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