There are a number of special sensors used in sodium — cooled power reactors. These are discussed in Vol. 2, Chap. 17. Most of the sensors are associated with monitor­ing sodium purity, e. g., the “plugging meter” that senses when impurities in the sodium have reached specific concentration levels, the electrochemical oxygen meter that monitors the activity of oxygen in the sodium coolant, the carbon meter that measures the carburizing potential in liquid sodium, etc. These are discussed in Chap. 17, Sec. 17-5.3, rather than in this chapter because of their rather specialized association with sodium-cooled reactors.

4-9.3 Special Sensors for Gas-Cooled Reactors

Gas-cooled reactors also require a number of specialized sensors. Sonic and acoustic thermometry have been noted elsewhere m this chapter. The critical importance of minimizing moisture in the primary gas coolant (analogous to the minimizing of oxygen in the sodium coolant in sodium-cooled reactors) has led to the development of moisture-sensing systems. These are discussed in Vol 2, Chap 18, Sec 18-3 3 In addition to moisture, coolant purity is also required This has led to the development of gas analyzing systems m the high temperature gas-cooled reactors These are also discussed in Sec 18-3 3

A number of inherent reactivity variations occur during the operation of a power reactor and must be considered in designing reactor control systems. Some of these can be used to assist in reactor control, others require attention in the control-system design.

A key effect to be considered is the temperature coefficient of reactivity. Temperature variations change neutron cross sections and dimensions of reactor materials and thus change the reactivity. A desirable condition is for the reactivity to decrease as the reactor temperature increases. Such a negative temperature coefficient has a stabilizing effect since, as the power increases and raises the reactor temperature, the negative temperature coefficient reduces the reactivity and tends to limit or level out the rise in power. Most of today’s reactors have a negative

temperature coefficient of reactivity, usually————- 1CT4/0F in

5k/k at operating temperatures

In boiling-water reactors (Vol. 2, Chap 16), the reac­tivity changes as the void volume in the core changes. Since the water (steam) acts both as neutron moderator and absorber, the void coefficient of reactivity can be either positive or negative

A generalization often used m preliminary calculations is to lump all the reactivity effects into a single power coefficient of reactivity, the change in reactivity resulting from a unit change in reactor power. This coefficient is typically ^10“4 decrease in 5k/k per megawatt (thermal) change in power level

A power reactor is inherently stable The degree of stability is temperature dependent since the reactivity coefficients are temperature dependent. Thus a reactor may be less stable when cold than at operating temperatures. When inherently stable, the negative temperature effects dominate the positive, and the requirements placed on the control system are less stringent. In fact, with a net negative coefficient of reactivity, some reactors may be controlled over a limited range without resorting to control-rod movement.

Long-time inherent changes in reactivity are those attributable to the increase of fission-product poisoning and fuel depletion. These can be controlled by chemical shimming or by incorporating burnable poisons in the fuel

7- 1.3 Methods of Reactivity Control

Most power reactors are controlled by rods that are inserted into or withdrawn from the reactor core The rods contain neutron-absorbing or fissionable material or a combination of the two Some power reactors have been controlled by the rotation of control drums on the core periphery, the control drums being made of combinations of neutron-reflecting and neutron-absorbing materials.

For power reactors where changes in neutron level may be accomplished over relatively long time periods, but where constant power levels are wanted once full power is achieved, burnable poisons and chemicals dissolved in the coolant (so-called “chemical shimming”) have proved ef­fective Burnable poisons can be added to the fuel elements to decrease fuel-element absorption of neutrons in propor­tion to the decrease in the fissionable material content of the fuel elements. Either type of control, chemical shimming or burnable poisons in the fuel, reduces the total reactivity that must be offset by the control-rod system

Joseph M Harrer and James G. Beckerley

1- 1 NUCLEAR AND FOSSIL FUELS

Many instrumentation systems are required to monitor, control, and regulate the nuclear and chemical processes of an operating nuclear power plant Although some of the systems are identical to those used in fossil-fueled power plants, many are entirely different

Perhaps the most important reason for differences between the instrumentation systems of conventional (fossil-fueled) and nuclear power plants is that conventional plants operate with continuous fuel feed and nuclear plants operate with stored feed In a conventional plant fuel is fed continuously to the combustion chamber, in present-day nuclear plants all the nuclear fuel necessary for many months of operation is in the reactor all that time Because of the large fuel inventory, an increasing nuclear reaction rate caused by equipment failure or malfunction will not be stopped by exhaustion of fuel Perhaps in future nuclear plants (e. g, those using fluid fuels), the inventory of fuel in the reacting region can be reduced and the associated hazard thereby diminished. In the meantime nuclear power plant instrumentation must be dependable to prevent damage.

Another reason for instrumentation differences is the concentration of heat energy in the two types of fuel About 40 billion Btu of heat is released in the fissioning of 1 lb of pure nuclear fuel On the other hand, about 14 thousand Btu is released in the burning of 1 lb of coal Since nuclear fuels are such concentrated heat sources, the heat flux from a nuclear fuel can exceed the capabilities of the coolant to remove heat Consequently, the details of nuclear-fuel performance must be measured The develop­ment of instrumentation systems for monitoring fuel performance has been a major effort in nuclear power technology.

The heat energy of a nuclear fuel comes almost entirely from the fission fragments At the time of their formation, the fragments have kinetic energies that correspond to particle tcmpcratuics of about 101 2°С In present-day solid fuels, the fission-fragment energies are immediately shared

CHAPTER CONTENTS

1-1 Nuclear and Fossil Fuels…. ……………………………………. 1

1-2 Definitions…………………………………………………………………………………………………… 2

1-2 1 Nuclear Terms…………………………………………………………………………. . 2

1-2.2 Fission-Process Terms……………………………………………………………………………… 3

1-2.3 Nuclear-Reactor Terms……………………………………………………………………………. 3

1-3 Nuclear-Reactor Kinetics…. ……………………………………. 4

1-3.1 Point Kinetics Without Delayed

Neutrons………………………………………………………………………………………………… 4

1-3 2 Point Kinetics with Delayed

Neutrons…………………………………………………………………………………………………. 5

1-3.3 Reactivity…………………………………………………………………………………………………. 6

1-3.4 The Inhour Equation. . . 8

1-3.5 Effects of Reactivity Insertions ……………………………………………………………… 8

1-3.6 Reactivity Changes………………………………………………………………………………….. 8

(a) Xenon 135……………………………………………………………………………………. 10

(b) Samarium-149 …………………………………………………………………………….. 15

(c) Fuel Burnup………………………………………………………………………………… 17

1-3.7 Three-Dimensional Kinetics. 18

1 4 Nuclear Power Plants………………………………………………………………….. . . 19

1-4 1 Types of Plants……………………………………………………………………………………….. 19

1-4.2 Sensed Vanables. .19

References………………………………….. … . . . 21 with the surrounding approximately 1022 atoms/cm3 of the fuel (usually uranium metal or oxide or carbide), and the average temperature of the nuclear fuel is many orders of magnitude less than the initial fission-fragment tempera­ture. In fact, the rate of coolant flow is regulated to keep the interior temperature of the nuclear fuel in the same general range (a few thousand degrees centigrade) as typical fossil-fuel temperatures Should coolant flow be impeded, however, the nuclear fuel temperature could become much higher. One of the primary purposes of nuclear power reactor instrumentation is to prevent this

