Caros et al 2019b - Revision history

Rimni at 13:07, 24 November 2020

2020-11-24T13:07:18Z

Rimni at 13:04, 24 November 2020

2020-11-24T13:04:18Z

Rimni: /* 4. Results */

2020-11-24T13:03:31Z

‎4. Results

Rimni at 12:42, 24 November 2020

2020-11-24T12:42:30Z

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Scipediacontent at 10:43, 16 April 2020

2020-04-16T10:43:49Z

Scipediacontent at 10:33, 16 April 2020

2020-04-16T10:33:56Z

Rimni at 11:14, 21 January 2020

2020-01-21T11:14:22Z

Rimni at 11:10, 21 January 2020

2020-01-21T11:10:20Z

Rimni at 11:05, 21 January 2020

2020-01-21T11:05:44Z

Rimni at 11:05, 21 January 2020

2020-01-21T11:05:00Z

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 Hypersonic flight vehicles such as the X-43, require profound studies on each technological part. Examples of the depth of such studies are, the optimization of the internal engine flow channel via employing genetic algorithms, which was undertaken by Ahuja et al. <span id='citeF-1'></span>[[#cite-1|[1]]]. Aeroelastic and aerothermoelastic-acoustics simulations based on new computational Fluid Mechanics models, were presented in <span id='citeF-2'></span><span id='citeF-3'>[[#cite-2|[2]],[[#cite-3|3]]]. The pressure distribution over this particular aircraft was numerically determined by Elizarova and Shirokov <span id='citeF-4'></span>[[#cite-4|[4]]], where they implemented a method which introduced artificial dissipation coefficients. The resulting overall lift and drag coefficients for several angles of attack were obtained when solving the three dimensional Navier-Stokes equations by <span id='citeF-5'></span><span id='citeF-6'></span>[[#cite-5|[5]],[[#cite-6|6]]], the comparison with the experimental measurements gave a very good agreement. The flight dynamics affecting a 2D hypersonic vehicle resembling the X-43, were described in <span id='citeF-7'></span>[[#cite-7|[7]]], where the non linear equations of motion were derived. An increase of the aerodynamic efficiency of the hypersonic aircraft (HA) was obtained in <span id='citeF-8'></span>[[#cite-8|[8]]], via adding energy in front of the bow of the HA. It was observed that the addition of energy weakened the shock wave. In Kotov et al. <span id='citeF-9'></span>[[#cite-9|[9]]], the shock-wave structures appearing around the same (HA) studied by the rest of the researchers cited in this paper, were filmed using a high-speed video camera. Visualizations of the flow at the engine entrance throat, where the shock waves reflect, were particularly interesting.
-In the present study, given the Mach number and the altitude at which the X-43 simplified shape aircraft performs, the aerodynamic forces acting on the aircraft will be calculated based on the mathematical formulation defined in section II. In the next step, these forces will be optimized, computing this formulation with a python code and using the RMOP optimizer (http://tts.cimne.com/rmop). The optimization will be based on the variation of the main geometrical parameters of the aircraft, presented in Figures 1 and 2. The shape of the chosen aircraft, was as well optimised for different possible flight altitudes and Mach numbers.
+In the present study, given the Mach number and the altitude at which the X-43 simplified shape aircraft performs, the aerodynamic forces acting on the aircraft will be calculated based on the mathematical formulation defined in section II. In the next step, these forces will be optimized, computing this formulation with a python code and using the RMOP optimizer (http://tts.cimne.com/rmop). The optimization will be based on the variation of the main geometrical parameters of the aircraft, presented in [[#img-1|Figures 1]] 1 and [[#img-2|2]]. The shape of the chosen aircraft, was as well optimised for different possible flight altitudes and Mach numbers.
 ==2. Mathematical model==
@@ Line 189: / Line 189: @@
 ==4. Results==
-The conditions at which the aircraft was initially optimised were, <math display="inline">Mach = 7</math> and a flight altitude of <math display="inline">h = 30000 m</math>. Following the International Standard Atmosphere (ISA), the thermo-physical values were obtained; a temperature of <math display="inline">T = 226.65 K</math>, a pressure of <math display="inline">P = 1171.87 Pa</math> and a gravity of <math display="inline">g = 9.715 m/s^2</math>. In reality the optimization was undertaken at another three different altitudes, 25000 m, 35000 m and 40000 m. Table [[#table-2|Table 2]] presents the air properties at all studied altitudes.
