Numerical Study of Accelerating Turbulent Boundary Layers

Abstract

This thesis focuses on the prediction of favourable pressure gradient turbulent boundary layer flows. Particularly, the focus is on mild favourable pressure gradient turbulent boundary layers and relaminarising turbulent boundary layers (where the favourable pressure gradient is relatively large.) The calculations were performed on ANSYS FLUENT software, and the turbulence models used are the Spalart-Allamaras model and k-ω ​SST model. Furthermore, an integral method called Green's Lag Entrainment method is also used, which was originally designed for the prediction of turbulent flows. A MATLAB code was developed to simulate the test cases using Green's Lag Entrainment method (1977). A limited set of mild favourable pressure gradient experiments on a low-speed wind tunnel and the measurements were made using Particle Image Velocimetry. It should be noted that in the PIV experiment, the flow acceleration was mild (owing to mild FPG), and hence it stayed turbulent and did not relaminarise. In the present study, three re-laminarisation experiments/DNS computations were considered as test cases. 1)An initial zero-pressure turbulent boundary layer of Re_θ=1120=, ​subjected to a strong favourable pressure gradient over a region in the wind tunnel relaminarised at x = 73cm from the leading edge of the flat plate. This was originally studied by Patwardhan using experiments, and he also re-created in direct numerical simulations, and the agreement between them was good. We will refer to this case as the Low Re case of Patwardhan (2014). 2) Similarly, the initial zero pressure gradient turbulent boundary layer of Re_θ=1900, ​subjected to strong favourable pressure gradient different in magnitude (whilst keeping the same non-dimensional free-stream velocity distribution) over a much larger region than the Low Re case of Patwardhan re-laminarises at x = 87cm from the leading edge of the flat plate. Again, this also was originally studied by Patwardhan using experiments and direct numerical simulations, and the agreement between them was good. We will refer to this case as the High Re case of Patwardhan. 3)An experiment published in literature by Bourassa & Thomas (2009) where the initial Reynolds is much higher, perhaps the highest in the whole literature concerning re-laminarising flows of Re_θ=4590.​ Studies using RANS turbulence models and Green's Lag Entrainment method were performed on all the above cases. The overall conclusion is that while the prediction upstream of the onset of relaminarisation is fairly good. But it is interesting to see that the integral method agrees more closely with the experiments and DNS computations than the RANS turbulence models for all three cases upstream of relaminarisation. After relaminarisation, for all three cases, both the RANS turbulence models and the integral method fared poorly. Since the model didn't fare well downstream of the relaminarisation, another set of FLUENT calculations was devised where the flow was calculated without any turbulence model, i.e., a laminar model is solved. The results from these laminar calculations showed a good agreement in the relaminarisation zone for Patwarhdan's Low and High Re cases. This is consistent with the Ranjan & Narasimha (2018) improved version of the quasi-laminar theory, which was developed to explain the later stages of flow relaminarisation.

References: [1] Green J. E., Weeks D. J., Brooman J. W. F., “Prediction of Turbulent Boundary Layers and Wakes in Compressible Flow by Lag Entrainment Method, A. R. C., R & M. No. 3791, 1977. [2] Patwardhan S. S., “Effect of favourable pressure gradients on turbulence in boundary layers”, A Ph.D. Thesis, Indian Institute of Science, Bangalore, 2014. [3] Bourassa, C. & Thomas, F. O., An experimental investigation of a highly accelerated turbulent boundary layer. J. Fluid Mech. 634, 359–404. 2009. [4] Rajesh Rajan & Roddam Narasimha, "An assessment of the two-layer quasi-laminar theory of relaminarization through recent high-Re accelerated TBL experiments, arXiv preprint arXiv:1611.09746, 2018.