N 84 - 19 60 6

NASA Contractor Report 168221

Comparisons of Rational Engineering Correlations of ThermophoretlcallyAugmented Particle Mass Transfer with STAN5-Pred1ct1ons for

Developing Boundary Layers

Siileyman A. Gb'koglu

Analex Corporation

Cleveland, Ohio

and

Daniel E. Rosner

Yale University

New Haven, Connecticut

January 1984

Prepared for

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

Lewis Research Center

Under Contract NAS3-23293 and NAG3-201

https://ntrs.nasa.gov/search.jsp?R=19840011538 2018-05-11T19:30:56+00:00Z
COMPARISONS OF RATIONAL ENGINEERING CORRELATIONS OF

THERMOPHORETICALLY-AUGMENTED PARTICLE MASS TRANSFER

WITH STAN5-PREDICTIONS FOR DEVELOPING BOUNDARY LAYERS1

Siileyman A. Gokoglu2

Analex Corporation

Cleveland, Ohio 44135

and

Daniel E. Rosner^

Yale University

Chemical Engineering Department

New Haven, Connecticut 06520

SUMMARY

Fouling (and corrosion) of gas turbine (GT) bladlng often results from

the deposition of materials derived from Inorganic Impurities 1n the fuel

and/or Ingested air. When the depositing material 1s 1n the form of a submicron "aerosol" (dust or mist) 1t has been found that the rates of deposition

on cooled surfaces can be augmented by some 100-1000-fold via the mechanism of

thermophoresls (particle migration down a temperature gradient). For this

reason, 1n earlier papers we reported the development of rational, yet simple,

engineering correlations of thermophoretlcally-augmented particle transport

across both laminar boundary layers (LBLs) and turbulent boundary layers

(TBLs). While developed based on theoretical considerations, and numerical

computations of self-similar LBLs and law-of-the-wall (Couette flow-like)

TBLs, these mass transfer coefficient (Stm-) correlations, when applied

locally, may also prove useful 1n making engineering mass transfer predictions

for more complex geometries, Including GT-blades. Pending additional controlled experiments, Insight Into the local applicability of these correlations can be gained by selected comparisons with numerical predictions for

developing BLs. This paper reports on our (a) modification of the code STAN5

to properly Include thermophoretlc mass transport, and (b) examination of

selected test cases of developing BLs which Include variable properties,

viscous dissipation, transition to turbulence and transpiration cooling.

Under conditions representative of current and projected GT operation, local

application of our Stm/Stm 0- correlations evidently provides accurate

and economical engineering design predictions, especially for suspended

particles characterized by Schmidt numbers outside of the heavy vapor range

(say, Sc>10).

Supported by NASA Lewis Research Center Contract NAS3-23293 [Analex]

and Grant NAG3-201 [Yale U.].

^Research scientist.

3Professor of Chemical Engineering, Director, High Temperature Chemical

Reaction Engineering Laboratory.
INTRODUCTION

Accurate predictions of mass transport rates 1n nonIsothermal forced

convection systems are now essential to the gas turbine (GT) Industry, among

other technologies. Recently, a dramatic enhancement 1n small particle d1ffuslonal transport rates due to thermophoresls (particle drift down a temperature gradient) has been predicted for both Internally cooledand transpiration-cooled surfaces across both self-similar laminar boundary layers

(LBLs) (refs. 1 and 2) and law-of-the-wall turbulent (ref. 3.) boundary layers

(TBLs), Including viscous dissipation (ref. 4). The magnitude and temperature

dependence of this thermophoretlc augmentation has been experimentally

confirmed for L6L flow of combustion products containing submlcron

MgO-part1cles (ref. 5).

To facilitate engineering predictions, simple rational correlations have

recently been developed (refs. 6 and 7). Until now their accuracy and

applicability limits have been demonstrated using "exact" numerical

calculations for self-similar BLs (refs. 1 and 4). One of our purposes here

Is to examine their behavior and accuracy 1n more complex BL-flows, under

conditions representative of current and future GT-technology.

