parasitedrag

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parasitedrag [2018/04/25 08:29] jgravett Adds Dynamic Viscosity Equation |
parasitedrag [2020/05/27 16:15] (current) ramcdona |
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+ | ====== Parasite Drag Tool ====== | ||

+ | |||

+ | Parasite drag is a combination of form, friction, and interference drag that is evident in any body moving through a fluid. Although VSPAERO includes an estimate of parasite drag in the calculation of the zero lift drag coefficient, the Parasite Drag tool provides much more advanced options and capabilities. The Parasite Drag Tool GUI is accessed by clicking "Parasite Drag..." from the Analysis drop-down on the top menu-bar. | ||

+ | |||

===== General Overview ===== | ===== General Overview ===== | ||

+ | |||

$ c_i \equiv \mbox{Chord length at span station} $\\ | $ c_i \equiv \mbox{Chord length at span station} $\\ | ||

$ b_i \equiv \mbox{Section span} $\\ | $ b_i \equiv \mbox{Section span} $\\ | ||

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$ D \equiv \mbox{Diameter} $\\ | $ D \equiv \mbox{Diameter} $\\ | ||

$ X_{area} \equiv \mbox{Max cross sectional area} $\\ | $ X_{area} \equiv \mbox{Max cross sectional area} $\\ | ||

- | $ F \equiv \mbox{Fineness ratio} $\\ | + | $ FR \equiv \mbox{Fineness ratio} $\\ |

$ Re \equiv \mbox{Reynolds number} $\\ | $ Re \equiv \mbox{Reynolds number} $\\ | ||

$ V_{inf} \equiv \mbox{freestream velocity} $\\ | $ V_{inf} \equiv \mbox{freestream velocity} $\\ | ||

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$ S_{ref} \equiv \mbox{reference area} $\\ | $ S_{ref} \equiv \mbox{reference area} $\\ | ||

$ C_D \equiv \mbox{coefficient of drag} $\\ | $ C_D \equiv \mbox{coefficient of drag} $\\ | ||

+ | |||

+ | {{ :parasitedraggui.png?900 |}} | ||

+ | |||

+ | Visible on all tabs of the GUI is the parasite drag table, which identifies individual components and their inputs in the parasite drag calculation. The table may be sorted by Component, S_wet, or % Total by selecting the toggles at the top of the table. Clicking on a geometry in the Component column of the table will break up the geometry into its surfaces and sub-surfaces. Below the list of components, excrescences are identifies, for which the Excrescence tab is available to add, remove, and adjust excrescences. Once the table has been setup, the "Calculate CDO" button on the bottom left of the GUI will run the parasite drag calculation. Once finished, the results will update in real time in response to changes in input values, such as the flow condition. However, if a component is added, removed, or modified, the tool must be rerun. The entire Parasite Drag table, excrescence list, and total results can be exported by selecting "Export to *.csv". Next to this button, the Export Sub-Components toggle is available to include or ignore component breakup in the export file. On the bottom right of the GUI, the total form factor, drag coefficient, and percent contribution to total drag is listed for all components, excrescences, and the combination of both. | ||

=== Wetted Area === | === Wetted Area === | ||

- | Wetted areas for all components are taken from comp geom and as such as are appropriately trimmed. | + | Wetted areas for all components are taken from executing Comp Geom for the indicated geometry set and as such as are appropriately trimmed. |

+ | | ||

+ | ==== Grouping ==== | ||

+ | Utilizing this feature the user is able to combine the wetted area of any geometry with that of another. Currently, geometries can only be grouped with their ancestors and geometries of the same shape type. | ||

+ | | ||

+ | This can be used for example if the gear pod is modeled seperately from the fuselage but the wetted area of the gear pod should be applied with the drag qualities (e.g. length, form factor, etc.) of the fuselage. | ||

+ | {{ :grouping_example_geometry.png?nolink |}} | ||

+ | | ||

+ | ==== Sub Surface Handling ==== | ||

+ | By default, subsurfaces are incorporated as a part of the geometry as a whole. In other words, the surfaces do not subtract any wetted area from the geometry or have any of their own unique properties. However, the parasite drag tool let's the user choose these as options if they desire. | ||

+ | | ||

+ | The three options are: | ||

+ | * Treat as Parent | ||

+ | * Separate Treatment | ||

+ | * Zero Drag | ||

+ | | ||

+ | **Treat as Parent**: The default option, incorporates the wetted area of the subsurface as part of a continuous geometry. | ||

