Category Archives: Handbook Nuclear Terms

PRINCIPLES OF GAS IONIZATION SENSORS

Most detectors in common use in nuclear power reactors are ionization chambers.5 ‘7 Since the principles of the ionization chamber apply broadly to gas-filled de­tectors, only ionization chambers are considered in this section. Specific characteristics of other types of gas-filled detectors are discussed in Sec. 2-4.

2-2.1 Ionization Chambers

Ionization chambers are used to collect and measure the electric charge of ions and electrons that result from the interaction of incident radiation and secondary radiation from the chamber structure with the fixed, known volume of gas in the chamber. The quantity of collected charge is a measure of the incident radiation.

I he sensitivity of ionization chambers can be increased by incorporating materials8 into their structure which interact with the incident reactor radiation to create energetic ions or electrons These materials can be coated as a thin film on the electrodes of the chamber or they can be included in the chamber as a gas For the detection of thermal neutrons, 2 3 5 U and 10B in various degrees of isotopie enrichment are used Other materials ean be used if it is desired to increase the ehamber sensitivity to fast neutrons Table 2 1 is a partial listing of materials that can

Table 2 1—Threshold Energies of Materials for East-Neutron Detection

Thermal <1 MeV >1 MeV

2 3 3 U 2 3 4 U 2 3 2 rh

23SU 2 3 7 Np 23SU

235Pu

be used in fast neutron detectors Of the isotopes listed, 2 38 U is available commercially in a limited number of chamber configurations 2 3 9 Pu and 2 3 7 Np can be obtained by special order

Many isotopes of the heavy elements are of potential value in fast neutron detection Of these, the most likely candidates are 2 3 6 U, 241 Am, 2 40 Pu, and 24 1 Pu The list is

Basically, an юш/ation chamber consists of at least two insulated electrodes sealed within a metallic case or enclosure Connections are made through electrical seals designed for minimum charge leakage Typical resistance between electrodes and case is high, of the order of 101 ohms or greater A guarded structure can be used for the seals if very low signal levels are anticipated Such a structure consists of insulated conducting guard rings or cylinders surrounding each lead The guard rings are maintained at the potential applied to the corresponding electrode Figure 2 3 shows the structure of a fission chamber

The electrodes must be designed and placed so there is a uniform electric field within the sensitive volume of the chamber Auxiliary electrodes can be used to help attain field uniformity, which is particularly important when the sensitive volume of the chamber must be well defined and when uniform ion collection rates are needed In practical detector designs for reactor service, electrode spacing is small compared to the electrode dimensions As a con sequence, the fringing electric field at the edges of the electrodes does not seriously compromise performance Possible errors are usually small compared to other un­certainties in reactor flux measurements Because of this, auxiliary electrodes for field shaping are not used in normal commercial practice

235u-coated 235u-coated

image25

Fig 2.3 —Fission ionization chamber (Courtesy Wcsttngbouse l lectrtc Corp )

 

limited by the availability of accurate fission cross section data, by interfering alpha radiation, and, in some instances, by spontaneous fission

Fast neutron measurements must be interpreted with caution Some of the above isotopes are available onlv bv separation from thermally fissionable isotopes For example, 2 3 6 U and 240Pu may have traces of 2 35 U and 239Pu, respectively These traces may cause errors A second reason for caution is that these isotopes are sensitive to the entire neutron spectrum above the fission threshold Thus, information about the entire neutron spectrum is contained in the signal

High voltage, the magnitude depending on the chamber design and application, is applied to one of the electrodes, and the other electrode is operated close to ground potential This high voltage may be quite low for a chamber of small physical dimensions and low gas pressure (<100 volts) For good performance, the minimum voltage on a large chamber with high gas pressure may be many hundreds of volts Since the gas pressure is fixed to optimize performance (Fig 2 4), the high-voltage limits are also fixed The maximum voltage is limited by the danger of breakdown The applied voltage is usually negative for counters since the collection of electrons is desired at the

Подпись:low-voltage electrode For other types, the voltage mav be positive or negative The value of the applied voltage depends on the plateau of the chamber

Free electrons and positive ions are produced in the gas fill of the chamber Because ions are much heavier than electrons and not as mobile, electrons are normally col­lected faster 9 However, in some gases there is a tendency for the free electrons to associate with the molecules of the gas, producing negative ions ‘I hese negative ions are also relatively immobile The gas fill of the chamber is therefore commonly selected from one of the electron-free gases, such as the inert gases helium and argon Nitrogen also has good properties and is frequently used A number of gas mixtures promote electron mobilit) to an extent much greater than possible with any pure gas and have found great favor in ionization chambers 10

In general, gases whose chemical activity is enhanced by radiation are avoided since they may be gettered by the metals of the electrodes and the chamber enclosure Gases that are chemical compounds may be dissociated in a high radiation field, recombination is not spontaneous m most of these gases, and their use is avoided A BF^ counter or chamber, for example, ma have a short life 1 1

Подпись: Fig 2.5—Counter pulse height vs supply voltage [From H Etherington (Ed ), Nuclear Fngmeenng Handbook p 8-54, MtGraw-Hill Book Company, Inc , New York, 1958 I

