APPENDIX C Optimization of Rectangular Offset-Strip, Plate-Fin Surfaces

Transcription

1 APPENDIX C Optimization of Rectangular Offset-Strip, Plate-Fin Surfaces Directions in which to move C.1 Fine-tuning of rectangular offset-strip fins The generalized Manglik & Bergles (1990) correlations for heat transfer and flow friction allow exploration of the effect of varying surface geometries on final core size. For the same thermodynamic performance, the optimum surface geometry is sought for the following geometric parameters: minimum block volume (overall dimensions) minimum block length minimum frontal area minimum plate surface Choice of exchanger A two-stream compact plate-fin heat exchanger with single-cell rectangular offsetstrip fin surfaces on each sides was chosen as the model. In operational mode 1, the hot fluid was made the high-pressure fluid (corresponding to a cryogenic exchanger). In operational mode 2, the hot fluid was made the low-pressure fluid (corresponding to a gas turbine recuperator). The only change in operational parameters between the two modes will be to swap the inlet pressure levels of the fluids. Pressure loss on one side of the exchanger was kept constant while the pressure loss on the other side was allowed to float and find its correct level at the design point. This search arrangement was applied to both sides of the exchanger. In design it is best to seek coincidence of pressure loss curves on the direct-sizing plot, which makes both pressure losses controlling. Hence only performance characteristics for controlling sides are given in the figures which follow. LMTD reduction for longitudinal conduction was not applied as interest is for trends at this time. Exchanger specifications Thermal parameters A 200 kw contraflow exchanger with an effectiveness of 0.86 was chosen with hot inlet temperature T h \ = K and cold inlet temperature T c2 = K. Advances in Thermal Design of Heat Exchangers: A Numerical Approach: Direct-sizing, step-wise rating, and transients. Eric M. Smith Copyright 2005 John Wiley & Sons, Ltd. ISBN:

2 406 Advances in Thermal Design of Heat Exchangers Pressure levels (which were swapped to complete the investigation) were 1.1 and 6.0 bar. One outlet temperature was forced using the effectiveness of 0.86, and a forced mean specific heat was obtained from spline-fits of physical property data. One forced mass flowrate was then found using the thermal duty Q = 200 kw. Then an arbitrary mass flowrate ratio of 1.15 was selected, to produce the missing mass flowrate. Parameters still required were an outlet temperature and mean specific heat of one fluid. The outlet temperature was iterated and an estimated mean specific heat obtained from a spline-fit until the required thermal duty of 200 kw was matched. Surface geometries The effects of changing fin thickness might be explored, but it was thought that the credibility of the Manglik & Bergles correlations might be pushed too far. Keeping cell width flow area constant it was found that varying high-pressure fin thickness had virtually no effect on surface area. Small low-pressure fin thickness helped minimize surface area. The result is inconclusive because the work of Kelkar & Patankar (1989) and Hesselgreaves (1993) needs further study, however, it is to be noted that thin fins also cause less longitudinal conduction. Surface geometry was varied according to the following scheme (Table c.l). Nominal sizes for both sides: b = 5.00 (mm), c = 2.0 (mm), x = 6.00 (mm) Plate material Plate thickness, mm tp = 2.00 Fin thickness, mm tf = 0.15 Density Al alloy, kg/m 3 p = Observations concerning all dimensional parameters stem from validity of the Manglik & Bergles correlations, and the scatter of data should be noted in Figs 4.5 and 4.6. Also, the approach of varying one parameter at a time and then selecting a combination of these to optimize against a particular requirement may find the Table C.I Range of geometrical parameters, variation about nominal - (one dimension at a time) Plate spacing b (mm) Cell pitch c (mm) Strip length x (mm)

3 Optimization of Rectangular Offset-Strip, Plate-Fin Surfaces 407 general area of best performance, but may miss a true optimum configuration. Automatic optimization techniques can encounter the problem of changing limits on Reynolds number validity during iteration, which may cause problems. Here a manual search was used. C.2 Trend curves Primary design parameters of interest are block volume, block length and block frontal area. Secondary parameters include block mass, block porosity, plate surface area and total surface area. The objective is to indicate the most profitable direction in which changes in the local geometry of rectangular offset-strip fins may be made when optimizing thermal performance of an exchanger. The computational scheme employed covered both single- and double-cell ROSF geometries. Graphs were generated by changing the dimensions of plate spacing '&', cell width 'c' and strip length V, one at a time while the other values remained at a median position. Thus the reader should not expect to find that selection of three individually-optimized parameters will lead to a fully-optimized design. To obtain a complete picture of the situation, readers should refer to the set of 20 figures presented in Smith (1997, 99). Cool et al. (1999) provide a complete set of search parameters using generic algorithms, but their results are presented in scatter plots. There has been no attempt to explore the effect of varying fin thickness on exchanger performance. Although this could have been done, it might have pushed the Manglik & Bergles correlations just a little too far. However, there is no reason why such work should not be done so that results obtained can be compared with other papers directly concerned with the effect of fin thickness on exchanger performance (Xi et al., 1989). Minimization of block volume In the study of block volume there emerged from the complete set of four figures (Smith, 1997) clear-cut evidence that cell width, c, could be minimized on both sides without affecting other parameters. This implied a minor pressure loss penalty, which could easily be accommodated through larger values in cellheights b and strip-lengths x. Minimization of block length The same situation applies to block length as with block volume, if we ignore the behaviour of strip-length x. Minimization of block mass Here the situation is less clear, for a reduction in cell width c with a modest increase in cell-height b on one side, is coupled with an increase in cell-width c and a decrease of cell-height b on the other side. There is also an indication that a marginally higher value is required for cell-widths (c = 1.5 mm instead of 1.0 mm).

