Applicability of the Wright Polynomial Correction for Time-Resolved Laser-Induced Incandescence in the Transition Regime

2012 ◽  
Author(s):  
K. J. Daun ◽  
S. C. Huberman
Keyword(s):  
Heat Conduction ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Mean Free Path ◽  
Knudsen Layer ◽  
Transition Regime ◽  
Time Resolved ◽  
Laser Induced Incandescence ◽  
The Mean ◽  
Gas Molecules

Sizing aerosolized nanoparticles through time-resolved laser-induced incandescence (TiRe-LII) requires an accurate model of the heat conduction from the laser-energized particle to the surrounding gas. Under transition regime conditions this is often done using Fuchs’ boundary-sphere method, which requires the analyst to specify the thickness of a collisionless layer surrounding the particle, representing the Knudsen layer. Traditionally the boundary layer thickness is set to the mean free path of the gas at the boundary temperature, but recently some TiRe-LII practitioners have adopted a more complex treatment that accounts for particle curvature and directional distribution of gas molecules. This paper presents a critical reassessment of this approach; while this modification is more representative of the true Knudsen layer thickness, it does not improve the accuracy of heat conduction rates estimated using Fuchs’ boundary sphere methods under conditions prevailing in most TiRe-LII experiments.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Direct simulation of the turbulent boundary layer along a compression ramp at M = 3 and Reθ = 1685

2000 ◽  
Vol 420 ◽  
pp. 47-83 ◽  
Author(s):  
NIKOLAUS A. ADAMS
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Shear Stresses ◽  
Numerical Representation ◽  
Computational Domain ◽  
The Mean ◽  
Compression Ramp

The turbulent boundary layer along a compression ramp with a deflection angle of 18° at a free-stream Mach number of M = 3 and a Reynolds number of Reθ = 1685 with respect to free-stream quantities and mean momentum thickness at inflow is studied by direct numerical simulation. The conservation equations for mass, momentum, and energy are solved in generalized coordinates using a 5th-order hybrid compact- finite-difference-ENO scheme for the spatial discretization of the convective fluxes and 6th-order central compact finite differences for the diffusive fluxes. For time advancement a 3rd-order Runge–Kutta scheme is used. The computational domain is discretized with about 15 × 106 grid points. Turbulent inflow data are provided by a separate zero-pressure-gradient boundary-layer simulation. For statistical analysis, the flow is sampled 600 times over about 385 characteristic timescales δ0/U∞, defined by the mean boundary-layer thickness at inflow and the free-stream velocity. Diagnostics show that the numerical representation of the flow field is sufficiently well resolved.Near the corner, a small area of separated flow develops. The shock motion is limited to less than about 10% of the mean boundary-layer thickness. The shock oscillates slightly around its mean location with a frequency of similar magnitude to the bursting frequency of the incoming boundary layer. Turbulent fluctuations are significantly amplified owing to the shock–boundary-layer interaction. Reynolds-stress maxima are amplified by a factor of about 4. Turbulent normal and shear stresses are amplified differently, resulting in a change of the structure parameter. Compressibility affects the turbulence structure in the interaction area around the corner and during the relaxation after reattachment downstream of the corner. Correlations involving pressure fluctuations are significantly enhanced in these regions. The strong Reynolds analogy which suggests a perfect correlation between velocity and temperature fluctuations is found to be invalid in the interaction area.

scholarly journals Slip boundary condition of heat flux in Knudsen layers

2014 ◽  
Vol 470 (2161) ◽  
pp. 20130578 ◽  
Author(s):  
Mingtian Xu
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Mean Free Path ◽  
Knudsen Layer ◽  
Boltzmann Transport ◽  
Slip Boundary ◽  
The Mean ◽  
Solid Walls

In a Knudsen layer with thickness comparable to the mean free path, collisions between heat carriers and solid walls play an important role in nanoscale heat transports. An interesting question is that whether these collisions also induce the slip of heat flow similar to the velocity slip condition of the rarefied gases on solid walls. In this work based on the discrete Boltzmann transport equation, the slip boundary condition of heat flux on solid walls in the Knudsen layer is established. This result is exemplified by the slip boundary condition of heat flux in nanowires, which has been proposed in a phenomenological way.

scholarly journals Maximum Possible Colling Rate in Ultrafast Chip Nanocalorimetry: Fundamental Limitations Due to Thermal Resistance at the Membrane/Gas Interface

2021 ◽  
Author(s):  
Alexander A. Minakov ◽  
Christoph Schick
Keyword(s):  
Thermal Resistance ◽  
Cooling Rate ◽  
Materials Science ◽  
Mean Free Path ◽  
Heat Conducting ◽  
Controlled Cooling ◽  
Fundamental Limitations ◽  
The Mean ◽  
Gas Molecules ◽  
Hot Zone

Ultrafast chip nanocalorimetry opens up remarkable possibilities in materials science by allowing samples to be cooled and heated at extremely high rates. Due to heat transfer limitations, controlled ultrafast cooling and heating can only be achieved for tiny samples in calorimeters with a micron-thick membrane. Even if ultrafast heating can be controlled under quasi-adiabatic conditions, ultrafast controlled cooling can be performed if the calorimetric cell is located in a heat-conducting gas. It was found that the maximum possible cooling rate increases as 1/r0 with decreasing radius r0 of the hot zone of the membrane. The possibility of increasing the maximum cooling rate with decreasing r0 was successfully implemented in many experiments. In this regard, it is interesting to answer the question: what is the maximum possible cooling rate in such experiments if r0 tends to zero? Indeed, on submicron scales, the mean free path of gas molecules lmfp becomes comparable to r0, and the temperature jump that exists at the membrane/gas interface becomes significant. Considering the limitation associated with thermal resistance at the membrane/gas interface and considering the transfer of heat through the membrane, we show that the controlled cooling rate can reach billions of K/s, up to 1010 K/s.

