a vortex in the centrifuge.

5

hot

cold

increasing density

resultingconvective flowlocal effect

hot

cold

increasing density

hot

cold

increasing density

resultingconvective flowlocal effect

drag

resulting convective flowlocal effect

dragdrag

resulting convective flowlocal effect

Figure 4-a: thermal counter-current Figure 4-b: mechanical counter-current

Internal components of the rotor The centrifuge is operated in steady regime, the gas being continuously fed and extracted. The

feed F enters the machine by an axial pipe and is injected in the vacuum core of the rotor through apertures of the pipe (fig. 5).

scoop

baffle

scoop

baffle

internalflow

P chamber

W chamber

separationzone

scoop

baffle

scoop

baffle

internalflow

P chamber

W chamber

separationzone

Figure 5: internal components of the rotor

The enriched product P and the depleted product W are extracted near both ends of the rotor by

pipes ended by scoops, which are small pitot tubes whose apertures face the rotating gas flow. Even if the static pressure of the gas is low in front of the scoop because of the sharpness of the radial pressure profile, the stagnation pressure is much higher because the gas rotation velocity is hypersonic (for example, in the Rome centrifuge where Ωr≈600 m/s, Mach≈7); the extracted gas crosses a strong shock and is compressed to this stagnation pressure before it enters the scoop, which allows the gas to flow into the scoop, then to flow out of the machine.

The bottom scoop which extracts the depleted product is also used to generate the mechanical counter-current, as it exerts a drag on the rotating gas. To avoid that the top scoop generates an opposite counter-current which would damage the axial enrichment, this scoop is confined in a chamber by a screen plate, or baffle, which spins with the rotor. A bottom baffle may also be used to prevent the bottom scoop from disturbing the rotation of the gas in the middle part of the rotor; this baffle is provided with apertures near its periphery, so that the gas flowing down along the rotor wall can enter the chamber.

6

The two baffles divide the rotor into three parts: the scoop chambers at each end, whose functions are to extract the gas products and to create the mechanical counter-current, and the middle part which occupies most of the rotor length and whose function is the separation itself.

Operating conditions In order to increase the centrifuge separation capacity, the counter-current drives must be adjusted

by an appropriate choice of operating conditions. First, let us consider the middle separation zone only and omit the scoop chambers. Then, the

centrifuge is characterised by its geometry (rotor radius, length between the two baffles, internal radii of the baffle, location and size of the peripheral apertures of the bottom baffle, height and size of the feed injection), by its rotational velocity, and by gas characteristics (wall pressure pw, or rotor hold-up, and working temperature T0). The operating conditions are the feed flow rate F, the enriched product flow rate P, the depleted product flow rate W, and those related to the counter-current drives: the temperature difference ∆T between the two baffles (which drives the thermal counter-current), the recirculation flow R (which goes out of the separation zone into the chamber near the peripheral wall, and enters the separation zone from the chamber inside the rotor, and which drives the mechanical counter-current). These operating conditions are the optimisation parameters which allow maximising the separation capacity of the centrifuge.

In a more complete approach, the scoop chambers are considered together with the separation zone. Then, the operating conditions are more complicated to describe: the mechanical counter-current depends on the geometry of the bottom scoop and of its chamber; the product flow rates P and W depend on the geometry of each of the chambers and scoops and on the pipes which connect the scoops to the exterior of the machine.

Separation performance modelling The separation performance of a gas centrifuge results from the gas mixture dynamics and from

the diffusion of the isotopes among the mixture. Apart from the vacuum core, the gas dynamics is described by the steady, compressible, viscous and laminar Navier-Stokes equations. Most parts of the centrifuge present a cylindrical symmetry, but near the scoops and near the feed injection. The three-dimensional problem is commonly simplified in these zones by considering a similar axisymmetric one, which allows modelling the whole internal flow in bi-dimensional geometry.

The internal fluid dynamics may be modelled through Onsager’s equation which approximates the Navier-Stokes equations: the counter-current flow is then assumed to be a small perturbation to the rotating flow. This model is restricted to the separation zone between the two baffles, as it cannot deal with the vicinity of the scoops where the gas rotation is strongly slowed down. In the French code named “Tryphon” [6], it is integrated by a finite element method on a structured rectangular grid, without using the “pancake” approximation.

Otherwise, the full Navier-Stokes equations are handled to model the scoop chambers together with the separation zone. In the French code named “Molina” [7], their discretization is performed on three staggered rectangular grids and the integration by a finite volume method. The bi-dimensional scoop model is based on an orthoradial averaging of the flow taking into account the product withdrawal and the drag (by means of a mass sink and of a force acting on the gas).

