Multiple pass and cross flow heat exchangers

Transcription

1 Multiple pass and cross flow heat exchangers Parag Chaware Department of Mechanical Engineering of Engineering, Pune Multiple pass and cross flow heat exchangers Parag Chaware 1 / 13

2 Introduction In order to increase the surface area for convection relative to the fluid volume, it is common to design for multiple tubes within a single heat exchanger. Figure: 1-2 pass shell and tube type of heat exchanger Multiple pass and cross flow heat exchangers Parag Chaware 2 / 13

3 Corrected LMTD I In shell and tube exchangers, the flow pattern is a mixture of cocurrent, counter current, and crossflow, so the LMTD does not directly apply. Instead, a corrected LMTD must be used. The appropriate mean temperature difference can be obtained by introducing a correction factor F to log mean temperature difference with same hot and cold fluid temperatures in such cases T lm = F T lm Q = UA(F T lm ) The correction factor F depends on geometry of heat exchanger and inlet and outlet temperatures. The value of F varies from 0 to unity. Multiple pass and cross flow heat exchangers Parag Chaware 3 / 13

4 Corrected LMTD II The correction factor F for a heat exchanger is a measure of deviation of T lm the from the corresponding values for the counter-flow case. The value of F can be obtained by plots given by Kern, Jakob. In these plots the abscissa is dimensionless ratio P which represents the thermal effectiveness of tube side fluid. It is expressed as P = t o t i T i t i where T represents to shell side temperatures, t represents the tube side temperatures. Parameter R referents the heat capacity ratio, is expressed as, R = m hc p,h or T 1 T 2 m c C p,c t 2 t 1 Multiple pass and cross flow heat exchangers Parag Chaware 4 / 13

5 Corrected LMTD III Figure: Correction factor chart for cross flow heat exchanger Multiple pass and cross flow heat exchangers Parag Chaware 5 / 13

6 NTU Method I When outlet temperatures of the heat exchanger is not known for given mass flow rate and size of the heat exchanger, The LMTD method requires lot of iterations and is tedious to use Kays and London invented a method in 1955 called the NTU method, which can be used for such analysis. This method is based on a dimensionless parameter called the heat transfer effectiveness ɛ, defined as; ɛ = Q = Q max Actual heat transfer Maximum possible heat transfer Effectiveness relations of the heat exchangers typically involve the dimensionless group UAs / Cmin. This quantity is called the number of transfer units NTU and is expressed as; Multiple pass and cross flow heat exchangers Parag Chaware 6 / 13

7 NTU Method II NTU = UA s C min NTU is proportional to As. Therefore, for specified values of U and Cmin, the value of NTU is a measure of the heat transfer surface area As. Effectiveness relations have been developed for a large number of heat exchangers. The effectiveness of some common types of heat exchangers are also plotted, which can be used for analysis of heat exchanger. Multiple pass and cross flow heat exchangers Parag Chaware 7 / 13

8 Parallel and counter flow heat exchanger Figure: Effectiveness Chart for Parallel and counter flow heat exchanger Multiple pass and cross flow heat exchangers Parag Chaware 8 / 13

9 Cross flow heat exchanger Figure: Effectiveness chart for cross flow heat exchanger Multiple pass and cross flow heat exchangers Parag Chaware 9 / 13

10 Exercise I In a heat exchanger, hot fluid enters at 180 C and leaves at 118 C. The cold water enters at 99 C and leaves 119 C. Find LMTD, NTU effectiveness in following cases; i) One shell pass and multiple pass tube ii) Two shell pass and multiple pass tube iii) Cross flow both fluids unmixed iv) Cross flow cold fluid unmixed T h,i = 180, T h,o = 118, T c,i = 99, T c,o = 119 For counterflow arrangement θ 1 = T h,i T c,o = 61 C θ 2 = T h,o T c,i = 19 C Multiple pass and cross flow heat exchangers Parag Chaware 10 / 13

11 Exercise II LMTD = θ 2 θ 1 θ 2 /θ 1 = 36 C 1 One shell pass and multiple pass tube a) P = t 2 t = T 1 t = 0.25 R = T 1 T = t 2 t = 3.1 From charts F = 0.88, T lm = = 28.8 C b) Effectiveness ɛ = T h,i T h,o = T h,i T c,i Multiple pass and cross flow heat exchangers Parag Chaware 11 / 13

12 Exercise III c) NTU C = Cmin /C max = From charts for C= and ɛ = NTU = Two shell pass and multiple pass tube a) P = t 2 t = T 1 t = 0.25 R = T 1 T = t 2 t = 3.1 From charts F = 0.85, thus T lm = = 30.6 C Multiple pass and cross flow heat exchangers Parag Chaware 12 / 13

13 Exercise IV b) Effectiveness c) NTU ɛ = T h,i T h,o = T h,i T c,i C = Cmin /C max = From charts for C= and ɛ = NTU = 1.7 Multiple pass and cross flow heat exchangers Parag Chaware 13 / 13