Heat Transfer Analysis for Thruster

Abstract

This analysis is designed to evaluate the proposed thruster design that was created by MSD Team P08454 in respect to its thermal dynamics. From this analysis, an understanding of the heat flow through the design and how much power can be put into the thruster while still keeping the designs components under maximum working parameters. Four test cases will be looked at, each in four different outside flow environments. The test cases will include, the bare thruster with no additional thermal dissipation, adding a heat sink to the motor to increase conduction to the housing, changing the inner fluid of the thruster to increase convection (air to oil), and combining the heat sink and change of fluid. The outer flow conditions will change as well as the ROV will not always operate in standard conditions. The extreme temperatures ranging from surface conditions (75oF) to bottom conditions (38oF) are important, along with the flow of the water over the housing body, which will range from 0.5 to 3.0 knots.

Assumptions

For all Cases:

·  The temperature of all components (TM, TMC, THB) is not to exceed 90oC (194oF)

·  Neglect effects of radiation; the heat transfer then depends on the modes that are being looked at in the analysis (conduction and convection)

·  Heat Generation throughout each component is homogeneous and steady state

·  Look at steady state conditions so that the convective coefficients for both fluids (inner and outer) can be considered to be roughly constant

·  The partition of the housing that separates the motor from the electrical components is adiabatic (based on the fact that the gradient between the two compartments is minimal when compared to the temperature gradient of the compartments versus the outside)

·  Look at the extreme outside temperatures: 38oF (3.3oC) < To < 75oF (23.9oC)

·  Aluminum housing [k ~ 136 Btu/hr-ft-F (240 W/m-K)]

·  Motor is made mostly of steel [k ~ 26.58 Btu/hr-ft-F (46 W/m-K)]

·  Inner fluid of thruster has little to no movement so looking at the worst case convection [Air: h ~ 1.057 Btu/hr-ft2-F (6 W/m2-K), Soybean Oil: h ~ 34.74 Btu/hr-ft2-F (197.25 W/m2-K)]

·  Assume Lumped thermal capacitance for the housing as:

o  The characteristic length needed to calculate the Biot number:

o  At the inner surface:

o  At the outer surface when flow conditions are optimum for heat transfer:

·  Outside fluid is homogenous water that is not fully developed, but the boundary layer is small enough to neglect for thermal analysis and moving at constant speeds of 3 knots [5.06 ft/s] and 0.5 knots [0.844 ft/s], as these speeds correspond to a horizontal thruster at full power (3 knots) and the vertical thruster at full power (0.5 knots). If the flow is looked at as flowing over a flat plate with a width of infinitely small size, , then the following Reynolds numbers are found:

o  At 38oF and 3 knots:

o  At 38oF and 0.5 knots:

o  At 75oF and 3 knots:

o  At 75oF and 0.5 knots:

·  The temperature of the outer surface of the housing can be modeled as an isothermal flat plate as the aluminum is highly conductive and will spread heat through itself easily and the assumption of Lumped Thermal Capacitance has already been shown. Using this assumption, an equation to find the Nusselt number for this scenario exists, which will lead to finding the convective coefficients:

o  ,

o  Prandtl number at 38oF = 10.916

o  Prandtl number at 75oF = 5.9429

o  ßValues tabulated in Data Worksheet

Test Cases:

Case 1: No Heat Sink and No Dissipative Fluid

Solution:

Find equivalent resistance for the entire circuit:

Case 2: Heat Sink on the Motor and No Dissipative Fluid

Solution:

Find equivalent resistance for the entire circuit:

Case 3: No Heat Sink and a Dissipative Fluid

Same Figures as Case 1 and same solution only using instead of for the motor circuit

Case 4: Heat Sink on the Motor and a Dissipative Fluid

Same Figures as Case 2 and same solution only using instead of for the motor circuit

Results/Conclusions:

The heat dissipation of this design is very pivotal and can influence whether the final design is successful. In this early look, the design as is appears to be acceptable in allowing adequate heat loss to the surroundings to keep all components under their maximum operating temperatures. Table 1 gives a brief look at the results for all test cases at the four outside flow conditions:

Maximum Heat Transfer
To = 38F, 5.06 ft/s / To = 38F, 0.844 ft/s / To = 75F, 5.06 ft/s / To = 75F, 0.844 ft/s
[Btu/hr] / [Btu/hr] / [Btu/hr] / [Btu/hr]
Test Case 1 / 2555.419456 / 2014.891366 / 1970.900084 / 1566.8808
Test Case 2 / 2836.744439 / 2160.773271 / 2192.084696 / 1684.280308
Test Case 3 / 2794.251693 / 2139.458663 / 2158.615643 / 1667.087282
Test Case 4 / 1019.796889 / 978.3337086 / 666.135427 / 636.0220741

In the first two outside flow conditions, the heat flows are at their highest because of the larger temperature gradient. The higher speed shows the highest heat flow because this flow condition allows for a higher heat transfer coefficient of the fluid.

The heat transfer for all cases seems to be more than adequate for the heat load that will be introduced into the housing of the thruster, a mere 58.01 Btu/hr. Curiously, the heat transfer for when both a heat sink and dissipative fluid are used is very low. This could be a result of extra resistance to heat flow added by adding the heat sink in the way of the more efficient convection of the oil. But it seems that best, safest and cheapest solution to adding more heat transfer from the housing is to added a simple disc of aluminum to the end of the motor as a heat sink to help conduct heat to the housing surface.

Sources:

Note: Any table or page reference in this document refers to the book:

·  Fundamentals of Heat and Mass Transfer, Sixth Edition . Incropera, Frank P., DeWitt, David P., Bergman, Theodore L., Lavine, Adrienne S. . 2007 . Jon Wiley and Sons Inc.

·  “Fluid Properties Calculator” . 1997 . Microelectronics Heat Transfer Laboratory . http://www.mhtl.uwaterloo.ca/old/onlinetools/airprop.html

·  “Basic Mechanical and Thermal Properties of Silicon” . Virginia Semiconductor Inc. . http://www.virginiasemi.com/pdf/Basic%20Mechanical%20and%20Thermal%20Properties%20of%20Silicon.doc