Convective heat flux determination using surface temperature history measurements and an inverse calculation method

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Virginia Tech


Effective gages to measure skin friction and heat transfer have been established over decades. One of the most important criteria in designing such a gage is the physical size of the gage to minimise the interference of the flow, as well as the mass of these devices. The combined measurement of skin friction and heat flux using one single gage on the other hand, present unique opportunities and with it, unique technical problems.

The objective of this study is therefore to develop a cost-effective single gage that can be used to measure both skin friction and heat flux. The method proposed in this study is to install a coaxial thermocouple into an existing skin friction gage to measure the unsteady temperature on the surface of the gage. By using the temperature history and a computer program the heat flux through the surface can be obtained through an iterative guessing method. To ensure that the heat flux through the gage is similar to the heat flux through the rest of the surface, the gage is manufactured of a material very similar to the rest of the surface.

Walker developed a computer program capable of predicting the heat flux through a surface from the measured surface temperature history. The program is based on an inverse approach to calculate the heat flux through the surface. The biggest advantages of this method are its stability and the small amount of noise induced into the system. The drawback of the method is that it is limited to semi-infinite objects. For surfaces with a finite thickness, a second thermocouple was installed into the system some distance below the first thermocouple. By modifying the computer program these two unsteady temperatures can be used to predict the heat flux through a surface of finite thickness.

As part of this study, the effect of noise induced by the Cook-Felderman technique, found in the literature were investigated in detail and it was concluded that the method proposed in this study is superior to this Cook-Felderman method. Heat flux measurements compared well with measurements recorded with heat flux gages. In all cases evaluated the difference was less than 20%. It can therefore be concluded that heat flux gages on their own can measure surface heat flux very accurately. These gages are however too large to install in a skin-friction gage. The method introduced in this study is noisier than the heat flux gages on their own, but the size which is very important, is magnitudes smaller when using a coaxial thermocouple, to measure the surface temperature history.



transient, surface temperature, finite thickness, inverse, Heat flux