Unsteady velocity measurements of model-scale supersonic exhaust jets in military-relevant configurations

Abstract

Of the utmost importance is the need to better understand the high temperature, high velocity flow fields generated by military tactical aircraft during “run up” and take-off that gives rise to extremely hazardous conditions for personnel and equipment within the vicinity of the aircraft. The present study aims to fill the need for high frequency, two velocity component measurements throughout the flow fields produced by university-scale supersonic jets exhausting from nozzles in configurations relevant to practical, full-scale application. Specifically, this work focuses on studying the supersonic jets operating in two basic configurations: horizontal, free jets and jets impinging normal to a ground plane reminiscent of current short-takeoff and vertical landing aircraft. Experiments are conducted at nozzle operating conditions similar to those of full-scale aircraft. Both mean velocities and turbulence components are measured in both flow fields using a laser Doppler velocimeter. Axial components of the mean flow and turbulence are measured in the free jet. In the single impinging jet flow field two-component mean velocity and turbulence components are measured in the jet plume, impingement region, and outwash flow. Free jet velocity measurements show good consistency with 50% increase in jet Reynolds number. Turbulence intensities up to 15% of the mean jet exit velocity are observed at the nozzle exit plane. Laser Doppler measurements in the outwash of an impinging jet show turbulent fluctuations produce unsteady velocities well above the mean value. Two-component impinging jet unsteady velocity spectra show a distinct peak at the same frequency as the impingement tone observed in prior impinging jet acoustic field measurements.

Keywords

Laser Doppler velocimetry supersonic jet impinging jet unsteady velocity measurements

Introduction

Experiments led by Dr. Dennis K. McLaughlin have been underway at Penn State University for a number of years on the aerodynamics and aeroacoustics of supersonic jets. In general, the research at Penn State is of a fundamental nature but addresses issues related to the flow fields of Navy aircraft currently in service. Tactical aircraft that operate from aircraft carriers produce noise levels on take-off that endanger the hearing health of Naval personnel who work on the flight line. The introduction of F-35B, STOVL aircraft during shipboard operations has required better understanding of the high speed, high temperature impinging jet flow field. Although the noise produced by such aircraft is an annoyance, the downwash of the powered lift system is of great concern to the Navy. This paper describes experiments using small scale, geometric replicas of aircraft engine exhaust nozzles, with similar operating conditions, in both free and impinging jet configurations, that were conducted in the Penn State aeroacoustics facility.

Navy shipboard personnel may be exposed to the aerodynamic and acoustic environment surrounding both the more conventional catapult-assisted take-off and arrested recovery aircraft as well as STOVL aircraft. Efforts at Penn State are being made to better characterize the flow field dynamics and acoustics of both supersonic free and impinging jets. Experiments in the Penn State facility have provided data to guide and evaluate numerical simulations of supersonic free jets with noise reduction technologies.^1,2 More recently, the capability of the Penn State aeroacoustics facility has broadened to include experiments to characterize aerodynamic hazards in the shipboard operation of a new generation of STOVL aircraft.³ Penn State has designed and fabricated a generic scale model of the tandem main vertical jets. Experimental data collected will guide and eventually validate the CFD flow field simulations being developed to assist the shipboard operation engineering.³ The focus of the present measurements includes supersonic, free jet flows and flows of a single, cold, over-expanded supersonic impinging jet in the wall impingement region and in the radially flowing wall jet.

Alvi and Iyer⁴ describe the three major regions of the impinging jet flow field: (i) the primary jet plume that retains the characteristics of a free jet, (ii) the impingement zone, characterized by strong velocity gradients and a turning of the flow parallel to the ground plane, and (iii) the wall jet or outwash flow parallel to the plate. Donaldson and Snedeker⁵ proposed that the mean properties of the jet plume remain unchanged upstream of any strong local interaction effects that are a result of impingement. It can be expected that the noise generated by high subsonic and supersonic impinging jets has characteristics of their free-jet counterparts (i.e. turbulent mixing noise, broadband shock-associated noise, BBSAN, and jet screech) in addition to aeroacoustic phenomena unique to jet–surface interactions including impingement tones, ground plate scrubbing noise, and positive/negative reinforcement of noise sources.

Unique to impinging jet flows is the closed-loop resonant phenomenon generally referred to as impingement tones. Instabilities traveling in the shear layer of the jet plume may impact the ground plane and generate strong acoustic waves that propagate upstream back to the nozzle exit or lift plate further exciting instabilities of the same frequency. Particle image velocimetry (PIV) images obtained by Krothapalli et al.⁶ showed large scale turbulent structures in the jet plume impinging on the ground plane. These large scale structures retained coherence upon traversing laterally into the outwash region. High speed shadowgraph visualization provided evidence that upstream-propagating acoustic waves originated in the stagnation region of the impinging jet. The findings of Krothapalli et al.⁶ are in agreement with the earlier model of impinging jet tone production proposed by Tam and Ahuja.⁷ The authors developed a theoretical model to attempt to predict whether the loop is closed by feedback waves traveling up the jet column or acoustic fluctuations propagating through the quiescent medium.

Henderson et al.⁸ studied supersonic impinging jets using time-resolved particle image velocimetry (TRPIV) and shadowgraphy. The authors reported results supporting.⁶ Large scale instabilities were observed to result due to wall jet oscillations. Phase-locked shadowgraph images showed sound waves originating from the boundary between the oscillating wall jet and ambient air that propagate back to the nozzle lip. More recently, large-eddy simulations (LES) by Gojon et al.⁹ captured impingement tone frequencies and mode jumps observed in earlier experiments. The presence of these impingement tones can increase overall sound pressure levels by several decibels and be a source of unsteady loading on the aircraft. It is worth noting that pressure and total temperature measurements in free jets by Glass¹⁰ provided evidence that strong acoustic tones can increase supersonic jet spread rates by as much as 50%.

Predictions of supersonic jet noise, using either models such as acoustic analogies or computational fluid dynamics (CFD), depend on accurate experimental databases. Specifically, advanced statistics such as the spectral characteristics acquired from space–time correlations for the broad range of jet conditions required for current prediction methods are largely unavailable.¹¹ Furthermore, the complex flow fields encountered in the present impinging jet scale model experiments have turbulence components for which no accurate turbulence models have been developed.

Numerous unsteady velocity measurements have been conducted with various instruments in subsonic cold jets. Harper-Bourne¹² described hot-wire measurements in a low speed unheated jet. Turbulence measurements along with detailed statistics were given and used to model the source term in Lighthill’s acoustic analogy. Morris and Zaman¹³ also performed hot-wire measurements at several locations within the jet along both the lip and centerline. Their study compared the relationship between second and fourth order correlations and deduced the corresponding length scales. While both studies were very extensive, hot-wire measurements in supersonic heated jets are impractical due to the fragility of the sensors. Molecular Rayleigh scattering has also been used to investigate the turbulence characteristics of jet exhausts, specifically in Panda and Seasholtz¹⁴ and Panda et al.¹⁵ However, this technique has proved to be very difficult and time consuming for many researchers and has additional limitations when applied to high speed jet flows.

Turbulence measurements were performed using the optical deflectometer as described originally in Doty and McLaughlin¹⁶ and later in Veltin et al.¹⁷ The optical deflectometer relies on the Schlieren principle; photo detector signals within the image plane are related to density fluctuations within the jet. Two point space–time correlations were performed and the convection velocity calculated for a large range in frequency. This technique was applied to cold supersonic jets. The optical technique is physically measuring the integrated refractive index of the air throughout the entire beam path. This works very well with pure air jets, however with helium-air mixture jets, success was limited. This is believed to be due to the fact that the refractive index is more heavily dependent on the helium concentration at the measurement location rather than the density fluctuations. Thus, reliable and accurate convection velocity measurements for heat-simulated jets within the jet shear annulus could not be obtained.

Two instruments that measure the velocity of small particles seeded into air (and water) streams are the laser Doppler velocimeter (LDV) and the particle image velocimeter (PIV). The LDV is occasionally referred to as a laser Doppler anemometer (LDA). For the past decade, PIV has been used extensively by many research groups to characterize the mean velocities and turbulence levels of jet exhausts. A major advantage of this technique is that it provides unsteady velocity information for extensive regions of flow fields so that spatial correlations can be obtained quite accurately. This technique has now been further developed into TRPIV, which uses a more extensive electro-optical setup and only focuses on part of the flow field. As described and documented in detail by Bridges and Wernet,^18,19 TRPIV allows for the time resolved spectral characterization of the flow field. However, due to the massive amount of data throughput required for these systems, current state of the art systems only sample the velocity field up to 10–20 kHz.²⁰ For a moderate scale jet, this allows the spectral velocity field to be resolved to a Strouhal number just less than 1. Brock et al.²¹ had limited success with multiple time synchronous simultaneous PIV systems that achieved sampling rates approaching 1 MHz. To obtain velocity measurements at higher frequencies, TRPIV is not as versatile as a classical LDV system. This is especially important when accounting for the small jet diameter and higher characteristic frequency used in typical university research facilities.

Laser Doppler systems have been used in the past to study the flow field of supersonic exhaust jets. Excellent data have been previously acquired by Lau et al.²² and Lau,²³ but turbulent spectra and convection velocity as a function of frequency were not presented. Kerhervé et al.²⁴ performed two-point space–time correlations within a supersonic Mach 1.2 cold jet. Thus, while this study was very thorough, the pursuit of spatio-temporal characteristics for a heated supersonic exhaust jet still continues. Recently, LDV has been used by Brooks et al.²⁵ and Brooks and Lowe²⁶ to measure turbulent statistics in a new facility with cold and electrically heated over-expanded supersonic jets. Doppler Global Velocimetry, a derivative technique of LDV, has been used by the same researchers in Ecker et al.^27,28 to obtain fourth-order statistics and velocity spectra with a frequency resolution that exceeds 100 kHz.²⁹

In order to obtain measurements at high sampling rates in the small scale High Speed Jet Aeroacoustics Facility, a laser Doppler system was built and developed for supersonic flow. The development and testing of the LDV system with convergent subsonic jets was performed by Karns.³⁰ Further development and measurements with supersonic jets was performed by Karns et al.³¹ These measurements were compared and validated against steady RANS simulations documented in Miller and Veltin.³²

A LDV system has been developed for these experiments predominantly because of the high speed/frequency requirement as well as the need to make near wall measurements where reflections can often prove difficult for PIV systems. To this point, all measurements have been performed with cold supersonic jets only. However, the goal during development of the system was to eventually test in heat-simulated helium-air mixture supersonic jets.

