IMPACT OF BOUNDARY-LAYER IMPACT OF BOUNDARY-LAYER CUTTING ON FREE-SURFACE CUTTING ON FREE-SURFACE BEHAVIOR IN TURBULENT BEHAVIOR IN TURBULENT LIQUID SHEETS LIQUID SHEETS S.G. DURBIN, M. YODA, and S.I. ABDEL-KHALIK G. W. Woodruff School of Mechanical Engineering Atlanta, GA 30332-0405 USA
Thick Liquid Protection (HYLIFE-II) Oscillating pocket Protective lattices Picture courtesy of Ryan Abbott ( LLNL ) 2
Motivation • Provide effective thick liquid protection � Minimize interference with beam and target propagation ⇒ smooth jets • What type(s) of flow conditioning are necessary to produce jets that meet HYLIFE-II requirements? � Is boundary-layer cutting required? � If so, can boundary-layer cutting be optimized? 3
Objectives • Estimate amount of turbulent breakup at free surface (“hydrodynamic source term”) • Quantify free-surface fluctuations • Optimize effectiveness of boundary-layer (BL) cutting � Determine minimum “cut” mass flux to meet propagation requirements � Minimize surface ripple 4
Flow Loop • Pump-driven D recirculating flow loop E E • Test section height ~ 1 m F F • Overall height ~ 5.5 m G G A Pump H 400 gal tank C B Bypass line I Butterfly valve C Flow meter J 700 gal tank H B D Pressure gage K 20 kW chiller I E Flow conditioner E Flow conditioner F Nozzle F Nozzle K J A G Liquid sheet G Liquid sheet 5
Experimental Parameters z • Char. length scale δ = 1 cm y δ x • Re = U o δ / ν = 120,000 • We = ρ L U o 2 δ / σ = 19,000 • Re 50% and We 20% of HYLIFE-II values y z • ρ L / ρ g = 850 • Near field: x / δ ≤ 25 matching extent of HYLIFE-II protective pocket x • BL cutter removal rate: � � m / m = 0– 1.9% g cut fl • σ z standard deviation in z -position of free surface 6
Flow Conditioning Elements • Round inlet (12.7 cm ID) to PP 3.9 cm rectangular cross-section 10 cm HC × 3 cm ( y × z ) 3.0 cm • Perforated plate (PP) FS � Open area ratio 50% with staggered 4.8 mm dia. holes • Honeycomb (HC) 14.7 cm � 3.2 mm dia. × 25.4 mm staggered circular cells • Fine screen (FS) � Open area ratio 37.1% � 0.33 mm dia. wires w/open cell width of 0.51 mm (mesh size 30 × 30) z � “Standard design” • Contracting nozzle y x � Contraction ratio = 3 7
Turbulent Breakup Flow • Turbulent primary breakup Nozzle mechanism � Formation of instabilities followed by ligaments and finally droplets x i � Possible sources of instabilities – Vorticity imparted at nozzle exit – Instability in boundary layer – Sudden velocity profile relaxation • Onset of breakup, x i � Location of first observable droplets � x i ↓ as We ↑ 8
Beam Propagation • Droplets travel into beam footprint • Jet standoff distance, ∆ z s Beam-to-jet standoff x i � Measured from distance nominal jet surface x • Equivalent number Beam density dependent on footprint x and ∆ z s ∆ z s � Ignores jet-jet interactions 9
Atomization Work • Considerable database from combustion and spray research group at UM (Faeth et al.) � Most recently: Sallam, Dai, & Faeth, Int. J. of Multiphase Flow, 28 : 427 – 449 (2002) • Correlations developed for � Round and annular jets � Fully-developed turbulent flow at exit � No flow conditioning, contraction/nozzle or BL cutting � Jets issue into air at atmospheric pressure � Working fluids: water and ethanol 10
Surface Breakup Efficiency Factor • Radial droplet velocity relative to jet surface ~ ≅ v 0 . 045 U r o • Surface breakup efficiency factor � Gives a measure of the flux of droplets from free surface � ε = 1 indicates droplets are forming over entire surface area of liquid surface G = ≡ ε G mass flux of droplets � ρ v L r • Efficiency factor correlation (valid for We d = 235–270,000) x = d h = hydraulic diameter ε 0.272 ( ) 1 2 d We h d 11
Mass Collection • Cuvette opening = 1 cm × 1 cm w/ 1 mm walls 5 y 4 3 • 5 cuvettes placed side by side z 2 1 � Cuvette #3 centered at y = 0 • Located at x , ∆ z s away from nominal jet position x � ∆ z s varied from ~ 2.5 – 15 mm θ • Shallow angle of inclination, θ = 6.5 ° • Samples acquired over 0.5 – 1 hr • Collected mass used to calculate: ∆ z s Cuvettes � Mass flux, G [kg / (m 2 ·s)] � Equivalent number density, N [m -3 ] 12
