Exam 1

Module 54

Look at this!

Annular: when boiling from saturated liquid to saturated steam, the flow is in the annular regime for the widest range of quality and, therefore, in most of the volume of the equipment. Annular flow modeling is dominated by ___________ and ________________________

thin film phenomena, droplet entertainment and deposition

Bubbly: bubble transport and its effects on heat transfer are key in this regime. It is predominant in ________ and can occur in _______ as well. (Subcooled boiling: rods are ________, bulk fluid ________ – _________ are created, but don’t survive for long.) Bubbly flow models often have some applicability in related regimes, such as ___________.

BWR cores; PWR cores; above saturation; below saturation; bubbles; slug flow

Regime changes might occur in two forms, what are they and give an example.

Smooth transitions like wavy to wavy-annular in horizontal flow; sudden transition, frequent in counter current two phase flow

Some regimes vanish completely at different diameters (no bubbly at very small ___; no slug at very large ____

D, D

Effect of flow development – the range of flow rates for which ______ is present decreases as ____ increases. It may vanish completely at very large L/D, but such experiments are very expensive and this question is of little industrial relevance.

churn flow, L/D

Transitions in Taitel Map: Line A; Lines B and C; Line D; Line E

Bubbly to slug; bubble/slug/churn to dispersed bubble; slug to churn; slug/churn to annular

define v_0

rise velocity of large bubbles

Define v_b

Taylor (slug) rise velocity

This ____ is larger than __ in a rod bundle, which would seem to contradict observations of a bubbly regime observed in reactor geometry.

This highlights the distinction between ______________ flow seen in experiments and ________ flow seen in a reactor. Were there enough unheated length above the core, bubbles would coalesce into slugs.

D; De; fully-developed; developing

This is another criterion based on _____________ of bubbles (i.e., _________). When bubbles are close-packed (simple cubic), they have a packing fraction of π/6 ≈ 0.52. If the fraction of volume occupied by bubbles, {α}, exceeds this, the bubbles must _______ into (non-spherical) shapes that can pack more tightly.

Since this line occurs at high liquid flow, a zero relative velocity assumption (i.e.; HEM) is employed for the _____________,

packing fraction; void fraction; fine bubbly regime

The majority view on the ___________ regime is that it occurs when the Taylor bubbles (_____) become unstable. This occurs when the ____ between them becomes thin.

Strongly time-dependent liquid flow velocities occur, similar to _______ and __________. In some churn cases, liquid flow moves both ___________ locally, varying as a function of time.

The Taitel map is based on the minority (but not rare) view that given enough _______________, churn flow would eventually disappear into ___ flow

Depending on the ________________, Lines D can exist up to ___ of 1000 or more

churn flow; slug; film; flooding; flood reversal; downward and upward; development length; slug flow; diameter and fluid; L/D

The line E transition to annular is hypothesized to occur when the _______ on liquid droplets by a __________ exceeds the ________ on the droplet

drag force; rising gas core; gravity forse

The nuclear specific map (_______), its axes are _______ on the y and ________ on the x

RELAP-5; mass flux; void fraction

At relatively ______ (BWR range), the familiar _____________regimes are joined with transition regions and a “_____” regime, in which nearly all the liquid flows as droplets.

low mass fluxes; bubbly, slug, and annular; mist

At _________ (PWR range), the __________ regimes (both possible to model with HEM) are coupled with a “__________” regime.

high mass fluxes; bubbly and mist regimes; churn-turbulent

For the Taitel model, for very large ___, there is no ____ regime. Instead a “_________” regime exists in which highly deformed bubbles are large but do not occupy the whole cross-section. It is seen in some of the largest diameter pipes in ___________.

De; slug; cap-bubbly; nuclear reactors

For Taitel, at very _____ {jv}, a _________ regime may exist, in which the _________ in the vapor core exhibit some form of structure. They have been variously reported as “____” or “_______” in flow imaging experiments.

high; wispy annular; droplets; clouds; lines

The concepts of two-phase averaged parameters, such as {__} and , are most useful in the __________ regimes, as is φ2lo. {α} is most useful here because its value is far away from 1 and, often, far away from 0 – less fractional uncertainty on data.

alpha; S; bubbly and slug

At high ____________, bubbly flow is well-modeled with the HEM

mass flux and pressure

At lower _____________, the _______ model is recommended in the bubbly regime

Mass fluxes and BWR pressures; drift flux

________ (three-phase interaction among vapor, liquid, and [solid] wall

contact angles

In the momentum transport equation, some terms are dependent on ________, others on ______________

volume; interfacial area

In the momentum transport equation, area-based terms include an ____________ term, with dimensions of ___________ – unit (surface) area per unit volume.

Physically, the interfacial area concentration is inversely related to a characteristic distance between ______________.

Since mass, momentum, and energy transfer between phases occurs at these interfaces, this term is important for understanding the relative importance of the __________ terms, as compared to volume-based terms and those that depend on the surface area of ____________

interfacial area concentration; inverse length; gas-liquid interfaces; interphase area; fixed boundaries

Since some phenomena depends on surface area and others on volume or mass, not all bubble size distributions are _____________

interchangeable

__________________ (IATE): The interfacial area transport equation (IATE), advanced by Ishii and Kocamustafagullari (among others), develops a analogy between the transport of ___________ (such as ________) and _________ transport.

The explicit ____________________ terms are similar to the typical transport equation (as bubbles flow in and out of the volume and can accumulate).

Interfacial Area Transport Equation; interfacial area; bubbles; particle; time dependence and convection

Qualitatively different bubbles can be assigned to different ______. This is analogous with neutron transport. Extending the analogy, a ________ approach is the most common. However, for bubbles, both __________ can be distinguishing factors among groups, making the distinctions among groups somewhat more challenging to make.

These can be coupled with analogous terms to ______________.

groups; two-group; size and shape; capture/scattering/generation

bubble breakup

large bubble splits and generates smaller bubbles like fission

Bubble coalescence - no direct analogy IATE is a __________ Boltzmann equation (neutron transport is _________).

non-linear, linear

in annular flow: Liquid – ______ (base film and waves), __________-

Gas – __________- (dominant) and _____________.

film; entrained droplets; gas core; entrained bubbles

the triangular relationship considers what three charateristics

average (film) thickness; film flow rate (entrained fraction); interfacial shear stress (presssure gradient) (given any two the third can be computed)

The link between film thickness and shear stress is termed the ____________. This asserts that interfacial shear is enhanced by the film, which acts as a rough surface. Often ignored: the velocity profile within the film is not known. (_____________, ___________.) This an exceptionally challenging measurement

film roughness concept; laminar vs turbulent; steady vs unsteady

Liquid is divided between film and entrainment. By mass conservation,______ film flow rate means _____ entrainment. At a sufficiently low {__}, the film flow rate is the entire liquid flow – no entrainment is necessary to transport the liquid. This film appears to be ______.

An alternate version of this concept is phrased this way: the liquid not in the base film must be either in _______. As a result, at high {jl}, more ____________ are present. How the extra liquid is distributed between these two phenomena is poorly understood.

more; less; jl; wave-free; waves or droplets; waves and entrainment

for adiabatic flows, φ2lo is predominant when the flow can be characterized as “___________”. φ2go would be used for “____________”. Annular flow has been correlated fairly well with both classes of model

liquid with some gas in it; gas with some liquid in it

For roughness correlations in annular flow: Assumption: roughness is proportional to _________________ (to a power C, which is usually set to 1). Note the use of ______________ factors, f ′ = f /4 (more familiar Moody friction factor).

average film thickness; fanning friction

For film thickness measurements: Typical approach: __________. _________ often have very different (electrical) conductivities. By measuring the conductance of a certain area, the _________ can be estimated. In annular flow, a qualitative shape is assumed (gas flowing over liquid), which allows the film thickness to be computed.

conductance probes; liquid and gas phases; void fraction;

Designs fall into two categories: (1)___________ (invasive) and (2) ___________ (can have poor resolution for large films). Either type of measurement has uncertainty on the calibration.

