Sid Sharma.CV
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Schematic only: the planar PIV arrangement that the study evaluated on the micro-turbojet exhaust. No PIV measurement was made.
Conceptual diagram: tracking favors small particles and light scattering favors large ones. The native exhaust particles sit on the optically weak side.
Measured data: unstripped exhaust size distributions for Jet A-1 and FT-SPK at 100% speed, from earlier campaigns. Most particles are below 100 nm.

PIV Feasibility Study: Can Native Exhaust Aerosol Seed the Jet?

Course project

A course project in turbulent shear flows. Lubrication-oil-derived material in the P200-SX exhaust complicates the emissions measurements. I asked whether that native aerosol could instead seed particle image velocimetry (PIV) of the jet. On paper, it does not pass, so the study supports controlled external seeding.

Result
A negative feasibility result. The native aerosol was not established as suitable for quantitative PIV. It tracks the flow well on paper. But its optically useful fraction is a small tail, and its survival to a laser sheet, uniformity and composition are unknown. No PIV measurement was made.
My role
Sole author. I did the literature review, the tracer-gate analysis, the response, scattering and image-density estimates and the staged test plan. The particle data came from earlier campaigns of the emissions program.
Methods & tools
PIV theory · round-jet scaling · SMPS particle data · Stokes-number and Mie size-parameter analysis · Keane–Adrian image density · uncertainty propagation
Report breakdown

WhyCould a measurement problem become a tracer?

The P200-SX has an open-loop lubrication system [22, 30]. Material derived from the lubrication oil reaches the exhaust, and this complicates the particle and emissions measurements. This project turned the problem around. Could that same particle population act as a native tracer for PIV of the jet?

A velocity field would be useful. In a round jet, centerline decay, spreading, shear-layer structure, entrainment and the organization of turbulence are spatial properties of the plume. A point sensor gives local fluctuation levels. It cannot show how momentum and entrained air reorganize the plume in space [23, 24, 26, 37].

In a hot exhaust the need is sharper. The region that carries the transport physics also carries the experimental penalties: strong convection, density variation, tracer survival limits and difficult optical access.

The transport logic is compact. The velocity splits into a mean and a fluctuation. The turbulent kinetic energy summarizes the fluctuation level. The production term is the rate at which the mean flow feeds the turbulence:

\[\begin{gathered}u_i(\mathbf{x},t)=\overline{u}_i(\mathbf{x})+u_i'(\mathbf{x},t),\\[6pt]k=\tfrac12\overline{u_i'u_i'},\\[6pt]P=-\overline{u_i'u_j'}\,\frac{\partial\overline{u}_i}{\partial x_j}\end{gathered}\]

In an axisymmetric jet, the Reynolds stresses and the mean gradients across the outer shear layer dominate production. A field measurement recovers the mean motion, the fluctuations and the gradients in one dataset.

The exit scales of the P200-SX are already demanding: \(D_j\approx67\) mm, \(U_e\approx490\) m s⁻¹ and \(Re_D\sim\mathcal{O}(10^5)\). The question was narrow. Can PIV work credibly in this plume, with the oil-derived particles as the only seed [22, 30]?

ScopeFour particle populations, kept separate

The word “aerosol” covers several different things here. I keep four of them apart:

  • Native unstripped aerosol. This is what the study used. The SMPS sampled the exhaust with the catalytic stripper bypassed. It can hold soot, oil-derived droplets, condensate and other semivolatile material in unknown proportions. It is not a volatile-only distribution.
  • Stripped (non-volatile) aerosol. A catalytic stripper removes most of the volatile material before the instrument. The non-volatile distributions on the nvPM page are of this type. This study did not use them.
  • Inferred volatile fraction. A comparison of stripped and unstripped scans can give an operational estimate of the volatile part. This study made no such estimate.
  • Artificial PIV seed. A controlled external tracer of known material and size, for example a refractory powder or an oil-droplet aerosol. The study recommends it as the benchmark. No seed was used.