The availability of high-speed, large capacity computers has made 1t

possible to examine the reliability of self-similar heat transfer correlations

when applied locally to developing BL situations. Indeed, computer codes

for both multidimensional laminar and turbulent flows have been developed by

exploiting finite-difference techniques (refs. 8 and 9). Recently, with

Increased Interest 1n GT blade fouling and/or corrosion problems, greater

attention Is being focused on small particle mass transfer across twodimensional BL's (ref. 10). To make such predictions we have adapted the

two-dimensional BL code STAN5 (ref. 11), which has previously been widely

used for gas-side convectlve heat transfer predictions. This necessitated

modifying the program to now Include thermal (Soret) diffusion

("thermophoresls" for small particles) 1n the suspended particle mass conservation (particle-phase "continuity") equation. Toward this end, STAN5

predictions over the suction surface of a typical stator blade are here

compared with the predictions of our earlier correlations (refs. 6 and 7) when

applied locally to such developing BL situations. Of course, experimental

data, both for blade cascades and operational turbines, will be the ultimate

arbiter of whether our correlations and/or numerical BL codes (e.g., STAN5)

presently and properly Include all of the phenomena which dictate mass

transport rates 1n the challenging GT environment.

NOMENCLATURE

B^ real blowing parameter, eq. (5)

-BT thermophoretlc suction parameter, eq. (6)

c mass fraction of particles 1n the local gas mixture

D Brownlan diffusion coefficient of particles

Da effective Damkohler number, eq. (7)

Le Lewis number (ratio of particle Brownlan d1ffus1v1ty to host gas

heat d1ffus1v1ty)
m" mass flux at station e or w

Ma Hach number

p pressure

r radius (for axUymmetrU BL flow)

R nose radius of the turbine blade

n

S source; eq. (3)

Sc Schmidt number (ratio of host gas momentum d1ffus1v1ty (kinematic

viscosity) to particle Brownlan (mass) d1ffus1v1ty)

St. Stanton number for heat transfer h

St Stanton number for mass transfer, Including thermophoresls

m

St Stanton number for mass transfer without thermophoresls and/or

m,o

transpiration cooling

T absolute temperature

T temperature at the outer edge of Brownlan diffusion boundary layer

m

u fluid velocity 1n x-d1rect1on (parallel to wall)

v fluid velocity 1n y-d1rect1on (normal to wall)

x distance along the surface (measured from the forward stagnation

point)

y distance normal to surface

a thermal diffusion factor of the particle/host gas combination

p dynamic viscosity of host gas

p density of host gas

y stream function coordinate, pur = 3\|»/3y, pvr = -3^/3*

w nondlmenslonal stream function coordinate, («M» )/(^ -«l» ) W C iw

Subscripts:

e pertaining to the outer edge of the boundary layer

eff effective

o pertaining to reservoir conditions (transpiration coolant)

w pertaining to the surface (wall)

oo pertaining to gas mixture at upstream "Infinity"

Miscellaneous:

BL boundary layer (L, laminar; T, turbulent)

GT gas turbine

PDE partial differential equation

RHS right hand side
ADDITION OF THERMOPHORESIS TO STAN5 BL CODE

Here we focus only on the suspended particle mass conservation PDE,

which must Include the thermophoretlc flux term. Upon time-averaging, the

simultaneous fluctuation of the thermophoretlc speed and particle concentration produces a new "correlation" term. But this latter term (which may be

called "eddy thermophoresls") 1s neglected based on arguments given 1n

references 12 and 13. In the same notation as reference 11, the time-averaged

particle mass conservation equation for the BL can then be written:

ac x ac 1 a_[

 yeff acV 1 a /rpaTDc aj_ pu ax * pv ay

 = r aylr Sceff ay/* r a7\ T ay, (1)

where the second term on the RHS of equation (1) 1s the added thermophoretlc

flux. Upon Introducing the nondlmenslonal stream function as the transverse

coordinate (cf. ref. 11) equation (1) becomes:

ac

r PU yeff

.(*.- /SC

eff

ac

3 co

a

3 co

" 2 2

r p ua,Dc

_<v v2 T 31

du

(2)

In the numerical solution of equation (2) the thermophoretlc flux term on

the RHS will be treated as a "source" term. Although the source Itself 1s

explicitly c-dependent, c-values obtained from the previous (upstream)

Integration step are used 1n Its evaluation. This simple treatment of the

thermophoretlc flux term 1s compatible with numerical approximations already

Incorporated 1n STAN5. For flow near the wall, where STAN5 switches to

simplified Couette-flow equations (with no streamwlse variation of the

dependent variable, and constant r), the thermophoretlc flux term 1s Included

1n the particle mass conservation equation, again as the "source" defined by:

(3)

