FUNCTIONAL REYNOLDS STRESS MODELING

  by Joan G. Moore and John Moore    

Comments, Questions and Discussion from several people who have emailed us. Nov 2006 - Feb 2007.

  • 3-D Implementation of the RSM Models   Feb. 2007
        "A general comment, the key impediment to the industrial use of RSMs is their cost-benefit relation. The expense due to numerical stability/convergence related to the clear benefit over 2-equation models "tuned" for specific applications. Has the model been implemented into a commercial code (Fluent or CFX)?"

    Reply.   I have implemented early versions of all the models (MC, MA, MR, MARV) in a 3-d steady flow code. I did this early on (2001) to make sure that the models were going to be usable in 3-d codes, and that I could converge steady flow solutions.
        The models are more friendly to implement than other models in the literature because of the choice of variables, q, omega and bij. The near-wall variations are mild compared with dissipation and the Reynolds stresses. Omega and the bij equations depend on q only through the turbulence Reynolds number Rt. The dissipation in the q equation is proportional to q. The MC and MR models will be the easiest to implement, and perhaps the most robust, due to their simplicity and the use of isotropic diffusion for turbulence properties.
        The major CFD companies, ANSYS in Germany (which I believe now owns Fluent) and NUMECA in Belgium have copies of the book.

  • Robustness   Feb. 2007
        "I was a surprised at how well the RSM model did in representing RDT cases within the "W=0" class of flows. As I understand it you blended the model coefficients with those from a related model for flows with rotation, the "W=S" class of flows. How robust would you think the model is to arbitrary initial anisotropy and imposed gradient conditions? I didn't get as clear a picture on the performance of the model for elliptic flows (chapter 18)."

    Reply.   The number of coefficients considered (c1, c3, c4, c5, c6) in the pressure-strain model was intentionally limited to make sure the model wouldn't give silly results. Similarly the ranges of values the coefficients take were also limited. For example, I didn't pursue extending the model basis to higher W/S values, as this might have triggered choosing negative values for c3.
        Elliptic flows are not in general captured by the models. With c5=0 the model has the same peak location, consistent with the maximum elliptical instability. There it overdoes the turbulence production, otherwise in general it underestimates it. The best I could offer were parameters which could be used to evaluate whether or not the flow considered would be subject to elliptical instabilities. I had a look at trying to adjust c5 to model elliptical instabilities, but it would be a nightmare in terms of robustness.

  • Functional Space   Feb. 2007
        "Your comments in Sect 10.5 are exactly right. There is existing data and calculations (DNS) only in a very limited region of the functional [g, fw, fB] space. An interesting pictorial (although useful?) would be to define the regions in this space occupied by a particular application."

  • Glyph Applications   Jan. 2007
        "It is very good to see your 3D (glyphic?) extension of Mohr's circle (will this soon appear in mechanics/materials texts as well?) A fine idea and I am still trying to get my intuition fully trained to read the shapes; will have to ponder further the full implications of Fig. 1.2.5."

    Reply.   In response to your question on our glyphs. We got the idea from Ron Kriz's work on scientific visualization. If you go to our homepage http://moore64.home.comcast.net then click on "Reynolds stress tensor glyphs", this takes you to a page we first put out about 10 years ago, where we presented some Reynolds stress measurements in a tip leakage turbine cascade as glyphs. At the bottom of that page is a "tensor glyph" link which takes you to Ron Kriz's work.

  • Equation Format   Nov. 2006
        "I enjoyed to read your book. It's quite a contribution to this class model. I have a question about the way you wrote some equations, for example, in equation (19.2.3), the (9-2). Does the expression (9-2) mean the value 7? What's the reason that use (9-2) instead of 7?"

    Reply.   Yes, the 9-2 means 7. I wrote it this way to emphasize both the high and low turbulence Reynolds number values of c1, 9 and 2 respectively. Similarly in Eq. 19.2.5, 1.83-1.4 is 0.43.

    From the Homepage of J&J Moore, http://moore64.home.comcast.net. April 2007