Glossary

Axial turbines

Angle, blade inlet: Angle between the tangent of the camber line at a flow station and the axial direction.
Angle, deviation: Difference between the relative outlet flow angle and the metal angle at the trailing edge.
Angle, flaring: Angle defined by the increase of blade height in the axial
Angle, flow: Angle between the absolute or relative velocity vector at a flow station and the axial direction.
Angle, incidence: Difference between the relative inlet flow angle and the metal angle at the leading edge.
Angle, metal: Angle formed by the blade surface of a blade relative to a reference direction.
Annulus: Annular duct defined by the shroud and the hub surfaces.
Blade: Aerodynamic profile used in turbomachines to change the velocity and direction of the working fluid. Depending its function, a blade can either be stationary (stator blades) or rotate (rotor blades).
Blade Tip: End section of the blade. Rotor-blade tip sections are at the shroud and stator-blade tip sections are at the hub.
Blade, Aspect ratio: Ratio of the blade height to the chord length of the blades.
Blade, Axial aspect ratio: Ratio of the blade height to the axial chord length of the blades.
Blade, Axial chord length: The length of the chord’s projection aligned with the turbine’s axial direction.
Blade, Axial pitch-to-chord ratio: Dimensionless ratio comparing the axial chord length of a blade to the spacing between adjacent blades in a cascade.
Blade, camber: Distance between the camber line and the chord line measured perpendicular to the chord line.
Blade, Camber length: The distance measured along the camber line from the leading edge to the trailing edge.
Blade, Camber line: Curve half-way between the suction and pressure surfaces of the blade.
Blade, Chord length: The straight-line distance between the blade’s leading and trailing edges.
Blade, Chord line: A straight line connecting the blade’s leading and trailing edges.
Blade, Height: Difference between the blade radius at the tip and the blade radius at the root.
Blade, Hub-to-tip ratio: Ratio of the blade radius at the hub to the blade radius at the tip.
Blade, Leading edge: The foremost point where the suction and pressure surfaces of the blade meet.
Blade, Pitch: Same as blade spacing
Blade, Pitch-to-chord ratio: Dimensionless ratio comparing the blade spacing to the chord length of a blade. This parameter has a string influence on the profile losses within a cascade.
Blade, Pressure side: The concave surface of the blade characterized by higher pressure and lower velocity, typically experiencing stable flow conditions.
Blade, Root: Section of the blade attached to the casing for stator blades (shroud) and to the disks for rotor blades (hub).
Blade, Rotor: Rotating blade that deflects the fluid and extract work due to the fluid’s change in angular momentum. Rotor blades are also known as buckets.
Blade, Setting angle: Same as stagger angle.
Blade, Solidity: The reciprocal of the pitch-to-chord ratio
Blade, spacing: The circumferential distance separating corresponding points on consecutive blades within a cascade.
Blade, Stagger angle: Angle formed between the chord line and the axial direction. It relates the actual and axial chord lengths, such that the cosine of this angle equals the ratio of the axial chord to the actual chord length. Angle between the chord line and the turbine axial direction. The cosine of the stagger angle is equal to the ratio of axial chord to true chord.
Blade, Stator: Stationary blade that deflects and accelerates the fluid, preparing it for the subsequent rotor blade. Stator blades are also know as vanes or nozzles.
Blade, Suction side: The convex surface of the blade with reduced pressure and increased velocity, potentially prone to flow instabilities and separation.
Blade, thickness: Distance between the pressure and suction surfaces, measured perpendicular to the camber line.
Blade, Trailing edge: The rearmost point where the suction and pressure surfaces converge.
Cascade: Row of circumferentially spaced blades designed to guide and modify the direction and/or velocity of the fluid.
Cascade, Annular: Configuration where turbine blades are assempled in a ring-like arrangement. Annular cascades are found in actual turbomachines or in annular test rigs that emulate the geometry of turbomachines.
Cascade, Linear: Configuration where turbine blades are aligned in a straight row, typically employed for aerodynamic testing under two-dimensional flow conditions.
Cascade, Rotor: Row of rotating blades that extracts energy from the fluid and transforms it into mechanical work.
Cascade, Stator: Row of stationary blades that guides and accelerates the working fluid to prepare it for the rotor cascade.
Casing: Stationary part of the turbine that contains the rest of the components.
Casing, Hub: Surface defining the inner diameter of the flow, see shroud.
Casing, Shroud: Surface defining the outer diameter of the flow, see hub.
Stage: A unit in a turbine that consists of a stator cascade followed by a rotor cascade.
Stage, Degree of reaction: Dimensionaless quantity defined as the ratio of the static pressure (or enthalpy) change across the rotor to the static pressure (or enthalpy) change across the entire stage. It can be interpreted as the fraction of fluid expansion that takes place within the rotor.
Stage, Impulse: A stage in which the majority of the pressure (or enthalpy) drop occurs in the stator, resulting in a degree of reaction close to zero. In such stages, the static pressure in the rotor cascade is approximately constant and work is produced due to the change of direction of the fluid.
Stage, Reaction: A stage in which both the rotor and the stator contribute to the pressure (or enthalpy) drop of the working fluid. The degree of reaction is between zero and one depending on the distribution of the energy conversion. Many reaction stages are designed with a degree of reaction about 50% at nominal conditions.
Stage, Spacing: Axial distance between the outlet of the stator stage and the inlet of the rotor stage.
Turbine: Machine that extracts energy from a fluid flow and converts it into useful work.
Turbine, axial: Turbine in which the flow is parallel to the shaft.
Turbine, mixed-flow: Turbine in which the flow is deflected from the radial to the axial direction.
Turbine, radial inflow: Turbine in which the flow is in the radial inward direction.
Turbine, radial outflow: Turbine in which the flow is in the radial outward direction.