The particle data come from earlier test campaigns at a downstream sampling point. They are not synchronized or co-located with any laser sheet. The data export also has no explicit dilution-ratio field.

HowChoosing a PIV modality

I judged each option by what it can realistically measure in this exhaust. The targets are centerline decay, jet spreading, outer-shear-layer structure, selected Reynolds stresses and the large motions that drive entrainment [5, 10, 23, 32].

Table 1 — PIV modalities for a hot turbulent round jet
ModalityComponentsOptical burdenSeeding burdenBest use in this exhaust
Planar 2C–2D\(u, v\) in sheetLowMost forgivingFirst campaign: mean decay, spread and shear-layer structure
Stereo 3C–2D\(u, v, w\) in sheetModerate–highGood image pairs in both viewsUpgrade for entrainment and three-component transport
Tomographic 3C–3D\(u, v, w\) in volumeHighDense, uniform volume seedingOnly after tracer quality is established
Time-resolved planar\(u, v\) in sheetHighLong-record stabilityCoherent structures and interface dynamics after a validated baseline
Time-resolved stereo\(u, v, w\) in sheetVery highHigh-quality paired views over long recordsOnly when seeding and calibration are reliable

Planar 2C–2D PIV is the defensible starting point. It recovers the most useful observables and puts the smallest demand on a tracer field of uncertain quality. Its main limit is the missing out-of-plane component [10, 27]. That matters only when the objective moves to entrainment paths or three-dimensional structure. Stereo, volumetric and time-resolved methods come later [3, 6, 24, 32, 36].

HowFive gates for a tracer

Hot-jet PIV usually fails at the tracer before it fails at the correlation algorithm. A usable tracer must pass five gates [1, 5, 27, 32]:

  • It follows the resolved motion.
  • It scatters enough light.
  • It survives the thermal path to the imaging plane.
  • It fills the light sheet densely and uniformly.
  • It stays interpretable as one tracer class.

Gate 1, dynamic response. In the Stokes-drag limit:

\[\tau_p\approx\frac{\rho_p d_p^{2}}{18\mu},\qquad St=\frac{\tau_p}{\tau_f}\]

Particle density \(\rho_p\), diameter \(d_p\), gas viscosity \(\mu\) and a characteristic flow timescale \(\tau_f\) [8, 27]. Low inertia is necessary but not sufficient.

Gate 2, scattering. The size parameter sets the regime. In the Rayleigh limit, the scattered intensity falls with the sixth power of the diameter:

\[x=\frac{\pi d_p}{\lambda},\qquad I_s\propto\frac{d_p^{6}}{\lambda^{4}}\quad(x\ll1)\]

Half the particle diameter means 1/64 of the signal [12, 27]. The plausible range for lubricant-derived particles here is roughly 50–500 nm. That is well below the low-micron size usually preferred in gas-phase PIV.

Gate 3, thermal survival. Refractory solids (alumina, titania, zirconia) tolerate high temperature. Their high density gives a longer relaxation time. Liquid tracers such as DEHS or glycol–water are bright at modest size. But in a hot flow they evaporate, change chemically and suffer thermophoretic loss [5, 27].

Gate 4, spatial adequacy. This gate is statistical. Correlation responds only to the particle images inside each interrogation window. Sparse, patchy or dim seeding broadens the peaks and biases the statistics [17, 36].

Gate 5, interpretive control. The signal can come from a mix of droplets, soot aggregates and condensate. Then neither the drag scale nor the optical scale belongs to one particle class [31, 33, 38].

