Spalart-Allmaras Turbulence Model for Disaggregated Mesh 58 Figure 4-24: Flow angle around the suction side of the vane 59 Figure 4-25: Pressure distribution from aerodynamic analysis using. Spalart-Allmaras model for exit Mach number=0.75 60 Figure 4-26: Pressure distribution from aerodynamic analysis using. Spalart-Allmaras model for exit Mach number=1.04 60 Figure 4-27: Temperature distribution from aerodynamic analysis for.
LIST OF TABLES
NOMENCLATURE
CHAPTERl
INTRODUCTION
In 1930 Sir Frank Whittle an English aeronautical engineer and pilot patented a design for a gas turbine for jet propulsion. At the age of 22, Frank Whittle first thought of using a gas turbine engine to power an airplane. The gas turbine engine works according to the principle of the Brayton cycle, where compressed air is mixed with fuel and burned in the combustion chamber under almost constant pressure.
Combustor ompressor
Turbine
Analyzing the thermal design of a blade begins with understanding the complex flow field around the blade. This thesis aims to develop a CFD model using a commercially available numerical code to solve the flow field and heat load to the blade. The maximum equivalent stress that occurred in the blade was plotted against time along with the TIT profile for the cycle.
LITERATURE SURVEY
Introduction
Overview of Lumg Models
- Integrated Lifing Analysis for Gas Turbine Components
- FACE
- Lif'mg Model
From the CFD analysis of gas flow through the gas turbine, values for heat transfer coefficients or temperatures are obtained at specific locations in the component. The choice of lifmg model ultimately depends on the expected failure mechanism of the component under consideration. The accuracy of the temperatures calculated by the FE thermal model is mainly determined by the accuracy of the heat transfer coefficients calculated by the CFD model.
Turbine Blade Aerodynamics and Thermal Stress
Ganga performed a 2-D turbine blade aerodynamic analysis to calculate the temperature distribution on the turbine blade surface. For flow on a flat plate, the results of the k-E model agreed very well with the experimental data. Rodi and Scheuerer (1989) used a low Reynolds number version of the thek-E turbulence model developed by Lam and Bremhorst (1981) to predict turbine blade heat transfer using the finite difference form of the boundary layer equations.
COMPUTATIONAL METHODOLOGY
Method Description
For the steady state model, it was decided to use the commercially available FV code FLUENT 6.1 for the aerodynamic analysis. The procedure used by Bohn for the steady state analysis can be extended to simulations where the TIT is unstable with respect to time. For the transient model, an unsteady aerodynamic analysis must be performed to obtain the unsteady turbine blade surface temperature distribution.
FLUENT
- Governing Equations
- Numerical Modelling of the Governing Equations
- Discretization
- The Segregated Solution Algorithm
- The Coupled Solution Algorithm
- Turbulence Models
- The Spalart-Allmaras Turbulence Model
- The k - E "Turbulence Models
- The k -0) Turbulence Models
Integration of the governing equations on the individual governing volumes to construct algebraic equations for the discrete unknown variables (such as velocity, pressure and temperature). The Realizablek - Emodel differs from the standard k -Emodel in two .. ways; it uses a new fonnulation for the turbulent viscosity and it uses a new transport equation for E. The tenn "Realizable" means that the model meets the mathematical constraints on the Reynold's stresses consistent with the physics of turbulent flow. The Standard and the SST k - 0) models have similar forms, with transport equations for k and 0). The standard k -0) model is modified for low-Reynold's effects.
NASTRAN
The performance of the threek-E models depends on the treatment of the viscous flow in the near-wall region. Where A is the thermal conductivity of the material in question, Q is the stored heat, and p and c are the density and specific heat, respectively. Only one type of material and element specifications for the thermal analysis require discussion as this relates to only one type of analysis.
