7. Glossary¶
- 2nd order low pass filter¶
A second order low pass filter is an input-output block that computes
˙x(t)=(r0−rr)x(t)+(−r0)u(t)and
y(t)=(0,1)x(t),where r is a positive real number. This causes the input signal u(⋅) to be converted to an output signal y(⋅) that is differentiable in time. See the plot of a filtered step response.
- compressible flow¶
The opposite of incompressible flow.
- incompressible flow¶
In fluid mechanics, incompressible flow refers to flow where the mass density is constant within a fluid volume that moves with the fluid.
- iterative solver¶
An iterative solver is a numerical solver that iterates until the approximate solution satisfies a convergence test. Examples include Newton solvers for nonlinear systems of equations, and ordinary differential equation solvers with adaptive time step length.
- numerical noise¶
In numerical solutions, numerical noise refers to fast but small changes in variables whose magnitude is typically smaller than the solver tolerance.
- regularization¶
By regularization, we mean approximating a non-differentiable function by another function that is differentiable and has continuous and bounded derivatives, i.e., a function that is continuously differentiable. Continuous differentiability is a necessary condition for Newton-based solvers to solve nonlinear equations.
- state variables¶
State variables are variables whose time rate of change is defined by a differential equation.
- thermo-fluid system¶
Thermo-fluid systems are systems that compute combined mass and energy flow, such as a heat exchanger in which heat is added to the medium that flows through it.
For a control valve, the valve authority N is defined as
N=Δpv(1)Δpv(1)+Δp0,where Δpv(1) is the pressure drop across the fully open valve, and Δpv(1)+Δp0 is the pressure drop across the whole flow leg whose mass flow rate is controlled by the valve. Valves should be designed such that N is around 0.5, but not higher.