AI AA-87-0294 A Wake Blockage Correction Method for Small Subsonic Wind Tunnels C. Q. Pass, General Dynamics Corp., Fort Worth, TX

AIM 25th Aerospace Sciences Meeting January 12-15, 19871Ren0, Nevada

For permission to copy or republish, contact the American Institute of Aeronautics and Aslmnautics 1633 Broadway, New York, NY 10019

A WAKE BLOCKAGE CORRECTION METHOD FOR SMALL SUBSONIC WIND TUNNELS

Clay Q. Pass* General Dvnamics/Fort worth Division

-Fort Worth. Texas

Abstract

A wake blockage correction method has been developed for use in small subsonic wind tunnels. Work on the method was initiated due to the extensive blockage effects encountered while testing prelim- inary design models in the General Dynamics 14 by 14 inch open circuit tunnel. A test program was conducted where base pressure data were measured on a series of non-lifting flat plates in order to confirm the theoretical basis of the method. Also, force and moment data were measured on a series of lifting wing plates and used in the development of empirical factors in the final correction equation. The resulting correction method incorporates the theoretical approach formulated by E. C. Maskell (Great Britain) but utilizes empirical terms adopted specifically for semispan tests of models with high blockage ratios. Results presented from tests of wings with block- age ratios up to 29 percent indicated the method will approximately double the range of blockage ratios where the Maskell method is considered valid. The method has shown to remain effective for a wide variety of wing planforms and demonstrates that reliable wake blockage corrections may be obtained by relatively simple and inexpensive means.

CL CL-a

2 kz, kc

Nomenclature

wing aspect ratio wing span parameters governing the shape of the required q-ratio curves cross-sectional area of wind tunnel test section mean aerodynamic chord uncorrected and corrected drag coefficient

u s profile, induced, and separation drag coefficients lift coefficient lift curve slope, & / 6 a pitching moment coefficient base pressure coefficient denotes a function of the parameters enclosed in the parenthesis uncorrected and corrected b y e pressure parameter, k =1-Cpb uncorrected and corrected dynamic pressure wing reference area

r-Engineer, Aeroanalyqfs Member AIAA

Copyright 0 American InslilYIe of A e r o n s u l i ~ ~ and AslrOnPUlics. h e . , 1987. All dghls resewed.

U velocity of the undisturbed stream

a angle of attack A denotes an increment due to

constraint wing leading- and trailing-edge sweep angles wake pockage factor, l/(kc -1)

A le, Ate

0

I. Introduction

Many small tunnels are in use throughout industry and academia and can be capable of obtaining results comparable of larger tunnels provided the proper wall boundary corrections are used. In partic- ular, the General Dynamics Aerodynamic Development Facility (ADF) tunnel has only a 14x14-inch cross section but is highly utilized in preliminary design studies Of advanced aircraft. Renewed interest in high angle of attack (40 to 90 degrees) aerodynamics has made the consideration of wall confinement essential even for much larger tunnels have been able to avoid large wall corrections by testing rela- tively small models at moderate angles of attack. This is not always possible in small tunnels where reduction in model size may lead to construction inaccuracy. For these cases, wall corrections are essential to obtaining "free-air" results.

the ADF tunnel often exceed 2 0 percent of the test section area. Testing these models at high angle of attack compounds an already significant blockage problem. Semispan testing is used so that the model scale may remain sufficiently large to help minimize construction inaccuracy. Cursory tests of several different Sizes of otherwise identical semispan models indicated that the wake blockage component of the wall correction method in use was inadequate for the test environment. consequently, the decision was made to explore how the correction method might be modified to better simulate free-air conditions.

Reference areas of models tested in

A significant portion of the effort was devoted to research of available wake blockage correction methods in order to determine what approach would be best suited to the ADF tunnel. Constraints used in the selection process were that the data acquisition equipment presently in use must be adaptable to the chosen method and the method must be relatively inexpensive to install and minimize data reduction time. The test environment of ADF is intended to provide quick visibil-

1

ity of results so that the engineer can adjust the model or test plan accordingly. This offers more freedom to apply spontan- eous design concepts than what is normallv possible in larger, more expensive to operate, tunnels.

obtaining sufficient test data to derive and evaluate a suitable wake blockage cor- rection method. The test articles were comprised of a parametric series of bluff and lifting flat plate configurations. The effort resulted in a correction method well suited to the ADF wind tunnel and other small tunnels where wall confinement effects may impose severe limitations on data reliability.