Another difference between nuclear and conventional power plants that affects instrumentation is the presence of strong nuclear radiation fields in certain regions of a nuclear reactor The interaction of these fields with sensors and with electrical components can cause a deterioration in signal and system performance Because of this, the materials and techniques used in nuclear power plant instrumentation often differ from those used in fossil- fueled power plants

1- 2 DEFINITIONS

Nuelear power plants are based on eoneepts that require eareful definition In subsequent ehapteis man) definitions of speeiali/ed terms are presented whenever relevant to the diseussion In this section definitions of a number of fundamental terms basie to an understanding of nuelear power plant operation are given The definitions are listed by eoneept rather than alphabetically Most of the defini­tions are taken verbatim from the American National Standard Glossary of Terms in Nuclear Science and Technology 1

The problems of manufacturing in core fission cham bers and ion chambers small enough to fit the allowable space, rugged enough to withstand the in core environment, and inexpensive enough to permit extensive coverage of a power reactor core have led to efforts to develop other types of devices to measure neutron flux at fixed locations in a power reactor One device developed to solve these problems is the self powered neutron detector

The self powered neutron detector uses the basic radioactive decay process of its neutron activated material to produce an output signal As the name implies, no external source of ionizing or collecting voltage is required to produce the signal current The construction of the detector is quite different from that of an m-core fission chamber There is no gas filled region where ionization takes place, instead, the detector is of solid construction with a neutron-sensitive material connected to a lead wire, both being separated from the detector outer sheath by hard packed ceramic insulation The resulting detector is like a mineial-insulated coaxial cable, small m size and rugged

The simplicity of construction and operating principle lead to a number of advantages, including low cost, simplicity of readout equipment, low burnup rate, long lifetime, and ease of reproducing sensitivity

(a) Operating Principles. As shown in Pig 3 10, a

typical self-powered neutron detector consists of four parts emitter, insulation, lead wire, and sheath (or collec­tor) The emitter is a material of reasonably high thermal-
neutron activation cross section which, after activation, decays b emission of high energy betas with a reasonably short half life The insulation is a solid that must maintain high electrical resistance m the in-core temperature and nuclear-radiation environment, it should ideally emit no betas or electrons (e g, from neutron activation) Both the lead wire and sheath, or collectoi must emit few betas or electrons compared to the emitter so that undesirable background signals are minimized

When the self-powered neutron detector is placed in a neutron flux and connected to ground through an electrical current meter, the current measured is proportional to the net beta escape from the emitter If the detector remains in the neutron flux until equilibrium beta emission is reached, the current is directly proportional to the incident-neutron flux

When the activity induced by thermal neutron absorp­tion m the emitter is from a single radionuclide with a single half life, the detector output after exposure to the neutron flux for a time t is (3 1) where I(t) = detector current (amp) at time t (sec)

К = a dimensionless constant determined by detec­tor geometry and materials aatt = thermal neutron activation cross section of emitter material (cm2)

Q = charge emitted by emitter per neutron ab sorbed (coulombs)

N = number of emitter atoms T^ = half life of radionuclide generated in emitter (sec)

ф = thermal-neutron flux (neutrons env2 sec 1)

Steady state is reached when the exposure time is several times the half-life, T^, of the radionuclide

I0(t) = Kaact QN ф

where I0(t) is the steady state detector current at time t The inclusion of t is made necessarv by the fact that the number of emitter atoms, N, is decreasing with time

N = N(t) = N0 exp (-Кффах) (3 3)

where Кф is the fraction of the detector constant К which accounts for the neutron self shielding m the emitter and о is the thermal neutron-absorption cross section of the emitter material Introduction of the factor Кф is necessary since atoms of the emitter are exposed to a neutron flux that has been attenuated by the intervening atoms of the sheath, insulation and the emitter itself Substitution of Eq 3 3 into Eq 3 2 gives the steadv-state detector current

I0(t) = K<7actQN0 exp (—Кффог) ф (t>l^) (3 4)

The sensitivity of a self powered detector is defined as the change in the steadv state detector current per unit change in the thermal-neutron flux

s(t) [KaactQN0 exp (—Кффог)]

x (1 — Кффаг) (3 5)

The detector sensitivity is seen to decrease (because of burnup of the emitter material) approximately exponen tially with time The rate of sensitivity decrease is deter mined by the thermal-neutron flux that the detector is exposed to, the thermal neutron-absorption cross section of the emitter material, and the neutron self shielding m the emitter

If the detector life is defined as the time during which the sensitivity decreases to a fraction f of its initial value when the detector is in a constant thermal-neutron flux, then Eq 3 5 shows that

f=e1/T(l-7) (3 6)

where T = detector life in constant thermal neutron flux (ф) f = S(t = T)/S(t = 0) = relative sensitivity at t = T t = /Кффа = time to complete burnup of emitter material assuming and ф arc constant

The lifetime T can be calculated as a function of f from Fq 3 6 The values of T corresponding to f = 0 9, 0 8 0 7, 0 6, and 0 5 are found to be 1 = 0 05r 0 llr 0 17т 0 24r and 0 31r respectively Thus for example, if the detector lifetime is defined as the time for the sensitivity to decrease to 60% of its initial value then the lifetime is 24% of its “complete burnup’ time or 1 = 0 24r = 0 24/Kффа

The constant К in the basic equation, Eq 3 1, takes into account several effects associated with the detector structure and materials Specifically, the detector current is reduced by a factor Кф because the emitter atoms are partly shielded from the neutron flux (incident on the detector) by the atoms nearer the detector surface The detector current is also reduced by a factor because some of the betas emitted by the radionuclides in the emitter are unable to escape from the emitter Finally, the detector current is reduced by a factor Kg because the geometry, particularly the insulation thickness, may not permit some betas to reach (or traverse) the detector sheath Thus the constant К = K^K^Kg

(b) Construction and Materials Self-powered neutron detectors can be manufactured in several ways using different construction materials and different manufactur­ing techniques Table 3 3 shows the various neutron — activated beta emitters that have been considered as potential candidates for the emitter material Of the materials listed, only 103Rh and 51 V have been used in commercial applications Each of the others has been

rejected for one or more undesirable characteristics Be cause each has a low thermal neutron-activation cross section, 7Li, 1 1 B, and 27A1 yield unacceptably low signal-to noise ratios With a 2 58-hr half life, 55Mn results in too long a time constant if used in a detector Since 99Tc does not occur naturally, it is not readily available,11 5 In is unsatisfactory because 76% of its beta decay has a 54 min half-life Silver has both an acceptable cross section value and acceptable half-lives, but it would be difficult to compensate for burnup with the 24-sec 1 9 Ag burning up three times as fast as the 2 4-min 10 7 Ag

Neither 103Rh nor 51 V has any of these undesirable characteristics Because of its larger thermal neutron- activation cross section, 103Rh is used where short detec tors are needed for measuring local flux Many 103Rh detectors distributed throughout the reactor core can provide three dimensional power distribution information The relatively lower signal level of 5 1 V is more suited to long detectors designed to average the neutron flux over the full core height Such detectors cannot be used to deter mine power distribution along the axis of the reactor core, although several 5 1 V detectors dispersed throughout the core can provide data on the radial power distribution

Figures 3 11 and 3 12 show the two types of construc­tion commonly used for self powered neutron detectors in commercial use today

