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Design of a Finned Radiator Assembly

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MAE 441 | Design of a Finned Radiator Assembly | Heat Exchanger Design Project | Thien Van TranChris LongfieldEric PacewiczOlivia Ching | | 4/3/2012 |

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Scope of the Project

The objective of the project was to design an effective radiator assembly to accommodate the Diesel-Engine Generator Set 1500-XC6DT2 by incorporating the use of tubes with inner fins in various geometries in order to meet the heat rejection requirements specified. This was done with consideration for minimizing cost, size, and complexity.

Initial Parameters

The initial parameters were the operating requirements of the Diesel-Engine Generator Set 1500-XC6DT2 are as follows: * Coolant capacity – The coolant chosen for our radiator is ethylene glycol (50/50 % by volume) * Its maximum operating temperature of 225F * Air flow rate – Since the generator is stationary as opposed to that used in an automobile application, a fan will be needed to provide the necessary flow rate. The required air flow rate specified by the engine is 9.383 m3/s in order to dissipate the heat generated * Coolant flow rate – The coolant flow rate is 17.914 kg/s through the radiator * The initial coolant temperature is assumed to be 212F, which is slightly below the operating temperature of the engine. The initial coolant temperature is taken as the ethylene glycol entering the radiator immediately after leaving the engine. * Pressure drop allowance – The * The total heat rejected to the coolant is 666kW * The outlet temperature of the coolant leaving the radiator was calculated to be 192F

Assumptions

In order to design a radiator for a specific operating condition, we assume the ambient temperature is 90F, which was the highest average temperature in Miami, Florida last year. This is accounting for the worst case scenario. We also assume that the ambient air density is constant throughout operation. We also assumed that there was no significant fouling on the inside of the tubes, so the heat transfer coefficient of the materials remains constant.

Design Methodology

Identification of Problem The heat rejection requirements were specified by the diesel-engine generator’s operating conditions. Our objective was to reduce construct a radiator that would provide better performance while functioning at a higher efficiency by reducing size and cost.

Selection of an Appropriate Heat Exchanger Classification The conventional and most effective form for a radiator in this application is the plate-fin and tube heat exchanger operating in cross-flow conditions. Rather than attempting to create a more innovative heat exchanger assembly while sacrificing simplicity, the present work aimed to improve and maximize the performance of the current heat exchanger type.

Material Selection The materials of each specific component were chosen based primarily on thermal conductivity as compared to price. The cost analysis of each material can be observed in Table 1 shown below.

Table1. Cost analysis of the selected materials Component | Description | Unit Size | Weight (lbs) | Price per Unit Size | Rel. Weight | Rel. Cost | Fins | ASTM B370 110 Copper Sheet, 0.08" thickness | 36" x 96" | 90.0239604 | $960.11 | 75.35208664 | $803.63 | Tubes | Seamless Brass 270 Tubing, 0.03" thickness | 96" x 0.5" OD | 15.7152 | $16.04 | 3771.648 | $3,849.60 | Cover Plates | ASTM B36 260 Brass Sheet, 1/16" thickness | 36" x 96" | 66.5280198 | $709.52 | 60.29101795 | $643.00 | | | | | | | | | | | | | 3907.291105 | $5,296.24 |

Table 2. The estimated manufacturing cost Manufacturing | | Hours | $/hr | Cost | | | | Design Time | 8 | 30 | $240.00 | | | | Machining Time | 2 | 12 | $24.00 | | | | Assembly Time | 10 | 15 | $150.00 | | | | Miscellaneous | 10 | 10 | $100.00 | | | | | | | $514.00 | | | | | | | | | | | | | | | | $5,810.24 |

The working fluid selected for the radiator was ethylene glycol (50% by mass), due to its prominent use in convective heat transfer applications, particularly in automobiles.

Selection of Provisional Dimensional Parameters
In order to design an ideal heat exchanger with minimal cost and size, preliminary measurements were chosen and initial calculations were run to provide a scope of the required parameters. The radiator core’s dimensions were determined by comparing the conventional radiator specified by the Diesel-Engine Generator. Its size was slightly reduced, since an increase in heat transfer in the tubes was anticipated in our design. The initial dimensions considered are listed in Table 3 below.

