Time-Dependent Reacotrs

Front 1

Changes in a nuclear reactor system associated with changes in the concentration of the fission products are called

Back 1

Medium-time Phenomena

Front 2

Changes in the neutron flux associated with control rod movements are:

Back 2

Short-time Phenomena

Front 3

Changes in a nuclear reactor system associated with the burnup and buildup of fissionable isotopes are:

Back 3

Long-term pehnomena

Front 4

Give the definition of reactor period if no delayed neutrons are present in the system. If the reactor period is 0.2 sec, how the reactor power will change in 1 second?

Back 4

If delayed neutrons are not present in the system, the reactor period is given as T= 1/(kinf - 1) . According to Eq.7.13 in the textbook, if T=0.2 sec, for time t=1 sec the power will increase e(t/T) times, or e(1/5)=148 times.

Front 5

In the prompt jump approximation, it is assumed that -

Back 5

1) The concentration of the delayed neutron precursors do not change over the time of the sudden rise in flux.

Front 6

In the prompt drop approximation, it is assumed that -

Back 6

The concentration of the delayed neutron precursors to not change over the time if the sudden drop in flux.

Front 7

When (1-B)k=1, the reactor is

Back 7

critical on prompt neutrons alone (prompt critical reactor)

Front 8

The two ways control rods are used are:

Back 8

1) To change the degree of reactor criticality for the purpose of raising or lowering the power level 2) To keep the reactor critical by compensating for the changes in the properties of the system with its lifetime

Front 9

Is the statement “Cluster control rods are used in PWR and they are inserted from the bottom of the core” true or false? Correct it if necessary

Back 9

False, they are inserted from the top

Front 10

Is the statement “Cruciform control rods are used in BWR and they are inserted from the bottom of the core” true or false? Correct it if necessary.

Back 10

True

Front 11

Is the statement “Cruciform control rods are used in both BWR and PWR; they are inserted from the bottom of the core” true or false? Correct it if necessary.

Back 11

False, cruciform control rods are only used in BWR, and they are inserted from the bottom.

Front 12

In PWR reactors, is the fuel temperature coefficient negative, or positive?

Back 12

It is inherently negative

Front 13

In PWR reactors, is the void coefficient negative, or positive?

Back 13

The void coefficient is desired to be negative

Front 14

In BWR reactors, is the moderator temperature coefficient desired to be negative or positive?

Back 14

Moderator temperature coefficient is desired to be negative.

Front 15

List the production and loss mechanisms for Xe-135

Back 15

Production - decay of I-135, and direct fission

Loss - neutron absorption, and radioactive decay

Front 16

List the production and loss mechanisms for Sm - 149

Back 16

Production - decay of Nd-149

Loss - Neutron Capture

Front 17

Explain the reactor dead time associated with Xe - 135

Back 17

The period after the reactor shutdown, when the reactor cannot be restarted because of the available positive reactivity of the control rods, which is less that the negative reactivity due to Xe-135 buildup after the I-135 decay.

Front 18

Reactivity Feedback

Back 18

The phenomenon that occurs when an originally applied reactivity changes the state of the system

Front 19

Reactivity coefficient

Back 19

The amount of change in reactivity per unit change in a given parameter

Front 20

Reactivity Defect

Back 20

The total reactivity change caused by a change in parameter

Front 21

Calculate the magnitude of the equilibrium Xe-135 poisoning effect for a U-235 fueled reactor. Assume that the reactor does not contain resonance absorbers and U-235 is the only fissionable material.

Back 21

p = (-1) (y(I) +y(Xe))/(vpe) = -1(0.0639 + 0.00237)/2.42 = -2.73 %

Front 22

Calculate the magnitude of the equilibrium Sm-149 poisoning effect for a U-235 fueled reactor. Assume that the reactor does not contain resonance absorbers and U-235 is the only fissionable material.

Back 22

p = (-1)(y(Pm)/(vpe) = -0.0107/2.42 = -0.442%

Front 23

Compute the prompt neutron lifetime for an infinite critical thermal reactor consisting of a homogenous mixture of U‐235 and (a) D2O, (b) Be, (c) graphite.