The goals of the experiments presented here are to make unsteady velocity measurements in the high shear regions of cold supersonic jets, operating in two basic configurations. First is a horizontal free jet operating with a geometry and operating conditions similar to those used in take-off by tactical aircraft on board an aircraft carrier. The second is a supersonic jet impinging normal to a ground plane as part of the dual impinging jet model flow field. Mean velocities and components of the turbulence are measured in both of these flow fields. The unsteady axial velocity component together with the axial component of the turbulence intensity is measured in the free jet, whereas two unsteady velocity (and turbulence) components are measured in the impingement region and the wall jet of the single impinging jet experiment. The following sections describe the two model configurations of the facility and the experimental approach for both series of experiments. The results of the experiments are then presented along with the discussion followed by conclusions of the study.

Technical approach

Facility description and acoustic measurements

Experimental results presented in this work were conducted in the Pennsylvania State University High Speed Jet Aeroacoustics Laboratory. This anechoic chamber facility is a $5.02 m \times 6.04 m \times 2.79 m$ room covered with fiberglass wedges producing a theoretical cut-off frequency of 500 Hz. At present, the facility can operate in two modes with a: (i) single, horizontal, free jet and (ii) twin jets in normal impingement to a ground plane. A top-down view of the aeroacoustics facility is shown in Figure 1. Specific details on the facility configuration, operation, and acoustic data collection and processing may be found in Powers and McLaughlin³³, Powers³⁴ and Hromisin et al.³⁵

Figure 1.

Top-down view schematic of the Pennsylvania State University High Speed Jet Aeroacoustics Facility.

Free jet experimental setup

The supply air is fed into a horizontal plenum mounted within the wall of the anechoic chamber as seen in Figure 1. The end of the plenum was designed in such a way that different geometry jet nozzles can be easily attached and operated.

LDV measurements were acquired in free jets issuing from nozzles representative of those found on the F404 family of low bypass ratio turbofan aircraft engines (used on the F-18 aircraft). Inner contours of the military-style nozzles were provided by General Electric Aviation under a previous contract. The divergent section of these nozzles contains a flap and seal configuration that consists of 12 straight, flat segments that are interleaved to facilitate area adjustment of the full-scale operational nozzles. The model-scale nozzle area ratio was selected to be 1.295. This is a typical configuration for a takeoff scenario of one of these aircraft. This results in a design Mach number, M_d, of 1.65. In this study, three different sized nozzles were used with exit hydraulic diameters, D_noz, of 18.0 mm (Gen1A-scale), 22.6 mm (Gen1B-scale), and 27.0 mm (Gen2-scale). A photograph of the LDV system configured for free jet measurements with Gen1B-scale model nozzle installed is shown in Figure 2. Nozzle geometries and operating conditions are tabulated in Table 1. Jet Reynolds numbers (Re) are based on jet conditions at the nozzle exit plane. Results presented for the Gen2-scale nozzle represent a 50% increase in scale and Reynolds number from the Gen1A-scale nozzle also used in this study.

Figure 2.

Photograph of the transmitting and receiving optics for the LDV system installed in the high speed jet aeroacoustics facility at Penn State.

Table 1.

Baseline nozzle descriptions.

Nozzle	D_noz (mm)	M_d	M_j	Reynolds number	Lip thickness (mm)
Gen1A BLA	18.0	1.65	1.36	$7.47 \times 10^{5}$	0.51
Gen1B BLF	22.6	1.65	1.36	$9.34 \times 10^{5}$	0.40
Gen2 BLA	27.0	1.65	1.36	$1.12 \times 10^{6}$	0.42

Impinging jet experimental setup

The dual impinging jet experimental model was designed to be representative of a generic military-style STOVL tactical aircraft, such as the F-35B, in hover. The experimental model consists of two vertically-oriented, stainless steel nozzles embedded in a rectangular lift plate of dimensions $15.2 \times 22.9 \times 0.64$ cm ( $6 \times 9 \times 0.25$ in). In lieu of a complex, aircraft-specific geometry, the flat, rectangular plate is used to mimic a generic aircraft underside. Using a simple experimental geometry also facilitates the grid generation process for CFD studies being conducted in parallel by the U.S. Navy.³

The nozzle is an axisymmetric, contoured, convergent-divergent nozzle with an exit diameter, D_r, of 11.9 mm (0.47 in) and design Mach number, M_d, of 1.34. This nozzle was operated at its design Mach number for this study. The nozzle protrudes 1 D_r below the surface of the lift plate. This is designed to approximately mimic the F-35B hover geometry in which the nozzle swivels downward when the aircraft performs a vertical landing. The subscript r is retained to denote the rear nozzle as opposed to the forward lift fan on the F-35B and as well differentiate the nozzle diameter from that used in free jet measurements.

Operating conditions for the jet are measured with a total pressure probe installed in each plenum pipe. The total pressure probe is installed approximately 28 cm (11 in or 22 D_r) upstream of the nozzle exit and is connected to a Setra Model 205-2 100 lbf/in² gauge pressure transducer. The entire model is rigidly attached to two angle iron supports at the top of the anechoic chamber.

An aluminum plate, with a smooth machined surface of dimensions $43 \times 61 \times 1.27$ cm ( $17 \times 24 \times 0.5$ in), was used to simulate a ground plane. Jets exhausting from the impinging jet model impact the ground plane at normal incidence. The ground plane was attached to four T-slot 80/20® rails. The rails were attached to two angle iron supports via rail clamps. This setup allows the distance between the ground plane and lift plate to be adjusted from 5-22 D_r.

A diagram of the coordinate system for impinging jet LDV measurements is presented in Figure 3(a). Non-dimensional nozzle separation or jet stand-off distance is $H / D_{r}$ and is measured from the nozzle exit plane to the ground plane. The reader is reminded that the nozzle protrudes 1 D_r below the surface of the lift plate. For this study, the impinging jet coordinate system is centered on the point on the ground plane directly on the centerline of the jet. Nondimensional height above the ground plane is $y / D_{r}$ . In all cases, radial position is positive to the right and is denoted as $r / D_{r}$ . $r / D_{r} = 0$ represents the centerline of the jet issuing from the nozzle. Radial velocities directed away from the jet axis are taken to be positive.

Figure 3.

Coordinate system and photograph of the LDV setup inside the anechoic chamber for impinging jet flow field measurements. (a) Coordinate system used for impinging jet LDV measurements. (b) Photograph of the LDV setup for impinging jet measurements.

To achieve velocity measurements within 1 D_r above the ground plane or less the aluminum plate holding the transmitting and receiving optics is attached to the scissor jack by way of two $15^{\circ}$ angle mounts so the optical equipment is “looking down” at the ground plane. A photograph of the LDV setup for impinging jet measurements is shown in Figure 3b. Without these mounts, the bottom half of the receiving probe lens would be below the ground plane. If this were the case, the ground plane would block a significant portion of the light scattered by the seeding particles thus significantly impairing signal-to-noise ratio (SNR) of the measurement. Orienting the probes in this angled fashion introduces a 3.4% error in vertical (axial) velocity measurements proportional to the cosine of the angle of inclination. This is deemed to be a reasonable trade-off for improved SNR for near-ground measurements. Velocities reported for near-ground plane measurements are reported as measured, without any angular correction applied to the data.

Laser Doppler velocimeter measurements

The LDV system used in this study was developed in-house and was designed with the capability to non-intrusively measure flow velocities ranging from low-speed to supersonic at high data rates in order to resolve both mean and time-varying velocity components. The development of the LDV used in the present study, including initial measurements as well as a more detailed description of the system are described in Karns³⁰ and Hromisin.³⁶ A more concise description of the system and the methodology for acquiring velocity measurements is provided below.

Description of laser Doppler system. The LDV system is powered by a 5 W rated Coherent Innova 90C-5 Laser System. A Bragg cell is incorporated in the setup just after the laser exit to split the beam and impart a shift frequency of 40 MHz into one of the beams to allow for negative velocities to be resolved. The frequency shifted beams are then passed through a double prism to split the light into separate pairs of blue and green wavelength (λ) light (488 and 514.5 nm wavelengths, respectively). The collimated green laser light beams are each focused into transmitting fiber optic cables and sent to the transmitting probe within the anechoic chamber through a small hole in the wall of the facility. All optical equipment is positioned on a heavy, vibration-resistant optics bench just outside the anechoic chamber.

Flow seeding is provided with a LaVision Aerosol Generator using di-ethyl-hexyl-sebacat (DEHS) particles. Nominal particle sizes range from 0.3 µm to 0.5 µm. In free jet experiments, seeding particles are introduced to the flow approximately 36 D_noz (84 cm) upstream of the nozzle exit. The feed line for the seeding particles is split to route particles to a second line attached to the outside of the nozzle. In the impinging jet configuration seeding particles for the core flow to the nozzle are introduced to 56 D_r upstream of the nozzle exit. The feed line for the nozzle is split to feed seeding particles to three holes in the lift plate surrounding the nozzle.

Entrainment flow seeding is provided so as to prevent bias towards higher velocity regions of the flow. For all measurements, a valve is attached to the entrainment flow seeding line to control the seeding of the entrainment flow independently of the core flow seeding. Thurow et al.³⁷ discuss the importance of uniform flow seeding for particle-based flow measurements in order to accurately determine convection velocities of large-scale turbulence structures. Seeding rates are optimized to achieve peak data rates before each series of tests.

The transmitting probe for the laser light within the anechoic chamber is 13.34 cm (5.25 in) in length overall with an interchangeable 7 cm (2.75 in) diameter achromatic doublet lens with a focal length of 30 cm (11.81 in). The back end of the transmitting probe is designed to accept up to two pairs of beam-carrying fiber optic cables. The transmitting probe focuses the coherent laser beam pairs exiting the fiber optic cables into an ellipsoid optical probe volume within the jet flow.

