-
Development of Computational Algorithms and Simulation Tools for
Annular Internal Condensing
FlowsResults on Heat-transfer Rates, Flow Physics,
Flow Stability, and Flow Sensitivity
Ranjeeth NaikPhD Candidate, Mechanical Engineering,
Michigan Technological University
PhD Defense22nd April, 2015
-
Outline
• Broad Perspective– Relevant Applications– Experimental
Observations– Need for Simulations– Key Computational Goals
• CFD Details– Simulation Tool Development– Simulation Strategy
and Data Management– Detailed Results
• Future Research Directions– CFD of Pulsatile Condensing,
Boiling and Adiabatic Flows – Enabling New Technology
• Conclusion
2
-
Example: Basic Refrigeration Cycle
Boilers/Condensers in Applications Where Gravity Effects are
Significant
vHeat Source
Heat Sink
3
-
Application Needs Where Gravity Effects are Minimal
Electronics/Data Center
Coolinghttp://www.pgal.com/portfolio/rice-university-data-center
Space Based Thermal Management Systems and Power Generation
Cycles
http://spaceflightsystems.grc.nasa.gov
• High heat removal requirements from small spaces• Phase change
flows with boilers and condensers is the way ahead• Miniaturization
– Shear/Pressure driven flows• Enables phase-change systems of high
heat removal and low weight requirementsLaser Weapon Cooling
http://www.darpa.mil/Our_Work/STO/Programs/High_Energy_Liquid_Laser_Area_Defense_System_(HELLADS).aspx
4
-
Challenges with Shear/Pressure Driven Condensing Flows
Traditional operation challenges• Large non- annular regime
lengths and associated heat transfer degradation• Lack of
repeatability due to extreme sensitivities in the coupled motion of
the two
phases Analogous boiling physics
Gravity Driven Condenser Shear/Pressure Driven Condenser
Inlet Exit
Annular Flow Regime Plug/Slug Regime
BubblyRegime
LcondenserLfc
(a) (b)
x
hxor
q’’w(x)
hxor
q’’w(x)
Annular flow regime
Non-annular regime
LCondenser LCondenserx
Non-annular regimeAnnular flow regime
5
-
How do we Address these Challenges?
q”w(t) h =
2 m
m
Heat Flux Meter (HFX)
Non-Annular ZoneVapor
Acoustic reflectors
HFXq”w(t)
Recirculating Vapor
Wavy Annular
TopView
Vapor LiquidMin
TopView
Wavy Annular Regime
Traditional Condenser Innovative Condenser
Plug/Slug and Bubbly
LiquidExit
VaporInlet
Pulsator
Valve
Key Ideas• Controlled recirculating vapor for annular
operations• Flow induced pulsations for high heat-flux realizations
- uses thin and large amplitude
waves on liquid films for microlayer physics
Experimentally proven method to achieve annularity – with and
without pulsations
Kivisalu et al., MGST, 2012 and Kivisalu et al., IJHMT, 2013
Analogous results for boiling flow operations are observed.
6
-
Heat Transfer Enhancements within Annular RegimesEffects of
externally imposed pressure-difference or inlet mass flow rate
pulsations
Kivisalu et al., MGST, 2012 and Kivisalu et al., IJHMT, 2013
Similar enhancements also observed for innovative
operations.
Imposed Pulsations
No Imposed Pulsations
∆p
q”w(t)Steady Cooling
Min
h =
2 m
m
Water Flow
IF-HA N-IF
Heat Flux Meter
Refrigerant VaporRefrigerant Liquid Interfacial Wave Motion
Non-Annular
End Zone
7
-
Need for Predictive/Simulation Capabilities
• “Non-pulsatile” conditions simulations– Reliable steady
annular flow predictions/correlations
• For design of innovative boilers/condensers• For different
fluid and thermal boundary conditions
– “Experiments – Theory” synthesized map of annular to
non-annular transition• Current Transition Maps – insufficient for
engineering purposes• Modified maps aids design/functioning of
innovative device operation (Gin =?, Xin =? Xout =?)
