Jet Engine hot parts IR Analysis Procedure (J-EIRP)

Appendix A - Basic Radiation Heat Transfer Concepts The following discussion briefly introduces some basic radiation heat transfer concepts. These radiation heat transfer concepts are used to define the solution technique and requirements for use in J-EIRP. The basic definitions, equations, units, and notation used to define the radiation characteristics were selected from reference 4.

The simplest mode of radiation heat transfer occurs when energy is emitted from a single flat surface in a vacuum where no reflected energy is involved. If the surface is a perfect absorber and emitter of radiant energy, it is called a blackbody.

This blackbody also emits the maximum amount of radiant energy to its surrounding hemisphere. The intensity of radiation emitted by a blackbody in any direction for a single wavelength is defined by Planck's Law as: i_ (_.,T)= 2Cl [ BTU ] (A1) _.5(eC_'T1) hr i_m ft = sr where C 1 and C2 represent Planck's spectral energy distribution constants, as shown:

hCo

C,=h C2= k

C_ = .18878x108 BTU _m 4 C 2 = 25897.84 _m ° R hr ft 2 The prime notation defines a directional quantity of radiation per unit solid angle for a single direction. The subscripted terms specify the quantity as spectral (_ - one wavelength), and the surface as a blackbody (b). The dependent variables are listed in the parentheses. The emissive power radiated from a blackbody over an entire hemisphere in a vacuum at a particular wavelength is defined as:

2,,c

exb(X,T ) = =

BTU 1 (A2) hr _m ft 2 _.5(eC_T_I) By integrating equation (A2) over the entire wavelength band, the total blackbody hemispherical emissive power at a specific surface temperature is then: (A3) o _.s(ec# -1) where o represents the Stefan-Boltzmann constant: I hr BTU__ 1 o = 0.17123x10 -8 °R4J Applying the emitting surface area to equation (A3) gives the total blackbody hemispherical emitted energy per unit time as: (A4) EbA_(TA) = /o-A, exb(X)d_" = A, oT_A [ BTU] L hrj For a real (non-blackbody) surface, thermophysical properties control the radiant energy absorbed, emitted, and reflected from the surface. These properties can be a function of incident and reflected angles, wavelength, and temperature.

Frequently, several simplifying assumptions can be made regarding the surface thermophysical properties. Averaged surface properties may be derived if one can average over all directions and wavelength bands. Applying these assumptions, a surface that absorbs and emits a fixed fraction of radiation from any direction and at any wavelength is now defined as a diffuse gray surface. The directional and spectral absorptivity and emissivity then become:

= eA(TA)

T,,.) = a A( TA)

From Kirchhoff's law the directional, spectral and hemispherical total values of absorptivity and emissivity are equal, thus: (A5)

e(TA)--

The dependence of the surface temperature on the surface emissivity value also may be averaged over the radiation heat transfer band.

Applying surface thermophysical properties results in the surface being defined as a non-blackbody. The total non-blackbody (diffuse-gray) hemispherical emissive power is: BTU l (AS)

e(T ) = = e,,o

-hT- j

The total non-blackbody hemispherical emitted energy is: EA,(TA) = _'A,¢Ae_,t,(X)d_. = AleAO _

(AT)

For radiation to be exchanged between surfaces, a geometric relationship (geometric configuration factor or view factor) between the surfaces must be defined.

The view factor for blackbody isothermal surfaces is the fraction of emitted radiant energy leaving a surface i that reaches another surface j. Since both surfaces are blackbodies or perfect absorbers of radiant energy, no reflected energy is introduced into the view factor value, FH. The total blackbody emitted energy from surface A 1 that is incident and absorbed by surface A 2 is then:

Eb A, - = A, FA, . [ BTU] (A8)

L-hT-j

For simple geometric configurations various view factor references are available. For complex geometric configurations, various computer techniques have been developed where the surfaces are defined, and mathematical or ray tracing techniques are applied to solve the surface relationships.

