Phenomenological modeling: Present and future Comment 1

Abstract

Professor Launder's position paper on phenomenological modelling is an impressive survey and valuable account of the status of second-moment closure, principally as applied to Reynolds Stresses. In this respect, it supplements and updates the monograph of Professor Rodi (1980), in which the emphasis is on the status of first-order closures, in particular the ~:-8 model, as of 10 years ago. Between them the two works provide an excellent reference source containing the equations; the rationale for modelling decisions that are made; tables of the constants that have been selected; displays of flow computations and their comparison with experimental measurements for a varied number of flows; and extensive reference lists. More than simply reference sources, the two works are critical accounts of difficulties, limitations and continuing efforts to improve performance. One is impressed by the effort, sophistication and ingenuity that is exercised in developing and in working over the equations for the turbulent correlations in order to discover the most effective and most economical ways to introduce the empiricism (the selection and evaluation of the constants) while satisfying various constraints; appropriate formulation of the latter is no small part of the overall exercise. The ten examples chosen by Launder for assessing the performance of second-order closure with respect to experiment, and for comparison with the ~c-e model, argue persuasively for the superior performance of second-order modelling, when one includes in the assessment the distributions of all quantities of interest, not just a single one, say a thickness distribution. It would be of interest and significance to know whether the contrary occurs, i.e. whether, for some flows, the overall performance of a first order model is better. It would be significant because one supposes that in second-order closure it is not just the larger number of constants that permits better "embodiment of experience" (one could have just as many constants at first order) but, 486 rather, that accuracies and uncertainties in modelling the higher order correlations will be smoothed out and diminished in the integration to the lower order correlations (here, the shear stress) and thus a broader class of flows can be modelled. By this logic, third-order closures would perform even better, and so on. However, as implied at the beginning of this statement, it is not really clear whether such