• “Pulsatile” conditions simulations – Needed to better
understand the physics of experimental heat-flux enhancements
xA
L = 1 m
Annular / Stratified Plug / Slug Bubbly All Liquid
X = 0
h = 2 mm
Liquid Exit
DPT–1
Condensing Plate
X = 40 cm DPT–2
HFX-1
Side view schematic of a shear-driven condensing flow
8
-
Computational Tools and Key Goals
-
Computational Tools
Computational Tools
Annular Boiling Flow (With suppressed nucleation)
Engineering 1D Tool
Scientific 2D CFD Tool
Steady Simulation
(Preliminary Tests)
Annular Condensing
Flow
Engineering 1D Tool
Scientific 2D CFD Tool
Steady Simulation
Correlation Developments - Heat Transfer
Coefficient- Annular Lengths
Unsteady Simulation
Qualitative Understanding and Design of
Innovative Devices
10
-
Annular Length (Stability Analysis) and Heat Transfer
Predictions
Run parameters: Fluid – FC72, Inlet Speed U = 1m/s, Temperature
Difference ΔT = 20 °C, Channel height h = 2 mm
Heat transfer estimates from 1-D ToolAccuracy for stability
analysis
0.02 0.04 0.06 0.08 0.1 0.12 0.141
1.5
2
2.5
3
3.5x 10-4
Film Thickness, ∆ (x,t)
Distance along the length of the channel, x (m)
Dis
tanc
e fro
m th
e co
nden
sing
sur
face
, y (m
)
Steady FilmInitial DisturbanceFilm at t = 0.29 sFilm at t = 0.57
s
0.03 0.032 0.034
1.55
1.6
1.65x 10-4
xA
Annular Zone (Stable)
Non-annular Zone (Unstable)
Heat Flux Predictions Dynamic Response to Initial Disturbance
θ(0)
Stability Analysis
Stable -- θ(t)→0
Unstable -- θ(t) grows
θ(0)
θ(0)
11
-
Computationally Develop Heat Transfer Correlations and Flow
Regime Maps
Vapor
Acoustic reflectors
HFXq”w(t)
Recirculating Vapor
TopView
Wavy Annular Regime
Innovative Condenser
VaporExit
Inlet
Pulsator
Non-dimensional transition map in Rein – X plane
Non-dimensional 3D transition Map and Correlations in Rein – �𝑥𝑥
– Ja/Pr1 plane
CFD Prediction of Transition Curve
Annular/Stratified Plug
Wavy Annular Slug
For ⁄ρ2 ρ1 ≅ 0.008, ⁄µ2 µ1 ≅ 0.0234, Su ≅ 6.44e6 and gnd ≅
6.36e6
Heat transfer correlations
Recirculating vapor flow rate control ensures the Vapor Quality
is in the range for the flow to stay in the wavy annular regime
12
-
Outline
• Broad Perspective– Relevant Applications– Experimental
Observations– Need for Simulations– Key Computational Goals
• CFD Details– Simulation Tool Development– Simulation Strategy
and Data Management– Detailed Results
• Future Research Directions– CFD of Pulsatile Condensing,
Boiling and Adiabatic Flows – Enabling New Technology
• Conclusion
13
-
Computational Problem
Inlet velocity U, pressure pin,Saturation temp. Tsat(pin)
Liquid
Superheated wall
Condensing Surface - known wall temp. Tw(x) < Tsat- known
wall heat flux q''w(x)
Channel gap (h)
Vapor
x
y
Vapor
Channel gap, h – 2 to 4 mmChannel Length, L – 10 to 100 cmInlet
Velocity, U – 0.1 to 3 m/sInlet Pressure, pin – 0.1 to 2 barVapor –
Refrigerant FC72, R113, etc.
14
-
Simulation Tool Development 2D/Engineering 1D
Wall for channel geometry or axis of symmetry for cylindrical
tube.
Vapor
Liquid
∆m
∆m
Heat released
P
P
∆x
For 1-D (mass and momentum balance is solved for the chosen
vapor velocity profile)
Thin film approximation (analytical solution of momentum and
energy balance are used)
Governing Equations : Mass, momentum and energy equations in the
fluid Interface Conditions : Flow physics restrictions on
mass-momentum-energy transfer,
definition of normal component of the surface velocity &
continuity of tangential velocity, and thermodynamic
restrictions
15
-
• Single phase domain approach solves CFD for each phase on
COMSOL using FEM and a fixed grid – all governing equations
• Solutions of the two domains “talk” to each other through
interface conditions – on MATLAB/COMSOL. This comes through
embedded interface conditions in the CFD formulation for each
domain
Scientific CFD Simulation Tool Development
• One of the interface conditions is the well known Interface
Tracking Equation - Solved on MATLAB on a separate x-grid (or x-y
grid for 2-D Level-set or x-y-z grid
for 3-D Level-set)- The grid is “fixed” for a set of
time-instants, but changes with marker time-
instant (current time instant)
16
-
Guessed/updated Interface Stress
Boundary Conditions
Data ExtractionMATLAB Sub-routines
Data ExtractionMATLAB Sub-routines
Converged Solution at t = t* + Δt
Algorithm Flow Chart
Guessed or Computed Interface Location ∑(t* + Δt)
Know values at t = { t*, t*- Δt, t*- 2Δt , t*- 3Δt }
Check Convergence
Liquid DomainCOMSOL
Vapor DomainCOMSOL
Compute Interface Velocity
Boundary Conditions
Update Interface
Liquid Domain –COMSOL/MATLAB
Vapor Domain –COMSOL/MATLAB
17
-
• All flow variables and interface location are known for t ≤
t*• One of the interface conditions associated with interfacial
mass flux equality
constraint: ṁLK = ṁEnergy• This leads to the popular interface
(where interface is located by ϕ x, y, t = 0)
evolution equation: 𝜕𝜕𝜕𝜕𝜕𝜕
+ veff.𝛻𝛻ϕ = 0, where flow CFD leads to a well defined veff• For
simplification ϕ(x, t) ≡ y − ∆(x, t) is used here and the interface
tracking
equation becomes: 𝜕𝜕∆𝜕𝜕𝜕
+ �u x, t 𝜕𝜕∆𝜕𝜕x
= �v x, t
Unsteady Simulation Approach – Interface Tracking
Liquid
TW(x) or q’’W(x) – cooling condition
p = pexit
Vapor
T = Tsat (p0)Velocity = UT = Tsat (p0) p0
∑(t*)
∑(t*+∆t)
∑(t*)
∑(t*+∆t)
∑(t*) ∑(t*+∆t) y
x
y =∆(x,t)
Explicit Definition, y- ∆(x,t) = 0
y
xNeed Implicit Definition ϕ x, y, t = 0
18
-
• Move the surface Σ t∗ to a new estimated Σ(t∗ + Δt), smoothly
“map” all the vapor domain flow variable (u, v, p, T) values at t*
to the new domain at t*+∆t.
