cmn_lecture.2 CAD OF DOUBLE PIPE HEAT EXCHANGERS

Transcription

1 cmn_lecture.2 CAD OF DOUBLE PIPE HEAT EXCHANGERS A double pipe heat exchanger, in essence, consists of two concentric pipes, one fluid flowing through the inner pipe and the outer fluid flowing countercurrently through the annular space between the two pipes. These exchangers are usually constructed in the form of hairpins. A hairpin consists of two sets of concentric pipes, the inner pipes being connected through a return bend (as shown in figure-2.1). A number of such hairpins can be connected in series. Figure (2.1) shows two such hairpins connected in series. Figure (2.1) Apart from heat transfer surface, the pressure drop through the exchanger is equally important design parameter since this decides the operating cost of the exchanger. In the case of double pipe heat exchangers, the pressure drop in the inner pipe, (-ΔP t ), can be estimated from the modified form of Fanning s equation:... (2.1) where, (-ΔP r ) = additional pressure drop due to flow reversal in return bends (taken equal to one velocity head per return bend) G t = mass velocity of inner pipe fluid, kg/m 2.s... (2.2)

2 ... (2.3) m = mass flow rate of inner pipe fluid, kg/s N rb = number of return bends... (2.4) It can be seen from figure (2.1) that when N hp = 2 (number of hairpins in series is two), the number of return bends (N rb ) is three. Therefore, if the number of hairpins used in series is N hp, then, the number of return bends N rb = (2N hp -1). The friction factor (f) depends on the Reynolds number (Re t ) and is given by,... (2.5) where,... (2.6) For nonisothermal flow through commercial pipes that have a given degree of roughness inside, the correlation constants (K and n) are given below in Table (2.1). TABLE 2.1 Correlation constants of Equation (2.5) for Nonisothermal flow through Rough commercial pipes Reynolds number K n In equation (2.1), L e is the total effective length of the exchanger. If L hp is the effective length of each hairpin, then... (2.7) By effective length, we mean the total pipe length used for constructing the hairpin, but excluding the return bend.

3 The annulus side pressure drop (pressure drop for flow of annulus fluid) may be estimated from a correlation similar to equation (2.1): where, G a = mass velocity of annulus fluid, kg/m 2.s... (2.8) m a = mass flow rate of annulus fluid, kg/s... (2.9)... (2.10) μ fa, μ wa = viscosity of annulus fluid at bulk temperature (T am or T cm ) and that at outer surface temperature (t wo ) of inner pipe respectively. D e = equivalent diameter of annulus ( for fluid flow ) The above equivalent diameter (D e ) differs from D e defined in equation (1.28) since D e is based on total wetted perimeter, whereas D e was based on wetted (and also heated) perimeter. Total wetted perimeter includes inside wetted perimeter of outer pipe as well. Thus,... (2.11)... (2.12)... (2.13) The annulus friction factor (f a ) depends on annulus Reynolds number (Re a ), as... (2.14) where,... (2.15) The values of correlation constants (K,n) can be obtained from Table (2.1) itself, but based on the magnitude of annulus Reynolds number, Re a.

4 If the inner pipe pressure drop happens to exceeds the maximum permissible limit, then a series-parallel arrangement of hairpins may be employed. A typical case is illustrated in figure (2.2). Here, the inner pipe fluid is divided into two streams (n t = 2) and each stream traverses only (N hp /n t ) number of hairpins. Here, (N hp /n t ) = (2/2) = 1.0. To note that though the heat transfer surface is halved, since the flow rate of the stream is also halved (equal to m/2), the outlet temperature of each stream shall be t 2 itself. In other words, the inner pipe fluid gets heated / cooled to the same temperature as in the series arrangement. However, since the flow rate (and thereby the mass velocity) of the fluid is halved, the pressure drop (see equation 2.1) becomes one-fourth. Also, since the total length of the travel of the fluid (L e ) is also halved, the pressure drop reduces to almost one-eighth of that in series arrangement. Figure 2.2 : Series parallel Arrangement of Hairpins However, unlike in series arrangement, the effective temperature difference, (-ΔT)(eff), shall not be equal to the logarithmic mean temperature difference, (-ΔT) ln, in a series-parallel arrangement. If the inner pipe fluid is the cold fluid and it is divided into n t streams, then (- T ) (eff) = ( 1 K P )( K R 1) ( T 1 t 1 ) / ( DIN )... (2.16) DIN = n t K R ln [ {(K R 1)/K R } ( 1/ K P ) n + ( 1/K R )] (2.16a) where,... (2.17)

5 ... (2.18)... (2.19) ΔT c = temperature difference between fluids at the cold end of the exchanger (see equation 1.37) ΔT(max) = maximum temperature difference... (2.20) Δt c, Δt h = temperature difference of cold fluid and that of hot fluid respectively. In the present case,... (2.21)... (2.22) If the inner pipe fluid is the hot fluid and that is divided into n t streams, then (- T ) (eff) = ( 1 K P ) ( 1 - K R ) ( T 1 t 1 ) / ( DIN )..(2.23) DIN = n t ln [ (1 - K R ) ( 1/ K P ) n + K R ] (2.23a) where,... (2.24)... (2.25) ΔT H = temperature difference between fluids at the hot end of the heat transfer surface (see equation 1.38) To note that in this case,... (2.26)... (2.27)

6 It is important to note that K P and K R are defined differently in equations (2.16) and (2.23). Also, the definition of K R is different from that given in equation (1.36).