+ | | ||

+ | **Separate Treatment**: Allows the user, to some extent, control the qualities of the subsurface. However, due to limitations of the methodology used, the geometry based qualities (e.g. L_{ref}, Re, etc.) are derived from the parent geometry. The user is allowed to change the form factor equation type, manually set the laminar percentage, and manually set the interference factor for the subsurface. | ||

+ | | ||

+ | **Zero Drag**:The subsurface wetted area is subtracted from the total wetted area of the geometry and no longer contributes to the drag of the component. | ||

=== Reference Length === | === Reference Length === | ||

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=== Laminar Percent === | === Laminar Percent === | ||

- | Laminar Percent takes a 0 to 100 value and at default is set to 0% for a fully turbulent flow. | + | Laminar Percent takes a 0 to 100 value and at default is set to 0% for a fully turbulent flow.According to Raymer, most aircraft have 10-20% laminar flow over lifting surfaces, and almost no laminar flow over the fuselage. However, an aircraft like the Piaggio GP180 can have up to 50% laminar flow over the wings and tail and 20-35% over the fuselage$^{22}$. |

The laminar friction coefficient is calculated using the following equation: | The laminar friction coefficient is calculated using the following equation: | ||

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$$ C_D = \frac{f}{S_{ref}} $$ | $$ C_D = \frac{f}{S_{ref}} $$ | ||

- | ==== Grouping ==== | + | ===== Coefficient of Friction Equations ===== |

- | Utilizing this feature the user is able to combine the wetted area of any geometry with that of another. Currently, geometries can only be grouped with their ancestors and geometries of the same shape type. | + | |

- | This can be used for example if the gear pod is modeled seperately from the fuselage but the wetted area of the gear pod should be applied with the drag qualities (e.g. length, form factor, etc.) of the fuselage. | + | Unfortunately, there is substantial opportunity for confusion around the equations for the skin friction coefficient. The primary source of confusion is inconsistent nomenclature in the literature around two related quantities -- the local skin friction coefficient vs. the flat plate average skin coefficient. Different references use inconsistent nomenclature to differentiate these quantities. A reader must be pedantic to verify that they understand the notation for any given publication. Often, the nomenclature is defined far away from where the equations are presented. |

- | {{ :grouping_example_geometry.png?nolink |}} | + | |

- | ==== Sub Surface Handling ==== | + | ^ Local ^ Average ^ Reference ^ |

- | By default, subsurfaces are incorporated as a part of the geometry as a whole. In other words, the surfaces do not subtract any wetted area from the geometry or have any of their own unique properties. However, the parasite drag tool let's the user choose these as options if they desire. | + | | $C_f$ | $C_D$ | White (3) | |

+ | | $C_{\tau}$ | $C_f$ | Hoerner (1) | | ||

+ | | ${c_f}'$ | $c_f$ | Schlicting (6) | | ||

+ | | $c_f$ | $C_f$ | Anderson (5) | | ||

+ | | $C_f$ | $C_D$ | White & Christoph (2) | | ||

- | The three options are: | + | This analysis is only concerned with the flat plate average skin friction coefficient, which will be denoted $C_f$ herein. |

- | * Treat as Parent | + | |

- | * Separate Treatment | + | |

- | * Zero Drag | + | |

- | **Treat as Parent**: The default option, incorporates the wetted area of the subsurface as part of a continuous geometry. | ||

- | |||

- | **Separate Treatment**: Allows the user, to some extent, control the qualities of the subsurface. However, due to limitations of the methodology used, the geometry based qualities (e.g. L_{ref}, Re, etc.) are derived from the parent geometry. The user is allowed to change the form factor equation type, manually set the laminar percentage, and manually set the interference factor for the subsurface. | ||

- | |||

- | **Zero Drag**:The subsurface wetted area is subtracted from the total wetted area of the geometry and no longer contributes to the drag of the component. | ||

- | ===== Coefficient of Friction Equations ===== | ||

$ x \equiv \mbox{distance along chord} $\\ | $ x \equiv \mbox{distance along chord} $\\ | ||

$ k \equiv \mbox{roughness height} $\\ | $ k \equiv \mbox{roughness height} $\\ | ||

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== Blasius (25) == | == Blasius (25) == | ||

- | $$ C_f = \frac{1.32824}{Re^{1/2}}\ $$ | + | $$ C_f = \frac{1.32824}{\sqrt{Re}}\ $$ |

==== Turbulent ==== | ==== Turbulent ==== | ||

== Explicit Fit of Spalding (3)== | == Explicit Fit of Spalding (3)== | ||

- | $$ C_f = \frac{0.455}{\ln^2(0.06\ Re)}\ $$ | + | $$ C_f = \frac{0.523}{\ln^2(0.06\ Re)}\ $$ |