COMPUTATIONAL FLUID DYNAMICS (CFD) MODEL DEVELOPMENT
Data for the Mark 11 NGV
The computational FEM mesh for the blade used higher order elements and contained 2032 elements with 6743 nodes. The simulation was done as a simple 2-D stress problem and took into account the temperature dependence of thermal conductivity, thermal expansion and Young's modulus. FEM simulation results are given as contours of blade temperature and equivalent stress ( With the flow in the model being transonic, the operating pressure was set to 0 Pascal's. The y+ values at the near wall for the first cell were all on the order of 300. The boundary layer mesh size depends on the type of turbulence model and near wall treatment used in the simulation. The results presented in the next section are those for a boundary layer mesh with the first cell size=0.00001. On the pressure side of the blade, the temperature at the stagnation point in the laminar region is over predicted by 8. The arrangements of the cooling holes lead to the local maxima and minima, as described for the pressure surface. The Spalart-Allmaras model again predicts the temperature particularly well in the turbulent region on the suction side. On the suction side, the model overpredicts the temperature by an enormous 12% in the laminae region. From the results, it can be argued that the Standard k - E model with improved wall treatment predicts the temperature in the laminae regions slightly worse (by 2 %) than the Spalart-Allmaras model. The Spalart-Allmaras model showed the best prediction in the turbulent region and was marked as the turbulence model for the validation. Another possibility was that the thermal boundary layer did not dissolve in the laminar regions. The same during prediction is then observed on the suction side in the turbulent region. CHAPTERS However, another code that forms part of the MSC family of FEM codes was available, namely MSC.NASTRAN 2004. Hohn mentions that one of the most difficult problems is the change in calculation grids in the solid region from the aerodynamic to the thermal analysis. The CSD applies the tensile force from the results of the thermal analysis (temperature distribution inside the blade) and uses the updated Lagrangian formulation to solve the displacements of the structure. It then only allows deformation in the x and y directions, with no movement of the cells in the z direction. The overall NASTRAN contour plot is accurate to Bohn's where the effect of the cooling holes can be seen as the temperature rises from the cooling holes to the blade surface. From the plot, higher stresses can therefore be expected towards the suction side of the blade. As expected, the maximum stress in the blade occurs at the minimum temperature, which is located at the edge of the second cooling hole. The temperature and stress contours are accurately predicted over the entire blade, with a constant underprediction of the stress. Both solvers solve the conduction heat equation for the thermal analysis, and the results between the two codes differ by only 2% to 3%. The result of the thermal analysis, which then forms the boundary condition for the mechanical analysis, was therefore the same in both solvers. The result of the steeper temperature gradient is a much higher voltage towards the suction surface, as shown in Figure 5-4. The temperature in the contour plot can be seen to increase behind the shock wave and therefore large temperature gradients are formed from the center of the blade to the suction surface. The time steps chosen depended on the time range and slope of the temperature changes. The stress is measured at the edge of the second cooling hole, in the center of the blade. Stress delays TIT by 2 to 3 s for the first 30 s of the simulation. The delay is then increased to between 6 and 8 s for the last 30 seconds of the simulation. The previous four cases showed the behavior of the stress curve due to a changing TIT profile, where three observations were made. The voltage is proportional to TIT, which is also dependent on the gradient of TIT. At 636 s there is an abrupt increase in TIT of 476 K, which initially results in a sharp increase in the stress curve. Most importantly, the behavior of stress in relation to changing TIT was also shown. The accuracy of thermal fatigue calculations depends on the accuracy of the thermal stresses used in the calculations. The overall accuracy of the transient voltage analysis depends on the separate models involved in the transient voltage analysis. Performing the transient stress analysis with a transient pressure boundary profile will undoubtedly increase the accuracy of the results. The results of the steady state aerodynamic analysis were in excellent agreement with the experimental data of Nealy et. All three turbulence models performed exceptionally well in the turbulent regions of the wing, where the Spalart-Allmaras model overpredicted Bohn's experimental data by approximately 1. Thus, it was shown that none of the FLUENT turbulence models could accurately predict the heat load to the wing, where this fmding is strongly emphasized throughout the open literature. The model predicted Bohn's experimental data by only 1% in the laminar regions of the leaf. The results of the Spalart-Allmaras and Laminar model were combined, resulting in the validation of the CFD model. The results of the steady-state FEM analysis were compared with Bohn's predicted results. The correct material and element characterization and accurate results of the aerodynamic analysis are extremely essential for the accuracy of the stress prediction. The success of the transient thermal stress points is mainly due to the discovery of the Laminar model. The accuracy of the aerodynamic analysis is the core of the work presented in this thesis. The combination of the Spalart-Allmaras and Laminar model for the aerodynamic analysis appears to be an accurate tool for predicting the heat load as well as the corresponding thermal stress. However, the relationship between stress and strain for the experimental work, as well as the relationship between temperature and stress for the prediction, provide a possible way to validate thermal stress. Equation A-18 shows that an increase in T4, the TIT, will result in an increase in overall cycle efficiency. APPENDIXB APPENDIXC APPENDIXD The idea was to change the angle at which the mesh BL grew away from the wall so that the mesh from either side of the corner TE could come together, as shown in the solution to the problem in Figure E-2 below. The Angle_Smooth_Factor setting has been adjusted in the default settings to allow for non-rectangular projections. This was then limited to two points at the corners of the trailing edge. Where the edges 64 to 73 are the edges that have the boundary layer attached and the vertices 134 and 135 are the tips at the corners of the trailing edge. APPENDIXF APPENDIXG APPENDIXH SOOK APPENDIXJ De Villiers1.E., Measurement and numerical validation of the flow and heat transfer on a transonic turbine blade, MScIng Final Report, Department of Mechanical Engineering, University of Natal, South Africa, 2002. Hah C., a Navier-Stokes -analysis of Three-Dimensional Turbulent Flow within Turbine Blade Rows at Design and Off-Design Conditions, Journal of Gas Turbine and Power Engineering, Vol pp 421-429. Incropera FP and De Witt D.P., Fundamentals of Heat and Mass Transfer, 4th edition, Wiley and Sons, 1996. Singh R., Managing Gas Turbine Availability, Performance and Utilization through Advanced Diagnostics, Gas Turbine Users Association Annual Conference, Dubai, UAB, May 9-14, 1999.Model Specification
FINITE ELEMENT METHOD (FEM) MODEL DEVELOPMENT
Introduction
Problem Definition and Boundary Conditions
THERMAL SHOCK AND TRANSIENT THERMAL STRESS
CONCLUSION
FUTURE WORK RECOMMENDATIONS
APPENDIX A
APPENDIXE
