Scaling of Gas Turbine from Air to Refrigerants using Similarity - PowerPoint PPT Presentation

Scaling of Gas Turbine from Air to Refrigerants using Similarity Concept By Choon Seng Wong Supervisor: Prof. Susan Krumdieck

Current turbine design and development process ORC Design Process Turbine Design Process

Similarity Analysis • Scale the turbomachine at different geometry  Predict the performance if the turbomachine is geometrically similar – number of blades, blade angle, machine size, blade thickness are scaled proportionally • Scale the turbomachine for different operating condition  Predict the performance at reduced inlet temp/pressure  To reduce the operational cost of the testing equipment Challenge • A turbomachine cannot be scaled to different fluids due to the variation in compressibility factor and Reynolds number

If we can scale the turbine for different working fluids ORC Design Process • Adapt the existing turbines for ORC and predict the performance using similarity analysis • Turbine performance testing using a simple compressed air test rig to reduce the cost

Objective • Explore the feasibility of utilizing the similarity concept to predict the turbine performance for refrigerants Dimensional Analysis • Reduce the group of variables representing some physical situation to a smaller number of dimensionless group. • Machine performance can be described in terms of the dimensionless groups.

Incompressible Fluid Machine Nomenclature • The performance of incompressible fluid machine is a function of 7 parameters. • The 7 variables were reduced to 4 dimensionless groups using dimensionless analysis.

Compressible Fluid Machine • The performance of compressible fluid machine is a function of the following parameters.       h , , P f N D m ( , , , , a , , ) Nomenclature 0 01 01 s Unit Description • The variables were reduced to the following: P Power Δ h 0s Enthalpy drop     η Isentropic efficiency 2 h ND P m ND      0 s 01 , , f , , , N Shaft speed    2 3 5 3   a a D ND a D Turbine diameter 01 01 01 01 01 ṁ Mass flow rate ρ 01 Inlet density a 01 Sonic velocity μ Dynamic viscosity γ Specific heat

Other Turbine Performance Dimensionless Group   h h h  • 0 01 02 Work coefficient h h 01 01 U  • Mach number Ma a 01 U U    • Velocity ratio  C 2 h is 0 s  h •   Stage loading coefficient 0 2 U C •   Flow coefficient m U

What is similarity concept? Complete similarity can be achieved when • complete geometrical similarity is achieved, in which the turbine is scaled up or scaled down proportionally, and • dynamic similarity is achieved, in which the velocity components and forces are equal. In this study • Three different approaches are derived from the dimensionless groups and attempted to scale the performance data from air to refrigerants

Method Perfect gas approach Constant specific Variable pressure speed approach Assume refrigerants are ratio approach perfect gas. Pressure ratio, blade speed coefficient, and Pressure ratio, velocity ratio, Ratio of enthalpy drop to the mass flow coefficients are hold and specific speed are hold squared of sonic velocity, blade constant to achieve similarity. constant to achieve similarity. speed coefficient, and mass 𝑞 02 flow coefficient are hold 𝑞 02 = constant 𝑞 01 = constant constant to achieve similarity. 𝑞 01  h  0 s constant ND  U U 2 constant a     constant 01 a  C 2 h 01 is ND 0 s  constant m a    constant 01 m    3 exit ND N constant m   01 s 0.75 h constant  0 s 3 ND 01

Example of Calculation Procedure (Perfect Gas Approach) Step 1 Air performance data Assumption • The correlation between efficiency and pressure ratio Total-to-static efficiency 0.9 is same for different working fluid. 0.8 Step2 ND 0.7 Calculate the shaft speed for refrigerant  constant a 01 0.6 m 2 3 4 5 6 7 8  Pressure ratio constant Calculate the mass flow for refrigerant  3 ND 01 Step 3 Total-to-static efficiency 0.90 Calculate the velocity ratio and specific speed for refrigerant Step 4 0.80 Plot the efficiency against velocity ratio 0.70 and specific speed for refrigerant 0.70 0.75 0.80 0.85 0.90 Velocity ratio

Compare the result from similarity analysis to CFD result to validate the similarity analysis approaches Performance Evaluation using CFD Analysis for R134a and R245fa CAD Meshing Physics Definition Solver Fluid flow field • Generation of • Hexahedral • Set up boundary • Solve Navier- • The result was solid model meshes were conditions Stokes transformed using ANSYS- formed on the equations in into velocity • Select suitable BladeGen fluid zone time and 3-D vector, equations of state across the space using k- ɛ temperature (EoS) for working blades. turbulence and pressure medium model. distribution.