== Explicit Fit of Spalding and Chi (2) == | == Explicit Fit of Spalding and Chi (2) == | ||

- | $$ C_f = \frac{0.225}{\log(Re)^{2.32}}\ $$ | + | $$ C_f = \frac{0.430}{\log(Re)^{2.32}}\ $$ |

== Explicit Fit of Schoenherr (1) == | == Explicit Fit of Schoenherr (1) == | ||

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== Implicit Schoenherr (1) == | == Implicit Schoenherr (1) == | ||

$$ \log\left(Re\ C_f\right) = \frac{0.242}{\sqrt{C_f}}\ $$ | $$ \log\left(Re\ C_f\right) = \frac{0.242}{\sqrt{C_f}}\ $$ | ||

- | |||

- | == Implicit Karman (2) == | ||

- | $$ \frac{1}{\sqrt{C_f}}\ = 4.15\log\left(Re\ C_f\right) + 1.70 $$ | ||

== Implicit Karman-Schoenherr (4) == | == Implicit Karman-Schoenherr (4) == | ||

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== Power Law Blasius (2) == | == Power Law Blasius (2) == | ||

- | $$ C_f = \frac{0.0592}{Re^{1/5}}\ $$ | + | $$ C_f = \frac{0.072}{Re^{1/5}}\ $$ |

== Power Law Prandtl Low Re (5) == | == Power Law Prandtl Low Re (5) == | ||

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== Power Law Prandtl Medium Re (3) == | == Power Law Prandtl Medium Re (3) == | ||

- | $$ C_f = \frac{0.027}{Re^{1/7}}\ $$ | + | $$ C_f = \frac{0.0315}{Re^{1/7}}\ $$ |

== Power Law Prandtl High Re (3) == | == Power Law Prandtl High Re (3) == | ||

- | $$ C_f = \frac{0.058}{Re^{1/5}}\ $$ | + | $$ C_f = \frac{0.0725}{Re^{1/5}}\ $$ |

== Schlichting Compressible (6) == | == Schlichting Compressible (6) == | ||

$$ C_f = \frac{0.455}{\log\left(Re\right)^{2.58}}\ $$ | $$ C_f = \frac{0.455}{\log\left(Re\right)^{2.58}}\ $$ | ||

- | |||

- | == Schlichting Incompressible (7) == | ||

- | $$ C_f = \frac{0.472}{\log\left(Re\right)^{2.5}}\ $$ | ||

- | |||

- | == Schlichting-Prandtl (2) == | ||

- | $$ C_f = \frac{1}{\left(2\ \log\left(Re\right) - 0.65\right)^{2.3}}\ $$ | ||

- | |||

- | == Schultz-Grunow High Re (2) == | ||

- | $$ C_f = \frac{0.370}{\log\left(Re\right)^{2.584}}\ $$ | ||

== Schlutz-Grunow Estimate of Schoenherr (1) == | == Schlutz-Grunow Estimate of Schoenherr (1) == | ||

$$ C_f = \frac{0.427}{\left(\log\left(Re\right) - 0.407\right)^{2.64}}\ $$ | $$ C_f = \frac{0.427}{\left(\log\left(Re\right) - 0.407\right)^{2.64}}\ $$ | ||

- | == White-Christoph Compressible (2) == | + | {{ :parasitefrictioncoefficientsfixed.png?850 |}} |

- | $$ C_f = \frac{0.42}{\ln^2\left(0.056\ Re\right)}\ $$ | + | |

- | | + | |

- | {{ :parasitefrictioncoefficients.png?850 |}} | + | |

=== Roughness === | === Roughness === | ||

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== Schlichting Avg (6) == | == Schlichting Avg (6) == | ||

$$ C_f = \left(1.89 + 1.62\ \log\left(\frac{l}{k}\right)\right)^{-2.5} $$ | $$ C_f = \left(1.89 + 1.62\ \log\left(\frac{l}{k}\right)\right)^{-2.5} $$ | ||

- | |||

- | == Schlichting Local (6) == | ||

- | $$ C_f = \left(2.87 + 1.58\ \log\left(\frac{x}{k}\right)\right)^{-2.5} $$ | ||

- | |||

- | == White (3) == | ||

- | $$ C_f = \left(1.4 + 3.7\ \log\left(\frac{x}{k}\right)\right)^{-2} $$ | ||

== Schlichting Avg Compressible (7) == | == Schlichting Avg Compressible (7) == | ||

Line 247: | Line 248: | ||

=== Body Equations === | === Body Equations === | ||

+ | |||

+ | Slender body form factor equations are typically given in terms of the fineness ratio (FR), which is the length to diameter ratio for the body. | ||

