Experimental and Modeling Results for Flow-Boilers (and Flow Condensers) that Operate in

Annular Regimes and in High Heat-Flux Modes

Narain, A., Naik, R., Kivisalu, M., Gorgitrattanagul, P., Bhasme, S. and Ranga Prasad, H.

Michigan TechAbstract Number HT2016-7464, Proceedings of 2016 ASME

Summer Heat Transfer Conference, July 10-14, Washington DCAcknowledgments

Grants: NSF-CBET-1402702, NSF-CBET-1033591, NASA-NNX10AJ59G

Talk Outline

Millimeter-scale Flow Boilers (and Condensers) Broad Outline

o Applications and Motivationso Proposed Innovative Operations

Experimental and Modeling /Computational Results for Innovative Flow-boilers

Modeling/Computational Details Conclusions

2

Examples of Contemporary Applications Needing Innovation

Ground-based miniaturization - requires use of millimeter scale hydraulic diameters and flow rates that lead to shear driven flow

Space - requires such devices at all hydraulic diameters Handling of high heat loads at high heat-fluxes is desired Low weight and size requirements typically need to be met

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

3

Innovation for shear/pressure driven flow-boilers and flow-condensers

Challenges with Traditional Shear/Pressure Driven Boiling Flows (mm-scale devices)

Traditional to shear/pressure driven operational challenges (channels heated from below) Loss of buoyancy assisted nucleate boiling and associated heat transfer degradation Increased lengths of ineffective non-annular regimes Lack of repeatability due to extreme sensitivities

4

Dh

Proposed innovative mm-scale flow-boilers:How do they address the identified challenges?

Key Ideas Controlled recirculation of vapor (at negligible pumping power) ensures annular flow

regimes. Induced resonant pulsations in the vapor & liquid phases allow low energy acoustics

mediated formation of: standing waves of large amplitudes on micron-scale liquidfilm flows. This leads to very high heat flux operations.

Interactions with adsorbed layer on the wetting heat-exchange surface allowsnucleate boiling type high heat-flux values through stable “sticking/dwelling” of thelow-pressure wave-trough regions and induced convective motions.

TopView

Innovative Boiler

Wavy Annular Regime

Wavy Annular (mostly) Bubbly/Large Bubble Bubbly

Flow Direction

Non – Annular Flow Regimes (mostly liquid)

Traditional Boiler

SideView

TopView

InletExitRecirculating Vapor

LiquidVaporAll liquid

inlet

q”w(t)

ExitingVapor

Vapor Pulsator

PulsatileLiquid Flow

Wavy Annular Regime (mostly)

XA* XNA

5

6

Innovative Annular Flow Boiling Basics

Annular(with nucleation)

Annular(suppressed nucleation)

2-D Simulations are made available(for the first time) for this x>0 region.

x = 0

Vapor

LiquidNon-pulsatile

How thin should this be ?Vapor recirculation rate = ?

How CHF/Dry-out instabilitycan be avoided?

x

Pulsatile Liquid

VaporLiquidVapor N-IF

IFVapor Exit

LiquidExit

Steady Heating

Closed end (for vapor acoustics enabled

formation of interfacial standing

waves )

Flow Physics Hypotheses for Pulsatile Boiler and Condenser Operations

The three intersecting circles represent: interaction zones of nm-scale, mm-scale, and macro-scale phenomena.

Between the liquid-vapor interface and the adsorbed layer, at the troughs, reduced pressure and shear allow enabling convective motion. The low-pressure is enabled both by the surface-tension and curvature effects as well as by adsorbed (yellow) layer through disjoining pressure effects.

Nucleation (of bubbles) is suppressed for thin annular boiling on wetting (or super-hydrophilic) surfaces – yet the contact-line physics (Stephan et al. 2012; etc.)advantages of nucleating bubbles are retained.

Near interface schematic of instantaneous spatial film thickness profile

Time-varying film thickness profileat location x = x*

LV

δ*

δ(x,t)

x=x*

x

Mv(x,t)

ML(x,t)x

δ**δads

Adsorbed layerδads ≈ 100-200 nm

x2

x1 L

V

δ

δ(x*): Time-averaged thickness at x=x*

t = 1/fp

∆t

tSignificant

throughflow

7

Motivation: Why is pool boiling effective when buoyancy is present?

