Prediction of model scale turbofan exhaust tone noise

In-duct tone levels

We begin this section by noting that the BPF tone is cut off for both fans for most of the conditions considered in this study and that the focus here is on the 2BPF tone. The BPF tone cut off is the result of the blade/vane count ratios for these fans. In theory, for perfectly identical rotor blades and perfectly identical stator vanes, the circumferential modes generated by the R/S interaction follow the Tyler-Sofrin ⁴³ rule given by the expression m = nB - kV where m is the circumferential mode order, B is the rotor blade count, V is the stator vane count, n is the BPF harmonic order, and k is an arbitrary integer (positive or negative). For a given B and n, V can be chosen so as to make the minimum | m | (i.e., that corresponding to k = 1 ) so large so as to make its constituent radial mode content evanescent (i.e., cutoff). ⁱ Naturally, this choice for V would also guarantee that radial modes corresponding to all larger | m | s (i.e., those corresponding to | k | > 1 ) are also cut off. Typically, the vane count is selected to be greater than twice the number of blades (with a sufficient margin) in order to ensure that the BPF tone is cut off at all subsonic tip relative speeds. ^j

Physically, the R/S interaction modes generated at a given BPF harmonics are the result of interference among the acoustic pressure waves emanating from the different vanes. When the interference is constructive, the mode is propagating and when the interference is destructive, the mode is evanescent. Figure 8 shows the distinction visually using predicted R/S interaction for the BPF and 2BPF tones for the ADP fan at the approach condition. The predictions, obtained using the LINFLUX code, are shown as contour plots of the real part of the harmonic acoustic pressure at 75% span. The left side of the figure shows the field for the BPF tone and the right side that for the 2BPF tone. The acoustic field generated at BPF, while intense in the vane passage, is decaying rapidly in both the upstream and downstream directions. By contrast, the field for 2BPF is propagating in both directions. OPEN IN VIEWER

The circumferential mode content for the 2BPF tone is determined by the relationship m = 2 B - kV . LINFLUX computations show that for the ADP fan only k = 1 corresponds to a propagating circumferential mode (i.e., mode m = - 9 ) at all rpm. For the SDT fan, LINFLUX results show that k = 0 , 1 correspond to propagating circumferential modes (i.e., modes m = - 10 , m = + 44 ). When the tip relative speed of the SDT fan is subsonic, predictions indicate that only m = - 10 is propagating, but when tip relative speed becomes supersonic (at 11,466 r/min), both m = - 10 and m = + 44 modes are predicted to be propagating. The mode corresponding to k = 2 (namely, m = - 64 ) is also propagating, but it is predicted to have comparatively little power. At supersonic tip relative speeds, there also exists a mode m = + 44 whose mechanism is not related to R/S interaction, but is instead related to the rotating pressure field associated with the mean loading on the rotor. This field is evanescent in the fan duct when tip relative speed is subsonic, but is propagating when it is supersonic as is the case for the SDT fan at the highest three rpm considered here. The scattering of this field by the OGV contributes to the overall acoustic power. The contribution of this mechanism is not computed by LINFLUX. The implications of this fact for the data–theory comparisons will be discussed later. Finally, another source mechanism associated with the rotor at supersonic tip relative speeds is the buzz saw noise (i.e., multiple pure tones), which contributes only to the inlet noise. This mechanism has also not been considered here.

We begin the presentation of the LINFLUX results with an illustrative example of the field solutions for the two fans. In Figure 9, contours of the real part of the 2BPF harmonic perturbation pressure are shown. The top row shows the result for ADP and the bottom row for SDT. For each fan, the propagating acoustic waves upstream and downstream of the OGV as well as the perturbation pressure distribution on all solid surfaces within the computational domain are shown. The results are for the approach rpm for both fans. For ADP, the upstream propagating acoustic field is composed of the three radial modes (−9, 0), (−9, 1), and (−9, 2), and the downstream propagating acoustic pressure is composed of only (−9, 0) and (−9, 1) radial modes, because mode (−9, 2) is cut off in the downstream direction. For SDT, the upstream propagating acoustic field is comprised of the radial modes (−10, 0), (−10, 1), (−10, 2), (−10, 3), (−10, 4), and (−10, 5), and the downstream propagating acoustic pressure is comprised of the radial modes (−10, 0), (−10, 1), (−10, 2), (−10, 3), and (−10, 4). Here we have used the notation (m, n) to identify a radial mode n belonging to the circumferential mode m. All other modes are predicted to be evanescent. For each fan, it is possible to discern the circumferential lobe pattern, i.e., the circumferential mode index (which is 9 for ADP and 10 for SDT), by counting the number of interlaced positive/negative peaks (i.e., the red and blue regions) in the contours of the upstream and downstream pressure or the pressure traces on the duct walls. The circumferential mode structure is less obvious for the pressure distributions on the stator vanes, though a careful examination of the regions with the same color does in fact reveal the circumferential order even on the vane surfaces. The minus sign of the circumferential mode index indicates that that the mode is counterrotating with respect to the rotor. The basic picture is the same at higher rpm, although the introduction of additional radial modes modifies the patterns somewhat. OPEN IN VIEWER