+The conditions at which the aircraft was initially optimised were, <math display="inline">Mach = 7</math> and a flight altitude of <math display="inline">h = 30000 m</math>. Following the International Standard Atmosphere (ISA), the thermo-physical values were obtained; a temperature of <math display="inline">T = 226.65 K</math>, a pressure of <math display="inline">P = 1171.87 Pa</math> and a gravity of <math display="inline">g = 9.715 m/s^2</math>. In reality the optimization was undertaken at another three different altitudes, 25000 m, 35000 m and 40000 m. [[#table-2|Table 2]] presents the air properties at all studied altitudes.
 <div class="center" style="font-size: 75%;">'''Table 2'''. ISA Atmosphere
 </div>
-<div id='tab-1'></div>
+<div id='tab-2'></div>
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
@@ Line 250: / Line 250: @@
 From the Pareto front configurations a range of values can be immediately discarded due to the incapacity of lifting the minimum weight necessary to build the aircraft. The weight of the real X-43 NASA aircraft is 1400 kg, so the results for lift values below 14kN can be discarded. However, having this weight reduced would imply the possibility of having configurations with lower values of drag, as can be seen on Figure [[#img-3|3]].
-Some of the design variables which conform the Pareto front with a possible optimum performance are presented in Table [[#table-3|Table 3]]. These parameters define the optimum geometries of the aircraft for the given objective functions. The total number of configurations obtained on the Pareto front is 420, therefore, the table just represents a overview of the optimum designs.
+Some of the design variables which conform the Pareto front with a possible optimum performance are presented in [[#table-3|Table 3]]. These parameters define the optimum geometries of the aircraft for the given objective functions. The total number of configurations obtained on the Pareto front is 420, therefore, the table just represents a overview of the optimum designs.
 <div class="center" style="font-size: 75%;">'''Table 3'''. Some of the design variables optimised values, taken from the Pareto front
 </div>
-<div id='table-1'></div>
+<div id='table-3'></div>
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
@@ Line 410: / Line 410: @@
-On the first column of [[#table-4|Table 4]] are shown the different altitudes at which the optimisation has been run, it has to be noted that it has also been run the optimisation for a 10km altitude but it has not been shown on the [[#img-4|Figure 4]]. This is due to the non viability of the aircraft at this altitude, as it will be seen on the power needed. On the second column it can be seen the range of different drag forces that can be achieved modifying the geometry as seen on [[#img-4|Figure 4]]. The third column of the Table shows the velocity at which the aircraft is flying, considering that the Mach number is 7, as mentioned before. Finally, on the last column are displayed the range of values of the power needed obtained from the drag force and the velocity.
+On the first column of [[#table-4|Table 4]] are shown the different altitudes at which the optimisation has been run, it has to be noted that it has also been run the optimisation for a 10km altitude but it has not been shown on the [[#img-4|Figure 4]]. This is due to the non viability of the aircraft at this altitude, as it will be seen on the power needed. On the second column it can be seen the range of different drag forces that can be achieved modifying the geometry as seen on [[#img-4|Figure 4]]. The third column of the table shows the velocity at which the aircraft is flying, considering that the Mach number is 7, as mentioned before. Finally, on the last column are displayed the range of values of the power needed obtained from the drag force and the velocity.
 These values approximate the order of magnitude of the power that would be needed at each altitude, it has to be noted that it changes drastically for different altitudes, having the lowest values at the highest altitudes as it happens with the drag force.

