Acoustic Modal Analysis Model Reference

表 1. Acoustic Modal Analysis Model Reference
Theory	See Acoustic Modal Analysis.
Provided By	Select after the CFD solution has converged: [physics continuum] > Models > Optional Models
Example Node Path	Continua > Physics 1 > Models > Acoustic Modal Analysis
Requires	A converged solution is required which uses (at least) the following models: Space: Any Time: Steady Material: one of Gas, Liquid, Multi-Component Gas, or Multiphase Flow: Any Equation of State: One of: Ideal Gas, Real Gas, or User-Defined EOS. (Any equation of state model that provides Speed of Sound). Viscous Regime: Any Energy: Any Turbulence (if required): Any When simulating a reacting flow, also include: Reaction Regime: Reacting Reacting Flow Models: Any
Properties	Key properties are: Number of Modes, Flame Transfer Function. See Acoustic Modal Analysis Properties.
Activates	Model Controls (child nodes)	Acoustic Frequency Table N-Tau Model / User N-Tau Model (Available when using the Reacting model).
	Boundary Inputs	See Boundary Settings.
	Solvers	Acoustic Modal Solver. See Acoustic Modal Solver Properties.
	Field Functions	Acoustic Pressure Normalized, Acoustic Pressure Normalized - Mode [n], and Acoustic Pressure Phase - Mode [n] . See Field Functions.
	Solution Views	Acoustic Modes View. See Solution Views.
	Simulation Operations	See Simulation Operations.

Acoustic Modal Analysis Properties

Number of Modes

The number of acoustic modes

\hat{P}

that are computed in Eqn. (4777)—a value of 5 represents the 5 lowest eigenvalues (acoustic frequencies

ω

).

Shift Frequency

Allows you to specify the frequency (/s or Hz) above which the nearest acoustic modes are calculated.

Flame Transfer Function

Available when using a reacting model. You specify the flame transfer function

D (ω)

in Eqn. (4777).

The methods available are:

Zero Source: No flame or heat source is accounted for in the acoustic modal solver. $D (ω)$ is omitted from Eqn. (4777).
N-Tau Model: Available when using the Reacting model with the Acoustic Modal Analysis model.; Calculates the flame transfer function/heat release source using Eqn. (4795).
User N-Tau Model: Available when using the Reacting model with the Acoustic Modal Analysis model.; Calculates the flame transfer function/heat release source using Eqn. (4801). Select this option if you have full details of the time lag profile and interaction index.

Secondary Gradients

When On, the secondary gradient contributions are included in the wave propagation term that involves the gradient of acoustic pressure (

\nabla\cdot ({\bar{c}}^{2} \nabla \hat{p})

in Eqn. (4774)). When Off, the secondary gradients are excluded from the acoustic wave equation.

N-Tau Model

Calculates the effect of the unsteady heat release source (due to combustion or an external heat source) on the acoustic pressure using N-Tau flame transfer functions Eqn. (4790) with the specified parameters.

Right-Click Actions

New: Creates a new N-Tau flame transfer function. You can create multiple flame transfer functions.; A new node N-Tau Model > [n-tau flame transfer function] appears in the simulation tree.

Properties

User Heat Release Rate: When activated, enables the Heat Release Rate Profile node which allows you to specify a user-defined heat release rate.

Child Nodes

Heat Release Rate Profile

Specifies the custom heat release input

\dot{q} (x)

in Eqn. (4794).

[n-tau flame transfer function] Properties

Reference Location: A reference location at the burner inlet, $x_{r e f}$ in Eqn. (4790).
Reference Direction: $n_{r e f}$ in Eqn. (4790).
Coordinate System: Defines the coordinate system in which $x_{r e f}$ and $n_{r e f}$ are specified.; See Coordinate Systems.
Index: (Read-only); The flame transfer function index.
Interaction Index: You specify the constant value for the amplitude of the flame response $n$ for the interaction index $n_{u} (x)$ (at location $x$ ). Within the flame, $n_{u} (x)$ is calculated by Eqn. (4791).
Time Delay: $τ$ in Eqn. (4795).

User N-Tau Model

Models the effect of the heat release fluctuations on the acoustic field using User N-Tau flame transfer functions Eqn. (4801).

Right-Click Actions

New: Creates a new N-Tau flame transfer function. You can create multiple flame transfer functions.; A new node User N-Tau Model > [user n-tau flame transfer function] appears in the simulation tree.

Properties

User Heat Release Rate: When activated, enables the Heat Release Rate Profile node which allows you to specify a user-defined heat release rate.