The receiving probe is aligned with the probe volume and focuses the scattered light onto a Hammamatsu photomultiplier tube (PMT). The receiving optics are placed next to the transmitting probe in a

30^{\circ}

backscatter configuration. The off-angle backscatter configuration reduces the effective probe volume length because the viewing path of the receiving optics “cut-through” the elliptic probe volume at an angle. The placement of a 200 µm pinhole just ahead of the PMT reduces the effective size of the probe volume and prevents extraneous light from reaching the PMT. With this arrangement it was estimated that using both the pinhole and the

30^{\circ}

off-axis receiver reduces the effective probe volume length for free jet measurements by about a factor of 5.³⁰ Off-axis receiving optics reduced the effective probe volume length in impinging jet measurements by nearly a factor of 11. The probe volume length is longer in the impinging jet measurements because a longer focal length lens was installed on the transmitting probe. Use of a longer focal length lens was driven by the desire to move sensitive optical equipment as far away as possible from the high speed, particle-laden outwash flow to mitigate lens fouling. All pertinent characteristics of the LDV system are listed in Table 2.

Table 2.

Laser Doppler velocimeter characteristics (green laser, $λ = 514.5 nm$ ).

Parameter	Impinging jet	Free jet
Beam separation	39.8 mm	39.8 mm
Transmitting focal length	500 mm	300 mm
Beam half angle	2.28°	3.92°
Probe volume length	5.40 mm	2.39 mm
Probe volume diameter	0.215 mm	0.215 mm
Effective probe volume length	0.5 mm	0.5 mm
Fringe spacing	$6.47 μ m$	$3.76 μ m$
Number of static fringes	33.3	43.7
Pinhole diameter	$200 μ m$	$200 μ m$

The data acquisition, A/D conversion, burst detection and processing are performed using the Studio Software Suite developed by AUR Inc. Scattered light is sent through the receiving probe and is measured directly by the PMT. The optimal PMT excitation voltage (i.e. sensitivity) is determined prior to each set of measurements to achieve the highest possible data rate and signal to noise ratio. The PMT signal is amplified using a Sonoma 310 high frequency amplifier. The analog signal is then read into a data processing computer purchased from AUR Inc. The data-acquisition computer digitizes the raw PMT data at a sampling-rate of 2 GHz. Proprietary burst detection algorithms are used to identify and record particle bursts and their properties. Output data from each run include the burst time, burst velocity, Doppler frequency, burst length, (SNR), and burst peak to peak ratio (P2P). The data acquisition and processing methodology directly calculates each particle’s Doppler frequency. The Doppler frequency is related to the particle velocity via the probe volume’s fringe spacing and beam half angle. The entire dataset output by the AUR software was then post-processed using MATLAB® to determine valid bursts based on SNR, P2P, as well as a notch filter to exclude any nonphysical measurements which seldom appear in the data.

Laser Doppler system calibration. The calibration process outlined here is derived from that described by Park et al.³⁸ The LDV system is calibrated against a known linear velocity. In this case, the reference velocity is provided by a Thorlabs model MC2000 optical chopper wheel. Using the theoretical and measured linear velocity of the blades at a known radial position and operational frequency, the actual spacing of fringes within the LDV probe volume may be determined. Using this fringe spacing, the half angle of the crossing laser beams may be calculated.

Data acquisition and processing. Acquired LDV velocity measurements are unevenly sampled in time as measurements are only acquired when a particle is present within the probe volume and produces a validated light burst. Measurements are subject to a bias error caused by the unequal particle arrival times, as originally identified by McLaughlin and Tiederman.³⁹ During this study, mean data rates of 40 kHz were observed but individual particle interarrival times were as short as 5 μs. To account for this, Kerhervé et al.²⁴ suggested a particle interarrival time weighting to calculate the mean and root mean square (rms) velocities as:

\bar{U} = \frac{\sum_{i = 1}^{N} u_{i} w_{i}}{\sum_{i = 1}^{N} w_{i}}, with w_{i} = t_{i} - t_{i - 1}

(1)

u_{rms} = \sqrt{\frac{\sum_{i = 1}^{N} (u_{i} - \bar{U})^{2} w_{i}}{\sum_{i = 1}^{N} w_{i}}} = \sqrt{\frac{\sum_{i = 1}^{N} u'_{i}^{2} w_{i}}{\sum_{i = 1}^{N} w_{i}}}

(2)

where t_i is the clock time of the ith velocity measurement and w_i is the time delay between the ith and

(i - 1) th

measurements. This bias correction is essentially equivalent to that originally suggested by McLaughlin and Tiederman,³⁹ although it might be more convenient to implement. For all further discussions, the axial (u) and radial (v) turbulence intensities, K, are defined on a percentage-wise basis as:

K_{u, v} = \frac{(u, v)_{rms}}{u_{j}} \times 100 %

(3)

where u_j is the theoretical, isentropic fully-expanded jet velocity.

After processing the data, the velocity probability density functions, PDF’s, are inspected to ensure no anomalies appear in the data (e.g. unphysical velocity peaks). Any unphysical velocities are manually excluded from post-processing. These unphysical velocities seldom appear in the data but may be present in regions of strong particle accelerations (e.g. near shock waves).

Estimation of velocity spectra. In order to perform meaningful spectral analysis on the unsteady velocity measurements, the data sets must effectively be converted into an equally-spaced (in time) data set. Sample-and-hold reconstruction of the signal is attractive in its simplicity, however, it involves signal contamination due to the addition of imprecise information. An alternative approach, used in this work, is a technique known as “fuzzy slotting” first introduced by Nobach et al.⁴⁰ Excellent overviews of the fuzzy slotting technique for LDV spectral estimation, its history, and implementation can be found in Benedict et al.⁴¹ and Nobach.⁴²

The fuzzy slotting autocorrelation estimation technique involves calculating all possible velocity cross-products. For each cross-product, the associated time lag is determined as well. The velocity cross-products are then organized into k number of bins (slots) equally spaced in time by $Δ τ$ . k is also the total number of points in the autocorrelation, where $k = N_{psd} / 2$ , where N_psd is the number of points used to calculate the velocity power spectral density (PSD). The time lag for each bin is defined as:

Timelag = k Δ τ for k = 0 to K - 1

For this study, $Δ τ = 4 μ s$ and $k = 2048$ resulting in an autocorrelation that extends out to nearly 8.2 ms for positive time delays only.

Within each bin, the cross-products are averaged resulting in equally spaced correlation coefficients in the correlation domain. The term “fuzzy slotting” is derived from the fact that the bins are triangular shaped in the correlation domain with the central peak (correlation value = 1) at the associated time lag ( $k Δ τ$ ). At the “base” of these bins (correlation value = 0), bins overlap each other by 50%. Products with time lags closer to the centers of bins contribute more heavily to the correlation estimate for that time lag (bin) than those towards the slot edges. Cross-products residing in regions where two bins overlap contribute to the correlation estimate for both bins. Similarly, cross-products in between bins, contribute to neither bin and get discounted. Kerhervé et al.²⁴ provide an excellent schematic of the “fuzzy slots.”

To calculate the velocity PSD, the data set are split into blocks. Calculating the PSD for each block and averaging them together reduces the variance of the PSD for the entire data set. For this study, data sets are split in to 10 to 20 blocks, depending on the total length of the data set, with each block containing on the order of 5000 valid velocity measurements. The mean velocity and rms velocity for each block is calculated using equations (1) and (2), respectively. The autocorrelation for each block is then calculated as:

{\hat{R}}_{k} = \frac{u_{rms}' 2 A}{\sqrt{BC}} fork = 0 toK

(4)

with

A = \sum_{i = 1}^{N - 1} \sum_{j = i + 1}^{N} u_{i} u_{j} w_{i} w_{j} b_{k} (t_{j} - t_{i})

(5)

B = \sum_{i = 1}^{N - 1} \sum_{j = i + 1}^{N} u_{i}^{2} w_{i} w_{j} b_{k} (t_{j} - t_{i})

(6)

C = \sum_{i = 1}^{N - 1} \sum_{j = i + 1}^{N} u_{j}^{2} w_{i} w_{j} b_{k} (t_{j} - t_{i})

(7)

where w_i is previously defined in equation (1) and

w_{j} = t_{j + 1} - t_{j}

(8)

The triangular fuzzy masking function, $b_{k} (t_{j} - t_{i})$ is defined as:

\begin{matrix} b_{k} (t_{j} - t_{i}) = {\begin{matrix} 1 - | \frac{Δ t}{Δ τ} - k | & for | \frac{Δ t}{Δ τ} - k | < 1 \\ 0 & otherwise \end{matrix} \end{matrix}

(9)

Once the autocorrelation is calculated (equation (4)), the scaled, single-sided PSD is determined using a discrete cosine transform. The unscaled PSD is calculated as follows:

\begin{matrix} \hat{G} (f) = 2 Δ τ ({\hat{R}}_{0} + 2 \sum_{k = 1}^{N_{PSD}} d_{k} (f) {\hat{R}}_{k} cos (2 π fk Δ τ)) \end{matrix}

(10)

The term $d_{k} (f)$ on the right-hand side of equation (10) is a frequency-dependent variable window originally recommended by Tummers and Passchier⁴³ to reduce the variance of the PSD. It is formally defined as:

\begin{matrix} d_{k} (f) = {\begin{matrix} 1 / 2 + 1 / 2 cos (\frac{π fk Δ τ}{κ}) & for | \frac{π fk Δ τ}{κ} | < κ \\ 0 & otherwise \end{matrix} \end{matrix}

(11)

The parameter κ in equation (11) is a “smoothing parameter” whose value can be chosen arbitrarily. A larger κ reduces the amount of “smoothing” the window applies to the PSD. The fuzzy slotting literature suggests κ = 6. However, for the data collected in this study, κ = 6 was found to provide far too much smoothing. As such, a value of κ = 50 is used for all spectra presented in this paper.

