Jack Hinze Advisors Professor Sanford Klein Professor Gregory Nellis Thermodynamic Optimization of Mixed Refrigerant for Joule Thomson Cycles Jack Hinze Advisors Professor Sanford Klein Professor Gregory Nellis

Outline Uses for Joule Thomson cycles How a Joule Thomson Cycle works Objective of research Overview of methodology Preliminary results Future work

Joule Thompson Cycle Uses Cryosurgical probes Cooling IR detectors for satellite and reconnaissance Any application that requires low temperatures and needs to be reliable and simple and cheap. First image from http://file.scirp.org/Html/10-1920150---13_33771.htm Second image from S.W. Stephens, Advanced design of Joule-Thomson coolers for infra-red detectors, Infrared Physics, Volume 8, Issue 1, March 1968, Pages 25-35, ISSN 0020-0891, http://dx.doi.org/10.1016/0020-0891(68)90047-X. (http://www.sciencedirect.com/science/article/pii/002008916890047X)

Joule Thomson Cycle Operation 2 1 1 5 Talk about the 5 states in cycle Maximum cooling load is the isothermal expansion of gas from high pressure to low pressure. 3 4 5 2 4 3

Advantage of Using a Mixed Refrigerant NEEDED???? K. Rule, “Empirical Modeling and System Optimization for a Precooled Joule-Thomson Cycle for Cryosurgery”, M.S. Thesis, Mech. Engr., UW-Madison, Madison, WI, 2014 Using a mixed refrigerant results in a larger isothermal enthalpy difference. Largest isothermal energy differences occur when the cycle passes through the vapor dome Mixed refrigerants can be selected to ensure that the cycle is expanded through the vapor dome Zeotropic – temp glide Azeotropic – no temperature glide

Optimization for thermodynamic cooling load only

Work done by Rodrigo Barraza has shown that heat transfer coefficients are a function of quality. Image supplied by Rodrigo Barraza Talk about past optimization lack of consideration of heat transfer in the recuperator. Results in needing a large recuperator or Poor cycle performance Enhance Heat Transfer Region

Optimizing for cooling load and enhanced heat transfer

Optimal Mixture Definition The optimal mixture is one that provides the largest possible cooling load at a given temperature while keeping the physical size of the recuperator as small as possible, by keeping the MR within the good heat transfer region of quality in the recuperator. Objective: Develop a way of visualizing design space so thermodynamic and heat transfer effects are evident Need a better title, neither of these is quantitative

Using a model, a parametric study is conducted to determine optimal mixture. Constant Variables Optimization variables Results of interest Mixture Components Mixture Composition Cooling Load / Displacement Rate Suction Pressure Discharge Pressure MR quality limits in Recuperator Load Temperature COP Supply Temperature Approach temperature This probably isn’t needed

The parameter space is defined to include every possible combination of composition and pressure Discharge Pressure: 1200-3500 [kPa] in 100 [kPa] intervals Choose Discharge Pressure Choose Mole Fraction Simulate results Repeat for all Mole Fractions Repeat for all Discharge Pressures

Quality and cooling load data are presented on the same contour plot. Methane, Ethane, Isobutane Parameter Value Supply temperature 240 [K] Load Temperature 150 [K] Approach temperature 0 [K] Suction Pressure 150 [kPa] Knowing which qualities define the recuperator, we know that any cycle that has these points operating within the optimal range will have all of its points operating in this desired range The x and y axises are the defining qualities of the cycle and in the parameter space contours of constant cooling power are plotted These contours are defined as the percentage of the maximum cooling power for that particular parametric study We can see that this seems to have some logical shape that follows closely to the saturation lines of the mixture It is clear that if we choose the thermodynamically optimized mixture that at least some of the recuperator will be outside of the desired 15-85% quality We then look to the point where we know that the entire recuperator is within the good heat transfer region however this point has the disadvantage of having only 45 percent of the cooling power of the maximum point So we then look to the other points along that line, it is likely that the actual maximum point will be somewhere along this line were most of the recuperator is in the 2 phase region

Quality limits always correspond to these point in recuperator Knowing which qualities define the recuperator, we know that any cycle that has these points operating within the optimal range will have all of its points operating in this desired range The x and y axises are the defining qualities of the cycle and in the parameter space contours of constant cooling power are plotted These contours are defined as the percentage of the maximum cooling power for that particular parametric study We can see that this seems to have some logical shape that follows closely to the saturation lines of the mixture It is clear that if we choose the thermodynamically optimized mixture that at least some of the recuperator will be outside of the desired 15-85% quality We then look to the point where we know that the entire recuperator is within the good heat transfer region however this point has the disadvantage of having only 45 percent of the cooling power of the maximum point So we then look to the other points along that line, it is likely that the actual maximum point will be somewhere along this line were most of the recuperator is in the 2 phase region

