Heat Flux Calibration Measurement Using the Noninteger System Identification Method for Cooled Surfaces

Abstract

ACTIVE cooling mechanisms are used in many applications for thermal protection of surfaces in combustion chambers, rocket nozzles, gas turbine blades, and only recently structures of reentry vehicles [1–4]. The basic principle is to inject a cooling fluid close to the wall to reduce the wall heat load. In literature, the three different effects, i.e., film, transpiration, or effusion cooling, are named to occur in actively cooled structures. These cooling mechanisms, however, complicate the problem of the determination of a heat transfer coefficient to thewall and thus a calculation of the heatflux to the wall becomes challenging. Although transpiration cooling has been proven theoretically as an effective cooling mechanism by many investigators, its technological application became recently of particular interest with the invention of high-temperature porous material [2]. The progress inmaterial development allows a very new approach to high-temperature environments. From rocket engine combustion chambers and nozzles to turbine blades, from thermal protection systems for reentry vehicles to fusion chamberwalls, in all these modern high-temperature environments, transpiration cooling is currently in the focus of research to overcome the principle problem of exceeding the wall temperature limit [4–8]. Regenerative cooling is state of the art in rocket engines. Liquid fuel is used to cool the nozzle and the heated fuel is injected in the combustion chamber at higher temperature, which again increases the combustion efficiency. Results of numerical analysis show that the efficiency of regenerative cooling compared with transpiration cooling can lower the wall temperature by more than 30%. Transpiration cooling means that the fuel is injected through the wall into the combustion chamber or nozzle. This is advantageous because a layer of relatively cool fuel close to the wall protects the wall [5]. With the invention of high-temperature porous media for rocket engines, those numerically proved improvements could be verified by experimental tests [3]. For high-speed aircraft, material and cooling issues for both airframe and engine are the key elements which force the designer to limit the flight Mach number [9]. All these engineering problems face the fact that the heatflux at the surface is a design critical value yet difficult to measure. In the high heat flux regimes, a direct measurement is not applicable, since no sensor is available to measure directly at the surface. The only solution is therefore, a temperature measurement using in-depth temperature sensors. However, an inversemethod has to be applied to determine surface heat flux. In the case of a transpiration cooling environment, however, the often applied one-dimensional analytical calculation is prone to error: The thermocouple position is of particular importance in this approach and particularly in a porous material very difficult to know with sufficient precision. Moreover, the porosity has to be known, which complicates this analytical problem further because there is not only the dependency from heat capacity, heat conductivity (both values needed for the porous material), but also from thematerial specific parameter of porosity. A numerical approach lacks a precise information of porosity of the material which is impossible to know for a particular sensor system. Finally, for such complex materials, the thermophysical properties are not known and difficult to determine. A recent publication of Shi andWang presents a solution for this inverse problem [10]. Here, the accuracy of themethod again depends strongly on the accuracy of the information about the specific heat capacity, heat conductivity, and coolant temperature. In this paper, an approach based on the calibration of the real environment will be presented. For the analysis of the calibration measurement, the noninteger system identification (NISI) approach is applied to a transpiration cooled environment. Using basic calibration experiments, the transpiration cooling is inherently covered by the NISI calibration process. It is shown for the first time that the knowledge of the coolant mass flow is sufficient to determine the surface heat flux.