This physics is being used by the thin film flow-boiler to reproduce similar convection –during part of the wave’s time-period (as it approaches wetting-surface) but throughout the device - to obtain high heat flux with “through” flows.

Very high heat flux at the contact line (of an initially growing and subsequently shrinking and detaching vapor bubble) are experimentally observed (Stephan, et al., 2012). Disjoining pressure assisted low-pressure in the micro-layer liquid films enable vigorous convective motion.

y

x

Liquid

or

Solid

VaporBubble

r

Heat

Macro region

Adsorbedlayer

Motion depending on advancing or receding contact line

Micro regionContact line σ

q”w(r,t)

8

Experimental Evidence of Significant Heat-flux Enhancements for Pulsatile Flows as Opposed to Non-pulsatile Flows

Characteristics of Experimentally Observed Pulsatile Flows: Much thinner mean film thickness achieved by pulsations (10 micro-meters). Controlled amplitude and frequency (1-15 Hz) for large amplitude standing waves. Heat-flux enhancement over entire 0 ≤ x ≤ L : Ongoing Expt.

q”40 cm(t)

h =

2 m

m

Steady HeatingHeat Flux Meter

VaporLiquidVapor

N-IFIF

40 cm

x

Liquid

q”40 cm(t)Steady Cooling

h =

6 m

m

Cold Water FlowHeat Flux Meter

VaporLiquidFC-72

Vapor

N-IFIF

40 cm

x

9

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.6 1.2 1.8 2.4 3 3.6

Mea

sure

d Lo

cal H

eat-F

lux

(W/c

m2 )

Measured Pulsation Amplitude (kPa)

3.0 Hz Imposed Fluctuations, Innovative Flow Boiler

q̅”̅W (x = 40 cm)data

q̅”̅W (x = 40 cm) trendEn

hanc

emen

t

No Imposed Pulsations

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1Ti

me

-Ave

rage

d H

eat F

lux

Mea

sure

d at

X =

40

cm (W

/cm

2 )

28.4 Hz Imposed Fluctuations, Innovative Condenser

10.6 Hz Imposed Fluctuations, Innovative Condenser

Pressure Amplitude at Heat Flux Meter location (kPa)No Imposed Pulsations

Expected Forthcoming experimental

results

10

First-principles basedsimulations (DNS & scientific)

Simplified results with approximate correlations

Empirically obtained/adjusted correlations

1D design solver

New Modeling Approach for Steady Innovative Operations

q"w(x) is positive for boiling &negative for condensation

Δx

q"w(x)

Boiling Condensationh

x

Definitions:

qw" x ≡ −k1𝜕𝜕𝜕1𝜕𝜕yp

≡ hx (𝜕w(x) − 𝜕sat(p0)

Nux ≡hx .hk1

; qw" (x) = qw" .Ψq(x)

│𝜕w(x) − 𝜕sat(p0)│ ≡ ∆𝜕 .θw x ; �x ≡xh

Bl ≡ qw"

G.hfg; Ja ≡ Cp1.∆T

k1; X �x ≡ Ṁv

Ṁin

yp=0

11

New Modeling Approach for Steady Innovative Operations (Contd.)

≡--- Temp. Prescription

--- Heat flux Prescription

Boiler (+)Condenser(-)

dXd�x

(x̂)

± NuxJa

Pr1.

1ReT−V

.µ1µ2

. θw(x)

�± Bl.Ψq(x

Combined solutions of Eq. (1) and Eq. (2) typically yieldspatial variations in X, hx etc.

xNu ≡2 2

x in1 1 1

ρ μJaNu X, , Re , ,Pr ρ μ

2 2x in

1 1

ρ μNu X,Bl,Re , ,ρ μ

--- Temp. Prescription

--- Heat flux Prescription

Experiments and/or DNS based correlations

Eq. (1)

Eq. (2)

12

Experimental/Modeling/Computations are given in:

Published scientific papers:

Kivisalu, M. T., Gorgitrattanagul, P., and Narain, A., (2014), International Journal of Heat and Mass Transfer, 75, 381-398.

