.. _nomenclature: Nomenclature ============ .. list-table:: :widths: 20 70 10 :header-rows: 1 :class: nomenclature-center * - Symbol - Description - Unit * - **Latin Symbols** - - * - :math:`a` - Speed of sound - m/s * - :math:`c` - Blade chord - m * - :math:`c_\mathrm{ax}` - Blade axial chord - m * - :math:`C_{\mathrm{f}}` - Diffuser skin friction coefficient - -- * - :math:`CR` - Contraction ratio in the :cite:`benner_empirical_2006` loss model - -- * - :math:`d_{\mathrm{m}}` - Turbine mean diameter - m * - :math:`d_{\mathrm{s}}` - Turbine specific diameter - -- * - :math:`F_t` - Tangential loading parameter in the :cite:`benner_empirical_2006` loss model - -- * - :math:`H` - Blade height - m * - :math:`h` - Static specific enthalpy - J/kg * - :math:`h_{0}` - Stagnation specific enthalpy - J/kg * - :math:`\Delta h_{\mathrm{ts},s}` - Total-to-static isentropic specific enthalpy change - J/kg * - :math:`\Delta h_{\mathrm{tt},s}` - Total-to-static isentropic specific enthalpy change - J/kg * - :math:`\dot{m}` - Mass flow rate - kg/s * - :math:`N` - Number of turbine stages - -- * - :math:`o` - Blade opening - m * - :math:`p` - Static pressure - Pa * - :math:`p_{0}` - Stagnation pressure - Pa * - :math:`PR` - Pressure ratio - -- * - :math:`r_{\mathrm{h}}` - Radius at the hub of the blades - m * - :math:`r_{\mathrm{m}}` - Turbine mean radius - m * - :math:`r_{\mathrm{t}}` - Radius at the tip of the blades - m * - :math:`s` - Blade pitch - m * - :math:`s` - Specific entropy - :math:`\mathrm{J/kg\,K}` * - :math:`s_\mathrm{ax}` - Axial spacing between cascades - m * - :math:`t` - Blade thickness - m * - :math:`T` - Static temperature - K * - :math:`T_{0}` - Stagnation temperature - K * - :math:`t_{\mathrm{max}}` - Maximum blade thickness - m * - :math:`t_{\mathrm{te}}` - Trailing edge thickness - m * - :math:`u` - Blade velocity - m/s * - :math:`v` - Absolute flow velocity - m/s * - :math:`v_{0}` - Isentropic velocity (also known as spouting velocity) - m/s * - :math:`w` - Relative flow velocity - m/s * - :math:`\dot{W}` - Actual power output - W * - :math:`\dot{W}_{s}` - Isentropic power output - W * - :math:`Y` - Stagnation pressure loss coefficient - -- * - :math:`Z_{\mathrm{te}}` - Passage vortex penetration depth at the trailing edge - m * - **Greek Symbols** - - * - :math:`\alpha` - Absolute flow angle - :math:`^{\circ}` * - :math:`\beta` - Relative flow angle - :math:`^{\circ}` * - :math:`\gamma` - Heat capacity ratio - -- * - :math:`\delta` - Flow deviation angle - :math:`^{\circ}` * - :math:`\delta` - Diffuser semi-divergence angle - :math:`^{\circ}` * - :math:`\delta` - Boundary layer thickness - m * - :math:`\delta^*` - Displacement thickness - m * - :math:`\delta_{\mathrm{fl}}` - Blade flaring angle - :math:`^{\circ}` * - :math:`\epsilon` - Blade wedge angle - :math:`^{\circ}` * - :math:`\epsilon_{\mathrm{cl}}` - Tip clearance gap - m * - :math:`\eta_{ts}` - Total-to-static isentropic efficiency - -- * - :math:`\eta_{tt}` - Total-to-total isentropic efficiency - -- * - :math:`\theta` - Metal angle - :math:`^{\circ}` * - :math:`\Delta \theta` - Camber angle - :math:`^{\circ}` * - :math:`i` - Incidence angle - :math:`^{\circ}` * - :math:`\lambda` - Hub-to-tip radii ratio - -- * - :math:`\mu` - Dynamic viscosity - Pa\,s * - :math:`\xi` - Stagger angle (also known as setting angle) - :math:`^{\circ}` * - :math:`\rho` - Density - kg/m^3 * - :math:`\tau_{\mathrm{w}}` - Wall shear stress - Pa * - :math:`\phi` - Flow coefficient - -- * - :math:`\phi^2` - Kinetic energy loss coefficient (:math:`\phi^2+\Delta\phi^2=1`) - -- * - :math:`\Delta\phi^2` - Complementary of the kinetic energy loss coefficient - -- * - :math:`\chi` - Incidence parameter in the :cite:`moustapha_improved_1990` loss model - -- * - :math:`\chi'` - Incidence parameter in the :cite:`benner_influence_1997` loss model - -- * - :math:`\psi` - Loading coefficient - -- * - :math:`\omega` - Angular velocity - rad/s * - **Abbreviations** - - * - CFD - Computational Fluid Dynamics - * - EOS - Equation of State - * - IP - Interior Point (optimization algorithm) - * - ODE - Ordinary Differential Equation - * - SQP - Sequential Quadratic Programming (optimization algorithm) - * - **Subscripts** - - * - :math:`0` - Stagnation state - * - :math:`1,2,3,\ldots` - Flow stations - * - :math:`\mathrm{cl}` - Tip clearance - * - :math:`\mathrm{error}` - Violation of an equality constraint - * - :math:`\mathrm{in}` - Inlet of the cascade or turbomachine - * - :math:`\mathrm{inc}` - Incidence loss - * - :math:`m` - Meridional direction - * - :math:`\mathrm{mid}` - Blade midspan - * - :math:`\mathrm{out}` - Outlet of the cascade or turbomachine - * - :math:`\mathrm{p}` - Profile loss - * - :math:`r` - Radial direction - * - :math:`\mathrm{rel}` - Relative to the rotating frame of reference - * - :math:`s` - Refers to isentropic quantities - * - :math:`\mathrm{s}` - Refers to specific quantitities - * - :math:`\mathrm{sec}` - Secondary loss - * - :math:`\theta` - Tangential direction - * - :math:`\mathrm{te}` - Trailing edge - * - :math:`x` - Axial direction -