Thermal Engineering

Different models used in calculating flows of a two-phase coolant are analyzed. A system of differential equations describing the flow is presented; the hyperbolicity and stability of stationary solutions of the system is studied. The correctness of the Cauchy problem is considered. The models’ ability to describe the following flows is analyzed: stable bubble and gas-droplet flows; stable flow with a level such that the bubble and gas-droplet flows are observed under and above it, respectively; and propagation of a perturbation of the phase concentration for the bubble and gas-droplet media. The solution of the problem about the breakdown of an arbitrary discontinuity has been constructed. Characteristic times of the development of an instability at different parameters of the flow are presented. Conditions at which the instability does not make it possible to perform the calculation are determined. The Riemann invariants for the nonlinear problem under consideration have been constructed. Numerical calculations have been performed for different conditions. The influence of viscosity on the structure of the discontinuity front is studied. Advantages of divergent equations are demonstrated. It is proven that a model used in almost all known investigating thermohydraulic programs, both in Russia and abroad, has significant disadvantages; in particular, it can lead to unstable solutions, which makes it necessary to introduce smoothing mechanisms and a very small step for describing regimes with a level. This does not allow one to use efficient numerical schemes for calculating the flow of two-phase currents. A possible model free from the abovementioned disadvantages is proposed.

The article considers the specific features related to operation of the power valve and orifice lines within turbine plant piping systems whose inlets receive water medium with saturation parameters (separated moisture or condensate). It is shown that transportation of working medium in these piping systems is accompanied by pressure drop, boiling, and formation of various two-phase flow patterns from bubble in the initial segment to dispersed-annual in the end segment. Under certain conditions, a slug flow pattern can occur, which behaves as a source of piping vibration. Practical experience has shown that the use of homogenizing inserts for suppressing vibration load in the heating steam condensate (HSC) discharge lines downstream of the moisture separator reheaters (MSRs) of nuclear power plant (NPP) turbines often leads to intensified local flow-accelerated corrosion and pipeline failures. The article considers examples illustrating failures of piping segments downstream of homogenizing inserts and presents statistical data on damageability of heating steam and separated moisture piping of NPP turbines. The steam–water flow patterns in the MSR HSC transportation line of an NPP turbine are determined. The results from hydrodynamic modeling of working medium flow under the conditions of an abrupt expansion at the outlet from the homogenizing insert channel are presented. It is shown that the location of zones characterized by the maximum wear of piping downstream of homogenizing inserts in the MSR HSC discharge lines is determined by the flow pattern and specific features of the working medium flow hydrodynamics. It has been established that droplet impingement erosion is the dominating mechanism causing destruction of stainless-steel piping segments downstream of the homogenizing inserts in the MSR HSC lines of NPP turbines. It is important to note that, if the pipeline is made of carbon or low alloy steel, its metal experiences a combined effect of droplet impingement erosion and flow-accelerated corrosion. The obtained study results can be used in elaborating measures aimed to prevent wear of piping components in the heating steam condensate and separated moisture discharge lines of NPP turbines.

The cooling of rock formations when extracting heat by a borehole heat exchanger and the restoration of the thermal field in the rock during the idle time of the well have been investigated. The heat in the rock during the summer downtime of the well is partially restored due to the influx of heat from the outside formation. The radius of the rock cooling front around the borehole in the heating period can reach 6–8 m. The temperature on the borehole wall is restored by approximately 50% in one month and by 80–85% in summer. Hybrid technology is proposed for the extraction and accumulation of thermal energy from the upper layers of the earth’s crust comprised of a shallow borehole heat exchanger, a heat pump, and solar collectors. The technology provides for both the extraction of heat from the rock during the heating period and transmission of this heat to the heating system with a heat pump and the restoration of the temperature field around the well during the interheating period by accumulating in the rock formation the heat fed to the borehole heat exchanger with hot water from the storage tank. This system was implemented in Makhachkala at the test site of the Joint Institute for High Temperatures, Russian Academy of Sciences, for supplying heat and hot water to cottage-type houses. The main components of the system are solar collectors with a total area of 20 m2, a heat-insulated hot water storage tank with a built-in heat exchanger, a 15-kW heat pump, and a 100-m deep borehole heat exchanger. The test results have demonstrated high efficiency of the system for supplying heat to low-power consumers not covered by central heating.

Experiments are carried out for simulating the efficiency of cooling the leading edge of a blunt streamlined body made of porous reticular material with an impermeable insert placed along the stagnation zone. Satisfactory results are obtained that make it possible to recommend the proposed method of organizing transpiration porous cooling of the leading edge of the blades used in high-temperature gas turbines for implementation.

The article discusses matters concerned with improving the performance of automatic closed-loop control systems of thermal plants with a time delay in responding to a change in the setpoint. The improvement is achieved by applying the fastest response algorithm (FRA) according to the Pontryagin maximum principle and using linear prediction of the controlled variable. It is shown that, during operation with switching the maximum control outputs applied to a plant with a time delay, linear prediction is inefficient, and self-oscillations may occur in the system. The technical solution proposed for eliminating self-oscillations implies the use of a hybrid closed-loop control system comprising an FRA, a PID controller, and an automatic controller tuning (ACT) unit, which performs the function of determining the plant model parameters and optimizing the controller parameters. The actuator is considered as a proportional section that is used as part of the plant. The control limitations are related to the level of the control output applied to the plant. The ACT unit comprises accelerated controller tuning algorithms that use active plant identification methods based on analyzing the response to an impulse input and two cycles of the excited self-oscillations. These algorithms make it possible to determine four parameters of the second-order plant model with a time delay. The self-oscillations occurring in systems with the FRA and plants with a time delay are eliminated at the end of the transient by making a switchover to PID control. Four embodiment versions of a system with the FRA are analyzed, specifically, those with and without control output reversal and also with using the plant simulation model without a time delay that is obtained from the ACT operating in parallel with the plant. For practical embodiment of the MSRA as part of a hybrid system, it is recommended to use its version without control output reversal. Relations for calculating the controlled variable prediction coefficient in terms of the plant model parameters in a wide range are obtained. Two examples of using the hybrid system equipped with industry-grade controllers for a temperature control system are given: one with the electric heater power controlled using a pulse-width modulator and the other with a constant speed actuator.