Naik, R., Narain, A., Mitra, S., (2016) Numerical Heat Transfer, part B: Fundamentals, 69(6), 473-494.

Naik, R., Narain, A., (2016) Numerical Heat Transfer, part B: Fundamentals, 69(6), 495-510.

Papers on correlations-based design tools:

Published: Narain, A., Naik, R.R., Ravikumar, S., Bhasme, S.S, (2015) Journal of Thermal Engineering, 1,

pp. 307-321.

Submitted: Ranga Prasad, H., Narain, A., Bhasme, S.S., Naik, R.R, (2016) International Journal of Transport

Phenomena.

DNS Modeling Requires Inlet ConditionsApproach: Assume Adiabatic Flows Followed by Different

Prior Heating Conditions Leading to Uniform Heating

13

(b)(c)

(a) Plot of the steady film thickness profile Δ(x) for a transverse gravity case of gy=-g.(b) Cross-sectional profiles for x-component of velocity uI, at xp = 0.02 & (c) Cross-sectional profiles for Pressure pI at xp = 0.02 m . (Run parameters: Fluid – FC-72, U = 1 m/s, p0 = 105.1 kPa, ΔT = 10°C,channel height = 2 mm)

Steady Flow Boiling Results Based on DNS

y=∆(x)

14

∆(x)

x=0.02 m

y

x

Vapor Liquid

I = 2

I = 1

(a)

Dis

tanc

e fro

m h

eate

d su

rface

, y (m

)

Dis

tanc

e fr

om h

eate

d su

rfac

e, y

(m)

Velocity, uI (m/s) @ xp = 0.02m (I – 1 or 2)Pressure, pI (m/s) @ xp = 0.02m (I – 1 or 2)

Film

Thi

ckne

ss, Δ

(m)

Distance along the length of the channel, xp (m)

Correlations are being developed for annular boiling.(On-going activity/Sample Reported)

Steady Flow Boiling Results Based on DNS (Contd.)

15

Distance along the length of the channel, xp (m)

Dis

tanc

e fr

om th

e he

ated

surf

ace,

y (m

m)

Velo

city

mag

nitu

de (m

/s)

h =

16

Figure: (a) Plot of the Heat Transfer Coefficient vs Non-Dimensional Distance (b) Plot of Heat Transfer Coefficient vs Quality (Run parameters: Fluid – FC-72, U = 1 m/s, p0 = 105.1 kPa, ΔT = 10°C, channel height = 2 mm)For xp > xe

p prior “heating method” effects are no longer present

Steady Flow Boiling Results Based on DNS (Contd.)

(a) (b)

xx

1

h .hNuk

≡ , non-dimensional pressure gradients, etc. are being correlated in forms discussed earlier.

�xe

�xe ≡ xep/h,where xe

p is heating methodassociated entrance length

Xe

Signature of Instability in Steady Base Flow: Energy Transfer Mechanisms and Flow Variables

Analyzing the steady base flows’ features for a number of cases: In the absence of transverse gravity, xA|0g corresponds to the extremum in the net mechanical work

terms per unit width, transferred primarily as the sum of net pressure work per unit width (Δx) terms (PWL-conv & PWL-int) & interfacial viscous work per unit width (Δx) term VWL-int. These are dissipated by equal and opposite outgoing net internal viscous dissipation per unit width term VDL. These are the predominant terms in the energy transfer mechanisms.

In the presence of transverse gravity, xA|1g approximately corresponds to the maximum associated with peaking and dropping nature of the characteristic wave speed. Its estimate provides an upper bound.

