Novel Approaches for sCO2 Axial Turbine Design

This work on novel approaches for sCO2 axial turbine design was first pre­sented at the ASME Turbo Expo in Phoenix, Arizona on July 17 – 21, 2019.

Intro­duc­tion

Con­ven­tional power plant cycles produce power from turbines using steam as the working fluid. Super­crit­i­cal carbon dioxide (sCO₂) cycles use CO₂ in a state where tem­per­a­tures and pres­sures are above a critical point – the super­crit­i­cal state. In this state CO₂ exhibits prop­er­ties in between gas and liquid and has high density and vol­u­met­ric heat capacity, which gives great poten­tial for higher cycle effi­ciency. Since the working fluid is more energy dense, the size of com­po­nents such as axial turbines can be reduced, leading to a smaller foot­print and lower costs. sCO₂ is also con­sid­ered to be a safe, abundant, and cost effec­tive medium. Thus, sCO₂ power plants have the poten­tial to replace steam power plants from both effi­ciency and cost perspectives.

The present work explores novel sCO₂ axial turbine designs for waste heat recovery (WHR) appli­ca­tions based on a 10 MW case study. A Kulfan Class Shape Trans­for­ma­tion (CST) for 2D axial blade profile design is employed, and con­sid­er­a­tions are under­taken for aero­dy­namic effi­ciency and mechan­i­cal stresses.

Axial Turbine Design Philosophy

Starting with spec­i­fi­ca­tions for size, capacity, oper­at­ing con­di­tions, etc. an in-house tool devel­oped at Triveni Turbines for 1D meanline cal­cu­la­tions was used. The results of the meanline cal­cu­la­tion form the basis for 2D blade profile design. The present study uses a 50% reaction turbine aero­dy­namic design and the flow regime is subsonic.

CAESES is used for the geo­met­ric modeling of the axial turbine and the 2D/quasi-3D flow solver MISES is used for the sim­u­la­tions. Within the CAESES envi­ron­ment, an IISc in-house Matlab script is used for pre-/post-pro­cess­ing. The CAESES automa­tion and opti­miza­tion platform encap­su­lates the entire process, to optimize for aero­dy­namic profile losses.

Several approaches are avail­able for para­me­ter­iz­ing axial turbine airfoils. A common method is shown in the fol­low­ing figure, which allows the direct control of mean­ing­ful para­me­ters such as flow and wedge angles, radii, thick­ness, etc. However, this approach has lim­i­ta­tions regard­ing the flex­i­bil­ity of geo­met­ric vari­a­tions, making it dif­fi­cult to explore more novel concepts. Other methods for example are B‑spline curves defined by a set of control points and CST. These approaches lead to greater flex­i­bil­ity and local shape control, which can lead to new and unex­pected designs in the opti­miza­tion process.

The present study used a workflow for para­me­ter­i­za­tion, sim­u­la­tion, and opti­miza­tion based on geome­tries uti­liz­ing B‑spline and CST approaches. The fol­low­ing steps were taken:

1. Import 2D baseline profile
2. Split­ting the baseline into pressure and suction sides
3. Auto­mat­i­cally fitting pressure and suction sides with B‑spline and CST
4. Assign­ing local coor­di­nate systems to the B‑spline control points to move them normal to the baseline profile
5. Applying another local coor­di­nate system for the B‑spline leading edge tangent points on pressure and suction sides to move these points tan­gen­tially and change the inlet wedge angle
6. Creating geo­met­ri­cal con­straints such as inscribed profile area and monot­o­nic­ity of cur­va­ture in certain areas
7. Creating design vari­ables for the dis­place­ment of control points and CST parameters
8. Setting up the software con­nec­tion which exports the profile to a Matlab script which in turn runs MISES
9. Using the DAKOTA global opti­miza­tion engine within CAESES to minimize airfoil profile loss

Feature def­i­n­i­tions created in CAESES automate steps 1 to 7, and specific user defined features were created for B‑spline and CST based airfoil design optimizations.

Surface cur­va­ture has a major influ­ence on pressure dis­tri­b­u­tions for subsonic airfoils. A unique cur­va­ture iden­ti­fi­ca­tion feature was created in CAESES and applied as a con­straint to have a rea­son­able number of para­me­ters and to ensure flex­i­bil­ity, while keeping the cur­va­ture dis­tri­b­u­tions rea­son­ably smooth. 