Qualities over 1 and less than 0 corresponds to distance away from the vapor dome hf hg h

The only mixtures we care about lie on the surface of the plot Methane, Ethane, Isobutane Parameter Value Supply temperature 240 [K] Load Temperature 150 [K] Approach temperature 0 [K] Suction Pressure 150 [kPa] Knowing which qualities define the recuperator, we know that any cycle that has these points operating within the optimal range will have all of its points operating in this desired range The x and y axises are the defining qualities of the cycle and in the parameter space contours of constant cooling power are plotted These contours are defined as the percentage of the maximum cooling power for that particular parametric study We can see that this seems to have some logical shape that follows closely to the saturation lines of the mixture It is clear that if we choose the thermodynamically optimized mixture that at least some of the recuperator will be outside of the desired 15-85% quality We then look to the point where we know that the entire recuperator is within the good heat transfer region however this point has the disadvantage of having only 45 percent of the cooling power of the maximum point So we then look to the other points along that line, it is likely that the actual maximum point will be somewhere along this line were most of the recuperator is in the 2 phase region

There must be a optimal mixture that balances good heat transfer and good thermodynamic cooling load

The design line can be used to estimate which mixtures will perform the best Methane, Ethane, Isobutane Parameter Value Supply temperature 240 [K] Load Temperature 150 [K] Approach temperature 0 [K] Suction Pressure 150 [kPa] This is an optimization problem that is best conducted experimentally. Too complicated to try to model all issues so instead experimental testing should be conducted along this line where thermodynamic cooling power is exchanged for heat transfer performance

Several other tests were to ensure the shape is normal to all J-T cycles Lower Suction pressure Non-precooled cycle Hydrocarbon Vs. Synthetic refrigerants Non-zero approach temperature difference For plots please see my thesis to be released August 2015 Not going to go into details Available in thesis

The mixture components have a drastic impact on how well this method works Nitrogen, Methane, Ethane Parameter Value Supply temperature 240 [K] Load Temperature 150 [K] Approach temperature 0 [K] Suction Pressure 150 [kPa]

The normal boiling point of the components selected has a dramatic impact on the results Refrigerant Normal Boiling Point (K) Nitrogen 77.3 Methane 111.67 Ethane 184.57 Propane 231.04 Isobutane 261.40 Butane 272.66 Pentane 309.21 Supply Temperature 240 K Load Temperature 150 K Need to pick components with boiling points above and below the supply and load temperatures

Conclusions The nature of a recuperative heat exchanger makes modeling and optimizing a MRJT cycle very difficult This simple model created should provide an accurate method of determining an initial mixture for experimental testing Choosing the proper components is very important to ensure proper operation of cycle

Future work Experimental verification of curve by testing mixtures along design line Further investigation of the relationship between the mixture component normal boiling points, cycle operating temperature, and cycle map

Questions? Contact Information Jack Hinze jfhinze@wisc.edu

Model created in EES Compressor model Heat exchanger model Tables created to prevent errors in REFPROP from affecting computation

The compressor model defined the mass flow rate in relation to the pressure ratio of the cycle Polytropic compressor model k = specific heat ratio

The cold head model breaks the recuperator into sub heat exchangers T, P ?, P 1 5 ?, P 2 T, P 4

What can this model/plotting technique tell us about the effect of Number of components in mixture Normal boiling point of components chosen

4 and 5 component mixtures Methane, Ethane, Propane, Isobutane 5 Component Methane, Ethane, Propane, Isobutane, Pentane

In this case, adding a fourth and fifth components does not effect the cooling power of the cycle Number of Components 3 4 5 Constraint Max 218.6 222.8 100-0 196.3 181.8 182.5 90-10 138.8 140.6 149.8 85-15 119.4 119.1 127.1

Suction Pressure

Room Temperature Cycle Methane, Propane, Pentane Parameter Value T1 300 [K] T4 170 [K] TAproach 0 [K] Psuction 150 [kPa]

Synthetic refrigerants Argon, R14, R218 Parameter Value T1 250[K] T4 150 [K] ΔTpp 0 [K] Psuction 150 [kPa]

Non-ideal recuperator The similar result for all of these cases show that the shape is normal to all JT cycles operating with an advantageous mixture.

P-h diagram for 85-15 percent quality constrained result. 2 1 3 4 5

P-h diagram for thermodynamic maximum point 2 1 3 4 5