For non-blackbody surfaces the blackbody view factor is replaced by the radiation interchange factor, Bi..j, which represents real surface radiation exchange.

The radiation interchange factor is the fraction of emitted energy by a real surface i that is absorbed by real surface j, including all reflections from other real surfaces including the emitting surface i. Computer programs are also available to calculate B_.j values. For the radiation exchange between two real surfaces, defined as A_ and A2, the total non-blackbody emitted energy from surface A 1 that is absorbed by surface A 2 is: [ BTU] (Ag)

EA' "_( TA') = A1B'_ "_e'& o T_ L--hFJ

This is where the g_.j term defines the relationship between the energy emitted from surface A1 that is absorbed by surface A 2 directly and indirectly. This indirect radiant energy may be in the form of multi-reflecting energy between A_ and A 2, and energy from A_ that is reflected from other surfaces to A 2. The radiation path for a multi- surface cavity configuration may include al! surfaces, which can result in a large number of total non-blackbody emitted energy terms: Energy Transfer From All Possible Radiation Paths = _ _ ¢,oA,B_.I(_) /=1 _1 The radiation exchange also can be evaluated within a particular wavelength region or fraction of the total emissivity power. This is done by simply using the total blackbody hemispherical emissive power, equation (A3), and modifying the limits of integration as shown:

d(x) (A10)

= f e,,d(x) = [ 2=C, _., )., _.s(eC'#_" T- 1) The non-blackbody hemispherical emitted energy within a wavelength band becomes: _2 'i2 (All) EA,(Z' T-'X27) = cA AA_fexbd(_. ) = eA AA,/ 2_C, x, x, Xs(e--_'--_ 1) d(_') Applying the radiation interchange factor results in the non-blackbody emitted energy from individual surfaces within a wavelength band: ;L 2 T-X27) = 2.c, ', _s(e C.J_T_I) _X ) (A12) The integration term can be solved using a numerical polynomial curve fit resulting in the total non-blackbody hemispherical emitted energy equation as: BTU] (A13) hr J where the P0-_,T is represented (ref. 4) as: (A14) C,, where x = --'- ZT Tabulated values of these polynomial approximations are also available as a function of wavelength-temperature products in reference 4.

Appendix B - The J-EIRP Solution Concept The programs that currently comprise J-EIRP solve the radiation heat transfer concepts described in appendix A. The same definitions, notations, and equations defined in appendix A apply, but a conversion factor modifying the units to watts has been included. The total non-blackbody hemispherical emitted energy in equation (A13) is the general form of J-EIRP solution concept.

To absorb, identify, and evaluate the radiation from an engine cavity, a sectioned hemisphere placed behind the cavity exit plane can be used. This multi- sectioned hemisphere reveals the uniform intensity over the finite hemispherical surfaces areas from the jet engine cavity. By selecting a distance where the emitted and reflected cavity radiation results in nearly normal intersections with the hemispherical surfaces, the radiant energy can be calculated as a function of solid angle. The equation describing the radiant energy emitted from a defined cavity surface to a defined hemispherical surface in terms of a solid angle is as shown: I/A_._(_.lT-*_.27") = eAA1BA_.A_[['o_x2TA-['o_x_T_]OT_A_ (.2931) r2_A= / (B1) I Watts] sr j In this equation r represents the distance from the source cavity surface area A 1 to the target hemispherical surface area A2 for a solid angle calculation. By calculating the radiant energy emitted and reflected from each jet engine cavity surface to each hemispherical surface and summing the hemispherical results, the jet engine cavity radiation emission is calculated. Equation (B1) summarizes all the basic concepts within J-EIRP. The radiation interchange factors (Bi.j values) are calculated using the NEVADA program which analyzes a model representing the jet engine cavity. The summed radiant energy from all the jet engine cavity surfaces to each hemispherical surface is calculated using the TRACK-E program. TRACK-E also evaluates the component radiant energy distributions over the hemispherical surfaces, and the radiant energy emitted and absorbed within the jet engine cavity.