Table 2 — Indicative tracer-property matrix (order-of-magnitude values at \(d_p=1\) µm in air)
MaterialTypeTypical \(d_p\)\(\rho_p\) [kg m⁻³]\(\tau_p\) at 1 µmSurvivable \(T\)Scattering
Al₂O₃Solid0.3–5 µm∼3900∼12 µsHighStrong
TiO₂Solid0.2–3 µm∼4200∼13 µsHighStrong
ZrO₂Solid0.3–5 µm∼5600∼17 µsVery highStrong
DEHSLiquid0.5–3 µm∼910∼2.8 µsLow–moderateModerate
Glycol–waterLiquid0.5–5 µm∼1030∼3.2 µsLow–moderateModerate
PolystyreneSolid0.2–2 µm∼1050∼3.2 µsLowModerate
SmokeMixed< 0.5 µmVariableVery smallVariableWeak
Lubricating oil (est.)Liquid / condensate0.05–0.5 µm∼850–950∼0.03–0.8 µsUncertainWeak

HowMeasurement limits

Different quantities fail at different points. Means converge first. Reynolds stresses need more samples and better peaks. Gradients, vorticity and entrainment metrics are the most fragile, because the estimator has already filtered the field they come from [23, 24, 36]:

\[u_i^{(\mathrm{PIV})}(\mathbf{x})=\int G_I(\mathbf{x}-\boldsymbol{\xi})\,u_i(\boldsymbol{\xi})\,\mathrm{d}\boldsymbol{\xi}\]

\(G_I\) is the effective interrogation-window kernel. Window size, overlap, deformation and image weighting set it [26, 27].

Uncorrelated measurement noise adds directly to the apparent fluctuation energy. Weak images therefore inflate the Reynolds stresses before they visibly distort the mean [16, 34, 36]:

\[\overline{u_m'^2}=\overline{u'^2}+\sigma_{n,u}^{2},\qquad \left(\frac{u'}{U}\right)_{\mathrm{meas}}=\frac{\sqrt{\overline{u'^2}+\sigma_{n,u}^{2}}}{U}\]

At \(u'/U\approx0.15\) and \(U=490\) m s⁻¹, noise of \(\sigma_{n,u}=5\) m s⁻¹ barely changes the intensity. The same noise matters much more in the outer plume, where \(U\) drops and the signal weakens. This is how weak native seeding can produce false turbulent kinetic energy that varies in space.

Sketch, not data: correlation-peak quality. Bright, repeatable particle images give a narrow peak and a stable sub-pixel estimate. Weak images broaden the peak and increase the displacement uncertainty.
Fig. 1 — Sketch, not data: correlation-peak quality. Bright, repeatable particle images give a narrow peak and a stable sub-pixel estimate. Weak images broaden the peak and increase the displacement uncertainty.

The dynamic velocity range turns that hierarchy into a design problem. The particle-image displacement and the range that one setup can resolve are [1, 27]:

\[\Delta x_{\mathrm{px}}=\frac{M_{\mathrm{opt}}\,U\,\Delta t}{p},\qquad \mathrm{DVR}=\frac{\Delta x_{\max}}{\sigma_{\Delta x}}\]

Magnification \(M_{\mathrm{opt}}\), local speed \(U\), pulse separation \(\Delta t\) and pixel pitch \(p\). No single \(\Delta t\) keeps both the 490 m s⁻¹ core and the slow entrained edge inside the preferred displacement band.

The first measurement window is therefore the early-development region, roughly \(x/D_j\approx2\text{–}6\). There, the shear layer is active and decay and spreading are emerging. The window also avoids the most hostile optical zone at the nozzle lip [15, 23, 24, 32].

Correlation is a windowed similarity estimate. A three-point Gaussian fit refines the peak to sub-pixel precision. A normalized-median test then validates the vectors before any replacement, smoothing or differentiation [17, 27, 34, 35]:

\[\begin{gathered}R_{12}(\Delta x,\Delta y)=\sum_{W}I_1(x,y)\,I_2(x+\Delta x,\,y+\Delta y),\\[6pt]x_{\mathrm{sub}}=x_{\mathrm{peak}}+\frac{\ln R_{x-1}-\ln R_{x+1}}{2\ln R_{x-1}-4\ln R_x+2\ln R_{x+1}},\\[6pt]r_0=\frac{|\mathbf{U}_{ij}-\mathbf{U}_{\mathrm{med}}|}{r_{\mathrm{med}}+\epsilon_0}\end{gathered}\]

The sub-pixel step only interpolates the peak that the image pair already made. When the peak is broad or noisy, the algebra still works, but the result loses physical credibility.