The complete propagating radial mode set and their SPL and PWL for the ADP fan are listed in Table 3 and those for the SDT fan are listed in Table 4. The PWLs are underlined for clarity. For ADP, up to five radial modes propagate in the swirling flow region upstream of the OGV and up to four modes in the shear flow region downstream of the OGV. The corresponding propagating mode content for SDT includes up to seven modes each in the upstream and downstream directions. The downstream propagating acoustic field can be rigorously associated with the exhaust noise as there are no obstacles in the path of propagating waves in that direction and we shall use the terms downstream and exhaust interchangeably henceforth. In contrast, the upstream propagating acoustic field cannot be directly equated with the inlet noise. That is because the effect of the rotor on the acoustic scattering, transmission, and reflection on the upstream propagating modes as well as the contribution of the other potential noise source mechanisms must be taken into account. A survey of literature suggests that there are no validated three-dimensional models of rotor acoustic transmission loss that can be used to estimate the inlet R/S interaction tone levels from the knowledge of acoustic field upstream of the OGV, especially in the presence of flow swirl. ^k

An inspection of the tabulated results indicates that, generally, there is no discernible pattern to the dependence of the predicted modal SPL and PWL on the fan rpm in the upstream direction. However, with a few exceptions, in the downstream direction the predicted modal SPL and PWL tend to increase with the increasing rpm in a fairly monotonic fashion. Unfortunately, there are no direct measurements of the modal SPL and PWL to which the predictions can be directly compared on a mode-by-mode basis. ^l However, it is possible to compare the predicted PWLs to the measured ones on the basis of the power level in the 2BPF tone. For this purpose, the LINFLUX modal power level predictions for the 2BPF tone were summed and compared with the 2BPF tone power level computed from the sideline SPL measurements.

It should be noted here that while the computation of the acoustic power from the measured (i.e., sideline) SPL data are straightforward, the same could not be said of the acoustic power calculations inside the fan duct. The reason is as follows. Where the sideline microphone track is located in the wind tunnel, the flow is essentially irrotational and nearly uniform. This allows for the use of the standard acoustic intensity formula ⁴⁸ for irrotational flows when calculating acoustic power. On the other hand, the flow through a realistic fan stage is nonuniform and rotational, a consequence of which is that the three possible families of unsteady perturbations (acoustic, vertical, and entropic) are coupled and the distinction between acoustic and convective waves is blurred. However, in view of the assumptions invoked in the LINFLUX code for computing the acoustic modes of the idealized base flows at the inflow and outflow planes of the computational domain, further approximations can be made to make the problem tractable. The idea is to take advantage of the weak coupling between the vortical and acoustic perturbations ^m riding on the idealized base flows in order to arrive at an estimate of the acoustic intensity. Essentially, the contribution of the pressure caused by the vortical disturbances is ignored and only the pressure associated with the acoustic disturbances is retained for the purpose of acoustic intensity calculations. However, as the acoustic mode sets associated with the idealized base flows do not form an orthogonal set (see literature^31,35), there is acoustic intensity in the cross products of the various modes. In LINFLUX, these cross-product terms are averaged over one axial wavelength and the resulting contribution is added to the acoustic intensity associated with the individual modes. That combined intensity is then used to calculate the acoustic power in LINFLUX. As an additional approximation, the irrotational flow intensity formula is used to calculate the axial component of the acoustic intensity for use in the power calculations.