Boundary-Layer Cutter • “Cut” (remove BL fluid) on one side of liquid sheet y • Independently control � m x removal rate: cut • Removed liquid diverted to side 13
Cutter Details • Aluminum blade inserted into flow � Remove high vorticity / low momentum fluid near nozzle wall Nozzle z y � Blade width ( y -extent) 12 cm vs. W o = 10 cm x � Blade edge 0.76 mm Diverted (cut) downstream of nozzle exit 7.5 mm � m fluid: cut • Relatively short reattachment length Cutter � Nozzle contraction length blade 63 mm 14
PLIF Results (Initial Conditions) • x / δ = 25 0.15 � � • = 1.9% m / m cut fl 0.10 • Large central σ z / δ fluctuation without 0.05 fine screen 0.00 � Fine screen has -5.0 -2.5 0.0 2.5 5.0 greater impact on σ z y / δ z y x No Screen Standard Design 15
Average PLIF Results 0.08 • Averaged over 0.06 central 75% of jet σ z / δ σ z / δ • Fluctuations 1.5 × 0.04 for no fine screen 0.02 • BL cutting reduces σ z by 33% for 0.00 standard flow 10 15 20 25 30 conditioner design x / δ � - No cutting Standard Design No Fine Screen � - 1.9% cut 16
PLIF Results (BL Cutting) 0.05 • Standard flow 0.04 conditioning 0.03 σ z / δ • σ z ↓ as ↑ � m cut 0.02 • Cutting as little as 0.01 � m = 0.6% cut 0.00 significantly 0.0 0.5 1.0 1.5 2.0 improves surface � � m / m (%) m cut / m flow (%) smoothness cut fl x / δ = � 15 � 20 � 25 17
Jet Profiles ( x / δ = 25) 1 cm • Std. flow conditioning Nozzle exit • Uncut jet inside nominal free surface No cutting • BL cutting results in large protrusions near edges of jet � Sharp transition to z 1.9% cut edges of jet y • Jet width ( y -extent) x decreases with cutting Vertical axis at 5 × magnification Notes: � ~6 mm at x / δ = 25 Average of 135 images over 4.5 s 18
Equivalent Number Density ( x / δ = 25) 5 mm beam-to-jet standoff [Latkowski & Meier (2001)] 10 23 • Turbulent breakup at free surface 10 22 � Ejected drops form 10 21 N (m -3 ) sparse aerosol around jet 10 20 • No fine screen: droplets N farther from free surface 10 19 Standard Design • BL cutting reduces No Fine Screen 10 18 hydrodynamic source term 0 0.5 1 1.5 � Effectively eliminates ∆ z s / δ breakup for “well � � m / m conditioned” jet cut fl � 0.0% � 1.0% � 1.9% 19
Model Comparison • Correlation over- 10 -3 predicts breakup 10 -4 � Correlation based on G exp / G corr fully-developed turbulent flow 10 -5 � Flow conditioning / Sensitivity Limit contracting nozzle 10 -6 may reduce breakup Standard Design by 10 3 - 10 5 No Fine Screen 10 -7 • Zero collected mass 0 0.5 1 1.5 within experimental ∆ z s / δ error for G exp / G corr < � � m / m 10 -6 cut fl � 0.0% � 1.0% � 1.9% 20
Conclusions Characterized boundary layer cutting in turbulent liquid sheets in the near field at Re = 120,000 • Optimum configuration: Standard flow conditioning with 1.0% of total mass flux cut from each face � Meets proposed upper limit of N = 6 × 10 21 m 3 � Surface ripple reduced by 31% • Boundary layer cutting changes free-surface geometry � Large protrusions near edges of sheet • Breakup correlation overestimates droplet mass flux (and number density) by 3 – 5 orders of magnitude � Reduction may be due to flow conditioning and nozzle � Demonstrates sensitivity of breakup to initial conditions 21
Correlation Mass Flux - I • Droplets follow ballistic path based on: � Absolute streamwise and radial velocities = ⋅ ≤ ⋅ � � u 0.78 U , v 0.089 U o o x i � Neglects gravitational and aerodynamic effects x • Droplet trajectory given by � v x set β = ≤ o arctan 6.5 � u β = 6.5 ° • Coordinate transformation −∆ ∆ z z ( ) β = ⇒ = + x x tan ( ) ( ) β set − tan x x set ∆ z 22
Correlation Mass Flux - II Solving for G and substituting for ε • x ( ) = ⋅ � G 0.272 ρ v ( ) L r 1 2 d We h d • Substituting for x ( ) ( ) ∆ β z tan ( ) ( ) ( ) ∆ = − ⋅ ρ � + G z x , 0.272 v G x ( ) set L r set 1 2 d We h d Valid for x set > x i and 0 < ∆ z < ( x set – x i ) · tan( β ) For average correlation mass flux at x / δ = 25 and ∆ z s = 5 mm • � x set = 25 cm � Use ∆ z = ∆ z s + 6 mm, for mass flux in center of cuvette Cuvette walls ∆ z s 5 mm 1 mm 23
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