Comparison for each approach (using R134a) R134a CFD Analysis (PR@5.7) R134a Perfect Gas Approach (PR@5.7) The optimal velocity ratio is underestimated using the 0.95 Perfect gas approach Total-to-static efficiency perfect gas approach. 0.85 0.75 Optimal velocity ratio (from perfect gas approach ): 0.48 0.65 Optimal velocity ratio from CFD: 0.6 0.55 0.45 0.40 0.50 0.60 0.70 0.80 Velocity ratio R134a CFD Analysis (PR@2.7) R134a Variable Pressure Ratio Approach (PR@2.7) 0.95 Total-to-static efficiency 0.85 0.75 Variable pressure 0.65 ratio approach 0.55 0.45 The optimal velocity ratio from the similarity 0.40 0.50 0.60 0.70 0.80 Velocity ratio analysis agrees to the value from CFD approach R134a CFD Analysis (PR@5.7) R134a Constant Specific Speed Approach (PR@5.7) with an error less than 10%. Constant specific speed approach 0.95 Total-to-static efficiency 0.85 0.75 0.65 0.55 0.45 0.40 0.50 0.60 0.70 0.80 Velocity ratio

Comparison for each approach (using R134a) -- Continued R134a CFD Analysis (PR@5.7) R134a Perfect Gas Approach (PR@5.7) 0.9 Total-to-static efficiency 0.8 0.7 0.6 Perfect gas approach 0.5 The trend of the performance curve is similar 0.4 to the result from the CFD simulation. 0.30 0.40 0.50 0.60 Specific speed R134a CFD Analysis (PR@5.7) R134a Constant Specific Speed Approach (PR@5.7) 0.95 Total-to-static efficiency 0.85 0.75 0.65 Constant specific speed 0.55 approach 0.45 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 Specific speed CFD result – shows that the turbine is sensitive to R134a CFD Analysis (PR@2.7) R134a Variable Pressure Ratio Approach (PR@2.7) the operating conditions. Total-to-static efficiency 0.9 0.8 Variable pressure ratio 0.7 Variable pressure ratio approach approach 0.6 - Shows that the turbine efficiency is fairly flat 0.5 0.30 0.35 0.40 0.45 0.50 0.55 between specific speed 0.3 to 0.45 Specific speed

Comparison for each approach (using R245fa) R245fa CFD Analysis (PR@5.7) R245fa Perfect Gas Approach (PR@5.7) R245fa CFD Analysis (PR@5.7) R245fa Constant Specific Speed Approach (PR@5.7) 0.95 0.95 0.85 Total-to-static efficiency Total-to-static efficiency 0.85 0.75 0.75 0.65 0.65 0.55 0.55 0.45 0.45 0.35 0.35 0.25 0.35 0.45 0.55 0.65 0.75 0.25 0.35 0.45 0.55 0.65 0.75 Specific speed Specific speed R245fa CFD Analysis (PR@4.0) R245fa Variable Pressure Ratio Approach (PR@4.0) 0.95 Total-to-static efficiency 0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.35 0.45 0.55 0.65 0.75 Specific speed Perform the comparison of each approach to the CFD simulation for R245fa.

Table : Numerical error for different scaling approaches Mass Working Pressure Optimal Optimal Maximum total-to- Average flow rate medium ratio velocity ratio specific speed static efficiency Error (%) (kg/s) Benchmark Air 5.7 0.6 0.42 0.85 0.29 R134a 5.7 0.46 0.35 0.85 3.46 Approach 1 Error (%) 23.3 25.5 11.8 4.6 16.3 (Perfect Gas) R245fa 5.7 0.38 0.29 0.85 3.75 Error (%) 31.9 35.9 18.4 9.0 23.8 R134a 2.7 0.6 0.37 0.85 3.46 Approach 2 Error (%) 7.7 9.8 6.6 4.7 7.2 (Variable R245fa 4.0 0.6 0.48 0.85 3.75 Pressure Ratio) Error (%) 2.9 13.5 9.4 9.0 8.7 R134a 5.7 0.6 0.42 0.85 2.99 Approach 3 Error (%) 0.0 10.6 11.8 17.6 10.0 (Constant R245fa 5.7 0.6 0.42 0.85 3.15 Specific Speed) Error (%) 7.5 7.2 18.4 23.5 14.1 2.7 0.65 0.41 0.91 3.63 R134a 5.7 0.60 0.47 0.76 3.63 CFD 4.00 0.58 0.42 0.78 4.12 R245fa 5.7 0.56 0.45 0.72 4.12

Lessons: Variable pressure ratio approach • Provides good prediction of optimal velocity ratio, optimal specific speed, optimal mass flow rate, and maximum efficiency. Constant specific speed approach • Provides better estimation of turbine performance away from the best efficiency point.

Discrepancy in Efficiency if a turbine is scaled from one fluid to another using Variable Pressure Ratio Approach Consider the effect of Reynolds number: 0.90 • Does not have significant effect on the turbine performance as the effect of viscosity and thermal Total-to-static efficiency conductivity can be neglected at high Reynolds number (Re) 0.85 • Re of air/steam usually in the magnitude of 1 x 10 6 Re of refrigerants usually between 1 x 10 6 and 100 x 10 6 • 0.80 0 20 40 60 80 100 Reynolds number (x 1e6)