An airfoil design program and a boundary layer analysis were developed. Boundary conditions were derived for ventilated transonic wind tunnels and performing transonic windtunnel wall calculations. A computational procedure for rotational transonic flow in engine inlet throats was formulated. Results and conclusions are summarized

Murman, E. M.

English

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FLOW RESEARCH COMPANY
A DIVISION OF FLOW INDUSTRIES, INC.
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(NA3A-CR-152041)	 STUDY OF DESIGN AND
N77-30086
A NALYSIS MF.THCDS FOR TRANSONIC FLOW Final
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HEADQUARTERS
P.O. Box 5wJ, 21414 68 th Ave. S.
Kent, ISeattlel WA 98031 (206) 8541370
Seattle Ex. 6221500 TWX 9104472762
PRINCETON COM-711STION LABS
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Flow Research Note No. 118
Study of Design and Analysis Methods for
Transonic Flow
by
Earll M. Murman
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Final Report
Contract NAS2-8847
July 1977
Submitted to
NASA Ames Research Center
Moffett Field, California 94035
Flow Research Company
A Division of Flow Industries, Inc.
P.O. Box 5040
Kent, Washington 98031
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(206) 854-1370
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F' 	 Flow Research Vote No. 118
Study of Design and Analysis Methods for
Transonic Flow
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Earll .4. Muroran
Final Report
Contract :1AS2-8847
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	 July 1977
Submitted to
NASA An-es Research Center
Moffett Field, California 94033
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Flow Research Company
A Division of Flow Industries, Inc.
P.O. Box 3040
Kent, Washington 98031
(206) 854-1370
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Flow Research Note No. 118
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Study of Design and Analysis Methods for Transonic Flow*
by
Earll M. Murman
Flow Research Company, Kent, Washington 98031
Summary
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During "' , e contract period, three tasks were completed. Task I
consisted of developing an airfoil design program and incorporating a
boundary layer analysis. Task II involved deriving boundary conditions
for ventilated transonic wind tunnels and performing transonic wind-
tunnel wall calculations. Task III consisted of formulating a compu-
tational procedure for rotational transonic flow in engine inlet throats.
The work accomplished during the contract, including significant conclusions,
is summarized below by task.
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Flow Research Note No. 113 	 a.
July 1977
`? 7
1.	 Task I - Airfoil Design Program
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	 An integral boundary layer method including a laminar boundary
layer, transition, a turbulent boundary layer, and a first-order shock-
wave boundary-layer interaction model was coded and coupled to the two-
dimensional airfoil program TSFOIL. The boundary layer program is a
modified version of the one written by McNalley (1970), which is well
documented. A Nash-Hicks turbulent shear stress model was added to the r'
program to account for "history effects" in the turbulent boundary
layer. In addition, a shock-wave boundary-layer interaction model developed by
Reshotko and Tucker (1955) also was added to the turbulent boundary layer
code to account for the jump in displacement thickness through the shock.
Smoothing of the resulting discontinuity was required to yield a realistic
solution. Figure 1 shows a calculated boundary layer result. An empirical
extrapolation of the displacement surface is required at the trailing
edge. A copy of this computer program was delivered to the Project
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Technical Monitor, Mr. Ray Hicks.
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The above program was coupled to TSFOIL, and calculations were
done for an NACA 0012 airfoil. A viscous wedge model was used in the
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inviscid calculation to properly locate the shock wave. The formulation
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of this model and the computed examples were reported in the progress
report for the sixth quarter of the contract. Coupling of the entire
viscous-inviscid program to the optmization program COPES was formulated,
and the subroutines were written. Flow charts for the boundary layer
calculation and design program are shown in figures 2 and 3.
There are several tasks which could be done to extend the above
work. The first is to incorporate the trailing edge "boundary layer"
model of Melnik and Mead (1977) to avoid ad hoc smoothing of the boundary
layer in this region. The second cask is to cou p le the boundary layer
program to Jameson's full potential equation code for two-dimensional
airfoils by using the conservative finite-volume method. Some work was
done in the early stages of this contract to accom p lish this for FL06,
but this work was not completed. The third task is to run more cases
to be compared with experiment. The fourth task is to extend the entire
method to transonic flows involving heat transfer, such as for turbine
blades. The ba.ic McNalley program already contains the heat transfer
capability.
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Flow Research Note No. 118
July 1977
-5-
Considerable effort was devoted to examining improved methods of
parametrically representing the airfoil geometry for optimization cal-
culations. These methods were fully reported in progress reports. The
methods studied included cubic splines, polynomials, super ellipses,
modified trigonometric functions, and quadratic splines. The most suc-
cessful methods are ones that are defined, and are smooth and continuous
over the entire airfoil surface. A calculation performed with the cubic
spline method is shown in figure 4.
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Fluw Research Note No. 118
July 1977
-7-	 7
2.	 Task II - Wind-Tunnel Wall Interference Study
Far-field formulae were derived for a source, doublet and vortex in
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a ventilated transonic wind-tunnel with contoured walls. These formulae
may be used for upstream and downstream boundary conditions for finite-
difference calculations of transonic wind-tunnel wall interference. The
"derivation" of the equations and discussion of the results were reported 	 l
by Smithmeyer and Murman (1976).
The general homogeneous wind-tunnel wall boundary condition was 	 ^=
incorporated in the program TSFOIL, and several representative calcula-
tions were completed. Three finite-difference formulations were con-
sidered, and two were tested. The calculations converged for a low
value of porosity (P = .25) but failed to converge for higher values of
porosity.
A number of calculations were done to test the sensitivity of wind-
tunnel wall calculations to the upstream and downstream boundary conditions.
If the boundaries are located far from the airfoil, there is no signifi-
cant effect on the airfoil pressure distribution. This result has led
to the concept of modeling an actual test section by using ¢ y = 0 for
the upstream boundary condition located at the test section entrance,
andQx or
	