The earliest, and in many respects the simplest, type of detector construction is shown in Fig 3 11 The 0 020-in — diameter rhodium wire emitter is fastened to the Inconel lead wire of a standard 0 040-in magnesium oxide in­sulated, Inconel sheathed, coaxial cable All parts are baked out before assembly and are maintained scrupulously clean during assembly The section of the detector sensitive to neutrons has a larger diameter than the coaxial cable The construction of a neutron-detector assembly containing several of these detectors can be complicated by the change in diameter

Figure 3 12 shows an alternate construction The neutron-sensitive emitter is fastened to the Inconel lead wire before the insulation is installed Magnesium oxide insulators are threaded over the emitter and lead wire The Inconel sheath is slid over the insulators, and the entire assembly is swaged down to a finished diameter of 0 062 in Bakeout before assembly and rigorous cleanliness during

• INCONEL LEAD WIRE 0 062 IN DIA

RHOD’UM WIRE (EMITTER) •

Fig 3 12—Self powered neutron detector

assembly are important procedures The resulting detector has a coTistant diameter over its length, and the magnesium oxide insulation is compacted tightly around the emitter

Only three insulation materials have been considered for self powered neutron detectors aluminum oxide, beryl­lium oxide, and magnesium oxide Aluminum oxide has been most frequently used when the detector is assembled as shown in Fig 3 11 Aluminum oxide is not suitable for detectors assembled as shown in Fig 3 12 because of the danger of damaging the emitter or lead wire during the swaging operation In addition, aluminum is activated by thermal neutrons and emits high-energy betas (see Table 3 3) which contribute to background and reduce the signal-to-noise ratio The characteristic 2 З-mm beta decay of aluminum has been observed during irradiation of cables insulated with aluminum oxide Whether or not this is tolerable depends on the accuracy desired in the detector output signal Beryllium oxide has no significant advantage other than its extremely low thermal-neutron cross section This advantage, however, is more than offset by its high cost and toxicity Magnesium oxide is the most satisfactory of the three insulation materials because of its low cost, high resistivity, workability, and low noise potential

The two most commonly used sheath materials in detectors for pressurized-water and boiling-water reactors are type-304 stainless steel and Inconel because both are compatible with the reactor coolant Inconel is now standard in all commercial detectors The use of 30 r stainless steel in the sheath of detectors intended for high-accuracy applications is problematical since manga­nese, which constitutes about 0 5 wt % of most stainless steels, is activated by thermal neutrons and emits betas (see Table 3 3 )

Inconel is used universally as the lead wire material, although Nichrome was used successfully in earlier detec­tors

(c) Sensitivity The initial sensitivity of a self powered detector is given by Eq 3 5, with t = 0

S(0) = KaattQNo0 (3 7)

The number of emitter atoms at t = 0 is

where p = density of emitter material (g/cm3)

A0 = Avogadro’s number = 6 02 X 1023 A = atomic weight of emitter d = diameter of emitter (cm)

/ = length of emitter (cm)

The emitter is assumed to be cylindrical and made of a pure element It is further assumed that the emitter decays with the emission of a single beta, і e , Q = 1 60 X 10 1 9 cou lomb, the electron charge

As noted at the end of Sec 3 3 3(a), the constant К is the product of Кф, Kp, and Kg, the constants that take into account the neutron self-shielding, beta self-shielding, and geometric effects Figure 3 13 shows the values of these constants as a function of emitter diameter for rhodium with 10 mils (0 25 mm) of MgO insulation Figure 3 14 shows the same constants for vanadium emitters

The initial sensitivity of a rhodium detector with a 20-mil (0 51-mm) emitter and 10 mils of MgO insulation can be calculated from Eqs 3 7 and 3 8 using К values from Fig 3 13 and the rhodium cross section from Table 3 3 (The density of rhodium is 12 4 g/cm3 ) The result is

у = 1 З X 1 (Ґ11 amp/(neutrons cnrf2 sec 1 )

A similar calculation for a vanadium detector with a 20 mil emitter and 10 mils of MgO insulation yields (vanadium density is 6 0 g/cm3)

C

— = 7 1 X 1CU2 3 amp/(neutrons cm"2 sec 1 )

This value, as well as the one for the rhodium detector, is in good agreement with experimental values

Because of the rapid decrease in К with increasing emitter diameter, detector sensitivity depends more on emitter surface area than on emitter volume This is evident from Fig 3 15, where the detector sensitivity is shown as a function of emitter diameter The relation is nearly a straight line

Figure з 16 shows the change in detector sensitivity when the detector length and diameter are varied but the emitter mass is kept constant

(d)

Emitter Burnup. The depletion of the neutron sensitive emitter caused bv its absorption of thermal

neutrons reduces the sensitivity of the detector (see Eq 3 5) In the derivation of Eq 3 5, it was assumed that all factors were constant except t However, the neutron self-shielding factor, K^, is not constant during prolonged exposure to neutrons it tends to increase as the emitter burnup increases because burnup removes (transforms) some of the self shielding atoms The resulting change m is not significant over a short period of operation, but it must be taken into account in am readout system that automatical^ compensates for detector burnup

From Eq 3 5 the relative detector sensitivity is

S(t)

^y=exp( K00ot)(l K00at)

= et/T(l (3 9)

where r = 1 /Кффо

For a rhodium detector with a 20 mil emitter and 10 mils of MgO insulation, the characteristic burnup time r is 0 913 X lO22/0 In an acerage thermal neutron flux 0 = 4 X 1013 neutrons cm”2 sec1 the value of r is 23 X 107 sec, or 7 18 years When the detector is exposed to this flux for one year, its sensitivity relative to its initial value decreases to exp (-1/7 18) X [1 —(1/7 18)1 =0 75 In other words, its sensitivity is now 75% of its initial value In two years, the sensitivity decreases to 55% of its initial value From this it follows that the emitter burnup time is longer than the normal reactor refuelling cycle The emitter burnup rates given in Table 3 3 are based on the assumption that Кф = 1 As noted earlier, Кф is less than 1, so the actual burnup rates will be lower than those given in the table

The product NQ in Eqs З 1 through 3 4 is equal to the total charge (betas) generated in the emitter before it is used up (all atoms activated) Since and Kg are the factors that identify how many betas escape to become useful detector output current, the total useful charge generated bv the detector is

q = K^KgQN (3 10)

If we use the К values from Fig 3 13 and calculate N from Eq 3 8, we find the total useful charge generated by a 20 mil rhodium detector with 10 mils of MgO insulation to be

q = 12 1 coulombs/cm of emitter length which is m good agreement with experimental values

(e) Response Characteristics The response character istics of a self powered neutron detector are directly related to the radioactive scheme of the radionuclides formed in the emitter

Figure 3 17 shows the decay scheme for self-powered detectors that use vanadium as the emitter material All neutron absorptions in the emitter material, 51 V, which has a thermal neutron-activation cross section of 4 9 barns, result in the creation of 52V The latter decays by beta emission to four excited states of 52Cr which then immediately go to the ground state by gamma emission The half life of this decay scheme is 3 76 min (226 sec) The 2 4 MeV beta accounts for almost 99% of the beta emission and provides energetic betas for a good signal to- noise ratio

Because the emitter radionuclide has a single beta decay period, the time response of the vanadium detector to a step change in thermal neutron flux from 0 to zero is

I(t) = I0e^ 69 31/2 2 6 =I0e 1/326 (3 1 1)

ind the time response to a step change in thermal neutron flux from zc ro to ф is

