Contact persons: Rene Pecnik, Piero Colonna

**INTRODUCTION**

The merit of using supercritical CO2 as the working fluid of a closed Brayton cycle gas turbine is widely recognized as an attractive new option for medium capacity energy conversion because of the very high efficiency reachable at moderate turbine inlet temperature and the very compact general assembly. scCO2 gas turbine power plants are an attractive option for solar, geothermal and nuclear energy conversion. Many challanges must be overcome in order to successfully bring this technology to the market, some of them being increasing the efficiency of the turbomachinery components as much as possible, the design of compact heat exchangers which must operate at high temperatures and pressures, and the dynamic control of the whole system. The aim of this project is the study, modeling and simulation of the entire scCO2 system as well as of specific single components.

**CFD SIMULATION OF TURBOMACHINERIES**

Accurate CFD analysis is of fundamental importance to study the performance of turbomachinery components. Their very small dimension (see figure 1) makes it very difficult to extrapolate data from larger machines. Moreover, due to the thermodynamic state of the working fluid which is very close to its critical point, real gas effects are predominant and must be taken into account. At the moment there are very few numerical studies which deals with real gas equations of state, and even less experimental data to compare with.

*Figure 1: Real geometry of the compressor under investigation. On the left side, the impeller only is shown. On the right side, the whole compressor is presented, including vaned diffuser.*

Due to strong variation of the thermodynamic properties in the supercritical region (figure 2), particular attention is focused on numerical aspects of solving the Navier-Stokes equations and on turbulence modeling (see also the related project *Direct numerical simulation of supercritical flows in developing pipes*), as common models have been introduced under the ideal gas assumption. The occurrence of condensation close to the critical point is also an interesting and challenging topic to tackle as part of this study.

*Figure 2: Thermophysical properties of CO2 at P = 8MPa. Left: density (solid) and isobaric specific heat (dash-dot). Right: dynamic viscosity (solid) and thermal conductivity (dash-dot).*

**Methodology**

A parallel solver for the compressible Reynolds-averaged Navier-Stokes equations on unstructured meshes based on a finite volume formulation and implicit time integration is used. Complex and accurate thermodynamic models are adopted to account for the strong nonlinearity of thermophysical properties close to the critical point. To reduce the computational cost, an accurate look-up table approach replaces direct evaluation of fluid properties during runtime. A robust and fully automated hybrid mesh generator suited for turbomachinery geometries has been developed. To ensure high quality grids, a geometry transformation is exploited. High level of fidelity is reached coupling the mesh generator with an external software which generates the blades and diffuser geometry. The tip clearance gap and the vaned diffuser are also modeled (see figure 5).

* Figure 3: Properties interpolation error using gradient **Figure 4: Average time per call. Colored lines*

*(dash-dot), bilinear (solid), and polynomial (dash) interpolation. are direct call to the interface library. Black lines*

*Triangles represent speed of sound, squares cp and circles represent tables interpolation for three different*

*specific internal energy. schemes: gradient (dashed), polynomial (dash-dot)*

* and bilinear (solid). Triangles indicates that a phase*

* check is performed on the input state. **( *

* *

*Figure 5: Computational mesh for one passage of the rotor and stator. The total number of control volumes is approximately 1 million and guarantees y+<1 at the wall in the whole domain.*

**Preliminary Results**

First simulations were performed using the geometry of the radial compressor operating at Sandia National Laboratories.

Initial conditions slightly above the vapor-liquid critical point lead to the occurrence of two-phase flow near the leading and trailing edge of the main blades. Despite a simplified geometry has been employed (no tip clearance and vaneless diffuser), efficiency values are reasonably close to experimental results. At the moment, the complete compressor geometry is under investigation and a preliminary steady state simulation shows larger regions of condensation then for the simple impeller only (see figure 7). The small gap between the rotor and stator blades suggests that an unsteady simulation is probably the best approach to study the considered compressor.

*Figure 6: Preliminary results for the impeller only. Computational points in the T-s diagram (left), pressure distribution at span = 15% (center) and condensation regions (right).*

*Figure 7: Preliminary results for the complete compressor. Pressure field in transversal sections (left) and condensation regions (right).*

**PERSPECTIVE**

Next steps of the project will be focused on improving the modeling of the entire system as well as of the fluid dynamics of supercritical fluids. Some fundamental aspects must still be tackled, like turbulence modeling in the supercritical region which is of major relevance, especially when heat transfer predictions are important. Furthermore, a complete and validated description of the condensation process close to the critical point would extend the range of problems which can be analyzed.

**PUBLICATIONS**

**Rinaldi, E., ****Pecnik, R., ****and Colonna, P**. Steady state investigation of a complete supercritical CO2 centrifugal compressor, *Submitted to ASME Turbo Expo Conference 2013.*

**Rinaldi, E., Pecnik, R., and Colonna, P.**, Eberhardsteiner, J., Böhm, H. J., and Rammerstorfer, F. G. (Eds.), Accurate and Efficient Look-up Table Approach for Dense Gas Flow Simulations, *6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012)*, Vienna University of Technology, Austria, 2012, 1-15

**Pecnik, R., Rinaldi, E., and Colonna, P**. Computational Fluid Dynamics of a Radial Compressor Operating With Supercritical CO2, *Journal of Engineering for Gas Turbines and Power*, *ASME*, 2012, *134*, 122301

**Casella, F., and Colonna, P.**, Development of a Modelica dynamic model of solar supercritical CO2 Brayton cycle power plants for control studies, *Supercritical CO2 Power Cycle Symposium*, Boulder Colorado, May, 2011

**Pecnik, R., and Colonna, P.**, Preliminary CFD Analysis of a Radial Compressor Operating with Supercritical CO2, *Supercritical CO2 Power Cycle Symposium*, Boulder Colorado, May, 2011