After calculating the velocity PSD, the PSD is rescaled such that its integral returns the mean square velocity, $u_{rms}' 2$ . A 3-point Savitzky-Golay smoothing filter is applied to the rescaled PSD to reduce the variance further. Because LDV does not sample regularly in time, incoming data rates may be as high as 200 kHz thus allowing spectra in this study to be resolved out to 100 kHz with a frequency resolution of 122 Hz.

Estimation of measurement uncertainty

Meaningful analysis and interpretation of experimental results can only be accomplished once there is a thorough understanding of the underlying uncertainties, σ, associated with the measurements. Reliability and repeatability of results is strongly dependent on the accuracy experiments. It is critical to understand expected outcomes and their associated uncertainties, especially when attempting to develop and validate an LDV system for supersonic exhaust jet measurements. General facility uncertainties for instruments crucial to flow metering and the LDV system are discussed in the following sections. A detailed analysis on the uncertainties associated with individual and mean velocities, and turbulence intensities measured using the LDV system is provided. The analysis is restricted to only the primary velocity component in each measured flow field. A more detailed derivation of the uncertainty equations may be found in Hromisin.³⁶

Facility uncertainties. General facility uncertainties are those associated with all gauges and transducers in the laboratory pertinent to high speed jet operation. Atmospheric pressure, temperature, and relative humidity are read off of analog gauges mounted within the anechoic chamber. The uncertainty in total nozzle operating pressure, P₀, is given by the manufacturer of the pressure transducer (Setra Model 205-2). Facility uncertainties are tabulated in Table 3.

Table 3.

Uncertainties of laboratory gauges and transducers.

Measurement	Uncertainty (σ)
Ambient temperature	$\pm 1 K$ (0.5°F)
Ambient pressure	$\pm 1000 Pa$ (0.15 lbf/in²)
Relative humidity	$\pm 1 % rh$
Pressure transducer	$\pm 690 Pa$ (0.1 lbf/in²)

Velocity uncertainty. Measurement uncertainty of mean jet velocity, $σ_{\bar{U}}$ , is assumed to be dependent on four primary sources: (i) uncertainty in operating the jet, $σ_{u_{j}}$ , (ii) uncertainty due to imperfections in the LDV probe volume and calibration, σ_LDV, (iii) errors due to titling the probe with respect to the velocity component being measured, $σ_{θ}$ , and (iv) mean velocities include an additional source due to the statistical error of the mean, σ_mean. These sources are summarized in equation (12). It is pertinent to note at this point that in the presence of shock waves or other strong velocity gradients, particle lag effects and LDV probe volume sizing become the dominating sources of experimental uncertainty.

σ_{\bar{U}} = \sqrt{σ_{u_{j}}^{2} + σ_{LDV}^{2} + σ_{θ}^{2} + σ_{mean}^{2}}

(12)

The uncertainty in a single realization of jet velocity, σ_u includes all uncertainty terms in equation (12) except for the statistical error of the mean term, σ_mean.

The fully-expanded jet velocity at any operating condition, T₀ and NPR, is shown in equation (13).

u_{j} = \sqrt{\frac{2 γ}{γ - 1} ℜ T_{0} (1 - {NPR}^{\frac{1 - γ}{γ}})}

(13)

The uncertainty in this term is representative of uncertainties in all measured axial velocities due to operating facility control hardware. The uncertainty is calculated using the data reduction equation described in Coleman and Steele.⁴⁴ In this way, the uncertainty of the jet velocity is dependent upon the uncertainty of each term within equation (13). The uncertainty in the fully-expanded jet velocity is:

σ_{u_{j}}^{2} = (\frac{\partial u_{j}}{\partial T_{0}})^{2} σ_{T_{0}}^{2} + (\frac{\partial u_{j}}{\partial NPR})^{2} σ_{NPR}^{2}

(14)

where the uncertainties in specific heat ratio and gas constant are assumed to be negligible with respect to those associated with nozzle pressure ratio and total temperature. Analytic solutions to the partial derivatives in equation (14) are given in Hromisin.³⁶

Because the supply air tanks and connecting lines are unheated and exposed to ambient conditions, then to a good approximation the total temperature of the jet can be assumed to be equal to ambient temperature. Therefore, the total temperature uncertainty, $σ_{T_{0}}$ , in equation (14) is equal to the uncertainty in atmospheric temperature listed in Table 3. However, σ_NPR in equation (14) must be determined. Given the definition of NPR, $P_{0} / P_{amb}$ , it is readily shown:

σ_{NPR}^{2} = (\frac{NPR}{P_{0}})^{2} σ_{P_{0}}^{2} + (\frac{{NPR}^{2}}{P_{0}})^{2} σ_{P_{amb}}^{2}

(15)

where

σ_{P_{0}}

and

σ_{P_{amb}}

are the uncertainties associated with the pressure transducer and ambient pressure gauge, respectively, and are tabulated in Table 3.

Beyond control of the jet, there is velocity uncertainty associated with the LDV probe itself, σ_LDV. This uncertainty stems from calibration of the LDV probe volume. During the calibration process, the linear velocity of the optical wheel is dependent on the distance of the LDV probe volume from the center of rotation. Given the finite diameter of the probe volume, the linear velocity of the wheel measured at the “bottom” of this volume is less than the linear velocity of the wheel measured at the “top” of the probe volume. Therefore uncertainty in wheel velocity is dependent on the uncertainty of the disk rotation frequency (f_whl) and the radial distance from the probe volume to the center of the wheel (r_whl). Uncertainties in linear wheel velocity will propagate into value of the corrected beam half angle. Lowe⁴⁵ describes the method used by the AUR Inc. system and shows that σ_LDV is proportional to the time duration of the particle burst, which can then be determined to be proportional to the minimum number of fringes encountered by the particle, N_f. The expression for σ_LDV is,

σ_{LDV}^{2} = u^{2} [(\frac{σ_{f}}{f_{whl}})^{2} + (\frac{σ_{r}}{r_{whl}})^{2} + (\frac{1}{10 N_{f}})^{2}]

(16)

where σ_f and σ_r are the uncertainties associated with the wheel rotation frequency and radius, respectively. u represents the measured velocity component.

Intentional misalignment of the LDV probe with respect to the velocity component being measured introduces alignment error, $σ_{θ}$ . Probe misalignment was discussed in detail in section “Impinging jet experimental setup”. Misalignment error is calculated simply from geometric relations. This error exists for axial velocities only, and only in the vicinity of the impinging jet ground plane when the probe was tilted and is zero otherwise.

The mean of a finite, discretely sampled variable will in general have a different value than the true mean of the continuous quantity being measured. The difference between the true mean and the sample mean leads to the standard error of the mean, σ_mean.⁴⁵ The expression for standard error is equation (17).

σ_{mean}^{2} = \frac{u_{rms}^{2}}{N}

(17)

with N being the total number of sample points, typically greater than 5000.

Table 4 lists uncertainty components as well as net mean velocity uncertainty for the free and impinging jets operating at their respective isentropic fully-expanded velocities. Estimated uncertainties are reported for a typical impinging jet centerline axial velocity in the near-ground region 1 D_r above of the ground plane where the angular alignment error,

σ_{θ}

is non-zero. Uncertainties are also tabulated for the radially-directed impinging jet outwash (wall jet) at a velocity typically observed within the first several radii. Uncertainty in impinging jet outwash velocity is estimated under the assumption that impinging jet velocity uncertainty,

σ_{u_{j}}

(middle column of Table 4) is a constant throughout the flow field. Or more physically, a one-to-one correspondence between u_j and outwash velocities is assumed.

Table 4.

Tabulated axial and radial velocity uncertainties.

Uncertainty component			Free jet	Imp. jet Jet plume	Imp. jet Near-ground	Imp. jet outwash
Uncertainty component			$u_{j} = 400 m / s$	$u_{j} = 395 m / s$	$u = 325 m / s$	$v = 160 m / s$
Jet velocity	$σ_{u_{j}}$	(m/s)	4.3	4.2	4.2	4.2
Center of wheel rotation	σ_r	(mm)	0.5	0.5	0.5	0.5
Wheel rotation frequency	σ_f	(Hz)	$4 \times 10^{- 4}$	$4 \times 10^{- 4}$	$4 \times 10^{- 4}$	$4 \times 10^{- 4}$
LDV ( $500 Hz, 25.4 mm$ )	σ_LDV	(m/s)	0.94	1.2	1.0	0.49
Alignment error	$σ_{θ}$	(m/s)	0	0	11	0
Standard mean error	σ_mean	(m/s)	0.57	0.51	0.51	0.23
Mean Vel. Uncertainty	$σ_{\bar{U}}$	(m/s)	4.4 (1.1%)	4.4 (1.1%)	11.8 (3.6%)	4.3 (2.7%)

In the absence of $σ_{θ}$ , the leading sources of experimental uncertainty generally stem from uncertainties in jet operating velocity, $σ_{u_{j}}$ and the LDV probe itself, σ_LDV. However, when present, the misalignment error, $σ_{θ}$ , is the leading order term in velocity uncertainty. Net mean velocity uncertainty values, $σ_{\bar{U}}$ , are on the order of $1 - 4 %$ of the measured velocity. If σ_mean is assumed to be negligible, the mean and instantaneous velocity uncertainties can be approximated as equal, $σ_{\bar{U}} \approx σ_{u}$ .

Velocity measurements in the vicinity of shock waves are susceptible to additional uncertainties due to particle lag effects and LDV probe volume sizing. Such sources of uncertainty are difficult to quantify prior to in-test measurements. Free jet LDV measurements in the vicinity of oblique shocks by Powers et al.¹ demonstrated two disparate velocity regions within the probe volume: one on either side of the shock wave. The effective uncertainty was taken to be the velocity difference between the two peaks in the probability density function and was up to 10% of the jet velocity.