I(t) = I0(l — e t/32 6 ) (3 12)

where t is in seconds l(t) is the detector signal current, and I0 is the steady state signal given in Eq 3 2 The mean life 326 sec, is the half life divided by 0 693, it is the time for I(t) to decrease by 1/e Figure 3 18 shows the response of a vanadium self powered detector to a step decrease m neutron flux (Eq 3 11) on a semilogarithmic scale T e vanadium detector response follows an exponential with a characteristic 3 76 min half-life (time constant = 3 76/0 693 = 5 4 min) and reaches 90% of the step change in 12 5 min Figure 3 19 shows the response of a vanadium self powered detector to a step decrease and a step increase in neutron flux, the curves are plotted on a linear scale

Figure 3 20 shows the decay scheme for rhodium emitters Neutron absorption by rhodium creates two radioisotopes of 104Rh The total neutron activation cross section of rhodium is 150 barns The cross section for the creation of the ground state 104Rh is 139 barns (92 7% of the 150 barns), and, for the creation of the metastable і 0 4 m Rh, tross section is 11 barns (7 3% of 150 barns) The metastable state decays by gamma emission to the ground state with a characteristic half life of 4 4 min (264 sec) The ground state 1 04 Rh decays by beta emission to the ground state 104 Pd with a half-life of 42 sec In this final beta decay process, 98% of the emitted betas have an

energy of 2.44 MeV, sufficiently high to provide adequate signal-to-noise ratio

Because it has an emitter with two beta-decay con­stants, the time response of a rhodium self-powered detector to step changes in neutron flux involves two

Figure 3 18 shows I(t)/I0 vs time on a semilogarithmic plot for a step decrease m thermal-neutron flux on a rhodium detector For the first 3 min after the step change, the detector signal is dominated by the 42-sec half-life (61-sec time constant), beyond 6 mm after the step change, the

rhodium detector signal follows the 4 4-min decay of 10 4m Rh slgna[ reaches 90% of the step change in less than 3 min The у-intercepts of the two half-life curves in Fig 3.18 correspond to the coefficients of each exponential in Eq 3 13 Figure 3 19 shows the time responses of a rhodium detector to step decreases (Eq 3 13) and to step increases (Eq 3 14) in flux, plotted on a linear scale

(f) Connecting Cables. The connecting cables required to bring the self-powered detector signals out of the core should produce as little background signal as possible As shown in Figs 3 11 and 3 12, the cables commonly used are 40 or 62 mils in outside diameter with magnesia insulation and Inconel lead wire and sheath The neutron cross section for Inconel is negligible, so neutron-induced signals are negligible The major sources of noise signals are

Compton electrons and photoelectrons generated when gamma rays are absorbed or scattered by the lead wire and sheath The noise signals are prompt in responding to changes m incident gamma flux

Compton electrons and photoelectrons originating in the wire and absorbed in the sheath produce positive background signals Electrons originating in the sheath and absorbed in the lead wire produce negative background signals Equal absorption of electrons in the wire and sheath would result in a zero background signal, ideal for maximum neutron signal The larger mass and surface area of the sheath tend to make a negative background signal for most connecting cables Appropriate selection of emitter and sheath materials and dimensions should make it possible to build cables with essentially zero background signal

In practice, temperature effects are not entirely separa­ble from the gamma effect If it is assumed that there is no need for gamma discrimination, at elevated temperature the cable insulation resistance is seen to decrease as the temperature increases whereas the breakdown voltage, which creates noise or a mean deviation, is relatively constant Thus the effect of noise is minimal whereas the mean current attributable to neutrons can be completely obscured by direct-current leakage.

Quantitative results have not been reported. The first reported use of MSV methods was for in-core units of about 1 cm3 volume operating at about 600°F (316°C) The mean signal was obscured by leakage, but the MSV signal was still present The gross effect has been discussed by DuBridge et al (see the Bibliography at the end of this chapter).

From these observations it can be concluded that, if neutron-sensitive chambers and their associated cables are to be operated at elevated temperatures, the proper method
is to use MSV measurements instead of mean-current measurements.

5- 5.4 Wide-Range Neutron Monitoring Channels

As noted in Sec 5-1, the large range of neutron-flux values to be monitored m a power reactor requires the use of several separate channels with two decades of overlap between the channels With the MSV technique it has been possible to develop monitoring systems that cover 10 decades of reactor power. The signal from a single fixed-position fission chamber is used with what has come to be called counting-MSV or counting-Campbelhng cir­cuits. The combination of count rate and MSV can be read out as a linear indication of power, much as is done with a range-switched picoammeter (see Sec 5-4.4), or a log output can be taken from which period can be derived.

The wide-range instrumentation permits the use of fewer sensors, recorders, meters, cables, and sensor thim­bles. This represents a significant saving in power-reactor instrumentation costs.System Descriptions and Components

Figure 5 21 is a block diagram of an average-magni­tude-squared channel that covers 10 decades of reactor power The MSV portion of the channel uses the combina­tion pulse-charge or current preamplifier, band-pass ampli­fier, rectifier, log amplifier, and d-c amplifier The noise level for the Campbell part of the channel is reduced by special shielding of the 40-ft cable between the chamber and the double-shielded preamplifier. The impedance and signal levels out of the preamplifier are such that essentially any reasonable length of conventional coaxial cable to the rest of the circuit may be used with good results As shown in Fig. 5.21, the wide-range log power channel consists of an LCR circuit and a log-Campbell circuit working out of the same fission chamber and preamplifier Their output signals are combined to give a single output indication of log power and, at the same time, to eliminate normal limiting errors of each one.

The high-frequency components of the signal pass through a conventional LCR circuit using a discriminator, flip-flop, and multiple-diode log pump circuit This circuit gives an output voltage, Ei, that is proportional to the log of the count rate from about 0.3 to 300,000 counts/sec. A biased diode, Db limiter is used to cut off that portion of the response which is adversely affected by resolution counting loss (usually about 2 X 10s neutrons cm 2 sec 1) As is customary with LCR circuits, the log diode pump uses fixed low-temperature-coefficient components to obtain the log relation. The pump circuit output passes through a d-c operational amplifier with adjustable gain and bias, so output volts per decade and volt level for a particular flux level can be established.

I LEVEL I TRIP I_ .__
ADJ BIAS	ADJ VOLT
jcOUNT-RATE SIGNAL ■<> |rms signal
PREAMP
TEST AND CALIB
I———— 1 y. LIN I Чпт PWR |£HANNELj
BAND­ PASS AMP
LEVEL TRIP (LOW)
LOG COUNT RATE LOGA-C OUTPUT COMBINED OUTPUT
VOLT­ METER
HIGH- VOLTAGE SUPPLY
Fig. 5.21—Wide-range log channel
LCRM
INPUT

The low-frequency components governed by the Campbell band-pass amplifier pass through the linear rectifier, filter (T = 50 msec), and through a stable d-c log amplifier to give a log indication of power from 2 X 10s to 2 X 1010 neutrons cm 2 sec 1 The diode D2 allows only signals above zero to pass, therefore, if the output of the log amplifier is biased, the lower end of the response curve below 2 X 10s neutrons cm-2 sec 1 can be eliminated. This portion of the curve may be adversely affected by gamma and alpha background, noise, imperfect rectification, and lack of pulse overlap. A gain adjust at the output of the log amplifier allows the slope of E2 to be properly adjusted to match that of Ej Since the bias cutoff points can be adjusted to coincide, a smooth, fast, all-electronic transition is made from counting to Campbelling or vice versa

Since misalignment or drift might produce an offset at the crossover point (2 X 10s neutrons cm2 sec1) and cause an exaggerated false period indication m that region, great emphasis has been placed on stability of the circuits and on a built-in calibration and test circuit that will allow proper alignment without the use of a reactor High-gain solid-state operational amplifiers (some integrated circuits) with feedback through stable circuit elements were used throughout. The principal temperature problem, as usual, was associated with the log amplifier in the Campbell circuit, and this was solved by using two operational amplifiers and two sets of logging diodes thermally coupled to obtain a temperature-compensated log response. Temper­
ature tests were performed between 50°F and 150°F (10°C and 66°C) Temperature drift results in an output error of less than 15% from 50°F to 120°F and only a slight further degradation up to 150°F.

