ISSN 0040-6015, Thermal Engineering, 2008, Vol. 55, No. 7, pp. 565–569. © Pleiades Publishing, Inc., 2008. Original Russian Text © A.S. Sedlov, Yu.A. Kuzma-Kichta, I.P. Il’ina, E.O. Kon’kov, A.V. Lavrikov, 2008, published in Teploenergetika.
Improvements in the Procedure for Design of Boiling-Type Evaporators for Highly Mineralized Media A. S. Sedlov, Yu. A. Kuzma-Kichta, I. P. Il’ina, E. O. Kon’kov, and A. V. Lavrikov Moscow Power Institute (Technical University), ul. Krasnokazarmennaya 14, Moscow, 111250 Russia Abstract—The dependences are obtained of the pressure drop in a vertical pipe under conditions of boiling aqueous solution of sodium sulfate on the flow velocity, steam quality, and concentration of the solution. DOI: 10.1134/S0040601508070069
The makeup water treatment in a steam power plant is performed using a chemical or thermal method. The thermal method of water treatment is largely realized using natural-circulation evaporators of the I type; in addition to makeup water treatment for the main loop, these evaporators are used for concentration of sewage. In this case, the evaporators utilize highly mineralized media. The procedure for analysis of evaporators operating with subcritical mineralization of concentrate and with pure water was developed by a team of specialists of the Chair of Thermal Power Plants of Moscow Power Institute under the leadership of L.S. Sterman. A comparison of heat-transfer coefficients in the evaporator, calculated by this procedure [1] and obtained in an I-600 evaporator under conditions of full-scale experiment [2] is given in Fig. 1. Increasing the mineralization of the working medium of evaporators causes a variation of its thermal properties, heat transfer, and hydrodynamics in boiling. This working medium is a multicomponent solution with sodium sulfate, chloride, and hydroxide as its main components.
One can see in Fig. 2 that a significant rise of pressure drop in the pipe is observed with the concentration of Na2SO4 increasing from 0 to 5 g/kg; with further increase in concentration up to 30 g/kg, the rise of the pressure drop and, therefore, of hydraulic resistance, slows down and stabilizes. Analysis of the data revealed that the increase in salt content of two-phase flow to 5 g/kg is accompanied by a variation in the structure of flow, caused by the increase in the amount of salt ions in the solution and by the emergence of additional ionic bonds. However, the number of ionic bonds increases up to a certain limit defined by the saturation of the interface by hydrated ions of salts and by the construction of “micelle,” which results in the stabilization of pressure drop with increasing concentration of the solution. These data are in good agreement with the results of measurements of the mass level in downward slot as a function of salt content [5] and with the tendencies of the dependence of the velocity of floating up of solitary bubble on the
Investigations of thermohydraulic processes occurring in an evaporator under conditions of high concentration of feedwater revealed special features of its hydraulic and thermal modes compared to operation with low-mineralized medium. However, the hydrodynamics under conditions of boiling of aqueous solutions in a pipe in a wide range of variation of salt content at low velocities and pressures have been hardly studied heretofore. We have determined the loss of pressure under conditions of boiling of aqueous solution of sodium sulfate in a pipe using an updated automated test bed [3]. To confirm the reliability of the resultant data, a series of experiments were performed involving pure water both with and without boiling. The pressure drop under conditions of water boiling in the pipe was calculated in accordance with the well-known recommendations [4]. 565
k × 10–3, W/(m2 K) 4 6 3
5
4
2 1
1 2 3
0
2
4
6
8
10
12
14 ∆t, K
Fig. 1. The calculated and measured overall coefficients of heat transfer in the evaporator as functions of temperature difference. Temperature of secondary steam, °C: (1, 4) 120, (2, 5) 140, (3, 6) 160; (1–3) data of [1], (4–6) calculation by the procedure of [2].
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concentration of aqueous solution, which were revealed in [1].