The remainder of the effort entailed

11. Background

Blockage effects are generally separ- vated into two categories. The first is called solid-body blockage and is assoc- iated with the restriction of flow in a test section by a streamlined body. This type blockage is of little consequence to the results of the present study due to its near absence when testing bluff bodies or lifting flat plate configurations. In contrast, the second category of blockage is referred to as wake blockage and is related to the flow restriction caused by the wake behind a body with separated flow. In both cases, the blockage causes local flow acceleration around the body and/or its wake. It is the flow velocity at the body that must be used during data reduction to obtain free-air results.

Figure 1 illustrates the effect of wake blockage. The amount of correction required is dependent on both the maximum cross-sectional area of the separation bubble and the location of the points of

Fig. 1 Illustration of Wake Blochage (Reproduced from Sketch 3 . 1 of R e f . 1)

flow separation. in drag accompanies flow separation, one can surmise that wake blockage can be related to the amount of separation drag present[l]. Sources differ on the amount of blockage that may be considered negligible. According to Lefebvre[21 the span of a straight wing should not exceed 7 5 % of the tunnel width and for swept wings, a blockage ratio (S/C) less than .os can usually be considered negligible. Other sources contend that blockage ratios greater than 1% cannot be considered negligible[l]. Much depends on the degree of accuracy required.

Since a marked increase

A principle common to many blockage correction methods is that of invariance under constraint. This principle states that the form of the pressure distribution over a body is independent of the amount of wall confinement imposed on the body[l]. It follows from this principle that the location on the body of the points of separation and the maximum cross-sectional area of the separation bubble are also invariant with constraint. These assumptions lead one to conclude that the effect of blockage is simply an effective increase in tunnel velocity. Review of available literature revealed that the principle of invariance under constraint may be considered valid for blockage ratios up to 15%[1].

v

111. Literature Search

Available methods were studied in depth in order to determine if any could fulfill the requirements of the ADF tunnel. Any particular method was judged according to whether it was, (1) applic- able within the desired range of blockage ratios, ( 2 ) valid for semispan testing, ( 3 ) simple to incorporate into the present data reduction system, ( 4 ) rapid during data reduction, and ( 5 ) inexpensive to install. Particular attention was given to the Maskell method, which was being used in the ADF tunnel, and the wall- pressure signature method, which repre- sents the latest technology available on wake blockage correction methods.

Wall-Pressure Signature Method

Many of the correction methods in use throughout industry are based on either simplified representation models or linear theory and have not kept pace with increasingly complex and demanding test conditions, such as the increased emphasis on high angle of attack aerodynamics for fighter aircraft[3]. The wall-pressure signature method is a fairly complex correction scheme but is reported to be applicable to geometrically complex con- figurations of blockage ratios up to 20 percent. However, it is a relatively new method with limited experimental data published in the literature that demon- strate its range of applicability. The method requires the measurement of static pressures along the tunnel walls which provide information about the shape of the wake behind a body with separated flow. Advantages of the method are that changes in seoaration oosition on the model and wake Geometry 'are automatically accounted Eor[l]. Hence, this method is applicable in the range where the assumption of invariance under constraint is no longer considered valid. Hackett, et a1.[4], give more insight to the use of the wall- pressure signature method with high angle of attack testing of three-dimensional models.

The wall-pressure signature method is based on representing the body and wake by J

2

source and sink distributions but, unlike other classical methods, it makes use of wall static pressures to solve for the required strengths. tunnel wall pressure survey is, the more detailed the representation of the model will become since more singularity points

v could be utilized. Anywhere from just a few pressure taps, for some simple shapes, to 30 taps or more for complex shapes may be required to evaluate the presence of a wake and body on the flow field. This requirement would vary depending on the particular model tested. Some reserva- tions exist concerning whether some shapes may be adequately modeled by a series of sources and sinks at all. Once the singu- larity strengths have been determined, an image method is used to calculate the interference flow field. Thus, instead of supplying the data correction method with a detailed description of model geometry and wake shape, these items can be re- solved from the static pressure measure- ments. The actual steps used to determine the correction parameters are not always straightforward. Hackett notes that the ability to determine the effect of the interference velocities on the model often depends on the availability of detailed aerodynamic data from the model.

correction parameters must be solved iteratively and require computations using about 3 seconds of computer time (CDC 1700) per data point. The entire pressure measurement and analysis task must be repeated for each angle of attack since the shape and size of the wake will vary

U with model attitude. Minimum instrumenta- tion requirements for the method consist of about two scanivalves, each with a capacity of 20 pressure taps or more. Realistically, an electronically scanned pressure module may be required instead, in order to provide sufficient accuracy and speed during data acquisition. During drag and pressure tests, sufficient infor- mation is provided by the measured data to apply the correction method. Additional data would be required to correct 6-degree of freedom balance data (forces and moments). For example, it may be required to isolate the loads on a particular model part, such as the horizontal tail, in order to adequately correct moment data. Pressure measurements on the model surface may be required to resolve problems related to adequate representation of the body by sources and sinks[3].