DSMC Simulation of Supersonic Gas Flow in Microchannel

2011 ◽  
Author(s):  
Mohamad M. Joneidipour ◽  
Reza Kamali
Keyword(s):  
Gas Flow ◽  
Characteristic Length ◽  
Flow Characteristics ◽  
Mean Free Path ◽  
Incoming Flow ◽  
Characteristic Length Scale ◽  
Flow Pressure ◽  
Supersonic Gas Flow ◽  
The Mean ◽  
Gas Molecules

The present study is concerned with the flow characteristics of a microchannel supersonic gas flow. The direct simulation Monte Carlo (DSMC) method is employed for predicting the density, velocity and temperature distributions. For gas flows in micro systems, the continuum hypothesis, which underpins the Navier-Stokes equations, may be inappropriate. This is because the mean free path of the gas molecules may be comparable to the characteristic length scale of the device. The Knudsen number, Kn, which is the ratio of the mean free path of the gas molecules to the characteristic length scale of the device, is a convenient measure of the degree of rarefaction of the flow. In this paper, the effect of Knudsen number on supersonic microchannel flow characteristics is studied by varying the incoming flow pressure or the microchannel height. In addition, the microchannel height and the incoming flow pressure are varied simultaneously to investigate their effects on the flow characteristics. Meanwhile, the results show that until the diffuse reflection model is used throughout the microchannel, the temperature and the Mach number in the microchannel entrance may not be equal to free-stream values and therefore a discontinuity appear in the flow field.

scholarly journals Experimental and theoretical studies of the behaviour of slow electrons in air. I

1949 ◽  
Vol 196 (1046) ◽  
pp. 402-426 ◽  
Keyword(s):  
Drift Velocity ◽  
Mean Free Path ◽  
Free Electrons ◽  
Direct Measurements ◽  
Electronic Motion ◽  
The Mean ◽  
Gas Molecules ◽  
Slow Electrons ◽  
Experimental And Theoretical Studies ◽  
Unit Pressure

This paper is an account of an experimental investigation of the motions of free electrons in air by the method developed by Townsend. An improved form of apparatus is described with the appropriate theory. The following parameters of the electronic motion were determined as functions of the ratio Z/p of the electric field strength Z to the gas pressure p : Townsend’s energy factor k r the drift velocity W , the mean free path at unit pressure L and the mean proportion n of its energy lost in collisions with gas molecules. The experimental data are given in the form of tables and curves. The drift velocity W is found by a new procedure based on the Hall effect and by comparing the velocities W so obtained with the direct measurements of W by Nielsen & Bradbury it is seen that the velocities of agitation are distributed approximately according to Druyvesteyn’s law when Z/p exceeds 0.5. Bailey’s factor G , which is of importance in ionospheric studies, is obtained from the experimental dependence of η on k r . Theoretical formulae are derived for k r and W in terms of L, G and Z/p . The theory of the new method for measuring W is given in an appendix.

The pre-transitional Klebanoff modes and other boundary-layer disturbances induced by small-wavelength free-stream vorticity

2009 ◽  
Vol 638 ◽  
pp. 267-303 ◽  
Author(s):  
PIERRE RICCO
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Streamwise Velocity ◽  
Matched Asymptotic Expansion ◽  
Two Dimensional ◽  
Mean Flow ◽  
Flow Distortion ◽  
The Mean

The response of the Blasius boundary layer to free-stream vortical disturbances of the convected gust type is studied. The vorticity signature of the boundary layer is computed through the boundary-region equations, which are the rigorous asymptotic limit of the Navier–Stokes equations for low-frequency disturbances. The method of matched asymptotic expansion is employed to obtain the initial and outer boundary conditions. For the case of forcing by a two-dimensional gust, the effect of a wall-normal wavelength comparable with the boundary-layer thickness is taken into account. The gust viscous dissipation and upward displacement due to the mean boundary layer produce significant changes on the fluctuations within the viscous region. The same analysis also proves useful for computing to second-order accuracy the boundary-layer response induced by a three-dimensional gust with spanwise wavelength comparable with the boundary-layer thickness. It also follows that the boundary-layer fluctuations of the streamwise velocity match the corresponding free-stream velocity component. The velocity profiles are compared with experimental data, and good agreement is attained.The generation of Tollmien–Schlichting waves by the nonlinear mixing between the two-dimensional unsteady vorticity fluctuations and the mean flow distortion induced by localized wall roughness and suction is also investigated. Gusts with small wall-normal wavelengths generate significantly different amplitudes of the instability waves for a selected range of forcing frequencies. This is primarily due to the disparity between the streamwise velocity fluctuations in the free stream and within the boundary layer.

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