Appendix C - The PIREP Solution Concept

The Preliminary Infrared Radiation Emissions Program (ref. 3) includes a

simplified method of calculating the jet engine cavity hot parts emission. The general

PIREP method applies Planck's Law directly to a solution where the jet engine cavity

geometry is simplified to represent a flat plate emitting energy at the size of the

exhaust nozzle throat. Therefore, this method evaluates only the directly emitted

energy from a flat plate and eliminates cavity wall reflections. To better understand the

general PIREPequation and results, the PIREPjet engine hot parts analysis method

will be derived in the following discussion.

The intensity of radiation emitted in any direction for a single wavelength is

defined by Planck's Law in equation (A1) as: i_xb(X,T) = 2C_ [ BTU ] XS(eCE_T-1) hr t_m ft 2 sr Applying Planck's spectral energy distribution constants as given in appendix A and converting units, equation (A1) becomes: J'_b(_,T) = 2(0"18878x108) (.2931 / = 76849.1917 Watts ] (Cl)

xS(e='7. 'Tc1) xs(e="97. *T-1)

This is the general form of Planck's Law used in PIREP. Planck's Law, which is for a single wavelength calculation, is normally integrated over the IR spectrum or wavelength band. To simplify the wavelength band integration, the integration is replaced with a wavelength delta. This assumes the wavelength band is small and that an average wavelength can be substituted into Planck's Law as follows: )'2 76849.1917 A_.

d_ _, f 76849.1917 i/b A1(_.1 T-" _L2 T ) _.s(e2s_7.s4/x T_ 1) xl _'s(e2'_97"e4/)`T-1) (C2) where: & _. = wavelength difference ;k = average wavelength This represents the intensity of emitted radiation per unit solid angle from a flat plate in all directions, where temperature is defined by the turbine exit total temperature. By introducing the exhaust nozzle throat area into equation (C2), PIREP evaluates the intensity from a jet engine cavity. This is shown in the following equation along with the notation changed to reflect PIREP's form.

J,o 76 9.1917 [ w .s 1 cca

i_ Ar(;h T-')_2T) = The PIREP method was designed as a fast approximation tool for calculating the emission from jet engine cavity hot parts. Alternative solution methods are required if component effects are to be evaluated, or increased analytical accuracy is required.

Equation (C3) differs slightly from the actual PIREP equation due to the use of updated values for Planck's spectral energy distribution constants (C 1 and C2).

References

1. Baumeister, J.F.: "Thermal Radiation Characteristics of Non-Isothermal

Cylindrical Enclosures Using a Numerical Ray Tracing Technique", NASA TM- 102527, 1990.

2. Turner, R.C.: "NEVADA Software Package User's Manual", Ninth Edition, Ver.

14, Turner Associates Consultants, 1988.

3. Anon.: "Preliminary Infrared Radiation Emissions Program (PIREP)", Volume I, Final Report, General Electric Company, Cincinnati, Ohio, ASD/XRoTR-76- 26, 1976. Distribution limited to U.S. Government agencies only.

4. Siegel, R., and Howell, J.R.: 'Thermal Radiation Heat Transfer", Second ed., Hemisphere Publishing Corporation, Washington, DC, 1981.

C Model ._

NEVADA SUPPLY SURFACE TRACKE 1_ TEMPERATURES I GRAPH I ROUTINES Figure 1. - Jet Engine IR Analysis Procedure (J-EIRP).

Figure 2. - Surface geometry of a sample cavity model.

Figure 3. - Surface geometry of sample hemisphere model section.

0" go. (Turbine/Nozzle Axis) 210" TURBINE PLANE

'" [- I

lm" I_'VERGENT NOZZLE Figure 4. - Sample cavity component radiation interchange factors.

O" 7j_l • gO • 2t0" 1_" _ TOTAL IR SPECTUM ] leo- Figure 5. - Sample cavity total radiation emission.