Another average-magnitude-squared channel is shown in Fig. 5.22. The circuit is divided into two portions, as shown in the figure The signal from the radiation sensor enters the instrument and is routed both to the log count rate circuit (LCRM) and the statistical level amplifier (MSV) Pulses within the range of 1 per second to 106 per second pass through the LCRM discriminator into a flip-flop, a driver network, and then to a Cooke—Yarborough diode pump log converter, where the pulse rate is converted to a d-c output At that point the signal is amplified to the desired output level and routed to the front panel meter and other instrument inputs When the input signal enters the MSV portion of the instrument, it is first applied to a filter that passes only the portion of the signal between 4 and 8 kHz This signal is then applied to a wide-range rectifier, thus providing a half-wave rectified signal to a smoothing filter, which then routes the d-c output to a log amplifier and hence to the output meter and other external devices The output of the MSV circuit is scaled to read two decades of output for each decade of input current to provide the square m the mean-square measuring technique

A third meter on the instrument measures the rate of change of both the LCRM and MSV channels alternately, switching from the LCRM channel to the MSV channel

automatically as the LCRM reaches near full scale and as the MSV channel begins to operate. Since this portion of the circuit is somewhat novel, it is detailed in Fig 5 23.

In operation the output levels from the LCRM and MSV circuits are each applied to a separate differentiator circuit that operates continuously. The two outputs are routed through a solid-state switching network that is controlled by the magnitude of the MSV input signal such that below a preset level of the MSV circuit the signal from the LCRM differentiator enters the output scaling amplifier and above this level the MSV differentiator controls the output scaling amplifier. The output of the scaling amplifier is fed to the rate-of-change meter, which reads from —1 to +9 decades per minute

Another feature of the rate-of-change circuit is the “LCRM suppress” feature This involves a circuit to suppress rate-of-change movements on the lower portion of the LCRM channel and thus has the effect of preventing rate-of-change meter movements where counting statistics cause an erratic signal

In addition to the rate-of-change circuits, the instru­ment generates pulses for calibrating the LCRM, ramp functions for checking the rate-of-change circuits, and a variable-level 5-kHz signal for calibrating the MSV circuit Furthermore, all meters have electronic level trip circuits that read the output level of a particular circuit and produce both an automatic resetting alarm and one that latches and must be reset manually after an alarm is
produced by an excessively high or low level reading on any one of the three front panel meters.*

Joseph F Mech

1- 1 INTRODUCTION

1- 1.1 Reactor-Power Measurement

Since a nuclear power plant generates power from the heat produced by nuclear fissions, the power level is commonly measured b> observing the “radiations” directly associated with the fission process Fnergetic fission fragments, neutrons, photons, and other particles are produced at the time each fission occurs 1 ’ The number of these radiations, or components of these radiations, is proportional to the number of fissions The rate of appearance of these radiations is proportional to the fission rate and, thus, to the reactor power level

Most fission fragments are radioactive and continue to emit betas and gammas long after the fission events m which they were created * In addition, the fission neutrons and some of the more energetic photons can induce radioactivity This induced radioactivity also persists long after the creating process The radiations from the total residual radioactivity, variously called afterglow, decay heat, or fission-product activity, contribute up to 5% of the reactor heat However, the decay heat is not an indicator of reactor power but is related to the history of operation of the reactor

The most desirable way to make any measurement is to use the most direct method Reactor power therefore should be measured by detecting the prompt fission radiations The fission fragments and beta radiations are short range and are stopped in the reactor fuel However, the neutrons and gamma rays accompanying fission are sufficiently penetrating to be detected at some distance The technology for reactor power measurement is based on the detection of neutrons or gammas or both.

‘Less than 1% of the fission fragments emit neutrons Most neutrons are emitted in the first few seconds after the fission event that created the fragments See Chap 1, Sec 132

CHAPTER CONTENTS

2 1 Introduction…………………………………………………….. …………. . .22

2-1 1 Reactor Power Measurement………………………………………………….. ……. 22

2 1.2 Interactions with Matter…. … 22

2 13 Accepted Detection Principles……………………………………………………….. 23

2 1.4 “Out-of (ore” Defined…………………………………………………………… ……… 23

2 15 Use of Out-of-Core Sensors in Reactors…. 24

2 2 Principles of Gas Ionization Sensors…. . -25

2-2 1 Ionization Chambers…. 25

2-2 2 Compensated Ionization Chambers………………………………………………. 28

2 2 3 Counters…………………………………….. … . … 3q

2-3 Mechanical Features of Gas Ionization Sensors… 32

2-3 1 Structural Design………………………………………………………………………………. 32

2 3.2 Materials of Construction…. . . -32

2-4 Other Radiation Sensors. … . … -33

2-4 1 Proportional Counters……………………………………………………………………… 33

2-4 2 Self-Powered Detectors…………………………………………………………………… 34

2-4.3 Activation Detectors………………………………………………………………………. 34

2-4.4 Solid-State and Scintillation Detectors…. 34

2-5 Installation……………………………………………………………………………………………………. 34

2-5.1 Cables……………………………………………………………………………………………….. 35

2-5 2 Hardware………………………………………………………………. ……….. 35

2 5.3 Circuits…. 35

2-5 4 Immersion in Coolant…………………………………………… ………. 35

2-6 Environment………………………………………………………………………………………………… 3 s

2 7 Life and Reliability……………………………………………………. …. -36

2-8 Typical Specifications of Commercial

Gas Ionization Sensors……………………………………………………… . * 36

References……………………………………………………………………………………………………………. 41

4- 4.1 Differential-Pressure Flowmeters

(a) Basic Considerations. All flowmeters are con­sidered to consist of two parts a primary element, which contacts the flowing fluid, and a secondary element, which indicates or otherwise displays the desired information.

In the common differential-pressure or head-type flow­meter, the primary element is an obstruction placed in the pipe to create a pressure drop, and the secondary element is a device to measure this pressure drop and convert it to rate of flow. The secondary element itself may consist of two parts, a transmitter and a receiver, in case the information is to be displayed at some distance from the point of measurement The primary element is usually one of three types orifice plate, flow nozzle, or Venturi tube.

(b) Orifice Plates. The orifice plate is a thin disk clamped between gaskets in a flanged joint, with a usually concentric circular hole smaller than the internal pipe diameter. This is the simplest type of primary element and the most easily reproducible. It can be used without individual calibration with the greatest assurance of accu­racy.