Turbulence intensity uncertainty. Estimation of turbulence intensity uncertainty is limited to the axial component, K_u. Uncertainty in axial turbulence intensity will be shown to be a consequence of the uncertainty in the jet operating velocity, $σ_{u_{j}}$ . Applying the data reduction equation outlined by Coleman and Steele⁴⁴ to the expression for turbulence intensity given by equation (3):

σ_{turb}^{2} = (\frac{\partial K_{u}}{\partial u_{rms}})^{2} σ_{u_{rms}}^{2} + (\frac{\partial K_{u}}{\partial u_{j}})^{2} σ_{u_{j}}^{2}

(18)

The partial derivatives in equation (18) can be evaluated analytically. Then, the only remaining unknown is the uncertainty associated with the rms velocity, $σ_{u_{rms}}$ . Using the definition of rms velocity, data reduction similar to what has already been shown may be applied to $σ_{u_{rms}}$ . If the prior approximation, $σ_{\bar{U}} \approx σ_{u}$ , holds, it can readily be shown that $σ_{u_{rms}} = 0$ . Finally, the second partial derivative in equation (18) may be evaluated to arrive at equation (19).

σ_{turb} = \frac{\partial K_{u}}{\partial u_{j}} σ_{u_{j}} = \frac{K_{u}}{u_{j}} σ_{u_{j}}

(19)

For an axial turbulence intensity of 16% and jet velocity u_j = 395 m/s, the uncertainty in turbulence intensity is 0.2%.

Experimental results from free jet measurements

This section presents the results of LDV measurements performed in jets issuing from military-style nozzles in a free jet configuration. Each nozzle was operated overexpanded at a nozzle pressure ratio (NPR $= P_{0} / P_{amb}$ ) of 3.0 resulting in a jet Mach number, M_j, of 1.36 with a theoretical isentropic fully-expanded velocity, u_j, of 400 m/s. The jets were operated unheated with a total temperature ratio, TTR, of 1. Corresponding jet Reynolds numbers based on fully-expanded jet conditions are tabulated in Table 1. A series of free jet LDV measurements were acquired in a vertical plane containing the jet centerline. The major axis of the probe volume was set to be parallel to the plane at the nozzle exit. This results in the small dimensions of the probe volume in the jet axial and radial direction (following the axial and vertical traverses). This allowed for the most regions of the flow to be accurately examined. Described below are results for unsteady velocity measurements acquired at the exit plane of the nozzles and along the jet centerlines.

Free jet measurements at the nozzle exit plane

Unsteady LDV measurements were acquired at the nozzle exit plane to examine the initial shear layer properties of jets exhausting from the military-style nozzles. Very little analysis has been performed in the past to attempt to understand this region of the flow for these small scale nozzles. It is hoped that interrogating the flow on the nozzle lip line near the nozzle exit will provide insight to the interior nozzle boundary layer thickness. Computational aeroacoustic simulations rely on accurate simulations (or approximations) of the upstream turbulent boundary layer within the nozzle.

Figure 4 presents mean axial velocity and turbulence intensity measurements radially through the nozzle lip line at an axial location (downstream of the nozzle exit) of $x / D_{noz} = 0.1$ . Presented are measurements for the Gen1A, Gen1B, and Gen2 nozzles, with equivalent nozzle exit diameters of 18.0 mm, 22.6 mm, and 27.0 mm, respectively. This represents a 50% increase in jet Reynolds number between the smallest scale (Gen1A) to the largest scale (Gen2) nozzles. It was observed that the shear-layer occurs at slightly different locations for each nozzle; likely due to small differences in centerline alignments between nozzles. Figure 4(a) depicts mean velocity, with a zeroed radial location, based upon the radial position where the local mean velocity is half of the centerline value. This representation shows an excellent collapse of the shear layers between the different nozzles. The high velocity flow within the jet core at $r / D_{r} = - 0.02$ decreases to 0 by $r / D_{r} = 0.02$ .

Figure 4.

Nozzle exit jet shear layer velocity and turbulence for different baseline nozzles. Shown are mean axial velocities and axial turbulence intensities calculated from LDV point measurements at $x / D_{noz} = 0.1$ . NPR = 3.0, $M_{j} = 1.36$ , TTR = 1, $u_{j} = 400 m / s$ . (a) Mean axial velocity. (b) Axial turbulence intensity.

For further interrogation, the axial turbulence intensity for the initial shear layer for the different baseline nozzles is examined. Figure 4(b) shows the shear layer thickness normalized by the nozzle exit diameter and zeroed by the half velocity point. The Gen2 baseline appears to have the thinnest non-dimensional initial shear layer thickness. This agrees with the fact that the boundary layer would be thinner relative to the nozzle diameter with increasing Reynolds number. When examining the dimensional shear layer thickness for each nozzle, it was observed that all are very similar except the Gen1A BLA and Gen2 BLA nozzles are slightly thinner. This can be observed in Figure 4(a) as both of these nozzles' velocity profiles overlap almost exactly, and is attributed to thinner lip thicknesses in these nozzles as documented in Table 1.

Mean velocity and turbulence measurements along jet centerline

A strong shock cell structure is present in the jet plume when the nozzle is operating overexpanded at $M_{j} = 1.36$ .³⁴ In order to better understand the shock structure within the flow field, Figure 5(a) shows the mean axial velocity along the jet centerline for the baseline nozzle operating at NPR = 3.0, $M_{j} = 1.36$ , TTR = 1.0. Measurement locations are noted with markers and connecting lines of the same color are used for clarity. Data for the Gen1B BLF nozzle ( $Re = 9.34 \times 10^{5}$ ) and the 20% larger diameter identical geometry Gen2 BLA nozzle ( $Re = 1.12 \times 10^{6}$ ) are presented. This measurement was performed to examine the initial Reynolds number effects as jet noise measurements and numerical simulations of jets at five times larger scale are planned in future work. Unfortunately, the length limitations of the axial traversing stage prevented measurements for the Gen2 BLA nozzle from being carried out as far downstream nondimensionally as those for the smaller-diameter Gen1B BLF nozzle.

Figure 5.

Free jet centerline velocity and turbulence intensity measurements for jet operating conditions: NPR = 3.0, $M_{j} = 1.36$ , TTR = 1, $u_{j} = 400 m / s$ . (a) Comparison of centerline velocity for different scale military-style nozzles. Calculated from LDV point measurements. (b) Comparison of centerline turbulence intensity for different scale military-style nozzles calculated from LDV point measurements.

From Figure 5(a), it can be readily observed that the mean velocity between the two different nozzle scales is remarkably consistent and highlights the reliability of the LDV system, measurement procedures, and processing methodology. The velocity just downstream of the nozzle exit reaches the nozzle design Mach number of 1.65 (A corresponding fully-expanded velocity of 459 m/s). The Mach disk present in the jet flow then decreases the centerline velocity to below 300 m/s. The shock cell amplitudes and lengths agree between all measured nozzles with the five shock cells persisting through the measurement range past 5 nozzle diameters.

Figure 5(b) presents the axial turbulence intensity along the jet centerline for the two different scale nozzles. Again, consistency between the measurements of different scale nozzles is observed. The increase of turbulence intensity reaches a maximum around 5 $x / D_{noz}$ , which would typically indicate the end of the potential core. However, the mean velocity at this point has not begun to decline. This could be the first indication of “spatial turbulence” or measurement fluctuations that may arise from velocity levels varying within the length of the probe volume (5% of the nozzle exit diameter). The Gen2 BLA nozzle, which has the largest D_noz, shows lower levels of turbulence between 2 and 4 $x / D_{noz}$ , which would support the hypothesis that some of this rise observed in the smaller diameter jet (issuing from the Gen1B nozzle) is due to “spatial turbulence.”

Experimental results from impinging jet measurements

This section reports on mean velocity and turbulence measurements made throughout the supersonic jet plume, impingement region, and wall jet for a single jet exhausting from an axisymmetric, 11.9 mm converging-diverging nozzle, impacting normally on a simulated ground plane, or impingement plate. Rear jet operating conditions for the LDV measurements were ${NPR}_{r} = 2.93, M_{j, r} = 1.34$ (design condition), and TTR_r = 1. The corresponding isentropic jet exit velocity is 395 m/s and jet Reynolds number is $5.25 \times 10^{5}$ . The reader is reminded that the forward jet in the impinging jet model was non-operational for the duration of this study. Data are presented for plate stand-off distances of 5 and 11 jet diameters.

Mean velocity and turbulence measurements in impinging jet plume and impingement zone

The two-velocity component mean flow characteristics of the impinging jet plume and impingement region for jet stand-off distances of $H / D_{r} = 5$ and 11 were investigated. Vector fields and mean velocity contours were generated for the impinging jet plumes. Figure 6(a) and (b) shows the vector fields and contours for lift plate stand-off distances of 11 D_r and 5 D_r, respectively. Open circles mark the locations of the data points used to generate the contours. Unit vector arrows indicate flow directionality whereas contour color denotes velocity magnitude. Contours are generated by interpolating between measurement locations. Due to the sparse matrix of measurement locations, contours are meant to only yield a qualitative representation of the flow field. Within 0.5 D_r of the ground plane, there remains a strong axially directed component of velocity on the order of 250 m/s for both jets indicating that impingement effects occur very near the surface of the ground plane. Although in this same region, a significant redirecting of the flow can start to be seen at radial locations greater than 1 D_r away from the jet centerline.

Figure 6.

Velocity magnitude contours for $H / D_{r} = 11$ and 5 with unit vectors indicating flow directionality. Open circles denote measurement locations used to generate contours. Contour color levels are identical for both plots. Jet operating conditions are: ${NPR}_{r} = 2.93, M_{j, r} = 1.34$ , TTR_r = 1, $u_{j} = 395 m / s$ . (a) Two-component velocity vector field and velocity magnitude contour for H/D_r = 11. (b) Two-component velocity vector field and velocity magnitude contour for H/D_r = 5.

Axial turbulence intensity contours for jet stand-off distances of 11 and 5 jet diameters are shown in Figure 7(a) and (b), respectively. In both cases, measurements begin 4 D_r downstream of the nozzle exit plane. Turbulence intensity contours are generated using the same points as those shown in Figure 6. For a plate stand-off distance of 11 D_r the strongest mixing in the jet shear layer exists greater than 5 D_r above the surface of the ground plane. However, for plate stand-off distances of both 11 and 5 diameters, turbulence intensities greater than 14% exist throughout the jet down to 0.5 D_r above the impingement plate. This is especially pronounced at stand-off distance of $H / D_{r} = 5$ . At this height, there is a strong concentration of elevated turbulence levels 0.5 D_r above the plate surface.

