上海交通大学：《多相流和传热 Multiphase flow and heat transfer》课程教学资源_Chapter 3 Bubble or droplet translation

Bubble or droplet translation

Bubble or droplet translation

Introduction Forces on particle can radically modified them,and in turn to change the interaction between particles and continuous phase. This chapter consider the translation of disperse phase consists of deformable particles

Introduction • Forces on particle can radically modified them, and in turn to change the interaction between particles and continuous phase. • This chapter consider the translation of disperse phase consists of deformable particles

Dimensional analysis Translation stress may deform particles ●Need to consider -Deformation parameters Impacts on translation velocity and shape Surface tension will be force restrain the deformation ·Assumptions: Steady translation Driven by gravity

Dimensional analysis • Translation stress may deform particles • Need to consider – Deformation parameters – Impacts on translation velocity and shape • Surface tension will be force restrain the deformation • Assumptions: – Steady translation – Driven by gravity

Dimensional analysis Surface tension force,SR When magnitude of deform force approaches SR, deformation happens. For Re>1,the deform force PLW2R2 So define We =2pLW2R/S For Re>1,deformation happens when We ~1 Therefore woo need to be defined,so F(Re,We,Fr)=0 To define a new parameter We3 Hm Fr2Re4 mp PLu PL S3

Dimensional analysis • Surface tension force, SR • When magnitude of deform force approaches SR, deformation happens. – For Re>1, the deform force • So define – For Re>1, deformation happens when We ~1 • Therefore need to be defined, so To define a new parameter

Hm 108 HELIUM-4 -TOLUENE FREON-12 OXYGEN OXYGEN NITROGEN NITROGEN 10 HELIUM-4 METHANE WATER SODIUM MERCURY 0.2 0.4 0.6 0.8 1.0 REDUCED TEMPERATURE. （T-T,)/(Te-T) Filtered Water 0.25×10-10 Turpentine 2.41×10-9 Methyl Alcohol 0.89×10-10 Olive Oil 7.16×10-3 Mineral Oil 1.45×10-2 Syrup 0.92×106

Hm

Bubble shapes and terminal velocities When the departure from sphericity happens ·Re1 in some irregular case,therefore deformation happens ·Re>>1 Fr≈O(1) We>1→Re>Hm If Hm1,deform happens since Re<<1

Bubble shapes and terminal velocities • When the departure from sphericity happens • Re1 in some irregular case, therefore deformation happens • Re>>1 – If Hm1, deform happens since Re<<1

Bubble shapes and terminal velocities Experimentally,deformation causes ellipsoidal bubbles oscillation both in shape and trajectories. When bubble size increases further reaching We=20, it acquires a new shape,spherical-cap bubble w=子gRc)=(gR)话 Where for a spherical gas bubble with same volume Woo =(8gRB/3Cp)=2.3(gRB) -BUBBLE VOLUME

Bubble shapes and terminal velocities • Experimentally, deformation causes ellipsoidal bubbles oscillation both in shape and trajectories. • When bubble size increases further reaching We=20, it acquires a new shape, spherical-cap bubble – Where for a spherical gas bubble with same volume

Bubble shapes and terminal velocities Spherical-cap bubble -Woo/(gRB)constant Re>200 90 80 60 50 0 60 ★。 12 2.0 10 24 0.8 0.5 10 102 103 10 105 REYNOLDS NUMBER,Re=2 WooRa/v

Bubble shapes and terminal velocities • Spherical-cap bubble – constant Re>200

Bubble shapes and terminal velocities Terminal velocity function F(Re,Hm,CD)=0 Hm LIQUID A 9.2X105 SYRUP 24 0 1.45X102 MINERAL OL 0 7.2X103 OLIVE OIL 0 1.5X10→ WATER+CORN SYRUP 2.1x103 E 1.75x102 WATER+56%GLYCERINE 4.18×109 WATER+42%GLYCERINE LN3IO30 10 Co-36 Hm LIQUID G1.17x109 WATER+13%ETHYL ALCOHOL H 2.41x109 TURPENTINE 4.3x1010 VARSOL K 1.08x1010 COLD FILTERED WATER 0.89x1010 METHYL ALCOHOL M0.25x1010 FILTERED WATER 10L 101 1 10 102 103 10 REYNOLDS NUMBER,Re

Bubble shapes and terminal velocities • Terminal velocity function

Marangoni effects Marangoni effects,force due to the surface tension e gradient affects the translation velocity. The gradient can be caused by temperature gradient, electric potential. The thermocapillary effects For most liquid,surface tension decreases linearly with temperature -ds/dT,for pure liquid/vapor interfaces (in kg/s2 K). Water 2.02×10-4 Methane 1.84×10-4 Hydrogen 1.59×10-4 Butane 1.06×10-4 Helium-4 1.02×10-4 Carbon Dioxide 1.84×10-4 Nitrogen 1.92×10-4 Ammonia 1.85×10-4 Oxygen 1.92×10-4 Toluene 0.93×10-4 Sodium 0.90×10-4 Freon-12 1.18×10-4 Mercury 3.85×10-4 Uranium Dioxide 1.11×10-4

Marangoni effects • Marangoni effects, force due to the surface tension gradient affects the translation velocity. • The gradient can be caused by temperature gradient, electric potential. • The thermocapillary effects – For most liquid, surface tension decreases linearly with temperature