3.THE PERFORMANCE CURVES OF THE CROSS-FLOW COOLING TOWERS

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1 3.THE PERFORMANCE CURVES OF THE CROSS-FLOW COOLING TOWERS Longin IONESCU... Reader Ph. D. - UPB Gheorghe LAZAROIU - Lecturer Ph. D. - UPB A Iosif BILCAN,., P. Eng..!e ISPE l.introduction Cooling towers of conventional thermal power plants are currently used, above all in the case of the closed or mixed circuit cooling. An inefficient operation. of the cooling process in the tower results in a continuous decrease in the power generated by the plant, therefore a low efficiency entailing financial repercurmons. For any type of cooling tower the efficiency curves can be raised, as they are useful for surveying the variation of water and air parameters in its active zone. The present paper approaches the crossflow cooling towers involving a bidimensional flowing model, in which water circulates vertically from top to bottom and the air horizontally (through the active zone). In this case the parameters of the heat earners vary both vertically and horizontally... The calculation model for the efficiency curves The calculation method is based on the principle of the enthalpy difference as potential [I], consisting in determining, in every particular, the water temperature and air enthalpy in the tower. As the flowing model is bidimensional, practically the elements of a matrix will be assessed; these elements are three-size vectors, T, Na, Hs, respectively. Those sizes mean the following: - T [ C] is the water temperature in the point under survey; -Na [kj/kg of humid air] is the air enthalpy; -Hs [kj I kg ofhumid air] is the air enthalpy at saturation and water temperature. The pattern for the matrix used in the analysis of the cross-flow cooling towers operation bears n lines and m columns. To calculate the following hypotheses are made []: 1. On the first line of the matrix the water temperature is considered to be constant, therefore also the saturation air enthalpy is constant at the water temperature, and only the air enthalpy varies;.0n the first column of the matrix the air enthalpy is considered constant, while the other parameters vary. The calculation algorithm is the following: a) For the first line of the matrix:.. the water temperature at the tower inlet is known, as well as the saturation air enthalpy at the water temperature, respectively; - the air enthalpy is assessed by a recursive relation. b) For the first column of the matrix: - the air enthalpy at tower inlet is known; - the other parameters are assessed by a recursive-iterative calculation as the saturation air enthalpy depends on the water temperature; 39

2 c) For the points inside the matrix: the parameters on the first column, the first line, respectively, are known; - the parameters in the points inside the matrix are assessed by a recursive-iterative calculation. The equations and procedure for the thorough analysis of the water and air parameters in the cross-flow cooling tower are: 1.F or the first line of the matrix the hot water temperature is introduced and the saturation air enthaply corresponding to this temperature is assessed from the humid air diagrams. The average enthaply, for the AX calculation pitch and the matrix meters (m, n), is: AX H (m - l n) - --(H (m - 1 n) + H (m n) - 11 (m -- 1 a '? s ' s' a.., n)'\ 'J H ( m, n ) = --= M (1) For the first column of the matrix the air enthalpy at tower inlet is known. The water temperature and saturation air enthalpy, at the water temperature, can be calculated by the relation: t{m,n)= t{m,n-1)- - /J.Y [Hs(m,n-l)-Hs(m,n)-H(m,n-1)-H(m,n)} ( ) cp where: - cp [kj/kg C] is the specific water heat; - A Y is the calculation pitch. Initially the water temperature is assessed. The first attempt may be: t(m,n)= t(m,n-1) t(m,n-l)-t (4) Corresponding to this temperature Hs(m, n) results. Then it is introduced in equation [] and the temperature is calculated. If t assessed = t calculated, the following point is calculated, and if not, calculating is resumed, as the new temperature assessed is the average between the value assessed initially and the calculated one. 3.F or calculating the points inside the matrix, the air enthalpy is calculated: H(m,n)=H(m-1,n)+ AX (4) +-[Hs (m-1,n)-h(m-1,n)+hs (m,n)-h(jl\n)] and water temperature, t (m,n)= t(m,n-1)- /J.Y (5) - l cp[hs(m-l,n)-h(m-l,n)+h 5 (m,n)-h(m,n)] The difference H (m, n) - H {m, n) = Hs (m-1,n) - H (m-1,n), is assessed, as it is introduced in equations ( 4) and ( 5). For the value t (m. n), resulted from the equation (5), Hs (m, /) is assessed. Hs (m, n) - H (m,n) is calculated and compared with the value assessed. If the difference between the two values is not included in the tolerance interval, the new value assessed may be the average between the value previously assessed and the calculated one. The equations presented above, as well as the calculating procedure were introduced by an algorithm into the computer. The calculations can be made in a computer as the calculating relations are given under a recursive fonn, considering a dimensionless pitch, arbitrarily chosen. 40