Figure 7.

Axial turbulence intensity contours for $H / D_{r} = 11$ and 5. Jet operating conditions are: ${NPR}_{r} = 2.93, M_{j, r} = 1.34$ , and TTR_r = 1. (a) Axial turbulence intensity contour for H/D_r = 11. (b) Axial turbulence intensity contour for H/D_r = 5.

The impinging jet shadowgraph images presented in Hromisin³⁶ are focused on the jet impinging on the ground plane for plate stand-off distances of 11 and 5 diameters. For a 5 D_r plate separation, a stand-off shock was observed in the jet plume above the surface of the ground plane. Closer inspection of this shadowgraph places the stand-off shock at approximately 0.5 D_r above the ground plane surface. Oscillations in the stand-off shock position around the position of the probe volume would produce strong fluctuations in the local velocity which could explain the higher turbulence intensities observed just off the surface of the ground plane. Although not observed directly in this work, Henderson and Powell⁴⁶ and Henderson et al.^47,8 have shown jet instabilities originating upstream can cause significant stand-off shock oscillations and thus strong oscillations in the surrounding flow.

Mean velocity and turbulence measurements in impinging jet outwash flow

It is important to quantify the mean velocity in the outwash flow of the impinging jet flow field; however, obtaining the gusts associated with turbulent fluctuations gives a more complete picture of what is happening. Of practical concern to the U.S. Navy in operating STOVL aircraft in confined spaces, such as the flight deck of ships, is the effect of the outwash on the surrounding environment. In full-scale environments, it is the outwash produced by the exhaust of the STOVL aircraft that convects the high speed, high temperature flow towards personnel and equipment in the vicinity of the aircraft. As well, Worden et al.⁴⁸ note that other researchers have observed the outwash flow being an additional source of high amplitude Mach wave radiation noise if the turbulence convection velocities are supersonic. The U.S. Navy has spent considerable effort in defining the areas around a hovering aircraft where it is potentially dangerous for ground crew or equipment to be located.⁴⁹ These personnel and equipment hazard zones are typically defined by a pressure or wind speed that limits the position of a person or object within a certain distance from the operating aircraft. Preston et al.⁴⁹ discuss the importance of using unsteady velocity data to “provide more meaningful and realistic statistical metrics for outwash force,” than what can be obtained using averaged outwash velocity profiles. The basis for this work was to determine the aerodynamic drag force that personnel may be exposed to if they were immersed in a given outwash flow field.

To this end, unsteady radial-component velocity measurements were performed in the wall jet, or outwash flow region, of the flow field for a lift plate height of 11 jet diameters. Rear jet operating conditions were ${NPR}_{r} = 2.93, M_{j, r} = 1.34$ , and TTR_r = 1. Measurements were taken from 2 to 12 diameters radially outward from the centerline of the jet in 1 D_r increments. Logarithmic vertical spacing of measurements above the ground plane allowed for good resolution of the wall jet velocity profile both near the wall and in the entrainment shear layer. These data supplement the steady outwash flow measurements previously performed by Myers and McLaughlin⁵⁰ using a 5-probe Pitot rake. Because of the relatively small probe volume size, the LDV technique is able to measure within 0.02 D_r of the ground plane whereas the Pitot probe is physically limited to measurements no closer than $y / D_{r} = 0.1$ for the nozzle used in this study.

Outwash flow measurements between $8 \leq r / D_{r} \leq 12$ are compared to Pitot rake data in Figure 8. Pitot rake measurements in the outwash flow were previously reported by Myers and McLaughlin.⁵⁰ The exact radial position of Pitot rake measurements is indicated on each graph in red, italicized font. There is excellent agreement between the LDV and Pitot probe measurements in the outwash region, particularly above $y / D_{r} = 0.5$ .

Figure 8.

Mean outwash flow LDV measurements compared to Pitot rake data at similar locations for $H / D_{r} = 11$ and $M_{j} = 1.34$ . The radial position of Pitot rake measurement is listed in each plot in red.

However, at nearly all positions, peak velocities measured using LDV are higher than those observed in the Pitot rake measurements. This is likely due to spatial averaging in the Pitot probes near the point of maximum velocity. Because the Pitot-probe tip is larger than the size of the LDV probe volume, Pitot probe measurements are averaging over a larger vertical section of the wall jet. As such, the Pitot probes may not be able to accurately resolve the peak velocity in a wall jet of this scale. It is important to note that the authors of Myers and McLaughlin⁵⁰ believe the impinging jet apparatus may not have been oriented perfectly vertical at the time Pitot rake measurements were taken. This would introduce angularity in the resulting outwash flow such that there would be a non-negligible velocity component tangential to the Pitot rake that could not be measured.

Figure 9(a) presents a contour plot of the mean radial velocity in the wall jet. Velocities as high as 125 m/s are observed out as far as 6.5 D_r from the jet centerline. Furthermore, velocities as high as 25% of the nozzle exit velocity persist out to 9 diameters. The wall jet is largely confined close to the ground plane, $y / D_{r} \leq 0.25$ . Significant upward spreading of the outwash flow is observed where the peak wall jet velocity begins to rapidly decay: near $r / D_{r} = 6$ .

Figure 9.

Mean radial velocity contour and scaled radial velocity profiles in outwash flow region for $H / D_{r} = 11$ and $M_{j, r} = 1.34$ . (a) Outwash flow mean radial velocity magnitude contour. (b) Scaled outwash flow radial velocity profiles for: mean velocity (black) and 99th percentile velocity (red).

Scaled outwash flow velocity profiles are shown in Figure 9(b) in black. Each profile is zeroed to its corresponding $r / D_{r}$ location on the abscissa. The radial positions of the measurements is also noted at the top of the figure near each pair of velocity profiles. The spacing of major vertical ticks corresponds to 80% of the jet exit velocity. Also shown are the $99 th$ percentile velocity, $\bar{V} + 3 v'_{rms}$ , (red) velocity profiles. These profiles give an indication of the maximum jet speeds that could be experienced in the wall jet due to turbulent velocity fluctuations. Within the first five diameters from the jet centerline, mean velocities are about 50% of the jet exit velocity but with turbulent fluctuations may be as high 80%. Maximum velocities are initially largest near the ground plane. However, at larger radial distances from the impingement center, the velocity fluctuations are largest at higher heights above the ground plane. Interestingly, between 6 and 8 diameters radially outward, peak velocities due to turbulent fluctuations occur higher above the ground plane ( $y / D_{r} \approx 0.25$ , red) than the position of maximum mean velocity ( $y / D_{r} \approx 0.125$ , black).

Scaled radial outwash turbulence intensity profiles are shown in Figure 10. Each profile is zeroed to its corresponding $r / D_{r}$ location on the abscissa. Again the radial positions of the measurements are also noted at the top of the figure near each profile. The spacing of major lateral ticks corresponds to 10% turbulence intensity. Peak radial turbulence intensity increases up to $r / D_{r} = 4$ then decreases with increasing $r / D_{r}$ as the wall jet spreads and loses momentum due to entrainment of the quiescent air. Turbulence intensities as large as 12% persist in the wall jet out to 7 D_r. There is a steady increase in the position of peak turbulence intensity above the ground plate with increasing radial distance for $r / D_{r} \leq 7$ . Turbulence intensities are seen to become more uniformly distributed throughout the height of the wall jet as the boundary layer and entrainment shear layer converge. When the two shear layers converge, the outwash flow may be considered “fully-developed”.

Figure 10.

Scaled outwash flow radial turbulence intensity profiles for $H / D_{r} = 11$ and $M_{j, r} = 1.34$ .

To further inspect the development of the outwash flow, normalized mean radial outwash velocities and radial turbulence intensities are presented in Figures 11 and 12, respectively. Mean radial outwash velocities are normalized by the maximum velocity observed at the corresponding radial station, $v / v_{max}$ ( $r / D_{r}$ ). Similarly, radial turbulence intensities, are normalized by the peak turbulence intensity at each radial station, $K_{v} / K_{v max} (r / D_{r})$ . The vertical distance above the ground plane is nondimensionalized by $y_{0.5}$ : the height above the ground plane at which the local mean velocity is equal to half the peak mean velocity (v_max) at a given radial position. That is, $y_{0.5} = y (\frac{1}{2} v_{max})$ . A collapse of the data using these parameters has been interpreted by Miller and Wilson⁵¹ to indicate that the wall jet has become fully-developed.

Figure 11.

Normalized radial velocity profiles of the outwash flow for $H / D_{r} = 11$ and $M_{j, r} = 1.34$ .

Figure 12.

Normalized turbulence intensity profiles of the outwash flow for $H / D_{r} = 11$ and $M_{j, r} = 1.34$ .

Figure 11 presents the normalized mean radial outwash velocities. It is clear that the outwash flow velocities between $2 \leq r / D_{r} \leq 12$ collapse on to three distinct curves. This is indicative of three regions in the wall jet: (1) the early wall jet, extending radially outwards to 5 D_r (Figure 11(a)), (2) intermediate or developing wall jet between 6 and 8 D_r (Figure 11(b)) and (3) the fully-developed wall jet (Figure 11(c)) beyond approximately 9 D_r. When presented nondimensionally in this manner, the early wall jet, $2 \leq r / D_{r} \leq 5$ is characterized by a “concave-up” profile with a maximum velocity occurring near $0.1 y_{0.5}$ . Moving outwards to the intermediate, or developing, wall jet region, $6 \leq r / D_{r} \leq 8$ , the profile has an essentially linear profile above the point of peak nondimensional velocity. Interestingly, this intermediate region appears to have two distinct heights at which the flow speed reaches a maximum: $0.1 y_{0.5}$ and $0.4 y_{0.5}$ .

At radial distances greater than 9 D_r, the outwash flow is fully-developed. This is in agreement with Myers and McLaughlin⁵⁰ who observed fully-developed flow from $r / D_{r} = 8.3$ to 24. The velocity profile takes on the classic wall jet boundary layer shape with a “bending back” of the data above and below the position of peak velocity. Maximum velocity in the wall jet occurs at $0.3 y_{0.5}$ above the ground plane, in the fully-developed region. This is nearly the same as the height of the second velocity peak in the intermediate wall jet region.