When a voltage is applied to an ionization chamber and the resulting current is measured in a constant radiation field, the current is found to van with the voltage A graph of pulse amplitude vs voltage (Fig 2 5) shows the pulse amplitude increasing with voltage in a very characteristic

fashion [2] Ac low voltages competing gas processes hold the current down As voltage is increased, the current increases rapidly, and, then, as the voltage is increased further, the current remains nearly constant, increasing only slightly The flat region of nearly constant current is known as the plateau, and the region where the current begins to flatten is called the knee of the plateau The voltage just above the knee is the minimum operating voltage Normally, the operating voltage is selected, somewhat arbitrarily, to be considerably above the minimum

As the chamber voltage is increased along the plateau, assuming that voltage breakdown does not occur, a point is reached where the current again begins to increase Voltages above this point cause gas multiplication This voltage or the breakdown voltage, whichever is smaller, determines the maximum voltage In turn, the maximum rated voltage must normally be considerably below the breakdown voltage for reliable operation, again a somewhat arbitrary choice Since the reactor radiation field tends to promote voltage breakdown, operation at minimum voltage is preferred

If the voltage plateau for a given chamber12 is deter­mined for a number of radiation-field values, it is found that the voltage at the knee increases with radiation intensity, as shown m Fig 2 6 This is caused by recombination and space-charge effects, which increase rapidly with radiation intensity It is important to recognize this fact and to select an operating voltage that is on a plateau at the maximum radiation intensity experienced during operation At this voltage, again somewhat arbitrary, the magnitude of the chamber current is a faithful indicator of radiation in­tensity

Radiation emitted bv neutron-induced radioactivity within the chamber may, under some circumstances, increase the background and limit the range of usefulness of the chamber 1 3 Figure 2 7 shows the residual current due to the induced activity in the fission chamber

Hardness

(a) Definition. Dissolved salts of calcium and magne­sium impart the property of “hardness” to water. Hardness is characterized by the formation of insoluble precipitates, or curds, with soaps. Temporary hardness, caused by calcium and magnesium bicarbonate, is removed by boiling, which causes these salts to decompose, liberating C02 and

image215
image216

precipitating carbonates. Permanent hardness is due to the sulfates, chlorides, and all the soluble calcium and magne­sium salts other than the bicarbonates. Permanent hardness is not removed by boiling.

(b) Measurement Techniques. Total hardness is deter­mined by adding a standard soap solution to a measured amount of sample and shaking the mixture vigorously between additions of the soap solution until an unbroken lather is maintained for 5 mm on the water surface. The volume of soap used is referred to a chart or multiplied by a factor. The result is expressed in parts per million.

Chloride concentration is determined by titrating a measured volume of sample with standard AgNC>3 solution, using potassium chromate as an indicator The end point is red coloration.

Equivalent sodium sulfate determination is made by titrating with sodium hydroxide solution, with phenol — phthalein as indicator, after adding an excess of benzidine sulfate to a measured sample. The benzidine sulfate precipitates the sulfate in the sample. After standing, filtering, and washing, the precipitate is titrated with NaOH. Turbidity-measuring instruments, described in Sec. 4-7.6, can be used for sulfate determination Barium

image142

9 1 9 3

pH AT 25°C

Fig. 4.50—Theoretical relationship between pH and conduc­tivity for ammonia (From J. H. Hicks, Babcock and Wilcox Nuclear Power Generation Division Water Chemistry Manual, Part 13, Curves, 1969.)

Подпись: Fig. 4 51—Relationship between conductivity and pH for ammonia solutions. (From J H. Hicks, Babcock and Wilcox Nuclear Power Generation Division Water Chemistry Manual, Part 13, Curves, 1969 )
Подпись: SAMPLE TEMPERATURE °F 50 60 70 80 90 100 110 120 Fig 4.49—Temperature correction to 25°C for pH (ammonia solutions). (From J H Hicks, Babcock and Wilcox Nuclear Power Generation Division Water Chemistry Manual, Part 13, Curves, 1969 )

chloride and hydrochloric acid added to the measured sample cause a white precipitate of barium sulfate to form. The resulting turbidity is measured and is an indication of sulfate concentration.

4- 7.6 Turbidity

A turbidity transmitter depends upon the principle that suspended solids in a liquid absorb and scatter part of any light passing through the liquid. The transmitter is ar integral assembly of a light source, a flow tube, and a light-intensity detector (Fig. 4.52). The change in radiant energy reaching the detector varies the resistance in one arm of a Wheatstone bridge A compensating filament m the second arm of the bridge corrects for ambient tempera­ture.

FREQUENCY ANALYZERS

6- 6.1 Usage

In the preceding section analyzers suitable for handling data in the time domain were considered. These analyzers

are used mostly for correlations or for obtaining transfer functions from single-frequency excitation However, there is an alternative approach, used primarily foi data having a continuum of frequencies, in which the various frequencies in the signal are separated and analyzed in the frequency domain Correlators seek the amount of correlation at various time intervals, whether within one signal or between two signals Frequency analyzers, on the other hand, seek the relative amounts of various frequencies in one signal or existing in a related fashion in two signals In both approaches Table 6.1 is used to compute the corresponding functions in the time or frequency domain from those functions which are obtained by experiment

The analyzers discussed in this section are most often used for directly obtaining the spectral power density, Px(f), and the cross spectral power density, Pxy(f) This implies that, in the system being analyzed, a continuum of excitation frequencies exists and has been generated by either internal or external excitation sources In manv instances the spectral power density contains the required information about the dynamics of the reactor system In other instances both Pxy(f) and Px(f) are determined, and then, by using Eq 6 20, the transfer function between x and у is obtained

