FEASIBILITY OF COMPONENTS CLARA ECHAVARRIA & JONATHON LOCKE.

FEASIBILITY OF COMPONENTS

CLARA ECHAVARRIA & JONATHON LOCKE

Efficiency Estimation Functional Diagram: Part 1Cooling Load Required

Inputs/Givens1. Volume of Ice

(3.5 gal)2. Density of Ice

(736 kg/m3)3. Latent Heat of Ice, hsf

(333.6 KJ/kg)4. Melt time of 1 hour

(3600 s)

Constraints and Assumptions1. Steady State2. Ice can be melted in 1 hour

Output1. Cooling Load

(900 W)

Governing Equations

Efficiency Estimation Functional Diagram: Part 2Fan/Pump sizing

Inputs/Givens1. Heat Flux (900W)2. Fluid properties of air

and water

Constraints and Assumptions1. Ideal gas2. Incompressible flow3. Constant Pressure (Cp)4. Uniform Flow5. Steady State6. Ambient air Temp of 22⁰C

and output temp of 13⁰C 7. Water temp of 0⁰C from

ice box8. Ice can be melted in 1

hour

Output1. Air Flow Rate

(255 CFM)2. Coolant Flow Rate

(1 GPM -> at least 0.5)

Governing Equations

Input data1. Cooling Load (900 watts)2. Coolant Flow rate (1

GPM -> at least 0.5 GPM)3. Fan power (40W)

Constants Density of Water

(1000 kg/m3)

Constraints and Assumptions

1. No pumping losses2. 65% pump

efficiency (low)3. Fan at 100% power4. Steady State5. 2x calculated pump

power to accommodate losses

6. z (H) of water in pumping loop equal to 1m (would be less in actual unit)

OutputCOP = 10

Governing Equations

Efficiency Estimation Functional Diagram: Part 3COP calculation

Preliminary testing

Initial Water Volume (mL) Vo 1600 Initial Water Volume (mL) Vo 3785 Initial Water Volume (mL) Vo 1600 Initial Water Volume (mL) Vo 9463.5Initial Water Temperature (⁰C) To 20.5 Initial Water Temperature (⁰C) To 7.22 Initial Water Temperature (⁰C) To 20.6 Initial Water Temperature (⁰C) To 21.1Initial Ice Volume (mL) Vice 5000 Initial Ice Volume (mL) Vice n/a Initial Ice Volume (mL) Vice 5000 Initial Ice Volume (mL) Vice 18927

Flow Rate In (mL/s) 43.47826 Time elapsed (s) t 70Time of Water to Drain (s) to 37.7 Time of Water to Drain (s) to 435 Time of Water to Drain (s) to 21.7 Final Temperature (⁰C) Tf 0Volume Drained (mL) Vd 1000 Volume Drained Vd 2900 Volume Drained (mL) Vd 1000Final Temperature (⁰C) Tf 0 Final Temperature (⁰C) Tf 0 Final Temperature (⁰C) Tf 0

End Ice Volume (mL) 4000

mL/s 26.5 mL/s 6.7 mL/s 46.1m^3/s 0.0000265 m^3/s 0.000007 m^3/s 0.000046gpm 0.4204 gpm 0.1057 gpm 0.7303

Mass flow rate kg/s 0.0265 kg/s 0.0067 kg/s 0.0461Heat Flux Q [Watts] 2283.8 Q [Watts] 202.2 Q [Watts] 3967.7

Test 4Steady-State Test

PurposeDump water over bucket of ice. Measuring the mass flow rate through the two holes in the bottom of the bucket. Recording time it takes for one liter of water to come out and measure the output temperature.

Pre-cool water to about 43⁰F. Try spray pattern of pasta strainer. Maintain a flow rate of 1 gpm over ice.

Dump water over bucket of ice. Measuring the mass flow rate into the bucket and out of the bucket. Recording time it takes for one liter of water to come out and measure the output temperature. Same as test 1 with an input flow rate.

To find the time required for water to hit steady-state output of 0⁰C. Water at 21.1⁰C was chosen for dramatized results. At actual system water output of less than 12⁰C, the system will reach 0⁰C quickly enough to validate the radiator inlet assumption of 0⁰C.