The tone power levels from the theory and experiment are listed in Table 5. The data–theory agreement in the upstream direction is surprisingly good at the two lower rpm for both fans. This is likely because the rotor transmission loss is small at these lower rpm. Interestingly, for the ADP fan, the transmission loss is highest at the mid-range rpm (7525) and begins to decrease as the rpm increases indicating another aspect of the three-dimensional acoustic transmission physics at work. This aspect is likely related to the fact that the rotor, unlike the OGV, is not simply a passive barrier to the incident acoustic waves. Instead, due to its motion, it is also an active participant in reradiating the incident acoustic waves. This reradiation (i.e., scattering) could occur at higher radiation efficiencies resulting in elevated levels of the transmitted tones thus making for a smaller effective acoustic transmission loss. In contrast to the ADP case, for SDT, the rotor acoustic transmission mechanism is completely overwhelmed by the rotor-locked acoustic pressure field and multiple pure tones (MPT) noise at the supersonic tip relative speeds. The net effect is the higher levels of tone noise in the inlet than can be attributed to R/S interaction alone.

In the downstream direction, where a direct comparison is meaningful, the data–theory agreement is remarkably good for the ADP fan at all rpm and for the SDT fan for subsonic tip relative speeds with the agreement being to within 1 dB for all but one case where it is 2 dB. Recall that the tip relative speed is subsonic for all ADP speeds considered here. As the experimental uncertainty in the sideline SPL (and hence PWL) measurements in the 9 ft × 15 ft wind tunnel has been established to be ±1dB, ⁴⁹ the PWL data–theory agreement in the exhaust is in fact excellent. When the tip relative speed is supersonic for the SDT fan, the acoustic field associated with the propagating rotor-locked pressure field scattered by the OGV could also contribute to the exhaust tone levels raising the combined measured levels above the contribution from the R/S interaction source alone. The tabulated levels in Table 5 are plotted in Figure 10 to more clearly convey the trends with the fan rpm. The predicted and measured SDT power levels in the inlet have been plotted less than 5 dB to avoid overlap with the ADP inlet power level curves. OPEN IN VIEWER

Comparisons with a R/S analytical model

At this point, we digress to examine the validity of employing the classical plug-flow duct mode description that is typically used in analytical or semi-analytical models of the R/S interaction tone noise. Recall that, in contrast, LINFLUX relies on numerically computed swirl or shear flow duct modes to represent the upstream and downstream propagating acoustic waves. To ensure a valid comparison of the results between the two types of duct mode descriptions, we have used the three-dimensional unsteady loading distributions on the OGV computed by LINFLUX as well as the three-dimensional geometry of the vanes as input to the analytical model. Recall that the analytical/semi-analytical models of R/S interaction noise typically rely on highly simplified descriptions of the OGV loading and geometry as well as on the analytical duct mode description. The goal here is to eliminate the limitations imposed by the simplified loading and geometry and focus solely on the effect of the duct mode description on the predicted mode levels.

The mathematical derivation of the frequency-domain analytical formula for calculating the acoustic field generated as a result of rotor wake impingement on the OGV is fairly straightforward and can be readily found in the literature. Here, we shall use the formula derived in literature ³⁴ (equation 4.25): ⁿ

p ' ( x ; ω ) = ∫ ∫ S ( x s ) n ∧ s · ∇ G ( x | x s ; ω ) f ( x s ; ω ) ds ( x s )

(1a)

G ( x | x s ; ω ) = ∑ m = - ∞ ∞ ∑ n = 0 ∞ 1 π ( r T 2 - r H 2 ) ( ω / c D ) 2 - β D 2 κ mn 2 Ψ mn ( r , θ ) Ψ mn * ( r s , θ s ) e ik mn ± ( x - x s )

(1b)

Ψ mn ( r , θ ) = [ AJ m ( κ mn r ) + BY m ( κ mn r ) ] e im θ

(1c)

k mn ± = 1 ( 1 - M D 2 ) ( M D ω / c D ± ( ω / c D ) 2 - β D 2 κ mn 2 ) , β D 2 = 1 - M D 2

(1d)

The acoustic pressure p ' in the duct, at the frequency ω, is given by the surface integral in equation (1a) where f is the harmonic loading on the vane, n ∧ s the unit outward normal to the vane surface. G, given by equation (1b), is the Green’s function, which provides a modal description of the sound field inside the duct in terms of the acoustic modes of a constant cross-sectional area annulus with a uniform (plug) flow inside it. The modes are denoted by Ψ mn and are expressed in terms of the Bessel functions of the first and second kind (equation 1c) and are associated with the radial eigenvalue κ mn . The integration is over the surface of the vane S ( x → s ) . r_H and r_T denote the hub and tip radii of the annular duct, and M_D and c_D designate the duct Mach number (for plug flow) and duct ambient speed of sound. x → = ( x , r , θ ) and x → s = ( x s , r s , θ s ) are the observer (i.e., field point) and source coordinates. k mn ± in equation (1d) denotes the axial wavenumber of a mode with the minus sign indicating an upstream propagating mode and plus sign a downstream propagating mode. The term under the square root sign is the mode cut-off condition, which can be rewritten as ( ω / c D ) 1 - 1 / ξ 2 with ξ = ( ω / c D ) / β D κ mn denoting the mode cut-off ratio. For ξ < 1 , the mode is cut off (i.e., k mn ± is complex and the mode is evanescent). For a hard wall duct, the coefficients A and B are given by either one of the two equivalent sets:

A = 1 B = - J ' m ( κ mn r H ) Y ' m ( κ mn r H ) , or A = - Y ' m ( κ mn r T ) J ' m ( κ mn r T ) and B = 1

(1e)

If the distribution of the aerodynamic pressure f on the vane surface is known, the integration in equation (1a) can be explicitly carried out and the tone sound field inside the duct resulting from R/S interaction can be computed. As was stated earlier, we have used the three-dimensional geometry of the vane and the associated loading distributions that were computed with LINFLUX for that purpose. In fact, for convenience, we have used the vane surface grid from the LINFLUX simulations for calculating the surface integral in equation (1a). The SPLs and PWLs calculated by LINFLUX and those form the analytical model (i.e., equation 1a) for all the propagating modes (as determined by each model) are listed in Tables 6 through 9. The LINFLUX levels are the same as those listed in Tables 3 and 4. The analytical model levels are underlined for clarity.

The mode SPL comparisons indicate that, save for incidental agreement in a few instances, there is no discernable pattern of agreement between the LINFLUX and analytical mode results in either the upstream or downstream directions. The comparison is only marginally better for PWL in the upstream direction. However, in the downstream direction, there is much more consistent agreement between the PWL computed using LINLFUX and the analytical model results for a large number of modes or, at least, for the modes with the highest power levels. These comparisons suggest that for the purpose of computing the SPLs, the plug-flow assumption does not correctly model the modal content (i.e., the amplitudes and phases) of the tonal sound field inside the fan duct (upstream or downstream). This despite that fact that the tone power levels are reasonably well-predicted in the downstream direction using the classical mode theory if the vane surface pressures are accurate. These observations are reconcilable by noting that the PWL is a global (i.e., an integrated) quantity whereas the SPL is, in a sense, a local quantity. On the basis of these results, it is expected that on the basis of the tone power level (i.e., the sum of power levels in all the propagating modes), there would be a good agreement between the LINFLUX predictions and the analytical model predictions in the downstream direction. That is indeed the case as shown in Figure 11. The agreement in the downstream direction is quite good, whereas it is only marginal for the upstream direction. OPEN IN VIEWER

These comparisons suggest that, whereas the plug-flow mode description in the upstream direction substantially misrepresents the physics of the swirling flow duct modes, in the downstream direction (where there is mostly shear flow) it does seem to model the acoustic power reasonably well. Of course, the principal reason for the good agreement is that the source amplitudes (i.e., the vane surface pressure distributions) are the same in both cases. The comparisons would not be nearly as good if a simpler source model (such as the flat plate strip analysis) was used to calculate the unsteady loading on the vanes in the analytical model. The salient point here is that the three-dimensional high-fidelity calculation of the vane surface pressure is crucial in developing a robust and accurate model for predicting the R/S interaction tone levels.