1.30
We suggest the following correlation for the calculation of pressure loss in a vertical pipe in boiling of aqueous solution of sodium sulfate under the conditions being investigated:
1 2
1.25
3 4
1.20
∆ p Na2 SO4 = ( 1 + K )∆ p H2 O ,
1.15 1.10
6
5
1.00
where 0
5
10
15
20
3.93 × 10 C Na2 SO4 ------------------------------------------2 p –2
1.05 25 30 CNa2SO4
Fig. 2. The ratio of pressure drop in the vertical working section in boiling of aqueous solution of Na2SO4 and pure water as a function of concentration of sodium sulfate with steam quality x = 0.5. Continuous lines indicate calculation by formula (1); flow velocity, m/s: (1) 0.19, (2) 0.17, (3) 0.15, (4) 0.12, (5) 0.10, (6) 0.09.
K
(1)
=
0.4
0.4 '' x 2 ⎛ 7.14 × 10 –5 + ρ ----- ----------- w ⎞ at C ≥ Ccr; ∆ p Na2 SO4 and ⎝ ρ' 1 – x ⎠
∆ p H2 O denote the pressure drop in boiling of aqueous solution of Na2SO4 and pure water, respectively, Pa; ρ" and ρ' denote the density of steam and water on the saturation line, respectively, kg/m3; p is the pressure in the working section, Pa; x is the steam quality; w is the velocity of two-phase flow, m/s; and C Na2 SO4 is the concentration of sodium sulfate in aqueous solution, g/kg. The experimental data are described by correlation (1) with a deviation of 14% or less. For correcting the procedure of analysis of naturalcirculation evaporator at supercritical values of salt content of concentrate, we took into account the dependences for the region of deteriorated heat transfer [1], as well as the equation for pressure drop obtained by Vasin [2] used by us for the stabilization region.
Input data
Preassign w
For all regions
Preassign qi Calculation of hydrodynamics and heat transfer in the ith region
– qi| ≤ ∆q |qcalc i
No
Figure 3 gives the algorithm of thermohydraulic analysis of evaporator by the corrected procedure. For determining the heat-transfer coefficient on the external surface of pipes in the region of deteriorated heat transext fer, the number Re det for the condensate film is calculated by the formula q det L det ext Re det = -----------------, rρ ' ν '
Yes |∆ploss – ∆pheat.sect| ≤ ∆(∆p) Yes Calculation of evaporator average values of coefficients of heat transfer
where qdet is the heat flux in the region of deteriorated heat transfer, Ldet is the length of the region of deteriorated heat transfer, r is the heat of vaporization, and ν' is the coefficient of kinematic viscosity of condensate. The coefficient α det of heat transfer from heating steam to the external surface of pipes of the heating section is determined in accordance with [4], ext
1 ---
Fig. 3. Algorithm of thermohydraulic analysis of evaporator for supercritical mineralization of concentrate.
