Which formulas are appropriate for design of a single stage turbine? To match components of a thermodynamic cycle for off-design calculations, what are the proper equations?
You need the graph of mollier for the substance of work. For the design there is necessary both the minimal pressure and minimal temperature and the maximum pressure and maximum temperature. On having identified all the points of the cycle brayton and the needs of wished power it can do the design,
Talieh. You can find your target in Dixon. The book explains the mechanisms of compressor/turbine blades thermodynamically using the well-known velocity triangles. I can send you the book if your are interested. You can also find a preliminary scheme of jet propulsion devoted do the study of the turbojet engine Avon 500 of Rolls Royce at https://www.academia.edu/5500183/Dimensionnement_du_turboreacteur_Avon_500_de_Rolls_Royce
Energy conservation, mass conservation, impulse conservation, cinetic momentum conservation. You need also a diagram/software for thermodynamic properties of the work fluid.
I highly recommend "Gas Turbine Theory" by HIH Saravanamuttoo, CFC Rogers and H. Cohen. I am now on the 5th edition - I have been using it since 1972 and encourage all new hires to my group to work through the Turbine Meanline Calculation example in Chapter 7.
Which formulas are appropriate? Is an unsolvable question. So. I think the best option is to recommend a good book. Apart of the before referred material I suggest Lakshminarayana's book. "Fluid dynamics and heat transfer of turbomachinery". In my opinion the most complete and deeper book of the subject ever written. Although nor easy nor of quick reading. For a deep understanding and implementation of it, you need to have fresh and sharp knowledges of fluid mechanics and computer programming. If you're in a hurry, I suggest the first 3 chapters of NASA-SP 290. "turbine design and applications". A very accessible and understandable text.
having read this and other question about flow in turbines, I strongly suggest the NASA-SP 290 and a series of reports from Arthur Glassman and Warner Stewart (in NACA). Apart of these, the paper of Carter "Analysis of geometry and Design point performance of axial-flow turbines..." NASA-CR 1456 is of stunning utility.
In NATO ASI series E 97A. "thermodynamics and fluid mechanics of turbomachinery" (vol II) you will find excellent material of preliminary design and quick estimation of performances. For example the paper of Sieverding "axial turbine performance prediction methods".
Being you in Italy, you can easily consult the works of Ennio Macchi, or maybe at the same Mr. Macchi at Politecnico di Milano. He is a pioneer in ORC.
From the Russian school I think the book from Deitch (or Deijch) and Troyanovki "turbines" (1973) is an excellent choice. All them in the "classical side" of turbine design and analysis (no CFD).
I think we should stop entertaining this topics..if she is reading for Ph. D ,she should be able to sort references herself....this is not a specialist topics .
What is it that you are really seeking? Who designs turbines other than OEMs? They have access to years of experience, laboratory testing and development, etc. .
I can tell you who designs turbines other than OEMs. My company, conceptsnrec.com, is a 50 year-old company that designs and manufactures turbines (and compressors, pumps, fans) for various customers. These customers include large OEMs, VC-funded startups, and medium-sized businesses.
We also sell the world's only complete line of turbomachinery design and manufacturing software (1-D, 3-D etc. CAE, as well as CAM software). Again, customers include large OEMs, VC-funded startups, and medium-sized businesses (and colleges/universities.)
Finally, we also sell books and offer classes on turbomachinery, etc. I believe we offer a 33% educational discount to students and educators.