Figure 12 presents the normalized radial turbulence intensities. In the early wall jet, Figure 12(a), there is a very rough collapse of the data. Although, this is an aerodynamically complex region of the flow with significant turning and strong velocity gradients so a collapse of turbulence intensities is not necessarily expected. Figure 12(b) shows the normalized radial intensities for $r / D_{r} \geq 6$ . There is an excellent collapse of the data onto a single curve. It appears that outwash flow turbulence becomes fully-developed more quickly than the mean flow velocities. Comparison with Figure 11(b) and (c) shows that peak turbulence intensity occurs near or just above the position of peak velocity, i.e. in the entrainment shear layer. There is a distinct local maxima in turbulence intensity near $y / D_{r} = 0.1$ in the boundary layer as well.

Impinging jet velocity spectra

Velocity spectra have been calculated from unsteady measurements taken in the impinging jet plume, impingement region, and wall jet for stand-off distances of $H / D_{r} = 5$ and 11. Rear jet operating conditions were ${NPR}_{r} = 2.93, M_{j, r} = 1.34$ , and TTR_r = 1.

Because the LDV system was built in-house it is imperative to qualify unsteady velocity measurements and the fuzzy slotting spectra-estimating method. To this end, velocity spectra taken in the impinging jet plume for a lift plate stand-off of 11 D_r are compared with available velocity spectra data obtained by other researchers in supersonic round jet flows. Velocity spectra comparisons are summarized in Figure 13 – adapted from Papamoschou et al.⁵² with permission. Spectra were normalized by their mean square values. The two impinging jet plume velocity spectra shown were obtained on the centerline and lip line 4 D_r downstream of the nozzle exit. The impinging jet flow closely resembles a free jet flow at this location. Impinging jet LDV spectra are compared with free jet spectra measured on the lip line at $x / D_{noz} = 6$ using an optical deflectometer,⁵² an LDV probe,²⁴ a Rayleigh scattering system,¹⁴ and a hot-film probe.⁵³

Figure 13.

LDV impinging jet plume velocity spectra compared with free jet velocity spectra using other measurement techniques. Figure adapted from Papamoschou et al.,⁵² with permission. (a) u = 258 m/s, $u'_{rms}$ = 46.7 m/s, Axial velocity. (b) v = 73.4 m/s, $v'_{rms}$ = 73 m/s, radial velocity.

The shapes and normalized magnitudes of the impinging jet velocity spectra agree remarkably with free jet velocity spectra measured above M_j = 1.75. As well, all spectra exhibit a $- 5 / 3$ decay to a varying extent. The close agreement of results presented in Figure 13 provides the necessary qualification of the LDV system for accurate velocity spectra measurements.

For a lift plate stand-off of 5 D_r, spectra have been calculated from axial measurements in the impingement region and radial measurements in the wall jet shear layer. Experimental parameters correspond to those used by Myers et al.⁵⁴ for impinging jet acoustic measurements. A $20 dB$ impingement tone was observed in the acoustic data. LDV spectra obtained at two positions within the flow field are presented in Figure 14 in blue. Also included on each graph is the acoustic spectrum, in red, obtained from acoustic field measurements using a microphone located 100 D_r aft of the nozzle. The scale for the acoustic measurements is along the right ordinate. Figure 14(a) shows a velocity spectrum determined from axial velocity fluctuations in the impingement region near the jet centerline while Figure 14(b) presents a velocity spectrum obtained from radial velocity fluctuations in the early wall jet shear layer. The exact coordinates of where spectra were obtained within the flow field are indicated in the lower-left corner of each figure.

Figure 14.

Blue spectra: Velocity spectra obtained from LDV measurements for $H / D_{r} = 5, M_{j, r} = 1.34, {NPR}_{r} = 2.93$ , TTR_r = 1, characteristic frequency, $f_{c} = 31.8 kHz$ . LDV measurement positions are indicated on each graph. Frequency resolution is 122 Hz. Red spectra: Acoustic field measurements taken directly aft of the model for the same plate separation and jet conditions. Frequency resolution is 74 Hz. (a) u = 258 m/s, $u'_{rms}$ = 46:7 m/s, Axial velocity. (b) v = 73:4 m/s, $v'_{rms}$ = 73 m/s, Radial velocity.

Both graphs show a distinct tone present in the velocity spectra. This tone shows excellent agreement with the acoustic measurements of Myers et al.⁵⁴ Both measurements indicate a tone frequency of 12.7 kHz. The amplitude of this tone appears greatest close to the jet centerline near the approximate location of the stand-off shock ( $y / D_{r} = 0.5$ ) (Figure 14(a)). Recall that Figure 7(b) shows increased axial turbulence levels near this position as well. When moving outward radially, the tone decreases in magnitude, as seen in Figure 14(b). By 2 D_r radially outward from the jet centerline a tone was no longer evident in velocity spectra. These findings are in agreement with Krothapalli et al.⁶ and Henderson et al.⁸ who showed that velocity fluctuations associated with the impingement tone retain coherence into the wall jet.

Summary and conclusions

Mean velocity and turbulence measurements were performed using a laser Doppler velocimetry instrument throughout the flow fields produced by university-scale supersonic jets exhausting from nozzles in configurations relevant to practical, full-scale application.

Axial-component mean and unsteady laser Doppler velocimetry measurements were performed in the supersonic core and shear layer of overexpanded jets exhausting freely from military-style nozzles. Mean velocities and turbulence intensities measured near the lip line at the nozzle exit plane showed good consistency when jet Reynolds number was increased by 50%. Mean axial velocities along the jet centerline, including modulations in mean flow velocity due to the quasi-periodic shock cell structure, compared well for a 20% increase in jet Reynolds number.

Two-components of mean velocity and turbulence were measured in the jet plume, impingement zone, and wall jet region of a single, on-design supersonic jet impinging normally on flat plate. Up to moderate jet stand-off heights, the impingement region was found to remain within 0.5 D_r above the ground plane. Axial turbulence measurements showed elevated flow fluctuations in the approximate vicinity of a stand-off shock above the plate. In the outwash flow, turbulent fluctuations were found to elevate unsteady velocities well above the local mean velocity. Velocity spectra were obtained from unsteady axial and radial velocity measurements throughout the flow. Both fluctuation components showed a distinct peak at the same frequency as the jet impingement tone measured in prior acoustic field measurements. This peak was found to be most distinct near the impingement zone and decayed further out in the wall jet.

Continuing unsteady LDV measurements would benefit from companion hot-wire measurements as a comparison point to better understand the accuracy of rms and PSD data. Further simultaneous multi-velocity component or multi-point measurements are warranted. Multi-component measurements would allow for determining off-axis components of the Reynolds stresses. Multi-point measurements would yield convection velocities and correlation length scales of the large scale structures within the flow fields. These properties are relevant to the development of accurate turbulence models and aeroacoustic prediction codes.

Footnotes

References

Powers RW, Hromisin SM, McLaughlin DK, et al. Mean velocity and turbulence measurements of supersonic jets with fluidic inserts. In: 54th aerospace sciences meeting, January 2016, pp.1–22. DOI: 10.2514/6.2016-0001.

Kapusta MJ, Powers RW, Morris PJ, et al. Numerical simulations for supersonic jet noise reduction using fluidic inserts. In: 54th aerospace sciences meeting. AIAA Paper No. 2016-0758, San Diego, CA, January 2016, pp.1–38. DOI: 10.2514/6.2016-0758.

Crowell AR and Myers LM. Computational analysis, model reduction, and experimental comparison of model scale impinging jets. In: 54th AIAA aerospace sciences meeting, January 2016, pp.1–21. DOI: 10.2514/6.2016-0310.

Alvi FS and Iyer KG. Mean and unsteady flowfield properties of supersonic impinging jets with lift plates. In: 5th AIAA/CEAS aeroacoustics conference. AIAA 99-1829, Bellevue, WA, 10–12 May 1999.

Donaldson

Snedeker

. A study of free jet impingement. Part 1. Mean properties of free and impinging jets. Journal of Fluid Mechanics 1971; 45: 281–319. DOI: 10.1017/S0022112071000053.

Flow field and noise characteristics of a supersonic impinging jet. Journal of Fluid Mechanics 1999; 392: 155–181. DOI: 10.1017/S0022112099005406.

Tam CKW and Ahuja KK. Theoretical model of discrete tone generation by impinging jets. Journal of Fluid Mechanics 1990; 214: 67–87. DOI: 10.1017/S0022112090000052.

Henderson

Bridges

Wernet

. An experimental study of the oscillatory flow structure of tone-producing supersonic impinging jets. Journal of Fluid Mechanics 2005; 542: 115.DOI: 10.1017/S0022112005006385.

Gojon R, Bogey C and Marsden O. Large-eddy simulation of underexpanded round jets impinging on a flat plate 4 to 9 radii downstream from the nozzle, 21st AIAA/CEAS aeroacoustics conference. AIAA Paper No. 2015–2210, Dallas, TX, 22–26 June 2015; 1–18.

10.

Glass

. Effect of acoustic feedback on the spread and decay of supersonic jets. AIAA Journal 1968; 6: 1890–1897.

11.

Bridges JE and Wernet MP. Establishing consensus turbulence statistics for hot subsonic jets. In: 16th AIAA/CEAS aeroacoustics conference. AIAA Paper No. 2010-3751, Stockholm, Sweden, 2010. DOI: 10.2514/6.2010-3751.

12.

Harper-Bourne M. Jet noise turbulence measurements. In: 9th AIAA/CEAS aeroacoustics conference and exhibit. AIAA Paper No. 2003-3214, Hilton Head, SC, 2003.

. Velocity measurements in jets with application to noise source modeling. Journal of Sound and Vibration 2010; 329: 394–414. DOI: 10.1016/j.jsv.2009.09.024.

14.

Panda

Seasholtz

. Experimental investigation of density fluctuations in high-speed jets and correlation with generated noise. Journal of Fluid Mechanics 2002; 450: 97–130. DOI: 10.1017/S002211200100622X.