@@ Line 258: / Line 258: @@
 {| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
-!  <math>\boldsymbol{\alpha _1}^{[\circ ]}</math> !! <math>\boldsymbol{\alpha _2}^{[\circ ]}</math> !! <math>\boldsymbol{\alpha _3}^{[\circ ]}</math> !! <math>\boldsymbol{\alpha _4}^{[\circ ]}</math> !!  <math>\boldsymbol{d_1} [m]</math>  <math>\boldsymbol{d_2} [m]</math>
+!  <math>\boldsymbol{\alpha _1}^{[\circ ]}</math> !! <math>\boldsymbol{\alpha _2}^{[\circ ]}</math> !! <math>\boldsymbol{\alpha _3}^{[\circ ]}</math> !! <math>\boldsymbol{\alpha _4}^{[\circ ]}</math> !!  <math>\boldsymbol{d_1} [m]</math>  !! <math>\boldsymbol{d_2} [m]</math>
 |-
 | style="text-align: center;" |7.0

@@ Line 215: / Line 215: @@
 | style="text-align: center;" | 277.522
 |-
-| style="text-align: center;" |   '''Density [kg/m3] '''
+!  style="text-align: center;" |   Density [kg/m3] !! style="text-align: center;" | Sound speed [m/s] !! style="text-align: center;" | Viscosity [Pa.s]
-| style="text-align: center;" | '''Sound speed [m/s] '''
-| style="text-align: center;" | '''Viscosity [Pa.s]'''
 |-
 | style="text-align: center;" |  0.0394658

@@ Line 134: / Line 134: @@
 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 60%;"
 |-
-|style="padding: 10px;"|[[Image:Draft_Pons Prats_614556693-X43dimensions.png|450px|Design variables on the simplified shape of the X-43.]]
+|style="padding: 10px;"|[[Image:Caros_et_al_2019b_3741_Figura2.png|450px|Design variables on the simplified shape of the X-43.]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding: 10px;"| '''Figure 2'''. Design variables on the simplified shape of the X-43

@@ Line 132: / Line 132: @@
 <div id='img-2'></div>
-{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;"
+{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 60%;"
 |-
 |style="padding: 10px;"|[[Image:Draft_Pons Prats_614556693-X43dimensions.png|450px|Design variables on the simplified shape of the X-43.]]

@@ Line 146: / Line 146: @@
 {|  class="floating_tableSCP wikitable" style="text-align: center; margin: 1em auto;min-width:50%;font-size:85%;"
-|- style="border-top: 1px solid;"
+|- style="border-top: 2px solid;"
 | style="text-align: left;" |
 | '''Lower limit'''
 | '''Upper limit'''
 | '''Variable step'''
-|-style="text-align: center;border-top: 1px solid;"
+|-style="text-align: center;border-top: 2px solid;"
 |  <math>\alpha _1</math>, <math display="inline">\alpha _3</math>
 | 7
@@ Line 161: / Line 161: @@
 | 40
 | 0.1
-|-style="text-align: center;border-bottom: 1px solid;"
+|-style="text-align: center;border-bottom: 2px solid;"
 |  <math>d_1</math>, <math display="inline">d_2</math>
 | 4.2

@@ Line 22: / Line 22: @@
 ==2. Mathematical model==
-In the present section, the required equations able to determine the lift and drag of the simplified shape X-43 aircraft, for a given initial geometry, free-stream Mach number and for a certain altitude, will be introduced. Further information regarding the equations development is to be found in <span id='citeF-10'></span><span id='citeF-11'></span><span id='citeF-12'></span>[[#cite-10|[10,11,12]]. It has to be noted that oblique reattached shock waves will appear at the leading edge. Expansion waves will appear both in extrados and intrados of the aerodynamic body. Figure [[#img-1|1]] shows graphically the main features of the problem under study.
+In the present section, the required equations able to determine the lift and drag of the simplified shape X-43 aircraft, for a given initial geometry, free-stream Mach number and for a certain altitude, will be introduced. Further information regarding the equations development is to be found in <span id='citeF-10'></span><span id='citeF-11'></span><span id='citeF-12'></span>[[#cite-10|[10,11,12]]]. It has to be noted that oblique reattached shock waves will appear at the leading edge. Expansion waves will appear both in extrados and intrados of the aerodynamic body. Figure [[#img-1|1]] shows graphically the main features of the problem under study.
 <div id='img-1'></div>

