Macro Heat Exchanger Model Theory
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Some salient features of Macro Heat Exchanger Model Theory. Macro Heat Exchanger Model Theory --------------------------------- A. *************** Givens: 1. Heat Exchanger Performance Curve: NTU_full (mdot_air_full) 2. NTU-E Curve Even if full exchanger is multi-pass, a macro is always single-pass. So NTU-E of single-pass can be applied on a heat exchanger that has multiple passes. NTU - Number of Transfer Units E - Effectiveness B.*************** Determining NTU_macro The NTU_full (mdot_air_full) curve is for the full heat exchanger and does not directly apply to the macro. However, using simple ratios, we can relate NTU_macro to the NTU_full curve. NTU_macro = NTU_full * A_macro/A_full * Cmin_full/Cmin_macro where A is the surface area at which heat transfer takes place, which would be the fins, tubes, etc. For homogeneous core, the ratio of the areas has to equal the ratio of the volumes: A_macro/A_full = V_macro/V_full. Also, NTU_full has to be evaluated at local flow rate (mdot_macro * Af_total/Af_full), where Af is the frontal inlet let area. NTU_macro = NTU_full * V_macro/V_full * Cmin_full/Cmin_macro NTU_macro = V_macro/V_full * Cmin_full/Cmin_macro * NTU_full C. *************** Given NTU_macro, calculate effectiveness of the macro using NTU-effectiveness relations. E_macro = f (NTU_macro, R_macro), where R_macro = Cmin_macro/Cmax_macro D. *************** Calculate heat rejection of the macro. Q_macro = Cmin_macro * E_macro * ( Tcoolant-in_macro - Tair-in_macro) E. *************** Calculate heat rejection/added for each cell within a macro. Q_cell = Q_macro * Vcell/Vmacro where Vcell, and Vmacro are volumes of cell and macro, respectively. Notes: -To properly account for variable density, mdot, not velocity, is used. -The above assumes fixed coolant flow rate. -Only one performance curve is used for a single coolant flow-rate is used. -If it is a multi-pass heat exchanger, use multi-pass NTU-E relation to convert raw heat exchanger data into NTU_full (mdot_air_full) for Step A. -The macro always uses single-pass NTU-E relation, where both fluid are unmixed. The curve is: E = 1-exp[(1/Cr)(NTU)^.22{exp[-Cr(NTU)^.78] - 1}], |
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