Linearized Euler Model
Use the Linearized Euler Model to set up the governing equations, define the background mean flow, the ideal gas fluid properties, and select gradient term suppression stabilization, if needed. The governing equations solved are (in the time domain):
(4-1)
where ρt, ut, and pt are the acoustic perturbations to the density, velocity, and pressure, respectively. The subscript “t” refers to the fact that the acoustic variables are the total fields, that is, the sum of possible Background Acoustic Fields and the scattered fields.
In the frequency domain the time derivatives of the dependent variables is replaced by multiplication with iω. The variables with a zero subscript are the background mean flow values, γ is the ratio of specific heats. The right-hand-side source terms Sc, Sm, and Se are zero. They can be defined in the Domain Sources node. Details about the physics interfaces and references are found in the Theory Background for the Aeroacoustics Branch section.
Model Inputs
In order to model the influence of the background mean flow on the propagation of the acoustic waves in the fluid the background mean flow temperature T0, absolute pressure p0, and velocity field u0 need to be defined.
All the background flow parameters can be functions of space. They can be either analytical expressions (user defined) or they can be picked up from a flow simulation performed using the CFD Module. By default they are set to the quiescent background conditions of air.
Enter User defined values for the Background mean flow temperature T0 (SI unit: K), Background mean flow pressure p0 (SI unit: Pa), and Background mean flow velocity u0 (SI unit: m/s). The defaults are 293.15 K, 1 atm, and 0 m/s, respectively.
Note that the Background mean flow density also needs to be defined or entered in the Fluid Properties section below.
When modeling aeroacoustics it is important how the Mapping Between CFD and Acoustics Mesh is done from a numerical perspective.
Fluid Properties
Select an option for the Background mean flow density ρ0 (SI unit: kg/m3) — Ideal gas (the default), From material, User defined (default value 1.2 kg/m3), or it can be picked up from a flow interface, for example, from a High Mach Number Flow model as Density (hmnf/fluid1). As the flow is assumed to be an ideal gas, the background density ρ0 is readily defined as
where Rs is the specific gas constant, it can also be defined as a material input and is then defined as ρ0 = ρ0(p0,T0), or it can be picked up from a flow model.
Define the remaining fluid properties necessary for defining an ideal gas. Select the Gas constant type: Specific gas constant (the default) or Mean molar mass. The defaults take values From material or for User defined enter another value or expression:
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Specific gas constant Rs (SI unit: J/(kg⋅K)). The default is 287.058 J/(kg⋅K)).
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Mean molar mass Mn (SI unit:  g/mol). The default is 28.97 g/mol), which calculates Rs = R/Mn, where R is the gas constant.
Select an option from the Specify Cp or γ list: Ratio of specific heats (the default) or Heat capacity at constant pressure. The defaults take values From material or for User defined enter another value or expression:
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Ratio of specific heats γ (dimensionless). The default is 1.4.
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Heat capacity at constant pressure Cp (SI unit: J/(kg⋅K)). The default is 1005.4 J/(kg⋅K)), which calculates γ = Cp /(Cp - Rs).
Gradient Term Suppression Stabilization
When the linearized Euler (LE) equations are solved in the time domain (or in the frequency domain with an iterative solver), linear physical instability waves can develop, the so-called Kelvin-Helmholtz instabilities. They are instabilities that grow exponentially because no losses exist in the LE equations (no viscous dissipation and no heat conduction). Furthermore, they are limited by non-linearities in the full Navier-Stokes flow equations. It has been shown that the growth of these instabilities can be limited, while the acoustic solution is retained, by canceling terms involving gradients of the mean flow quantities. This is known as gradient terms suppression (GTS) stabilization.
More details in Ref. 9, Ref. 10, Ref. 11, and the Theory Background for the Aeroacoustics Branch section.
Select the following check boxes to activate the applicable gradient term suppression (GTS), which is a form of physical stabilization where certain terms involving gradients of the background mean flow properties are removed:
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Suppression of mean flow density gradients
This option sets the following terms in the governing equations to zero:
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Suppression of mean flow velocity gradients
This option sets the following terms in the governing equations to zero:
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Suppression of mean flow pressure gradients
This option sets the following terms in the governing equations to zero: