Direct numerical simulation of a turbulent axisymmetric jet with buoyancy induced acceleration

Abstract

Abstract. Direct numerical simulations of an axisymmetric jet with off-source volumetric heat addition are presented in this paper. The system solved here involves a three-way coupling between velocity, concentration and temperature. The computations are performed on a spherical coordinate system, and application of a traction free boundary condition at the lateral edges allows physical entrainment into the computational domain. The Reynolds and Richardson numbers based on local scales employed in the simulations are 1000 and 12 respectively. A strong effect of heat addition on the jet is apparent. Heating causes acceleration of the jet, and an increased dilution due to an increase in entrainment. Further, the streamwise velocity profile is distorted, and the cross-stream velocity is inward for all radial locations for the heated jet. Interestingly, the maximum temperature is realized off-axis and a short distance upstream of the exit of the heat injection zone (HIZ). The temperature width is intermediate between the scalar and velocity widths in the HIZ. Normalized rms of the concentration and temperature increases in the HIZ, whereas that of streamwise, crossstream and tangential velocities increases rapidly after decreasing. Both mass flux and entrainment are larger for the heated jet as compared to their unheated counterparts. The buoyancy flux increases monotonically in the HIZ, and subsequently remains constant.

Detection of turbulent/non-turbulent interface for an axisymmetric turbulent jet: evaluation of known criteria and proposal of a new criterion

“…The same code as developed by Boersma et al (1998), Lubbers et al (2001) and used earlier by Agrawal et al (2005), has been employed for the present work. The simulations are performed on a spherical grid of size 270 9 80 9 48 in r, h, / directions, respectively, for a jet.…”

“…The exit Reynolds number (=U 0 d/m, where U 0 is the exit velocity, d is the orifice diameter, and m is the kinematic viscosity of the fluid) is 1000 and Schmidt number (=m/D where D is the molecular diffusivity of the dye) is unity, in the present simulations. The current simulations are able to resolve the Kolmogorov length and concentration scale sufficiently (Boersma et al 1998;Agrawal et al 2005). The data set comprised 37 time frames taken after the jet had become stationary.…”

A Conceptual Model for Entrainment in Cumulus Clouds

“…Mixing of ambient and cloud air may still occur just beyond the cloud base. In the author's experience with an off-source volumetrically heated jet, which was studied in an effort to understand entrainment in cumulus clouds (Agrawal et al 2004b;Agrawal and Prasad 2004), mixing at the beginning of the heat injection zone is actually much higher for the heated case as compared to its unheated counterpart. Therefore, at least some entrainment should occur in cumulus clouds for a small downstream extent beyond the cloud base.…”

“…The proposed expression is obtained by a suitable modification of the velocity profile for volumetrically heated jets described in Agrawal et al (2004b): 1 1 The velocity profile U/U c ϭ (1 ϩ B 1 2 ) exp(Ϫ 2 ) was obtained empirically by Agrawal et al (2004b) for a volumetrically heated jet to describe the flattened Gaussian streamwise velocity profile. This profile correctly predicted the cross-stream variation of the radial velocity and temperature.…”

“…This profile correctly predicted the cross-stream variation of the radial velocity and temperature. It was however realized that the expression is not suitable for cumulus clouds because it predicts a larger than normal mass flux with heating, which was subsequently corroborated by the experiments of Agrawal and Prasad (2004) and numerical simulations of Agrawal et al (2004a). However, the model becomes appropriate for cumulus clouds upon addition of a fourth-order term.…”