Throttling Thermodynamics Professor Lee Carkner Lecture 22

PAL #21 Refrigeration  Refrigerator cycle where P = 120 kPa and x = 0.3 before the evaporator and 60 C after the compressor  Start at point 4, P 4 = 120 kPa, x = 0.3, look up h 4 =  h 3 = h 4 = 86.83, for a saturated liquid this means P 3 =  Since P 2 = P 3 and T 2 = 60, look up h for superheated vapor, h 2 =  At point 1, P 1 = P 4 = 120 kPa, saturated vapor, h 4 =

PAL #21 Refrigeration  Mass flow rate if W’ in = 0.45 kW  W’ in = m’(h 2 -h 1 )  m’ = (0.45)/( ) =  Find COP from W’ in and Q’ L  Q’ L = m’(h 1 -h 4 ) = ( )( ) = kW  COP = Q’ L /W’ in = (1.091)/(0.45) =

Cascade Systems   For larger commercial systems, efficiency becomes more important   e.g., deep freeze   Called cascade cycles

Two-Stage Cascade

Cascade Efficiency  The condenser of cycle B (points 1-4) is connected to the evaporator of cycle A (points 5-8)   m’ A (h 5 -h 8 ) = m’ B (h 2 -h 3 )   COP Cascde = m’ B (h 1 -h 4 )/[m’ A (h 6 -h 5 )+m’ B (h 2 -h 1 )]

Multistage Compression   Some fluid is vaporized and is sent back to the high pressure compressor   Can also use just one compressor and multiple throttle valves and evaporators for multiple temperatures

Gas Refrigeration   We can also us a reverse Brayton cycle   Isentropic compression   Isentropic expansion in turbine 

Reversed Brayton Cycle

Gas Refrigeration Efficiency   w net,in = w comp – w turb = (h 2 -h 1 )-(h 3 -h 4 )  COP = q L /w net,in = (h 1 -h 4 ) / [(h 2 -h 1 )-(h 3 -h 4 )] 

Heat Pumps  COP HP = Q H /W net,in = Q H / (Q H – Q L ) COP HP,Carnot = 1 / (1 – T L /T H )  Often designed as dual heat pump/air conditioners   Low COP if the outside temperature is very cold   Can also push the heat extraction underground

Reversible Heat Pump

Joule-Thompson Expansion   Can be achieved by a pump circulating fluid through a pipe with an expansion valve in the middle   We know that in this case, h i = h f  What will be the final properties of the fluid?

Isenthalpic Curve   If the apparatus is changed a little, a new P f and T f are produced   The curve represents possible beginning and ending points for a throttling process   A series of isenthalpic curves can be produced for a substance

Inversion Curve  Each curve has two regions  T f >T i  T f < T i   In between, the slope, or Joule-Thompson coefficient (  ), is zero:   For a series of isenthalpic curves, a curve connecting  =0 points is the inversion curve

Liquefying Gasses  In order to cool a gas, its temperature must start below the maximum inversion temperature   T M.I. is near room temperature for many gasses   Some gasses have to be pre-cooled 

Heat Exchanger  How is gas liquefied?   Throttled and cooled   Cold gas runs back through the heat exchanger cooling the incoming gas   Cycle starts over 

Next Time  Read:  Homework: Ch 11, P: 35, 56, Ch 12, P: 8, 27