In the final assessment of the wall- pressure signature method, it was con- cluded by the author that the method was inappropriate for use in the ADF tunnel. The maior contributors to this decision

The more detailed the

The equations governing the blockage

< - -... were, (1) the greatly increased data acquisition and reduction time due to the additional data measurement requirements and the iterative nature of the correction method, ( 2 ) the lack of specific guide- lines on measurements required to adequately correct 5-component balance

v

data, and (3) the increased complexity and expense of the required data acquisition equipment.

Slotted or Adaptive Walls

One awwroach to reducincr wall con- finement is-to use adaptive funnel walls that will conform to the shape of the streamlines produced by the body and any wakes. Determining the wall contours re- quired is often very challenging. tive wall technology is well developed for two-dimensional testing, but consideration of an additional component of velocity gradient makes the three-dimensional prob- lem much more difficult. In both cases, measured wall data are used to determine the velocity gradients and calculate any required changes in the test section con- tour[4]. The complexity required for such a variable contour surface would be pro- hibitively expensive for a tunnel such as the ADF and, in comparison to the wall- pressure signature method, does not de- crease the reliance on measured wall data.

Adap-

An approach more applicable to ADF testing may be the use of porous walls in the test section. Since blockage correc- tions for open and closed test sections are known to be opposite in sign, one can minimize the effects of blockage by using porous tunnel walls[3]. Disadvantages of such a system include determining the amount of porosity required for the par- ticular model tested since it would be a function of wake geometry and blockage ratio. Provisions must be made to either vary the porosity or detect and correct any residual wall confinement effects.

boundary conditions has not been elimi- nated with either the porous or adaptive wall system and the mechanical complexity would be greatly increased, these systems would not be recommended for use in the ADF tunnel.

Semi-Empirical Methods

Since the requirement to measure wall

Pietzman describes in his report how a blockage correction method was needed in the Northrop 7x10-foot low-speed tunnel for high angle of attack testing[5]. Using two YF-17 models of different scale, Pietzman found through data analysis that he could empirically modify his correction method until the data from the two models agreed with one another. The use of dif- ferent sized models to "back-out" required corrections is typical of the approach used in empirical methods. The implied assumption is that the smaller model has negligible blockage. This assumption may or may not be valid depending on the blockage ratio, wake geometry, and other characteristics of the smaller model.

tion methods of this type is that the method may only apply to the particular model and tunnel that were utilized[ll.

Another apparent drawback to correc-

3

In addition, much experimental data on many different configurations may be re- quired to obtain a generalized correction method. While this may prove to be expen- sive and time consuming, testing of this type is normally required to confirm the validity of any blockage correction method whether theoretical or empirical[l]. De- spite some disadvantages, good results aDneat to be attainable and the simule ~ ~ . ~ _ ~

approach and application meet the objec- tives for the ADF tunnel.

Free-Streamline Methods

The free-streamline method was first proposed by Fackrell[6] who chose to represent the confined flow by the use of an image system. The method is not lim- ited to the assumption by some other methods that blockage is related to a simple increase in dynamic pressure. assumption that is required is that the bodies to be modeled have slope discontin- uities only at the stagnation point and at or behind the point of flow separation[6]. This may not be too severe a restriction for most aerodynamic shapes of interest.

The body is modeled by a continuous distribution of vorticity and the wake by sources located on the vortex sheet. The induced wall effects are represented by an image system of these vortices and sources and the assumption of zero total vorticity is applied. A further requirement is that the velocities at the pre-determined sep- aration locations be specified. The largest disadvantage of this method is the need to have base pressure and separation locations known for the model tested. For a lifting wing, these parameters would change with angle of attack, thereby pre- venting their measurement by any simple means.

One

Assuming that the measurement prob- lems can be overcome, the average run time that would be required for a solution at each angle of attack is about 10 seconds on a cDC 6400 computer[6]. that ADF calculations are done with a desktop computer, this requirement along with the previously discussed measurement problems would prevent the efficient use of the free-streamline method in the ADF tunnel.

Momentum Balance Methods

al. have shown that the wake behind a bluff body approaches an axisymmetric shape at some downstream distance despite wide variations of the bluff body geome- try[7]. He performed extensive investiga- tions of the shape and formation of wakes by measuring wake pressure and velocity profiles. These investigations provide the basis for many simplified wake block- age correction schemes of which the Maskell method is included.

