Stefan Löhle

Heat flux sensor calibration using noninteger system identification: Theory, experiment, and error analysis

This paper concerns the improvement of the calibration technique of null point calorimeters generally used in high enthalpy plasma flows. Based on the linearity assumption, this technique leads to calculate the impulse response that relates the heat flux at the tip of the sensor according to the temperature at the embedded thermocouple close to the heated surface. The noninteger system identification (NISI) procedure is applied. The NISI technique had been well described in previous study. The present work focuses on the accuracy of the identified system in terms of absorbed heat flux during the calibration experiment and of the estimated parameters in the model. The impulse response is thus calculated along with its associated standard deviation. Furthermore, this response is compared with that of the one-dimensional semi-infinite medium, which is classically used in practical applications. The asymptotic behavior of the identified system at the short times is analyzed for a better understanding of the noninteger identified system. Finally, the technique was applied to a new sensor geometry that has been developed particularly for high enthalpy plasma flows and it is shown that the method can be applied to any geometry suitable for a certain test configuration.

Oxidation Behavior of Siliconcarbide-Based Materials by Using New Probe Techniques

Hysteresis of passive to active and active to passive transition of SiC oxidation behavior has been investigated theoretically, numerically, and experimentally. Theoretical and experimental investigations show a strong interaction between transition and catalysis. Dependence on plasma composition is shown.Arecently developed reaction model has been implemented in the advanced nonequilibrium Navier–Stokes code URANUS. Results are presented for the highly dissociated flow around the MIRKA capsule. In this case, radiation adiabatic surface temperatures have been found to be 120Khigher for active oxidation conditions as compared to passive oxidation conditions. To investigate transition behavior in detail, various new probe measurement techniques have been developed. Important additional observations have been made in chemical nonequilibrium.Within plasma wind-tunnel testing, a sudden temperature increase of up to 400 K was found with the transition from passive to active oxidation. Theoretical and numerical predictions show good qualitative and quantitative agreement with experimental results.

Two-Photon Absorption Laser-Induced Fluorescence Investigation of CO2 Plasmas for Mars Entry

Two-photon absorption laser-induced fluorescence measurements have been conducted to investigate atomic oxygen temperature and number density in a CO2 plasma relevant to Martian entry. The high-enthalpy plasma flow has been produced by an inductively heated plasma generator. This paper describes the experimental setup and shows the applicability of laser diagnostics to Mars-relevant plasmas. Particular emphasis is put on the use of the generated data for the numerical simulation of the aerothermal chemistry of a Martian entry. Relative fluorescence signals are calibrated by a procedure using xenon as a reference. This calibration method allows the in situ experimental determination of the instrumental broadening of the spectroscopic setup and thus an accurate temperature measurement. The acquired, highly resolved line profiles of the fluorescence signal yield a translational temperature of 2777  K±400  K and a mean number density of 1.55·1019m−3±60%.

Estimation of High Heat Flux in Supersonic Plasma Flows

The objective of this study is to ameliorate transient heat flux measurements up to 60 MW/m2 in high enthalpy plasma wind tunnels. Usually so-called null-point calorimeters are used, which means the temperature inside a known material is measured with a thermocouple and by solving the heat conduction problem under the assumption of one-dimensional, semi-infinite heat transfer the surface heat flux can be calculated. The surface heat flux in the present case is determined by solving the inverse heat conduction problem of the system using a non integer identified model as a direct model for the estimation process. Therefore, calibration measurements using a known variable heat flux are applied. The advantage of the system identification process is, that critical design aspects of the sensor which lead to significant disturbances in the assumption of one-dimensional, semi-infinite heat conduction, are accounted for. In the paper, a classical null-point calorimeter as well as a new sensor design adapted for the present plasma wind tunnel configuration are described in detail. Using finite element modelling, calculations of both sensors are presented and the system identification procedure is demonstrated. The amelioration of the measurements are clearly outlined, e.g. an asymmetry in the measured radial profile using the classical approach of one-dimensional, semi-infinite heat conduction is not measured using the novel approach

Laser-Induced Fluorescence Measurements of Atomic Oxygen Using Two Calibration Methods

Number densities of atomic oxygen have been measured in pure oxygen plasma, using two-photon laser-induced fluorescence measurements. In this paper, two calibration techniques are compared: the sensitivity of the experimental setup is calibrated using scattering experiments, and reference measurements on xenon are performed using two-photon laser-induced fluorescence measurements. The theoretical background and the experimental setup are described in detail. The advantages and drawbacks are herewith outlined. Applied to high-enthalpy, pure oxygen plasma, the evaluated number densities show fairly good agreement; however, because a constant discrepancy is measured between the results when using the two calibration approaches, a systematic error is probable. Possible reasons for this error are discussed (e.g., the cross-sectional ratio, in the case of xenon reference measurement calibration). One main conclusion is that measurements that are performed using the reference measurements on xenon are preferred, because they have much fewer experimental factors to be taken into account.

Local Enthalpy Measurements in a Supersonic Arcjet Facility

Results of the application of a mass-injection probe to estimate the local mass-specific enthalpy in a supersonic air plasma flow are presented. Up to now this probe has only been applied to subsonic flows. Numerical calculations to interpret the probe behavior are shown and compared to experimental results. Furthermore, to interpret the measured local mass-specific enthalpies, classical enthalpy estimation methods are used together with analytical calculations of the turbulent free plasma jet and fairly good agreement is found.