Child Nodes

Heat Release Rate Profile

Specifies the custom heat release input

\dot{q} (x)

in Eqn. (4794).

[user n-tau flame transfer function] Properties

Reference Location

A reference location at the burner inlet,

x_{r e f}

in Eqn. (4790).

Reference Direction

n_{r e f}

in Eqn. (4790).

Coordinate System

Defines the coordinate system in which

x_{r e f}

and

n_{r e f}

are specified.

See Coordinate Systems.

Index

(Read-only)

The flame transfer function index.

Bulk Velocity

U_{b u l k}

in Eqn. (4802).

Child Nodes

Interaction Index Profile: You specify the interaction index field profile $n_{u} (x)$ in Eqn. (4801).
Time Lag Profile: You specify the spatially distributed time delay field profile $τ (x)$ in Eqn. (4801).

Boundary Settings

All Boundary Types

Acoustic Impedance Specification

Method	Corresponding Physics Value Nodes
Perfectly Reflecting (Default for Wall, Contact, and Symmetry boundaries). The boundary perfectly reflects acoustic pressure at a hard wall according to Eqn. (4786).	None
Zero Acoustic Pressure (Default for all boundary types except Wall, Contact, and Symmetry boundaries). The acoustic pressure is zero at the boundary—which reflects acoustic waves perfectly, but with a phase-shift of 180 degrees Eqn. (4787).	None
Specified Impedance Specifies the magnitude and phase of the reflected acoustic wave, independent of frequency.	Acoustic Impedance Allows you to specify the complex impedance $Z$ in Eqn. (4788) using a composite polar profile or a composite rectangular profile.
Quadratic Impedance Profile Specifies the magnitude and phase of the reflected acoustic wave as a quadratic function of frequency.	Acoustic Impedance Z0 Allows you to specify $Z_{0}$ in Eqn. (4789) using a composite polar profile or a composite rectangular profile. Acoustic Impedance Z1 $Z_{1}$ in Eqn. (4789) using a composite polar profile or a composite rectangular profile. Acoustic Impedance Z2 $Z_{2}$ in Eqn. (4789) using a composite polar profile or a composite rectangular profile.

Acoustic Modal Solver

Properties

Tolerance Scaling Factor: Scales the default convergence tolerance of the eigenvalue solver.
Iteration Scaling Factor: Scales the default maximum number of iterations of the eigenvalue solver.
Stop if Not Enough Memory: When activated, the computation stops if there is insufficient memory.

Specific Right-Click Actions

Solve for Acoustic Modes: Runs the acoustic modal solver with the parameters that are specified. When solved, the frequencies and growth rates of each acoustic mode are printed in the Output window.

Field Functions

Acoustic Pressure Normalized: Available when the scalar scene representation is set to Acoustic Modes View. You can use the Solution Views > Acoustic Modes View node to edit the acoustic mode number that is displayed in scalar scenes which use this field function.; Displays the normalized acoustic pressure throughout the associated region (the acoustic pressure is scaled from 0–1).; See Solution Views.
Acoustic Pressure Normalized - Mode [n]: Displays the normalized acoustic pressure for mode [n] (the acoustic pressure is scaled from 0–1).

Acoustic Pressure Phase - Mode [n]: Displays the phase (in deg) of the acoustic pressure for mode [n] (the acoustic pressure is scaled from 0–1). This value is; $φ$ in Eqn. (4783).

Acoustic Frequency Table

Once the acoustic modes are solved, the acoustic frequency table is displayed in the output window and the Acoustic Modal Analysis > Acoustic Frequency Table node also appears which provides the following functions:

Right-Click Actions

Export: Allows you to export and save a table of acoustic frequencies in .csv format.
Tabulate: Displays tabular data in a pop-out window.; The following example shows 6 modes and their associated frequencies and growth rates. If the growth rate (imaginary part of the acoustic frequency $ω_{i}$ ) is positive, the associated mode is unstable—as highlighted in the example below:

Properties

Extracted: (Read-only). Provides a list of the column names in the extracted table.

Solution Views

Acoustic Modes View

Representation: (Read-only). Displays the Acoustic Modes View representation.
Acoustic Mode: The acoustic mode number that is currently displayed in scalar scenes with the Acoustic Pressure Normalized field function active and in which Representation is set to Acoustic Modes View (available after running the Acoustic Modal Solver).; Editing the acoustic mode number, dynamically edits the acoustic mode number that is displayed in the associated scalar scene. The associated scalar scene also displays text stating which acoustic mode is currently displayed, for example: