Mishra, Analysis of the transport of a train of short-pulse radiation of Gaussian temporal profile through a 2-D participating medium, Heat Transfer Engineering (submitted) 2008. In the past, effects of the transport of a single pulse in a participatory medium was studied in detail.
TH-0531_RMUTHUKUMARAN
Transmission and reflectance signals are analyzed for the effects of the extinction coefficient and the scattering albedo. In a practical situation, the spatial intensity distribution of the incident collimated radiation can be a Gaussian function.
Contents
- The General 3D FVM Formulation for a Short-pulse Laser Transport through a Participating Medium
- Transient Response of a 1-D Planar Participating Medium Subjected to a Train of Short-Pulse Radiation
- Propagation of a Laser Wave through a 1-D Planar Participating Inhomogeneous Medium
- Effects of the Incidence of a Short-Pulse Laser Wave on a 2-D Rectangular Homogeneous Participating Medium
- Effects of the incidence of a short-pulse laser wave on a 2-D Rectangular inhomogeneous Participating medium
- Thermal Signatures of an Inhomogeneous 2-D Participating Medium under the Influence of a Short-Pulse Laser – Effects of Shapes and
- Effects of the incidence of a Gaussian-temporal short-pulse laser of different spatial profiles on a 2D rectangular inhomogeneous
Effects of the incidence of a short-pulse laser wave on a 2-D homogeneous rectangular participant medium. Homogeneous rectangular participant medium. Effects of the Incidence of a Short-Pulse Laser Wave on a Rectangular Inhomogeneous Participating Medium 2-D Rectangular Inhomogeneous Participating Medium.
215 Figure 8.5: Spatial distribution of transmittance and reflectance results for cases 11, 12 for two different extinction coefficient values.
List of Tables
Nomenclature
Introduction
- Radiation as a Mode of Heat Transfer
- Surface and Volumetric Radiation
- Transient Radiative Heat Transfer
- A summary of the specific applications of pulse radiation
- Numerical Methods for Solutions of Pulse Radiation Transport through a Participating Medium
- Objective and Organization of Thesis
- Summary
Details of the FVM methodologies used in this work can be found in [80] and [103]. The results of the present work for a single pulse were compared with those available in the literature.
The General 3D FVM Formulation for a Short- pulse Laser Transport through a Participating
Introduction
A basic mathematical model for the transport of a short pulse laser through a participating medium is essential for the solution of a variety of problems. This chapter presents a mathematical formulation in the finite volume method for the transport of a short pulse laser through a three-dimensional absorbing-emitting-scattering medium.
Formulation
These effects are taken care of, mathematically, by introducing the Heaviside function into the above equations. I r t is given by and calculated from. 2.23), the first and second terms represent respectively radiated and reflected components of the boundary intensity.
Summary
The short solution methodology for an FVM solution for short pulse laser transport through a participating medium is presented as a flowchart in Figure 2.
Introduction
Further, his study was limited to an approximate step pulse and the effect of albedo scattering was not considered. For the four combinations of radiation (diffuse and coarse) and time variations (step and Gaussian), the transmission and reflection signals are analyzed.
Problem
Transmittance and reflection signals at the boundaries received by the detectors were not taken into account in his study. This chapter deals with the study of a train of diffuse and collimated pulses with a stepwise or Gaussian time variation.
Formulation
When the short-pulse radiation propagates through the participating medium, the time-dependent diffuse radiation manifests itself and its lifetime in the medium is of the order of the pulse width of the radiation source. The changes in the formulation for diffuse radiation will be emphasized where their need is felt. For a linear anisotropic phase function p(Ω Ω = +, ′) 1 acos cosθ θ′, the source term Sc in terms of the incident radiation Gc and the heat flux qc is written as. s = z θ is the geometric distance in the direction θco of the collimated radiation, δ is the Dirac delta function and H is the Heaviside function defined as.
I r t is given and calculated from it. 3.21), the first and second terms represent the transmitted and reflected components of the boundary intensity.
Solution Procedure
Results and Discussions
- Validation of results for a single pulse
- Results with a train of pulses
- Effect of the extinction coefficient β
- Effect of the scattering albedo ω
In this case, the northern boundary of the planar medium is exposed to a single diffuse or collimated pulse. On the following pages, the results of transmittance q Z tt*( ), * and reflectance qr*( )0,t* with a set of pulses for different values of extinction coefficient β and scattering albedoω are given. It is observed that similar to the diffuse step pulse results, the transmittance magnitude.
Further, like diffuse step pulses (Fig. 3.3e), for the same reason, for a higher value of the extinction coefficient (β =5.0), multiple maxima and minima are not observed.
![Figure 3.2: Comparison of results with literature[1,97,101,104]](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10465100.0/73.918.142.755.110.869/figure-comparison-of-results-with-literature-101-104.webp)
Summary
Introduction
In all the above cases, the analyzes were performed for a single pulse or a multi-pulse laser. A laser pulse train finds potential applications in the emerging fields such as laser tissue welding and brazing, laser metal surface treatment, laser metal marking and engraving, nanophotonics and fiber optic communication [1-99]. In contrast to numerical studies with a single pulse laser, where the transmittance and reflectance signals have mainly been analyzed, studies with pulse trains are scarce.
In this chapter, research with a single and a series of four laser pulses is presented.