Table 3. The initial dimensions chosen to gauge heat rejection rates Width (m) | 2.2098 | Height (m) | 2.4384 | Depth (m) | 0.12065 | Number of Fins | 1140 | XL (m) | 0.0254 | Xt (m) | 0.0254 | t (m) | 0.0001 | OD (m) | 0.0127 | The use of previously derived correlations for the inner-finned tubes was the primary means of determining heat rejection requirements. The pitch for the ribs was calculated using,

p=πdinstanβ (1)

where represents the angle of each rib’s alignment with respect to the axial direction of the tube. The Reynolds number was derived by,

Re=mdiμ (2)

where the mass flow rate is that of the ethylene glycol. The friction factor for flow inside the tubes can be determined using the following equation.

f=1.58lnRe-3.28-2μbulkμwall-0.25 (3)

This correlation is valid for turbulent flows within tubes, and relates the pressure loss due to friction in the tubes to wall shear stress.

∆p=2fm2Lρdi (4)

This pressure drop can be determined using the preceding equation. This pressure drop in turn governs the pumping power required for the coolant mass flow rate. The Nusselt number required to find the heat transfer coefficient needed to determine heat transferred from the engine to the coolant to the air is given by the following correlation for turbulent flow.

Nu=αptdik=f2Re-1000Pr1+12.7f212(Pr2/3-1)μbulkμwall0.14 (5)

The local heat transfer coefficient for finned tube as compared to the coefficient for plane tubes is illustrated by the following equation.

αftαpt=1+2.64Re0.036edi0.212pdi-0.21β900.29Pr-0.02471/7 (6)

The friction factor for the finned tubes can be determined using the original friction factor through the following correlation.

fftf=1+29.1Re(0.67-0.06pdi-0.49β90)edi(1.37-0.157pdi)pdi(-0.00000166Re-0.33β90)β90(4.59+0.00000411Re-0.15pdi)1+2.94ncornerssinβrib15/1616/15 (7)

Design Optimization

For the preliminary design of our radiator, some optimization was performed for the heat transfer in the coolant tubes, fins, inner ribs, as well as other surface areas. Local heat transfer coefficient was calculated and compared for various cases of inside tube diameters, rib angles, and rib heights, as well as the number of ribs. These results can be observed in figures 4 and 5.

Figure 4. Local heat transfer as a function of rib number

Figure 5. Local heat transfer coefficient as a function of rib angle

The pressure drops were also calculated for different tube diameters as well as rib angles. These can be viewed in figures 6 and 7.

Figure 6. Pressure drop vs. number of ribs for various pipe diameters

Figure 7. Pressure drop vs. number of ribs for various rib angles

Preliminary Results

Using the prescribed parameters above with a coolant mass flow rate of 17.915 kg/s and an air flow rate of 29 kg/s, we found the tube side convection coefficient of 1252.1 W/m2K. We found the air side convection coefficient to be 122.265 W/m2K with an overall fin efficiency of 0.5066. Using these values and assuming that additives in the ethylene glycol coolant render the fouling resistance negligible, an overall heat transfer coefficient times area was found to be 14256.87 W/m2K. The required UA value was 13,816 W/m2K. These initial parameters allowed our radiator to reject a total of 764,025.8 W. This much higher than the required 666 kW heat rejection specified by the diesel-engine generator.

References 1. "Brass Tube Brass", OnlineMetals.com, 2012, http://www.onlinemetals.com/merchant.cfm?pid=1548&step=4&showunits=inches&id=84&top_cat=79 2. "Brass Sheet", "Copper Sheet", Discount Steel, 2012, http://www.discountsteel.com/ 3. Liu, Hongtan. Heat Exchangers: Selection, Rating, and Thermal Design. 2nd ed. Boca Raton: CRC, 2000. Print. 4. Enhanced Single-Phase Turbulent Tube-side Flows and Heat Transfer. Engineering Data Book III. Wolverine Tube Inc. Web. 4 Apr. 2012.

Appendix

Figure A1. A close-up view of the finned tube array

Figure A2. A top view of a single fin plate, with holes for the tubes

Figure 3A. A cross-sectional view of the inner-ribbed tubes

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