Sideline tone directivities

In the previous section, data–theory comparisons could only be carried out on the basis of PWL. In this section, we have used the exhaust SPLs computed by LINFLUX as input to an acoustic radiation model and projected them to the sideline locations in the wind tunnel where tone SPL had been measured in order to carry out a data–theory comparison on the basis of SPL. We have used an aft-duct radiation code developed by Eversman ⁵⁰ for that purpose. This code is based on a frequency-domain, finite element formulation for the problem of acoustic radiation from an axisymmetric exhaust duct. The Eversman code solves weighted residual formulations for the mean flow and acoustic perturbations. To calculate a solution, in addition to the geometry of the exhaust duct (which must include the aft nacelle profile), the in-duct acoustic pressure distribution is needed at an appropriate axial plane, which serves as the input plane to the computational domain for the Eversman code. In this study, the input plane is taken to be the outflow boundary of the LINFLUX computational domain. The acoustic pressure specification in the Eversman code is accomplished via the analytical duct mode description given by equation (1c) using only the cut-on modes in one circumferential mode m at a time. Note that, only the pressure specification at the boundary is in terms of the classical duct modes. The subsequent evolution of the acoustic modes in the Eversman code is on the basis of a nonuniform mean flow, which depends on both the axial and radial coordinates. It should be noted that the mean flow, which is computed as part of the solution, is modeled as irrotational.

The presence of the nozzle shear layer poses special challenges as the dynamic of a real shear layer is highly complex and beyond the scope of the theory underlying the Eversman code. As a result, some simplifications are necessary to make the problem tractable. The shear layer is assumed infinitely thin and extending a finite distance downstream of the nozzle and terminating well before the end of the computational domain. Where it is assumed to exist, the shear layer marks the boundary between an “inner” and an “outer” flow region. The inner flow region is taken to be an extension of the exhaust duct flow and the outer flow region encompasses the rest of the external computational domain. The velocity potential is discontinuous across the shear layer, but becomes continuous when the shear layer ends. The inner and out flows are permitted to mix on a potential flow basis downstream of the shear layer termination point. The extent of the shear layer is chosen to provide acoustic wave refraction across the layer while minimizing the effect of the artificial flow mixing on the acoustic waves. The presence of the shear layer also necessitates the specification of two continuity conditions along the layer. These are the continuity of the acoustic pressure and the continuity of the shear layer displacement. Under these conditions, the layer effectively behaves as an impermeable boundary to the mean flow, but transmits the acoustic perturbations across by virtue of its local motion (see literature ⁵⁰ ).

Because the theory models the aft-radiated noise, the computational domain does not include the inlet region either internal or external to the fan duct. Inside the fan duct, the domain begins at the outflow boundary of the LINFLUX computational domain. External to the fan duct, a “baffle” is introduced to isolate the aft-radiated acoustic field from the inlet. The baffle location is chosen sufficiently far away from the nozzle to minimize its influence on the solution. Additionally, the aft centerbody is shortened and tapered in order to reduce the size of the computational domain and improve the quality of the finite element mesh. The recommended rule for specifying the mesh density in the Eversman code is that there should be at least five elements per wavelength in the principal direction of propagation, which is axial in the duct and radial in the external domain. The formula relating the number of elements per wavelength ( N λ ) to number of elements per unit length ( N R ¯ ) is given by N R ¯ = η N λ / 2 π ( 1 + M ) where η = ω R ¯ / c ∞ is the nondimensional frequency, ω is the harmonic frequency, R ¯ is a reference length (usually taken to be the duct radius at the input plane), c ∞ is the freestream speed of sound, and M is the local Mach number in the domain. For the calculations presented in this paper, N λ was set to 10 for the highest 2BPF frequency considered and the resulting grid was used for all lower speed calculations. Figure 12 depicts a typical arrangement of the computational domain including the changes discussed above as well as the finite element grid used in the radiation calculations. The example shown is for the ADP fan, but the SDT domain is similar. OPEN IN VIEWER

Finally, it should be noted that to ensure a good-quality finite element mesh, the coordinate origin had to be shifted downstream (the red dot in Figure 12) from its normal position (the black dot in Figure 12), which is the stacking axis of the fan. The shift used here is equal to one input plane radius, which is R ¯ = 11 . 3 ″ (0.29 m) for the ADP fan, and it is R ¯ = 11 . 0 ″ (0.28 m) for the SDT fan. The farfield boundary of the computational domain is set sufficiently far to ensure that the target sideline microphone positions are all located within the radiation domain. Of course, due to the presence of the baffle, only angles equal to or greater than 90° will be considered in the data–theory comparisons that will follow in order to minimize the influence of the baffle on the results.

