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PREDICTION OF THE PRESSURE LOSS COEFFICIENT OF WIND T U N N E L TURBULENCE REDUCING SCREENS

Samer Aljabari* Arizona State University, Tempe, Arizona

CT

Various studies have shown that screens can b e used very cffectivcly as turbulence rcducing devices for wind tunnel applications. Analysis o f data oblained from various sources in addition to data generatcd by an experiment that was conducted a t the Technology Wind Tunnel a t Arizona State Universily has been completed. A mathematical model for predicting the pressure loss coefficient (K) of a screen was derived based on the work of Davis, Strouhal and Von Karman. The results arc valid for single and multiple screens with solidities greater than 0.2 and less than 0.6 a t wire Reynolds numbers below 600. When comparing the derived mathematical model results against the measured and collected data, the average error was 0.1% and the standard deviation was 13%. One percent error in thc prediction of the coefficicnt of pressure loss (K) will result only in 0.25% to 0.3% error in the prediction of the turbulcnce reduction factor.

Screen mesh spacing (distance between the centers of neighboring wires in inches) Number of screens Static pressure upstream of the screen Static pressure downstream of the screen Free stream Reynolds Number Screen wire Reynolds number Critical screen wire Reynolds number Solidity (closed area / total area) Strouhal number Temperature in degrees Fehrenhcit Time interval of vortex passage (sec) Entry turbulence (%) Screen generatcd turbulence (%) Velocity of vortex moving downstream Free stream velocity Distance downstream from a screen (in) Porosity (open areabotal area) Density

Introduction

Constant for calculating drag dependent on Reynolds number Drag coefficient Wire diamcter (in) Voltage (volts) Turbulence reduction factor Cross flow vortex spacing Pressure loss coefficient Measured pressure loss coefficient Pressure loss coefficient dependent on screen solidity Predicted pressure loss coefficient Average error in estimating K against K, Pressure loss coefficient after correction for solidity Pressure loss coefficient dependcnt on wire Reynolds number Longitudinal vortex spacing

'Graduate Student. A I M Member Copyriglit@1992 by the American Institute of Aeronautics and Astronautics, lnc. All rights reserved

Since the turbulence reduction capability of a screcn depends on the pressure drop across it, the pressure loss coefficient (K) of the screen must be evaluated in order to evaluate its turbulence reduction factor. The pressure loss coefficient (K) can be measured experimentally or predicted mathematically. The main objective of this paHxr is to develop a mathematical model that would enable users to accurately predict the pressure loss coefficient of single screens. Once the pressure loss coefficient is predicted, the turbulence reduction factor can b e evaluated. Among the first to recognize the effectiveness of screens as velocity uniformity controlling devices was Prandtl'. Researchers including Dryden2, Schubauer3 et. al, Tan- Atichat4 et . al. and others have attempted to predict screen performance with varying success. In general, they all agree that the turbulence reduction performance of a screen is dependent o n the pressure loss coefficient of the screen which is clearly related to the geometry of the screen. T h e prediction techniques developed by these researchers were useful in illustrating the principles. T h e main proplcm with those techniques was that they would have large errors when compared with actual measured

1

In 1981, a research team led by Derbunovichs published a paper o n single screens in which a n important relationship between the screen's generated turbulence and upstream turbulence was presented. In that paper, a mathematical model was derived that enables users to predict the turbulence reduction factor for a single screen provided that the pressure loss coefficient is known. T h e predictions agreed with experimental data to within 10%.

Since most wind tunnels use multiple screens, a study conducted by Salmirs and Herrick6 verified that Derbunovich's prediction techniques were not only valid for a single screen but can also be used o n multiple screen systems if the pressure loss coefficient (K) of each screen was measured.

A literature search was conducted to study the previous work and techniques developed by various scholars. Then, an experiment was dcsigned to obtain sufficient data that could be compared with the prcvious work. A test box was designed and built to measure pressure loss coeflicient (K) of three different scrcens with dillerent physical properties over a range of Reynolds numbers. The wire Reynolds number, R,, based o n the flow velocity through the wire grid and wire diameter, was used. That Reynolds number is considered more representative of the local flow around the screen wires and is more directly related to drag. Tests were performed below, near and above critical Reynolds numbers. T h e critical Reynolds number was defined by DerbunovichS as the Reynolds number, R,, beyond which the screen generated turbulence lcvcl downstream of the screen became constant. Tha t critical Reynolds number, R,,,, is approximatcly 175.

