FSAE Cooling System Design and Development Purpose and Motivation The FSAE racer goes through many different stress and performance tests at less-thanideal conditions throughout the competition so it is crucial that its motor functions at the peak of its ability throughout the competition. As an ICE (internal combustion engine) the engine of the FSAE car rejects a large amount of heat as a result of the chemical explosions that continuously occur within it. If the engine is not cooled properly, it may overheat. The consequences of which could be mild or catastrophic to the life of the engine. Thus, the design and development of a proper cooling system is vital to the performance and life of the FSAE racer. This cooling system should not only keep the engine from overheating but also keep it at an optimum performance temperature determined through calculation. Design and Calculation Before design of the cooling system can begin, certain design requirements needed to be determined. These requirements included the average heat rejection of the engine, engine efficiency, tube size, coolant flow rate, radiator size and average vehicle speed. The amount of heat that was rejected by engine was calculated by assuming that engine’s power output was 1.5 and efficiency is about 20%. Now, based on the engine’s fuel consumption the power lost to heat was calculated by using the following equation (
) (
) ( )
(1)
where SG is the specific gravity of the fuel, CV is the caloric value of the fuel and V is the volume of the fuel. Solving this equation with the known values of V = 5.7 L, CV = 48 MJ/kg, and SG = 0.75 yields a power value of 97,714 Watts. However, since we assume that the engine is a typical ICE, its efficiency is assumed to be 0.2 therefore the actual power lost to heat is 19.5 kW. Now, in order to determine the cooling rate of the air around the radiator the mass flow rate of the air through the radiator and temperature difference of the air at the inlet and outlet of the radiator were determined. In order to determine the mass flow rate
the volume flow
rate through a projected 12”x12” radiator by using the following equation (2)
where FA is the flow area and u is the velocity of the air flow plus the velocity of the air. Solving this equation for known values yields a volume flow rate of 1320 be rewritten as 0.62
⁄ . To determine the mass flow rate,
. In SI units this value can
the volume flow rate was
multiplied by the density of air at 20°C, 1.2 , and the final value was 0.748 . This value was then multiplied by the constant-pressure specific heat and the temperature difference between the inlet and the outlet of the radiator in order to solve for the rate of heat transfer between the projected radiator and the surrounding air which can be defined by the following equation (3) where is the difference in temperature between the inlet and outlet tube of the radiator which had a value of 83 K and was 1.01 . These temperatures were measured at a point where the engine had an rpm that corresponded to a vehicle speed of 15 mph. Solving Eq. 3 for the given values yielded a cooling rate of 60 kW. Since this value is much greater than amount of heat rejected by the engine, a 12”x12” radiator should be sufficient to cool the engine during competition. Now, for cooling the engine while the car is stationary, the cooling fan must be able to move the air around the radiator at a sufficient rate. The first step in calculating this rate was manipulating Eq. 3 so that it could be used to solve for the necessary mass flow rate of air through the radiator to cool the engine. The new equation is (4)
where
in this case is the amount heat rejected by the engine or 19.5 kW. Dividing this mass
flow rate by the density of air yielded the required volume flow rate for the cooling fan: 723.6 . In order to determine the true size of the radiator that would be used, the effectivenessNTU method for heat exchangers was utilized. NTU is a dimensionless grouping called the number of transfer units and can be expressed as (5) where U is the overall heat transfer coefficient, is the heat transfer surface area of the heat exchanger, and is the smaller of Ch and Cc. Ch and Cc are the heat capacity rates of the hot
and cold fluids involved in a heat exchanger where, in this case, the hot fluid is the water leaving the engine and the cold fluid is the air traveling through the radiator. C is defined as (6) The ultimate goal of this method is to solve for the surface area of the heat exchanger. This will allow for the selection of the size of radiator. NTU can also be determined from graphs that relate NTU with the heat transfer effectiveness ε and with known values of Cmin and Cmax. The heat transfer effectiveness is defined as (7) where (8)
The mass flow rate for the water traveling through cooling system is 2.39 GPM and then converted to SI units for a value of 0.1449 . This mass flow rate for the water, the volume flow rate for the air and the tabulated specific heats for water and air are sufficient to solve Eq. 6 to obtain values for Cmax and Cmin. (9)
(10)
Therefore,
Using this result along with Eq. 8 yields
Eq. (3) was used with properties of air and a
of 27K and the result was (11)
Finally, the heat transfer effectiveness was calculated using Eq. 7 and the result was (12)
Now, using this value and the ratio (13) a value for NTU could be determined by looking up a value from the following graph
Figure 1: Heat transfer effectiveness as a function of NTU (C*= Cmin/Cmax) From the graph, (14) Using this value, an overall heat transfer coefficient of 60(
)
, and Eq.5 the heat transfer
surface area of the radiator could be solved for and the result of which was (15) Now, assuming 1” diameter tubes with 0.05” walls, the total length of the tubes within the radiator can be calculated so that the size of the radiator can be finalized.
( ) (16) So, the required total lengths of tubes is L = 200 in. If the base of the radiator is kept to 12” then in order to satisfy the total length the height must be 18”. And thus, the final size of the radiator is 12”x18”. References [1] A. Ghajar, Y.A. Cengel. Heat and Mass Transfer. 4th ed. New York: McGraw-Hill, 1961. [2] Yang, Zhen, Zhenxing Zhao, Yinhe Liu, Yongqiang Chang, and Zidong Cao. "Convective Heat Transfer Characteristics of High-pressure Gas in Heat Exchanger with Membrane Helical Coils and Membrane Serpentine Tubes." Experimental Thermal and Fluid Science 35.7 (2011): 1427434.
