Articles with tag: "Python"

1. Anti-Ice Heat Required Calculations with LEWICE

   
   Public domain image by Donald Cook.

   Prerequisites

   You need to have completed Anti-Ice Heat Required Calculations.

   Introduction

   Here, we will see that the values calculated by a multi-node analysis in LEWICE are comparable to the values calculated previously.

   Running LEWICE for anti-icing calculations involves (necessarily) more complex inputs. The user has to select which set of external heat transfer assumptions to use. The detailed output files require post-processing to extract the total heat required value.

   Discussion

   The LEWICE manual describes "deicer" cases that also may be used for anti-ice heat requirement analysis.
   An input is the "IDEICE" value in the case.inp file. By default, this is 0, and an unheated surface ice analysis is performed. However, with IDEICE > 0, ice protection analysis is performed, as detailed in a cased.inp file. A key input in that file is ievap, which for the cases below is set to ievap=1 …

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2. Anti-Ice Heat Required Calculations

   
   Public domain image by Donald Cook.

   Prerequisites

   You need to have completed Anti-Ice Heating Calculations Theory.

   Introduction

   For this we will use "Engineering Summary of Airframe Icing Technical Data", ADS-4, as the anti-ice examples are more detailed than those in the "Aircraft Icing Handbook", DOT/FAA/CT-88/8-1.

   The ADS-4 analysis method uses NACA-TN-2799, from 1952, for the heat and mass balance calculations. This method implements solutions as nomographs (for more details, see the post NACA-TN-2799). We will not be using the nomographs. The heat balance equations are similar to the Standard Computational Model, which we will use.

   The calculations are implemented in the file "aircraft_a_ads4.py" (and associated files) available at github.com/icinganalysis/icinganalysis.github.io. Readers are encouraged to run the analysis to the duplicate results.

   Discussion

   "Aircraft Icing", AC 20-73A, briefly mentions the terms Qa and Qr:

   Qa Heat available
   Qr Heat required

   Heat required is …

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3. Analysis Toolset

   
   Figure 15 of NACA-TN-2904 ntrs.nasa.gov.

   Summary

   You will have to choose a toolset to perform the example analyses.

   Example calculations are provided in the Python programming language, and using the NASA-provided LEWICE code.

   Introduction

   You are highly encouraged to perform the analysis described in the examples (and not just read the examples). Some examples can be accomplished with hand calculations, while other require computational capabilities.

   You need to select your toolset.

   Consider your current and future uses

   A toolset is an investment of your time and resources. By performing the calculation of the examples used here, you will build your personal and software capabilities and skills.

   Your toolset at a particular time may not be entirely your choice. Your company, institution, or customer may have policies on which kinds of software are required, encouraged, discouraged, or prohibited. Some codes have by-country use restrictions. You may have signed an …

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4. The Effects of Humidity in Icing Wind Tunnel Tests

   "a condition of supersaturation, which promotes the growth of frost deposits"

   Summary

   Supersaturated humidity can affect icing wind tunnel results.

   Key Points

   1. Some observations of supersaturated humidity conditions were made in the NACA-era.
   2. Supersaturation was associated with frost on test article afterbodies.
   3. Recirculating icing wind tunnel conditions are calculated to tend to be supersaturated.
   4. Some potential effects of supersaturation are calculated.

   A brief primer on humidity

   A measurement of water vapor in the air is humidity. Relative humidity is the most common measure. In everyday life 30% to 60% relative humidity is generally considered to be comfortable. Lower humidities feel dry, and higher humidities feel wet or "humid".

   The most water vapor that can usually exist at a given static temperature is termed "saturated", and that condition has 100% relative humidity. Given sufficient time and condensation surfaces, any surplus vapor above this value will condense as liquid water.

   Natural icing …

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5. NACA-TN-3024-revisited

   "evaporation losses are ... very small (less than 1 percent) in the case of smaller obstacles (of icing-rate-measurement-cylinder size)."

   "Maximum Evaporation Rates of Water Droplets Approaching Obstacles the Atmosphere under Icing Conditions" Evaporation calculations ¹

   

   Summary

   Less that 1% of drops evaporate approaching an obstacle for most cases.

   Key points

   1. Equations are detailed for the evaporation of water drops approaching an obstacle.
   2. The equations were coded into a python program.
   3. Less that 1% of drops evaporate approaching an obstacle for most cases.
   4. A water drop that approaches on the stagnation line but does not impinge is predicted to evaporate away.

   NACA-TN-3024 was reviewed previously, herein we will concentrate on comparing our own code to the results in NACA-TN-3024.