Plot of significant Energy Transfer Mechanism Terms in the presence of transverse gravity

Plot of Characteristic Wave Speed and Viscous Dissipation rates in the presence of transverse gravity

17

xA|1g

xA|0g

xA|0g

XA ≡ ”NA-A” transition location

Cha

ract

eris

tic S

peed

, �u(m

/s)

18

Instability analysis gives Xcr|NA-A & steady solution gives ∆0.Xcr|NA-A & ∆0 are being correlated and reported in IJTP 2016/2017 and JTEN 2016/2017

papers. Known correlations allow Ṁv-recirc to be adjusted to satisfy:

Xin > Xcr|NA-A & keep ∆0 ≅ O (100µm)

Steady/Unsteady Flow Boiling Results Based on DNS (Contd.)

Vapor Recirculation

Vapor

Inlet

Annular

Non-annular

Xin Xcr|NA-AVapor Recirculation

Inlet

VaporAnnular Liquid

XinXcr|NA-A

Ṁv-recirc

∆0Xin > Xcr|NA-A

Xin < Xcr|NA-A

Unsteady Simulations: Instability Identification Capability

Unsteady 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

19

Velo

city

mag

nitu

de (m

/s)

Not available for Flow-boiling. Expected to be analogous to the ones in flow-condensation.

We have proposed simulations-experiments synthesis based heat transfer coefficient (HTC) correlations (J. Therm. Sci. & Engg. App., 2015) for non-pulsatile annular condensing flows.

Parameter Space: 800 ≤ Rein ≤ 23,000, 0.005 ≤JaPr1

≤ 0.021, 0.000466 ≤ 𝜌𝜌2𝜌𝜌1

0.01095,

0.012013 ≤ 𝜇𝜇2𝜇𝜇1≤ 0.03898, 376491 ≤ 𝑆𝑆𝑆𝑆 ≤ 25520263

Non-Dimensional hx or Nux correlation for Non-pulsatile case

𝑁𝑁𝑆𝑆𝑥𝑥 = 0.1 (1 − X)−0.59𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖0.122𝐽𝐽𝐽𝐽𝑃𝑃𝑃𝑃1

0.3 𝜌𝜌2𝜌𝜌1

−0.73 𝜇𝜇2𝜇𝜇1

0.069for X𝑐𝑐𝑃𝑃−𝐴𝐴|1𝑔𝑔 ≤ X ≤ 1

Non-Dimensional hx or Nux correlation (Pulsatile, ongoing)

|𝑁𝑁𝑆𝑆𝑥𝑥 𝑝𝑝𝑆𝑆𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑅𝑅 = 𝑁𝑁𝑆𝑆𝑥𝑥 + 𝑅𝑅𝑒𝑒𝑝𝑝𝑝𝑝𝑒𝑒𝑝𝑝𝑒𝑒𝑝𝑝𝑝𝑝 % 𝑅𝑅𝑒𝑒𝑒𝑝𝑝𝑒𝑒𝑒𝑒𝑅𝑅𝑒𝑒𝑅𝑅𝑒𝑒𝑝𝑝 𝑓𝑓𝑆𝑆𝑒𝑒𝑒𝑒𝑝𝑝𝑝𝑝𝑓𝑓𝑒𝑒𝑒𝑒𝑓𝑓𝑒𝑒 − 𝑑𝑑𝑝𝑝𝑒𝑒𝑅𝑅𝑒𝑒𝑝𝑝𝑝𝑝𝑓𝑓𝑒𝑒𝑝𝑝𝑝𝑝 𝑝𝑝𝑒𝑒𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑆𝑆𝑑𝑑𝑅𝑅,𝑒𝑒𝑓𝑓𝑒𝑒 − 𝑑𝑑𝑝𝑝𝑒𝑒𝑅𝑅𝑒𝑒𝑝𝑝𝑝𝑝𝑓𝑓𝑒𝑒𝑝𝑝𝑝𝑝 𝑓𝑓𝑒𝑒𝑅𝑅𝑓𝑓𝑆𝑆𝑅𝑅𝑒𝑒𝑒𝑒𝑓𝑓

Xcr-A|1gcorrelation

X𝑐𝑐𝑃𝑃−𝐴𝐴|1𝑔𝑔 = 1 − 1.78 ∗ 𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖−0.02𝐽𝐽𝑝𝑝𝑃𝑃𝑒𝑒1

−0.564 𝜌𝜌2𝜌𝜌1

0.42 𝜇𝜇2𝜇𝜇1

0.335

Above correlations are in reasonable agreement with existing HTC correlations and flow-regime maps and with our own experiments.

