Analytical Approach for Aero-Optical & Atmospheric Effects in Supersonic Flow Fields. Gupta, A. & Argrow, B. Technical Report abstract bibtex Radio blackout is commonly associated with interference from plasma created around high-speed aerospace and re-entry vehicles. Alternative communication means, including lasers at optical frequencies, has emerged as promising counter to the problem. The refractive index of a medium, such as air, governs the angular shift in the path of an optical signal. For a fluid, the refractive index is a function of the thermodynamic state. Drastic changes in the thermodynamic variables across the shock wave changes the downstream refractive index. This paper presents an investigation of how changes to the thermodynamic state of air for high-speed flow (not including chemical reactions) affects optical propagation. Analytical expressions for horizontal deviation and angular shifts induced by-shock layer, shock wave and atmosphere, are derived for an optical signal that travels from a high-speed vehicle to the ground. The formulation has been verified computationally for the supersonic flow about a wedge and cone that capture effects from flow gradients. I. Nomenclature α = communication angle [deg] α * = inflex communication angle [deg] β = shock angle [deg] ˆ θ = estimated angle to ground [deg] θ c = semi-vertex angle of the body [deg] θ d m = approach angle to shock [deg] θ u0 = refraction angle after shock [deg] θ u n = approach angle to ground [deg] ∆θ = small angular difference between consecutive rays in shock layer [deg] κ = Gladstone-Dale constant [m 3 /kg] ˆ φ = estimated approach angle to shock wave [deg] φ * d m = inflex approach angle [deg] φ * u0 = inflex refraction angle in upstream [deg] φ di = incident angle at the interface of i th and (i + 1) th sub-layer of shock layer [deg] φ dir = refraction angle at the interface of i th and (i + 1) th sub-layer of shock layer [deg] φ u0 = refraction angle in upstream [deg] ω = angular shift [deg] ω = augmented angular shift [deg] n d m = downstream refractive index of m th sub-layer of shock layer n u0 = upstream refractive index at the cruising altitude n u n = upstream refractive index of n th atmospheric layer x = actual horizontal distance on surface [m] ˆ x = estimated horizontal distance on surface [m] x u = actual horizontal distance before reaching first atmospheric layer [m] x r i = actual horizontal distance in i th atmospheric layer [m]
@techreport{gupta,
title = {Analytical {Approach} for {Aero}-{Optical} \& {Atmospheric} {Effects} in {Supersonic} {Flow} {Fields}},
abstract = {Radio blackout is commonly associated with interference from plasma created around high-speed aerospace and re-entry vehicles. Alternative communication means, including lasers at optical frequencies, has emerged as promising counter to the problem. The refractive index of a medium, such as air, governs the angular shift in the path of an optical signal. For a fluid, the refractive index is a function of the thermodynamic state. Drastic changes in the thermodynamic variables across the shock wave changes the downstream refractive index. This paper presents an investigation of how changes to the thermodynamic state of air for high-speed flow (not including chemical reactions) affects optical propagation. Analytical expressions for horizontal deviation and angular shifts induced by-shock layer, shock wave and atmosphere, are derived for an optical signal that travels from a high-speed vehicle to the ground. The formulation has been verified computationally for the supersonic flow about a wedge and cone that capture effects from flow gradients. I. Nomenclature α = communication angle [deg] α * = inflex communication angle [deg] β = shock angle [deg] ˆ θ = estimated angle to ground [deg] θ c = semi-vertex angle of the body [deg] θ d m = approach angle to shock [deg] θ u0 = refraction angle after shock [deg] θ u n = approach angle to ground [deg] ∆θ = small angular difference between consecutive rays in shock layer [deg] κ = Gladstone-Dale constant [m 3 /kg] ˆ φ = estimated approach angle to shock wave [deg] φ * d m = inflex approach angle [deg] φ * u0 = inflex refraction angle in upstream [deg] φ di = incident angle at the interface of i th and (i + 1) th sub-layer of shock layer [deg] φ dir = refraction angle at the interface of i th and (i + 1) th sub-layer of shock layer [deg] φ u0 = refraction angle in upstream [deg] ω = angular shift [deg] ω = augmented angular shift [deg] n d m = downstream refractive index of m th sub-layer of shock layer n u0 = upstream refractive index at the cruising altitude n u n = upstream refractive index of n th atmospheric layer x = actual horizontal distance on surface [m] ˆ x = estimated horizontal distance on surface [m] x u = actual horizontal distance before reaching first atmospheric layer [m] x r i = actual horizontal distance in i th atmospheric layer [m]},
author = {Gupta, Anubhav and Argrow, Brian},
}