Based on the procedures outlined 1n reference 14, new subroutines have

been added to STAN5 1n order to calculate the suspended particle thermal

diffusion factor, oj, and the Brownlan diffusion coefficient, D (as well

as the Schmidt number, Sc), Including their respective temperature

dependencies.
The modification In particle deposition rate due to thermophoresls

depends both on particle size (hence Schmidt number) and the ratio of

mainstream-to-surface-temperature. Therefore, under typical turbine operating

conditions, 1n order to see an appreciable thermophoretlc effect one needs to

consider particles heavier than ordinary vapor molecules. However, as 1s well

known, when the particle size Increases (enough to cause Sc » 1), the mass

transfer (Brownlan diffusion) BL 1s completely Imbedded within the momentum

(or heat) transfer BL, the thickness ratio being proportional to Sc~1/3

(or Le*1/3). In fact, 1t can be readily shown (ref. 1) that 1n the

presence of "strong" thermophoresls (I.e., aj [(Te/Tw) - 1] » 1) the

Brownlan diffusion BL 1s even much thinner than In the absence of

thermophoresls. with the thickness ratio scaling becoming proportional to

Sc-1 (or Le*'). These observations Imply that a finite-difference

scheme with a much finer mesh size 1s required for an accurate solution of the

small particle concentration profile and the associated mass transfer Stanton

number. Moreover, to preserve accuracy for a two-dimensional Integration

process, a thinner BL requires a smaller step-size 1n the x-d1rect1on —

1.e.. x-d1rect1on step-size 1s restricted by the smallest of the momentum,

heat and mass transfer BL thicknesses. Consequently, a moderate Increase 1n

the particle size (via Sc) Increases the computation time dramatically. In

order to achieve a reasonable balance between (a) sufficient thermophoretlc

deposition rate enhancement (to test the accuracy of our correlations) and (b)

required computation time, we have therefore adopted a Schmidt number of about

26 for most of our trials (except for one case with Sc = 100, see "Results

and Discussion"). Accordingly, the dimensioning of STAN5 has been Increased

up to 1000 mesh points 1n the y-d1rect1on (from the originally programmed

maximum of 60 mesh points)4.

RESULTS AND DISCUSSION

For all results presented here a mainstream velocity distribution

obtained from reference 15 for a turbine stator blade 1s used as Input to

STAN5. Except for figure 6, the nose radius, Rn, of the blade used for the

Illustrative calculations was taken to be 0.152 cm. Integrations were carried

out along the suction surface up to about 10 nose rad11 from the blade stagnation point. In these cases the predicted BL flow remained laminar. To

examine the consequence of transition to turbulence (by x/Rn«5), for

figure 6 the blade was magnified to Rn = 0.366 cm and the stagnation

pressure was Increased from 4 atm. to 20 atm.

In all figures, results aj. the stagnation point (x = 0) are obtained from

the self-similar solutions of reference 1 (because STAN5 1s singular at x =

0). STAN5 calculations are started at x = 10-1 Rn. Downstream results

are very sensitive to the Initial starting profile specified (see also

4For the fastest commercially available computer, CRAY-1, using 800

mesh points 1n the y-d1rect1on and taking the step-size along the x-d1rect1on

to be 10"1 times the local momentum BL thickness, Integration of LBL

equations by STAN5 along the suction surface of a typical turbine blade to

about 10 nose rad11 downstream from the stagnation point required a CPU time

of about 8 minutes with thermophoresls and 4 minutes without thermophoresls.
ref. 16). To be on the safe side, only STAN5-values beyond one nose radius

from the stagnation point were considered reliable (Initial profile Insensitive). Moreover, by moving one nose radius away from the stagnation

point we avoid any anomal1t1es that may result due to (a) lack of accuracy 1n

the mainstream velocity near the stagnation point (ref. 15), and (b) an unrealistic curve-fit generated by the cubic splines that STAN5 employs (ref.

17). The automatic starting profile generating subroutine of STAN5 (ref. 16)

was used for the Initial velocity and temperature profiles, and the velocity

profile was scaled (via Sc~1/r3) to obtain the Initial concentration profile.