Recognizing

Experimental observations by Fail, et

BY utilizing the empirical observa- tions of Fail, a much simplified model of

bluff body flow was proposed by Maskell and is shown in Figure 2[81. The free- stream velocity is U and accelerates to ku

Fig. 2 Maskell's Model of B l u f f Body Flow

at the maximum cross-sectional area of the flow separation bubble. Using the assump- tion of an axisymmetric wake at the down- stream plane and neglecting some higher order terms, Maskell was able to show that the momentum equation governing the flow reduced to a much simplified form. A further empirical equation, relating to distortion of the wake under constraint, was used to obtain the final form of the correction equation. This equation, given below, simply relates the change in tunnel dynamic pressure to the drag due to flow separation, the blockage ratio, and a base pressure parameter (kc2).

An assumption used throughout the derivation is that the separation location of any given body and wake system is not affected by the degree of wall confine-

confinement had little effect on wake shape for a sphere with a blockage ratio of 13.7% and results given by Modi and El Sherbiny[B] indicate little change in separation location for circular cylinders with blockage ratios up to 36%. bodies that are less rounded than a cir- cular o linder or sphere, it can be expectei that separation location will be even lass affected by confinement. This assumption appears to be reasonable for most shapes of interest. For a wing at fixed anole of attack. one would exwect

ment. It was noted by Hackett[4], that v

For

the effect of-wall confinement on separ- ation location to be small.

Other authors have suggested that the Maskell method requires modification to make it more applicable to data from models of high blockage ratio. A method given by Lefebvre[2] differs from Maskell's by the addition of a term that only bECOmeS significant for high blockage ratios. His equation is given as,

L.3. ; CDS S I C 2 q k, - I (I-S/C)

The effect of the squared term in the denominator would be of special interest for ADF testing. Krishnaswamy, et al. have also proposed a slight variation of the Maskell correction method [IO]. Their report suggests that the basic formula should be dependent on model location in v

the tunnel in addition to the other parameters. For the specific case of semispan testing their correction reduces to

V Most sources agree that the basic Maskell method can be considered valid for block- aae ratios uu to about 10%. but it is e;idenr. that'some modificaiion of his equation will be required before its use in the ADF tunnel.

A problem associated with the Maskell method concerns determining values for the different components that makeup his equa- tion, in particular the base pressure parameter. Maskell eliminated the cumber- some problem of having to measure base pressure for each model tested by the sub- stitution of an empiricaJly derived block- age factor ( @ ) for l/(kc -1). This block- age factor was proposed to be a function of aspect ratio, but for most wings r3 = 512 was thought to be sufficient. remaining complication is the ability to accurately isolate the component of drag due to flow separation from the total measured dragtll].

Maskell suggests calculating the separation Brag component by plotting CL versus C and extrapolating the linear region oP the curve as shown in Figure 3 .

The

CD Fig. 3 Graphical Method of Separating TO^

Drag Into Its Components Complications arise when a configuration has significant flow separation even at low angle9 of attack. entire C versus C curve would be non- linear, tireventing ehe accurate calcula- tion of separation drag. Configurations that would present this type of problem are those with high-lift devices, spoilers, jets, etc. For these cases, Maskell suggests as an approximation to first test the clean model (no flap de- flections, etc.) to establish the linear region and then use the difference between this level and the total drag of the full configuration to obtain the separation

For these cases th0

- drag component.

It was concluded by the author that the Maskell-type approach held the most promise of obtaining corrections suitable for the typical configuration tested in the ADF tunnel. Several suggestions pro- vided in the literature offer the possi- bility that the Maskell method can be slightly modified to give improved results for semispan testing and high blockage ratios.

Iv. Experimental Method and Results

A test plan was chosen in order to provide data both to explore why the Maskell method was inadequate for high blockage ratios and formulate a new method if necessary. while reviewing the liter- ature it was found that the Maskell method, as well as other methods, were based on rather limited test data where little attempt was made to explore para- metric effects of either body geometry or blockage ratio. In order to derive a correction method suitable for a wide range of geometries and blockage ratios it was necessary to conduct extensive tests using a large matrix of flat plate configurations.

configured to provide data with which to confirm the basic principles Maskell used in the derivation of his method. A series of 2 7 rectangular and triangular flat plates (shown in Figure 4 ) were tested as

The first phase of testing was

Fig. 4 Test Matrix of Non-lifting Flat Plates bluff bodies (90 degrees to the flow) in order to evaluate his assumption of invariance under constraint and his find- ings regarding the relations of base pressure and separation drag with blockage ratio and plate geometry. The second phase of testing involved obtaining data for a series of 4 3 lifting flat plate wings (shown in Figure 5) at up to 60 degree. angle of attack. Them data were intended to be used to evaluate the effectiveness of any data correction method that may have resulted from the first phase of testing and to determine if correction methods suitable at low angles of attack were also sufficient at high angles of attack.

