1 1 INTRODUCTION TO MULTIPHASE FLOW Mekanika Fluida II -Haryo Tomo-
2 2 Definitions Multiphase flow is simultaneous flow of Matters with different phases( i.e. gas, liquid or solid). Matters with different chemical substances but with the same phase (i.e. liquid-liquid like oil-water). Primary and secondary phases One of the phases is considered continuous (primary) and others (secondary) are considered to be dispersed within the continuous phase. A diameter has to be assigned for each secondary phase to calculate its interaction (drag) with the primary phase (except for VOF model). Dilute phase vs. Dense phase; Refers to the volume fraction of secondary phase(s) Volume fraction of a phase = Volume of the phase in a cell/domain Volume of the cell/domain
3 Rushton CD-6 BT-6 3 Why model multiphase flow? Multiphase flow is important in many industrial processes: Riser reactors. Bubble column reactors. Fluidized bed reactors. Scrubbers, dryers, etc. Typical objectives of a modeling analysis: Maximize the contact between the different phases, typically different chemical compounds. Flow dynamics.
4 Two-phase Flow Applications The practical importance in many common engineering and industrial applications are: Steam generators and condensers, steam turbines ( Power Plants ). Refrigeration. Coal fired furnaces. Fluidized bed reactors. Liquid sprays. Separation of contaminants from a carrier fluid
5 Free surface flows, where sharp interfaces exist. pumping of slurries. pumping of flashing liquids. raining bed driers. oil industry two phase flow occurs in pipelines carrying oil and natural gas. energy conversion. paper manufacturing. food manufacturing. medical applications.
6 The laws governing two phase flow are identical to those for single phase flow. However, the equations are more complex and/or more numerous than those of single phase flow.
7 The description of the two-phase flow is complicated due to the existence of interface between the phases depending on a large number of variables such as : 1. quality (x). 2. phase physical properties. 3. flow patterns. 4. pipe geometry. 5. orientation of flow.
8 A general classifications divide two-phase flow into four groups depending on the mixtures of phases in the flow. The four groups are the flow of gas-liquid, gas-solid, liquid-solid and immiscible liquid-liquid mixtures. The last case is technically not a two-phase mixture, it is rather a single phase two-component flow, but for all practical purposes it can be considered as a two-phase mixture.
11 11 Flow Regimes in Vertical Flow Multiphase flow can be classified by the following regimes: 1. Bubbly flow: Discrete gaseous or fluid bubbles in a continuous fluid 2. Droplet flow: Discrete fluid droplets in a continuous gas 3. Particle-laden flow: Discrete solid particles in a continuous fluid 4. Slug flow: Large bubbles (nearly filling cross-section) in a continuous fluid 5. Annular flow: Continuous fluid along walls, gas in center 6. Stratified/free-surface flow: Immiscible fluids separated by a clearly-defined interface slug flow annular flow bubbly flow droplet flow particle-laden flow free-surface flow
12 Slug Bubble Separated Annular
13 Two Phase Flow Regimes Mapping Mapping of flow patterns that occur in pipe flow has always been a popular means of describing the behaviors of flow at different conditions. The superficial velocity of the gas and liquid are usually put on the two different axes, and supply an efficient method of comparing and contrasting the effects of different flow conditions.
15 15 Flow regimes: vertical gas-liquid flow Evaporator 3 Q( m / s) Superficial Velocity : vsg ( m/ s) 2 A( m ) 3 Q( m / s) Q( VVM ) 60 3 V ( m )
16 16 Multiphase flow regimes User must know a priori the characteristics of the flow. Flow regime, e.g. bubbly flow, slug flow, annular flow, etc. Only model one flow regime at a time. Predicting the transition from one regime to another possible only if the flow regimes can be predicted by the same model. This is not always the case. Laminar or turbulent. Dilute or dense. Secondary phase diameter for drag considerations.
17 Increased complexity 17 Modeling approach Empirical correlations. Lagrangian. Track individual point particles. Particles do not interact. Algebraic slip model. Dispersed phase in a continuous phase. Solve one momentum equation for the mixture. Two-fluids theory (multi-fluids). Eulerian models. Solve as many momentum equations as there are phases. Discrete element method. Solve the trajectories of individual objects and their collisions, inside a continuous phase. Fully resolved and coupled.