Conceptual diagram, not data: the uncertainty chain. Low photon yield lowers the correlation quality, the sub-pixel variance increases, and the apparent fluctuation energy exceeds the true value.
Fig. 2 — Conceptual diagram, not data: the uncertainty chain. Low photon yield lowers the correlation quality, the sub-pixel variance increases, and the apparent fluctuation energy exceeds the true value.

HowEngine context and the seeding hypothesis

Table 3 — Working design point (campaign-planning inputs)
QuantityWorking design value
Nozzle diameter, \(D_j\)67 mm
Exit speed, \(U_e\)≈ 490 m s⁻¹
Hot kinematic viscosity, \(\nu_h\)(0.8–1.0) × 10⁻⁴ m² s⁻¹
Reynolds number, \(Re_D=U_eD_j/\nu_h\)\(\mathcal{O}(10^5)\)
Target image shift6–8 px
Estimated pulse separation≈ 0.8–1.3 µs

For a first-order plume analysis, the nozzle is a turbulent round-jet source. The exit momentum is approximately conserved, while the mass flow grows by entrainment [11, 19, 24, 37]:

\[\begin{gathered}J_e\approx\rho_eU_e^{2}A_e,\\[6pt]\dot m(x)=2\pi\int_0^{\infty}\bar\rho\,\widetilde U(x,r)\,r\,\mathrm{d}r,\\[6pt]\frac{\mathrm{d}\dot m}{\mathrm{d}x}=2\pi\rho_a\,b(x)\,U_c(x)\,\alpha,\\[6pt]\frac{\dot m(x)}{\dot m_e}\approx1+2\alpha\frac{x}{D_j}\end{gathered}\]

Jet width \(b(x)\), centerline velocity \(U_c(x)\) and entrainment coefficient \(\alpha\). These are what PIV must recover to be useful. With the 6–8 px target shift, the displacement relation gives an inter-frame delay of about 0.8–1.3 µs. The report does not state the image scale behind this range, so it is a planning value only.

Sketch, not data: round-jet development with entrainment. It shows the potential core, centerline decay, spreading and entrained mass.
Fig. 3 — Sketch, not data: round-jet development with entrainment. It shows the potential core, centerline decay \(\widetilde U_c(x)\), spreading \(b(x)\) and entrained mass \(\mathrm{d}\dot m/\mathrm{d}x\).
Engine schematic from Lieder et al., ASME Journal of Engineering for Gas Turbines and Power (accepted, GTP-26-1516). The open-loop lubrication system, the hot-gas path and the nozzle define how lubricant-derived material can enter the plume.
Fig. 4 — Engine schematic from Lieder et al., ASME Journal of Engineering for Gas Turbines and Power (accepted, GTP-26-1516). The open-loop lubrication system, the hot-gas path and the nozzle define how lubricant-derived material can enter the plume.

The hypothesis is narrow. The engine does not inject a controlled, monodisperse tracer. Downstream material can come from survival, cracking, reformation and condensation of the oil, and from mixing with soot or other semivolatile species [31, 33, 38].

A native tracer matters only if the material at the imaging plane passes all five gates. The particle data can test only part of that chain.

ResultsWhat the particle data show

The data are three usable long-DMA SMPS scans per fuel at the matched 100% point, over 9.06–465.55 nm. They are loss-corrected and given as \(\mathrm{d}N/\mathrm{d}\log d_m\). That is mobility-diameter space, which differs from optical diameter [13, 14, 21, 30].