Evaluation of the Non-Lifting Data

normal to the flow) provides a means of isolating the component of drag due to flow separation and also provides for reliable base pressure measurement. In these cases the measured drag is Cus. All tests were conducted in the ADF tunnel, which has an average velocity of about 165 fps and a corresponding Reynolds number of approximately 1 million per foot. loss through the diffuser screens of the open circuit tunnel was assumed to be negligible. Consequently, the total pressure in the tunnel is equal to atmos- pheric and the dynamic pressure may be measured by use of a static orifice at the entrance of the test section.

The testing of bluff bodies (plates

Energy

Drag and base pressure were measured for each plate where great emphasis was placed on obtaining accurate data. drag points were taken for each plate and averaged to obtain the final value. Following the drag measurements, an average of 15 base pressure taps were distributed over the downstream side of each plate in an attempt to account for pressure differentials at the plate edges and the interference of the tunnel floor. Data from these taps were weighted and averaged to obtain a single value of base pressure for each plate.

of invariance under constraint and equation (I), one must show that both cp b and Cus are linearZfunctions of CD (S/C) . 19 addition, CDS/k must be constaat with k . Fiaures 6 and 7 comnare results

Twenty

In order to validate the assumption

obtainei in the ADF tunnel with values given by Maskell. The Maskell data represent results for square plates from 1.5 to 5.6 percent blockage ratio mounted in the tunnel center. It is evident that the ADF data, taken for up to 2 0 percent blockage ratio, represent a much wider range of flow conditions. Although there is some data scatter, the ADF data appears to retain linear characteristics. Examin- ing the data more closely, one also finds a significant aspect ratio effect for the rectangular plates that is absent for the triangular plates. From these plots it

CDs(S/C) lrig. 6 Drag and Base Pressure as a Function

of the Wake Blockage Parameter

0 WSKELL DATA FOR SWARE PLATES

0 ADF DATA FOR RECTANGULAR PLATES

2 k

Fig. 7 CDs/k2 as a Function of k2 was concluded that the basic principles upon which Maskell developed his correction method were still valid for higher blockage ratios but needed to be more dependent on model geometry and proximity to the tunnel wall.

Analysis of the non-lifting data continued by determining the blockage factor ( G ) for each plate by solving Maskell's transcendental equation for k, and substituting into the equation for 0 as shown below,

f ( k c 2 ) = 1 + & c - 2 4 S k2 ( 4 )

0 = l / ( k c 2 - l ) ( 5 ) For several of the plates, no solution could be found for equation ( 4 ) and as an approximation a minimum value was used

V

LJ

W

W

W

v-

instead of the true zero. Blockage factor is plotted versus aspect ratio in Figure 8 for the rectangular plates and compared to values recommended by Maskell[8,12]. The data show the same trend with aspect ratio as the Maskell values but it is evident that the data are appreciably affected by blockage ratio. For increasingly higher blockage ratio, the blockage factor

A s p e c t R a t i o ( A R )

with Values Given by Maskell Fig. 8 Comparison of ADF Blockage Factors

becomes smaller. This plot gives the first evidence that Maskell's blockage factor, should be a function of S/C as well as aspect ratio.