18 18 Coupling between phases One-way coupling: Fluid phase influences particulate phase via aerodynamic drag and turbulence transfer. No influence of particulate phase on the gas phase. Two-way coupling: Fluid phase influences particulate phase via aerodynamic drag and turbulence transfer. Particulate phase reduces mean momentum and turbulent kinetic energy in fluid phase. Four-way coupling: Includes all two-way coupling. Particle-particle collisions create particle pressure and viscous stresses.
19 19 Modeling multiphase flows What is the goal of the simulation? Which effects are important? Controlled by which hydrodynamic effects? Controlled by which other transport phenomena effects? All these factors influence which model to choose for the analysis. Flow Specific bubbly droplet particle-laden slug annular stratified/free surface rapid granular flow? Process Model Specific Lagrangian Dispersed Phase Algebraic Slip Eulerian Eulerian Granular Volume of Fluid Specific Separation Filtration Suspension Evaporation Reaction
20 20 Physical effects in dispersed systems Hydrodynamics: Change in shape. Diameter. Particle-wall collision. Particle-particle collision. Coalescence. Dispersion and breakup. Turbulence. Inversion. Other transport phenomena: Heat transfer. Mass transfer. Change in composition. Heterogeneous reactions.
21 21 Multiphase formulation Two phases Fluid Solids Fluid Three phases Solids - 1 Solids - 2
22 22 Sediment transport under unidirectional flows I. Classification of sediment load The sediment that is transported by a current. Two main classes: Wash load: silt and clay size material that remains in suspension even during low flow events in a river. Bed material load: sediment (sand and gravel size) that resides in the bed but goes into transport during high flow events (e.g., floods). Bed material load makes up many arenites and rudites in the geological record.
23 Three main components of bed material load. Contact load: particles that move in contact with the bed by sliding or rolling over it. 23
24 Saltation load: movement as a series of hops along the bed, each hop following a ballistic trajectory. 24
25 When the ballistic trajectory is disturbed by turbulence the motion is referred to as Suspensive saltation. 25
26 Intermittent suspension load: carried in suspension by turbulence in the flow. Intermittent because it is in suspension only during high flow events and otherwise resides in the deposits of the bed. 26 Bursting is an important process in initiating suspension transport.
27 27 II. Hydraulic interpretation of grain size distributions In the section on grain size distributions we saw that some sands are made up of several normally distributed subpopulations. These subpopulations can be interpreted in terms of the modes of transport that they underwent prior to deposition.
28 28 The finest subpopulation represents the wash load. Only a very small amount of wash load is ever stored within the bed material so that it makes up a very small proportion of these deposits.
29 29 The coarsest subpopulation represents the contact and saltation loads. In some cases they make up two subpopulations (only one is shown in the figure).
30 30 The remainder of the distribution, normally making up the largest proportion, is the intermittent suspension load. This interpretation of the subpopulations gives us two bases for quantitatively determining the strength of the currents that transported the deposits.
31 31 The grain size X is the coarsest sediment that the currents could move on the bed. In this case, X = -1.5 f or approximately 2.8 mm. If the currents were weaker, that grain size would not be present. If the currents were stronger, coarser material would be present. This assumes that there were no limitations to the size of grains available in the system.
32 32 The grain size Y is the coarsest sediment that the currents could take into suspension. In this case, Y = 1.3 f or approximately 0.41 mm. Therefore the currents must have been just powerful enough to take the 0.41 mm particles into suspension. If the currents were stronger the coarsest grain size would be larger. This assumes that there were no limitations to the size of grains available in the system.
33 33 To quantitatively interpret X we need to know the hydraulic conditions needed to just begin to move of that size. This condition is the threshold for sediment movement. To quantitatively interpret Y we need to know the hydraulic conditions needed to just begin carry that grain size in suspension. This condition is the threshold for suspension.
34 The threshold for grain movement on the bed. 34 Grain size X can be interpreted if we know what flow strength is required to just move a particle of that size. That flow strength will have transported sediment with that maximum grain size. Several approaches have been taken to determine the critical flow strength to initiate motion on the bed.