Both stat ic and total head pressure measurements were taken in front of the test screcn and a t various locations behind the screen. Based on the data collected, a value of the pressure loss coeflicientwas calculated and compared to data obtained from other references. Screens were also tested in pairs below, near and above critical Reynolds numbers based o n the front screen characteristics. Data were analyzed in the same fashion as single screens.

An analysis of the collected data was conducted and related to the work of Davis7, Von KarmanR and Strouhal"(pg. 31). Two mathematical models wcre derived. T h e first model, based on Davis' work, could be used to evaluate K based o n the geometrical properties of the screen. T h e second model, based o n Von Karman's inviscid cylinder drag analysis and Strouhal vortex frequency, could be used to evaluate K based on the R, effect.

experimental and analytical investigations to better understand the behavior of wind tunnel turbulence screens. All researchers since Prandtl (1933) have concluded that the capability of a screen in reducing turbulence is related to the pressure loss across it. To predict the turbulence reduction factor of a screen, the energy loss, represented in terms of static pressure loss across the screen must be evaluated. This energy loss may be represented as a pressure loss coefficient (K) using the equation:

ps, - ps2 K= Z P v 2

where P,, and PS2 a re the static pressures measured upstream and downstream, respectively, from the screen. The pressure loss coefficient (K) was used by the various researchers to predict the turbulence reduction factor of a screen.

Prandtl' was among the first to recognize that screens can be used to obtain a uniform velocity profile. This is a consequence of the fact that the higher upstream velocities will encounter higher resistance when passing through the screen. T h e resulting downstream velocity is therefore more uniform. T h e total head loss across the screen is dependent o n the screen pressure loss coefficient and the number of screens. This total head reduction factor is rcprescnted by:

v3= 1 (1 + K ) "

where v, and v, a r e the drop in total head upstream and downstream from the screen. T h e total head drop implies a change in the static pressure across the screen:

1 2 APs = PSI - P,, = n K z p V (3)

Prandtl also showed that a system of "n" multiple screens with lower K would provide a higher reduction factor than a single screen with a pressure loss coefficient equal to nK. In addition to explaining the multiple screen behavior, Prandtl pointed out the need to place screens in the settling chamber where the flow velocity is minimum. This minimizes energy losses and results in less power requirements by the wind tunnel.

Following Prandtl, Collar]" addressed thc problem of selccting a best value of (K). He used a momentum theory developed for propellers to derive an cquation that cstimatcs the total head reduction factor as shown below:

V a r i o u s r e s e a r c h e r s have conduc ted

2

In 1981, a research team led by Derbunovich5 publishcd a papcr o n single screens in which a n important relationship between the screen's generated turbulencc and upstream turbulence was presented. In that paper, a mathematical model was derived that enables users to predict the turbulence reduction factor for a single screen provided that the pressure loss coefficient is known. T h e predictions agreed with experimental data to within 10%.

Since most wind tunnels use multiple screens, a study conducted by Salmirs and Herrick6 verificd that Derbunovich's prediction techniques were not only valid for a single screen but can also be uscd o n multiple screen systems if the pressure loss coefficient (K) of each screen was measured.

A literature search was conducted to study the previous work and techniques developed by various scholars. Thcn, a n experimcnt was designed to obtain sufficient data that could be comparcd with the previous work. A tcst box was designcd and built to measure pressurc loss coefficient (K) of three different screens with different physical properties ovcr a range of Rcynolds numbers. The wirc Rcynolds number, R,, based o n the flow velocity through the wirc grid and wire diameter, was used. Tha t Reynolds number is considered more representative of thc local flow around the screen wires and is more dircctly related to drag. Tests were performed below, near and above critical Reynolds numbers. The critical Reynolds number was defined by DerbunovichS as the Rcynolds number, R,, beyond which the screen generated turbulence level downstream of thc scrccn became constant. That critical Reynolds number, R,,,, is approximatcly 175.