The correlation values shown 1n all figures (with negligible viscous

dissipation) are calculated from (refs. 6 and 7):

St -(B + B )

~

 m exp(-Da) (4)

Stm,o ] - «' <Bm * BT>

where:

<PV)

and:

St. T - T

n 6 W

m, o w

T - T

Oa = (<*TLe)e • T (7)

m

The Schmidt numbers reported 1n the figures correspond to particles

(assumed spherical) made up of N32S04 "monomer units" 1n a1r^. The

ratio a-j-Le (of the thermophoretlc d1ffus1v1ty of the particles to the heat

d1ffus1v1ty of air), required for our correlations (ref. 6) was estimated to

be 0.4 and temperature-Independent for all reported cases here. For

simplicity 1n the correlation scheme, throughout this paper the ratio:

Stn/Stm 0, of the Stanton number for heat transfer to the Stanton number

for mass transfer without thermophoresls, was approximated to be equal to the

prevailing value of Lew ~

2/3 for laminar BL flows. However, for

transitional and fully turbulent flows, local Stn and Stm 0 values

(as calculated by STAN5) are used for the correlation calculations.

To "calibrate" STAN5, we first ran the case of a flat plate (constant

mainstream velocity), with the results shown 1n figure 1. The abscissa Is the

distance along the flat plate made nondlmenslonal by the stator nose radius

Rn = 0.152 cm to allow comparisons with the abovementloned turbine blade

example. The ordlnate 1s the ratio of mass transfer Stanton numbers

5SCa> = 26 corresponds to 102 and Sc = 100 corresponds to 8xl02

N32S04 monomer units 1n a cluster.
(obtained with thermophoresls and without thermophoresls, respectively).

Under the prevailing conditions there 1s more than a two-fold enhancement 1n

the deposition rate due to thermophoresls. For this "self-similar" case the

result obtained from the exact numerical calculations of reference 1 1s shown

by the dash-dot line (x-1ndependent). The correction-predicted value 1s the

dashed line. The only difference between the results of reference 1 and STAN5

should be that due to the somewhat different treatment of variable host gas

(air) thermodynamlc and particle transport properties for this "cold" wall

(TV/TO, = 0.6) self-similar case6. However, 1n Interpreting subsequent

comparisons, the reader should recall that STAN5 does not quite give a

constant (x-1ndependent) enhancement.

Figure 2 displays the results of calculations for the suction surface of

a stator blade, using the same environmental conditions as 1n figure 1. For

the prevailing conditions the Mach number Is calculated to be about Mae =

0.72 at x/Rn = 10 (less for smaller x/Rn). To display the effect of

the Mach number STAN5 was also run Including viscous dissipation. As expected

(ref. 4), at these Mach numbers viscous dissipation 1s seen to have a small

effect on the thermophoretlc enhancement of deposition rates. Comparison of

our correlations with STAN5 both with and without viscous dissipation shows

that the local difference 1s always less than 10 percent. The shape of the

curves (1.e.. the fact that the effect of thermophoresls decreases as x/Rn

Increases) can be explained by the mainstream static temperature cooling.

Although Ty/T,,, 1s fixed for our calculations, the difference between

the mainstream static temperature, Te (which gets cooler as the flow

accelerates under adlabatlc conditions), and the wall temperature, Tw

(constant), gets smaller, which reduces the effect of thermophoresls. Of

course, our correlations are also applied locally, with the relevant local

temperature being Te rather than T'COa*

Figure 3 1s constructed for the same conditions as figure 2 except that

the wall temperature 1s higher (Ty/To, = 0.8), corresponding to a smaller

enhancement 1n deposition rate due to thermophoresls. The agreement between

the predictions of STAN5 and our correlations 1s excellent.

In figure 4 an Increased particle size 1s considered (Sc^ = 100),

keeping all remaining parameters the same as 1n figure 3. The corresponding

effect of thermophoresls 1s now even greater than 1n the colder wall case

(TV/TO, = 0.6) with Sc,,, = 26 (shown earlier 1n fig. 2). Yet, the

agreement between our correlations and STAN5-pred1ct1ons 1s even better, with

local differences being less than 4 percent for all x/Rn-values. This may

be related to our observation (ref. 6) that for self-similar cases these

correlations Improve as Tw/Too -»1, regardless of particle size (Sc).

To consider even larger departures from self-similarity a variable

(x-dependent) wall temperature was considered, with the results shown 1n

figure 5. Tw 1s varied 1n such a way that the wall 1s hottest at the

stagnation point (Ty/T^ = 0.8) and gets colder as x/Rn Increases,

becoming lv/'Ia> = 0.5 at x/Rn = 10. Not surprisingly, the

thermophoretlc effect Increases as the wall gets cooler (although the

Reference 1 assumes that the host gas thermodynamlc and particle

transport properties have simple power-law temperature dependencies.
mainstream static temperature drops as the flow accelerates, the reduction 1n

the assumed wall temperature 1s greater, resulting 1n a steeper temperature

gradient across the BL). While departures between the correlation and

STAN5-pred1ct1ons Increase as the wall-to-malnstream-temperature ratio departs

from unity (ref. 16), remarkably enough, the effects due to "nonselfs1m1lar1ty" act 1n such a way that the agreement between STAN5 and the

correlations Improve as Tw drops.