35 Hjulstrom s Diagram 35 Based on a series of experiments using unidirectional currents with a flow depth of 1 m. The diagram (below) shows the critical velocity that is required to just begin to move sediment of a given size (the top of the yellow field). It also shows the critical velocity for deposition of sediment of a given size (the bottom of the yellow field).
36 Note that for grain sizes coarser than 0.5 mm the velocity that is required for transport increases with grain size; the larger the particles the higher velocity that is required for transport. 36 For finer grain sizes (with cohesive clay minerals) the finer the grain size the greater the critical velocity for transport. This is because the more mud is present the greater the cohesion and the greater the resistance to erosion, despite the finer grain size.
37 37 The problem is that the forces that are required to move sediment are not only related to flow velocity. Boundary shear stress is a particularly important force and it varies with flow depth. t o = rgdsinq Therefore, Hjulstrom s diagram is reasonably accurate only for sediment that has been deposited under flow depths of 1 m.
38 Shield s criterion for the initiation of motion 38 Based on a large number of experiments Shield s criterion considers the problem in terms of the forces that act to move a particle. The criterion applies to beds of spherical particles of uniform grain size. Forces that are important to initial motion: r 6 1. The submerged weight of the particle ( 3 ( ) which s r ) gd resists motion. 2. t o which causes a drag force that acts to move the particle down current. 3. Lift force (L) that reduces the effective submerged weight.
39 What s a Lift Force? 39 The flow velocity that is felt by the particle varies from approximately zero at its base to some higher velocity at its highest point.
40 Pressure (specifically dynamic pressure in contrast to static pressure) is also imposed on the particle and the magnitude of the dynamic pressure varies inversely with the velocity: 40 Higher velocity, lower dynamic pressure. Maximum dynamic pressure is exerted at the base of the particle and minimum pressure at its highest point.
41 The dynamic pressure on the particle varies symmetrically from a minimum at the top to a maximum at the base of the particle. 41
42 This distribution of dynamic pressure results in a net pressure force that acts upwards. 42 Thus, the net pressure force (known as the Lift Force) acts oppose the weight of the particle (reducing its effective weight). This makes it easier for the flow to roll the particle along the bed. The lift force reduces the drag force that is required to move the particle.
43 A quick note on saltation 43 If the particle remains immobile to the flow and the velocity gradient is large enough so that the Lift force exceeds the particle s weight.it will jump straight upwards away from the bed. Once off the bed, the pressure difference from top to bottom of the particle is lost and it is carried down current as it falls back to the bed. following the ballistic trajectory of saltation.
44 44 Example: bubble column design Gas A bubble column is a liquid pool sparged by a process stream. Liquid 2 < L/D < 20 U G,sup up to 50 cm/s Liquid Pool U G,sup >> U L,sup Sparger Gas Liquid/Slurry Inlet Gas Inlet
46 46 Bubble column design issues Design parameters: Gas holdup. Directly related to rise velocity. Correlations of the form a ~ u sga r lb s c m l d are commonly used. Mass transfer coefficient k l a. Correlations of the form k l a ~ u sga r lb s c m l d m ge D f Dr g are commonly used. Axial dispersion occurs in both the liquid and gas phase, and correlations for each are available. Mixing time. Correlations are available for a limited number of systems. Volume, flow rates and residence time. Flow regime: homogeneous, heterogeneous, slug flow.
47 47 Bubble column design issues - cont d Accurate knowledge of the physical properties is important, especially the effects of coalescence and mass transfer affecting chemicals. Although good correlations are available for commonly studied air-water systems, these are limited to the ranges studied. Correlations may not be available for large scale systems or systems with vessel geometries other than cylinders without internals. Furthermore, experimental correlations may not accurately reflect changes in performance when flow regime transitions occur.
48 48 Bubble size At present, bubble column reactors are modeled using a single effective bubble size. Coalescence and breakup models are not yet mature. Statistical approach. Solve equation for number density. Population balance approach. Application of population balance with two-fluid models with initial focus on gas-liquid. The gas phase is composed of n bubble bins and share the same velocity as the second phase. The death and birth of each bubble bin is solved from the above models.
49 49 Example - gas-liquid mixing vessel Combinations of multiple impeller types used. Bottom radial flow turbine disperses the gas. Top hydrofoil impeller provides good blending performance in tall vessels.