O" o _r/,O ° IlO" WAVELENGTH >G.0 t_m I lao 80 pro< WAV_mRG'I'H >12.O _n Figure 6. - Sample cavity wavelength band radiation emission.

O" _'_° I I _ TOTAL ENGINE ,.. DIVERGENT NOZ21.E I 180" I Figure 7. - Sample cavity divergent nozzle effect on radiation emission.

(3.0 i_m<wavelength<5.0 pm) Form Approved REPORT DOCUMENTATION PAGE OMe No.0704-0188 Public reporTir_g burden f_ ih_ collection of information is estimated to average I hour pe_" reeponse, including |he lime for reviewing ;nsZrucl;ons. sesrching existing d_na source, gathering and malntaintn_ the data needed and completing and reviewing the collectionof information. Send comments r egar.ding this burden e st=mate or any other aspS,, of this collection of information, including sL)ogeslions for reducing this burden, to Washington Headquarters Serv_cos. D_rectorate Tor _nformat_on uperat_ons and Heports, 1215 Jenersen Davis Highway, Suite 1204. Adington,VA 22202-4302. and 1o the Office of Management and Budgel, Paperwork Reducl_on Protecl (0704-0188), Washington, DC 20503, 3. REPORTTYPE AND DATESCOVERED 1. AGENCY U'sE ONLY (Leave blank) 2. REPORT DATE Technical Memorandum February 1993 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS Jet Engine Hot Parts IR Analysis Procedure (J-EIRP) WU- 505--62 6. AUTHOR(S) Joseph F. Baumeister 8. PERFORMING ORGANIZATION 7. PERFORMINGORGANIZATION NAME(S)ANDADDRESS(ES) REPORT NUMBER National Aeronautics and Space Administration Lewis Research Center E-7605 Cleveland, Ohio 44135-3191 10. SPONSORING/MONITORING 9. SPONSORING/MONITORING AGENCYNAMES(S)ANDADDRESS(ES)" AGENCY REPORT NUMBER National Aeronautics and Space Administration NASA TM- 105914 Washington, D.C. 20546-0001 11. SUPPLEMENTARY NOTES Responsible person, Joseph F. Baumeister, NASA Lewis Research Center (216) 433-2179.

12b. DISTRIBUTION CODE 12a. DISTRIBUTION/AVAILABILITY STATEMENT Unclassified- Unlimited Subject Category 05, 34 13. ABSTRACT (Maximum 200 words) A thermal radiation analysis method called Jet Engine IR Analysis Procedure (J-EIRP) was developed to evaluate jet engine cavity hot parts source radiation. The objectives behind J-EIRP were to achieve the greatest accuracy in model representation and solution, while minimizing computer resources and computational time. The computer programs that comprise J-EIRP were selected on the basis of their performance, accuracy and flexibility to solve both simple and complex problems. These programs were intended for use on a personal computer, but include the ability to solve large problems on a mainframe or super-computer. J-EIRP also provides the user a tool for developing thermal design experi- ence and engineering judgment through analysis experimentation, while using minimal computer resources. A sample jet engine cavity analysis demonstrates the procedure and capabilities within J-EIRP, and is compared to a simplified method for approximating cavity radiation. The goal is to introduce the terminology and solution process used in J-EIRP, and provide insight into the radiation heat transfer principles used in this procedure.

15. NUMBER OF PAGES 14. SUBJECTTERMS 2O Infrared radiation; Nozzle design; Jet engines; Numerical analysis; 16. PRICE CODE Statistical analysis A03 20. LIMITATION OF ABSTRACT 17. SECURITYCLASSIFICATION 18. SECURITYCLASSIFICATION 19. SECURITY CLASSIFICATION OF REPORT OF THISPAGE OF ABSTRACT Unclassified Unclassified Unclassified Standard Form 298 (Rev. 2-8g) NSN 7540-01-280-5500 Prescribed by ANSI Sial. Z39-18 298-102