• Considering the domain at t*+∆t to be “fixed,” solve the
unsteady governing equations using the initial conditions known at
t* and boundary conditions (at inlet, interface, walls, etc.)
available for t* and t*+∆t.
• Extract the stresses (τVi , pVi ↔ FVxi , FVyi ) at the
interface from the solution.
• Compute the stresses on the liquid-side of the interface (τLi
, pLi ↔ FLxi , FLyi ) using the x and y component of the interface
condition for momentum balance.
Vapor Domain Solutionp = pexit
Vapor
T = Tsat (p0)Velocity = UT = Tsat (p0) p0
∑(t*)
∑(t*+∆t)
uVi
vVi
T2iτVi
pVi
BCs known at t* and t*+∆t
Internal governing equations – mass, momentum, energy solved on
Comsol
19
-
• Move the surface Σ t∗ to a new estimated Σ(t∗ + Δt), smoothly
“map” all the liquid domain flow variable (u, v, p, T) values at t*
to the domain at t*+∆t.
• Considering the domain at time instant t*+∆t to be “fixed,”
solve the unsteady governing equations using the initial conditions
known at t* and boundary conditions (at inlet, interface, walls,
etc.) available for t* and t*+∆t.
• Extract the components of the velocity (uLi , vLi ) at the
interface from the solution.• Compute the velocity components
(𝐮𝐮𝐕𝐕𝐢𝐢 , 𝐯𝐯𝐕𝐕𝐢𝐢 ) on the vapor side of the interface,
using the interface conditions - continuity of tangential
velocity and interfacial mass condition (ṁVK = ṁEnergy).
Liquid Domain Solution
Liquid
TW(x) or q’’W(x) – cooling condition
∑(t*)
∑(t*+∆t)τ Li
pLiT1i uLi
vLi
BCs known at t* and t*+∆t
Internal governing equations – mass, momentum, energy solved on
Comsol
20
-
Interface Tracking• Reduced form of interface evolution
equation: 𝜕𝜕𝜕
𝜕𝜕𝜕+ �u x, t 𝜕𝜕𝜕
𝜕𝜕x= �v x, t
• Solved by the “Method of Characteristics” on a spatially fixed
x-grid and temporally moving grid
• Numerical integration of the evolution equation is done along
the underlying characteristic curves - xc(t) that satisfy:
dxcd𝜕
= �u xc(t), t - obtained as “RS” by 1st order explicit method
and then obtained as “P''',…P,Q” curve by 4th order Implicit RK4
method
• The interface evolution equation along xc(t) becomes: dd𝜕
Δ xc t , t = �v xc t , t -Numerical integration is implemented
using a 4th order Simpson rule (4-interval & 5-points)
t*-3∆t
t*-2∆t
t*-∆t
t*
t*+∆t
x
t
P'''
P''
P'
P
Q
R
S
∆xfg
xc(t) - Explicit
∆(t = t*+ ∆t)
xc(t) - Implicit
∆(t*- 3∆t)
• Accurate interface location ∆(x,t) is predicted for t = t*+∆t
where �u and �v come from the CFD for the liquid-vapor domains
t*-2∆t
t*-∆t
t*
t*+∆t
t*+2∆t
x
t
P'''
P''
P'
P
Q
R
S
∆xfg
xc(t) - Explicit
∆(t = t*+ 2∆t)
xc(t) - Implicit
∆(t*- ∆t)
21
-
• Convergence of solution at t*+∆t means that all the
steady/unsteady governing, boundary conditions (interface, inlet
and wall conditions) and interior flow variables are satisfied.
• Converged interface location indicates: - The interface
evolution equation ṁLK = ṁEnergy is satisfied.- The choice of a
“smooth” domain mapping function from t* t*+∆t is such that
different choices leads to a unique interface location and flow
field at t*+∆t.
