jet

class description

class jet.Jet

Bases: object

static jet_mixing(source, theta, inputs: openmdao.vectors.default_vector.DefaultVector) → numpy.ndarray

Compute jet mixing noise mean-square acoustic pressure (msap).

Parameters

• source (Source) – pyNA component computing noise sources

• inputs (openmdao.vectors.default_vector.DefaultVector) – unscaled, dimensional input variables read via inputs[key]

Returns

msap_jet_mixing

Return type

[n_t, settings.N_f]

static jet_shock(source, theta, inputs: openmdao.vectors.default_vector.DefaultVector) → numpy.ndarray

Compute jet mixing noise mean-square acoustic pressure (msap).

Parameters

• source –

• inputs (openmdao.vectors.default_vector.DefaultVector) – unscaled, dimensional input variables read via inputs[key]

Returns

msap_jet_shock

Return type

[n_t, settings.N_f]

theory

Jet mixing noise

Jet mixing noise accounts for the noise generated by turbulent jet fluid exiting a nozzle creating a shear layer with the surrounding fluid. The SAE ARP876 method is used to estimate mean-square acoustic pressure of the the jet mixing noise:

\[<p^2(r_s^*)>^* = 10\log_{10}\left[\frac{\Pi^*_{jet}A_{jet}^*}{4\pi (r_s^*)^2p_{\textrm{ref}}^2} \frac{D(\theta,V_{jet}^*) F(S_c, \theta,V_{jet}^*,T_{jet}^*)}{1-M_0 \cos(\theta-\delta)} \left(\frac{V_{jet}^*-M_0}{V_{jet}^*}\right)^{m(\theta)} \right]\]

where:

\[\Pi_{jet}^* = (6.67\cdot 10^{-5}) (\rho_{jet}^*)^{\omega(V_{jet}^*)} (V_{jet}^*)^8 P(V_{jet}^*)\]

The density exponent, \(\omega\), accounts for the effect of density on noise in heated jets. The Strouhal number, \(S_c\), used in the spectral distribution function, \(F(S_c, \theta,V_{jet}^*,T_{jet}^*)\), is given by \(S_c = \frac{f^*d_{jet}^*}{\xi(V_{jet}^*)(V_{jet}^*-M_0)}\). The directivity function, \(D(\theta, V_{jet}^*)\), the spectral distribution, \(F(S_c,\theta,V_{jet}^*,T_{jet}^*)\), the density exponent, \(\omega(V_j^*)\), the power deviation factor \(P(V_{j}^*)\), the Strouhal correction factor \(\xi(V_{jet}^*)\), and the forward velocity index \(m(\theta)\) are tabulated online.

Jet shock-cell noise

Supersonic jets that are not perfectly expanded will create a shocks cell structure that interact with the turbulent jet flow. This interaction is the main driver of the shock-cell noise. The SAE ARP876 method is used to estimate jet-shock cell mean-square acoustic pressure for supersonic exhaust Mach numbers (\(M_{jet}>1\)):

\[<p^2(r_s^*)>^* = 10\log_{10} \left[ \frac{1.92\cdot10^{-3} A_j^*}{4\pi(r_s^*)^2p_{\textrm{ref}}^2} \left[\frac{1+W(\sigma,\theta,V_j^*)}{1-M_0 \cos(\theta-\delta)}\right] \beta^\eta H(\sigma) \right]\]

The pressure ratio parameter, \(\beta = \sqrt{M_{jet}^2-1}\), indicates that shock noise will only be produced with a supersonic exhaust velocity. The frequency parameter, \(\sigma = 7.8\beta(1-M_0 \cos \theta) \sqrt{A_{jet}^*}f^*\), where \(f^* = f\sqrt{A_e}/c_0\). The pressure ratio parameter, \(\eta\), is given by:

\[\begin{split}\eta = \begin{cases} 1 & \textrm{if } T_{jet}^* < 1.1 \text{ and } \beta > 1 \\ 2 & \textrm{if } T_{jet}^* \leq 1.1 \text{ and } \beta > 1 \\ 4 & \textrm{if } \beta \leq 1 \end{cases}\end{split}\]

The shock-cell interference function, \(W(\sigma, \theta, V_{jet}^*)\), is given by:footnote{This equation is an updated version of Eq. 6 on page 8.5-4 in Zorumski. To obtain the shock cell interference function graph on Figure 4 in Zorumski, one factor textit{b} in the denominator should be omitted.}

\[\begin{split}\begin{split} W = \frac{4}{N_s b} \sum_{k=1}^{N_s-1} \left[C(\sigma\right]^{k^2} \sum_{m=0}^{N_s - (k+1)} \frac{\sin (b\sigma q_{km}/2)}{\sigma q_{km}} \cos(\sigma q_{km}) \hspace{0.5cm} \textrm{where} \\ \hspace{0.5cm} q_{km} = \frac{1.7k}{V_{jet}^*} \left[ 1 - 0.06 \left( m + \frac{k+1}{2} \right) \right](1 + 0.7V_{jet}^* \cos \theta) \end{split}\end{split}\]

The correlation coefficient, \(C(\sigma)\), and the group source strength spectrum, \(H(\sigma)\), are tabulated online.