Other problems stem from the violations of the assumed geometry (______________) and the difficulty in assessing the amount of axial-direction averaging inherent to conduction-based methods.

inverted into the flow; flush mounted; drops in the gas core and bubbles in the film

film thickness is represented by what greek letter

lowercase delta

Annular flow does not show the sort of ____________ of a rough metal tube/pipe. Direct measurements of local τw indicate _____ oscillations in a wide range of fluids, geometries, and flow rates. The frequency of these oscillations is consistent with the _____________. Waves are 2-5 times thicker than ________ (2 on average, 5 at the peaks of large waves).

Some researchers have proposed multi-zone modeling, in which base ___________ are considered separately. Each zone has a local film thickness (distribution), a local roughness, a local shear, a local pressure gradient, etc

homogenous roughness; factor-of-4; passage of waves; base film; film and waves;

y+ < 5

viscous sublayer

5 < y < 30

buffer layer

v*

friction/shear velocity

v+

universal velocity

A different velocity profile must be used if there is turbulence in the film (_________) than if there is not (laminar profile).

UVP or something similar

In a wave, assume δ doubles and τ quadruples. _____ increases by a factor of 8 (4x from ______, 2x from _______), and ___ increases by factor of 16! As a result, _______ are (probably) turbulent structures, but base film may not be

u; shear; film thickness; Re; waves

Vertical slug flow: _______ flow models are often extended into the slug flow regime. There are some concerns relating to ______________. The wall is sometimes covered by liquid (_____) and sometimes a very thin film (________) that may move downward or stagnate.

As we’ll see, these two situations are dealt with very differently in the CHF correlations.

bubbly; heat transfer and CHF; bubbly-like; annular-like

Vertical Churn flow: two different flow patterns are called churn flow. One is an _________ flow where the ______ is moving downward some fraction of the time. A gas core is generally maintained. The second, termed “________” (particularly in the nuclear world) resembles the typical, chaotic drawing of churn flow and becomes more frequent at high ___

annular-like; liquid film; churn-turbulent; G

of the four main vertical regimes, _____ has the least industrial relevance

churn

The __________ (also plug) regimes in horizontal flow are similar to their vertical versions, except with gas tending to congregate towards the top of the tube.

A smooth transition has been observed from stratified (smooth) to wavy to wavy-annular to annular flow in horizontal flow. Frequently (e.g., by Mandhane), these regimes are reduced to stratified-wavy-annular. Stratified implies ______ and annular refers to any flow with continuous _________

bubbly and slug; smooth; top-wetting

There is general agreement that the wavy flow regime implies ____________. The wavy to wavy-annular transition is an increasing function of ________ up to D ≈ 50 mm. The circumferential dependence of film thickness extends well into annular flow.

Note: wavy-annular is not any annular flow with (disturbance) waves. Indeed, most annular flows show disturbance waves. Instead, wavy-annular refers to ________ between two regimes: the wavy regime and the annular regime.

no continuous top-wetting; tupe diameter; a transition

Multi-dimensional flow is briefly discussed in your text and occurs (for example) due to ______________. This produces uneven void fractions, slip ratios, pressures, etc. and allows cross-flow. Such conditions are typically understood highly ______

uneven heating between rods; empirically

Counter-current flow: Flow regime transitions in counter-current flow tend to be _______, indicative of fluid instability-based changes. The transition from counter-current (gas upward, liquid downward) to mixed upward/downward liquid is termed __________.

The transition from co-current (upward) to mixedupward/downward liquid is termed __________. Small-scale flow reversals may be linked to the transition from annular to (both types of) ____ flow

sudden; flooding; flow reversal; churn

The Kutateladze number and Wallis number are tied to what

non-dimensional film thickness

The wallis and porteous correlations are for what

increasing gas flow (flooding)

Pushkin and Sorokin, and Wallis correlations are for what

decreasing gas flow (flow reversal)

One area of particular relevance for counter-current flow and flow reversal is in the ________ of a PWR __________. Vapor generation in the core leads to gas traveling upwards into the pressurizer. The gas is then condensed in the pressurizer and flows downward as a liquid. When the flow rate(s) is sufficiently large, ________ occurs in which ______ can be (violently) ejected upwards into the pressurizer. This condition is undesirable and may provide a more restrictive limit on operation than would maximum pressurizer condensation ability.

pressurize, during an accident, flooding, liquid