 

SIGNAL TO BE ANALYZED x(t)

 

image225

P(f,) THE TIME-AVERAGED (OVER A TIME T) VALUE OF THE D-C COMPONENT OF THE INTEGRATOR INPUT

 

image367

Fig 6 15—Operation of the three essential elements (filter, detector, and averager) in a spectrum analyzer

 

resolution band, Af, then it is desirable that B(f) resemble the ideal filter of Fig 6 16 as closely as possible (This is discussed further in Sec 6-6 4 )

Spectrum analyzers that have been used in reactor experiments can be classified as follows specially designed and constructed,62 based on commercially available analog-

 

image226

DEVIATION OF FREQUENCY FROM BAND CENTER

Fig. 6.16—Shapes of some spectral windows used in spectral analysis Here rm is the maximum lag used in the correlation function associated with the spectra

 

image369

(6 37)

 

where B(f) is the spectral-window function of the analj/er If P(f) is a function varying substantially within the

Подпись: Fig. 6.17—Operation of the four essential elements in a cross-spectrum analyzer

computer components,48 and a commercially available spectrum analyzer 11 7 Some spectrum analyzers use elec­trical filters resonant at the desired frequency, fj, others use a heterodyne technique in which the signal modulates a high-frequency carrier, fc, that is subsequently filtered in a narrow band. Since all these approaches perform the same P(f) determination, such factors as cost, convenience, and availability are usually the deciding factors for ex­perimenters

Neutron Sensors — In-Core

Howard H Stevens

3- 1 INTRODUCTION

In core neutron sensors accomplish one or more of the following (1) confirm calculated core performance (2) confirm core operating safety margins, (3) provide input data for fuel management and (4) detect the existence of xenon induced power asymmetries or oscillations (see Chap 1, Sec 1 — 3 6(a) for a discussion of xenon)

The first of a kind power reactor core is usually more thoroughly instrumented than cores of duplicate or similar reactors because of the need to confirm calculated nuclear and thermal performance This practice has become preva lent as core designers have become more dependent on computer codes for nuclear and thermal data and less dependent on critical experiments data The first of-a-kind plant therefore serves as a field laboratory to confirm design calculations It is not intended to generate new experimental data

When reactor complexity, size, power output, power density, or neutron flux level increases beyond certain limits, safe operation of the reactor over its lifetime cannot depend on data from out of core instruments The reactor operator must have available to him the outputs from in-core neutron sensors so he can determine if the core is operating within prescribed safety limits

In large power reactors in-core neutron sensors provide the data needed for carrying out an effective fuel manage ment program and monitor for the existence of xenon induced power asymmetries or instabilities It is normally possible to detect the presence of such asymmetries or instabilities with out of-core instruments, but in-core sen sors must be used to ascertain their exact nature and to provide the data from which an operator can carry out effective control actions (l e, equalizing asymmetries or damping out oscillations) In-core neutron sensors also provide the data for correlating core performance with the response of the out of-core sensors

To be effective, the in-core sensors should provide data continuously or, at a minimum, at periodic intervals while the reactor is operating in its normal mode Reactor

CHAPTER CONTENTS

З 1 Introduction 42

3 2 In Core Environment 42

3 3 In Core Neutron Flux Sensing 43

3 3 1 In Core Fission Chambers 44

(a) Uranium Form 44

(b) Uranium Enrichment 44

(c) Uranium Surface Area 45

(d) Type of Till Gas 45

(e) Fill Gas Pressure 45

(f) Emitter Collector Gap 45

(g) Dimensional Tolerances 45

(h) Operating Characteristics 45

(l) Operating Ranges 47

(j) Traveling In Core Fission Chambers 49

3 3 2 Boron Lined Chambers 49

3 3 3 Self Powered Neutron Detectors 50

(a) Operating Principles 50

(b) Construction and Materials 51

(c) Sensitivity 52

(d) Emitter Burnup 53

(e) Response Characteristics 54

(f) Connecting Cables 56

shutdown should not be required to collect the data, such as would be the case if activation foils were used for flux distribution measurements or if gamma scanning of fuel elements were used for determining irradiation history

Calibration and Checkout Control

(a) Log Count-Rate Meter. The LCRM has a count-rate circuit for control and readout, it will also have period and level circuits that must be calibrated periodically to ensure proper alignment of the unit

The counting circuits can be checked by using a built-in oscillator to provide pulses at two or more repetition rates to the discriminator output The frequency of the oscillator can be verified by using scaler output and a scaler The meters and recorders can then be calibrated

The period circuits can be calibrated from a built in ramp generator The ramp generator provides signals that increase linearly with time and at various rates The signal is applied to the operational amplifier that feeds the differen­tiator The period circuit differentiates this signal and provides a constant period indication for calibration of the readout circuits This also provides a means for setting the period trip level.