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This paper presents an investigation of how changes to the thermodynamic state of air for high-speed flow (not including chemical reactions) affects optical propagation. Analytical expressions for horizontal deviation and angular shifts induced by-shock layer, shock wave and atmosphere, are derived for an optical signal that travels from a high-speed vehicle to the ground. The formulation has been verified computationally for the supersonic flow about a wedge and cone that capture effects from flow gradients. I. Nomenclature α = communication angle [deg] α * = inflex communication angle [deg] β = shock angle [deg] ˆ θ = estimated angle to ground [deg] θ c = semi-vertex angle of the body [deg] θ d m = approach angle to shock [deg] θ u0 = refraction angle after shock [deg] θ u n = approach angle to ground [deg] ∆θ = small angular difference between consecutive rays in shock layer [deg] κ = Gladstone-Dale constant [m 3 /kg] ˆ φ = estimated approach angle to shock wave [deg] φ * d m = inflex approach angle [deg] φ * u0 = inflex refraction angle in upstream [deg] φ di = incident angle at the interface of i th and (i + 1) th sub-layer of shock layer [deg] φ dir = refraction angle at the interface of i th and (i + 1) th sub-layer of shock layer [deg] φ u0 = refraction angle in upstream [deg] ω = angular shift [deg] ω = augmented angular shift [deg] n d m = downstream refractive index of m th sub-layer of shock layer n u0 = upstream refractive index at the cruising altitude n u n = upstream refractive index of n th atmospheric layer x = actual horizontal distance on surface [m] ˆ x = estimated horizontal distance on surface [m] x u = actual horizontal distance before reaching first atmospheric layer [m] x r i = actual horizontal distance in i th atmospheric layer [m]","author":[{"propositions":[],"lastnames":["Gupta"],"firstnames":["Anubhav"],"suffixes":[]},{"propositions":[],"lastnames":["Argrow"],"firstnames":["Brian"],"suffixes":[]}],"bibtex":"@techreport{gupta,\n\ttitle = {Analytical {Approach} for {Aero}-{Optical} \\& {Atmospheric} {Effects} in {Supersonic} {Flow} {Fields}},\n\tabstract = {Radio blackout is commonly associated with interference from plasma created around high-speed aerospace and re-entry vehicles. Alternative communication means, including lasers at optical frequencies, has emerged as promising counter to the problem. The refractive index of a medium, such as air, governs the angular shift in the path of an optical signal. For a fluid, the refractive index is a function of the thermodynamic state. Drastic changes in the thermodynamic variables across the shock wave changes the downstream refractive index. This paper presents an investigation of how changes to the thermodynamic state of air for high-speed flow (not including chemical reactions) affects optical propagation. Analytical expressions for horizontal deviation and angular shifts induced by-shock layer, shock wave and atmosphere, are derived for an optical signal that travels from a high-speed vehicle to the ground. The formulation has been verified computationally for the supersonic flow about a wedge and cone that capture effects from flow gradients. I. Nomenclature α = communication angle [deg] α * = inflex communication angle [deg] β = shock angle [deg] ˆ θ = estimated angle to ground [deg] θ c = semi-vertex angle of the body [deg] θ d m = approach angle to shock [deg] θ u0 = refraction angle after shock [deg] θ u n = approach angle to ground [deg] ∆θ = small angular difference between consecutive rays in shock layer [deg] κ = Gladstone-Dale constant [m 3 /kg] ˆ φ = estimated approach angle to shock wave [deg] φ * d m = inflex approach angle [deg] φ * u0 = inflex refraction angle in upstream [deg] φ di = incident angle at the interface of i th and (i + 1) th sub-layer of shock layer [deg] φ dir = refraction angle at the interface of i th and (i + 1) th sub-layer of shock layer [deg] φ u0 = refraction angle in upstream [deg] ω = angular shift [deg] ω = augmented angular shift [deg] n d m = downstream refractive index of m th sub-layer of shock layer n u0 = upstream refractive index at the cruising altitude n u n = upstream refractive index of n th atmospheric layer x = actual horizontal distance on surface [m] ˆ x = estimated horizontal distance on surface [m] x u = actual horizontal distance before reaching first atmospheric layer [m] x r i = actual horizontal distance in i th atmospheric layer [m]},\n\tauthor = {Gupta, Anubhav and Argrow, Brian},\n}\n\n\n\n","author_short":["Gupta, A.","Argrow, B."],"key":"gupta","id":"gupta","bibbaseid":"gupta-argrow-analyticalapproachforaeroopticalatmosphericeffectsinsupersonicflowfields","role":"author","urls":{},"metadata":{"authorlinks":{}}},"bibtype":"techreport","biburl":"https://bibbase.org/zotero-group/khanquist/4882481","dataSources":["qwkM8ZucCwtxbnXfc"],"keywords":[],"search_terms":["analytical","approach","aero","optical","atmospheric","effects","supersonic","flow","fields","gupta","argrow"],"title":"Analytical Approach for Aero-Optical & Atmospheric Effects in Supersonic Flow Fields","year":null}