   Abstract

   When a closed body or a duct envelope moves through the atmosphere, air pressure and temperature rises occur ahead of the body or, under ram conditions, within the duct. If cloud water …

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6. AEDC1DMP

   "The third part of the study comprised some numerical computations of two-phase, dilute, air and entrained water particle flows, using a new version of the AEDC one-dimensional, multiphase flow code, AEDC1DMP."

   

   The AEDC 1-Dimensional Multi-Phase code (AEDC1DMP) and the iads1dmp

   Abstract

   The AEDC1DMP calculates the water drop speed and evaporation in an icing wind tunnel. The AEDC1DMP is described in "Second Report for Research and Modeling of Water Particles in Adverse Weather Simulation Facilities" ¹. AEDC is the Arnold Engineering Development Complex, formerly the Arnold Engineering Development Center.

   1.0 INTRODUCTION TO THE RESEARCH
   This report describes a continuation of research into the modeling of water particle freezing for application to adverse weather simulation facilities. The research was initiated in FY1996 to investigate the physics of freezing of submillimeter supercooled water particles or droplets in both natural and artificial or simulated adverse weather environments. The first phase of the research …

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7. Let's Build a 1D Water Drop Trajectory Simulation

   

   "The discrepancies are of the magnitude to be expected from ... the step by step integration". ¹

   Let's build a 1D water drop trajectory simulation

   Summary

   Water impingement values on a cylinder are calculated with step-by-step integration.

   Key points

   1. 1D equations of motion were implemented.
   2. Results agree well with the minimum drop size required for impingement.
   3. Water drops may contact the cylinder at very low K values.
   4. The methods appears accurate enough to use for other applications.

   Discussion

   We are going to start with a one dimensional simulation along a single line, the stagnation line of flow around a cylinder, y=0 in the figure above.

   We will implement the equations of motions for a drop around a cylinder from "Mathematical Investigation of Water Droplet Trajectories" ¹.

   Readers unfamiliar with "Mathematical Investigation of Water Droplet Trajectories" may wish to review it before proceeding further herein, especially to be familiar with the …

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8. NACA-TR-1215 Thermodynamics

   "... the effect on final results of droplets that do not freeze completely on the cylinders"

   

   "Impingement of Cloud Droplets and Procedure for Measuring Liquid-Water Content and Droplet Sizes in Supercooled Clouds by Rotating Multicylinder Method" [Thermodynamics topics] ¹

   Summary

   Conditions where not all water drops freeze are considered.

   Key points

   1. Conditions where not all water drops freeze on the multicylinder instrument are considered.
   2. Rotating cylinder Ludlam limits are compared to flight test data.

   Abstract

   Evaluation of the rotating multicylinder method for the measurement of droplet-size distribution, volume-median droplet size, and liquid-water content in clouds showed that small uncertainties in the basic data eliminate the distinction between different cloud droplet-size distributions and are a source of large errors in the determination of the droplet size. Calculations of the trajectories of cloud droplets in incompressible and compressible flow fields around a cylinder were performed on a mechanical analog constructed for the study …

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9. NACA-TN-2914

   "The effects of frictional heating were analyzed to determine the conditions under which ice formations can be prevented"

   

   NACA-TN-2861 "Analytical Investigation of Icing Limit for Diamond Shaped Airfoil in Transonic and Supersonic Flow" ¹

   and

   NACA-TN-2914 "A Method for Rapid Determination of the Icing Limit of a Body in Terms of the Stream Conditions" ²

   Summary

   The warmest ambient temperature at which ice can accumulate is calculated.

   Key points

   1. The warmest ambient temperature at which ice can accumulate is calculated.
   2. Compressibility effects were included.
   3. Analysis showed good results compared to test data at transonic Mach numbers.

   Abstract

   Calculations have been made for the icing limit of a diamond airfoil at zero angle of attack in terms of the stream Mach number, stream temperature, and pressure altitude. The icing limit is defined as a wetted-surface temperature of 32F and is related to the stream conditions by the method of Hardy.
   The …

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10. A Brief Digression on Unit Systems

    "I'm burning through the sky, yeah. Two hundred degrees, that's why they call me Mister Fahrenheit. I'm travelling at the speed of light."

    from Queen, "Don't Stop Me Now".

    Standard weights and other measurements in use. ¹

    Summary

    The unit system used herein is detailed.

    Preferred units (primary SI units):

        mass: kg
        force: N
        length: m
        tk: temperature, K
        time: seconds, s
        p: air static pressure, Pa (N/m^2)
        u: free-stream air speed, m/s
        altitude: pressure altitude, m
        energy: J or N-m
    

    Icing specific, entrenched exceptions:

        d_drop: water drop diameter, micrometer (1e-6 m)
        lwc: liquid water content, g/m^3
    

    The NACA publications systems of units

    The units in the NACA publications vaguely follow "US Customary" units, although there are often exceptions:

        mass: g, kg, lbm, slug
        force: N, lbf
        length: micron, inch, foot, mile, nautical mile
        temperature: F, R
        time: s, hour
        air static pressure, lbf/in …

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11. NACA-TN-2799

    "Solution of the heat and mass transfer from a wetted surface is quite involved and tedious."