Test 3

Purpose

Test 1 Test 2

Purpose

Spray pattern test

Purpose

Drain Test Flow Test

Heat Exchanger selection

• Size: 12”X12”• 99.9% pure copper• 3/8” seamless tubing, 3 core construction• High flow of 12 GPM, 175 psi and can handle up to 350F• Aluminum fins are 12 per inch, 22 gauge galvanized steel

frame• The design enables heating loads of 50,000-60,000 BTU per

square foot

12X12

CFM 600 800 1000

APD (w.c.) 0.35 LAT 0.58 LAT 0.85 LAT WPD (ft. w.)

GPM 5 BTU 44542 133 51846 124 57659 118 1.01

10 47978 138 56895 130 64294 124 3.64

12 48607 139 57836 131 65550 125 5.11

Constants and givens (from vendor)

1. CFM air, GPM water, rating (q)

2. Inlet temperatures (used to figure out the densities of the fluids and the specific heat capacities)

Constraints and Assumptions- Ideal gas- Incompressible flow- Constant Pressure (Cp)- Uniform Flow

OutputUA value at different flow rates of air and water

Governing Equations

Heat Exchanger Feasibility Calculations: Part 1

Data Analysis

• The value of UA depends on the flow conditions and fluid properties. • Assume an empirical relationship between UA and mass flow rates using

the results previously obtained for UA.• Assuming a polynomial equation of the form:

• Use Excel’s solver to find the coefficients A, B, C, D, E, F.

0 2 4 6 8 10 12 14320.0

340.0

360.0

380.0

400.0

420.0

440.0

460.0

480.0

Variation of UA with water and air flow

GPM (Water)

UA (W

/m*K

)

• Pump and fan selection is driven by the selected heat exchanger.

• The air and water flow rates used need to be in the ranges of the heat exchanger testing data in order to minimize deviation of the analytical calculations.

12”X12”

CFM 600 800 1000

APD (w.c.) 0.35 LAT 0.58 LAT 0.85 LAT WPD (ft. w.)

GPM 5 BTU 44542 133 51846 124 57659 118 1.01

10 47978 138 56895 130 64294 124 3.64

12 48607 139 57836 131 65550 125 5.11

Fan selection

• The heat exchanger model fits best between 600 CFM and 1000 CFM. • DC fans that can handle this flow at the required pressure drops are

easier to find than AC fans that can do the same. • AC fans are more expensive, but DC fans require a car battery or a

power converter.

Fan Selection: AC Axial Fan

Both the radiator pressure drop versus flow and the fan pressure capabilities versus flow were plotted together to show the optimum flow point. The point where the two curves intersect is at 645 CFM and 0.41” of water.

Based on the Flow Selection Analysis:Static Pressure of System : 0.41” waterAir Flow @ S.P. : 645 CFMVoltage: 115 VACPower: 160 W

400 600 800 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

ΔP

(w.c

.)

GPM COP Cooling load (W)

Run time (min)

Air outlet temperature (⁰F)

1.0 12.8 3270.3 75.8 49.9

2.0 15.6 3988.8 62.1 52.2

3.0 17.0 4345.2 57.0 50.5

4.0 17.8 4538.7 54.6 49.5

5.0 18.5 4715.1 52.6 48.6

6.0 18.9 4814.4 51.5 48.1

7.0 19.3 4931.3 50.3 47.5

8.0 19.6 4990.6 49.7 47.3

9.0 19.9 5073.8 48.8 46.8

10.0 20.0 5108.2 48.5 46.7

11.0 20.3 5166.9 48.0 46.4

12.0 20.3 5182.6 47.8 46.3

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.00.0

5.0

10.0

15.0

20.0

25.0

Variation of COP with water flow

GPM

COP

Pump Selection: system losses considered

1. Radiator pressure drop 2. 7 Sharp radius PVC elbows3. Straight piping length4. Entrance loss

5. Sudden contraction (after pump)

6. Tee loss

7. Gate valve loss

8. Δ Height of the system

Important Equations

Friction loss formulas

1. Equivalent length method

2. Loss coefficient method

Where H = head lossf = friction factorL = length/equivalent length v = velocityD = pipe diameterg = gravitational constant K = loss coefficient

System Properties and Results

As seen above, the system losses are minimal.

