Reply to Discussion by Duarte et al. of “CFD analysis of the effect of nozzle stand-off distance on turbulent impinging jets”

The authors would like to thank the discussants for their interesting suggestions. The discussants have carried out experiments on impinging jets and have compared their results with the CFD results presented in the paper. In addition, discussants have also presented a solution for the differences observed between the CFD and experimental results in the core portion of the jet. The discussants’ experiment includes measurements on impinging water jets with a 72 mm diameter (D) circular nozzle anda stand-off distanceofH/D=9.58. Issuance velocities ranged from 5 to 22m/s. The discussants have also questioned the use of Reynolds StressModel (RSM) formodeling the turbulence in thepaper.Herein, the reasons for choosing this turbulence model in our simulations are explained. Based on the H/D ratio, different regimes occur in the flow field of impinging jets (Fig. 1 from Shademan et al. 2013). For H/D 8), Beltaos and Rajaratnam (1974, 1977) classified the flow into three different regions: the free jet portion (region I, Fig. 1 in Shademan et al. 2013), the impingement zone (region II, Fig. 1 in Shademan et al. 2013), and the axisymmetric wall jet portion (region III, Fig. 1 in Shademan et al. 2013). As a result, each region has specific characteristics and the objective of the study was to best capture the features in all the regions with a single turbulence model. The purpose of the paper was also to identify some of the issues and difficulties associated with previously used turbulence models in solving turbulent flow in impinging jets. Numerical simulation of a circular impinging jet using RANS simulations has been of interest to many researchers. As a result, these simulations formed part of the 2nd ERCOFTAC-IAHRWorkshop on Refined Flow Modelling in 1993. Later, Craft et al. (1993) published their research on impinging jets using different turbulence models. They reported that due to the weakness associated with the eddy viscosity stress–strain relationship in the turbulence models, the results were not in good agreement with the available experimental data. Similar issues were reported by Cooper et al. (1993), who reported that the k– model over-predicts the turbulent kinetic energy near the stagnation point. To sort out the issues reported by previous researchers in modeling impinging jets, different turbulence models were implemented in the current study. Models that take into account the low-Re effects in the flow were selected. In addition, the selected models take into consideration the anisotropic nature of the turbulent viscosity, which is ignored during Reynolds averaging. The Realizable k– model (Shih et al. 1995), the k– SST (Shear Stress Transport) model (Menter 1994), and the Reynolds Stress Model (RSM) (Launder et al. 1975) were implemented in the simulations. Each of the commonly used turbulencemodels has some advantages and disadvantages. Considering that RSM is a fully anisotropic turbulencemodel, which solves the transport equations for all three fluctuating velocity components, the issues resulting from applying the Boussinesq approximation is removed. Basically, the strength of this model compared to the Boussinesq based turbulencemodels is its capability in producing the fluctuating velocity components in the results. The other reason for using the RSM model is the analysis of wall jet region, which was of interest to the authors. Following impingement, the flow undergoes a large deflection, which is associated with the initiation of the wall jet portion of the flow. This causes the turbulence components to be highly anisotropic in this part of the flow. Therefore, irrespective of the minor weakness observed in the RSM results (Fig. 3 in Shademan et al. 2013), the authors decided to implement this model for the analysis of the entire domain to benefit from both an anisotropic turbulence model and also extracting the fluctuating velocity components. These would not have been possible by choosing either the k– SST or the Realizable k– turbulence models. The authors appreciate the idea of the new length scale (xc) for synchronizing results from different numerical and experimental studies. Indeed this method can help future researchers for comparing the results in an appropriate way. As the discussants have shown, this way of comparison solves the ambiguity observed in the results in the free jet region. However, as noted in the paper and by others, the nozzle design always plays a significant role on the development of the flow in the core and in the free jet region of the flow (Xu and Antonia 2002).

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