bubble pump modeling for solar hot water heater system design

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Figure 5: Vertical Two-Phase Flow Regimes (Collier & Thome 1996) Figure 6: Bubble Pump System Layout A series of momentum and mass flow balances can be performed to model the operation of the bubble pump system based on the definitions of the state locations in Figure 6. These equations are provided in detail as follows: Momentum equation from P sys to 0 gives: 176
P 0 2 V0 Psys LgH L [1] 2 Where: V 0 is the velocity (m/s) at point 0 (liquid solution) Momentum equation from 0 to 1 yields (including pressure drop from friction): P 1 P0 LV0 ( V1 V0 ) TP gHFP [2] Where: V 1 is the velocity (m/s) at state 1 D 0 is the diameter (m) of the water entrance line ρ L is the density (kg/m 3 ) of the water entrance line ρ TP is the density (kg/m 3 ) of the two phase mixture in flat panel H FP is the height (m) of the water level in flat panel Conservation of mass from state 0 to 1 yields: A [3] L Where: 0V0 L A0V 1 Therefore: Area of the water entrance line (m 2 ): A 0 = πD 0 2 /4 [4] V0 V 1 [5] Conservation of momentum from state 1 to 2, neglecting friction in this transition: 2 P1 V1 V2 V1 P TP [6] where ρ TP is the homogeneous density of the two-phase flow. Since the velocities of each phase in the region between 1 and 2 are approximately equal (slip, S=1) a homogeneous density is used in this momentum equation. This expression for the homogeneous density can be found from the conservation of mass from 0 to 1. Conservation of mass from state 0 to 1 for the system yields: A [7] L 0V0 TP A0V1 177
Page 1 and 2: BUBBLE PUMP MODELING FOR SOLAR HOT
Page 3 and 4: P Q Pressure (bars) Volumetric flow
Page 5 and 6: Figure 1: US Energy Consumption by
Page 7 and 8: Figure 3 : Thermosyphon Solar Hot W
Page 9: METHODOLOGY Two-phase flow is the m
Page 13 and 14: A L 1 [15] A 2 Now the momentum eq
Page 15 and 16: [24a] [24b] Bubbly flow then occurs
Page 17 and 18: m L [kg/s] m L [kg/s] 0.12 Mass Flo
Page 19 and 20: fluctuates throughout the day, the
Page 21: White, S.J., 2001. Bubble Pump Desi

bubble pump modeling for solar hot water heater system design

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