Fundamental Modeling/Simulation Supported Correlation: Flow-Condensation

20

Parameter Space: 616.5 ≤ Rein ≤ 9880.7, 0.0048 ≤JaPr1

≤ 0.0424, 0.00466 ≤𝜌𝜌2𝜌𝜌1

0.0097, 0.0216 ≤ 𝜇𝜇2𝜇𝜇1≤ 0.0295, 0.5 ≤ Xin ≤ 0.86

Non-Dimensional hx or Nux correlation for Non-pulsatile case

𝑁𝑁𝑆𝑆𝑥𝑥 = 1.13 ∗ X1.652𝑅𝑅𝑅𝑅𝑖𝑖𝑖𝑖0.0776𝐽𝐽𝐽𝐽𝑃𝑃𝑃𝑃1

−0.0963 𝜌𝜌2𝜌𝜌1

−0.423 𝜇𝜇2𝜇𝜇1

0.4833for X ≤ 1

Non-Dimensional hx or Nux correlation (Pulsatile, ongoing)

|𝑁𝑁𝑆𝑆𝑥𝑥 𝑝𝑝𝑆𝑆𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑅𝑅 = 𝑁𝑁𝑆𝑆𝑥𝑥 + 𝑅𝑅𝑒𝑒𝑝𝑝𝑝𝑝𝑒𝑒𝑝𝑝𝑒𝑒𝑝𝑝𝑝𝑝 % 𝑅𝑅𝑒𝑒𝑒𝑝𝑝𝑒𝑒𝑒𝑒𝑅𝑅𝑒𝑒𝑅𝑅𝑒𝑒𝑝𝑝 𝑓𝑓𝑆𝑆𝑒𝑒𝑒𝑒𝑝𝑝𝑝𝑝𝑓𝑓𝑒𝑒𝑒𝑒𝑓𝑓𝑒𝑒 − 𝑑𝑑𝑝𝑝𝑒𝑒𝑅𝑅𝑒𝑒𝑝𝑝𝑝𝑝𝑓𝑓𝑒𝑒𝑝𝑝𝑝𝑝 𝑝𝑝𝑒𝑒𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑆𝑆𝑑𝑑𝑅𝑅,𝑒𝑒𝑓𝑓𝑒𝑒 − 𝑑𝑑𝑝𝑝𝑒𝑒𝑅𝑅𝑒𝑒𝑝𝑝𝑝𝑝𝑓𝑓𝑒𝑒𝑝𝑝𝑝𝑝 𝑓𝑓𝑒𝑒𝑅𝑅𝑓𝑓𝑆𝑆𝑅𝑅𝑒𝑒𝑒𝑒𝑓𝑓

Xcr-A|1gcorrelation

Forthcoming for Flow-boiling. Result types are analogous to the ones for flow condensation.

Fundamental Modeling/Simulation Supported Correlation: Flow-Boiling

21

Channel gap, h – 2 to 4 mmChannel Length, L – 10 to 100 cmInlet Velocity, U – 0.1 to 3 m/sInlet Pressure, pin – 1 to 2 barVapor – Refrigerant FC72, R113, etc.

Modeling / DNS CFD Approach Outline(for Annular Flow Boiling)

22

Simulation Tool Development 2D/Engineering 1D

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

23

P

P

Δm

Δm

Δx

Vapor

Liquid

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)

Wall for channel geometry or axis of symmetry for cylindrical tube.

Heat transferred

• Single phase domain approach solves CFD for each phase on COMSOL using FEM – all governing equations

• Solutions of the two domains “talk” to each other through interface conditions –arrange on MATLAB/COMSOL program. The “talk” results from embedded interface conditions in the CFD formulation for each domain

• One of the interface conditions is the well known Interface Tracking Equation which is 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). For unsteady simulation, the grid is “fixed” for a set of time-instants, but changes with marker time-instant (current time instant).

