An experiment in cooling of gas turbine nozzle guide vanes was modelled numerically with a conjugate viscous-flow and solid-material heat conduction solver. The nozzle vanes were arranged in a cascade and operated in high-pressure, hot-temperature conditions, typical for first turbine stage in a flow of controlled-intensity, artificially-generated turbulence. The vane cooling was internal, accomplished by 10 channels in each vane with cooling-air flow. Numerical simulations of the experiment were conducted applying two turbulence models of the k-omega family: k-omega-SST and Transition SST implemented in the ANSYS Fluent solver. Boundary conditions for the simulations were set based on conditions of experiment: total pressures and total temperature on inlet to cascade, static pressure on the outlet of the cascade and heat flux on the surface of cooling channels. The values of heat flux on the surface of cooling channels were evaluated based on Nusselt numbers obtained from experiment and varied in time until steady-state conditions were obtained. Two test cases, one with subcritical outlet flow, and another one, with supercritical outlet flow were simulated. The result of experiment – distributions of pressure, surface temperature, and heat transfer coefficients on the vane external surface were compared to results of numerical simulations. Sensitivity of the vane surface temperatures and heat transfer coefficients to turbulence models and to boundary-condition values of parameters of turbulence models: turbulence energy and specific dissipation of turbulence energy was also studied.
A method of modelling of nozzle and rotor blade rows of gas turbine dedicated to simulations of gas turbine performance is proposed. The method is applicable especially in early design stage when many of geometric parameters are yet subject to change. The method is based on analytical formulas derived from considerations of flow theory and from cascade experiments. It involves determination of parameters of gas flow on the mean radius of blade rows. The blade row gas exit angle, determined in turbine design point is a basis for determination of details of blade contour behind the throat position. Throat area is then fixed based on required maximum mass flow in critical conditions. Blade leading edge radius is determined based on flow inlet angle to the blade row in the design point. The accuracy of analytical formulas applied for definition of blade contour details for assumed gas exit angle was verified by comparing the results of analytical formulas with CFD simulations for an airfoil cascade. Losses of enthalpy due to non-isentropic gas flow are evaluated using the analytical model of Craig and Cox, based on cascade experiments. Effects of blade cooling flows on losses of total pressure of the gas are determined based on analytical formulas applicable to film cooling with cooling streams blowing from discrete point along blade surface, including leading and trailing edges. The losses of total pressure due to film cooling of blades are incorporated into the Craig and Cox model as additional factor modifying gas flow velocities.
A mathematical model for simulation of icing dedicated to simulation of ice accretion and its effects on aircraft aerodynamic characteristics in conditions of rime icing is presented. Pure rime icing occurs at lower temperatures than glaze icing and results in higher roughness of the surface of deposited ice. The model accounts for increased surface roughness, in terms of equivalent sand grain roughness, caused by deposited rime ice, which influences generation and dispersion of heat in the boundary layer. Increase of surface roughness is determined by analytical models created upon experimental data obtained in icing wind tunnels. Increased generation of heat is a result of increased tangential stress on the surface and is quantified in the temperature recovery factor determined numerically by a CFD solver. Effects of surface roughness on the intensity of forced convection are quantified by application of Colburn analogy between heat and momentum transfer in the boundary layer, which allows assessment of heat transfer coefficient for known friction coefficient, determined by CFD. The computational method includes determination of the surface distribution of mass of captured water in icing conditions. The model of freezing of captured water accounts for generation of heat due to latent heat of captured water droplets, temperature recovery in boundary layer and kinetic energy of captured droplets. The sinks of heat include forced convection, heating of super cooled droplets, conduction of heat through the ice layer and sublimation. The mathematical model is implemented as user-defined function module in ANSYS Fluent solver. The results include effects of deposited ice, including increased surface roughness on aerodynamic characteristics of an airfoil.
Janusz Sznajder, Adam Sieradzki and Wieńczysław Stalewski
Simulations of ice accretion on airfoil in icing conditions were conducted using ice accretion model implemented by authors in ANSYS FLUENT CFD solver. The computational model includes several sub-models intended for simulations of two-phase flow, determination of zones of water droplets impinging on the investigated surface, flow of water in a thin film on airfoil surface and heat balance in air-water-ice contact zone. The method operates in an iterative loop, which enables determination of effects of gradual deformation of aircraft surface on airflow over the surface, which has impact on distribution of collected water, flow of water film over the surface and local freezing rates. The implementation of the method in CFD solver made it necessary to complement the mathematical model of determination of local rates of deformation of aircraft surface with modification of computational mesh around the surface, which must conform, to the deformed surface. Results of simulated ice accretion on NACA 0012 airfoil were compared with results of experiment conducted in icing wind tunnel for a 420 s long process of ice accretion in steady-flow, steady angle-of-attack conditions. Close agreement of values and location of maximum ice thickness obtained in experiment and in the flow, simulations can be observed. For the airfoil deformed with ice, contour determination of its aerodynamic characteristics at several other angles of attack was conducted proving dramatic degradation of its aerodynamic characteristics due to ice deformation.