Both static and total head pressure measurements wcre taken in front of the test screen and a t various locations bchind the scrccn. Based on the data collcctcd, a value of thc pressure loss coefficient was calculated and compared to data obtained from other referenccs. Screens were also tested in pairs below, near and above critical Reynolds numbers based on the front screen characteristics. Data wcrc analyzed in the samc fashion as single screens.

An analysis of the collected data was conductcd and related to the work of Davis', Von KarmanR and Strouhal"(pg. 31). Two mathematical modcls wcre dcrived. The first model, based o n Davis' work, could b c used to evaluate K based on the geometrical propcrties of the scrccn. T h e second model, based Karman's inviscid cylinder drag analysis and vortex frcqucncy, could be used to evaluate K the R, effect.

on Von S t ro u ha 1

based o n

o m UTE

V a r i o u s r e s e a r c h e r s have conduc tcd

expcrimcntal and analytical investigations to better understand the behavior of wind tunnel turbulence screens. All rcsearchers since Prandtl (1933) have concluded that the capability of a screen in reducing turbulence is related to the pressure loss across it. To predict the turbulence reduction factor of a screen, the energy loss, represented in terms of static pressure loss across the scrcen must be cvaluated. This cnergy loss may be rcpresented as a pressure loss coefficient (K) using the equation:

where P,, and P,, are thc static pressures measured upstream and downstrcam, respectively, from the screen. The pressure loss coefficient (K) was used by the various researchers to predict the turbulence reduction factor of a screen.

Prandtl] was among the first to recognize that screens can be used to obtain a uniform velocity profile. This is a consequence of the fact that the higher upstream velocities will encounter higher resistance when passing through the screen. The resulting downstream velocity is thercfore more uniform. T h e total head loss across the scrcen is dependent o n the scrcen pressure loss coefficient and the number of screens. This total head reduction factor is represented by:

v3= 1 "1 (1 +K)"

whcre v, and v3 arc the drop in total head upstream and downstream from the screen. The total head drop implies a change in thc static pressure across the screen:

APs = P,, - P,, = n K z p 1 2 V (3 )

Prandtl also showed that a system of "n" multiple scrcens with lower K would providc a higher reduction factor than a single scrcen with a pressure loss coefficicnt equal to nK. In addition to explaining the multiple screen bchavior, Prandtl pointed out the nccd to place screens in the settling chamber where the flow velocity is minimum. This minimizes energy losses and results in less power requirements by the wind tunnel.

Following Prandtl, Collar1" addressed the problem o f sclccting a best value of (K). He used a momentum theory developed for propellers to dcrive an equation that estimatcs the total head reduction factor as shown below:

(4)

2

A screen with K = 2 would remove all variations in the flow. His main contribution was showing the dependence of K o n the geometric properties of the screen. To describe the geometrical properties of a screen, Collar defined a term "porosity" which represents the ratio of open to blocked area of the screen as follows:

By plotting the pressure loss coefficient versus porosity, Collar was able to obtain the following empirical relationship:

( 1 -p , K = 0.9 - p2

His technique for estimating the pressure loss coefficient served as a model for subsequent investigations.

Annand" investigated new techniques for predicting K depending heavily o n graphical data obtained from various sources. In much the same way as Collar's work, Annand reduced the data to a n empirical equation:

(7)

Annand made the constant, C, in Eq. 7 vary with wire Reynolds number, R,. Values of (C) were obtained from a nomogram h e provided in that paper. Annand's work provided a means of incorporating Reynolds number effects. T h e major problem with his technique is that his analysis was based o n graphical data obtained from various sources each of which conducted a slightly different experiment which resulted in large variations.