Solution Convergence
Liquid
TW(x) or q’’W(x) – cooling condition
p = pexit
Vapor
T = Tsat (p0)Velocity = UT = Tsat (p0) p0
∑(t*)
∑(t*+∆t)
∑(t*)
∑(t*+∆t)
∑(t*) ∑(t*+∆t)
22
-
Guessed/updated Interface Stress
Boundary Conditions
Data ExtractionMATLAB Sub-routines
Data ExtractionMATLAB Sub-routines
Converged Solution at t = t* + Δt
Algorithm Flow Chart
Guessed or Computed Interface Location ∑(t* + Δt)
Know values at t = { t*, t*- Δt, t*- 2Δt , t*- 3Δt }
Check Convergence
Liquid DomainCOMSOL
Vapor DomainCOMSOL
Compute Interface Velocity
Boundary Conditions
Update Interface
Liquid Domain –COMSOL/MATLAB
Vapor Domain –COMSOL/MATLAB
23
-
MATLAB
COMSOL
Interface Tracking-4th order accuracy in time- Unique mix of
explicit and implicit methods
Problem Definition
Processing- Data extraction- Interaction between domain through
interface conditions
Vapor Domain- Laminar Flow/ Single-Phase Flow Branch
Liquid Domain-Laminar Flow/ Single-Phase Flow Branch- Heat
Transfer in Fluids
Logistical Framework for the Algorithm
24
-
Convergence and Grid Independence
Criteria needed to avoid numerical diffusion and achieve
accurate solution: • Spatial discretization: ∆h
-
Comsol Grid Independence Study
• Mesh size needed for convergence:• Liquid – ∆sL• Vapor –
∆sV
• The chosen mesh size for the problem ∆s* is smaller than ∆sL
and ∆sV• Relationship to spatio-temporal grid sizes for interface
tracking is such that they are
larger than the grid sizes for the CFD. Accurate location of
interface is possible through smoothing of CFD obtained variables.
Thus numerical diffusion is avoided.
-2.2
-1.7
-1.2
-0.7
-0.2
0.8
0.805
0.81
0.815
0.82
0.825
0.83
0 0.0005 0.001 0.0015 0.002 0.0025 0.003
Average y-component of velocity x 10
-3(m/s)
Aver
age
x-co
mpo
nent
of v
eloc
ity (m
/s)
Average element size (m)
Average x-componentof velocityAverage y-componentof velocity
less than 3 % change in flow variables
∆sV = 0.0006 m
∆s* = 0.0001 m
10.551
10.552
10.553
10.554
10.555
10.556
10.557
10.558
10.559
10.56
22.5839
22.5840
22.5841
22.5842
22.5843
0 0.0001 0.0002 0.0003 0.0004
Average y-component of velocity x 10
-6 (m/s)Aver
age
x-co
mpo
nent
of v
eloc
ity x
10-
3(m
/s)
Average element size (m)
Average x-component ofvelocityAverage y-component ofvelocity
∆s* ≈ 0.0001 m
less than 1% change in flow variables
∆sL = 0.00018 m
Vapor Domain Liquid Domain
26
-
Unsteady Grid Independence
0.02 0.04 0.06 0.08 0.1 0.121
2
3
x 10-4
Distance along the length of the channel, x(m)
Dis
tanc
e fro
m th
e co
nden
sing
sur
face
, y(m
)
Steady film thicknessInitial disturbanceFilm at tp = 0.3 s, ∆tp1
= 0.01 s
Film at tp = 0.3 s, ∆tp2 = 0.005 s
0.035 0.04 0.045 0.05
1.6
1.7
1.8
1.9
2x 10-4
Mesh 1 Mesh 2N1 ∆tp1 N2 ∆tp230 0.01 s 60 0.005 s
Number of time steps and time-step size
Film thickness plot for the two different time-step sizes
showing grid independence.
27
-
Convergence of Interface Conditions
Location
x ṁLK ṁVK ṁEnergy u2i u1
i + ….. p2i p1
i + …..m kg/m2s kg/m2s kg/m2s m/s m/s Pa Pa
0.0223 0.1199 0.1199 0.1199 0.002 0.0361 0.0361 1E-07 1.3186
1.3167 0.1410.0486 0.0819 0.0824 0.0824 0.644 0.0426 0.0426 2E-06
1.7975 1.7572 2.2410.0749 0.0662 0.0662 0.0662 0.003 0.0435 0.0435
6E-07 1.9991 1.9992 0.0070.1012 0.0554 0.0554 0.0554 0.001 0.0435
0.0435 6E-07 2.0155 2.0156 0.0030.1275 0.0477 0.0477 0.0477 0.005
0.0428 0.0428 5E-07 1.8991 1.8992 0.002
Max % Diff.
Interfacial Mass flux
% Diff.
Continuity of Tangential Velocities
Normal Component of Momentum Balance
% Diff.
Location
t ṁLK ṁVK ṁEnergy u2i u1
i + ….. p2i p1
i + …..s kg/m2s kg/m2s kg/m2s m/s m/s Pa Pa
0.0533 0.0846 0.0847 0.0847 0.102 0.0426 0.0426 1E-07 1.8311
1.8449 0.7540.1367 0.0784 0.0774 0.0774 1.271 0.0415 0.0415 4E-06
1.8072 1.7851 1.2260.2200 0.0832 0.0833 0.0833 0.096 0.0408 0.0408
2E-08 1.8658 1.9156 2.6700.3033 0.0809 0.0808 0.0808 0.090 0.0428
0.0428 1E-08 1.8504 1.7926 3.1200.3867 0.0745 0.0744 0.0744 0.107
0.0395 0.0395 4E-09 1.9308 1.9591 1.468
Max % Diff.
% Diff. % Diff.
