Superheated steam, at a mass flow rate of 15.0 kg/s, enters an insulated mixing chamber at 500 kPa and 200oC. In the chamber, the steam is mixed with liquid water at 500 kPa and 40oC. Determine the mass flow rate of the entering liquid water required for the combined flow to exit as a saturated liquid at 500 kPa.

Question

State 1: Steam inlet; State 2: Water inlet; State 3: Outlet
Given: T1 = 200oC; P1 = P2 = P3 = 500 kPa; m?1 = 15.0 kg/s; T2 = 40oC; x3 = 0.0 Assume: Q? = 0 (insulated). Also, given no other information regarding the mixing chamber, make the following common assumptions: W? = ?KE = ?PE = 0
Also, assume the mixing chamber is a multiple-inlet, single-outlet, steady-state, steady-flow device.

What will be an ideal response?

Answer 1

The First Law for Open Systems reduces to m?1h1 + m?2h2 = m?3h3

The conservation of mass yields: m?1 + m?2 = m?3
For water:
h1 = 2855.4 kJ/kg
h2 = 167.57 kJ/kg (Consider this a slightly compressed liquid, and just use hf @ T2)

Then, the heat out of the steam is into the coolant (so the sign changes as the system changes): Q?cool = ?Q?s = 2213 kW
For each coolant, to minimize the mass flow rate, we need to maximize the change in enthalpy. This is done with using the maximum quality for the R-134a, and the maximum temperature for the air.
R-134a: T3 = T4 = 0oC ; x3 = 0.0; x4 = 0.60 (assumes a constant pressure process) Then, h3 = 50.02 kJ/kg; h4 = 168.35 kJ/kg
For the heat input to the R-134a, the First Law yields: m?R134a =Q?cool/(h4?h3) = 18.7 kg/s
Air: T3 = 15oC, P3 = 100 kPa; T4 = 75oC
Consider the air to be an ideal gas with constant specific heats: cp = 1.005 kJ/kg-K
For the heat input to the air, the First Law yields: m?air =Q?cool/(h4?h3) = 36.7 kg/s

While the flow rates may not seem much different at first, the fact that the air is a gas while the volume of the R-134a is primarily a liquid means that the R-134a system is more practical from a size-standpoint. One would need approximately 30 m3/s of air to go through the system, but only approximately 0.015 m3/s of R-134a to enter the system.