WeighardtI2, who was working on the problem around the same time as Annand, agreed that the pressure loss coefficient is dependent on both Reynolds number and porosity. Weighardt's empirical equation was the same as Collar's with the exception that the constant (C) was dependent o n the wire Reynolds number, R,, based on the local velocity through the screen. The wire Reynolds number was evaluated by dividing Re by the porosity. T h e resulting equations are:

The consideration of local rather than free stream Reynolds numbcr resulted in data with a higher degree

of correlation. T h e most recent work o n the prediction of

pressure loss Coefficient of a screen was done by Davis'. Davis treated the flow through the screen openings as an inviscid rapid expansion. In his work, Davis showed that both the geometrical properties and the Reynolds number have independent effccts on the pressure loss mechanism. Davis provided two terms for estimating K. T h e first term was based on the fact that K approaches a constant, &, a t high Re values. Thc value K, is related only to the porosity of the screen:

T h e constant C, the "throttling coefficient", was given a value of 0.95 and is used to account for the variations in the geometric characteristics of the screen. The second term was based o n the contribution of Re. This term was derived from a n empirical relationship that was derived by plotting K-KO versus Re with values of K obtained experimentally. T h e resulting mathematical model for this relationship is:

K r = K - K -- 55.2 O - Re

EQ.(11) was found to give satisfactory results for 5 0 i R e < 2 0 0 . T h e main concern about Davis' work was that he dealt with screens with very high solidity. Screens with high solidities behave erratically a t the low Reynolds number range used in his experiment. Although his techniques resulted in higher correlation, the margin of error was large for general screen applications. In gencral, Davis work resulted in a better understanding of the behavior of screens and the mechanism of pressure loss.

Researchers have not only been dealing with the prediction of K but also with methods to improve the prediction of the turbulence reduction factor of a system of screens. The latest development was done by a group of Russian researchers led by Derbunovich5. Derbunovich, e t al. dealt mainly with developing a mathematical model that would enable wind tunnel designers and users to predict the turbulence reduction factor, F. In their equation, shown below, once the screen geometry is defined, the turbulence reduction factor can be evaluated only if K is known.

F =

A major benefit from their paper was the very good

3

numerical data of turbulence and static pressure measurements for diffcrent screens at different Rw. By using Derbunovich's equation, one can accurately predict the value of F for a single screen.

A recent study conducted at Arizona State University by Salmirs and Herrick6 demonstrated that Derbunovich's method was correct and accurate for single and multiple screen systems, provided that K is known.

deals mainly with improving the prediction technique of Davis so that better results could bc obtaincd when predicting F.

This paper

The Tcchnolom Wind Tunnel The Technology wind tunnel a t Arizona State

University has a test section which is 50 inches wide, 3.5 inches high and 8 feet long. T h e tunnel is powered by a 7.5 horsepower electric motor which rotates a variable pitch, four blade fan a t a constant speed of S96 RPM. The flow accelerates from the plenum section into the test section through a 7:1 contraction ratio. The wind tunnel can achieve a maximum test speed of 220 ft/sec. The test section speed is varied by manually changing the pitch of the fan. T h e turbulence level in the test section is approximately 0.8%. This high turbulence levcl is because there a re prescntly no scrccns in the settling chamber. A picture and a schematic of the wind tunncl is shown in Figures 1 and 2.

Figure 1. ASU Technology Wind Tunnel

Test Box Construction The main purpose of the test box was to hold

the test screens, the static pressure ports and total head tubes located a t specified locations relative to the scrccn position (Fig. 3) . T h e plywood box had an inner cross section of 1 foot square. Upper and lower steel brackets

were used to hold the wooden removable individual

Figure 2. Schematic of The ASU Wind Tunnel

sections in place (Fig. 4).

constructed in four major sections: 1) Flow smoothing section 2) Entry scction 3 ) Screen tcst section 4) Exit section

The wooden portion of the tcst box was

1 Total Hea I

I I

p r b u l e n c .5 cm) I Control j 1 Screens

i I

I b- 37" (94.0 cm) -4

Figure 3. Internal Schcmatic o f T h e Test Box

The first section, the smoothing section, was 11 inches long with two smoothing screens 5 inches apart installed a t the front of the box as can be seen in Fig. 3. The two screens wcrc used to ensure a niorc uniform velocity profile a t the face of thc test screen.

The entry section which was 5 inches long, was installcd downstream of the smoothing section. The entry section had a rounded nose to provide smooth unseparatcd entry flow.