Interfacial Mass fluxContinuity of Tangential
VelocitiesNormal Component of
Momentum Balance
Satisfaction of interface variables for different locations at a
specific time t = 0.15s
Satisfaction of interface variables for different time instants
at a specific distance x = 0.05m from the inlet
28
-
Unsteady Simulation Capability – Interfacial Mass Flux
Resolution
Interfacial mass flux (kg/m2s)ṁVK - Based on kinematic
constraints on the interfacial values of vapor velocity fieldsṁLK -
Based on kinematic constraints on the interfacial values of liquid
velocity fieldsṁEnergy - Based on net energy transfer
constraint
ṁEnergy = 1/hfg . k1 [∂T1/∂n]|i
ṁVK = -ρ2 (v2i – vsi).n̂
ṁLK = -ρ1 (v1i – vsi).n̂ Liquid
Vapor
Interface
Condensing Surface
Inlet Velocity,U 2
10.12 0.14 0.16 0.18 0.2 0.22 0.24
0.045
0.05
0.055
0.06
Time = 0.036 s
Distance along the length of the condenser, x (m)
Inte
rfac
ial M
ass F
lux,
(kg
/m2 s
)
MLiqMVapMEnergy
ṁLK
ṁEnergy ṁVK
Naik et.al., 2013 Algorithm Features
29
-
Results
-
Base Flow Predictions for gy = -g are in Agreement with
Experimental Runs
Validation with Experiments (Annular Regime)xA
L = 1 m
Annular / Stratified Plug / Slug Bubbly All Liquid
X = 0
h = 2 mm
Liquid Exit
DPT–1
Condensing Plate
X = 40 cm DPT–2
HFX-1
Side view schematic of a shear-driven condensing flows
Ṁin
g/s kPa ° C ° C W/cm2 W/cm2
Error ± 0.05 ± 0.15 ± 1 ± 1 ± 25%1 0.702 99.98 48.63 7.94 0.181
0.188 4.12 0.700 99.99 49.78 6.79 0.157 0.136 13.43 0.700 99.99
49.95 6.62 0.149 0.132 11.54 0.698 99.99 50.70 5.90 0.120 0.115
4.25 1.000 101.07 43.97 13.03 0.401 0.399 0.66 1.198 142.02 49.96
18.90 0.507 0.491 3.37 1.202 142.00 50.90 17.96 0.545 0.549 0.8
% Diff. Expt. And
Theory
ΔTCase
q�w |Theory′′
@ x = 40 cmq�w |Exp𝜕′′
@ x = 40 cmp�inṀ�in T�w
31
-
Physics Understanding of Condensing Flow Differences
0.02 0.04 0.06 0.08 0.1 0.12 0.14
0.5
1
1.5
2
2.5
3
3.5
4x 10-4
Distance along the length of the condenser, x(m)
Dis
tanc
e fro
m th
e co
nden
sing
sur
face
, y(m
) Film Thickness
Horizontal Channel, gy = 0
Horizontal Channel, gy = - 9.81 m/s2
Inclined Channel, α = 2 deg
0 0.5 10
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10-3
Velocity, uI (m/s)
Dis
tanc
e fro
m th
e co
nden
sing
sur
face
, y (m
)
0 5 100
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10-3
Relative pressure, pI - p0 (Pa)310 320 3300
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10-3
Temperature, TI (deg C)
Cross-sectional Profiles for gy = 0 and gy = -9.81 m/s2 at x =
0.08 m:• Velocity and temperature profiles
show a similarity in behavior• Cross-sectional pressure
profile
shows a difference • Leads to difference in unsteady
behavior
Steady film thickness profile:• For moderate ∆T ≈ 20 deg C,
film
thickness values for gy = 0 and gy = -9.81 m/s2 are nearly the
sane over the annular length
• Inclined Channel with an inclination of 2 deg shows a much
thinner film
* Solid black line – gy = 0 and Dashed grey line – gy = -9.81
m/s2
32
-
Physics Understanding of Condensing Flow Differences
Velocity Magnitude
(m/s)
Distance along the length of the condenser, (m)
Dist
ance
from
the
cond
ensin
g su
rface
, (m
)
Velocity Magnitude
(m/s)
Distance along the length of the condenser, (m)
Dist
ance
from
the
cond
ensin
g su
rface
, (m
)
Shear Driven Gravity Driven
Horizontal channelgy = - g and gx = 0
y
xTilted channel, 2 deggy = - g cos (2°) and gx = g sin(2°)
Flow Situation
33
-
Unsteady Simulation - Wave Resolution CapabilityUnsteady flow
streamline patterns
Run parameters: Fluid – FC72, Inlet Speed U = 1m/s, Temperature
Difference ΔT = 20 °C, Channel height h = 2 mm, gy = -9.81 m/s2
34
-
Annular to Non-annular Transitions/Stability Analysis
• Unsteady response of the flow is assessed for arbitrary
spatial wavelength forms of externally imposed initial interfacial
disturbance– Predominant growth frequency and wavenumber obtained
from DFT analysis
• The unsteady response of the flow is better assessed for the
special predominant growth spatial wavelength (identified earlier)
initial interfacial disturbance
• The above results are independently assessed through:–
Characteristic curves intersection– Liquid kinetic energy and its
rate of change analyses
35
-
Unsteady Simulation – Response to Initial Disturbance
Run parameters: Fluid – FC72, Inlet Speed U = 1m/s, Temperature
Difference ΔT = 20 °C, Channel height h = 2 mm, gy = -9.81 m/s2
0.02 0.04 0.06 0.08 0.1 0.12 0.141
1.5
2
2.5
3
3.5
x 10-4Film Thickness, ∆ (x,t)
Distance along the length of the channel, x (m)
Dis
tanc
e fro
m th
e co
nden
sing
sur
face
, y (m
)
Steady FilmInitial DisturbanceFilm at t = 0.24 sFilm at t = 0.48
s
0.05 0.055 0.06 0.065 0.07
1.61.8
22.22.4
x 10-4
xAL
Annular zone
Non-annular Zone
100 200 300 400 500 600 700
2
4
6
8
10
12x 10-6
Wavenumber, k (1/m)
Mag
nitu
de o
f DFT
of ∆′ (x
,t)
DFT of ∆′(x,t) for 0< x < L
t = 0 st = 0.09 st = 0.35 st = 0.46 s
Plot of film evolution as a response to imposed initial
disturbance along the length of the condenser. Initial disturbance
∆'(x,0) ≈ a1. sin(2πx/λ1) with λ1 = 0.1 m and a1 = 1.2e-5 m
superposed on the steady solution.
