Approximate expressions for the logarithmic mean void fraction

The logarithmic mean void fraction (LMe) was introduced in literature by El Hajal et al. (El Hajal, J., Thome, J. R., Cavallini, A., Condensation in Horizontal Tubes, Part 1: Two-Phase Flow Pattern Map, International Journal of Heat and Mass Transfer 46 (2003) 18, pp. 3349-3363). In the present study, approximate expressions for the logarithmic mean void fraction (LMe) will be presented because the original formula for the computation of the logarithmic mean void fraction in finite precision floating-point arithmetic may suffer from serious round-off problems when both differences (eh and era) are very close to each other. This situation corresponds to very low values or very high values of mass quality (x). The analogy between the logarithmic mean temperature difference (DTLM or LMTD) in heat exchangers and the logarithmic mean void fraction (LMe) in two-phase flow will be used. These approximations of the LMe can be applied in the computational studies.