7. GlossaryΒΆ
- 2nd order low pass filter
A second order low pass filter is an input-output block that computes
\[\begin{split}\dot x(t) = \begin{pmatrix} r & 0 \\ -r & r \end{pmatrix} \, x(t) + \begin{pmatrix} -r \\ 0 \end{pmatrix} \, u(t)\end{split}\]and
\[y(t) = (0, \, 1) \, x(t),\]where \(r\) is a positive real number. This causes the input signal \(u(\cdot)\) to be converted to an output signal \(y(\cdot)\) 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.
- 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
\[N = \frac{\Delta p_v(1)}{\Delta p_v(1) + \Delta p_0},\]where \(\Delta p_v(1)\) is the pressure drop across the fully open valve, and \(\Delta p_v(1) + \Delta p_0\) 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.