Plot of the magnitude of DFT of ∆'(x,t) ≡ ∆(x,t) - ∆Steady(x)
with respect to x and time t as a parameter. The plot shows high
growth at a predominant wavenumber, kmd ≈390 m-1.
36
-
Unsteady Simulation – Contour Plot of Wave Growth
Plot showing the change in magnitude of ∆'(x,t)/∆steady(x) with
time and distance along the length of the condenser.
Contour plot of magnitude of ∆'(x,t)/∆steady(x) showing the
highest values of the contours at x ≈ 0.0675 m.
37
-
0.02 0.04 0.06 0.08 0.1 0.12 0.141
1.5
2
2.5
3
3.5x 10-4
Film Thickness, ∆ (x,t)
Distance along the length of the channel, x (m)
Dis
tanc
e fro
m th
e co
nden
sing
sur
face
, y (m
)
Steady FilmInitial DisturbanceFilm at t = 0.29 sFilm at t = 0.57
s
0.03 0.032 0.034
1.55
1.6
1.65x 10-4
xAL
Annular zone
Non-annular zone
100 200 300 400 500 600 700
1
2
3
4
5
6
7
8
9
10
11x 10-6
Wavenumber, k (1/m)
Mag
nitu
de o
f ∆′ (x
,t)
DFT of ∆′(x,t) for 0< x < L
t = 0 st = 0.13 st = 0.43 st = 0.57 s
Plot of film evolution as a response to imposed initial
disturbance along the length of the condenser.
Initial disturbance ∆'(x,0) ≈ a. sin(2πx/λmd) with λmd = 1/kmd
and a1 = 9.28e-7 m superposed on the steady solution.
Plot of the magnitude of DFT of ∆'(x,t) ≡ ∆(x,t) - ∆Steady(x)
with respect to x and time t as a parameter. The plot shows high
growth at a predominant wavenumber, kmd ≈390 m-1.
Unsteady Simulation – Response to Initial Disturbance
38
-
Transition from Annular to Non-annular Regime Through
Characteristic Curves - XA
0.04 0.05 0.06 0.07
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
xc (m)
t (s)
The plot shows characteristic curves. The characteristics
intersect at around point xA ≈ 0.065 m indicating multi-valued
nature and is the zone where transition occurs.
39
-
Energy Analysis for the Condensing Flow
Spatially averaged value of KE'L(x, t) over [0, xA] shows a
tendency to plateau
Energy analysis for the condensing flow control volumes CV1(t)
and CV2(t) of width “∆x.”
0 0.1 0.2 0.3 0.4 0.5
1
1.5
2
2.5
x 10-3
Time, t(s)
Spa
tial a
vera
ge
valu
e of
KE
L′|[0
,xA]
0 0.1 0.2 0.3 0.4 0.5
5
10
15
x 10-3
Time, t(s)
Spa
tial a
vera
geva
lue
of K
EL′
|[xA,x
L]
Liquid
Vapor
Interface
Condensing Surface
Inlet Velocity,U 2
1
x Δx
CV1(t)
CV2(t)
0xA xL
Disturbance kinetic energy in the condensate control volume
CV1(t):
KEL′ x, t ≡ KEL x, t − KEL−s𝜕 x where
KEL x, t ≡ ∫0∆(x,𝜕) �1
2ρ � u1 2 +
Spatially averaged value of KE'L(x, t) over [xA, xL] shows a
tendency for exponential growth and eventual breakup of the annular
regime
40
-
Unsteady Simulation – Critical Spatial and Temporal
Frequency
2-Dimensional DFT of KE'L (x,t) over xAL< x < xL and its
planar view • Used to identify the predominant
wavenumber and frequency.