TO investigate the effects of semi- span testing, the data were compared to Values given by Krishnaswamy, et al. for plates adjacent to the tunnel wall[lO]. Fisure 9 aives this comnarison in a nlot . ~ - ~ ~

~~~ ~ ~~ ~ ~~~~~ ~ ~~ ~~~ ~~

of-CDS/ (kr-l) versus S4C. Krishnaswamy has stated that CoS/(k -1) 9hould be invariant (instead of Cnc/k )for semispan models. the ADF data and aaain the nrinciDle

This is clearlynot the case ;ith

reason appears to 6e the hish blockage ratios.

s/c Fig. 9 ComParlson of ADF and Krishnaswamy Data

for Plates Adjacent t o the Tunnel Wall

The results given in this section appear to contradict what is known from experience about the effects of high blockage ratio. Normally as the blockage ratio is increased, a greater amount of correction is needed to simulate free-air

conditions. This will be proven in the next section. If Maskell's blockaae factor decreases with increasing biockage ratio, then his basic equation must require an additional term or terms that would increase the total correction with blockage ratio. It can not be resolved at this point what those terms should be.

Evaluation of the Lifting Wing Data

A total of 4 3 lifting wing plates were tested as semispan models where 5-component balance data were obtained that included all forces and moments except side force. The wings were part of a parametric matrix where each was constructed of several different sizes ranaina from 7 to 29 uercent blockaae ratio ;Figure 5 ) . uncorrected results that are typical of all the configurations tested.

Figures 10 t o 122show

Fig. 10 Uncorrected L i f t and Moment Curves f o r the 45 Degree Delta Wings

Fie. 1 1 Uncorrected Drag Polars for the 05 Degree Delta Wings

The basic Maskell method was first applied to the uncorrected data in order to evaluate the corrections being used at the time in the ADF tunnel. Good correla- tion was seen for the S/C=.15 data uu to

F i g . 12 Uncorrected High Angle of Attack i lrag Polars fo r the 45 Degree Delta Wings

The uncorrected data shows trends typical of increasing blockage ratio. As the blockage ratio increased, lift-curve slope and maximum attainable lift prior to wing stall (CL ) increased accordingly. For some of thZa?arger wings, the lift for points beyond QmaX continued to increase with angle of attack. The pitching moment curves tended to have a negative shift for points beyond CL , but up until this point remained r88gtively unaffected by blockage ratio. When examining the drag polars at constant a , it was found that both the drag and lift increased with blockage ratio resulting in an improved polar shape. one can easily see how blockage ratio can have a tremendous effect on the measured aerodynamic data. The data obtained from this phase of testing played a crucial role in establishing the form of the final wake blockage correction method.

V. Correlation of the Selected Method

Many different correction methods were investigated by application to the uncorrected lifting wing data. The decision was made to evaluate their performance by their effect on lift curves. This was done because it was felt that the lift was the most accurately measured component of the data (due to low balance loads) and is most often utilized in the preliminary design studies under- taken in the ADF tunnel. The ideal correction method, assuming zero data scatter, would cause all the curves from different sizes of the same wing to collapse onto one line. This curve would then be representative of unconfined flow. Correlation of the pitching moment curves and the drag polars was also highly desired, but played a secondary role in the selection process. It was acceptable that the correction applied to the remaining forces and moments merely "f&ll-out" of the correction applied to the lift curve.

CL begs# to appear. . 2 2 and . 29 , discrepancies were evident

but beyond this point discrepakies

W For the wings with S/C =

for points below CL as well. For the 2 2 % wings the diffep8fice in CL compared to the 7% wings was approximatg89 5 % . This difference increased to about 12% for the 29% wings. Since models normally tested in the ADF tunnel usually range from 20% to 30% blockage ratio, this represents an undesirable inaccuracy in

and c -a prediction. Points beyond ELLmax showek even greater percent differ- en?% which would adversely affect high angle of attack studies. It was also noted, when comparing corrected to uncor- rected data, that the Maskell method had negligible effect below C . This leads one to conclude that the k@#ell method is best suited for wings with fully separated flow and bluff bodies. A more general correction method is needed that will apply to the entire range of angles of attack.

A short investigation of replacing the empirically derived 5 / 2 , used by Maskell for 0 , with other constant block- age factors was completed with little improvement in the results. Blockage factors that gave good correlation at high a ' s tended to over correct the data at low a ' s . It was concluded that any suitable correction method would require at minimum a blockage factor that varied with angle of attack. An attempt was made to use the " base pressure data obtained in the first phase of testing as a function of separ- ation drag (i.e. angle of attack) in calculating the required blockage factors: however, it was already noted from Figure 8 that this would result in a lower value of 0 . An application of these data con- firmed that the resulting correction was indeed too low at all angles of attack.