For the radial mode amplitude specification at the input plane, theoretically, the pressure distribution at the LINFLUX outflow plane should be expanded in the terms of the radial modes of the classical theory. In other words,

∑ n = 0 N P ' mn ( x inputplane , r ; ω j ) e im θ | LINFLUX = Π ' m ( x inputplane , r , θ ; ω j ) | LINFLUX = ∑ n = 0 M p ' mn ( x inputplane , r ; ω j ) e im θ | ClassicalTheory

(2)

The aft radiation calculations were carried out for both fans, but for the SDT fan, the calculations were restricted to the subsonic tip relative speeds because for the supersonic tip relative speeds, the contribution of the rotor-locked pressure field is missing from the predicted in-duct levels (see Figure 10 and the associated discussion).

We begin the presentation of the sideline results with Figure 13, which shows the predicted directivity of the 2BPF tone on the 89.3″ (2.27 m) sideline for the ADP fan at the 8750 r/min. The abscissa is the sideline (geometric) angle and the ordinate is the SPL on the sideline. The purpose of this plot is to show the relative contributions of the constituent (propagating) radial modes to the overall tone level and the way the relative phase among the modes can affect the tone directivity. OPEN IN VIEWER

The comparisons of the predicted and measured sideline SPLs for the 2BPF tone are shown in Figure 14 for the ADP fan and in Figure 15 for the SDT fan. We remind the reader that the radiation calculations were carried out for all speeds for ADP, but only for two subsonic tip relative speeds for SDT. As indicated earlier, the sideline levels were computed using the input mode levels calculated by the LINFLUX code. It should be noted that the angular resolution of the computed directivities is far higher than the measured directivities (0.1° vs. 2.5°). As such, the definition of the peaks and valleys in the SPL directivity are much better resolved in the computations than they are in the measurements. As a result, the relatively coarse measured directivities do not necessarily represent the true behavior of the tone directivities if they were viewed on finer angular increments. In spite of this limitation in the data, for the most part, the data–theory agreement is reasonable especially for sideline angles greater than 120°. While there are substantial discrepancies at some sideline angles for some speeds, the overall trends with speed are well captured. OPEN IN VIEWER

OPEN IN VIEWER

Figure 15.

Comparisons of predicted and measured 2BPF sideline sound pressure levels for the SDT fan at the subsonic tip relative speeds. LINFLUX mode amplitude predictions were used as input to the Eversman radiation code. BPF: blade passing frequency; SDT: source diagnostic test.

Generally speaking, the comparisons are encouraging for several reasons. First, the chain of calculations, from the RANS flow simulations for estimating the rotor wakes, to the linearized Euler simulations for computing the in-duct levels, to the linearized potential field simulations for computing the exhaust acoustic radiation to the sideline, has not been calibrated in any way. Second, as Figure 13 indicates, the nature of the tones is such that they are dependent on the relative phases of their constituent radial modes requiring a precise prediction of the modal phases, which is a difficult task especially in view of the next two observations. Third, an examination of the sideline measurements of the tones in the wind tunnel indicates that the fan tones are inherently “unsteady” due to the slight, but ever present, variations in the fan rpm resulting from fluctuations in the wind tunnel environment. The ADP and SDT fan tests in the 9 ft × 15 ft wind tunnel were conducted by holding the target rpm, known as the corrected rpm (denoted by RPM_c) constant. RPM_c is related to the physical (i.e., actual) rpm (denoted by RPM_a) via the relationship RPM c = RPM a / T a / T 0 , where T_a is the ambient total temperature and T₀ the standard day temperature. Therefore, small fluctuations in the tunnel conditions require constant adjustment of the actual rpm in order to ensure that the corrected rpm remains constant throughout a run. These small variations in the actual rpm result in small but detectable change in the tone levels and their sideline directivities making tone levels and their directivities inherently nonstationary in time. ⁵¹ In effect, the measured tone levels (extracted from the microphone data) represent averaged snapshots of tone spectra over a finite acquisition time. Fourth, and perhaps most importantly, given the nature of sound refraction through a region of velocity gradient, the shear layer generated downstream of the fan exhaust nozzle lip plays an important role in determining the directivity of the fan exhaust tones in the freefield. As such, the shear layer model embedded in the Eversman code while practical to use, oversimplifies the physics of refraction of the sound waves through a real exhaust stream potentially affecting the accuracy of the predicted sideline results.