Cycle Thermodynamic Model | Contents | Cycle Thermodynamic Performance

Bubble Pump Performance

BUBBLE PUMP PERFORMANCE

The previous chapter provides sufficient information to create a model of the bubble pump. This model is first used to determine the performance for bubble pumps with varying physical parameters. Also, the model is compared to the bubble pump built and tested in the conceptual demonstration prototype, and it was shown to provide a reasonable estimate of the heat input necessary to provide a given liquid flow rate.

Analytical Results

Using the analytical model, the performance of the bubble pump is evaluated for different heat inputs, tube diameters, and submergence ratios. Figure 4-1 shows the performance of a bubble pump which has a pump tube 8.6 mm in diameter submerged in ammonia water.

The submergence ratio of the bubble pump is a measure of how far the pump is submerged relative to its length. With increasing submergence ratio, the relative height to which the pump must lift the liquid decreases, so the liquid flow rate increases. For a fixed submergence ratio, the liquid mass flow rate increases with increasing heat input, reaches a

Figure 4-1: Bubble Pump Performance (for a tube diameter = 0.0086 m,
and submergence ratios, h/l = 0.1, 0.2, 0.3. System Pressure = 4 bars)

maximum, and then decreases with further heat input increase. This maximum flow occurs when the increase in the frictional pressure drop caused by increased vapor flow rate exceeds the increased buoyancy effect of the vapor to pump the liquid (Stenning and Martin, 1968).

Figure 4-2: Bubble Pump Performance (for a tube diameter = 0.0086 m,
and submergence ratios, h/l = 0.1, 0.2, 0.3. System Pressure = 4 bars)

Figure 4-2 shows the mass flow rate of liquid versus the mass flow rate of vapor for the same pump. The mass flow rate of vapor which the heat input produces to pump the liquid is needed for the conservation of mass and energy in both the generator and condenser. The vapor mass flow rate is generally much less than the liquid mass flow rate.

Figure 4-3: Bubble Pump Performance for Varying Tube Diameter and a fixed h/L = 0.2

The performance of the bubble pump also depends on the diameter of the tube, as shown in Figure 4-3. As diameter increases, the friction factor decreases thereby increasing the efficiency of the pump. However, the largest possible diameter bubble pump for ammonia-water in which slug flow will occur is predicted by equation 3-22 to be 50 mm.

As discussed in the previous chapter, there are four flow regimes for two phase vertical flow in a pipe. The bubble pump model presented here assumes all flow to take place in the slug flow regime. Somewhere to the left of the maximum, transition to bubbly flow will occur while somewhere to the right of the maximum, transition to churn flow and then annular flow occurs. At first, it may seem that a larger diameter pump tube would always be advantageous. However, increasing the diameter with a fixed liquid flow will eventually cause transition from the assumed slug flow to bubbly flow. Therefore, a bubble pump will always be assumed to operate at its maximum liquid flow rate for a fixed h/L of 0.2. If the liquid flow rate needs to increase or decrease, then the diameter and vapor flow rate of the pump will be chosen such that this liquid flow rate is the maximum.

The vapor flow rate which produces the greatest liquid mass flow rate for any given diameter tube can be linearly related to the liquid mass flow rate as seen by the straight line drawn through all the maximums in Figure 4-3. The thermodynamic model of the cycle requires the bubble pump's heat input and mass flow rates. The following linear equation is useful in this study.

(4-1)

The liquid mass flow rate in equation 4-1, , is the mass flow of vapor in kg/min leaving the bubble pump, and , is the mass flow of liquid in kg/min leaving the bubble pump. Equation 3-40 is then utilized to calculate the heat input required to provide these mass flows.

Experimental Setup

The first component of the conceptual demonstration prototype constructed was the bubble pump. The prototype's bubble pump is a stainless steel tube with a 7.62 mm inner diameter, and a length of 0.736 meters. Before completion of the conceptual demonstration prototype, its bubble pump was tested with water at a submergence ratio, h/L, of 0.2. An electric heater clamped to the base of the tube provided heat input while a dimmer switch and a power meter provided control and monitoring of this input. A large reservoir of boiling water was used to keep the liquid saturated and the submergence ratio constant during pumping. A stopwatch and a graduated cylinder were used to measure the mass flow rates of the liquid pumped.

Results

Liquid flow rates were measured for heat inputs between 0 and 200 watts and are shown in Figure 4-4. The performance for this pump predicted by the model is also shown in Figure 4-4. The value of K, using equation 3-45 for the friction factor, is 10.3. By adjusting K to a value of 17, the model more closely matches the data points.

Figure 4-4 shows that the analytical model for the bubble pump developed in Chapter III provides sufficiently accurate predictions without the need for experimental measurements. With experimental measurements K can be adjusted to account for additional losses and create an accurate model of an actual bubble pump.

Figure 4-4: Actual and Analytical Bubble Pump Performance


Cycle Thermodynamic Model | Contents | Cycle Thermodynamic Performance