Optimization

Degrees of freedom: The number of independent parameters that can vary in a system or optimization problem. It represents the number of independent directions in which the system can move.
Design variables: Another term for independent variables, specifically in the context of design optimization. These are the parameters that can be modified to achieve the optimal design.
Equality constraint: A type of constraint in an optimization problem that requires a specific condition to be exactly met. It is typically represented as ( g(x) = 0 ).
Feasibility: The condition of satisfying all constraints in an optimization problem. A feasible solution meets all equality and inequality constraints.
Finite differences: A numerical method used to approximate the derivatives of a function by using the differences in function values at specific points. It is commonly used in gradient-free optimization methods.
Gradient vector: A vector that contains the partial derivatives of the objective function with respect to all the design variables. It points in the direction of the steepest ascent or descent.
Gradient-based optimization: An optimization method that uses the gradient of the objective function to guide the search for the minimum or maximum. It typically involves iterative steps in the direction of the negative gradient for minimization problems.
Gradient-free optimization: An optimization method that does not require the gradient of the objective function. These methods are useful for problems where the gradient is not available or difficult to compute. Examples include genetic algorithms, simulated annealing, and particle swarm optimization.
Hessian matrix: A square matrix of second-order partial derivatives of a scalar-valued function. It describes the local curvature of the objective function and is used in second-order optimization methods.
Independent variables: The variables in an optimization problem that can be adjusted or controlled in order to find the optimal solution. They are also known as decision variables.
Inequality constraint: A type of constraint that restricts the values of the variables to a certain range, typically represented as ( h(x) leq 0 ) or ( h(x) geq 0 ).
Jacobian matrix: A matrix of all first-order partial derivatives of a vector-valued function. In optimization, it represents the gradients of the constraints with respect to the design variables.
Lagrangian function: A function used in constrained optimization problems that combines the objective function and the constraints using Lagrange multipliers. It is used to convert a constrained problem into an unconstrained one.
Line search: An iterative optimization technique that involves moving along a search direction to find an acceptable step size that reduces the objective function.
Objective function: The function that is being optimized, which can be either minimized or maximized. It represents the goal of the optimization process.
Optimization bounds: The constraints that define the minimum and maximum values that the design variables can take. These bounds limit the search space for the optimization process.
Step size: The magnitude of the change applied to the design variables in each iteration of an optimization algorithm. It determines how far the variables move in the search space during each iteration.
Trust region: An optimization technique where the search for the optimal solution is restricted to a region around the current point, and this region is adjusted based on the success of the optimization steps.