Flow 5gpm

0.000316m3/s

PVC 1in

0.0254m

Area 0.000507m2

Velocity 0.622647m/s

Relative roughness 0.000007me/d 0.000276 µ 0.00152kg/(m*s)Re 10404.8 Friction factor 0.03099

Radiator losses 0.3079mElbow losses 0.0227mPipe losses 0.0377mEntrance losses 0.0198mS.C. losses 0.0781mTee losses 0.001mGate valve losses 0.0004mΔ Height 0.6858mTotal losses 1.1534m 3.784ft

Pump Selected

Tiny Might Spa Pump

Properties:• 1/16 HP• 115 volt, 0.8 amps• 92 Watts• Capable of 0-20 GPM• Capable for 0-23.1 ft of Head

Dimensions:

This pump is easily capable of the required head at Q=5 GPM. A valve will be used to control the flow. This is the cheapest, smallest, and lowest power pump available that will meet system requirements. The flow capability of the pump provides flexibility for testing and data collection.

Pump Head vs. Flow Curve

Feet

of h

ead

Flow (GPM)

Constants and givens1. Flows from fan and pump

(645 CFM, 5 GPM)2. Inlet temperatures

Constraints and Assumptions- Ideal gas- Incompressible flow- Constant Pressure -Uniform Flow

OutputHeat exchanger

cooling load

Governing Equations

Heat Exchanger Feasibility Calculations: Part 2

Constants and givens1. Latent Heat of Ice, hsf

(333.6 KJ/kg)2. Volume of ice (16 gal)3. Density of Ice

(736 kg/m3)4. Cooling load of heat

exchanger(4715.1 W)

Constraints and AssumptionsSteady-State

OutputTime required to melt the ice in the tank = 52.6 min

Governing Equations

Run Time

Measured data1. T of water in and out

of radiator2. Win from “plug power

meter”3. Water flow rate4. Output air

temperature5. Air speed

Constants and givens1. Area (A) of air flow2. Fluid properties of air

(density, Cp)3. Ambient air

temperature

Constraints and Assumptions• Ideal gas• Incompressible flow• Constant Pressure (Cp)• Uniform Flow

OutputFinal/Overall COP of unit

Governing Equations

Final Efficiency Functional Diagram (Final Testing)

InsulationBox Insulation

Pipe InsulationR Value 5.78 h*ft2*oF/BtuFoam Ins. 1.0179 m2*K/WInt. Temp 0⁰CExternal Temp 30 ⁰CDelta T 30 ⁰CDelta T 30 KFront/Back 572 in2

Sides 360 in2

Top/Bottom 440 in2

Total Area 1372 in2

Total Area 9.5 ft2

Total Area 0.885 m2

Heat Loss Q 26.1 WHeat Loss Q 89.0 BTU/hr

System Heat Transfer

4361.7 W

% of System 0.60

This is an acceptable percentage. Note that the air and metal/plexiglass will add

additional resistance (although minimal)

Insulation Information

1.5" Insulfoam 1-1/2-in x 2-ft x 4-ft Expanded Polystyrene Insulated Sheathing8ft2 for $4.42

R Value 3.33 (h*ft2*oF/Btu)/inch Inches 0 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000 inFoam Ins. 0 0.073 0.147 0.220 0.293 0.367 0.440 0.513 0.586 m2*K/WInt. Temp 0 0 0 0 0 0 0 0 0CExternal Temp 30 30 30 30 30 30 30 30 30 CDelta T 30 30 30 30 30 30 30 30 30 KTotal Area 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 0.0122 ft2

Heat Loss Q - 4.98 2.49 1.66 1.24 1.00 0.83 0.71 0.62 WHeat Loss Q - 16.98 8.49 5.66 4.25 3.40 2.83 2.43 2.12 BTU/hrSystem Heat Transfer 4361.7 4361.7 4361.7 4361.7 4361.7 4361.7 4361.7 4361.7 4361.7 W

% of System - 0.11 0.06 0.04 0.03 0.02 0.02 0.02 0.01 %