In figure 6 the nose radius of the stator blade and the pressure have

been Increased to 0.366 cm and 20 atm, respectively. The corresponding BL

flow becomes transitional at about x/Rn = 2.9 and "fully" turbulent at

about x/Rn = 5.0. A lower wall temperature (Ty/To, = 0.5) 1s considered

to provide a stringent test of the present correlations, based (ref. 6) on

self-similar Integrations for Tw/T,n > 0.5. We observe that the

agreement between STAN5 and our correlations Improves for turbulent BLs. In

this connection 1t should be recalled that our correlations describe the

results of law-of-the-wall Couette-flow TBL Integrations with even better

accuracy than 1n otherwise corresponding LBL situations. When compared

locally with STAN5 results, even for Ty/T,,, = 0.5, agreement 1s within

10 percent for the laminar portion, and within 4 percent for the fully

turbulent portion of the flow. The agreement 1s still better 1n the

transitional region. Note that the effect of thermophoresls on mass transfer

(over and above the already efficient transfer mechanism by turbulent eddies)

is smaller than 1n the corresponding laminar BL case.

Figure 7 displays the results of our calculations on the effect of

transpiration cooling and/or thermophoresls on the deposition rate of small

particles (Sc«a = 26). For this purpose STAN5 was run with the wall

boundary condition specified as a flux (Instead of a level), where the

reservoir temperature of the coolant air was taken to be 600K (TQ/TO, =

0.4). The correlation curve without thermophoresls 1s representative of how

the blowing rate was varied along the blade surface. The blowing rate was set

higher near the stagnation point, was reduced along the suction surface, and

near the trailing edge (7 < x/Rn < 10) was chosen such that the real blowing

parameter, Bm (defined by eq. (5)), was constant.

If attention 1s first focused on the STAN5 and correlation curves without

thermophoresls, observe that STAN5-pred1ct1ons "lag" 1n responding to local

blowing rate variations when compared with the correlation (which 1s based on

an "Instant" assumed adjustment to the local blowing rate). Specifically,

for 7 < x/Rn < 10, although the correlation predicts a constant reduction

1n the deposition rate, STANS-values steadily Increase, ultimately approaching

the correlation prediction, but remaining below them due to "recollection" of

the "history" of higher upstream blowing rates. For a two-dimensional

developing BL each x-1ntegrat1on station provides the starting profile for

the next station 1n the forward "marching" process. Therefore, the flow

cannot Instantaneously adapt Itself to the "new" (continuously varying)

boundary conditions. A better example 1s provided 1f the cross-over points of

the curves with and without thermophoresls are compared for the correlation

(x/Rn«7.4) and STAN5 (x/Rn«8.2). Because of mainstream static temperature cooling and the small blowing rates used 1n this example, the wall

temperature becomes hotter than the mainstream static temperature at about

x/Rn«7.4. Although thermophoresls enhances small particles deposition

rates toward colder walls ("suction" effect, ref. 6), for hot walls the
deposition rate 1s reduced due to what we have called "thermophoretlc

blowing." The correlation curve with thermophoresls, of course, exhibits an

Immediate reaction to the hotter wall, and crosses the correlation curve

without thermophoresls at x/Rn«7.4 (Tw/Te =1). However, STAN5-w1th

thermophoresls responds to the change to a hotter wall further downstream at

x»8.2 and predicts lower deposition rates than STAN5 - without thermophoresls

from then on. We estimate the "lag" 1n the reaction of STAN5 to be about 9 to

10 local momentum BL thickness for the conditions Investigated here. For a

blowing rate distribution with more abrupt changes we can therefore expect

even larger local disparities between STAN5-pred1ct1ons and such correlations. However, 1n such cases (with sharp boundary condition variations)

1t should be recalled that the reliability of STAN5 results themselves becomes

questionable7. Considering the cost and accuracy features of both methods,

the comparisons shown 1n figure 7 suggest that local applications of our correlations will be satisfactory for most engineering design predictions on

transpiration-cooled objects.

