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