Heat transfer in packet of parallel plates in the short-term processes

The description of the experimental stand (laboratory regenerative air preheater), the method for measuring the unsteady flow temperature and the results of experimental heat transfer studies of a package of plates (nozzles) of alloy steel AISI-430 with a 2 mm thickness for short-time periods with different durations are presented. The experimentally obtained mean Nusselt numbers are generalized by the criterial equation.


Introduction
In many power plants thermal processes take place during a limited period of time. Such power plants include regenerative air preheaters (RAPH) used in steam generators, air cooling and air separation machines, gas turbine engines, metallurgical furnaces, ventilation and heating systems [1][2][3].
Due to a cyclic heat exchange of the nozzle with a cold and hot heat carrier the heat transfer process in each cycle period is unsteady. It is known that the unsteady nature of external conditions qualitatively and quantitatively affects on local heat transfer [3][4][5][6][7]. Therefore, the heat transfer coefficient of the nozzle averaged over the period, which is important for the calculation and design of the RAPH, becomes dependent, among other factors, on the duration of the periods, that is, on the frequency of regeneration [3,4]. However, this dependence is not fully understood and in most cases is not taken into account by the developers of industrial RAPH [1,2].
The work elaborates on the description of the test bench, experimental procedure and data processing in measurements of the heat transfer coefficient of the plate pack surface in the laboratory RAPH. We also demonstrate the effect of the regeneration cycle duration on the heat transfer coefficient averaged over the period, obtaining the criterion dependence of the Nusselt number on the duration of the period and the flow regime of the heat transfer agent for a specific packing.

Stand with a laboratory RAPH
The stand consists of air blowers, air ducts with flowmeters, a heater on one of the air ducts, a working area, a moving unit, an automatic control system (ACS) and an automated measuring system (AMS). In the working area, the body of which is molded from fiberglass and having a cavity of a square section of 50 × 50 mm, the test nozzle is located. Thermocouples are installed in the inlet and outlet of the working area to measure the non-stationary temperatures of air flows at the inlet and outlet of the RAPH. In addition, in front of the working site there are standard thermometers. The air flow was measured with the help of narrowing devices with low-flow diaphragms [8]. The flow switching, that is, the periodic connection of the RAPH to the ducts of the cold and hot air ducts, is carried out by means of electric drives.
AMS includes a personal computer (PC) and an I / O device from National Instruments PCI-6251, connected to the PCI bus of the PC [9]. To create the AMS software, the LabVIEW graphical programming environment was used (License agreement number: 777455-03 Serial number: M71X16236). The readings from mV to degrees were carried out according to the individual calibration characteristics of thermocouples. AMS registered the following parameters: flow temperatures at both nozzles of the working section, the surface temperature and the center of the nozzle, pressure differences on the flowmeters and the RAPH. Readings of stationary parameters (barometric pressure, temperatures and relative humidity of ambient air, temperatures and pressures before flowmeters, standard thermometers) were taken manually.
The explored packing was a package of parallel plates of alloy steel AISI-430 1 mm thick and 100 mm long. The plates are welded in pairs by contact welding, forming 13 plates 2 mm thick, set at a distance of 2 mm from each other. Thermocouples are welded between thin plates and on the surface of one of them to measure the temperatures of its central point and surface. Thermocouples from chromel-kopel wires with a diameter of 0.2 mm are welded by a contact welding machine.

Method for measuring the heat transfer coefficient of the nozzle of the RAPH
The heat transfer coefficient of the nozzle surface in a separate period is given by the formula where  is the heat transfer coefficient, W / (m 2 K); Q is the heat load transferred through the nozzle from the hot heat carrier to the cold, W; w F is the complete surface of the nozzle, m 2 ; is the average temperature of heat carrier, °C; ' f T and " f T are the temperatures of the heat carrier at the inlet and outlet of the working section in the period under review, °C; w T is the average surface temperature of the nozzle, °C.
The thermal load can be represented as the thermal power perceived or transmitted by the nozzle at the current time ( Here w M is the mass of the nozzle, kg; w c is the specific heat of the packing, J / (kg K); w T is the average nozzle temperature, K.
The stand allows to measure all the quantities entering into formulas (1)

Calculation of the actual values of rapidly varying flow temperatures
The works [10][11][12][13] are devoted to the method of measuring non-stationary flow temperatures.
The equation of thermal conductivity for a thermocouple junction in relative variables has the form [11]: where ; T is temperature of the junction, К;  T is temperature of the heat carrier at the end of the transition period, К; is temperature scale, К; max T and min T are the maximum and minimum temperatures, respectively, of the hot and cold flows, К;  is time from the beginning of the period, s; p  is duration of the transition period, s; characteristic thermocouple time, s;  is density, kg/m 3 ; c is the heat capacity, J/(kg K); F and V are the surface area, m 2 , and volume, m 3 , of the junction. The general solution of the ordinary differential equation (3) Here is the true dependence of the flow temperature on time, in which we use the exponential The required coefficients 0 a and 1 a are found from the comparison of solution (4) with the regression equation that approximates the thermocouple readings   where l b is the regression coefficients.

Determination of the coefficients of the exponent (5)
Integration of equation (4) after substitution of the function (5) gives an expression for the calculated thermocouple temperature: To find the unknowns 0 a and 1 a , two conditions are set: from which we obtain the equations   The solution of these equations allows to find the unknown coefficients 0 a and 1 a . Here  is the average temperature of the flow during the period

Results of correction of thermocouple readings and their analysis
The coefficient of heat transfer of the thermocouple junction, necessary for calculating the characteristic time of the thermocouple *  , was calculated from the formulas [15]: When determining the characteristic time of thermocouples *  , the thermophysical properties of their junctions were calculated on the assumption of the equality of volume fractions of metals [16][17][18]: Here   is the temperature limit at the end of I or III of the calculation period; the sign "+" before the exponent corresponds to the cold period, the sign "-", to the hot period; the polynomial on the right-hand side determines the calculated temperature in the II or IV calculation period. The character of the dependence of the heat transfer coefficient on time, shown in figure 3, qualitatively agrees with the classical concepts [5] explaining such a behavior of the heat transfer coefficient by increasing the thickness of the boundary layer in time tending to the steady-state value. A similar character of the change in the heat transfer of a plate when the temperature of the coolant changes abruptly is confirmed by theoretical studies [6].     Figure 4 (for the notation, see figure 4).