Flow through a sharp-edged orifice plate is character­ized by a change in velocity, which reaches a maximum at a point slightly downstream from the orifice. At this point, called the vena contracta, the flowing stream has its greatest convergence. Beyond this point the flowing stream diverges until it again fills the entire pipe area, the velocity is reduced back to its original value (assuming fluid density and pipe cross section are the same upstream and down-

• •

*MCT CORE MOVES TOWARD PRIMARY A ON MEASURED VARIABLE INCREASE.

ACTUAL DIRECTION OF TRAVEL DEPENDS UPON LINKAGE REQUIRED FOR PARTICULAR INSTRUMENT.

□ CUSTOMER CONNECTIONS

Fig. 4.23—Schematic of a linear voltage differential transformer (LVDT) and demodulator circuit.

■*— IRON — CORE

BAKELITE OR CERAMIC COIL FORM

COILS

LEADS-

ALUMINUM SHIELD

VARIABLE-INDUCTANCE INDUCTANCE-RATIO UNIT ELEMENT

MUTUAL-INDUCTANCE ELEMENT

A-C VOLTMETER 0.1 V
FULL SCALE

0. 10

0. 08

>

l_" 0.06

Э

ь 0.04 О

0. 02

0

PHASE RELATIONSHIP IN MUTUAL-
INDUCTANCE ELEMENT

BOURDON TUBE /

CIRCUIT CONNECTIONS USED IN SIMPLE
PRESSURE-INDICATING SYSTEM EMPLOYING
MUTUAL-INDUCTANCE ELEMENT

Fig. 4.24—Examples of inductance elements for LVDT’s

stream of the orifice), and the pressure increases to a value less than its original value.

Several locations for metering connections are shown in Fig 4 25.

Vena Contractu Tapi, The high-pressure connection is one pipe diameter upstream from the orifice, and the low-pressure connection is at the vena contracta. This tap arrangement is commonly used, particularly in the power industry. It has a slight advantage in that the connections are in regions of nearly constant velocity, thereby offering some tolerance in tap location without a noticeable change in differential pressure

ID and %D Taps These are an approximation of vena contracta taps. The high-pressure connection is one pipe diameter upstream from the orifice, and the low-pressure connection is one-half pipe diameter downstream from the orifice inlet.

Flange Taps These have connections drilled through the edges of the flanges 1 in. from the adjacent orifice surface. Flange taps are widely used in the gas and chemical industries because they are convenient to use and install “Orifice flanges” are readily available with pressure con­nections and jackscrews to spread the flanges to facilitate orifice replacement

Corner Taps These have effective connections im­mediately adjacent to the orifice plate. Corner taps are
commonly used in Europe but are seldom used in this country because they require special flange machining. They are used in some small orifice pipe assemblies furnished by several instrument manufacturers

(c) Flow Nozzles. The flow nozzle, usually of ASME long-radius high-ratio design (Fig 4.26), has an elliptically flared inlet and a cylindrical throat section. There is no vena contracta effect, because maximum velocity takes place in the throat. The flow nozzle passes approximately 60% more flow than an orifice with the same differential pressure and the same ratio of throat diameter to internal pipe diameter. (This latter ratio is the (3 of the flow nozzle, see Sec. (e) below.) A flow nozzle can be installed in welded piping but cannot be used to meter flow in either direction. The flow nozzle can be used successfully in some installations where limited length of straight pipe would not be suited to the use of an orifice.

A throat-tap nozzle, with downstream connection installed directly in the wall of the flow nozzle throat (Fig 4.27), has been developed by turbine engineers and is strongly recommended by them for the performance testing of turbines.

(d) Venturi Tubes. A Venturi tube has conical sections between the cylindrical pipe and throat, with curved transitions (Fig. 4.28) Its capacity is similar to that of a

flow nozzle, but pressure restoration is more complete because of minimized turbulence in the outlet cone. The Venturi tube may have piezometer rings or annular cham­bers surrounding the inlet and throat to average pressures at four or more points. These rings also have the beneficial

effect of permitting an installation to be made with a minimum length of straight pipe.

A nonstandard Venturi tube, with equal angles of taper in the inlet and outlet cones, can be used to meter reversing flow.

L, i D or L, i(D/4 +10") z ;D/2i D/4 for 4’і 0*6"

0/40; D/2 for 6"i D г 32"

Lt* d/3 у * d/6

5/32" ї 8 < 25/64" ond
8 < 0.1 D or 013 d

Fig. 4.28—Herschcl or classical Venturi tube. (From Fluid Meters, Fig II III 26, p. 231, American Society of Mechanical Engineers, N Y, 1971.)

Several modified Venturi tubes or flow tubes, shorter than the standard Venturi tube but claiming a lower unrecovered pressure drop, are now available. One such tube is shown in big 4.29 In general, these tubes take advantage of (1) an impact component to increase the pressure felt at the high-pressure connection and (2) a change in direction of the flow in the boundary layer at the low-pressure connection to decrease the pressure at that point. The result is that, for a specified differential pressure and flow rate, the throat diameters of these modified Venturi tubes are larger than those of conventional tubes, thus the overall pressure loss for a given flow rate may be less.

(e) Sizing Primary Elements. The basic equation for a differential-pressure flowmeter, using an orifice, flow noz­zle, or Venturi tube, may be stated

This equation exists in other forms, e. g., for convenient use in gas measurement where flow rate in volumetric units and density at standard or base conditions are involved

The coefficient of discharge, C, may be presented by curves or in tables as a function of pipe Reynolds number, Ro, or of throat Reynolds number, Rq Sometimes C is replaced by’ a combined coefficient, already divided by the denominator of Lq 4.12, then it is labelled the “coefficient К with velocity-of-approach factor included ” Rather than including here sufficient information to permit complete and accurate flow determinations to be made by measuring differential pressure across a primary element of any type and dimensions, this text is limited to presenting a method for determining approximate dimensions. These are suitable for estimating purposes or for assessing the acceptability of a proposed piping installation for flow-measurement pur­poses. ’

The diameter ratio, (3, is determined from Fig 4 30 with a calculation of the capacity factor, I, from the applicable equation For liquids

_ W 1 “ D2(h7f^

or

I = Ql7s

7.48D2 (h7f)1’4

For steam

,______ w___

D2 (h/v)’*

For gases

QgTs

D2(h7f)^

or

Qg [G(T + 460)1*
21 5D2 (hP)^

where D =mternal pipe diameter (in.)

G = specific gravity (dimensionless)

I = capacity factor (dimensions consistent with above equations)

P = pressure at primary-element inlet (psia)

Qq = gas flow rate [ft3 /hr at standard or base con­ditions, often abbreviated “scfh” (standard con­ditions are usually 30 in Hg and 60°F)]

Ql = liquid flow rate [gal/hr at standard or base temperature (usually 60°F for petroleum prod­ucts, but flowing temperature for water)]

T = temperature (°F) v = specific volume (ft3/lb)

7S = density (lb/ft3 at standard or base conditions)

7f = density (lb/ft3 at flowing conditions)

In general, a primary-element /3 ratio of 0 50 to 0 70 may be considered normal. Higher ratios may be expected in high-pressure or high-temperature applications where pipeline economics suggests using the smallest acceptable size with consequent high velocities. An extremely low /3 value might indicate that the pipe size is larger than required or that a meter of lower differential-pressure rating would be preferable. The low /3 ratios of throat-tap nozzles are desirable in turbine testing to provide high differential pressure which may be read with accuracy on a manometer. The high differential pressure can be tolerated during the short duration of a test (after which the nozzle is removed)

The minimum and maximum limits of the diameter ratio, (3, for various primary elements are shown m Table 4.18. These (3 values are important in the selection of maximum meter differential pressure. For compressible fluids (steam, air, and gases), the value of the maximum differential in inches of water should not exceed the operating pressure in psia in order to avoid inaccuracies due to variations in the expansion factor, Y, that are not taken into account.

