Self-similarity, momentum scaling and Reynolds stress in non-premixed turbulent spray flames

An experimental study was conducted in a turbulent spray flame in which dro plets were produced ultrasonically at low velocity relative to the host gas . In this fashion, injector-specific effects on the two-phase flow were min imized and a scenario generally characteristic of the far held of practical spray systems could be simulated. Close to the burner exit, the spray flam e appeared as a dense column of drops burning with an envelope flame. Furth er downstream, it opened up slowly in the radial direction and developed a turbulent 'brush' appearance. Measurements of the size, velocity and concen tration of the droplets, and of gas-phase velocity and temperature were mad e by combining a Phase-Doppler interferometric technique with Stokes/anti-S tokes Raman thermometry. The experimental data were used to derive scaling and self-similarity for the Reynolds-averaged continuity and momentum equat ions using suitable transformations. Results showed three distinct regions, on the basis of the behaviour of the gas axial velocity in the spray flame. In the lower part of the flame, the gas momentum increased because of vaporization. In the intermediate region of the spray flame, the axial velocity decayed along the centreline as an inverse power of the distance from the virtual origin, with exponents small er than unity. In the upper part of the spray flame, the flow held recovere d the axial velocity decay that is typical of incompressible jets, namely a s an inverse of the axial distance. Self-similar behaviour held for the axi al velocity throughout the intermediate region. The vapour source term in t he gas continuity equation scaled approximately as an inverse power of axia l distance, and exhibited self-similarity throughout the spray flame. As a result, a simple model of the Reynolds stress term could be formulated, in which two competing contributions appear: one, that is due to turbulent tra nsport, tends to increase the value of the velocity correlation; another, t hat is due to the vaporization term, tends to reduce the value of the veloc ity correlation and can be construed as a vaporization-induced tendency tow ards relaminarization. The first term is modelled by a classic gradient-tra nsport approach yielding an empirical mixing length relating the velocity c orrelation to the average velocity gradient. Model and experiments are foun d to be in good agreement, especially sufficiently far from the injector, w here one-way coupling between the two phases holds.