CONCLUDING REMARKS

To examine the behavior and accuracy of our recently proposed

Stm/Stm ^-correlations of particle mass transport (ref. 6) when applied

locally'to developing GT-boundary layer situations, we have embarked on a

program of selected numerical computations and controlled laboratory

experiments (ref. 5). Progress 1n the former category 1s reported here, and

1n view of the widespread familiarity and use of the two-dimensional BL code

STAN5 (ref. 11 and 9) for GT heat transfer predictions, we have described

how STAN5 has been adapted for mass transfer (deposition) rate predictions for

cooled combustion turbine blades. Most Importantly, the program has been

modified to Include thermal (Soret) diffusion ("thermophoresls" for small

particles) 1n the suspended particle mass conservation equation. The

transport properties (I.e., Brownlan diffusion coefficient, thermal diffusion

factor) of small particles (considered simply as "heavy molecules") are

calculated allowing for their variation with temperature across the boundary

layer. The program dimensioning 1s Increased to accurately obtain the suspended particle concentration profile Inside the much "thinner" (cf., thermal

and momentum boundary layer thickness) mass transfer (Brownlan diffusion)

boundary layer for small particles (Sc » 1).

STAN5 predictions of mass transfer coefficients are then used to examine

the behavior and accuracy of correlations we recently developed to predict the

enhancement 1n deposition rates due to thermophoresls 1n the presence of

variable properties, transpiration cooling and/or viscous dissipation. These

correlations, which successfully described results for self-similar laminar

boundary layers, and law-of-the-wall turbulent boundary layers (ref. 6), are

here found to be quite satisfactory and very economical, when applied locally

to developing laminar and turbulent high Schmidt number mass transfer boundary

layers.

Whatever 1s projected for electronic computational capabilities, more

realistic system predictions/optimizations will Inevitably require subroutines

7See reference 18 for a comparison of STAN5 predictions with

experimental heat transfer around a gas film-cooled cylinder 1n cross-flow.
which economically Incorporate the results of prior BL Integrations. In

view of the complexity and the often prohibitive cost of running repetitive

PDE simulations for day-to-day engineering design calculations, the comparisons discussed here suggest that local application of our previous mass

transfer correlations (ref. 6) can cover typical cases of GT-1nterest with

acceptable accuracy.

REFERENCES

1. Gokog'lu, S. A. and Rosner, 0. E., "Thermophoretlcally-Augmented Forced

Convection Mass Transfer Rates to Solid Walls Across Non-Isothermal

Laminar Boundary Layers," AIAA Journal, (submitted, 1983).

2. Gokoglu, S. A. and Rosner, D. E., "Effect of Partlculate Thermophoresls

1n Reducing the Fouling Rate Advantages of Effusion-Cooling,"

International Journal of Heat and Fluid Flow, vol. 5, no. 1, Mar. 1984,

pp. 37-41,.

3. Gokoglu, S. A. and Rosner, D. E., "Thermophoretlcally Enhanced Mass

Transport Rates to Solid and Transpiration-Cooled Walls Across Turbulent

(Law-of-the-Wall) Boundary Layers," Industrial and Engineering Chemistry

-Fundamentals (1n press, 1984).

4. Gokog'lu, S. A. and Rosner, 0. E., "Viscous Dissipation Effects on

Thermophoretlcally-Augmented Particle Transport Across Laminar Boundary

Layers," International Journal of. Heat and Mass Transfer (1n press, 1984).

5. Rosner, D. E. and K1m, S. S., "Optical Experiments on Thermophoretlcally

Augmented Submlcron Particle Deposition from 'Dusty1 High Temperature Gas

Flows," Chemical Engineering Journal (Lausanne), vol. 28, (1n press,

1984).

6. Gokoglu, S. A. and Rosner, D. E. "Correlation of ThermophoretlcallyMod1f1ed Small Particle D1ffus1onal Deposition Rates In Forced Convection

Systems with Variable Properties, Transpiration Cooling and/or Viscous

Dissipation," International Journal of Heat and Mass Transfer vol. 27,

no. 5, 1984, pp. 639-645,.

7. Rosner, D. E., Gokog'lu, S. A. and Israel, R., "Rational Engineering

Correlations of D1ffus1onal and Inertlal Particle Deposition Behavior 1n

Non-Isothermal Forced Convection Environments," Fouling o_f Heat Exchange

Surfaces. Engineering Foundation, New York, 1983, pp. 235-256.

8. Cebed, T., Smith, A. M. 0., and Wang, L. C., "A Finite-Difference Method

for Calculating Compressible Laminar and Turbulent Boundary Layers, Part

I," Report No. DAC-67131, McDonnell-Douglas Co., Aircraft D1v., St.

