Thermal Systems Design and Analysis EN 535.452 James Richards Jr 12 May 2015 Optimization of a Residential Geo-Thermal Heat Pump Introduction The objective of this project is to design a residential geothermal heat pump system and optimize that design in order to find the best design combination of the components and characteristics used for this system. Background A geo-thermal heat pump (GTHP) or sometimes known as a ground source heat pump is a thermal system which utilizes the nearly constant temperature of the ground as a heat reservoir. The GTHP utilizes a coil of polyethylene piping that is buried under ground called the ground source heat exchanger in order to transfer heat into and out of the ground. The ground serves has a heat reservoir where heat can be reclaimed into the system or rejected by the system depending on whether the system is in cooling or heating mode. During the heating season, heat from the ground is brought into the system through the ground source heat exchanger into the heat pump system and where it is used to heat up the air that is distributed into the house. During the cooling season, heat is removed from the house into the heat pump system and rejected to the ground through the ground source heat exchanger. Design Requirements The design of the geothermal heat pump must meet the following requirements. In heating mode the system will provide a minimum of 85 degree air leaving the condensing coil and in cooling mode the system will provide a minimum of 55 F degree air leaving the evaporating coil. The system shall provide a minimum of 1700 CFM to the main air supply duct. General Overview The GTHP in heating mode transfers heat from the ground into the ground HX (1). The brine solution in ground HX carries the heat to a water to refrigerant HX (2). The brine transfers the heat energy to the refrigerant. The refrigerant is heated and then compressed by the compressor (3). The hot liquid refrigerant flows through the condenser coil (4) where it transfers heat to the air supplied by the fan. 4 1 2 3 Current designs The current existing designs of residential geothermal heat pumps differ primarily in the configuration of the ground heat exchanger. A. B. C. D. Closed loop vs Open Loop Vertical vs Horizontal Straight vs Slinky Loop Underground vs Underwater Design Selected for Modeling a Workable Solution The design I selected to model is a horizontal closed loop system of straight rows of piping underground. I selected the fluid as 9% brine solution which prevents freezing up to 15 F. Design Parameters • • • • Temperature of ground is set 55F Length of HDPE piping is set at 300 ft Heating and Cooling loads are set at 48000 BTU/hr (4Tons) Assume system is in steady state Design Variables D (diameter of ground heat exchanger piping) mbrine (mass flow rate of brine for heat exchanger) mair(mass flow rate of air) Governing Equations 1. Heat Transfer from ground to ground pipe HX mb · cpb · ( Tbout – Tbin ) – Upipe · C 12 Tg=55F Upipe from pipe manufacturer (0.24 BTU/hr ft oF) Surface Area of piping (Circum/12*300ft) cp(brine): .8837 BTU/lbm-F · L · Tbout – Tg – ( Tbin – Tg ) ln Tbout – Tg Tbin – Tg = 0 2. Heat from Evaporator (water to refrigerant HX) Qevap – mb · cpb · ( Tbout – Tbin ) = 0 3. Heat from Condenser Coil Qcond – mair · cpair · ( Tain – Taout ) = 0 Tain=70F (Ambient house temperature) Taout= 85F(Design air temperature leaving condenser coil) Cpair=.24 BTU/lbm-F 4. Ground HX pump performance curve (from pump curve) dp – 0.003 · ( mb · 7.19 ) 2 + 0.3748 · mb · 7.19 – 41.746 = 5. Ground pipe system and water to refrigerant HX curve dp – fc · L D · vbrine 32.2 2 – 14 · vbrine 32.2 2 = 0 12 * pressure loss equation for pipe flow + pressure loss from water to refrigerant HX 0 6. Heat gained by evaporator equal heat rejected by condenser Qevap + Qcond = 0 Equipment selected Pump used for analysis: VR 20, 1/3 -1 HP motor Curve fit equation for VR-20 pump performance: y=.0004x2-.2986x+47.538 7. Operating point for supply fan and duct system 0.000007 · CFM 2 – 0.0201 · CFM + 13.959 – 4.0 x 10 –7 • Supply fan 1/3 HP, Forward Centrifugal , 1770 Max CFM • Duct system 160 ft of 12” round duct with 8 elbows • Condenser coil adds .7 in of pressure drop · CFM 2 – 0.0004 · CFM + 0.2692 + 0.7 = 0 Use EES to model thermal system using Newton-Raphson method Workable solution results The Tbout represents the temperature of the brine solution leaving the ground loop heat exchanger. I had to set Tbout max limit to 54F to keep EES from stopping. I also had to set max limit of Tbin to 53 to keep EES from stopping. I need to troubleshoot my equations to determine why temperature of brine in converging so close to the ground temp 55F. Optimization of Design For this design my objective was to optimize the design to find the design that provide the maximum amount of heat transfer for the lowest first unit cost. (Qcond/Unit first cost). Objective equation: Qcond/Unit first cost= mair*cpair*(Taout-Tain)/(Pipe Cost+HX cost+Compressor Cost+….) Design Variables: mair(mass flow rate of air, lbm/s), mbrine (mass flow rate of brine, lbm/s), D (diameter of piping) Direct Constraints: a. Taout= 85F b. Tg=55F Component characteristics: a. Qevap-mb*cpb*(Tbout-Tbin)=0 b. Qcond-mair*cpair*(Tain-Taout)=0 c. Qhx-(Upipe*(C/12)*L*(((Tbout-Tg)-(Tbin-Tg))/ln((Tbout-Tg)/(Tbin-Tg)))) d. deltap-.003*(mb*7.19)^2+.3748*(mb*7.19)-41.746=0 e. 4E-07*CFM^2 - 0.0004*CFM + 0.2692