Consideration was next given to modifications of the Maskell method that were suggested by Lefebvre and Krishnaswamy. The Lefebvre method, given bv Emation ( 2 1 , resulted in ureatlv over c&r&ted data' for points beyond with little effect on points below Fax The method of Krishnaswamy (Equationpgrj gave results similar to the Maskell method. It was concluded that all these methods were best suited for Strictly bluff body type flow and not for data from the entire range of a ' s .

At this point, correction methods suggested in the literature were abandoned in favor of an empirically derived correction method. If one assumes that the smallest (7%) wing has negligible blockaue. as is suuaested bv Ref. 3. then one ma? calculate f6e change in q rkquired at each angle of attack for the lift of each wing to exactly match that of the 7% W

wing. If the required q-ratio is plotted versus Maskell's blockage parameter, CuS ( S / C ) , then the validity of his equation, where Aq/q is a linear function of c D , ( S / c ) , may be investigated. This was done in Figure 13 for the 45 degree delta wings. by Maskell's equation.

A l s o shown is the line given The slopes of the

0 .00 0 . 0 4 0 .08 0.12 0.16 0.20 0.24 0 . 2 8 0 . 3 2 0.36 0 . 4 0 CDs ( S I C )

Fig. 13 Required q-ratios for the 45 Degree Delta W n g s

linear portions of these curves correspond to 13, the blockage factor. The results are typical of those obtained for the remain- ing wings. There are three important characteristics to be observed concerning the curves shown. First, for low values of the blockage parameter, the required o-ratio is aooroximatelv constant but of ciifferent vaGes depending on blockage ratio. This implies that at low a the correction required is more a function of plate geometry and blockage ratio than separation drag. Second there is a distinct transition oeriod between low and high a's during whic; C however, the transitionip)@nts do not appear to be explicitly related to the

is reached:

stall point. this region is much greater than the 5 / 2 used by Maskell and is actually closer to 4 times that amount. The third character- istic of the curves begins to appear when the wing more closely resembles a bluff body (i.e. totally separated flow). In this region the required q-ratios begin to approach a linear function of CD (S/C) with slopes about 2/3 of the Masijell value. The lower value of blockage factor in this third region is well supported by the base pressure data obtained during the first phase of testing (Figure 8 ) . If one extrapolates these linear regions, it is easily seen that the intercepts are not zero as is suggested by the Maskell equation. However, from the trends shown with blockage ratio, one might expect data from a wing with much lower blockage ratio to begin to approach the characteristics of the line given by Maskell.

q-ratio versus C D (S/C) that an additional term is required fn the Maskell equation

The slope of the curve in

One can conclude from the plots of

v

that, along with 0, must be a function of both blockage ratio and wing geometry. help correlate an empirical approach to the desired correction method, plots were made of the characteristics of the required q-ratio curves using the nomenclature established in Figure 14.

To

b l u f f body reglon

r s g l o n I I 1 I

CDs ( S / C )

Fig . 14 Notation Used t o Describe q - r a t i o Curves

These plots are shown in Figures 15 to 17. The intercepts for the low-a region were divided into groups which differentiated between sweep and tapered or delta wing planforms. The rationale behind this was that of low a's the onset of separation and the formation of vortex flow is known to be sensitive to these planform parameters. Wings of low sweep tend to have more two-dimensional flow whereas highly swept wings (greater than 6 0 degrees) tend to have vortex dominated flow. Physically what occurs is that for wings with AleM.0 the wake (vortex wake in this case) decreases in size with increasing sweep angle resulting in less confinement of the flow and less required correction (b ) . The oppositg is true of wings with sw8ep less than 60 the wake originates from a different source. Once the region of massive flow separation has been reached, the effect of sweep becomes negligible and it is only important to differentiate between tapered and delta wings. This latter observation is well supported by data obtained during the base pressure tests of rectangular and triangui -Lr plates.

the q-ratio curves is to establish where the transition boundaries occur. These boundaries are probably defined by the first occurrence of rapid movement of the wing's separation location with a and the ensuing deterioration to fully separated flow. Since it is difficult to obtain data on separation location without pressure or flow visualization data, an attempt was made to relate the transition boundaries to the amount of separation

although

The final item in the correlation of

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s /c F i g . 15 m 8 5 a runction of S i c f o r a l l W1ni:~,

drag present. When this was done it was found that there was no apparent relation between the amount of separation drag present at the boundaries and wing geomet- ry or blockage ratio. This resulted in the use of average values of CD for these boundaries. wing was considered in the low-a region until CDs = .049, in the transition region until Cu = .193, and in the bluff body region wilen CD~>. 193.

To obtain the final correction method, linear approximations with S/C and AR were made for the curves of Figures 15 to 17 and resulted in the procedure and equations given below.