    "Simple Graphical Solution of Heat Transfer and Evaporation from Surface Heated to Prevent Icing" ¹

    

    Figure 1. - Graphical solution of anti-icing heat and mass transfer from surface subject to impingement and heated above freezing.

    Summary

    Simplified ice protection equations allow graphical solutions.

    Key points

    1. Simplified ice protection equations allow graphical solutions.
    2. The effects of varying local surface pressure and velocity are included.

    Abstract

    Equations expressing the heat transfer and evaporation from wetted surfaces during ice prevention have been simplified and regrouped to permit solutions by simple graphical means. Working charts for quick and accurate anti-icing calculations are also included.

    Discussion

    INTRODUCTION Solution of the general problem of heat and mass transfer from a wetted surface in forced convection is quite involved and tedious. The calculations that often must be made point by point along …

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12. Python coding style guide

    "Beautiful is better than ugly."

    

    Summary

    For the Thermodynamics tread and on, I will be using this style guide. Previous code may eventually be upgraded to this.

    Python target version:

    Target python version 3.7, and the corresponding Anaconda stack (version 2021-11). Avoid modules with deprecation warnings (there are not many of them). This is a balance between current installations and future-proofing. The goal is to be applicable for all 3.7+ uses.

    (Note: 3.10 is the latest available version, as of April 2022).

    Code should be portable, and not use operating system specific functions.

    General guidelines

    • simple

      • use simple functions over classes
      • out-source complexity where possible
        • use built-in data structures (list, dict)
        • use numpy and scipy, anything in the anaconda stack
      • promote reuse
        • anything used more than once should be put in an importable module
        • use the "if __name__ == '__main__:" block idiom
          • to have clean (no side effect …

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13. Messinger

    ""freezing-fraction" denotes the proportion of the impinging liquid which freezes in the impingement region"

    B. L. Messinger, "Equilibrium Temperature of an Unheated Icing Surface as a Function of Airspeed" ¹

    

    Modes of energy transfer for an unheated airfoil in icing conditions.

    Summary

    The term "freezing fraction" is defined

    Key points

    1. Heat balance equations for a wet surface are presented.
    2. The term "freezing fraction" is defined
    3. Example calculations are provided
    4. Icing wind tunnel test data is provided

    Abstract

    The thermal analysis of a heated surface in icing conditions has been extensively treated in the literature. Except for the work of Tribus, however, little has been done on the analysis of an unheated icing surface. This latter analysis is significant in the design of cyclic thermal deicing systems that are attractive for small high-speed aircraft for which thermal anti-icing requirements have become severe. In this paper, a complete analysis of the temperature …

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14. Ludlam

    "The rotating-cylinder technique of determining water content and drop-size distribution cannot therefore be used without consideration of the heat economy"

    

    F. H. Ludlam, "The Heat Economy of a Rimed Cylinder" ¹

    Summary

    Various "Ludlam Limits" have been implemented, but they produce different results.

    Key points

    1. Calculations are laid out for finding the "critical" LWC where not all available water freezes on a cylinder.
    2. The critical LWC is often termed the "Ludlam limit", although Ludlam did not use that term.
    3. Various "Ludlam Limits" have been implemented, but they produce different results.

    Abstract

    A method is described for calculating the surface temperature of a slender cylinder which is moved through a supercooled cloud and becomes covered with rime ice. When the surface temperature reaches 0°C the ice formation proceeds at the maximum possible rate; the associated liquid-water content of the cloud is calculated and found to be usually less than the …

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15. NACA-TR-831

    "It has been shown that the temperature of the surface of the wing in conditions of icing can be predicted with considerable exactitude from the temperatures measured in clear air."

    "An Analysis of the Dissipation of Heat in Conditions of Icing from a Section of the Wing of the C-46 Airplane" ¹

    

    Summary

    Two-dimensional heat balance equations for ice protection are detailed.

    Key points

    1. Heat balance equations for ice protection are detailed.
    2. An assumption about water drop temperature approaching an object is made.
    3. A cylinder approximation for an airfoil leading edge is used for water drop impingement.