Back 23

t = t(dm)(1-f) = t(dm)(1-(1/Nt))

Front 24

Express the following reactivities of a U235‐fueled thermal reactor in percent: (a) 0.001, (b) $2, (c) ‐50 cents.

Back 24

A) The reactivity of 0.001 is 0.1%

B) $2 = x/B --> x = 2(0.0065) = 0.013 = 1.3%

C) x = (-.50)*(0.0065) = -0.00325 = -0.325%

Front 25

A U235‐fueled reactor originally operating at a constant power of 1 milliwatt is placed on a positive 10‐ minute period. At what time will the reactor power level reach 1 megawatt?

Back 25

w = 1/T = 1/(600seconds) = 0.001667 Hz

P=Po*e^wt

t = ln(P/Po)/w = 12431 s

Front 26

List the three most important differences between prompt and delayed neutrons.

Back 26

1. Time delay of neutron emission after the fission: prompt neutrons – 10‐15 sec; delayed neutrons – up to 80 seconds (Ba)

2. Energy ‐ delayed neutrons are emitted on the average with considerably smaller energies than prompt neutrons

3. Fraction ‐ delayed neutrons are less than 1% of the total neutron production in fission

Front 27

HW 5 - Finding power based on period and reactivity change

Back 27

For odd numbered P, use: P3/P2 = (1-p1)/(1-p2)

For even numbered P, use P4 = P3e^(-t/T)

Front 28

How to solve power defect compensation problem

Back 28

Subtract the lowest temperature mentioned to from the other two. Multiply the two remaining temperatures by their respective coefficients, then add them together

Front 29

Differential Rod worth

Back 29

Shaped like a bell. For each interval, the number of pcm/inch must be determined. For example, in the first interval (0 inches to 2 inches), 10 pcm is added. Therefore, the differential rod worth equals an average 5 pcm/inch. This value of differential rod worth is plotted at the center of each interval. The center of the interval 0 inches to 2 inches is 1 inch. The values of pcm/inch for each interval are then listed as shown below and plotted on the figure below.

Front 30

Integral Rod Worth

Back 30

Shaped like an S. To plot the integral rod worth, merely develop a cumulative total of the reactivity added after each interval and plot the summed reactivity insertion vs. rod position as shown in the figure below.

Front 31

Neutron Generation time

Back 31

Integral property of the reactor, fast reactors --> 10^-7 - 10^-8 seconds. Thermal reactors --> 10^-3 - 10^-4 seconds. Depends on the number of scattering collisions before leakage or absorption.

Front 32

Prompt neutron lifetime (Lp)

Back 32

The average time between the emission of a prompt neutron and its absorption or leakage.

Front 33

Mean diffusion time - Td

Back 33

The average lifetime of a thermal neutron in an infinite system. In a fast reactor, td = 0. and in a thermal reactor lp = td

Front 34

Reactivity's relation to criticality

Back 34

p = k-1/k. Reactivity depends on reactor size, amounts and densities of various materials, and cross-sections for fission, scattering, and absorption.

Front 35

Delayed neutrons are important because

Back 35

Static reactor problems - the prompt and the delayed fission neutrons always appear together as the total number of fission neutrons

Front 36

Delayed neutron precursor

Back 36

The parent of the daughter nuclei that produce delayed neutrons

Front 37

The delayed neutron fraction

Back 37

B = vd/v

v = vd + vp

Front 38

Simplified Neutron cycle

Back 38

See looseleaf.

Front 39

"inherent" reactivty feedback

Back 39

Reactivity feedback is called inherent if its occurrence is based on an unavoidable and thus totally reliable physical phenomenon

Front 40

"Prompt" reactivity Feedback

Back 40

Reactivity feedback is called "prompt" if it directly follows the fuel temperature changes.

Front 41

"delayed" reactivity feedback

Back 41

Reactivity feedback is "delayed" if it follows 80 seconds after the prompt feedback.

Front 42

Control Rod worth

Back 42

The change in reactivity caused by control rod motion.