3 3.Results and conclusions To assess the distribution of water temperature and air enthaply it is considered that the water temperature at the tower inlet is 8 [ C] and the water temperature at the tower outlet is 0 [ C]. It results that the air enthaply, calculated according to formula [3 ], at the tower inlet is [kj/kg] and at tower outlet is [kj/kg]. Fort (m, n) == t (I, I) = t z = 8 [ C] results Hs (m, n) = Hsz = 90.5 [kj/kg]. Figures 1 and, resulted from calculations, may help surveying the variation of water and air parameters in the active zone of a cross-flow cooling tower. Figure 1 shows the water temperature variation in the active zone, depending on the "relative height" and "relative ray 11 If one considers a rectangular axis system with the positive sense of the ordinate in the direction of the water flow and the positive sense of the abscissa in the direction of the air flow, then the "relative height'' represents the ratio between the current ordinate of the point considered and the total height of the active zone (for instance, considered HJ= 7.85 m) and the "relative ray" represents the ratio between the abscissa of the point considered and the ray of the cooling tower opposite the active zone (R=3.15n1). By analysing the curves one notices that the water temperature decreases approximately linearly in the active zone of the cross-flow cooling tower. This variation is larger, as it is obvious, on the vertical rather than on the horizontal (Fig. I).,_..., u 0 i (!) (!) """ 4 E.B 3 (1) «1 i 1 c Relative ray [%] 0 [%} [%] 4-40 [%} 5-50 [%] 6-60 [%) 1-70 [%) 8 - B 0 [%] g [%] 1 O 1 00 [% 1 0,. 19 l Relative height [%] BO Fig.1 Water temperature distribution in the active zone of the cooling tower 41

4 To assess the water temperature in a point inside the active zone situated, for instance, at h = 5. l [ m] from inlet (on the vertical) and atr = 6 [ m] from the tower edge (air input), the following is to be done: - calculating the "relative height": _I'_! 100 = SJ 100:;::: 65 [%} H calculating the "relative ray": 100 ::: = 8 [%j R from the abscissa point 65 [%] (point A) a vertical goes up to meet the curve of 8 [%] (point B); - from point B a perpendicular is drawn on the ordinate, resulting in point C, where the water temperature is read, t =.9 [ C]. The saturation air enthalpy at water temperature is read analogously with the water temperature reading namely : - from the abscissa point 65 [%](point A) a perpendicular goes up to meet the 8 [%) curve (point B); - from point B a perpendicular is drawn on the ordinate (point C), where the saturation air enthalpy is read: Hs 64.9 [kj/kg] Finally one can draw the conclusion that this study method makes it possible, by its approach, to analyse step by step the heat transfer taking place in the cross-flow cooling tower, in other words, makes it possible to-sense the essence of the process in the active zone of the tower, which is a great advantage ,.._, 85 "--' ;;;...) ;9 c:: <l) lo-i. (tj 0.+j ro 9 r/)_ I 70 l c l 3 Relative ray [%] - 0 [%] - 30 [%] [%] 5-50 [%] 6 - so [%] [%] B - 80 [%] [% J [%] Relative height [%] Fig. Distribution of saturation air enthalpy 4

5 1. References. ZIVI, S.M.; BRAND, BURCE B. - An Analysis of the Cross-Flow Cooling Tower, 3. Refrigerating Engineering, HALLETT, G.F. - Performance Curves for Mechanical Draft Cooling Towers, Jownal of Engineering for Power, Oct LECA, A.; PRISECARU, L - Proprietati termofizice i tennodinamice: solide, lichide i gaze, Vo!., Ed. Tehnica, Bucure}ii,