(b) Channel Checkout. Some means should be pro­vided at the preamplifier input for checking and calibrating the complete channel Ideally, a neutron source inserted near the neutron sensor would provide complete system checkout. Since this is generally not possible, the system is checked from the preamplifier A calibrated pulser provides the input signal to the preamplifier, and meter, recorder, and scaler readings are verified Level and period trips are also verified

5- 2.8 Control and Safety Circuits[14]

A start-up channel system is shown in Fig 5 15 The system consists of independent channels for control and local indication but with a common recorder for switch selection of a desired readout channel. The three channels provide the redundancy necessary to satisfy safe operation of the reactor and also provide for sufficient channels so that loss of a single instrument need not result in lost reactor operating time. The shutdown circuits associated with the three channels are arranged in a two-out-of-three shutdown logic, i. e., two instruments must trip before scram is initiated. The initiating shutdown circuit is shown in Fig 5.15

Rod-Position Indicators

Two aspects of position indication are essential for the operation of control rods in a reactor the measurement of control-rod position with respect to the core and the determination of rod position with respect to the drive mechanism The first is far more important. The second is relevant to systems where the rod can be separated from

FLEXIBLE ROD BUNDLES

image244

ROD

Fig. 7.8—Magnetic-jack configuration.

the drive, as is often the case in drive systems that satisfy both the shim or control and safety requirements.

Pickup or release of a control rod and full insertion or full withdrawal are usually indicated by panel lights controlled by relays or sensing switches actuated by magnetic or mechanical coupling to the control rod. These switches or relays generally have auxiliary contacts used in the control logic circuits. An example is the logic that initiates movement of a bank of shimming control rods when the automatic regulating rod has exceeded its normal control range. Another is a permissive logic circuit that often takes the form of withholding control power at start-up until all rods are completely down or fully inserted in the reactor and all drives are down and engaged to their respective rods.

Whenever more than one group of shim rods is used on reactor start-up, limit-sensing switches can be used to permit or initiate movement of a second bank of rods when the first has reached a programmed “full-out” position.

Once the condition of major rod position and attach­ment to drives has been satisfied, knowledge of the position of rods with respect to the core is essential to reliable control of a reactor. Both absolute position and relative movement must be measured with an accuracy sufficient to establish safe conditions during start-up and power adjust­ment and to establish predetermined power distribution patterns in the core. The position of rods relative to each other can also be used to diagnose reactivity anomalies within the core. A study of the history of the reactor operating characteristics makes it possible to predict rod position under various operating conditions. If an indica­tion differs markedly from its expected value, it is usually a sign of anomalous behavior in the core, control system, instrumentation, or rod-drive system. Analysis can often pinpoint the malfunctioning item.

Position indication may be direct, when the control rod actuates the sensing device, or indirect, when the position sensor is coupled to the drive mechanism. The control system is arranged so that after rod release the drives are automatically returned to zero position.

In all reactor operation, indication of rod position is displayed at the control console. Panel-mounted dial indicators driven by synchro-receiver units with the synchro-transmitters directly geared or coupled to the driven mechanisms, synchro-driven bar indicators, tapes, or digital counters are conventional. The bar or tape indicators give an immediate and graphic nonambiguous indication of absolute rod position, thereby minimizing possible operator error.

In conjunction with the previously mentioned “all-in” and “all-out” position indication and indication of relative position, position switch sensing of intermediate position is valuable for interlocking with rod-programming circuits and for giving the operator an independent indication of where the rods are under all circumstances. Intermediate position measurements can be used to signal definite rod positions on a bar or tape indicator, thereby providing a backup measurement that also prevents operator misinterpretation of absolute rod position.

Rod-position sensing in sealed systems, in which the drive as well as the rod is in a pressurized high-tem­perature coolant environment, is usually accomplished magnetically. Here extreme in/out positions and also intermediate points may be indicated by having magnetic coupling to coils located at the various points along the pressure-seal housing around a control-rod extension. Ac­curate and continuous sensing of rod position along the entire length of travel, however, is more difficult.

An example of rod-position sensing and indication in a sealed system is the magnetic-jack control rod in the San Onofre Atomic Power Plant (see Sec. 7-4.2). Lights on the control panel indicate rod position. Thirty transformers are mounted around the control-rod-extension pressure hous­ing. Each of the 30 secondary windings is connected to its own individual light on the control panel. As the magnetic portion of the control-rod extension passes each trans­former, the coupling between primary and secondary windings is increased to the point where each lamp in the row is successively lighted and stays lit as rod movement progresses. Although these lights give only approximate position, there is no ambiguity. A secondary scheme for securing indirect position indication uses synchro-repeater indication of the rotation of the cam shaft that actuates the jacking mechanism from the power supply.

Another magnetic readout device for a sealed system uses a winding distributed around the thimble (pressure housing) around the rod extension. The winding is part of an induction bridge with readout on a panel meter. As the rod is withdrawn, the magnetic portion enters the solenoid and changes the inductance of the winding as it progresses. Through suitable design of the coil, its spacing and number of turns, the indication can be made approximately linear with rod displacement.

image245

CONTROL-

ROD

DRIVE

MECHANISM

CONTROL-

ROD

SHROUD

ASSEMBLY-

CONTROL-

ROD

SHAFT

ASSEMBLY-

OUTLET

NOZZLE-

CONTROL-ROD ASSEMBLY-

BLANKET

ASSEMBLY-

FMI PIPING

PRESSURE — VESSEL HEAD

-FMI CONDUIT

-HOLD-DOWN

BARREL

-CORE-SUPPORT

SPRING

-CORE CAGE

-SEED CLUSTER

INLET

NOZZLE

Fig. 7.9—Shippingport Pressurized Water Reactor, center­lines section. (From The Shippingport Pressurized Water Reactor, p. 62, Addison—Wesley Publishing Company, Inc., Reading, Mass,, 1958.)