    Abstract

    A method is given for calculating the temperature that a surface, heated internally by air, will assume in specified conditions of icing. The method can be applied generally to predict the performance, under conditions of icing, of the thermal system for protecting aircraft. Calculations have been made for a section of the …

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16. NACA-ARR-5G13

    "A method is given for calculating the temperature of a surface wetted ... by a pure liquid, such as water"

    "Kinetic Temperature of Wet Surfaces A Method of Calculating the Amount of Alcohol Required to Prevent Ice, and the Derivation of the Psychrometric Equation" ¹

    

    Summary

    Psychrometric equations are presented to calculate the thermal effects of evaporation from wet surfaces at high air speeds.

    Key Points

    1. The wet surface equilibrium "datum" temperature is defined.
    2. Psychrometric equations are presented to calculate the thermal effects of evaporation from wet surfaces.
    3. The calculations are implemented in python code.

    Abstract

    A method is given for calculating the temperature of a surface wetted either by a pure liquid, such as water, or by a mixture, such as alcohol and water. The method is applied to the problem of protecting, by alcohol, propellers and the induction system of the engine against ice. The minimum quantity of alcohol …

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17. A Langmuir B drop size distribution is (almost) a normal distribution

    "Upon comparing this chart with Langmuir's tables, it was found that his selections of the representative radii for the various sub-divisions of the volume were in error." ¹

    Summary

    The Langmuir B drop size distribution is almost a normal distribution.

    Key points

    1. The Langmuir B drop size distribution is almost a normal distribution.
    2. Perhaps it was originally intended that it be exactly a normal distribution.
    3. The proposed alternatives in NACA-TN-2708 appears to have larger errors, rather than correcting errors.
    4. The other Langmuir distributions (C, D, E) do not fit a normal distribution as well.

    Discussion

    Normal drop size distributions

    Normal distributions show up many places in nature, so it is not surprising that drop sizes in clouds can approximate a normal distribution.

    In NACA-TN-2708 ¹, it was "presumed" that water-volume distribution with the drop size is a Gaussian [normal] distribution:

    Drop-Size Distribution. - In the present report it is presumed, following …

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18. Implementation of multicylinder calculations in Python

    "This effect would be expected if the droplets were of non-uniform size, since the largest droplets could reach the largest collector while those of average size could not." ¹

    Summary

    The calculations to determine drop median volumetric diameter with a multicylinder instrument are implemented in Python.

    Key points

    1. A manual method of multicylinder calculation is illustrated.
    2. The drop median effect diameter is reproduced well from a multicylinder example in "Mathematical Investigation of Water Droplet Trajectories"

    Discussion

    Manual method of drop size analysis

    By measuring the differential rates of ice collection on cylinders of different sizes the drop median volumetric diameter (MVD) can be determined.

    Some typical multicylinder instruments (from NACA-TN-2708 ¹):

    "Mathematical Investigation of Water Droplet Trajectories" ² provides an example of the multicylinder calculations method in the section "Example of the Application of the D.A. Data to Experimental Data".

    The method has been revised as a result of …

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19. A Detailed Comparison of Water Drop Impingement Calculations

    "The discrepancies are of the magnitude to be expected from ... the step by step integration"

    Summary

    Water drop impingement calculations on a cylinder from "Mathematical Investigation of Water Droplet Trajectories" ¹ and NACA-TN-779 ² are compared.

    Key Points

    1. There are differences in conditions in Table IV(a) of "Mathematical Investigation of Water Droplet Trajectories" compared to NACA-TN-779.
    2. When the conditions are revised to match, the comparison with NACA-TN-779 data improves.

    Discussion

    NACA-TN-779

    In NACA-TN-779, the water drop impingement on a cylinder 12 inch in diameter, with an airspeed of 200 mph, was analyzed. The altitude was not noted. Water drop diameters from 0.002 inch (about 8 micrometer) to 0.1 inch (about 4000 micrometer) were considered, as shown below.

    

    The “swept area of cleared drops” represents what fraction of the water drops in the forward projected area of the cylinder impinge on the cylinder. In more modern terms, this …

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20. Implementation of cylinder impingement correlations in Python

    "The equations were found to fit the experimental data over a wider range of values..." ¹

    Summary

    The correlations for water drop impingement on a cylinder from "Mathematical Investigation of Water Droplet Trajectories" ¹ are implemented in the Python programming language.

    Key points

    1. The cylinder impingement correlations were implemented and reproduced values from "Mathematical Investigation of Water Droplet Trajectories"
    2. A subtlety about calculations with drop size distributions is noted.

    Discussion

    Implementation of cylinder impingement correlations

    Alas, I do not have access to a differential analyzer as was used in ¹, so I will have to use a modern, digital computer. Also, we will not be integrating the water drop equations of motion; we will be using the data in ¹ to determine water drop impingement on a cylinder.

    The Anaconda distribution of Python version 3.7 was used ², as this includes the third party modules matplotlib, numpy, and scipy …

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