= 0 on the downstream boundary located at the test
section exit. Previous work had been directed at modeling tunnels
extending to infinity in the upstream and downstream directions. The
use of these simple upstream and downstream boundary conditions will
allow the use of more complicated forumlae in place of the classical
homogeneous tunnel wall bo •Aa	 _^^a4«;--- -- -.,a.,,	 e
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Flow Research Note No. 118
July 1977
-8-
3.	 Task III - Rotational Flows
Several fo • mulations for computing rotational inviscid transonic
flows were studied. Results showed that internal transonic flows with
subsonic exit boundary conditions are fundamentally different from
external transonic flows. For example, for one-dimensional converging-
diverging nozzle floors, it is well known that no isentropic solution
exists for a wide range of downstream boundary conditions. In contrast
to this, no such non-existence proofs are known for external flows. Thus,
internal transonic flow calculations require some fundamentally different
equations, difference algorithms and iteration procedures. These were
studied in the course of the work and have been written in report form.
The report by Rizk and Nurman (1977) will be distributed soon. A one-
dimensional calculation was completed and is shown in figure 5. This
model problem uses the ngmerical procedures that will be extended to
two-dimensional calculations under separate funding from NASA-Ames.
As part of the wo:-k of this task, the suitability of transonic
small-disturbance theory for internal flows was critically examined.
It was found that, because of the non-uniqu:ness of isentropic internal
flows under some conditions, the range of applicability of small-
disturbance theory to internal flows in solid wall channels is limited
to a small class of flows. It is believed that if the exit conditions are
subsonic, the usual small-disturbance theory may be restricted to con-
ditions where the embedded supersonic zones do not extend all the way
across the channel.
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Flow Research Note No. 118
July 1977
-10-
4.	 Other Related Activities
Three talks were presented as a direct result of work done on this
contract. They are:
Murman, E. M. "Review of Some Numeric Solutions of the Transonic Small-
Disturbance Equation," presented at Symposium Transsoniccum II,
Gottingen, Germany, September 1975.
Murman, E. M. "Calculations of the Transonic Small-Disturbance Equations,'
presented at the ONR Transonic Flow Conference, UCLA, March 1976.
Rizk, M. H. and Murman, E. M. "Rotational Transonic Flows in Ducts and
Nozzles," presented at the Third AIAA Computational Fluid Dynamics
Meeting, Albuquerque, New Mexico, June 1977.
Five visits were made to NASA Ames to work joiatly with the project
officer Ray Hicks and to execute computations on the Ames CDC 7600.
Flow Research Note No. 118
July 1977
-11-
References
McNalley, W. D. (1970) "FORTRAN Program for Calculating Compressible
Laminar and Turbulent Boundary Layers in Arbitrary Pressure
Gradients," NASA TN D-5681.
Melnik, R. E. and Mead, H. R. (1977) "Theory of Viscous Transonic Flow
Over Airfoils at High Reynolds Number," ALL Y. Paper 77-680, June.
..	 Reshotko, E. and Tucker, E. (1955) "Effect of a Discontinuity on
Turbulent Boundary Layer Thickness Parameters With Applications
to Shock Induced Separation," NACA IN 3454.
Rizk, M. and Murman, E. M. (1977) Transonic :Ion-Insentropic Internal
Flows, Flow Research note to be published.
Smithmeyer, M. G. and Murman, E. M. (1976) "Far-Field Boundary Conditions for
Airfoils in Transonic Wind Tunnels." Flow Research Report No. 78,
December.
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Study of design and analysis methods for transonic flow

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