Problem
Step Pulse- Results and Discussions
- Validation of results
- Results with 1- and 4-pulse laser train
This accounts for the differences in the peak sizes (Figs. 4.3a and 4.3c) of the transmission signals at the southern boundary. With a single pulse, the minimum corresponding to inhomogeneities in the medium is observed only in the case of Fig. The inhomogeneities are presented by considering distinct values of the distribution albedo in the three layers.
As a result, a significantly larger difference in the magnitudes of the reflectance q*r( )0,t* signal in Fig.
Gaussian Pulse-Results and Discussions
The temporal span of the reflectance signals for all cases depends on the overall scattering character of the medium. The temporal spans for the reflectance qr*()0,t* signals for all four cases have the same tendency as for the transmittance q Z tt*( ), * signals. The time spans for the signals turn out to be almost the same for all the cases.
The layer adjacent to the northern boundary which contributes the most, the peak magnitudes of the reflectance q*r( )0,t* signals are the same in all the cases.
Summary
The time span of the transmission signals was found to depend on both the optical depth and the scattering albedo. However, the time span of the reflection signals appeared to depend more on the scattering albedo of the layer adjacent to the northern boundary. These signals are strongly dependent on the radiation properties of the layers and the location of the layer relative to the incident boundary.
However, the time span of the transmittance signals showed a strong dependence on the scattering albedos of the layers.
Introduction
Regarding the two-dimensional rectangular geometries, no research has been done so far on the effect of multiple pulses on transmission and reflection signals. One of the boundaries of the medium is subjected to diffuse or collimated radiation. The temporal profile of the short pulse radiation at the incident boundary is a step or Gaussian function.
This chapter also presents formulation specific to the transport of a pulse radiation through a 2-D participating medium.
Problem
2-D geometry represents a more realistic situation, but on the other hand, it introduces additional mathematical complexities. The work in Chapter 5 deals with the analysis of the interaction of a laser train of short pulses in a 2-D rectangular homogeneous cooperating medium.
Formulation
In this work, we have considered the southern boundary of the 2-D medium exposed to either a diffuse or a collimated radiation. The transport of the collimated radiation in the medium and its decay results in diffuse radiation. The source term Sc, resulting from the collimated radiation Ic, expressed in the incident radiation Gc and heat flux qc, for a linear anisotropic phase function p(Ω Ω = +, ′) 1 acos cosθ θ′ is given by.
If t* =βct and t*p =βctp are dimensionless times, equation 5.8), N is the number of pulses and Tp*=βcTp is the dimensionless time period of the pulse train.
Results and Discussion – Step pulse train
- Validation of results
- Results with 1-4 pulse train
With distribution albedoω=1.0, for 1-4 pulses, these results are shown for three values of the extinction coefficient β. A distinct difference in the peak magnitudes of signals for multiple pulses is observed for β =5.0 and 10.0. It is further observed that the peak heat flux magnitudes are still found within the medium near the northern boundary.
Like the transmittance, the magnitudes of the reflected signals increase with increasing ω.
Results and Discussion – Gaussian pulse train
- Validation of results
- Results with 1-4 pulse train
A comparison of the q*r(0,5,0,0,t*) reflectance signals shows no discernible effect of ω on the peak shape and time spans for any pulse train. Since the size of the incident pulse is a Gaussian function, a gradual increase in the signal is observed. Unlike the transmittance q*t (0,5,1,0,t*), the maximum values of the reflectance signals q*r(0,5,0,0,t*) increase with increasing β, and there are also different peaks and drops are different for all values of β.
Like transmittance, the magnitude of the reflectance signals is also found to increase with the increase inω.
Summary
Effects of the Incidence of a Short-Pulse
Radiation Transport through a 2-D Rectangular Inhomogeneous Participating Medium
Introduction
Furthermore, the effect of the location of the inhomogeneity in the medium was also not reported for a single or multiple pulses. An investigation of the transport of a train of short-pulse radiation through a 2-D rectangular participating medium consisting of local inhomogeneities is presented in this chapter. The pulse width and the period of the incident radiation are of the order of a nano-second.
The formulation for the problems considered in this chapter is the same as that presented in Chapter 5.
Problem
Although a few studies involving the presence of inhomogeneities in 2-D rectangular cooperating media are found in the literature studies of the effects of multiple pulses on 2-D geometries with local inhomogeneities and thus their thermal signatures, viz. permeability and reflectivity have never been done until now.
Results and Discussion – Step pulse train
The southern boundary of the 2-D medium is subjected to a short-pulse laser incident normal to the boundary. The scattering albedo of the medium and its inhomogeneity are opposite to those for the results in Fig. X results along the boundaries are plotted for three different values of the extinction coefficient β.
In all three figures, the area of the negative heat flux can be seen concentrated near the southern boundary.
Results and Discussion – Gaussian pulse train
While for a medium with less attenuation (β = 1.0), the reflection signal q*r(0.5,0,0,t*) depends strongly on the location of the inhomogeneity. Due to the presence of a strong scattering inhomogeneity in the lower right corner of the geometry, a trend with a skew toward the eastern boundary emerges, similar to that in Figure 6.16b. Since in this case the radiation has already encountered the inhomogeneity, the heat flux contours in the vicinity of the inhomogeneity are affected at an early stage.
However, due to the Gaussian temporal nature of the incident profile and high diffusion in the medium, the heat flux concentration is smaller.
Summary
