ESDU 69012+Amendment(A&B)-1973 气动加热对飞行器平衡温度的影响

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69012



EFFECTS OF KINETIC HEATING ON EQUILIBRIUM TEMPERATURE OF FLIGHT

VEHICLES

1. NOTATION AND UNITS

Any set of consistent units may be used. Two sets are indicated below.

SI British

Stefan-Boltzmann radiation constant, taken as

W/m2K4Chu/ft2s K4

factor in Equations (2.3), taken as

kg/m3K2.5 slug/ft3 K2.5

factor in Equations (2.3), taken as

m2K4/W ft2s K4/Chu

specific heat capacity at constant pressure,

taken as 103 J/kg K

(7.72 Chu/slug K) for air

J/kg K Chu/slug K

non-dimensional parameter,

Mach number at edge of boundary layer

local forced convection heat flux intensity W/m2Chu/ft2s

solar radiation heat flux intensity W/m2Chu/ft2s

gas constant, taken as 287 J/kg K

(3090 ft lbf/slug K) for air J/kg K ft lbf/slug K

temperature recovery factor

local Stanton number,

wall temperature K K

equilibrium wall temperature K K

recovery temperature, K K

temperature at edge of boundary layer K K

B5.67 10 8– W/m2K4

2.78 10 12– Chu/ft2s K4

×()

2.83 10 12– kg/m3K2.5

5.47 10 15– slug/ft3 K2.5

×()

1.76 107m2K4/W×

3.60 1011ft2sK4/Chu×()

1εBT1

2.5/St ρ1cpγR

K2αsqs/εBT1

()T

∞

()

1–+

St q/ρ1u1cpTwr Tw

–

()

Twr T11r γ1–

()

------------------ M1

Issued October 1969

With Amendments A and B, July 1973

ESDU product release: 2005-02. For current status, contact ESDU. Observe Copyright.

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69012



2. NOTES

Figures 1 to 3 present data for estimating the equilibrium temperature distribution on flat plates, wedges,

cylinders and cones in constant velocity flight in air. The equilibrium temperature is attained (see Item

No. 69009 for a full discussion) when the effects of forced convection heat transfer and solar radiation to

the surface are balanced by the difference between radiation from the surface and atmospheric radiation to

the surface. The heat balance equation under these conditions is

For the purposes of this Item it will be assumed that the emissivity of air, , is unity and that the absorptivity

of the surface, , is equal to the emissivity, . The above equation therefore reduces to

. (2.1)

Substitution for and in Equation (2.1) yields, with some rearrangement

(2.2)

temperature of uniform flow upstream K K

velocity at edge of boundary layer m/s ft/s

normal total surface absorptivity

normal total solar absorptivity

ratio of specific heat capacities, taken as 1.4 for air

normal total surface emissivity

gas emissivity, taken as unity for air

density at edge of boundary layer kg/m3slugs/ft3

T∞

αs

εG

ρ1

St ρ1u1cpTwr Twe

–

()α

BTwe

4 αεGBT∞

–=

εG

αε

St ρ1u1cpTwr Twe

–

()α

(4 T∞

–=

u1Twr

Twe

---------







------- Twe

---------

------- 1r γ1–

()

---------------

+ M1

2 K

)0=+––+

ESDU product release: 2005-02. For current status, contact ESDU. Observe Copyright.

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69012



in which the parameters and are given by

Note that contains the total effect of solar heating in addition to part of the effect of surface incidence

in supersonic flow.

Solutions of Equation (2.2) for are presented in Figure 1 as functions of in the range

and in the range for . Data for and 10 are given in Figures 2 and 3

respectively. The broken and solid lines are for laminar (r = 0.85) and turbulent (r = 0.89) boundary layers

respectively. For the two sets of data in which the data for are given separately for clarity.

The curves for the turbulent boundary layer only are given, the differences from those for the laminar

boundary layer being too small to plot.

Figure 1 provides data for estimating the equilibrium temperature distribution in the special case of the flat

plate at zero incidence with no solar heating , i.e. . The effect in practice of

deviations of from unity in (e.g. wedge and cone flow) is small, amounting to less than about

5 per cent in the worst case.

The effect of solar radiation on equilibrium temperature is found in practice to be small at other than fairly

low Mach numbers (e.g. 2 or 3 per cent is typical for a flat plate at a Mach number of 3). Values for ,

the intensity of solar radiation at any point within the earth's atmosphere, may be obtained by reference to

Item No. 69015 in the Structures Sub-series.

The ranges of data given cover most practical cases. For cases outside the data presented Equation (2.2)

should be solved directly.

Tables 6.1 and 6.2 (extracted from Derivation 1) give a list of values of the normal total emissivity, , for

various surfaces at the stated surface temperatures. Also given are values of the normal total solar

absorptivity, , for each surface. More extensive data for these parameters will be found in References 1

to 5.

The method of solution for equilibrium temperature using this Item is of necessity an iterative one since

the Stanton number required in , and obtained from Item Nos 69010 and 69011 for laminar and turbulent

boundary layers respectively, is itself a function of wall temperature. Convergence is rapid, however, and

seldom are more than three iterations required.

where = ,

and (2.3)

where = .

K1K2

εBT1

2.5

Stρ1cpγR

--------------------------- C1

εT1

2.5

ρ1St

------------











C12.83 10 12– kg/m3K2.5 5.47 10 15–

×slug/ft3K2.5

()×

εBT1

------------- T∞

-------







1–+= C

εT

----------- T∞

-------







1–+

21.76 107 m2K4/W 3.60 1011

×( ft2s K4/Chu×)

we/T1K10K10.2

≤≤

≤≤ K

20=

25=

≠M

≤

∞

()

∞

ESDU product release: 2005-02. For current status, contact ESDU. Observe Copyright.

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标签： #飞行

摘要：

ESDU 69012+Amendment(A&B)-1973 是一份由 ESDU（工程科学数据单元）发布的重要技术标准，详细阐述了气动加热对飞行器平衡温度的影响。该文档适用于高速飞行器设计与热防护系统评估，涵盖气动加热的基本原理、热平衡分析方法以及温度预测模型。通过本规范，工程师可以理解飞行器在高速飞行过程中，表面因与空气摩擦产生的热流如何影响其结构温度分布，进而优化材料选择与隔热设计。该标准特别适用于航空航天领域，帮助设计者在飞行器早期设计阶段预测热环境，确保安全性与性能。

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ESDU 69012+Amendment(A&B)-1973 气动加热对飞行器平衡温度的影响

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