Reactivity

When a nuclear power-reactor plant is generating electrical energv at a steadv or constant rate, the reactor is in a steady state m which the neutron density is fixed, the temperatures at various positions in the reactor are con­stant, etc Equations 1 7 and 1 8 show that, since dn/dt = dC,/dt = 0 in this steady state, the effective multi­plication factor is just 1 If the effective multiplication factor increases above 1, n will increase with time Similarly, when к < 1, n decreases with time

s к is increased above 1, it reaches a value where the first term of Eq 17 becomes zero, then, for higher values of k, the term becomes positive When k(l — (3) — 1 is positive, the neutron density increases with time at a rate depending on the ratio of the prompt-neutron lifetime, /, to k(l — (3) — 1 Under these conditions the reactor is prompt critical, and, because / is so small (/ ^ 10 4 sec for a thermal reactor, / A? 10 7 sec for a fast reactor), n increases very rapidlv with time for anv appreciable positive value of k( 1 — /3) — 1 The value of the effective multiplication factor when the reactor is just prompt critical is 1/(1 — (3) Since power reactors are always kept below prompt criticality, the practical range of the effective multiplication factor is between 1 and 1/(1 —/3) when the reactor is operating and between 0 and 1 when the reactor is being started up or shut down

In place of the effective multiplication factor it is more convenient to refer to the reactivity, or the fractional deviation of the effective multiplication factor from unity, (k — l)/k,

к — 1 5k, ,

Reactivitv = p = —:— = — (19)

к к

When the effective multiplication factor varies from 1 to 1/(1 — 13), the reactivity varies from 0 to /3 In other words, the reactivity increases by (3 as the reactor goes from delayed critical to prompt critical It is convenient to designate this change of reactivity as “one dollar” = $1 = unit of reactivity equal to the reactivity difference between the prompt critical (k = 1/1 — (3) and the delayed critical (k = 1) conditions of a reactor The dollar is further subdivided into 100 cents, a change in reactivity of 1$, for example, is Др = 0 01/3 from the values of (3 in I able 1 3, it follows that a l<f reactivity increment is 0 000064 for a 2 3 5 U-fueled reactor

frequently the terms “excess k,” “5k/k,” and “reac tivity ” are used interchangeably As fq 19 shows, the second and third terms are exactly equivalent 1 he use of “excess k” or “5k” as equivalent to reactivity is approxi­mately correct, since p = 5k/k = 5k/(l + 5k) = 5k — (5k)2 , etc, and 5k < 1 in all practical cases

Table 1 2—Delayed-Neutron Half-Lives and Yields in hast I ission*7

Delayed Group Relative Absolute

Isotope

neutrons/

fission

index

(0

Half-life <T^>, see

Decay constant

(X), sec 1

abundance

(a)