Louis, MO, Mar., 1969.

9. Patankar, S. V. and Spaldlng, D. B., Heat and Mass Transfer 1n Boundary

Layers: A General Calculation Procedure. 2nd Ed., Intertext, London,

1970.

10. Mengutiirk, M. and Sverdrup, E. F., "A Theory for Fine Particle Deposition

1n Two-Dimensional Boundary Layer Flows and Application to Gas Turbines,"

Journal of Engineering for Power, vol. 104, no. 1, Jan. 1982, pp. 69-76.

11. Crawford, M. E. and Kays, W. M., "STAN5 — A Program for Numerical

Computation of Two-D1mens1onal Internal and External Boundary Layer

Flows," NASA CR-2742, 1976.

12. Rosner, D. E. and Fernandez de la Mora, J., "Small Particle Transport

Across Turbulent Nonlsothermal Boundary Layers," Journal of Engineering

for Power, vol. 104, no. 4, Oct. 1982, pp. 885-894.

13. Fernandez de la Mora, J., "Deterministic and Diffusive Mass Transfer

Mechanisms 1n the Capture of Vapors and Particles," Ph.D. Dissertation.

Yale University, 1980.

10
14. Gb'koglu, S. A., "Thermophoretlcally Enhanced Deposition of Participate

Matter Across Nonlsothermal Boundary Layers," Ph.D. Dissertation, Yale

University, 1982.

15. Haas, J. E. and Kofskey, M. G., "Cold-A1r Performance of a

l2.766-Cent1meter-T1p-D1ameter Axial-Flow Cooled Turbine II-Effect of A1r

Ejection on Turbine Performance," NASA TP-1018, 1977.

16. Gaugler, R. E., "Some Modifications to, and Operational Experiences with,

the Two-Dimensional, Finite-Difference, Boundary-Layer Code, STAN5," NASA

TM-81631, 1981 .

17. McCartln, B. J., "Applications of Exponential Splines 1n Computational

Fluid Dynamics," AIAA Journal, vol. 21, no. 8, Aug., 1983, pp. 1059-1065.

18. Stepka, F. S. and Gaugler, R. E., "Comparison of Predicted and

Experimental External Heat Transfer Around a Film Cooled Cylinder 1n

Crossflow," ASME Paper 83-GT-47, 1983.

11
00

y. v

2.5

2.0

1.5

i1. n0

Sc,, - 26

T W /T0 0=0.6

Tm = 1500 K

^INITIAL p<"=4atm

_ / POINT

~~ STAN 5

SELF-SIMILARITY (REF. 1)

CORRELATION

I 1 1 1 1 1 1 1 1

312345678 9

X/Rn

1

10

FIG. 1 Accuracy of STAN 5 [11] and correlations [6,7] in predicting

the thermophoretic enhancementof particulate mass transfer rates

when compared to self-similar laminar boundary layer calculations

[11 for a flat plate; Sc^* 26, TW/T00= 0.6.

3.0 i—

o

E"

</>

2.5

2.0

1.5

1.0

STAN 5

CORRELATION

Sc^ = 26

Tw/Tm = 0.6

TO T =1500K

p = 4 atm

WITH VISCOUS DISSIPATION

WITHOUT VISCOUS DISSIPATION-^

1 1

5

X/R

10

n

FIG. 2 Comparison of correlations [6,7] with STAN 5 [11] predictions

of mass transfer rate enhancement due to thermophoresis both with

and without viscous dissipation; GTstator [15], Sc^' 26, Tw/Tm= 0.6.
2.0

1.5

1.0

STAN 5

CORRELATION

I I I

Scro - 26

Tw/i.-as

TO T=1500K

p = 4atm

I I I

0 1 3 8 10

X/Rr

FIG. 3 Comparison of correlations [6,7] with STAN 5 [11] predictions

of mass transfer rate enhancement due tothermophoresis; GT stator

[15], Sc00=26, Tw/Tro=0.a

CO

3.0

2.5

2.0

1.5

1.0

STAN 5

CORRELATION

I I I I I I I I I

5

X/R

10

n

FIG. 4 Comparison of correlations [6,7] with STAN 5 [11] predictions

of mass transfer rate enhancement due tothermophoresis; GT stator

[15], Scro = 100, T/T r o - 0. a
3.0

2.5

2.Q

1.5

1.0

STAN 5

CORRELATION

0 1

TJTW

J

4 5

X/R

8 9 10

n

FIG. 5 Comparison of correlations [6,7] with STAN 5

[11] predictions of mass transfer rate enhancement

due to thermophoresis for a variable wall temperature, GTstator [15] (T^T. - 0.8—-0.5).

