Exergy Balance: Control Volumes
By Alva Murphy
They are different from closed systems as they also have exergy transfer due to mass flow. The rate of exergy change in a control volume is equal to the rate of exergy transfer through the control volume boundary by heat, work and mass flow minus the rate of exergy destruction.
***This exergy balance equation can be stated as the rate of exergy change if all the variables are in the rate form***
In a steady flow system, the exergy in is equal to the exergy out plus exergy destroyed. If the system is reversible the exergy destroyed is zero! This means that the work W is equal to the reversible work Wrev.
o So, for a single stream steady flow device…
Control volumes don't change mass, energy, entropy, volume or exergy during processes. Therefore, dVcv/dt = 0 and dXcv/dt = 0. This causes the rate form of the exergy balance equation to decrease to the following. This is also due to the knowledge that the rate exergy from heat is the rate of heat energy multiplied by the Carnot efficiency of the device:
In addition we know the rate exergy of mass and hence find:
Reversible work can be found from the equation above as exergy destroyed is zero. If you input that and rearrange you get the following equation.
o For an adiabatic single stream device…
Single stream devices have one inlet and one outlet which allows us to simplify the exergy balance equation. The mass flow rate is the same and there is only one flow exergy in and one flow exergy out.
Reversible work can be found from the equation above as exergy destroyed is zero. Also, adiabatic systems have no heat transfer so the exergy due to heat can be removed from the equation. If you input that and rearrange you get the following equation.
Second law efficiencies of steady flow devices that have control volumes can be found from the general efficiency definition:
o This is for kinetic and potential energies being negligible, and devices being adiabatic
o These efficiencies can be calculated from many different variables that may be known for the flow devices. Specifically the change in flow exergy can be used to show either the exergy recovered or the exergy expended depending on the device.
o For an adiabatic turbine the exergy recovered is equivalent to the work out of the system and the exergy expended is equivalent to the loss of flow exergy…
o For an adiabatic compressor work is put in to compress the fluid so this is the exergy loss in the compressor and the exergy recovered is the change in flow exergy…
o For an adiabatic heat exchanger of two unmixed fluid streams where the recovered exergy is the cold stream exergy increase and the exergy expended is the hot stream exergy decrease…
o For an adiabatic mixing chamber where hot stream 1 mixes with cold stream 2 to make a mixture 3 the exergy recovered where the exergy expended is the loss of exergy from the hot stream and the recovered exergy is the exergy increase of the cold stream…