group yield,

%

33u

0 0070 4 0 0004

і

55 11 +

1 86

0 0126 4 0 0004

0 086

4 0 003

0 06 4

0 003

2

20 74 +

0 86

0 0334 4 0 0014

0 274

4 0 005

0 192 ±

0 009

3

5 30 4

0 19

0 131 + 0005

0 227

4 0 03 5

0 159 4

0 025

4

2 29 4

0 18

0 302 4 0 024

0 317

4 0 011

0 222 ±

0 012

5

0 546 +

0 108

1 27 4 0 266

0 073

4 0 014

0 051 4

0 010

6

0 221 +

0 042

3 13 4 0 675

0 023

± 0 007

0 016 4

0 005

2 3 5 и

0 0165 ± 0 0005

1

54 51 4

0 94

0 0127 + 0 0002

0 038

4 0 003

0 063 4

0 005

2

21 84 +

0 54

0 0317 00008

0 213

4 0 005

0 3 51 ±

0 Oil

3

6 00 4

0 17

0 11 5 4 0 003

0 188

4 0 016

0 310 4

0 028

4

2 23 ±

0 06

0 311 4 0 008

0 407

+ 0 007

0 672 ±

0 023

5

0 496 4

0 029

1 40 4 0 081

0 128

4 0 008

0 211 4

0 015

6

0 179 4

0 017

3 87 4 0 369

0 026

4 0 003

0 043 4

0 005

2 3 8 U

0 0412 4 0 001 7

1

52 38 +

1 29

0 01 32 4 0 0003

0 013

4 0 001

0 054 4

0 005

2

21 58 +

0 39

0 0321 4 0 0006

0 137

+ 0 002

0 564 ±

0 025

3

5 00 4

0 19

0 139 0 005

0 162

4 0 020

0 667 ±

0 087

4

1 93 ±

0 07

0 3 58 0 014

0 388

4 0 012

1 599 4

0 081

5

0 49 +

0 023

1 41 4 0 067

0 225

4 0 013

0 927 4

0 060

6

0 172 +

0 009

4 02 4 0 214

0 075

+ 0 005

0 309 4

0 024

2 3 9 l’u

0 0063 + 0 0003

1

53 75 4

0 95

0 0129 ± 0 0002

0 03 8

4 0 003

0 024 4

0 002

2

22 29 ±

0 36

0 0311 4 0 0005

0 280

4 0 004

0 176 ±

0 009

3

5 19 4

0 12

0 134 4 0 003

0 216

4 0 018

0 136 ±

0 013

4

2 09 4

0 08

0 331 4 0 012

0 3 28

4 0 010

0 207 4

0 012

5

0 549 4

0 049

1 26 4 0 115

0 103

+ 0 009

0 065 ±

0 007

6

0 216 +

0 017

3 21 0 255

0 03 5

+ 0 005

0 022 4

0 003

2 4 0 Pu

0 0088 + 0 0006

1

53 56 4

1 21

0 0129 4 0 0004

0 028

4 0 003

0 022 +

0 003

2

22 14

0 38

0 0313 4 0 0005

0 273

4 0 004

0 238 ±

0 016

3

5 14 4

0 42

0 135 4 0 011

0 192

4 0053

0 162 ±

0 044

4

2 08 4

0 19

0 333 + 0 031

0 3 50

4 0 020

0 315 4

0 027

5

0 511 4

0 077

1 36 + 0 205

0 128

4 0 018

0 119 4

0 018

6

0 172

0 033

4 04 4 0 782

0 029

4 0 006

0 024 ±

0 005

2 3 2 1 h

0 0496 + 0 0020

1

56 03 4

0 95

0 0124 0 0002

0 034

0 002

0 169 4

0 012

2

20 75 4

0 66

0 0334 0 0011

0 150

4 0 005

0 744

0 037

3

5 74 4

0 24

0 1 21 4 0 005

0 155

4 0 021

0 769 4

0 108

4

2 16 4

0 08

0 321 4 0 01 1

0 446

0 015

2 212 4

0 110

5

0 571 4

0 042

1 21 + 0 090

0 172

4 0 013

0 853 4

0 073

6

0 211

0 019

3 29 4 0 297

0 043

4 0 006

0 213 4

0 031

* bast fission is defined as fission induced by a continuous neutron spectrum similar to a prompt fission neutron spectrum

Tabic 1 3—Delayed-Neutron Fractions and Yields* +

Fission

nuclide

(Eeff

Fast fission ~ fission spectrum)

Thermal neutron induced fission

n/1

V

0

n/F

V

/3

2 3 9 pu

0 0063 0 0003

3 08 4

0 04

0 0020,

± 0 0001,

0 0061 4 0 0003

2 82„

0 02,

0 0021, 4

0 0001,

2 3 3 u

0 0070 4 0 0004

2 61 4

0 03

0 0026„

4 0 00016

0 0066 4 0 0003

2 46, 4

0 020

0 0026, 4

0 0001,

2 4 0 Pu

0 0088 4 0 0006

3 3 4

0 2

0 00266

4 0 0002,

241 Pu

0 0154 4 0 0015

3 14 4

0 06

0 0049 4

0 0005

2 3 3 U

0 0165 4 0 0005

2 59 4

0 03

0 0063,

+ 0 00022

0 0158 4 0 0005

2 43„ 4

0 001

0 0065„ ±

0 0002,

4 3 8 u

0 0412 + 0 001

2 80 >

0 13

0 0147

4 0 0009

2 3 2 Th

0 0496 0 0020

2 42

0 20

0 0205

4 0 0019

*From

H C Paxton and

C, R

Kecpin

Tin Technology of

Nuclear Reactor Safety Vol

1 P

267 The M I

1 Press

Cambridge Mass 1964

tSymbols n/b = delayed neutrons per fission v = average total neutrons per fission 0 = n/I v = fraction of total neutrons that arc delayed

Подпись: TkПодпись: 2 ;= і Подпись: PПодпись: (1.13)

Range Selection

A common practice is to specify the pressure interval in which the sensor is to be used so that the sensor is normally operating at a pressure between % and of the range span. Data for the elastic-metal sensors are given in Table 4.16. The basic ranges shown in the table may be modified.

Table 4.16—Typical Ranges of Elastic-Metal Pressure Sensors

Range span

Maximum over-range pressure, psig

Design

available

Min.

Max.

Thin diaphragm

316 s. s

0 5 in HjO

10 in. H20

50

Thick diaphragm

316 s. s.

25 psig

2000 psig

500 to 4000*

Bellows

Inconel or AM350 steelt

10 in H20

1000 in h2o

6000$

Bourdon tube

Ni-Span C,§ 316 s. s., or beryllium — copper

30 psig

8000 psig

Max. range x 1.25

‘See discussion of force balance in Sec. 4-3 2

tModified type-304 stainless steel adapted for welding and stress relieving. $And 100 psig on gases § Constant-modulus alloy.

image94

Fig. 4.17—Catenary-diaphragm sensing element and typical bridge circuit. (From D. M. Considine, Process Instruments and Controls Handbook, p. 3-42, McGraw-Hill Book Company, Inc., New York, 1957.)

 

Modifications include ranges having an elevated zero (com­pound range) and suppressed ranges where the minimum pressure is greater than atmospheric zero.

Motion balance refers to the mechanical system where­by the sensor motion is transferred by linkage or other means to a pointer, recording pen, or transducer mecha­nism, such as an armature or core (see Fig. 4.24). Typical motion-balance mechanisms are shown in Figs. 4.18, 4.19, and 4.20. Where restraining members are used, they are limited to providing means for adjusting /его or permitting calibration within the initial range capability of the sensing
element, in no way should the restraining members restrict the sensing action within the intended range span of the device.

