.AixLib.Fluid.MassExchangers.MembraneBasedEnthalpyExchangers.BaseClasses.Functions.CoefficientCrossToCounterFlow

Information

This function calculates an coefficient to derive the heat/mass transfer of a cross-flow enthalpy exchanger out of the heat/mass transfer of a counter-flow enthalpy exchanger.

The coefficient calculation is based on the effectiveness correlations for the NTU-Method[1].

The effectiveness of a counter-flow heat exchanger can be expressed as:

ε = (1 - exp[- NTU (1 - C_r )]) ⁄ (1 - C_r exp[- NTU (1 - C_r )])

for (C_r < 1)

ε = NTU ⁄ (1 + NTU)

for (C_r = 1)

With

C_r = (ṁ c_p )_min ⁄ (ṁ c_p )_max

The effectiveness of a cross-flow heat exchanger can be expressed as:

ε = 1 - exp[(exp(- NTU ^0.78 C_r ) - 1 ) ⁄ (NTU ^-0.22 C_r )]

By dividing the correlation for the cross-flow heat exchanger through the correlation for the counter-flow heat exchanger it is possible to derive the efficiency of a cross-flow heat exhcanger from the efficiency of a counter-flow heat exchanger.

C = ε_cross ⁄ ε_counter = f(NTU,C_r)

The coefficient C was evaluated for different NTU and C_r . It has shown, that for C_r near to 1 the coefficient can be approximated through a polynom of third degree:

C = -9 · 10 ^-5 NTU ³ + 0.0023 NTU ² - 0.0207 NTU + 0.956

[1]: Incropera, F.P.; De Witt, D.P.; Bergman, T. L.; Lavine, A. S. : Fundamentals of Heat and Mass Transfer ; 6th Edition; 2007; John Wiley & Sons, Inc.

Interface

function CoefficientCrossToCounterFlow
  input Real NTU "number of transfer units";
  output Real coeCroCou "coefficient for reduced efficiency in quasi-counter flow";
end CoefficientCrossToCounterFlow;

Revisions

• August 21, 2018, by Martin Kremer:
  First implementation.