The next section was the segmcntcd screen test section which contained thc tcst screens. The total length of the scgmentcd scction was 10 inches. The

4

segments varied in length from 1 to 4 inches to allow moving the downstream screen to the various positions. There were two 1-inch segments, two 2-inch segments and one 4-inch segment. Three static ports were located a t a spacing of 0.25 inch o n the side of the upstream 1- inch segment. T h e 2-inch and the 4-inch segments had two and four static pressure ports respectively.

T h e exit section was 11 inches long with gradual expanding taper toward the rear of the box for pressure recovery. In addition to the static pressure ports behind the test screen, a static pressure port and a total head tube were located in front of the upstream screen to take free stream measurements (Fig. 3). Behind the test screen, a movable total head tube was installed to take total head measurements behind the screen a t the same locations as the static pressure ports.

Figure 4. Test Box in The Test Section

Pressure and Temperature Measurements Two types of pressure measurements were taken

during this experiment, total head and static. Static pressure measurements were taken upstream and downstream of thc test screen. One measurement was taken upstream for free stream calculations and various static readings were taken behind the test screen a t the locations shown in Table 1. All prcssure ports and tubes were connected to a scanivalve. The scanivalve connected the pressure ports in sequence to a Validyne prcssurc transducer. T h c delay time for each port before a pressure reading was taken, which was computer controlled, was two seconds where ten samples of data were collected. T h e pressurc transducer used a 2 inch diameter diaphragm that had a full scalc range of 0.0 to 5.5 inchcs of water. One side of the transducer was connected to a tube that was open to thc ambient conditions in the control room. This was done so that all pressure measurement$ were referenced to the same room baromctric pressure.

The test section air temperature was monitored using a type K thermocouple which was installed in the wind tunnel test section. T h e temperature readouts were directly relayed to the computer via the HP-3497A Data Acquisition Control Unit for calculations of test air density and viscosity.

Table 1. Pressure Port Locations and Type

Pressure Downstream Pressure Type Port Location (in)

Total, upstream Static, upstream Totid, downstream Box zero Static, downstream Static, downstreani

1 0.00 2 0.00 3 4 0.00 5 0.25 6 0.50 7 0.75 8 1.50 9 2.50 10 3.50 11 4.50 12 5.50 13 6.50 14 7.50 15 8.50 16 9.50 17 10.50 18 11.50 19 12.50

--__I

The Data Acquisition svstems In order to create a link between the computer

and the pressure and tcrnperature transducers, data were sampled by a Hewlett Packard HP-3497A Data Acquisition Control Unit. The HP-3497A is capable of sampling data to a n accuracy of one part in lo5, converting to digital format and transmitting the digital data into the computer. T h e temperature and pressure signals were converted to digital in the HP unit and entered into the computer through a n IEEE-488 (GPIB) Data Bus. It can also transmit commands by the computer to various instruments. As shown in Fig. 5 , the HP-3497A was interfaced with a Zenith Z150 personal computer. The digital signals that were sent to and from the computer were handled by a software package called "ASYST Scientific". ASYST is a high order language which can perform bus operations, calculations, data analysis and plotting functions.

Test Screens Three different screens of a woven type were

used in this experiment. T h e physical characteristics of the screens a re shown in Table 2. T h e selection of these

5

screens was based o n comparison with the other references and to provide a wider range of data for low, medium and high solidity values. For single screen tests, the screen was fixed to the front of the 1-inch segment. For multiple screen tests, the second screen was fixed to the front of the 2-inch segment while the first screen was installed in the same manner as done in the single screen tests.

PRESSURE

Figure 5. Instrument System Schematic

Table 2 . Present Screen Characteristics

Screen d M S Reference Number inches mm inches mm

1 0.011 0.267 0.061 1.556 0.313 6 2 0.006 0.152 0.015 0.371 0.347 3 0.027 0.673 0.082 2.093 ,0.460

'FEST PROCEDURES

The format for conducting both single and multiple screen tests was essentially the same. Initially, calibration of the test equipment was completed. Following that, single screen tests were conducted and all necessary data were collected. After analyzing the single screen data, multiple screen tests were performed and data were collected. The details of each step in the procedure a re outlined in the following sections.