Forte balance refers to the system whereby the free motion of the sensor is limited and actively opposed by some mechanical or electrical means. In effect this reduces the actual mechanical motion of the sensor to a very few thousandths of an inch throughout its range. An example of such a device is shown in Fig. 4.21. The mechanism is capable of highly elevated ranges. One design features four interchangeable diaphragms or capsules (Table 4.17).

FIXED

Подпись:Подпись: ABSOLUTE-PRESSURE GAGE EVACUATED PIVOT і

/ у VACUUM

Подпись:image96/ <….. >

f ‘"’j’"

Подпись: SLACK-DIAPHRAGM GAGE image98

BELLOWS ABSOLUTE-PRESSURE GAGE

SLACK-DIAPHRAGM DIFFERENTIAL UNIT

Fig. 4.18—Typical bellows and diaphragm pressure gages. Sensor motion is transmitted to indicator by mechanical linkage (motion-balance mechanisms).

image163

LINK TO POINTER OR LVDT MECHANISM

image99

Fig 4.19—Sectional view of a motion-balance pressure gage. (I mm D. M. Considine, Process Instruments and Controls Handbook, p. 3 15, McGraw-Hill Book Company, New York, 1957.)

 

image100

Fig. 4.20—Types of Bourdon gages, (a) C type, (b) spiral, (c) helical. (From D M. Considine, Process Instruments and Controls Handbook, p 3-16, McGraw-Hill Book Company, New York, 1957.)

 

Power-Reactor Feedback

The neutron kinetics equations (Eqs. 6 11 and 6.12) that were applied to zero-power reactors also hold for power reactors However, additional relations exist here between reactor power and reactivity because the former is high enough to cause effects on the latter (see Fig. 6.4). This feedback of reactor power to reactivity is the

—*K+>

kfb

H, FEEDBACK

TRANSFER FUNCTION

Fig. 6.4—Relations between the feedback and the zero — power transfer functions which make up the transfer func­tion of a power reactor

important characteristic of power-reactor dynamics. As might be expected, transfer-function measurements are used to obtain information about this feedback.

Equations that relate power to reactivity can be numerous and complex, depending on the system. Specific forms for boiling — and pressunzed-water reactors have been summarized 74 Where commonly a set of linear differential equations adequately represent the system, the feedback transfer function from power to reactivity may be written

kfb(s) Y’ rijd+TgS)

Подпись:

Подпись: Method and excitation Reactors used Results Random pulsing of a neutron source GE Critical Assembly,5 Rubeole and Ulysse,6 UFTR,7,8 University of Florida subcnticals,9 0 0/1, subcntical reactivity Oscillating control CP-2,4 DFR,11 EBR-1 and EBR-2,1 2,1 3 EBWR,1 4 (t/l, verification of equip- rod Fermi,15 GTRR,1 6,17 KEWB,18 Kiwi-A,19 LPTR,20 LAMPRE-1,1 9 NORA,2 1 Pathfinder,2 2 Penn State,23 PTR,2 4 SHE,25 SPERT,2 6 Zephyr and Zeus11 ’2 7 ment performance Variance to mean (no excitation) AGN-201,28 Cornell,29 Ford,30 Homogeneous D2О Facility,31 NORA,21 32 Russian subcntical,33 SPERT-2 and SPERT-4,34'35 Tokyo Inst of Technology,36 ZPR-4,37,38 ZPR-537 0/1, absolute power level Pseudorandom con- ATSR,39 Brookhaven,40 Godiva-П,41 JRR-3 and (5/1, verification of equip- trol rod SHE,4 2 44 MSRE,443 Saxton,45 UFTR* ment performance Spectral analysis Atomics Int ,46 Babcock & Wilcox Test Reactor,47 0/1, subcntical re- and/or autocor* BSR,48-49 Battelle Plutonium Assembly,50 activity, absolute relation (no excitations) Brookhaven High Flux,5 0 a EBWR,51 Daphne and Jason,52,5 3 GLEEP,54, HFIR,55 HTR, JRR-1, SHE, and TRR-1,4 2 43'55a-55b ,owa State Umv _ UTR-10,5 6 KEWB and SRE,57 LFR,58 MSRE,59 NORA,2 1 ORNL Pool,6 0,61 Penn State,2 3 Savannah,62 Saxton,63 SPERT-1,34 SPERT-3, ATRC, ARMF-1, and PBF,64 SNAP-10A and ETR,65’66 UFTR,7’8 Westinghouse CES,67 ZPR-3, ZPR-4, ZPR-5, ZPR-7, and Argonaut,68 ZPR-66 8 a power level Two-detector cross GTRR,1 6 JPDR,55a Karlsruhe Argonaut,68b (i/l, subcntical reac- correlation (no ORNL Pool,69 Penn State,69a STARK,70 tivity, local power excitation) Savannah SR-305 Pile,71 TRR-1,72 ZPR-97 3 distribution
Подпись: Table 6.6—Results Achieved in Zero-Power Dynamic Studies

nfs)/N “ H(S) " 2j 7‘ П k (1 + Tlks)
1

Подпись: G(s) =Подпись:

