Articles with tag: "thermodynamics"

1. Aircraft Icing Handbook Energy Balance Examples

   
   Public domain image by Donald Cook.

   Prerequisites

   To learn the energy terms and equations, readers should first review the "Standard Computational Model", which combines the applicable sections original DOT/FAA/CT-88/8-1 and the update into one text.

   Introduction

   The term "standard computational model" has not seen wide use. Most recent literature refers to the "Messinger Model" or "Modified Messinger Model". That may or may not mean the "standard computational model" presented here. As noted for calculating evaporation:

   There are a variety of formulations of this term.

   That could also apply to several of the terms in the model. "Modified Messinger Model" could mean about anything, you would need to look at the details.

   The energy examples in the handbook are less detailed than the ones we previously saw for impingement.

   The "Standard Computational Model" is implemented here in the python programming language and is available via github.com/icinganalysis …

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2. Ice Shapes

   Types of ice shapes

   As ice accumulates on a wing, it changes the shape of the airfoil. The ice that forms is sometimes called an "Ice accretion" in the literature. The shape of the ice depends on details of the flight and icing conditions.

   At warmer temperatures (about -10°C to 0°C, depending on airspeed and other factors), ice shapes tend to produce "Glaze Ice" shapes with "horns". The nomenclature varies by domain. Pilot training materials generally note this type of ice as "Clear Ice".

   

   from "Pilot Guide: Flight in Icing Conditions", AC 91-74B faa.gov

   At colder temperatures, the ice appears milky and opaque, and is termed "Rime Ice".

   
   from "Pilot Guide: Flight in Icing Conditions", AC 91-74B faa.gov

   At temperatures in between, "Mixed Ice" can form.

   
   from "Pilot Guide: Flight in Icing Conditions", AC 91-74B faa.gov

   These types of ice can have varying effects on …

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3. 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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4. Conclusions of the Icing Thermodynamics Thread

   "The collection of ice by the cylinders is similar to the collection of ice by airplane components"

   

   Figure 1. Modes of energy transfer for an unheated airfoil in icing conditions.

   Conclusions of the Icing Thermodynamics Thread

   Summary

   Data from the post-NACA era are used to resolve open questions

   Key points

   1. The Icing Thermodynamics thread is summarized.
   2. Post-NACA era data is used to resolve some open questions.
   3. The "Messinger model" and extended Messinger models are prevalent in current icing analysis.

   Discussion

   Review of the Icing Thermodynamics thread so far

   In the Icing Thermodynamics thread, we saw:

   • Calculations of wet surface temperatures NACA-ARR-5G13
   • Two dimensional heated surface equations for ice protection NACA-TR-8311
   • Comparisons of natural icing flight data to 2D ice protection calculations NACA-TN-1472
   • The "Ludlam limit" for freezing all water impinging Ludlam, F. H.: The Heat Economy of a Rimed Cylinder
   • The term "freezing fraction" defined Messinger, B. L.: Equilibrium Temperature …

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5. ADS-4

   "these calculations, performed at several span stations, can become unnecessarily tedious"

   ADS-4, “Engineering Summary of Airframe Icing Technical Data” ¹

   

   Summary

   A single thermodynamic control volume is used for anti-ice calculations.

   Key points

   1. Ice shapes are classified (glaze, rime).
   2. A single thermodynamic control volume is used for anti-ice calculations.
   3. NACA icing publications are extensively used.

   Abstract

   This report provides, in a single reference document, an engineering summary of selected technical data on airframe icing conditions, methods of detecting, preventing, and removing ice from airframes in flight, and methods of testing ice protection systems to ensure their adequacy. An aircraft engineer can use this report to design adequate ice protection systems for any type aircraft for any flight mission profile.
   The work done in preparing this report covered a survey, study, analysis, and summary of the vast amount of technical literature on airframe icing available in the world today. Key technical …

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6. NACA-TN-3396

   "into the transonic and supersonic regimes, the frictional heating becomes of considerable importance to icing."

   "Icing Limit and Wet-Surface Temperature Variation for Two Airfoil Shapes under Simulated High-Speed Flight Conditions"

   ¹

   

   Summary

   Predictions of the icing limit temperature were "sufficiently accurate" in tests at Mach 1.35.

   Key points

   1. Surface temperatures in icing conditions are challenging to measure.
   2. Apparently small differences in pressure coefficient and recovery factor values are important at high Mach values.
   3. Partial surface wettedness makes comparisons between analysis and test challenging.
   4. Thermal conduction in the substrate affects runback ice.
   5. Predictions of the icing limit temperature were "sufficiently accurate" in tests at Mach 1.35.