Once the fluid dynamics of the gas mixture has been solved, the resulting convection flow is used in the diffusion equations; their integration provides the isotope composition fields inside the centrifuge, and the composition of the product flows. In both of the French codes previously mentioned, it is performed by a finite volume method.

Solving the gas dynamics model and the diffusion equations allows to compute the separation performance for given centrifuge characteristics and given operating conditions. An optimisation procedure [6] provides the optimal operating conditions which maximise the separation capacity of the centrifuge. As far as the separation of a binary mixture of uranium is concerned, the optimisation criterion

7

commonly used is the separation power defined by ∆U=PV(NP)+WV(NW)-FV(NF) where the “value function” is V(N)=(2N-1)ln[N/(1-N)].

0.0085

0.008

0.0075

0.0065

0.006

0.007

r (cm)z

(cm

)

19 21 23 250

100

200

300

400

500

Figure 6: streamlines and composition field in the Rome centrifuge

In the case of the Rome centrifuge, the optimisation leads to the temperature difference ∆T=2.7 K

and the optimal recirculation flow rate R=360 mg/s when the feed flow rate is F=100 mg/s and the cut θ=P/F=0.5; the computed separation power is then ∆U=59 SWU/y, corresponding to NP=0.00875 and NW=0.00547 when NF=0.00711 (so that α=1.233, β=0.768 and γ=1.606). The streamlines (fig. 6) show that the internal flow is rather complex, but the thermal counter-current vortex can be easily seen (near the peripheral wall), as well as the mechanical counter-current vortex (going upwards from the internal part of the bottom chamber to the top, then downwards along the peripheral wall). The composition field shows that the molar fraction of 235U increases from the periphery toward the axis (elementary radial separation) and from the bottom to the top (axial counter-current separation).

Centrifuge cascades In the nuclear fuel cycle, a separation plant is designed to enrich uranium from its natural

composition (0.71% of 235U) up to 3-5%. But a single centrifuge cannot perform such an enrichment: for example, the Rome centrifuge enriches uranium only from 0.71% to 0.87%. So, the isotope mixture must undergo successive separations which gradually increase its 235U fraction up to the required degree. To perform this succession of separations, centrifuges are connected in series so that the enriched product of each one is used to feed the next one. Similarly, the depleted product of a centrifuge is used to feed the previous one in this series, in order to limit the overall waste of depleted uranium. Moreover, several centrifuges are connected in parallel at each stage of this series, so that the plant produces the required rate of enriched material. Thus, the separation plant is a cascade composed of a great number of centrifuges grouped in stages where the elements are connected in parallel, while the stages are connected in series.

The cascade design (number of stages and number of centrifuges of each stage) is optimised in order to minimise the total number of centrifuges needed for the required plant production, or more generally to minimise the unit product cost.

An example of cascade design is presented on fig. 7. This cascade is composed of 10 000 Rome centrifuges grouped in 10 stages; it produces P=119 tons U/year of uranium enriched to NP=3.6 %, its

8

feed is F=915 t U/y of natural uranium, its waste is W=796 t U/y depleted to NW=0.28 % and its separation power is ∆U=570 000 SWU/y.

6711202

16221955

18791048

732482

283126

F

P

W Figure 7: cascade design, number of centrifuge per stage

(Rome centrifuges approached by α=1/β=1.6061/2)

References [1] D.G. AVERY – E. DAVIES, Uranium enrichment by gas centrifuge, Mills and Boon, London, 1973 [2] D.R. OLANDER, Technical basis of the gas centrifuge, Adv. Nucl. Sci. Technol., 6, 105-174, 1972 [3] Proceedings of the 5th Workshop on Separation Phenomena in Liquids and Gases, Fos de Iguaçu, Brazil, 1996 [4] Proceedings of the 3rd Workshop on Gases in Strong Rotation, Rome, Italy, 1979 [5] Proceedings of the 1st Workshop on Separation Phenomena in Liquids and Gases, Darmstadt, Germany, 1987 [6] F. DONEDDU – P. ROBLIN, Modeling of gas centrifuges by the Onsager's equation solved by a finite element method: the TRYPHON code, Proceedings of the 7th Workshop on Separation Phenomena in Liquids and Gases, SPLG’2000, Moscow, Russia, 2000 [7] P. OMNES – F. DONEDDU, Molina: a non-linear code to compute the internal hydrodynamics of a gas centrifuge, International Conference on Supercomputing in Nuclear Applications, SNA’2003, Paris, France, 2003