41
-
Annular to Non-annular Transition and Heat Transfer
Correlation Development
-
Comparison of Flow – Presence and Absence of Transverse Gravity
Component
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.11
1.5
2
2.5
3
3.5
x 10-4Film Thickness, ∆ (x,t)
Distance along the length of the channel, x (m)
Dis
tanc
e fro
m th
e co
nden
sing
sur
face
, y (m
)
Steady FilmInitial DisturbanceFilm at t = 0.2 sFilm at t = 0.4
s
0.02 0.04 0.06 0.08 0.1 0.12 0.141
1.5
2
2.5
3
3.5x 10-4
Film Thickness, ∆ (x,t)
Distance along the length of the channel, x (m)
Dis
tanc
e fro
m th
e co
nden
sing
sur
face
, y (m
)
Steady FilmInitial DisturbanceFilm at t = 0.29 sFilm at t = 0.57
s
0.03 0.032 0.034
1.55
1.6
1.65x 10-4
Unsteady film evolution - With transverse gravity Identified xA
≡ xA|1g ≈ 0.065 m
Unsteady film evolution – Absence of transverse gravity
Identified xA ≡ xA|0g ≈ 0.035 m
Are there signatures of instability in the steady base flow?
43
-
Signature of Instability in Steady Base Flow –Energy Transfer
Mechanisms and Flow Variables
0.02 0.04 0.06 0.08 0.1 0.12-5
-4
-3
-2
-1
0
1
2
3
4
5x 10-3
Distance along the length of the channel, m
Ste
ady
mec
hani
cal e
nerg
y te
rms,
W/m
KEL-convKEL-intPEL-gravPWL-convPWL-intVWL-convVWL-intVDL
Mech. energy into liquid throughthe interface due to net
viscousworking per unit length
Net viscous dissipation perunit length in the liquid
xA|0g
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Distance along the condenser, x(m)
u ste
ady
x2*
xA|1g
Analyzing the steady base flows’ features for a number of
cases:1. In the absence of transverse gravity, xA|0g corresponds to
the extremum in the net interface viscous work per unit width, as
transferred through the interface work term VWL-int, and net
internal viscous dissipation per unit width term VDL - which are
the predominant terms in the energy transfer mechanisms.2. In the
presence of transverse gravity, xA|1g corresponds to the peaking
and dropping nature of the characteristic wave speed and provides
an upper bound.
Plot of Energy Transfer Mechanisms for zero gravity
condition
Plot of Characteristic Wave Speed in presence of transverse
gravity
44
-
We have proposed simulations-experiments synthesis based heat
transfer coefficient (HTC) and annular to non-annular transition
correlations for non-pulsatile annular condensing flows.Parameter
Space: 800 ≤ Rein ≤ 23,000, 0.005 ≤
JaPr1
≤ 0.021, 0.000466 ≤ ρ2ρ1≤
0.01095, 0.012013 ≤ µ2µ1≤ 0.03898, 376491 ≤ Su ≤ 25520263
HTC correlation
Nux = 0.113 �x−0.433Rein0.503Ja
Pr1
−0.308 ρ2ρ1
−0.537 µ2µ1
0.443
for 0 ≤ �x ≡ xh≤ xA
xA|0g correlation
xA|0g = 0.0155 ∗ Rein0.9616Ja
Pr1
−1.1859 ρ2ρ1
0.4425 µ2µ1
0.3
xA|1g correlation
xA|1g = 2.9413 ∗ Rein0.8514Ja
Pr1
−2.1714 ρ2ρ1
1.031 µ2µ1
1.6366
• Above correlations are in reasonable agreement with existing
HTC correlations and flow-regime maps and with our own
experiments.
Modeling/Simulation Based Correlations
J. Therm. Sci. & Engg. App., 2015
45
-
Applications - Innovative Vapor Compression Cycle Design
• Proposed solution for a phase change thermal management system
requiring milli-meter scale boiler/condenser operations –
Electronic Cooling (Tsource > Tsink).
• The heat transfer and length of annular regime correlations
developed and presented here along with analogous boiling flow
correlations are being used to design the innovative systems.
Boiler
Condenser L/VpC
FMB1 and Pre-heater
Computer Controlled Condenser Recirculation Loop Compressor,
CCR
FMC1
FMCR
FMBR
L+V
L
V
Liquid-Vapor Separator /
Accumulator*
pBTsource
Tsink
Legend:FM: Flow MeterL : LiquidV : Vapor
L+V : 2-Phase Mixture
Vapor LineLiquid Line
Throttling ValveRecirculation Loop Vapor Line
Computer Controlled Flow Metering Valve, V1
Computer Controlled Liquid Recirculation Loop Pump, PLR
Recirculation Loop Liquid Line Computer Controlled
Liquid Pump, P1
46
-
Relation to Gravity Driven/Assisted Devices – Larger
Diameter Inclined and Vertical Channels
-
Gravity Driven Flow Results – 2 deg Inclined Channel
48
Flows in 2 deg inclined channel
Flows in horizontal channel
• Developed heat transfer and annular length correlations
• Annular to non-annular transition length, xA < L
• Flow simulations study was conducted for the same case as for
horizontal channel with a 2 deg inclination
• Significantly thinner film was observed• Flow was completely
stable through the
length of the channel indicating, annular to non-annular
transition length, xA >> L
g α = 2 deg
1g
L
xA < L
48
-
Gravity Driven Flow Results – Vertical Channel
Local Reynolds number: Reδ =4 ρ1umδ
µ1• The film is laminar with minor waves for
Reδ ≤ 30 and beyond it, the film becomes wavy and ripple
formation takes place in the condensate.