4 408 Advances in Thermal Design of Heat Exchangers Minimization of frontal area Increasing the value of length L would reduce block frontal area. There is evidence that cell-width c can be reduced on both sides, with the option of decreasing cellheight b on one side while maintaining a more or less constant b on the other side. For all of the above options, constraints in the selection of plain rectangular surfaces may be seen in Fig How to use the graphs Select the rectangular offset-strip, plate-fin geometry that you think may be suitable, and plot the values of (b, c, x) on the graphs. Now examine slopes of the graphs and from the ordinate and abscissae scales determine the direction in which it would be beneficial to alter the original surface specification. Fig.C.l Block volume versus (b, c, x) Fig.C.2 Block length versus (b, c, x) Fig.C.3 Frontal area versus (b, c, or) Fig.C.4 Plate surface area versus (b, c, x)

5 Optimization of Rectangular Offset-Strip, Plate-Fin Surfaces 409 C.3 Optimization graphs Sample trend curves (without pressure loss levels) are presented showing how block volume, block length, frontal area, and plate surface change as rectangular offset-strip-fin parameters (b, c, x) are varied. It is somewhat unexpected that changing strip length (x) hardly affects block volume or plate surface area, although it does affect block length and frontal area. For minimum block volume large values of plate spacing (b) and small values of cell pitch (c) are appropriate. More detailed discussion of optimization of plate spacing and cell pitch is to be found in Chapter 4 and Appendix J. Analysis of laminar flow heat transfer along a flat plate predicts infinite heattransfer coefficients at the leading edge, and a mean value of heat transfer over the plate to be twice that calculated at the trailing edge. Further investigation of ROSF geometries might be worthwhile. C.4 Manglik & Bergles correlations In the notation of this text:,.,, cell pitcn pitch /c\ Manglik & Bergles a = : = (-1 olates plates pacing oacine \b/ \b) fin thickness ftf\ Manghk & Bergles 8 = : = I I stop length' \xj fin thickness //A Manglik & Bergles y = = I I cell pitch \cj Flow friction: / = (Re) («) (8) (y) x [ x 10-8 (Re) (a) a920 (5) (y) a236 ] ai Heat transfer j = (Re) («) (S) (y) x [ x 10-5 (Re) L340 (a) (8) a456 (y) ] 0-1 where the Colburn y'-factor is 7 = St Pr 2 / 3. References Cool, T., Stevens, A., and Adderley, C.I. (1999) Heat exchanger optimisation using genetic algorithms. In 6th UK National Heat Transfer Conference, Institution of Mechanical Engineers, London.

6 410 Advances in Thermal Design of Heat Exchangers Hesselgreaves, J. (1993) Optimising size and weight of plate-fin heat exchangers. In Proceedings of the 1st International Conference on Heat Exchanger Technology, Palo Alta, California, February (Eds R.K. Shah, and A. Hashemi), Elsevier, Oxford pp Kelkar, K.M. and Patankar, S.V. (1989) Numerical prediction of heat transfer and fluid flow in rectangular offset-fin arrays. Int. J. Comp. Method., Pan A, Applied: Numerical Heat Transfer, 15(2), March, (Also, ASME Publication HTD-Vol.52, pp ) Manglik, R.M. and Bergles, A.E. (1990) The thermal hydraulic design of the rectangular offset-strip fin compact heat exchanger. Compact Heat Exchangers - a Festschrift for A.L. London (Eds R.K. Shah, A.D. Kraus, and D. Metzger), Hemisphere, New York, pp Smith, E.M. (1997, 99) Thermal Design of Heat Exchangers, John Wiley & Sons, Ltd, Chichester. Reprinted with corrections Xi, G., Suzuki, K., Hagiwara, Y., and Murata, T. (1989) Basic study on the heat transfer characteristics of offset fin arrays. (Effect of fin thickness on the middle range of Reynolds number.) Trans. Japan Soc. Mech. Engrs, Pan B, 55(519), November, Bibliography Manglik, R.M. and Bergles, A.E. (1995) Heat transfer and pressure drop correlations for the rectanglar offset strip-fin compact heat exchanger. Exp. Thermal Fluid Sci. 10,