Investigation of the inlet useful temperature difference effect on the distribution of hydrodynamic characteristics of the vapor-liquid flow inside the falling-film evaporator heating tube designed for a nitric acid solutions evaporation

We present the results of mathematical modeling of effect of inlet useful temperature difference on the vapor- liquid flow in the heat exchange tube of a vertical evaporating film apparatus, which is designed for evaporation of nitric acid solutions. Distributions obtained along the heat exchange tube length of local values of the: mass flow rate of the fluid and secondary steam, the velocity of the fluid film, the velocity of the secondary steam, the Reynolds criterion of the liquid and vapor phases, the absolute pressure depending on the values of this useful temperature difference. The study was carried out using numerical simulation. To study the effect of the initial useful temperature difference on the hydrodynamics of the vapor-liquid flow, the vertical evaporator equipped with the tube ø38x3 mm and length of L = 4 m was adopted. The linear nature of the distribution of hydrodynamic parameters along the length of the heat exchange tube is established. The absolute pressure in the tube space decreases along the heating tube due to pressure drop. The limiting factor in reducing the absolute pressure is the friction losses of the secondary vapor on the solution film surface. A decrease in the pressure in the tube space leads to decrease in the boiling point of the solution. This leads to increase useful temperature. This has a positive effect on the evaporation efficiency The obtained data should be used in the design of evaporation plants, which are designed for evaporation of nitric acid solutions.


Introduction
The main type of waste from galvanic production is washing water, which contains, among other things, salts dissolved in water.To evaporate these solutions, as a rule, evaporators with a remote heating chamber and natural circulation are used.However, during evaporation, there is a gradual increase in the concentration of impurities (anode sludge, corrosion products, etc.) in the evaporated process solution [1].
Currently, there is a tendency to evaporate such nitric acid solutions in direct-flow falling-film evaporators.The advantages of these devices are [2 -6]: -high heat transfer efficiency; -high productivity with small dimensions of the devices and the production area occupied by them; -the significant reduction in the residence time of the solution in the apparatus.
However, there is practically no data on the influence of technological modes on the hydrodynamics of the moving stream of the fluid film and secondary steam in the falling-film evaporator in the tube space in relation to the evaporation of nitric acid solutions.
This work is about the investigation the effect of the inlet useful temperature difference on the distribution of properties of the hydrodynamic this moving stream in the tube of the vertical falling-film evaporator designed for the nitric acid solutions evaporation.This work is the continuation of the complex of studies devoted to the vapor-liquid flow hydrodynamics in the film-type evaporators heating tubes [3, 4, 7 -9].As a result of the study, the technological characteristics distributions data along the heating tubes are obtained.

Research methodology
In this work we used a numerical simulation method.The mathematical model of the two phase vaporliquid flow with the interphase surface for the tube space is semi-empirical and describes changes in absolute pressure, the weight flow of the fluid film and secondary steam, the Reynolds criterion, the velocity of the fluid film and secondary steam, pressure drop along the heating tube [8]. Figure 1 shows the co-directional motion of the solution film and the secondary vapor.
To study the effect of the initial useful temperature difference on the moving stream hydrodynamics evaporator equipped with the heat exchange tube ø38x3 mm and length of L = 4 m was adopted.Table 1 shows the main process conditions of the vertical evaporation apparatus with the falling-film for evaporation of nitric acid solutions.The values of the Reynolds criterion of the solution film are inversely proportional to the values of the initial useful temperature difference, that is, with increase in the initial useful temperature difference, the Reynolds criterion will decrease at the corresponding points of the tube length (see Fig. 4).The Reynolds criterion of the solution film depends on J, and with increase in ∆t, J decreases in accordance with decrease in the liquid phase weight flow (see Fig. 2a).show that the tube space pressure decreases along the tube length with all the values of the useful temperature difference considered.At ∆t=25 o C, the greatest degree of this pressure decrease is observed, which is inversely proportional to the increase in ∆t.The minimum pressure in the tube space values is observed on the end part of heating tube.

Table 1. The process conditions of evaporation of nitric acid solutions
The absolute the tube space pressure decreases along the heating tube length due to drops: on the liquid phase film friction on the tube wall; on the friction on the on the interpase surface; on the change in the phases dynamic pressure.

Conclusion
New hydrodynamic characteristics dispensing data of the moving stream of the nitric acid solution and secondary steam by the heating tube with different values of the inlet useful temperature difference are obtained.
The absolute pressure in the tube space descends by the heating tube because of losses.The limiting factor of the absolute pressure descending is the friction vapor fraction losses due to interfacial friction.Decrease in the absolute pressure in the tube leads to the liquid phase boiling point decreasing and increasing of the useful temperature difference local values along the tube.The obtained data should be used in the design of evaporation plants, which are designed for evaporation of nitric acid solutions.

Figure 1 . 3 .
Figure 1.The downward moving stream of liquid and vapor phases in the falling-film evaporator tube; W1 -the liquid phase velocity, W2 -the vapour phase velocity.

Figure 2 .
Figure 2. Distribution along the length of tube of the liquid phase mass rate (A) and vapour phase mass rate (B) depending on different values of the inlet useful temperature difference.

4
The range of values corresponds to the turbulent flow regime of the solution film.The Reynolds criterion of secondary steam increases in linear manner.At the corresponding points by tube length, the values of the Reynolds criterion grow with increasing ∆t, reaching maximum values at the end of the tube.

Figure 3 .
Figure 3. Distribution along the length of tube of the film velocity of solution (A) and secondary steam (B) depending on different values of the inlet useful temperature difference.

Figure 4 . 5 Figure 5
Figure 4. Distribution by the tube length the Reynolds criterion of the solution film (A) and secondary steam (B) depending on different values of the initial useful temperature difference.

Figure 5 .
Figure 5. Pressure distribution in the tube space depending on the values of the inlet useful temperature difference along the heating tube.

Figure 6 .
Figure 6.Distribution of the fractions of the 3 components of the total pressure losses during evaporation of nitric acid solutions.