Table 4 — Unstripped SMPS observations at 100% speed
Jet A-1FT-SPK
Mode (unstripped)65.52 nm67.93 nm
Total number concentration4.12 × 10⁷ cm⁻³4.27 × 10⁷ cm⁻³
100–500 nm tail9.36 × 10⁵ cm⁻³1.76 × 10⁶ cm⁻³ (1.88×)
Fraction below 100 nm97.73%95.88%
200–465.55 nm sub-band9.01 × 10² cm⁻³7.73 × 10² cm⁻³
Measured data: integrated number concentration in the 100–500 nm interval. FT-SPK gives about 1.88 times the Jet A-1 concentration in this lower-bound band.
Fig. 5 — Measured data: integrated number concentration in the 100–500 nm interval. FT-SPK gives about 1.88 times the Jet A-1 concentration in this lower-bound band.

These concentrations give a first-pass image-density estimate. Take a volumetric concentration \(N_v\) in a light sheet of thickness \(\Delta z_0\). Use a representative 32 × 32 px window at 0.1 mm px⁻¹:

\[\begin{gathered}N_I=N_v\,\Delta z_0,\\[6pt]A_{IW}=(32\,s_{\mathrm{px}})^{2}\approx1.024\times10^{-5}\ \mathrm{m^2},\\[6pt]N_{IW}=N_I\,A_{IW}\end{gathered}\]

With \(\Delta z_0=1\) mm, the full 100–500 nm tail gives \(N_{IW}\approx9.6\times10^{3}\) (Jet A-1) and \(1.8\times10^{4}\) (FT-SPK). That is far above the Keane–Adrian guideline of 10–15 images per window [17]. The more optically promising 200–465.55 nm sub-band gives only \(N_{IW}\approx9.2\) and \(7.9\). These are upper bounds. They count every particle in the band as visible, and the concentrations apply at the sampling point.

Four limits stop this from being a positive result:

  • Mobility diameter is not the compact optical diameter for fractal soot [7, 13, 18, 21].
  • With the stripper bypassed, soot, oil-derived droplets and semivolatile material are counted together [31, 33, 38].
  • The SMPS counts what reached the instrument, which can differ from what crosses a laser sheet.
  • No data show that the optically useful fraction survives the path through the combustor, turbine and nozzle.

ResultsGate-by-gate verdict

A worked example: a 200 nm droplet-like particle, with Sutherland’s law for air at 800 K.

\[\begin{gathered}\mu(T)=\mu_0\left(\frac{T}{T_0}\right)^{3/2}\frac{T_0+S}{T+S}\;\Rightarrow\;\mu(800\,\mathrm{K})\approx3.62\times10^{-5}\ \mathrm{Pa\,s},\\[6pt]\tau_p=\frac{850\,(200\times10^{-9})^{2}}{18\,\mu}\approx5.21\times10^{-8}\ \mathrm{s},\\[6pt]St=\frac{\tau_p}{D_j/U_e}\approx3.81\times10^{-4}\end{gathered}\]

\(\mu_0=1.716\times10^{-5}\) Pa s, \(T_0=273.15\) K, \(S=110.4\) K, \(\tau_f=D_j/U_e=0.067/490\approx1.37\times10^{-4}\) s. The density of 850 kg m⁻³ is an assumed, droplet-like value.