+ | |||

+ | $$ FR = \frac{l}{d}$$ | ||

+ | |||

+ | For bodies of arbitrary cross section, an equivalent diameter is calculated based on the cross sectional area. | ||

+ | |||

+ | $$ d = 2 * \sqrt{\frac{A_{xsec}}{\pi}}$$ | ||

== Schemensky Fuselage (9) == | == Schemensky Fuselage (9) == | ||

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== Hoerner Streamlined Body (1) == | == Hoerner Streamlined Body (1) == | ||

- | $$ FF = 1 + \frac{1.5}{\left(\frac{l}{d}\right)^{1.5}} + \frac{7}{\left(\frac{l}{d}\right)^3} $$ | + | $$ FF = 1 + \frac{1.5}{\left(FR\right)^{1.5}} + \frac{7}{\left(FR\right)^3} $$ |

== Torenbeek (14) == | == Torenbeek (14) == | ||

- | $$ FF = 1 + \frac{2.2}{\left(\frac{l}{d}\right)^{1.5}} + \frac{3.8}{\left(\frac{l}{d}\right)^3} $$ | + | $$ FF = 1 + \frac{2.2}{\left(FR\right)^{1.5}} + \frac{3.8}{\left(FR\right)^3} $$ |

== Shevell (15) == | == Shevell (15) == | ||

- | $$ FF = 1 + \frac{2.8}{\left(\frac{l}{d}\right)^{1.5}} + \frac{3.8}{\left(\frac{l}{d}\right)^3} $$ | + | $$ FF = 1 + \frac{2.8}{\left(FR\right)^{1.5}} + \frac{3.8}{\left(FR\right)^3} $$ |

== Covert (4) == | == Covert (4) == | ||

- | $$ FF = 1.02\left(1.0 + \frac{1.5}{\left(\frac{l}{d}\right)^{1.5}} + | + | $$ FF = 1.02\left(1.0 + \frac{1.5}{\left(FR\right)^{1.5}} + |

- | \frac{7.0}{\left(\frac{l}{d}\right)^3 \left(1.0 - M^3\right)^{0.6}}\right) $$ | + | \frac{7.0}{\left(FR\right)^3 \left(1.0 - M^3\right)^{0.6}}\right) $$ |

== Jenkinson Fuselage (8) == | == Jenkinson Fuselage (8) == | ||

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Jenkinson suggests a constant Form Factor for typical nacelles on aft fuselages. | Jenkinson suggests a constant Form Factor for typical nacelles on aft fuselages. | ||

$$ FF = 1.50 $$ | $$ FF = 1.50 $$ | ||

- | |||

{{ :body_form_factor_api_output.png?nolink |}} | {{ :body_form_factor_api_output.png?nolink |}} | ||

- | ==== Atmosphere ==== | + | ===== Flow Condition ===== |

- | The parasite drag tool includes several options for atmosphere models as well as the option for the user to have control over 2 atmospheric qualities between Temperature, Pressure, and Density. | + | |

- | | + | |

- | == USAF 1966 (17) == | + | |

- | Upper Limit: 82,021 feet | + | |

- | == US Standard Atmosphere 1976 (16) == | + | On the Overview tab, the Parasite Drag Tool includes several options for atmosphere models as well as the option for the user to have manual control over certain atmospheric qualities. The freestream type is identified by the choice labeled "Atmosphere", and the sliders below will activate or deactivate depending on this selection. The first two freestream types are the US Standard Atmosphere 1976 and USAF 1966 atmospheric models, for which a comparison is shown below$^{16, 17}$. Note, the upper limit for the US Standard Atmospheric model is 84,852 meters, and the upper limit for the USAF model is 82,021 feet. Both require freestream velocity and altitude to be input, but an additional delta temperature input is available to offset temperature from the atmospheric model. The remaining atmosphere options require a series of manual inputs to calculate the atmospheric condition, but will not calculate and update the altitude slider. In addition, if the atmospheric choice type is "Re/L + Mach Control", no additional properties of the flow will be calculated (i.e. pressure and density). |

- | Upper Limit: 84,852 meters | + | |

{{ :standard_atmosphere_api_output.png?nolink |}} | {{ :standard_atmosphere_api_output.png?nolink |}} | ||

- | == Dynamic Viscosity (16) == | + | === Dynamic Viscosity (16) === |

$ \beta \equiv \mbox{}1.458E10^{-6} \frac{kg}{(s*m*K^{1/2})} $\\ | $ \beta \equiv \mbox{}1.458E10^{-6} \frac{kg}{(s*m*K^{1/2})} $\\ |

parasitedrag.1524670194.txt.gz · Last modified: 2018/04/25 08:29 by jgravett