Front 43

Control Rod Effectiveness

Back 43

depends largely upon the value of the ratio of the neutron flux at the location of the rod to the average neutron flux in the reactor

Front 44

A burnable neutron poison

Back 44

A material that has a high neutron absorption cross section that is converted into a material of relatively low absorption cross section as the result of neutron absorption

Front 45

Chemical Shim

Back 45

Soluble Poisons. - Boric Acid is most common. Decreases thermal utilization factor, increasing reactivity. If Boron concentration is increased, the coolant absorbs more neutrons, adding negative reactivity. Or if boron concentration is reduced, then positive reactivity is added. Reduces rod use

Front 46

Shim worth

Back 46

Pw = 1.92C x (10^3)(1-fo)

Front 47

Change in burnable poison worth during reactor cycle

Back 47

It cannot be done, but it can be with chemical shim.

Front 48

A non-burnable neutron poison

Back 48

A material that has relatively constant neutron absorption characteristics over core life. Example - hafnium.

Front 49

Doppler Effect

Back 49

The fuel temperature coefficient of reactivity is the change in reactivity per degree change in fuel temperature. The Doppler broadening of resonance peaks occurs because the nuclei may be moving either toward or away from the neutron at the time of interaction

Front 50

Moderator temperature effect

Back 50

The change in reactivity per degree change in moderator temperature.

Front 51

Void coefficient

Back 51

The void coefficient of reactivity is defined as the change in reactivity per percent change in void volume. The void coefficient is caused by the formation of steam voids in the moderator.

Front 52

Equilibrium Xe-135

Back 52

1. For Xe-135 to be in equilibrium, I-135 must also be in equilibrium 2. Equilibrium Xe-135 is not directly proportional to power level

Front 53

Sm-149 Equilibrium

Back 53

. Equilibrium Sm-149 concentration is independent of neutron flux and power level 2. The Sm-149 concentration will undergo a transient following a power level change, but it will return to its original value

Front 54

Response to shut-down

Back 54

Sm-149: Neutron flux goes to 0, Sm-149, no longer removed by burnup, produced by decay of Pm-149, and is stable. Xe -135 is no longer produced by fission, or removed by burnup, it is produced by the decay of remaining I-135, and is removed by decay.

Front 55

Xe-135 Oscillations

Back 55

Large thermal reactors with little flux coupling between regions may experience spatial power oscillations because of the non-uniform presence of Xe135.

Front 56

Nuclear Fuel Burnup

Back 56

(unit: MWd/t) is defined as thermal energy output (unit: MWd) per unitmass (unit metric ton, t) of heavy metal content in the initial fuel

Front 57

In a Uranium-fueled thermal reactor, the reactivity changes with burnup areassociated with the following factors:

Back 57

1. Depletion of 235U and transmutation of 238U2. Buildup of 239Pu

3. Buildup of 241Pu

4. Buildup of non-fissile nuclides - 240Pu, 236U, and 242Pu

5. Buildup of thermal neutron-absorbing FPs (135Xe and 149Sm)

6. Buildup of other FPs

Front 58

LWR Core Fuel Management - The core design for reactivity control

Back 58

Reactivity control predicts reactivity change duringreactor operation and determines its optimal control methods based oncalculations of reactivity change with fuel burnup

Front 59

Capacity Factor

Back 59

CF = integral of 0 to T, of (P(t)dt/(PoT))

Front 60

Effective full-power days

Back 60

CF x T(days)

Front 61

The chemical shim and BPs in PWRscompensate for the negative reactivitydue to 135Xe and 149Sm and for thereactivity decrease with fuel burnup

Back 61

If a chemical shim is present, adecrease in coolant density due totemperature rise will also lead to adecrease in boric acid concentration‒ Thus, it has a positive reactivity effecton moderator temperature coefficient

Front 62

Typical critical boron concentration with cycle burnup (100 % power)

Back 62

Downward sloping

Front 63

The excess reactivity is largest at no burnup and cold shutdown,because:

Back 63

1. burnup defect - the reactivity of the system is reduced due to theconsumption of fissile nuclides and the accumulation of FPs with fuelburnup2. temperature defect- negative feedback effect3. power defect - negative feedback effect