@@ Line 16: / Line 16: @@
 The aerospace industry is very demanding in terms of high performance, this is the reason why, optimisation techniques are particularly welcome in order to find the best design for each given situation. Optimisation algorithms allow improving new designs or designs already created, without the need of testing a large number of possible configurations.
-Hypersonic flight vehicles such as the X-43, require profound studies on each technological part. Examples of the depth of such studies are, the optimization of the internal engine flow channel via employing genetic algorithms, which was undertaken by Ahuja et al. <span id='citeF-1'></span>[[#cite-1|[1]]]. Aeroelastic and aerothermoelastic-acoustics simulations based on new computational Fluid Mechanics models, were presented in <span id='citeF-2'></span><span id='citeF-3'>[[#cite-2|[2]],[[#cite-3|3]]]. The pressure distribution over this particular aircraft was numerically determined by <span id='citeF-4'></span>[[#cite-4|[4]]], where they implemented a method which introduced artificial dissipation coefficients. The resulting overall lift and drag coefficients for several angles of attack were obtained when solving the three dimensional Navier-Stokes equations by <span id='citeF-5'></span><span id='citeF-6'></span>[[#cite-5|[5]],[[#cite-6|6]]], the comparison with the experimental measurements gave a very good agreement. The flight dynamics affecting a 2D hypersonic vehicle resembling the X-43, were described in <span id='citeF-7'></span>[[#cite-7|[7]]], where the non linear equations of motion were derived. An increase of the aerodynamic efficiency of the hypersonic aircraft (HA) was obtained in <span id='citeF-8'></span>[[#cite-8|[8]]], via adding energy in front of the bow of the HA. It was observed that the addition of energy weakened the shock wave. In <span id='citeF-9'></span>[[#cite-9|[9]]], the shock-wave structures appearing around the same (HA) studied by the rest of the researchers cited in this paper, were filmed using a high-speed video camera. Visualizations of the flow at the engine entrance throat, where the shock waves reflect, were particularly interesting.
+Hypersonic flight vehicles such as the X-43, require profound studies on each technological part. Examples of the depth of such studies are, the optimization of the internal engine flow channel via employing genetic algorithms, which was undertaken by Ahuja et al. <span id='citeF-1'></span>[[#cite-1|[1]]]. Aeroelastic and aerothermoelastic-acoustics simulations based on new computational Fluid Mechanics models, were presented in <span id='citeF-2'></span><span id='citeF-3'>[[#cite-2|[2]],[[#cite-3|3]]]. The pressure distribution over this particular aircraft was numerically determined by Elizarova and Shirokov <span id='citeF-4'></span>[[#cite-4|[4]]], where they implemented a method which introduced artificial dissipation coefficients. The resulting overall lift and drag coefficients for several angles of attack were obtained when solving the three dimensional Navier-Stokes equations by <span id='citeF-5'></span><span id='citeF-6'></span>[[#cite-5|[5]],[[#cite-6|6]]], the comparison with the experimental measurements gave a very good agreement. The flight dynamics affecting a 2D hypersonic vehicle resembling the X-43, were described in <span id='citeF-7'></span>[[#cite-7|[7]]], where the non linear equations of motion were derived. An increase of the aerodynamic efficiency of the hypersonic aircraft (HA) was obtained in <span id='citeF-8'></span>[[#cite-8|[8]]], via adding energy in front of the bow of the HA. It was observed that the addition of energy weakened the shock wave. In Kotov et al. <span id='citeF-9'></span>[[#cite-9|[9]]], the shock-wave structures appearing around the same (HA) studied by the rest of the researchers cited in this paper, were filmed using a high-speed video camera. Visualizations of the flow at the engine entrance throat, where the shock waves reflect, were particularly interesting.
 In the present study, given the Mach number and the altitude at which the X-43 simplified shape aircraft performs, the aerodynamic forces acting on the aircraft will be calculated based on the mathematical formulation defined in section II. In the next step, these forces will be optimized, computing this formulation with a python code and using the RMOP optimizer (http://tts.cimne.com/rmop). The optimization will be based on the variation of the main geometrical parameters of the aircraft, presented in Figures 1 and 2. The shape of the chosen aircraft, was as well optimised for different possible flight altitudes and Mach numbers.