Defined in this maher, a

2 Calculate C D ~ from the plot of CL versus Ci)

If CD < .049 then apply low-a corregtion, delta wings,Ale<60: b = .709S/C-.055AR + .ll8 d?lta wings, hle>60: b = .857S/C + .17OAR - .362 f8r tapered wings: b = (2.720 - .934AR)S/C + -073- - .902 AWq = bo

If CD > .193 then apply high-a corregtion, delta wings: bl = (-.294AR + 2.462)S/C +

.009AR - .208 . . ~ ~ ~~~

tapered wings: bl=(-l.OSSAR + 4.029)S/C +

.114AR - .406

s /c F i g . 16 The Effect of Wing Sweep and

T a ~ e r Ratio OD b,.

all wings: m = 1.547s/c + .318AR + .125 Aq/q = mCDi S/C + b l

( 4 ) If .049 < cD < .193 then apply a linear variation of A q / q with cos(S/C) from the last point of (2) to the first point of ( 3 ) as shown in Figure 14.

Using the above method, corrected data were obtained for the set of delta 45 wings and are shown in Figures 18 to 20. Discrepancies still exist but are accept- able considering that the method is based on a series of linear approximations to the required q-ratio curves which show considerable non-linearity. One will note that discrepancies at zero lift are un- accounted for by the chosen method since there would be a near absence of wake

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Fig. 19 Corrected Drag Polars for the 45 Degree Delta Wings

F i g . 17 1,1 as a Function of S I C f o r A l l Wings

F ig . 18 Corrected L i f t and Moment Curves f o r

formation and hence wake blockage correc- tion at those conditions. These zero lift discrepancies have been attributed to model construction and data measurement inaccuracies. Overall, the results were highly satisfactory when the correction was applied to the remaining wings even for blockage ratios up to 29%.

the 45 Degree Delta Wings

VI. Conclusions

A thorough investigation of litera- ture relating to available wake blockage correction methods was completed and it was determined that none adequately cor- rected data at high blockage ratios and were simple enough to use in the ADF - tunnel. However, the approach used by

Fig. 20 Corrected High Angle o f Attack Drag Polars fo r t h e 45 Degree Delta Wings

Maskell was selected for use because of its relative simplicity in both derivation and application. Several attempts were made to modify the Maskell equation by using the alternate equations suggested by Xrishnaswamy and Lefebvre, but these proved inadequate for use in the ADF tunnel. An empirical alteration of the Maskell approach was finally selected for use that was suitable for the range of wing planforms and blockage ratios tested. The selected method, developed specific- ally for semispan testing, shows great improvement over Maskell's original formu- lation and has demonstrated the capability to correct data from tests of models with approximately double the blockage ratio where the Maskell method is generally regarded as reliable. The selected method is simple to apply and readily adaptable to the data reduction equipment presently in use in the ADF tunnel and has shown to be of speed comparable to the original Maskell correction scheme.

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In order to apply the selected cor- rection equations to other low-speed tunnels, it is suggested that an abbrevi- ated test of several wings of different blockage ratios be performed and the data corrected to confirm the method's validity in other test facilities. Regardless of the outcome, the general empirical approach that was used should be applic- able to all low-speed tunnels where wings of high blockage ratios are commonly tested.

References

1.

2.

3 .

4.

5.

6.

7.

8.

9.

ESDU, "Blockage Corrections for Bluff Bodies in Confined Flows," Item No. 80024, Engineering Sciences Data Unit, London, NOV. 1980. Lefebvre, A.H., "A Method of Predicting the Aerodynamic Blockage of Bluff Bodies in a Ducted Airstream," COA. Rep. Aero NO. 188, College of Aeronautics, Cranfield. UK. NOV. 1965. Maarsingh; R.A., lVA Review of Research at NLR on Wind-Tunnel Corrections for High Angle of Attack Models," AGARD-R-692, Feb. 1981. Hackett, J.E., Wilsden, D.J., Stevens, W.A., "A Review of the 'Wall Pressure Signature' and Other Tunnel Contraint Correction Methods for High Angle-of- Attack Tests," AGARD-R-692, Feb. 1981. Pietzman, F.W., "Determination of High Attitude Wall Corrections in a Low Speed Tunnel," AIAA Paper No. 78-810, Apr. 1978. Fackrell, J.E., "Blockage Effects on Two-Dimensional Bluff Body Flow," Aeronaut. Quat., Vol. 26, Pt.4, pp. 243-253, Nov. 1975. Fail, R; , Lawford, J.A., Eyre, R. C. W., "Low-Speed Experiments on the Wake Characteristics of Flat Plates Normal to an Air stream," A.R.C. R.&M. 3120, Jun. 1957. Maskell, E.C., "A Theory of the Blockage Effects on Bluff Bodies and Stalled Wings in a closed Wind Tunnel," A.R.C. R.&M. 3400, Nov. 1963. Modi, V.J., El Sherbiny, S., "Effect of Wall Confinement on Aerodynamics of Stationary Circular Cylinders," Third International Conference on Wind Effects on Buildings and Structures, Vol. 1, Pt. 7 . 1971. - , - - . -.

l o . Krishnaswamy, T.N., Rao, G.N.V., Reddy, X.R., "Blockage Corrections for Large Bluff Bodies near a Wall in a Closed Jet Wind Tunnel," Journal of Aircraft, Vol. 10, No. 10, Oct. 1973.

ation of Low Speed Wake Blockage Corrections via Tunnel Wall Static

11. Hackett, J.E., Wilsden, D.J., "Determin-

Pressure Measurements," AGARD-CP-174, OCt. 1975.

12. Garner, H.C.,Rogers, E.W.E., Acum, W.E.A., Maskell, E.C., "Subsonic Wind Tunnel Wall corrections," AGARDograph 109, Oct. 1966.

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