Calibration of Tcst Equipment Calibration of the tcst equipment and

transducers was performed prior to testing to assure acquisition of reliable data.

T h e type-K thermocouple (chromel-alumel) was connected to the HP-3497A with shielded copper wires so voltage readings could be obtained. Calibration was

necessary because of the copper wire interfaces. T h e thermocouple was placed in iced water

along with a mercury thermometer. After the readings have stablized, temperature and voltage were recorded. Then, the temperature of the water was increased slightly by mixing it with some hot water. The water was left for some time to stabilize before taking the temperature and voltage readings. This procedure was repeated several times for a temperature rang of 34 to 200 degrees Fahrenhcit. After all data were collectcd, a plot of the voltage readings versus the temperature readings was generated. Regression results produced the following equations for voltage in millivolts as a function of temperature in degrees Fahrenheit:

Type K wire: E = -1.93415 + 0.024024 t

Reference Tables: E = -0.74623 + 0.022766 t

Based on the data taken, the values measurcd for type K wire agree well with those predicted by the tables with a -1.19 mv offset which was probably due to cold junction reference temperature difference. As a result, equation 13 was used in the program to calculate the temperature readings based o n the voltage readings from the HP- 3497A.

The Validyne pressure transducer had to b e calibrated periodically d u e to its high sensitivity. The calibration range was dependent on the type of diaphragm that was used in the pressure transducer. Since the diaphragm had a maximum pressure range of 5.5 inches of water a t 10 volts, the Validyne had to be adjustcd to read 10 volts when a pressure of 5.5 inches of water was applied o n the diaphragm. T h e first step was to connect the pressure transducer and a precision water manometer (DWYER model 424) through plastic tubing into a "T" fitting. T h e maximum pressure reading on the manometer was 10 inches of water. The other side of the pressure transducer was exposed to room pressure. Before applying any pressure o n the diaphragm, the transducer amplifier output reading was adjusted to read Lero volts. Maximum resolution of five significant figures was achieved. After that, pressure through the "T" fitting was applied to both the transducer and the water manomcter. When the reading o n the manometer showed 5.5 inchcs of water, the amplifier was adjusted to read exactly 10 volts. At that point, the Validyne pressure transduccr was satisfactorily calibrated and was ready to be used for the actual tests.

Single Screen Tests

different screens. T h e solidities of these screens were Single screen tests were conducted on only two

6

0.460 and 0.347. T h e third screen with a solidity equal to 0.313 was previously tested (Ref. 6). The test procedures started by installing the test screen o n the face of the 1- inch segment. After installing the screen in the box, the tubing from the total head and static pressure ports was connected to the scanivalve. The ports on the scanivalve were numbered from 0 to 48. The tubes were connected to ports 1 through 19 in order as shown in Table 1. The total head probe behind the screen was located a t the same location as the first static pressure port behind the screen.

T h e blade pitch was se t a t a low angle appropriate to the desired speed in the test section. Readings werc taken a t nominal freestream speeds of 20 - 50 ft/sec. When all instruments had been checked, the ASYST computer program was run to begin testing. Initially the program took "zero-offset'' readings and thcn requested the uscr to turn o n the wind tunnel. T h e program then commandcd the scanivalve to move to the appropriate port and pause for two seconds before taking 10 pressure readings. The scanivalve moved to the following port paused and then the data were read. Once all pressure readings werc collcctcd, the program requested the solidity and wire diameter of the screen in addition to the room barometric pressure. This input information was used by the program to calculate the screen's wire Reynolds number(R,), test density and air speed.

T h e first run was accomplished a t a speed that provided a Reynolds number below critical. Once the first run was completed, the total head probe behind the screen was moved to a location corresponding to the location o f the second static pressure port. The program was run again and data were obtained. The previous step was repeated and the total head probe was moved to the next static pressure port location. Tcsts were repeated to obtain data for the total head pressure behind the screen a t all the corresponding static prcssure port locations. T h e entire test was rcpeated a t R, near and abovc critical. The second screen was tested by following the samc steps.