(2)
ext α det
g ⎞ 3 ext - Re det = 1.18λ 'heat ⎛ --------⎝ ν '2 ⎠
1 – --3
at Re det < 100; (3) ext
heat
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1 ---
ext α det
g ⎞3 = 1.18λ 'heat ⎛ --------⎝ ν '2 ⎠ heat
2.4
(4)
1 --ext 3 0.16Pr heat Re det
ext
ext
--3 63.2Pr heat
1.8 1.6
where λ 'heat , ν 'heat , and Prheat denote the coefficients of thermal conductivity and kinematic viscosity and the Prandtl number of heating steam and g is the acceleration of gravity. In order to calculate heat transfer from the internal surface of pipes of the heating section to the steam– water mixture in the region of deteriorated heat transfer, the Reynolds number for this pipe segment is found, Re det = wdin/ ν det , in
av
(5)
where din is the inside diameter of the pipes of the heating section and ν det is the coefficient of kinematic viscosity of steam–water mixture in the region of deteriorated heat transfer. av
The convection component α det [W/(m2 K)] of the coefficient of heat transfer from the internal surface of pipes of the heating section to steam-water mixture in the region of deteriorated heat transfer is determined by the formula in
in α det
=
λ det ⎛ ρ ' wλ det d in⎞ - ------------------------0.023Pr0.8 ------d in ⎝
ν
⎠
0.8
,
(6)
where Pr is the Prandtl number of steam–water mixture and λdet is the coefficient of thermal conductivity of steam–water mixture in the region of deteriorated heat transfer. In view of thermal resistance of scale R, we have 1 in α det' = -------------------. 1 --------+R in α det
(7)
The overall coefficient of heat transfer in the region of deteriorated heat transfer related to the internal surface of pipes of the heating section kdet in W/(m2 K) is determined as follows: 1 k det = ------------------------------------------ , δ pipe 1 1 -------- + --------- + -------ext ' α det λ w α in det
(8)
where δpipe is the thickness of the wall of a pipe of the heating section and λw is the conductivity coefficient of the pipe wall. THERMAL ENGINEERING
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∆pheat.sect
2.0
- at Re det > 100, × -------------------------------------------------------1 Re det – 100 +
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1.4 0
∆ploss 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 w, m/s
Fig. 4. The determination of the velocity of circulation with the evaporator operating at supercritical mineralization of concentrate.
Therefore, the heat flux in the region of deteriorated calc heat transfer q det , in W/m2 may be calculated by the relation q det = kdet∆tdet, calc
(9)
where ∆tdet is the temperature difference in the region of deteriorated heat transfer. Then, the calculated heat flux in the region of deteriorated heat transfer is compared with the preassigned heat flux. In the case of difference in excess of 0.001 kW/m2, the calculation of heat transfer in the region of deteriorated heat transfer is repeated using the calculated value of heat flux as its new preassigned value. Because both the void fraction and the steam quality in the region of deteriorated heat transfer are close to unity and the heating section yields saturated steam, the pressure loss in this region may be ignored. The overall pressure loss in the circulation loop ∆ploss for water, which is used to find the pressure difference in pipes of the heating section during the evaporator operation with supercritical salt content of concentrate, is determined using Eq. (1) for the region of stabilization of pressure drop, ∆ p loss = --- 1 + 3.93 × 10 / p –2
2
0.4 – 5 ρ '' x 2 × ⎛ 7.143 × 10 ----- -----------w ⎞ ∆ p H2 O . ⎝ ρ' 1 – x ⎠
(10)
The pressure loss in pipes of the heating section is calculated by the following relation: ∆ p heat. sec t = 1 – 30.5 ( ρ '' w '' ) × ( H heat. sec t + h heat. sec t )
– 4.19
1.81
p
– 0.27
ρ ' gH heat. sec t ,
(11)
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k, W/(m2 K) 2500 5
6 7 8 9 10
4
2000 1500 1000 500
3 2
5
7
1
9
11
13
15
17 ∆t, K
Fig. 5. The overall coefficient of heat transfer in the evaporator as a function of temperature difference. Calculated data, tsec, °C: (1) 115, (2) 125, (3) 135, (4) 145, (5) 155; experimental data of [1, 2], tsec, °C: (6) 110–120, (7) 120– 130, (8) 130–140, (9) 140–150, (10) 150–160.
where w" is the velocity of steam in a pipe of the heating section, Hheat.sect is the mass level of the working medium of the evaporator, and hheat.sect is the height of pipes of the heating section. Then the pressure drops calculated by relations (10) and (11) are compared and the velocity w is found from the condition |∆ploss – ∆pheat.sect| ≤ 0.01. This is graphically illustrated by Fig. 4. The calculated values of the velocity of circulation at a high mineralization of the concentrate are low and amount to 0.01–0.1 m/s. The average heat flux qav in kW/m2 is determined by the formula q ec L ec + q int.ht L int.ht + q det L det -, q av = ---------------------------------------------------------------------L ec + L int.ht + L det
(12)
where qec and qint.ht denote the heat flux in the economizer region and in the region of intensive heat transfer, respectively, and Lec and Lint.ht denote the length of economizer region and of the region of intensive heat transfer. The average calculated temperature difference is ∆t ec L ec + ∆t int.ht L int.ht + ∆t det L det -, ∆t av = -----------------------------------------------------------------------------L ec + L int.ht + L det
(13)
and the average calculated overall coefficient of heat transfer in the evaporator in kW/(m2 K) is calc
k av = qav/∆tav.