Table 5 — Response time and scattering regime (\(\rho_p=850\) kg m⁻³, \(T=800\) K, \(d_p\approx d_m\) proxy)
Proxy \(d_p\)\(\tau_p\) [s]\(St\)\(x\) at 532 nmRegime
100 nm1.30 × 10⁻⁸9.52 × 10⁻⁵0.59Mie / transitional
200 nm5.21 × 10⁻⁸3.81 × 10⁻⁴1.18Mie / transitional
300 nm1.17 × 10⁻⁷8.57 × 10⁻⁴1.77Mie / transitional
500 nm3.26 × 10⁻⁷2.38 × 10⁻³2.95Mie / transitional
Table 6 — The native unstripped aerosol against the tracer gates
GateEvidenceVerdict
Tracking fidelity\(St=9.5\times10^{-5}\) to \(2.4\times10^{-3}\) over 100–500 nm, if the particles are droplet-likeFavorable
Scattering at 532 nm\(x=0.59\text{–}2.95\), but only 2.27% (Jet A-1) and 4.12% (FT-SPK) of particles are in 100–500 nmMarginal
Thermal survivalA population reaches the SMPS. Survival of the optically useful fraction to the sheet is unmeasured.Unknown
Spatial adequacyUpper-bound \(N_{IW}\approx9.6\times10^3\) and \(1.8\times10^4\). The 200–465 nm sub-band gives only ≈ 9.2 and 7.9.Unknown / unfavorable
Interpretive controlThe stripper bypass mixes soot, oil-derived and semivolatile material. \(d_m\) is not the optical diameter for aggregates.Marginal

The result is negative for quantitative PIV. The particles track well, and the 100–500 nm tail is not zero. The native aerosol might therefore show plume structure qualitatively. But the optically useful particles are a minority tail. Their survival and spatial uniformity are unknown, and the SMPS cannot separate soot from oil-derived material.

ResultsWhat the study supports

The study supports controlled external seeding for any quantitative PIV of this jet. The report described a gated test path to check this, shown below as a planning diagram. None of these phases was carried out.

Planning diagram, not a result: a gated path from a native-particle visibility check to PIV benchmarked against a controlled seed. Each phase sets a go or no-go condition for the next.
Fig. 6 — Planning diagram, not a result: a gated path from a native-particle visibility check to PIV benchmarked against a controlled seed. Each phase sets a go or no-go condition for the next.
  • Visibility check: native particles only, one sheet and one view, in the \(x/D_j\approx2\text{–}6\) window. The gate is repeatable plume structure. Isolated speckles do not count.
  • Benchmark: the same optics, field of view, pulse separation and processing, with a controlled external seed. Success means an acceptable vector yield and validation rate, and mean profiles that agree within the expected uncertainty.
  • Fuel comparison: planar PIV mapping of the plume for each fuel, with stereo only after the tracer is trusted.

RelevanceWhy the jet matters beyond the nozzle

Downstream of the nozzle, the exhaust is an entraining free jet. Species transport there follows momentum, mass and entrainment. The well-stirred and plug-flow idealizations used inside the combustor do not apply [22, 25]. The jet growth and centerline decay set the dilution history and the time available for chemistry, oxidation or condensation:

\[\begin{gathered}\frac{Y_k^{(m)}(x)}{Y_{k,e}^{(m)}}\approx\left(1+2\alpha\frac{x}{D_j}\right)^{-1},\\[6pt]\tau_c(x)=\int_0^{x}\frac{\mathrm{d}\xi}{U_c(\xi)},\\[6pt]\frac{\mathrm{d}\dot m}{\mathrm{d}x}=E(x),\quad \frac{\mathrm{d}\big(\dot m\,Y_k^{(m)}\big)}{\mathrm{d}x}=\dot\Omega_k+E(x)\,Y_{k,a}\end{gathered}\]

The last pair is a one-dimensional plume reactor that could extend a combustor reactor network. A measured jet growth would fix \(E(x)\), and a measured decay would fix \(\tau_c\). FANS and LES plume models need the same transport closure before their species, soot or ice predictions can be trusted [2, 3, 4, 20, 28].

This is the wider reason for the project. The jet spreads, its shear layers entrain air, and the mixing sets how fast the exhaust dilutes and cools. This transport is coupled to the fuel-dependent particle populations that the program measures.

Controlled-seed PIV plus matched native-aerosol measurements could constrain hypotheses about particle transport, evolution and activation. Matched means the same operating point, with known sampling positions and dilution, and both unstripped and stripped scans.

Size distribution and velocity alone do not determine cloud-condensation-nucleus activity or contrail ice. That also needs temperature, humidity, particle composition and hygroscopicity, and activation measurements or a suitably constrained model.

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