1.2) Considering the substrate to be a semi-infinite solid maintained at an initial temperature T i and is
2.2 Mathematical Modelling for Transient Heat Transfer Measurement
6. Application of coaxial surface junction thermocouple (internal combustion engine, hypersonic facilities, gas turbine)
7. Simulation-based study, and
8. Lastly, the assessment is focused on the work undertaken in IIT Guwahati considering advancement of coaxial surface junction thermocouple.
Taler (1996) defined the unified mathematical techniques of transient methods for measuring the surface heat transfer rates. Mainly, three heat flux gauges were discussed: thin film, thick-wall gauges placed on semi-infinite substrates and thin-skin calorimeters. The idea was to present a simple and accurate method for determination of the time-varying heat transfer coefficient (or heat flux) given an accurate temperature history of the body at a selected point beneath the surface. By solving the inverse heat conduction problem for the gauge, the measured interior temperature measurements were converted into local instantaneous heat transfer coefficients. The result of the inaccuracies in the measurement of the interior temperature was eliminated by using cubic spline smoothing or digital filtering of the raw interior temperature data prior to using it in the inverse heat conduction analyses. In general, the technique led to the development of closed-form equations for instantaneous surface heat flux or heat transfer coefficient.
Gulhan (1999) explained the fundamentals of heat transfer measurement techniques in high enthalpy flows. In addition, different heat flux measurement techniques were discussed with special focus on the design aspects. Further, a mathematical model for heat flux rate evaluation and application limits of each sensor type, in order to provide a useful and practical script for the reader with respect to the choice of an adequate sensor type for different requirements.
Furthermore, sensor calibration and comparative measurements using different heat flux sensors in the arc heated facility was presented.
Battisti and Bertolazzi (2001) reported a data reduction procedure for heat transfer measurements in short duration facilities. Single and double layer thin film thin-film sensors were utilized for this purpose. A simple finite element discretization was implemented and its ability to accurately reconstruct signals of known testing functions (as Heaviside signal with superimposed fluctuations) was checked. The obtained results seem to confirm the performance of the code presenting a very accurate signal reconstruction at a very low sampling frequency. Once the assumption of semi-infinite slab becomes invalid (i.e. leading edge of blades), the numerical discretization such as finite element approach becomes non-negotiable. Lastly, it was suggested to develop a 2-D scheme in order to consider problems where lateral conduction effects cannot be neglected, and the evaluation of the influence of heat flux generated by Joule effect into the sensor becomes important.
Schrijer (2003) investigated the hypersonic flow over an axisymmetric compression corner, with its related boundary layer separation as a reattachment phenomenon. The investigated model was DART (Delft Aerospace Re-entry Test vehicle), a re-entry demonstrator vehicle, designed and developed at the Faculty of Aerospace engineering of TU Delft. The vehicle, a blunted cone-flare made of Makrolon, was designed to be fully reusable with the task to collect the aero- thermodynamic flight data and test new thermal protection system concepts. Transient heat transfer measurements were conducted in a short duration hypersonic facility at Mach 9, and Schlieren visualization was used as a complementary tool. An infrared camera, which operated in the line- scan model to obtain an adequate sampling rate was used to get the surface temperature variation in time. Four different data reduction methods were used to get the heat flux data from the surface temperature. The result obtained with the different methods were within a maximum tolerance of about 10%.
Vasiliki (2005) developed two measurement techniques based on the applications of the thin film sensors. The first method involves the determination of wall heat transfer with two-layer gauge and the other technique involved measurement of flow temperature using dual thin film probe. The techniques were utilized in short duration tunnels of the Von Karman Institute (VKI) under-engine representative conditions and were able to resolve both time-averaged component and time- resolved component i.e. the periodic blade passing events at ~5-7 kHz with harmonics up to 50 kHz. Furthermore, to find out the wall heat flux with the two-layer gauge, the unsteady conduction equations were solved in the two-layer substrate using the measured value of the wall temperature as a boundary condition.
Buttsworth et al. (2005) formulated a one-dimensional transient heat conduction model to evaluate the transient surface heat flux from the measurements of surface temperature using an eroding ribbon surface thermocouple. The junction of the thermocouple was formed with low thermal inertia just near the surface by the use of abrasive wear. The impulse response was captured with the help of laser excitation; it was noted that the response of particular sensors may vary if new junctions were created with abrasive wear. In addition, the response of the sensors seemed to deviate substantially from the one-dimensional model and varied from the sensor to sensor. The impulse response was further simulated with greater conformity using a two-dimensional finite
variations on the derived heat flux was assessed for the case of measurements in an internal combustion engine; when the measured impulse response was used to derive the surface heat flux, the apparent reversal of heat flux during the expansion stroke does not occur. It was observed that for the time scales less than 0.1 ms, different thermocouple junctions created on the same sensor can produce very different responses, also for time scales between 0.1 ms and 1 ms, different junctions can still influence the sensor response, but the response was typically more consistent for time scales less than 0.1 ms. In short, the use of either one-dimensional/two-dimensional models for the sensor response will lead to substantial errors in the inferred heat flux results.
Saravanan et al. (2009) utilized a platinum thin-film gauge to study experimentally the surface convective heating rate on a missile shaped body flying at hypersonic. In addition, the effects of fins on the surface heating rates of missile frustum were investigated. The experiments were performed in a hypersonic shock tunnel at Mach number of 5.75 and 8, having stagnation enthalpy of 2 MJ/kg with 0° angle of attack. Further, the measured stagnation-point heat-transfer data compared well with the theoretical value, estimated using Fay and Riddell expression.
Furthermore, the measured heat-transfer rate with fin configuration was slightly higher than that of the model without fin; the normalized values of experimentally measured heat transfer rate and Stanton number compared well with the numerically estimated results.
Hubble and Diller (2010) described the development and evaluation of a novel hybrid method for obtaining heat flux measurements. It was noted from the obtained result that by combining the spatial and temporal temperature measurements of a heat flux sensor, the time response, accuracy, and versatility of the sensor could be improved. Further, sensors utilizing the hybrid method were able to make heat flux measurements on both high and low conductivity materials. In addition, by changing, the thermal conductivity of the backing material by four orders of magnitude caused only an 11% change in sensor response i.e. the hybrid method can enhance the time response of heat flux sensors. Furthermore, the temporal response was seen can increase by a factor of 28 compared with a standard spatial sensor. The developed hybrid method was tested both numerically and experimentally on high and low conductivity materials and it demonstrated significant improvement compared with operating the sensor as a spatial or temporal sensor alone.