50 50 Eulerian-granular/fluid model features Solves momentum equations for each phase and additional volume fraction equations. Appropriate for modeling fluidized beds, risers, pneumatic lines, hoppers, standpipes, and particle-laden flows in which phases mix or separate. Granular volume fractions from 0 to ~60%. Several choices for drag laws. Appropriate drag laws can be chosen for different processes. Several kinetic-theory based formulas for the granular stress in the viscous regime. Frictional viscosity based formulation for the plastic regime stresses. Added mass and lift force.
51 51 Eulerian-granular/fluid model features Solves momentum equations for each phase and additional volume fraction equations. Appropriate for modeling fluidized beds, risers, pneumatic lines, hoppers, standpipes, and particle-laden flows in which phases mix or separate. Granular volume fractions from 0 to ~60%. Several choices for drag laws. Appropriate drag laws can be chosen for different processes.
53 53 Fluidized-bed systems When a fluid flows upward through a bed of solids, beyond a certain fluid velocity the solids become suspended. The suspended solids: has many of the properties of a fluid, seeks its own level ( bed height ), assumes the shape of the containing vessel. Bed height typically varies between 0.3m and 15m. Particle sizes vary between 1 mm and 6 cm. Very small particles can agglomerate. Particle sizes between 10 mm and 150 mm typically result in the best fluidization and the least formation of large bubbles. Addition of finer size particles to a bed with coarse particles usually improves fluidization. Superficial gas velocities (based on cross sectional area of empty bed) typically range from 0.15 m/s to 6 m/s.
54 Fluidized bed example 54
55 55 Fluidized bed uses Fluidized beds are generally used for gas-solid contacting. Typical uses include: Chemical reactions: Catalytic reactions (e.g. hydrocarbon cracking). Noncatalytic reactions (both homogeneous and heterogeneous). Physical contacting: Heat transfer: to and from fluidized bed; between gases and solids; temperature control; between points in bed. Solids mixing. Gas mixing. Drying (solids or gases). Size enlargement or reduction. Classification (removal of fines from gas or fines from solids). Adsorption-desorption. Heat treatment. Coating.
56 Bed depth Freeboard 56 Typical fluidized bed systems - 1 Gas and entrained solids Gas Dust Solids Feed Disengaging Space (may also contain a cyclone separator) Separator Dust Fluidized Bed Gas in Solids Discharge Windbox or plenum chamber Gas distributor or constriction plate
57 57 Typical fluidized bed systems - 2 Gas + solids Riser section of a recirculating fluidized bed Solids Gas Uniform Fluidization Bed with central jet
58 Solids Return Solids Return Solids Return 58 Fluidization regimes U mf U mb U ch U U Gas Fixed Bed Particulate Regime Bubbling Regime Slug Flow Regime Turbulent Regime Fast Fluidization Pneumatic Conveying Increasing Gas Velocity
59 59 Fluidized bed design parameters Main components are the fluidization vessel (bed portion, disengagement space, gas distributor), solids feeder, flow control, solids discharge, dust separator, instrumentation, gas supply. There is no single design methodology that works for all applications. The design methodologies to be used depend on the application. Typical design parameters are bed height (depends on gas contact time, solids retention time, L/D for staging, space required for internal components such as heat exchangers). Flow regimes: bubbling, turbulent, recirculating, slugs. Flow regime changes can affect scale-up. Heat transfer and flow around heat exchanger components. Temperature and pressure control. Location of instrumentation, probes, solids feed, and discharges.
60 60 Fluidized bed - input required for CFD CFD can not be used to predict the: minimum fluidization velocity, and the minimum bubbling velocity. These depend on the: particle shape, particle surface roughness, particle cohesiveness, and the particle size distribution. All of these effects are lumped into the drag term. Hence we need to fine tune the drag term to match the experimental data for minimum fluidization or minimum bubbling velocity.
61 61 Fluidized bed - when to use CFD If the drag term is tuned to match the minimum fluidization velocity, CFD then can be used to predict: bed expansion gas flow pattern solid flow pattern bubbling size, frequency and population short circuiting effects of internals effects of inlet and outlets hot spots reaction and conversion rates mixing of multiple particle size residence times of solids and gases backmixing and downflows (in risers) solids distribution/segregation
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