o

E

3.0

2.5

2.0

1.5

1.0

STAN 5

CORRELATION

ScOT • 26

TvA,=0.5

Tro - 1500 K

p » 20 atm

LAMINAR

I I I I I I

5

X /R

10

n

FIG. 6 Comparison of correlations [6,7] with STAN 5 [11] predictions

of mass transfer rate enhancement due to thermophoresis allowing

transition to turbulence; GT stator [151, Sc^ 26, nm° 0.5.
•t-*

LO

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.1

TRANSPIRATION COOLING

,— /rWTH THERMOPHORESIS

STAN 5

CORRELATION

\/

^-WITHOUT THERMOPHORESIS

COLD WALL-

• HOT WALL

•26

= 0.4

I I

p = 4 atm

I _| I

5

X/R

8 10

n

FIG. 7 Comparison of correlations [6,7] with STAN 5 [111 predictions

of mass transfer rate reductions in the presence of gas transpiration

cooling, both with and without thermophoresis; GT stator [15],

Sc =26, 0.4.
1. Report No.

NASA CR-168221

2. Government Accession No. 3 Recipient's Catalog No

4 Title and Subtitle

Comparisons of Rational Engineering Correlations of

Thermophoretically-Augmented Particle Mass Transfer

with STAN5-Predictions for Developing Boundary Layers

5 Report Date

January 1984

6 Performing Organization Code

7. Authors)

Suleyman A. Gb'kocflu and Daniel E. Rosner

8 Performing Organization Report No

None

10 Work Unit No

9. Performing Organization Name and Address

Analex Corporation and Yale University

21000 Brookpark Rd. Chemical Engineering Dept.

Cleveland, Ohio 44135 New Haven, Connecticut 06520

11 Contract or Grant No

NAS3-23293 and NAG3-201

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546

13 Type of Report and Period Covered

Contractor Report

14 Sponsoring Agency Code

533-04-1A (E-1991)

15. Supplementary Notes

Final report. Project Manager, Carl A. Stearns, Materials Division, NASA Lewis

Research Center, Cleveland, Ohio 44135. Prepared for the Twenty-ninth

International Gas Turbine Conference sponsored by the American Society of

Mechanical Engineers, Amsterdam, The Netherlands, June 3-7, 1984.

16. Abstract

Fouling (and corrosion) of gas turbine (GT) bladin g often results from the

deposition of material s derive d from inorgani c impuritie s in the fuel and/or

ingested air. When the depositing materia l is in the form of a submicro n

"aerosol" (dust or mist) it has been found that the rates^ of depositio n on

cooled surfaces can be augmented by some 100-1000-foTd vTa the mechanism of

thermophoresis (particle migratio n down a temperature gradient). For thi s

Feason, In earlier papers we reported the development of rational , yet simple ,

engineering correlations of thermophoretically-augmented particl e transport

across both lamina r boundary layers (LBLs) and turbulen t boundary layers

(TBLs). Whil e developed based on theoretical considerations , and numerica l

computations of self-simila r LBLs and 1aw-of-the-wal1 (Couette flow-like )

TBLs, these mass transfer coefficient (St- ) correlations, when applie d

locally, may also prove useful in makin g engineerin g mass transfer prediction s

for more complex geometries, includin g GT-blades. PeruTTng additiona l

controlled experiments, insigh t into the local applicabilit y of these

correlations can be gained by selected comparisons with numerical prediction s

for developin g BLs. This paper reports on our (a) modificatio n of the code

STArTS to properly includ e thermophoretic mass transport, and (b) examinatio n

of selected test cases developin g BLs whic h includ e variabl e properties,

viscous dissipation , transitio n to turbulenc e and transpiratio n cooling.

Under conditions representative of current and projected GT operation, loca l

applicatio n of our St /St - correlations evidentl y provide s accurate

a nd economical engineerin g flesign predictions, especiall y for suspended

particles characterized by Schmidt numbers outside of the heavy vapor range

(say, Sc>10).

17. Key Word* (Suggested by Autbort.*))

Deposition; Boundary layer; Thermophoresis; Corrosion; Mass transfer;

Gas turbine

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Unclassified

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Unclassified

STAR Category

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Unclassified

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