The fol­low­ing figure shows the cur­va­ture dis­tri­b­u­tion from the fitted baseline profile where position‑0 rep­re­sents the trailing edge of the pressure surface and position‑1 rep­re­sents the trailing edge of the suction surface. A fairing routine is used to smooth the cur­va­ture dis­tri­b­u­tions (for B‑splines only). Monot­o­nic­ity of the cur­va­ture is esti­mated through the deriv­a­tive of the cur­va­ture distribution.

The cur­va­ture analysis is divided into separate zones around the profile, and con­straints are set up which judge the monot­o­nic­ity of these zones. A tol­er­ance is set up to allow for small non-monot­o­nous fluc­tu­a­tions. The fol­low­ing figure shows an example for a violated cur­va­ture con­straint (shown in red).

Aero­dy­namic Opti­miza­tion of Axial Turbine Blades

The turbine airfoils have been opti­mized to minimize profile losses. Separate opti­miza­tions were per­formed for the B‑spline and CST geo­met­ric para­me­ter­i­za­tion methods by assign­ing design vari­ables for the control points and CST para­me­ters respec­tively. Cur­va­ture monot­o­nic­ity was set as the con­straint. The DAKOTA sur­ro­gate-based opti­miza­tion method within CAESES was used. The profile loss coef­fi­cient Y_2‑norm is defined as the nor­mal­ized profile loss and is the ratio of each indi­vid­ual run’s profile loss divided by the baseline profile loss. Both the B‑spline and CST methods had a similar number of design vari­ables and con­straints and each para­me­ter­i­za­tion method involved 60 iterations.

The nor­mal­ized profile losses for the feasible designs from the B‑spline method are shown below. The range of vari­a­tion of each control point is 0.05 mm from the baseline value. The design with minimum profile loss was Y_2‑norm = 0.85, which means a 15% profile loss reduc­tion compared to the baseline. 

For the CST method, the para­me­ter vari­a­tion is in excess of 70% where the change in geometry is spread over the entire surface. As shown in the fol­low­ing figure, the opti­miza­tion found a minimum nor­mal­ized profile loss of Y_2‑norm = 0.83, indi­cat­ing a 17% improve­ment in profile loss relative to the baseline. The CST method was able to cover 40 feasible designs compared to 15 for the B‑spline method, and thus included more of the design space. The best CST design was 2% better in terms of profile losses compared to the best B‑spline design. 

Further Con­sid­er­a­tions

The project also con­sid­ered blade stress cal­cu­la­tions which form an integral part for the design of turbine blades, espe­cially for high energy density sCO₂ cycles. Cal­cu­la­tions for blade static stress as a sum­ma­tion of the cen­trifu­gal tensile stress and the bending stress due to fluid loading were undertaken. 

Studies were also carried out to under­stand the effects of increased power density on the turbine design when scaling from a 10 MW appli­ca­tion to as much as 50 MW. Changes in oper­at­ing con­di­tions, blade sizing, and blade mate­ri­als were con­sid­ered in the scal­a­bil­ity study.

Con­clu­sions

The present study on the design of axial turbine blades for sCO₂ turbines used for waste heat recovery appli­ca­tions has illus­trated the use of novel para­me­ter­i­za­tion methods and auto­mated opti­miza­tions in an effort to inves­ti­gate novel designs that exhibit sub­stan­tially lower profile losses and hence higher efficiencies.

The B‑spline based para­me­ter­i­za­tion gave a design with 15% reduc­tion in profile loss compared to the baseline. The class shape trans­for­ma­tion (CST) tech­nique yielded even better results with a 17% reduc­tion in profile losses compared to the baseline (i.e. 2% better than then the best B‑spline design).

Acknowl­edge­ment

We would like to thank the fol­low­ing authors for their con­tri­bu­tion to the paper which forms the basis for this tech­ni­cal blog post. 

Lead author:
Sharath Sathish, Indian Insti­tute of Science, Ban­ga­lore, India

Con­trib­u­tors:
Pramod Kumar, Indian Insti­tute of Science, Ban­ga­lore, India
Adi Narayana Namburi, Triveni Turbines, Ban­ga­lore, India
Lokesh Swami, Triveni Turbines, Ban­ga­lore, India
Pramod Chandra Gopi, Triveni Turbines, Ban­ga­lore, India
Carsten Fuet­terer, FRIEND­SHIP SYSTEMS AG, Potsdam, Germany

For Further Information

The full paper can be down­loaded from the ASME digital col­lec­tion portal for $25.00. 

Novel Approaches for sCO₂ Axial Turbine Design
Pro­ceed­ings of ASME Turbo Expo 2019: Turbine Tech­ni­cal Con­fer­ence and Expo­si­tion
GT2019-90606