Scientific CFD Simulation Tool Development

24

InterfaceLiquid

TW(x) or q''W(x) – heating condition

T = Tsat (p0)

p = pexit

Interface

VaporT = Tsat (p0)

Velocity - UT = Tsat (p0)

p0B

C

Internal Triangular Mesh

A

uVi

vVi

τLip Li

Lcomp

Inlet Condition-Extended Prior to Inlet & Assume Different Prior Heating Condition

25

Conclusions

Innovations proposed and demonstrated for mm-scale boilers and condensers.

Experimental and modeling support structure has been developed.

26

Thank you!Questions?

27

Governing Equations

28

Two dimensional flow with 𝐱𝐱𝐈𝐈 = xI ̂ı + yI ̂ȷ and 𝐯𝐯𝐈𝐈 = uI ̂ı + vI ̂ȷ

• Continuity Equation𝜕𝜕ρI𝜕𝜕t

+ 𝛻𝛻 ρ. 𝐯𝐯𝐈𝐈 = 0• Momentum Equation

ρI𝜕𝜕𝐯𝐯𝐈𝐈𝜕𝜕𝜕

+ 𝐯𝐯𝐈𝐈.𝛻𝛻 𝐯𝐯𝐈𝐈 = −𝛻𝛻𝛻 + ρIg + µI𝛻𝛻2𝐯𝐯𝐈𝐈

• Energy Equation

ρICpI𝜕𝜕𝜕I𝜕𝜕𝜕 + 𝐯𝐯𝐈𝐈.𝛻𝛻 𝜕I = kI𝛻𝛻

2𝜕I

Back

Interface Conditions

29

Explicit interface definition - ϕ x, t = y − Δ x, t = 0Unit normal at any point on the interface, when directed from the liquid towards the vapor, is denoted by �𝐧𝐧 ≡ 𝛻𝛻𝛻 / 𝛻𝛻𝛻• Continuity of tangential velocities - 1

u2i = u1i −𝜕𝜕Δ𝜕𝜕𝜕 (v2

i − v1i )

• Normal component of momentum balance - 1p1i = p2i + ṁp 2

1ρ2−

1ρ1

+ σ𝛻𝛻s. �𝐧𝐧 − 𝛻𝛻sσ. �𝐧𝐧 + 𝐒𝐒𝟏𝟏𝐢𝐢 − 𝐒𝐒𝟐𝟐𝐢𝐢 �𝐧𝐧. �𝐧𝐧

• Tangential component of momentum balance - 1𝐒𝐒𝟏𝟏𝐢𝐢 �𝐧𝐧. �̂�𝐭 = 𝐒𝐒𝟐𝟐𝐢𝐢 �𝐧𝐧. �̂�𝐭 + 𝛻𝛻sσ. �̂�𝐭

• Kinematic and energy constraints on interfacial mass flux and its equality - 2ṁVKp ≡ − ρ2 𝐯𝐯2

pi − 𝐯𝐯s . �𝐧𝐧

ṁLKp ≡ − ρ1 𝐯𝐯1

pi − 𝐯𝐯s . �𝐧𝐧

ṁEnergyp ≅

1hfg

k1 �𝜕𝜕𝜕1𝜕𝜕np

i

− k2 �𝜕𝜕𝜕2𝜕𝜕np

i

ṁLKp = ṁVK

p = ṁEnergyp ≡ ṁp

• Thermodynamic Restrictions - 2𝜕1i ≅ 𝜕2i ≡ 𝜕sat p2i

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Experimental and Modeling Results for Flow-Boilers (and Flow Condensers) that Operate in Annular Regimes and in High Heat-Flux ModesTalk OutlineSlide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12DNS Modeling Requires Inlet Conditions�Approach: Assume Adiabatic Flows Followed by Different Prior Heating Conditions Leading to Uniform HeatingSlide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Simulation Tool Development 2D/Engineering 1DScientific CFD Simulation Tool DevelopmentInlet Condition-Extended Prior to Inlet & Assume Different Prior Heating ConditionConclusionsThank you!�Questions?Governing EquationsInterface Conditions