   Abstract

   Frictional heating resulting from flight at high speeds effectively reduces the value of ambient-air temperatures at which ice forms on aircraft surfaces. An experimental study was made of the wet-surface temperature and the stream conditions that result in ice-free surfaces for bodies …

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7. NACA-TN-3104

   "there has been speculation concerning removing ice during flight in clear air at high altitudes by the process of sublimation"

   "Experimental Investigation of Sublimation of Ice at Subsonic and Supersonic Speeds and its Relation to Heat Transfer" ¹

   

   Abstract

   An experimental investigation was conducted in a 3.84- by 10-inch tunnel to determine the mass transfer by sublimation, heat transfer, and skin friction for an iced surface on a flat plate for Mach numbers of 0.4, 0.6, and 0.8 and pressure altitudes to 30,000 feet. Measurements of rates of sublimation were also made for a Mach number of 1.3 at a pressure altitude of 30,000 feet.
   The results show that the parameters of sublimation and heat transfer were 40 to 50 percent greater for an iced surface than was the bare- plate heat-transfer parameter. For iced surfaces of equivalent roughness, the ratio of sublimation …

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8. NACA-TN-3045

   "The evaporative cooling of surfaces by air streams at high speed is of considerable interest"

   "Analogy Between Mass and Heat Transfer with Turbulent Flow" ¹

   

   Summary

   For turbulent flow on a flat plate, ke/kh is about 1.1 to 1.05.

   Key points

   1. For turbulent flow on a flat plate, ke/kh is about 1.1 to 1.05.
   2. The result applies at Mach numbers up to 1.5.

   Abstract

   An analysis of combined heat and mass transfer from a flat plate has been made in terms of Prandtl's simplified physical concept of the turbulent boundary layer. The results of the analysis show that for conditions of reasonably small heat and mass transfer, the ratio of the mass- and heat-transfer coefficients is dependent on the Reynolds number of the boundary layer, the Prandtl number of the medium of diffusion, and the Schmidt number of the diffusing fluid in the …

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9. NACA-TN-3024

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

   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 droplets are encountered, droplet evaporation will result because of the air-temperature rise and the relative velocity between the droplet and stagnating air. It is shown that the solution of the steady-state psychrometric equation provides evaporation rates which are the maximum possible when droplets are entrained in …

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10. Fraser

    "[LWC] limits have been calculated for a rotating cylinder..., and the results show that rotating cylinder measurements are of limited usefulness and may, in fact, prove entirely misleading as regards both water content and droplet size."

    Fraser, et al., "Thermodynamic Limitations of Ice Accretion Instruments" ¹

    

    Summary

    The term "freezing fraction" is defined (but probably not the one that you expected).

    Key points

    1. The term "freezing fraction" is defined (but probably not the one that you expected).
    2. "Ludlam limits" for instruments are calculated.

    Abstract

    A number of instruments used for determining the supercooled water content of an icing cloud depend on measuring the rate of accretion of ice on an unheated body. It has been shown by Ludlam that, since only part of the supercooled water freezes on impact, and the rest cannot always be frozen by the limited convective and evaporative heat losses which are available, there are limiting …

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11. 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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12. 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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13. 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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14. 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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15. 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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16. NACA-TN-1472

    "... equations for calculating the rate of heat transfer from airfoils in icing conditions were verified"

    "The Calculation of the Heat Required for Wing Thermal Ice Prevention in Specified Icing Conditions" ¹

    

    Summary

    Natural icing flight tests with an instrumented test airfoil are compared to 2D thermodynamic calculations.

    Key points

    1. Thermodynamic equations for a heated surface with water impingement are detailed.
    2. Test flights in natural icing conditions measured surface temperature for a heated surface.
    3. Runback water characteristics were noted.
    4. Heat transfer coefficients in icing were be inferred from measurements and calculations.
    5. "the design of heated wings on a fundamental, wet-air basis now can be undertaken with reasonable certainty."

    Abstract

    As a result of a fundamental investigation of the meteorological conditions conducive to the formation of ice on aircraft and a study of the process of airfoil thermal ice prevention, previously derived equations for calculating the rate of heat transfer from airfoils …

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17. 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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18. 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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19. Icing Thermodynamics

    "ice formation can be redefined in more general terms as a thermodynamic problem" ¹ (1936)

    

    Icing Thermodynamics Thread

    Summary

    This thread will focus on the use of thermodynamic heat and mass balance for icing and ice protection calculations.

    There may be some overlap with ice protection systems, but the systems will not be detailed herein.

    NACA-ARR-5G13, Kinetic Temperature of Wet Surfaces A Method of Calculating the Amount of Alcohol Required to Prevent Ice, and the Derivation of the Psychrometric Equation."

    Psychrometric equations are presented to calculate the thermal effects of evaporation from wet surfaces.

    NACA-TR-831, An Analysis of the Dissipation of Heat in Conditions of Icing from a Section of the Wing of the C-46 Airplane

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

    NACA-TN-1472, The Calculation of the Heat Required for Wing Thermal Ice Prevention in Specified Icing Conditions

    Natural icing flight tests with an instrumented test airfoil …

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