. Investigation of noise sources in high-speed jets via correlation measurements. Journal of Fluid Mechanics 2005; 537: 349. DOI: 10.1017/S0022112005005148.

16.

Doty

McLaughlin

. Space–time correlation measurements of high-speed axisymmetric jets using optical deflectometry. Experiments in Fluids 2005; 38: 415–425. DOI: 10.1007/s00348-004-0920-1.

17.

Veltin J, Day BJ and McLaughlin DK. Correlation of flowfield and acoustic field measurements in high-speed jets. In: 15th AIAA/CEAS aeroacoustics conference (30th AIAA aeroacoustics conference), vol. 49, May 2009, AIAA 2009–3250. DOI: 10.2514/6.2009-3250.

18.

Bridges JE and Wernet MP. Effect of temperature on jet velocity spectra. In: 13th AIAA/CEAS aeroacoustics conference (28th AIAA aeroacoustics conference). AIAA Paper No. 2007-3628, Tallahassee, FL, 21–23 May 2007. DOI: 10.2514/6.2007-3628.

19.

Bridges JE and Wernet MP. Turbulence associated with broadband shock noise in hot jets. In: 14th AIAA/CEAS aeroacoustics conference (29th AIAA aeroacoustics conference). AIAA Paper No. 2008-2834, Manchester, Great Britain, 2008. DOI: 10.2514/6.2008-2834.

20.

Wernet MP. Time resolved PIV for space–time correlations in hot jets. In: 45th AIAA aerospace sciences meeting and exhibit. AIAA Paper No. 2007-47, 2007. DOI: 10.2514/6.2007-47.

21.

Brock B, Haynes RH, Thurow BS, et al. An examination of MHz rate PIV in a heated supersonic jet. In: 52nd aerospace sciences meeting. AIAA Paper No. 2014-1102, National Harbor, MD, 2014. DOI: 10.2514/6.2014-1102.

. Measurements in subsonic and supersonic free jets using a laser velocimeter. Journal of Fluid Mechanics 1979; 93: 1–27. DOI: http://dx.doi.org/10.1017/S0022112079001750.

23.

Lau

. Effects of exit Mach number and temperature on mean-flow and turbulence characteristics in round jets. Journal of Fluid Mechanics 1981; 105: 193–218. DOI: 10.1017/S0022112081003170.

24.

Kerhervé

Jordan

Gervais

et al.

Two-point laser Doppler velocimetry measurements in a Mach 1.2 cold supersonic jet for statistical aeroacoustic source model. Experiments in Fluids 2004; 37: 419–437. DOI: 10.1007/s00348-004-0815-1.

25.

Brooks DR, Ecker T, Lowe KT, et al. Experimental Reynolds stress spectra in hot supersonic round jets. In: 52nd aerospace sciences meeting. AIAA Paper No. 2014-1227, National Harbor, MD, January 2014. DOI: 10.2514/6.2014-1227.

26.

Brooks DR and Lowe KT. Fluctuating flow acceleration in a heated supersonic jet. In: International symposium on applications of laser techniques to fluid mechanics, 2014, pp.7–10.

27.

Ecker T, Lowe KT, Ng WF and Brooks DR. Fourth-order spectral statistics in the developing shear layers of hot supersonic jets. In: 50th AIAA/ASME/SAE/ASEE joint propulsion conference. AIAA Paper No. 2014-3742, Cleveland, OH, 2014. DOI: 10.2514/6.2014-3742.

28.

Ecker T, Brooks DR, Lowe KT and Ng WF. Spectral analysis of over-expanded cold jets via 3-component point Doppler velocimetry. In: 52nd aerospace sciences meeting. AIAA Paper No. 2014-1103, National Harbor, MD, January 2014. DOI: 10.2514/6.2014-1103.

29.

Ecker T, Brooks DR, Lowe KT and Ng WF. Development and application of a point Doppler velocimeter featuring two-beam multiplexing for time-resolved measurements of high-speed flow. Experiments in Fluids 55; 1819: 1–15. DOI: 10.1007/s00348-014-1819-0.

30.

Karns AM. Development of a laser Doppler velocimetry system for supersonic jet turbulence measurements. M.S. Thesis, The Pennsylvania State University, 2014.

31.

Karns AM, Powers RW and McLaughlin DK. Laser Doppler velocimetry in supersonic round jets. In: 53rd aerospace sciences meeting. AIAA Paper No. 2015-1483, Kissimmee, FL, 5–9 January 2015.

32.

Miller

SAE

Veltin

. Experimental and numerical investigation of flow properties of supersonic helium-air jets. AIAA Journal 2011; 49: 235–246. DOI: 10.2514/1.J050720.

33.

Powers

McLaughlin

. Acoustics measurements of military-style supersonic beveled nozzle jets with interior corrugations. International Journal of Aeroacoustics 2017; 16: 21–43. DOI: 10.1177/1475472X16680446.

34.

Powers RW. Experimental investigation of the noise reduction of supersonic exhaust jets with fluidic inserts. PhD Thesis, The Pennsylvania State University, 2015.

35.

Hromisin SM, Myers LM, McLaughlin DK, et al. A comparison of the aeroacoustic characteristics of free and impinging jets with noise reduction techniques. In: 54th aerospace sciences meeting, January 2016, pp.1–25. DOI: 10.2514/6.2016-0526.

36.

Hromisin SM. Laser Doppler velocimetry measurements of a scale model supersonic exhaust jet impinging on a ground plane. Master’s Thesis, Pennsylvania State University, 2015.

37.

Thurow

Jiang

Kim

J-HH

et al.

Issues with measurements of the convective velocity of large-scale structures in the compressible shear layer of a free jet. Physics of Fluids 2008; 20: 1–15. DOI: 10.1063/1.2926757.

38.

Park JT, Derradji-Aouat A, Wu B, et al. Uncertainty analysis: Laser Doppler velocimetry (LDV) calibration. ITTC – Recommended Procedures and Guidelines 2008; 7.5-01-03-02, pp.1–14.

39.

McLaughlin

Tiederman

. Biasing correction for individual realization of laser anemometer measurements in turbulent flows. Physics of Fluids 1973; 16: 2082–2088. DOI: 10.1063/1.1694269.

40.

Nobach H, Muller E and Tropea C. Correlation estimator for two-channel, non-coincidence laser Doppler anemometer. In: 9th international symposium on applications of laser technology in fluid mechanics, Lisbon, Portugal, 1998.

41.

Benedict

Nobach

Tropea

. Estimation of turbulent velocity spectra from laser Doppler data. Measurement Science and Technology 2000; 11: 1089–1104. DOI: 10.1088/0957-0233/11/8/301.

42.

Nobach H. A global concept of autocorrelation and power spectral density estimation from LDA data sets. Tech. rep., Dantec Measurement Technology, 2000.

43.

Tummers

Passchier

. Spectral estimation using a variable window and the slotting technique with local normalization. Measurement Science and Technology 1996; 7: 1541–1546. DOI: 10.1088/0957-0233/7/11/001.

44.

Coleman HW and Steele WG. Experimentation, validation, and uncertainty analysis for engineers. 3rd ed. Hoboken, New Jersey: Wiley, 2009. DOI: 10.1002/9780470485682.ch4.

45.

Lowe KT. Design and application of a novel laser-Doppler velocimeter for turbulence structural measurements in turbulent boundary layers. PhD Thesis, 2006.

46.

Henderson

Powell

. Experiments concerning tones produced by an axisymmetric choked jet impinging on flat plates. Journal of Sound and Vibration 1993; 168: 307–326. DOI: 10.1006/jsvi.1993.1375.

47.

Henderson BS, Bridges JE and Wernet MP. An experimental investigation of the flow structure of supersonic impinging jets. In: 7th AIAA/CEAS aeroacoustics conference and exhibit. AIAA Paper No. 2001-2145, Maastricht, Netherlands.

48.

Worden TJ, Gustavsson JPR, Shih C, et al. Acoustic measurements of high-temperature supersonic impinging jets in multiple configurations. AIAA Paper No. 2013-2187, Berlin, Germany, 2013, pp.1–18. DOI: 10.2514/6.2013-2187.

49.

Preston JR, Troutman S, Keen E, et al. Rotorwash Operational Footprint Modeling. Tech. rep., U.S. Army REDCOM, 2014.

50.

Myers LM and McLaughlin DK. Outwash measurements of a dual impinging jet scale model. In: 53rd aerospace sciences meeting. AIAA Paper No. 2015-1937, Kissimmee, FL, 5–9 January 2015, pp.1–19.

51.

Miller P and Wilson M. Wall jets created by single and twin high pressure jet impingement. Aeronautical Journal 1993; 97: 87–100.

52.

Papamoschou

Morris

McLaughlin

. Beamformed flow-acoustic correlations in a supersonic jet. AIAA Journal 2010; 48: 2445–2453. DOI: 10.2514/1.J050325.

53.

Seiner JM, McLaughlin DK and Liu CH. Supersonic jet noise generated by large scale instabilities. NASA TP 2072, 1982. DOI: 10.1016/S0022-460X(75)80020-4.

54.

Myers LM, Kuo C-W and McLaughlin DK. Far-field acoustic measurements of dual impinging scale model jets. In: 20th AIAA/CEAS aeroacoustics conference. AIAA Paper No. 2014-3200, Atlanta, GA, June 2014, pp.1–19. DOI: 10.2514/6.2014-3200.

Unsteady velocity measurements of model-scale supersonic exhaust jets in military-relevant configurations

Abstract

Keywords

Introduction

Technical approach

Facility description and acoustic measurements

Free jet experimental setup

Impinging jet experimental setup

Laser Doppler velocimeter measurements

Estimation of measurement uncertainty

Experimental results from free jet measurements

Free jet measurements at the nozzle exit plane

Mean velocity and turbulence measurements along jet centerline

Experimental results from impinging jet measurements

Mean velocity and turbulence measurements in impinging jet plume and impingement zone

Mean velocity and turbulence measurements in impinging jet outwash flow

Impinging jet velocity spectra

Summary and conclusions

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

References