(f)

Installation. Accurate flow measurements require that the primary element be in a “normally turbulent” flow pattern, with fully developed velocity profile and without spiral motion or velocity stratification. Because of this

straight pipe section of adequate length.

It is generally accepted that the required pipe length depends only on the diameter ratio, 13, and on the structure of the fitting or combination of fittings preceding the straight pipe. On this basis the curves of Fig 4.31, originally published by the American Society of Mechanical Engineers (ASME), have been developed. It should be emphasized that longer lengths are desirable when the arrangement of building and equipment permits, the mini­mum lengths represented by the curves are a compromise and may not result in complete removal of an abnormal inlet turbulence.

(g) Accuracy of Primary Elements. Any meter manu­facturer can be expected to furnish conventional primary elements (orifices, flow nozzles, or Venturi tubes) sized in accordance with the standard equations and discharge coefficients published by ASME These coefficients are average values that may be considered to be correct within tolerances that vary with /3, Reynolds number, and pipe size. The approximate accuracy of these coefficients is as follows

±1.0 for concentric orifices with flange or vena contracta taps, D ^ 2.0 m., 0.20 j3 3? 0.70 ±2.25% for same, (3 = 0.75 ±0.75% for Venturi tubes ±2.0% for flow nozzles ±1.4% for eccentric orifices, D > 4 in.

±2.0% for segmental orifices

When greater accuracy is required, the primary element in its pipe section may be calibrated at a hydraulic laboratory to establish, as nearly as possible, the true value of its individual coefficient of discharge. Ideally the calibration should be performed at Reynolds numbers corresponding to expected operating conditions. This may not be possible, however, because the application may involve the flow of steam, or high-temperature water, at low viscosity (hence a high Reynolds number), and in the
laboratory it is necessary to use low-temperature water with relatively high viscosity, which limits the maximum Reyn­olds number available in the calibration runs If the coefficient curve is stable and flattens out at the high flow rates available in the laboratory, it is considered satisfactory practice to extrapolate to obtain a coefficient at the higher Reynolds number expected m actual service. The uncer­tainty of a coefficient so determined may be approximately

0. 5%. Greater accuracy may be expected, although it is difficult to guarantee, in view of the number of variables that must be measured during the calibration.

(h) Pitot Tubes. The Pitot tube is a primary flow­sensing element. It consists usually of a small-diameter tube pointed upstream with a pressure tap in its side (Fig. 4.32). The second (static) connection may be a trailing connection inside the pipe. Sometimes both connections are in the sides of a straight cylindrical probe. The Pitot tube measures velocity pressure itself, rather than the change in static pressure resulting from a change in cross-sectional area and velocity.

The equation for the Pitot tube may be written

V = CpKp(2gH)* (4.14)

where V = average velocity in the pipe line (ft/sec)

Cp = ratio of average velocity to velocity at the Pitot tube tip

Kp = coefficient based on Pitot tube design H = differential pressure (in feet of flowing fluid) g = acceleration due to gravity (32.17 ft/sec2)

From Eq 4.14 an equation can be derived similar to the basic orifice equation

W= 359CpKpD2 (hw7f)’* (4.15)

where W = rate of flow (lb/hr)

D = internal pipe diameter (in.) hw = differential pressure (inches of water at 68°F)

7f = density at flowing condition (lb/ft3)

If the sensitive tip of the Pitot tube is located at or near the center of the pipe, Cp may be 0.70 to 0.81 The value of Kp is usually supplied by the manufacturer, it may be close to 1.00 for a laboratory Pitot tube such as that shown in Fig. 4 32, or approximately 0.82 for a commercial Pitot tube such as that shown in Fig. 4.33.

The Pitot tube is normally used in temporary installa­tions and for estimating. It is not generally accepted for permanent installation because (1) the small passages tend to plug, which makes the meter insensitive or inoperative,

(2) a traverse must be made across the pipe to establish the point of average velocity required to evaluate the correction factor, Cp, (3) the differential pressure usually encountered is small, and (4) the device cannot be adjusted to provide a given value of flow at a selected differential pressure.

ALL FITTINGS IN SAME PLANE

oo

SO

(i) Secondary Elements. In a nuclear plant, the selec­tion of a secondary element to measure and interpret the differential pressure is limited by the need to avoid the presence of mercury, a common flowmeter sealing fluid, and, in the majority of cases, the requirement for a remote transmission system between the measuring mechanism and the display equipment.

In a remote transmission system, the secondary element is considered to include both the transmitter containing the

measuring mechanism and the receiver (i. e., the compo­nents for recording, indicating, integrating, etc.). In effect, the direct mechanical connection of a self-contained secon­dary element is replaced by a pneumatic or electric position-transmitting mechanism.

As noted in Sec. 4-3.2, measuring mechanisms of differential-pressure transmitters are of two general classes: motion balance and force balance. In a motion-balance system, the differential pressure exerted on a bellows or diaphragm displaces it, and the displacement is opposed by a spring, the force exerted by the spring being directly proportional to the applied differential pressure. A typical motion-balance-type electric transmitter is shown in Fig. 4.34.

In a force-balance system, the output signal is supplied to a pneumatic bellows or electromagnet that opposes the force exerted by the measuring mechanism. In a typical pneumatic force-balance transmitter (Fig. 4.35), a change in differential pressure changes the air gap at a nozzle tip, thereby changing the nozzle pressure, which is then amplified to provide the output signal. The changed output pressure changes the force opposing the measuring force, restoring equilibrium at a new value of the opposing forces with only an imperceptible change in nozzle air gap.

The receiver of a flowmeter may contain two features peculiar to flow measurement, a square-root extractor and an integrator. The square-root extractor is required if the pointer motion is to be directly proportional to flow rate

instead of to differential pressure. The integrator is required to convert flow rate to total flow for accounting purposes.

Because the rate of flow is proportional to the square root of differential pressure, a flow scale on a differential-pressure meter is not uniform, the divisions at the low end of this scale are compressed close together and difficult to read. The square-root extractor interposes a variable gain between the measuring mechanism and the display, magnifying the motion significantly at lower flow rates to make the scale divisions uniform. The extractor may be in the transmitter of a transmitting system, in the receiver, or in a separate unit installed between transmitter and receiver. A simple mechanism that performs this function pneumatically is shown in Fig. 4.36 In the figure, the rise d is proportional to the differential pressure, and the pointer motion indicating flow is proportional to the angle a A cam follower operates through a vane and nozzle to maintain a light contact with the cam. For low values of a. (i. e., d is very small compared to the beam length R) the value of a is almost exactly proportional to the square root of d.

The integrator is a counter that is usually driven by a constant-speed motor through a friction clutch and cam — operated escape mechanism in such a way that the counter rotates during a portion of cam rotation, the duration being proportional to rate of flow or point of position. The amount registered during any time period therefore is the total flow m that period. A diagram of a typical integrator is shown in Fig. 4.37.

(j) Accuracy of Secondary Elements. Secondary — element accuracy may be represented as a single tolerance or as an individual tolerance for each component, such as transmitter, square-root extractor, receiver, and integrator.