• Beyond Reδ ≈ 1800, the film transitions from laminar to
turbulence.
• The simulation results are consistent with this well known
flow features. 1g
L
Reδ ≤ 30 – Laminar Minor Waves
30 ≤Reδ ≤ 1800– Laminar
Wavy/Oscillatory
x1*
49
-
Future Directions for CFD Work
• Level-set extension approaches of the proposed algorithm for
2-D/3-D problems under implicit representation Φ(x, t) = 0
• “Pulsatile” condensing flow simulations– Modeling for imposed
fluctuation cases– Study of enhancement phenomena (disjoining
pressure model effects, etc)– Pulsatile flow impact on annular to
non-annular regime transitions
• Analogous flow boiling simulations for numerous applications –
2D Steady CFD Simulation (Preliminary tests are done)– 2D Unsteady
CFD Simulation – Modeling for imposed fluctuation cases
50
-
Conclusions• Developed Fundamental 2-D steady/unsteady
predictive tools for annular flow
condensation. – With regard to convergence and satisfaction of
the interfacial conditions in the
presence of waves, it shows excellent accuracy (relative to
other methods).
• Validated the scientific tool by comparison with the
experimental data (MTU).
• Identified the transition from annular to non-annular regimes
using the stability analysis for shear/pressure driven flows.
• Proposed a method to identify the annular to non-annular
regime transition based on certain identifying features of the
steady solution.
• The results from the predictive tool has led to the
development of correlations for heat transfer coefficients and
transition maps for condensing flow regimes.
• Suitable integration of simulations and experiments will aid
in building of next generation thermal management systems involving
phase change.
51
-
Acknowledgments
• Dr. Amitabh Narain• PhD Committee Members – Dr. Fernando
Ponta, Dr. Dennis Meng,
Dr. Ranjit Pati• Department of Mechanical Engineering –
Engineering Mechanics• NSF Grant: NSF-CBET-1033591,
NSF-CBET-1402702• NASA Grant: NNX10AJ59G (Completed)• Computational
Research Group
– Dr. Soumya Mitra (Plasma Process Engineer, Hypertherm Inc.)•
Experimental Research Group
– Dr. Michael Kivisalu– Nook Gorgitratanagul, PhD Candidate
• Family and Friends
52
-
Thank You.
Questions?
53
Development of Computational Algorithms and �Simulation Tools
for Annular Internal Condensing Flows�Results on Heat-transfer
Rates, Flow Physics,�Flow Stability, and Flow
SensitivityOutlineSlide Number 3Slide Number 4Slide Number 5Slide
Number 6Slide Number 7Need for Predictive/Simulation
CapabilitiesComputational Tools and Key GoalsComputational
ToolsSlide Number 11Computationally Develop Heat Transfer
Correlations and Flow Regime MapsOutlineSlide Number 14Simulation
Tool Development 2D/Engineering 1DScientific CFD Simulation Tool
DevelopmentSlide Number 17Unsteady Simulation Approach – Interface
TrackingVapor Domain SolutionLiquid Domain SolutionInterface
TrackingSolution ConvergenceSlide Number 23Slide Number
24Convergence and Grid IndependenceSlide Number 26Slide Number
27Slide Number 28Unsteady Simulation Capability – Interfacial Mass
Flux ResolutionResultsValidation with Experiments (Annular
Regime)Slide Number 32Slide Number 33Slide Number 34Annular to
Non-annular Transitions/Stability AnalysisSlide Number 36Slide
Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number
41Annular to Non-annular Transition and Heat Transfer Correlation
DevelopmentSlide Number 43Slide Number 44Slide Number 45Slide
Number 46Relation to Gravity Driven/Assisted Devices – Larger
Diameter �Inclined and Vertical ChannelsSlide Number 48Slide Number
49Future Directions for CFD WorkConclusionsAcknowledgmentsSlide
Number 53Slide Number 54Engineering 1-D Simulation Tool
DevelopmentSlide Number 56Experimental Observations – Boiler
OperationsDifficulties in Satisfying Interfacial Mass Flux
EqualitiesAlgorithm Features that Aids in Satisfying Interfacial
Mass Flux EqualitiesGoverning EquationsInterface ConditionsSlide
Number 62Slide Number 63Slide Number 64Slide Number 65Slide Number
66Existing Simulation MethodologiesLimitations of FORTRAN Code and
Benefits of New CodeAssumptionsConsistency Between Different
Simulation ToolsHeat Transfer Enhancements – Using CFD/Physics
Knowledge Towards Qualitative Understanding as an Aid to
DesignSlide Number 72Slide Number 73Slide Number 74Slide Number
75Slide Number 76Slide Number 77Slide Number 78Slide Number 79