Untitled Deck Flashcards by Raffaella Binetti

What is a multiphase system characterized by?

Coexistence of two or more states of matter separated by distinct interfaces

This definition highlights the complexity of systems where multiple phases exist simultaneously.

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Define a homogeneous system.

Chemical and physical properties remain uniform throughout the process

Its properties do not change over time.

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Define a heterogeneous system.

Opposite of a homogeneous system

In a heterogeneous system, properties can vary throughout the system.

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What is a phase in the context of a multiphase system?

An homogeneous portion of a heterogeneous system

It is important to distinguish between phases and components.

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What are the three types of equilibrium conditions needed in a multiphase system?

Mechanical equilibrium (pressure)
Thermal equilibrium (temperature)
Chemical equilibrium (chemical potential)

Each type of equilibrium corresponds to different physical quantities.

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What is the Gibbs-Duhem Equation used for?

To express the relationship between entropy, volume, and chemical potential for each phase

The equation is written as: SdT−Vdp+Σ(Nidµi) = 0.

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What is the formula for the Degree of Freedom (dof)?

f = #qt−#eqs = m(r+ 2)−(m−1)(r+ 2)−m = r−m+ 2

This formula is known as the Gibbs Rule of Phases.

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In the case of a pure substance with r=1, what is the maximum number of phases (m) that can exist?

m ≤ 3

This includes single phase, two phase, and triple point scenarios.

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What is the Degree of Freedom (f) when there are 2 phases and 2 independent quantities?

f = 2

This scenario is relevant for gas-liquid flows.

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When analyzing a multiphase system, what is the significance of the interface?

Deformable (mechanical interaction)
Diathermic (thermal interaction)
Variable (chemical interaction)

The interface separates different phases and must respect these features.

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What is the mass flow rate expressed in?

[Kg/s]

It represents the quantity of mass flowing per unit time.

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What is the volume flow rate expressed in?

[m³/s]

It represents the quantity of volume flowing per unit time.

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Define phase density.

Pi = di

It relates to the mass flow rate and volume flow rate.

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What is the formula for average velocities?

ig = Q / Qi

The bar over the u indicates the average value.

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What does the mixture velocity represent?

Qg + QL = Qg + Q=1 + J

It includes superficial velocities or volumetric fluxes.

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What is the formula for actual mass flux for gas?

Gg = ρg·ug

It is expressed in [Kg/m²s].

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What is the formula for apparent mass flux for gas?

Γg = ρg·Jg

It is also expressed in [Kg/m²s].

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Define void fraction.

ε = Jg / Qg

It represents the flow of the gas.

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What is the formula for liquid holdup?

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Jl = ul / Ω = 1−ε

It indicates the proportion of liquid in the flow.

What is the volume quality for gas?

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xv = Qg / Q

It indicates the proportion of gas in the total flow.

What is the mass quality defined as?

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Γg = x * Γ

It is the ratio of the mass flow rates.

What is the relationship between the two volume flow rates expressed as?

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Ql / Qg = (1−x) / (x * ρl / ρg)

This ratio helps analyze the flow characteristics.

What does the average slip ratio represent?

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s = ug / ul

It is the ratio of the two phase velocities.

If **s = 1**, what type of flow do we have?

Homogeneous flow ## Footnote All phases are well mixed, like in an emulsion.

If **s < 1**, what does this indicate about the flow?

Bigger void fraction ## Footnote This describes the early stage of boiling in a vertical pipe.

If **s > 1**, what situation does this describe?

Annular flow ## Footnote The void factor tends to zero, with larger bubbles forming.

What is the **solid angle** represented by in the context of void fraction models?

dΩ = rdφdr ## Footnote This represents the differential solid angle used in calculations of local void fraction and liquid holdup.

Define **local void fraction** and **liquid holdup** in terms of solid angle.

* Local void fraction: ε = dΩg/dΩ * Liquid holdup: 1 - ε = dΩl/dΩ ## Footnote These quantities are essential for computing local velocities in two-phase flow.

How are **average local velocities** expressed using integrals on the solid angle?

* ug = (1/Ωg) ∫Ωg ug dΩg * ul = (1/(1-ε)·Ω) ∫Ω ug (1-ε) dΩ ## Footnote These equations help in determining the average velocities in a two-phase flow system.

What does the **slip ratio model** express?

s = f(ρg, ρl; µg, µl; Jg, Jl) ## Footnote This model relates the slip factor to the properties of the gas and liquid phases.

What are the two prominent models for void fraction?

* Slip ratio model * Drift flux model ## Footnote These models are foundational in analyzing two-phase flow in industrial applications.

In the **drift flux model**, what does the local drift flux represent?

jg - ε(jg + jl) ## Footnote This quantity indicates the relative motion of the gas with respect to the liquid.

What is the **distribution parameter** denoted as?

C∅ = ε·j / ε·J ## Footnote This parameter relates to how evenly the phases are distributed in the flow.

What is the **drift velocity** (slippage) represented by?

uD = jgl / ε ## Footnote This measures the slippage between the gas and liquid phases.

What are the two flow regimes analyzed in the context of drift velocity?

* Slug Flow * Bubbly Flow ## Footnote These regimes illustrate different behaviors of gas and liquid phases in vertical flow.

In **slug flow**, what drives the gas upward?

Buoyancy forces ## Footnote This flow regime is characterized by the gas displacing the liquid phase.

What is the relationship for **bubbly flow** regarding surface tension?

σ·Lc ∼ ρlu²cL²c ## Footnote This equation relates the surface tension to the characteristics of the bubbly flow.

What is the **Armand correlation** in the context of drift flux models?

ε = 0.833·εH ## Footnote This correlation links the void fraction to the homogeneous flow.

What is the **mean relative deviation (MRD)** formula?

MRD = (1/N) Σ(RDi) ## Footnote This measures the average deviation of predicted values from experimental data.

Which correlation showed the best prediction capability in inclined and vertical flow cases?

Toshiba correlation ## Footnote This correlation provided a very good agreement with horizontal experimental data.

What correction factors are introduced to address issues in the Dix correlation?

* Inclination factor: (1 + cos θ) * Pressure factor: (1 + sin θ) ## Footnote These factors account for variations in system pressure and inclination angle.

What are the **two correction factors** introduced to address issues in the experiments?

* Inclination factor (1 + cos θ) * Pressure factor (1 + sin θ) ## Footnote These factors help in adjusting the calculations related to pipe diameter and flow conditions.

What does the **Dix correlation** formula include?

USG ε= USG 1 + USL USG 0.1 ρG ρL 0.25· + 2.9 gDσ(1+cos θ)(ρL−ρG ) ρ2 L 1 (1.22 + 1.22 sin θ)Patm Psystem ## Footnote This formula is used to calculate the void fraction in a two-phase flow system.

What happens to the flow when **pressure increases** in the system?

* ρratio → 1 * C∅ → 1 * Flow becomes homogeneous ## Footnote Increased pressure leads to a more uniform flow condition.

If the **pressure of the system increases**, what happens to the **drift velocity**?

Drift velocity decreases (uD <) ## Footnote This indicates a relationship between pressure and flow characteristics.

When taking data, what is important to consider regarding the **measurements**?

Only measurements that fall on the straight line should be considered ## Footnote Measurements outside this range may need to be discarded.

What is confirmed about the **drift flux analysis method**?

It is a powerful tool for developing void fraction correlations and analyzing experimental data ## Footnote This method has shown effectiveness in correlation development.

Out of the six best performing correlations for the void fraction database, how many were developed based on the **drift flux model**?

All except one ## Footnote This highlights the model's significance in correlation development.

Untitled Deck Flashcards

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