For several tolerances to be combined, they must be expressed on the same basis, i. e, in terms of differential pressure or of flow, and as percent of maximum or of actual reading. The square root of percent maximum differential is percent maximum flow, and a tolerance in percent of maximum flow is divided by percent of scale to determine the percent of actual flow.

For instance, at mid-scale on a differential-pressure transmitter, a tolerance of ±1% of maximum would represent an actual flow tolerance of 1% since the square root of (0.50 — 0.01)/0.50 = 0.99, but, at 25% scale, the flow tolerance is 2% since the square root of (0.25 — 0.01)/0.25 = 0 98 The addition of individual toler­ances may be made on a root-mean-square basis and stated as such.

Because the high gam action of the square-root extrac­tor at low flow rates magnifies uncertainties as well as the flow signal itself, the rangeability, or turn-down ratio, of a differential-pressure meter is practically limited to about 25% of maximum flow (6.25% of maximum differential) When operation at wider range is required, multiple primary elements or multiple transmitters can be used with auto­matic switching, which simultaneously changes meter ca­pacity and integrator speed. Alternately, a meter with linear output might be specified.

6- 4.1 Excitation Signal

In experiments using external excitation, a plant con­trol device, often a reactor control rod, is moved in accordance with a prescribed signal while the prescribed signal and one or more output variables are recorded The signal is usually either sinusoidal or pseudorandom (such as Fig. 6.6) With the former the transfer function expressed in complex form is simply

G(co)=^-e10 (6 27)

A.

for an output variable В sin (cot + ф) With a pseudorandom signal the input and output must be cross correlated and a Fourier transform carried out on the result (see Set 6-3) As a signal generator in these experiments, one of the following may be used a function generator (of sine waves usually), a stored function on tape (usually pseudorandom), or a random or pseudorandom electronic noise generator It is important that the function-generator output not deviate significantly from a constant frequency and that it contain no significant harmonics The function generator might take any of the following forms a constant-speed motor driving a control actuator, an electronic oscillator driving a control-positioning circuit, or a square wave (“up” or “down”) or ternary signal (“up,” “hold,” or “down”) driving a control switch. Regarding pseudorandom noise generation, a stored tape has been used41 as well as an on-line generator107 Some experiments use commercial random-noise generators 84

An important characteristic of the excitation variable is its amplitude The amplitude must be large enough to overcome unwanted noise without requiring excessively long experimental times It will be shown in Sec 6-7 that the amplitude, unwanted noise, and test duration all combine to determine the accuracy of the result

The amplitude cannot be made arbitrarily large, how­ever, since nonlinear aspects of the system can complicate data analysis It can be shown91 that, because of non­linearities in the neutron kinetics equations, Eqs 6 11 and 6 12, one type of nonlinearity resulting from a sinusoidal reactivity excitation is a power function

N(t) = N0 + N, sin (2nft) + N2 sin (47rft + в) + (6 28)

where the harmonic to-fundamental ratio is

N2 _ 1 N, lG0(2f)l /А^Л

N, 2 N0 lG0(f)l ‘

This usually means that the harmonic content is of the same order of magnitude as the modulation fraction, N,/N„

Another important characteristic of the excitation signal is its frequency band The frequency content desired depends on the information to be obtained It is sufficient that frequencies cover the band

Ji_<2fff<_i — (6.30)

Unax Lmin

if rmax and rmin are the largest and smallest system time constants of interest In practice the amplitudes and frequencies attainable may not be those desired because of equipment limitations, so compromises may be required. Although there is little difficulty in attaining the lowest frequency desired, either the available power or the

limitations of materials are likely to place a limit on the highest frequency attainable. Also, the inverse relation between amplitude and frequency, if constant-speed motors are used (e. g., to drive a control rod in and out in a periodic triangular wave shape), places limits on the maximum frequency

linear rod speed 2 X frequency

A mild environment (low temperature and noncorrosive media) poses few problems Sensors are available with cable fittings, and the cable choice can be made easily Over extended periods of time, the nuclear radiation field can interact with the gaseous medium in the vicinity of a sensor and cause corrosion If the medium is air, elimination of moisture during installation and prevention of moisture accumulation after installation is advisable (see Chap 10) In a severe environment, a detector with an integral cable should be used In this case, the electrical parts of the sensor are effectively separated from the medium

2-5.2 Hardware

Radiological and mechanical requirements pose dif­ferent installation problems Frequently, some radiation conditioning must be provided, і e, gamma or neutron shielding at the detector location If the exact conditions are known, permanent shielding or neutron thermahzers can be built Usually, some permanent shielding is installed, and flexibility is provided by adjusting the detector position In this case, all possible locations of the detectors must be considered and shielded as needed

It is often possible to provide some gamma shielding or neutron thermahzation in the detector package A detector assembly is then needed The detector assembly must be positioned as a unit, which requires some provision for storing excess cable in or around the reactor shield This is particularly difficult for a detector with integtal cable For counters a preamplifier must also be mounted as close to the detector as possible Frequently, the excess cable and preamplifier space can be combined

For a detector that is positioned vertically, gravits can usually be relied on A load-bearing cable is then required to support the detector, relieving the electrical connections of any possible stress If positioning is horizontal or at some angle to the vertical, constraints m both directions must be provided This can be done by using a fixed or a temporary rigid member If the position might be disturbed, for example, by moving a second detector in the same general location, a rigid connection or possibly a hne-and pulley arrangement may be needed

2-5.3 Circuits

The more specialized circuits are covered m other chapters, particularly Chap 5, and the effects of reactor safety requirements are covered in Chap 12 Some special points are considered here

Interlocking circuits art customarily provided with each detector These interlocks provide a scram signal if the high voltage or signal connections to a detector are interrupted regardless of the cause of the interruption

Also it is generally desirable to prevent the establish­ment of a ground loop, і e, to prevent ground currents from flowing in the return or ground lead This is done by preventing the exposure of any bare metallic members of the return path Thus, cable connectors and the chamber itself are sometimes insulated The signal circuits are sensitive and of high impedance, so ground loops are a frequent source of trouble (see Chap 10)

К J Monarty, F H Just, and L J Christensen 5-1 INTRODUCTION chapter contents

Neutron flux measuring channels in nuclear power plants are generally classified according to the neutron flux range involved

Start up channel 10° to 10s neutrons cm 2 sec 1

Intermediate channel 104 to 1010 neutrons cm 2 sec 1 Power channel 106 to 1010 neutrons cm 2 sec 1

The channels successively overlap one another (Fig 5 1) to provide continuous measurements of the neutron flux level at all power levels (see also Chap 2 Sec 2 2 3)

Control circuits are provided in conjunction with one or more of the channels Reactor power is varied by the action of circuits associated with the neutron flux measuring equipment High power operation is controlled with the

power channel The neutron-measuring systems must be capable of providing alarm set points and annunciator units to warn the reactor operator

In conjunction with the alarm features are the reactor — protection mechanisms When an alarm set point is ex­ceeded, appropriate automatic action must be taken to reduce the reactor operating power to a safe level The type of protective circuits and action (see Chap 12) varies from reactor to reactor, from a simple reduction in reactivity (cutback) to a scram where essentially all the negative reactivity available is inserted.

The neutron-measuring equipment and circuits must be designed to minimize reactor downtime caused by unit maintenance, component failures, and spurious noise alarms Redundancy and independent systems are used for each power-level channel