(14)
If the measured overall heat-transfer coefficient obtained by the results of thermal tests of evaporator is related to the conditional area of heat transfer surface Fcond and to the difference between the saturated temperatures of heating steam theat and secondary steam tsec, it will be
kcalc, W/(m2 K) 2500 2250 2000 1750 1500 1250 1000 750 500 250 0
250
500
5%
–1
0% 0% +1
–1
5%
+1
750
1000
1500
1250
2000 1750 2250 kexp, W/(m2 K)
Fig. 6. Comparison of calculated and measured overall coefficients of heat transfer in the mode of evaporator operation at supercritical mineralization of concentrate.
cond
k av
πd in ( L ec + L int.ht )n pipe q av -, = --------------------= ---------------------------------------------------F cond t heat – t sec
(15)
where npipe is the number of pipes of the heating section. Figure 5 gives a comparison of the overall coefficients of heat transfer calculated by the procedure suggested in this paper with the data of a full-scale experiment involving the I-600 evaporator of the Saransk cogeneration power plant [1, 2]. The presence of maxima in Fig. 5 is due to the change of thermohydraulic mode of evaporator operation. A comparison of calculated and experimentally obtained overall coefficients of heat transfer is given in Fig. 6. The disagreement between them does not exceed ±15%, which confirms the validity of choice of the scale of circulation velocities for modes with supercritical salt content of concentrate of evaporators. CONCLUSIONS 1. As the salt content in aqueous solution of Na2SO4 increases, the pressure drop in boiling increases in the range from 0 to 20 g/kg and then stabilizes. An increase in the pressure drop in boiling of aqueous solution of Na2SO4 to 30% is observed under the investigated conditions. The effect of salt content on pressure drop under conditions of boiling of aqueous solution of Na2SO4 shows up to a greater extent at increased velocities of circulation. 2. The suggested improved procedure for analysis of hydrodynamics and heat transfer in boiling-type evaporators for supercritical mineralization of concentrate enables one to take into account the variation of thermohydraulic mode in the evaporator. THERMAL ENGINEERING
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REFERENCES 1. A. S. Kartsev, “Investigation of the Effect of Mineralization on the Hydrodynamics and Heat Transfer in Boiling-Type Evaporators,” Cand. Sci. (Tech.) Dissertation (Moscow, Moscow Power Institute, 2004) [in Russian]. 2. V. A. Vasin, “Investigation of Thermal and Hydrodynamic Processes and Development of Procedures for Analysis of Flow-Over Devices and Evaporators,” Extended Abstract of Cand. Sci. (Tech.) Dissertation (Moscow, 1993) [in Russian].
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3. A. S. Sedlov, Yu. A. Kuzma-Kichta, and Yu.A. Shkondin, “Investigation of Thermal Processes at Low Mass Flowrates and Refining of the procedure for Thermal Design of Evaporators,” Teploenergetika, No. 9, 38–42 (1998) [Thermal Engineering, No. 9, 750–754 (1998)]. 4. A. M. Kutepov, L. S. Sterman, and N. G. Styushin, Hydrodynamics and Heat Transfer in Vaporization (Vysshaya Shkola, Moscow, 1986) [in Russian]. 5. N. N. Demidov, E. K. Golubev, and A. G. Chernov, “The Static and Dynamic Characteristics of Surface-Type Evaporators in Variable Modes of Operation,” Energomashionstroenie, No. 3, 24–26 (1980).