Analysing inverse heat conduction problems by the analysis of the system impulse response

Abstract The paper presents the application of the non-integer system identification (NISI) method with a focus on the analysis of the system’s impulse response. The NISI method being first published in 2001 has been applied to very different inverse heat conduction problems. The results presented in this paper are new findings developed by considering the impulse response as the characteristic of the investigated system. This assumption allows a different view to the problems where the method so far has been restricted. Examples are shown for a system with variable thermophyiscal properties and a surface under transpiration cooling.

Improved Abel Inversion Method for Analysis of Spectral and Photo-Optical Data of Magnetic Influenced Plasma Flows

This paper presents the derivation of an alternative method called spline method to perform inverse Abel transformation of measured data sets. At first the general approach of Abel transformation is shown. The following section shows the principle of operation of the existing methods. Then the new spline method is derived, which is a combination of the known Fourier method and f-Interpolation method with polynomials with an analytical solution of the forward Abel transform. All methods are tested on three test cases: an off centered Gaussian function, a cubic function and photo-optical data of a plasma flow in front of a spherical probe head. The results of the different methods are compared, limitations are shown and their advantages are pointed out. The new method is advantageous for noisy data and due to its spline based approach no assumptions about the local distribution are needed.

Theoretical Approach to Surface Heat Flux Distribution Measurement from In-Depth Temperature Sensors

I NHIGH heat load environments such as combustion chambers of rocket motors or atmospheric entry, the determination of the net surface heat flux is an essential problem. Inmost cases, only in-depth temperature sensor data is available and derivation of heat flux requires the solution of what is known as the inverse heat conduction problem (IHCP). During the last 50 years, a wide array of analytical and numerical solutions for the IHCP have been developed [1,2]. However, most solutions are based on strict initial and boundary conditions. For example, some analytical solutions are only applicable to particular settings such as the semi-infinite half-space [3]. Furthermore, the knowledge of the thermophysical properties of the materials in use is a prerequisite. Finally, the temperature sensor position is very sensitive to the solution of such problems. Although promising solutions concerning the one-dimensional IHCP have been published at least for the semi-infinite half-space, there is still uncertainty in the material properties, contact resistance, and exact temperature sensor position [4]. Furthermore, given more complex geometric bodies, in which heat conduction in all three space dimensions cannot be neglected, these tools can not be applied. In this paper, an approach named the noninteger system identification (NISI) method is extended to a three-dimensional medium. The NISI method for one-dimensional problems has first been published byBattaglia et al. [5]. It has been shown that the basic idea of applying system identification as known from automatics and control as an alternative approach to solve IHCPs holds for several analytical problems, e.g., semi-infinte, sphere. It can even be applied to more complex systems since the system identification step accounts for effects as for example deviations from one-dimensional behavior or assembly issues of the thermocouple. During identification, the sensor system, i.e., the temperature sensor as mounted inside the probe body, is calibrated. That means, adhesive layers possibly in between the sensor and the probe body affecting the thermophysical properties, thermocouple position deviating from the specified position, or thermal contact resistancies of different materials are included in the calibration step and do not further influence the data analysis. More recently, the NISI method has successfully been applied to analyze the classical null-point calorimeter developed in the 1970s [6–8]. It has been shown that an asymmetry in the heat flux profile is an artificial effect arising due to radial heat fluxes to the temperature sensor. As a result of this investigation, modifications towards a miniaturized sensor aiming to measure radial heat flux profiles in other plasma flows has been developed and successfully applied [9,10]. Again this modification became possible, because the NISI method inherently takes effects as thermocouple mounting or thermal resistancies into account through the calibration step.Within the planned hypersonic flight experiment HIFiRE, a ceramic fin has been equipped with thermocouples and first investigations towards a NISI application have been conducted [11]. In the present investigation, it is tried to extend the method to a three-dimensional problem. In a simplified form a similar analysis has been published by Battaglia [12]. By simplifying the engineering problem and some further assumptions, the multidimensional approach had been considered as a series of one-dimensional problems. In the present study, we do not assume any symmetry or similarity from the experimental point of view. Using finite element analysis of a half-ellipsoid as a generic model featuring several virtually embedded temperature sensors, the method is applied in theory. In Fig. 1, the principal procedure is shown. A half-ellipsoid is the exemplary three-dimensional geometry. There are five surfaces and five temperature sensors defined. Using a commercially available finite element modelling software (Ansys), the system is first identified according to the NISI method applying a heat flux profile to each surface element and monitoring all five temperature sensors to calibrate the system. In a second step, an exemplary heatflux profile is applied to 1) all surface elements and 2) to only two surface elements. Finally, the temperature signal, which has been numerically calculated is used to determine inversely the preset heat flux profile. The following section describes the theory as an extension of the one-dimensional problem to more sensors andmore surface areas. In Sec. III the calibration based on numerical analysis is presented followed by the application to the numerical problem to solve the inverse problem.

Experimental setup for vacuum ultraviolet spectroscopy for earth re-entry testing

This paper presents the experimental system which has been designed to measure vacuum ultraviolet (VUV) optical emission spectra. It has been tested at the plasma wind tunnel PWK1 at the Institute of Space Systems. The setup, its calibration and qualification are reported. Wind tunnel experiments have been conducted with a local mass-specific enthalpy of 68.4MJ/kg and a stagnation pressure of 24.4 hPa. The radiation is collected through a magnesium fluoride window mounted close to the stagnation point of a sample. The received light is redirected to the spectrometer with a series of mirrors in an evacuated light path. The spectral range between 116-197 nm was investigated. The lower limit is due to the transmission of the window material. Measurements with a cooled copper and a carbon preform material sample are presented. The measured VUV spectra feature atomic nitrogen and oxygen lines for both the copper and the material sample. Atomic carbon lines are present in the case of the material sample.