Thermal feedback analysis

Waves of chemical reaction may travel through a reaction medium, but the ideas of important stationary spatial patterns are due to Turing (1952). They were at first invoked to explain the slowly developing stripes that can be exhibited by reactions like the Belousov-Zhabotinskii reaction. This (rather mathematical) chapter sets out an analysis of the physically simplest circumstances but for a system (P - A - B + heat) with thermal feedback in which the internal transport of heat and matter are wholly controlled by molecular collision processes of thermal conductivity and diffusion. After a careful study the reader should be able to ... 

Analysis of compound dynamic instabilities. As mentioned in the previous section, most of the compounded and feedback effects are built into computer codes for analyzing dynamic instabilities. These computer codes can be used to analyze compound dynamic instabilities such as BWR instability and parallel-channel instability. However, thermal instability between transition boiling and film boiling cannot be analyzed, because of the lack of phenomenological correlation of transition boiling. 

In the preceding chapters we investigated the basic patterns of behaviour which might be exhibited by a reaction scheme which involved a certain form of chemical feedback under isothermal conditions. Here we make a similar analysis for systems with purely first-order chemical reactions but under conditions in which the heat produced by the natural exothermicity can lead to departures from isothermal operation. Feedback is then provided from thermal coupling as the increase in temperature of the reacting mixture leads to an increase in the local value of the reaction rate constant. 

A block diagram for a feedback control furnace system, used in thermal analysis instrumentation, is shown in Figure 2.10. The SCR receives a control instruction, and in turn permits a... 

LMRs with oxide-fueled core Models modified and newly developed mto the code so far mclude models for reactivity feedback effects and pool thermal-hydraulics In order to venfy the logic of the models developed, and to assess the effectiveness of the inherent safety features based upon the negative reactivity feedbacks m achieving the safety design objectives of passive safety, a preliminary analysis of UTOP and ULOF/LOHS performance has been attempted... 

The principle of microcalorimetry is iUustraled with Fig. A.10.7 (pTA of TA Instruments, Inc.). The tip of an atomic force microscope, AFM, is replaced by a Pt-wire that can be heated and modulated, as is illustrated in detail with Fig. 3.96. A typical resolution is about 1.0 pm with heating rates up to 1,000 K min. A temperature precision of +3 K and a modulation frequency up to 100 kHz has been reached. The figure shows the control circuit for localized thermal analysis. In this case the probe contacts the surface at a fixed location with a programmed force, controlled by the piezoelectric feedback of the AFM. A reference probe is attached next to the sample probe with its tip not contacting the sample, allowing for... 

Over the last decade, it has been internationally accepted that the generic title for TA techniques whereby the heating rate is controlled using a feedback loop as some function of the rate of reaction or the chemical or physical process under study should be sample controlled thermal analysis (SCTA) and this title now embraces Q-TG, CRTA, SIA, and dynamic rate thermal analysis. 

One of the approaches described in this paper entails keeping the reaction rate and partial pressure of product gas constant during calcination by changing the tempo ature appropriately by means of a feedback loop. This technique has its origins in Controlled Rate Thermal Analysis (CRTA), which was developed by Rouquraol [4] to provide improved kinetic data and higher resolution in thermal analysis. He showed that constant reaction rate conditions could be of benefit also in preparing materials with specifiable surface areas. 

Pons, S. and Fleischmann, M. (1996) Calibration of the Pd-DjO system effects of procedure and positive feedback. Journal de Chimie Physique et de Physico-Chimie Biologique, 93, 711. Miles, M.H., Imam, M.A. and Fleischmann, M. (2000) Case studies of two experiments carried out with the Icarus systems. Proceedings, Itahan Physics Society Conference, vol. 70, p. 105. Miles, M.H. and Fleischmann, M. (2001) Calorimetric analysis of a heavy water electrolysis experiment using a Pd-B alloy cathode. Electrochemistry Society Proceedings, 2001-13,194. Szpak, S., Mosier-Boss, P.A., MUes, M.H. and Fleischmann, M. (2004) Thermal behaviour of polarised Pd/H electrodes prepared by co-deposition. Thermochimica Acta, 410, 101. 

Because it is based on well-established LWR technology and implements benchmarked thermal hydraulic safety analysis codes, and because each module is a relatively small reactor, it is possible that all of the information required for design certification may be obtained using a full-scale demonstration of a single module. Of significant interest for design certification would be the impact of neutronic feedback on flow stability, particularly during plant transients. 

The analysis of this thermogram can be done by applying a theoretical model that adequately describes the results from an TTC instrument with feedback system The capacity to correctly predict the respwnse of the calorimeter to any given thermal effect can allow us to satisfactorily analyze the obtained thermogram We demonstrated that for an isothermal calorimeter with dynamic power comp>ensation (feedback system) and a similar configuration as used here (VP-TTC from Microcal), the respwnse function to a power pulse (Wo) of finite duration ( ) can be expressed by the Eq. 24,... 

The elimination or at least minimization of the positive coolant density component of the temperature reactivity effect is a favourable factor in limitating the consequences of ULOF and UTOP. The negative reactivity feedback caused by a thermal expansion of the control rod drive lines also plays an important role. Analysis of a ULOF accident shows that sodium boiling and fuel melt are excluded because the core outlet temperature does not exceed 800 C. Nevertheless a refractory sodium-cooled tray beneath the core is provided to prevent release of corium beyond the reactor vessel boundary and formation of a critical mass. Preliminary safety analysis for the BN-1600M reactor plant shows that ... 

A variety of probe types have been developed for SECM-SICM. Eor one type of probe, gold was deposited onto one side of a nanopipette, which was then insulated entirely with aluminum oxide the nanopipette opening and a UME of the deposited gold were subsequently exposed via an EIB mill. A similar but simpler technique was also developed and used in SECM-SICM experiments— a nanopipette with a thin gold layer thermally evaporated on one side. Double-barrel carbon nanoprobes have also been fabricated, in which one barrel of the nanopipette is filled with a pyro-lized carbon electrode for the measurement of the faradaic current of SECM analysis and the other barrel filled with electrolyte solution to simultaneously measure the ion current for feedback and SICM analysis.269... 

The SSC-K code [4] has been developed by KAERI for the analysis of system behaviour during transients. The SSC-K code features a multiple-channel core representation coupled with a point kinetics model with reactivity feedback. It provides a detailed, one-dimensional thermal-hydraulic simulation of the primary and secondary sodium coolant circuits, as well as the balance-of-plant steam/water circuit. 

To facilitate modeling of the metal fuel used in KALIMER, several reactivity models are modified in SSC-K code. For neutronic calculations, SSC-K uses point kinetic equations with detailed reactivity feedback from each channel. Reactivity effects are required both for transient safety analysis and for control requirements during normal operation. Reactivity changes are calculated for control rod scram, the Doppler effect in the fuel, sodium voiding or density changes, fuel thermal expansion, core radial expansion, thermal expansion of control rod drives, and vessel wall thermal expansion. Figure 5 shows the components of reactivity feedback considered in the KALIMER core. The effect of fuel expansion becomes more significant when metallic fuel is used. 

The Super LWR employs separate large square water rods as neutron moderators. The time delay of the heat transfer to the water rod is much larger than that of the heat transfer to the coolant. Thus, the reactor system becomes less stable when a water rod model is included than when no water rod model is used. The descending water rods will have a significant effect on the coupled neutronic thermal-hydraulic stability because of the moderator density reactivity feedback from the large square water rods, and it needs to be considered in stability analysis of the Super LWR. 

Accident analysis calculations in which the thermal effect of a reactivity insertion may be determined are normally carried out by means of a computer code or combination of codes in which the reactor kinetics description is coupled with the thermal-hydraulics model. For example, the previously described vapor growth models become more meaningful for accident analysis if they are coupled with a reactivity feedback model 14). 

---