Подпись: Table 6.7—Results Achieved in At-Power Dynamics Studies Method and excitation Reactors used Results Oscillating control BORAX-4 and BORAX-5,’5’76 DFR,11 EBR-1 Stability study, feedback rod and EBR2,12’13 77 EBWR,H'n Fermi,15 GE BWR,79 HTR,80 JPDR,8oa SPERT l,26 SRE,81 VBWR8 2 determination Pseudorandom con- Kiwi-АЗ,41 MSRE,4 4a’8 3 Saxton,84 ,8 5 JRR-38sa Stability study, control- trol rod system study Spectral analysis BORAX-1,-2,-4, and -5,75 ’’ 6,8 6 Chapelcross,8 7 Stability study, noise- (no excitation) Dresden,88 EBR-2,89 EBWR,90-92 Elk River,9 3 GTR,9 4 HBWR,9 5 HFIR and ORR,5 9 ’*6,9 7 HFBR,98 HRE-2," HTR and JRR-1 and JRR-2,42 -4 з.8 0.1 0 0.1 0 0 a Indlan polnt> Savannah, and Yankee,62 JPDR,553'1 00a Kyoto Umv.,1 01 ML-1,102 Pluto,53 Saxton,63 SPERT-4,1 03 SRE,81 THOR,1 04 Trino,85 VBWR105’106 source determinations Pseudorandom Nerva,1 01 Phoebus 1A,1 08 SNAP109 Intervariable transfer plant control functions Cross correlation DFR,1 1 0 DMTR,11 oa SNAP,46 Pathfinder111 Stability study, inter- and spectral variable transfer analysis functions, noise- source determinations

where s = ICO and the values of т are time constants associated with a system variable that has a feedback reactivity change of y, percent for a 1% power change (in the limit of very slow transients).

The transfer function between an external excitation reactivity, kln, such as an oscillator rod, and the reactor power is the solution of Eqs 6 14 and 6.17 if к = 1 + kln + kfb is used

G0(s)

1 — G0(s) H(s)

Since G0 is well known, this equation is generally used to obtain H(s) or G(s) from the other

Compensated Ionization Chambers

One of the problems with ionization chambers is that the detector is indiscriminate and will detect any ionizing radiation If, for example, neutrons are to be detected m the presence of a strong gamma field and the neutron flux is to be related to the average current, then it is necessary to take into account the component of the current that is due to the gamma field

Part of the gamma-induced current is due to prompt gammas and is proportional to the neutron induced current This part is indicative of reactor power and is not detrimental However, the remainder of the gamma-induced current is relatively unchanging and creates a spurious signal, і e, a signal not indicative of the reactor power level

image28

OPERATING VOLTAGE, volts

Fig. 2.6—Typical neutron saturation curves, illustrating the change in plateau with increasing current (Courtesy Westing — house Electric Corp )

This, in turn, is not a problem at high power levels when the neutron field is much more intense than the back­ground gammas At low power levels, the gamma contribu­tion to the chamber current may be a large fraction of the chamber current and might exceed the neutron-induced current Thus the range of reactor power in which an ionization chamber can be used to measure the power level may be severely reduced

Two ionization chambers can be used to decrease the effect of the gamma background If an ionization chamber sensitive to gamma radiation only is installed near an ionization chamber that is primarily sensitive to neutrons, the signal from the gamma chamber may be used to cancel the gamma contribution to the neutron-chamber signal In practice, the chambers must be carefully matched and their relative positions must be properly fixed Chamber pairs for this purpose are commercially available

A common way of neutralizing or compensating for the effect of gamma radiation is to combine the two ionization chambers into a single unit called a compensated ionization chamber,1 4 1 s frequently abbreviated CIC A typical CIC is shown in Fig 2 8

A compensated ion chamber is essentially two ioniza­tion chambers m a single case One chamber collects the

image30

total current due to both neutrons and gammas. The other chamber is identical to the first in sensitive volume but lacks the neutron-sensitive materials. If electrons are col­lected in one chamber and positive ions in the other and if the resulting currents are summed, the gamma-induced currents are cancelled. In practice, it is normally immaterial whether the signal is obtained by collecting electrons or positive ions.

Theoretically, the cancellation could be complete. In practice, cancellation can be made complete at a given reactor power level. However, over the range of reactor power levels, most of the gamma effects can be nulled but a residual should be expected. The residual may be less than 1% of the signal or as great as 10% and depends on the
specific detector and the effort made to achieve good compensation. A reasonable state-of-the-art number is 2 to 3%, i. e., 97 to 98% compensation.

It is also possible to overcompensate. Figure 2.9 illus­trates the manner in which compensation varies as a function of operating voltage. Because of this voltage — sensitive feature, it is possible to use variable com­pensation.16 The variable-compensation feature has been commercially used.

Figure 2.10 shows one way in which compensation might vary over a portion of the reactor range. With fixed voltages, compensation is exact at only one point. Figure 2.11 is an illustration of the improvement gained from using a compensated ionization chamber. The figure

HV+ + 300 vl. HV_ — 250 vj *

image049
Подпись: Fig 2 9—Gamma compensation as a function of electrode voltages Measurements were made m a hot cell with a 60 Go source 1 3 fixed positive electrode voltage 300 volts Basic compensation 1 2%
Подпись: . Undercompensation

also provides insight for measuring and testing com­pensation in an operating reactor

The use of a gamma-compensated detector extends the range, compared to that of an uncompensated detector, by about two decades Depending on the reactor, an uncom­pensated detector may be expected to cover three or more decades, a properly located compensated chamber can reasonably be expected to measure the reactor power over at least five decades Recent practice has generally been to operate with fixed voltage and to design safety systems that avoid dependence on as r ach as two decades of compensation