Multiple Screen 'Tests Multiple screen tests were conducted in the samc

fashion as the single screen tests with few minor exceptions. First, no total head mcasurements were taken behirid the test screen. In the multiple screen tests, a combination of two scrcens were used with the 0.313 solidity screen always placed in the front. The second screen was o n e of the 0.313, 0.460 or 0.347 solidity.

The test procedures started by placing the 0.313 screen on the front of the 1-inch segment and the second screen was fixed to the front of a 2-inch segmcnt. This arrangement placed the screens with a spacing of one

inch. T h e program was run and data were collected for R, below critical based o n the first screen's wire diameter. Then, the spacing between the screens was changed to two inches by inserting another 1-inch segment between them. T h e test was repeated for spacings of 4, 6 and 8 inches. Upon the completion of the first five runs, tests were repeated for R, near and above critical. All three tests were repeated using a different screen o n the 2-inch segment.

Single Screen Pressure Results Plots of the static and total head pressure

readings upstream and downstream from the screens as a function of their relative locations to the screen were generated. These plots were used to analyze the pressure loss mechanism of the screen and to select the appropriate static and total pressure values to be used for evaluating K.

For high R,, there were slight variations in the longitudinaldistribution of static and total pressures from port to port downstream from the screen as shown in Fig. 6.

R n = 705, S 0.46

VI

0 n

i

nislnlrce d o w ~ l s t m t n , i l l .

0 1'1 t 1's

Figure 6. Single Screen Static Sr Total Pressure Loss

The static and total pressure variations were higher at the low range of R,. Interestingly, the pressure patterns were very similar for the different screens. After the air passed through the screen, it first experienced a very high drop in static and total pressure then a rise and then a drop that was lcss in magnitude than the first one (Fig. 6). Once downstream from that initial "wave", the static and total pressure variations were damped and stabilized.

That pattern was observed for all screens a t the different Reynolds numbers. This indicated that a standing wave had formed downstream from the screen.

7

No explanation of that phenomenon is offered at this time. Although S ~ h e i m a n ' ~ noted the same wave phenomenon, h e did not actually measure the pressures and likewise could not provide any explanation. When calculating the pressure loss of the screen using EQ. (1 j, only static pressure measurements were considered. T h e loss in total head was a more accurate measure of the screen losses since it accounts for the growth of the boundary layer and the resulting static pressure drop. The difference between total head loss and static pressure loss was less than three percent. Further, the total head measurements could not be compared to measurements obtained by the studies of References 3,

observed in the multi-screen tests confirms the existence of the phenomenon even in multiple screen case. The static pressure dropped after the first screen and dropped further after the second screen. In general, the pressure drop behavior for multiple screens was very similar to that for a single screen.

One major problem that was encountered in the multiple screen tests was the selection of static pressure values that were representative of the pressure loss behind the screens. This problem was encountered a t screen spacings of 1 inch and 8 inches since only three readings were available behind either screen.

S1=0.313, S2=0.46, Screen Spacing= I " 5 , 6 and others. T h e difference between K, derived from static pressures and that from total head

local boundary layer. Information on the details of the experiments necessary to determine boundary layer

Ri l l = 265, RII? = 050 measurements was related to the development of the

development was not available. For those two reasons, -0.15

the total head pressure estimate of the pressure loss

-0.M

-0.1

B -02 ;

pl -025

a

coefficient was not used in this study. P,, was evaluated as the average of static

pressure readings behind the screen. The first three

variations in their values. Measured values of K arc shown in Table 3.

h

-0.3

4 6 -0.35

UI

static pressure readings were neglected due to the high

-0.4

-0.45

-0.5 0.w 1.m 2.m 3.w 4.w 5.w 8.w 7 B S 10

Table 3. Present Data

Screen Rw Km Kp % Error

1 60 0.93 0.98 -5.4 108 0.80 0.73 8.9 266 0.65 0.65 1.1

2. 43 1.69 1.34 20.6 99 1.34 0.89 33.1 155 0.97 0.76 21.9 239 0.86 0.79 7.4

3 105 1.85 1.61 12.8 113 1.73 1.59 8.4 123 1.43 1.56 -9.0

516 1.30 1.26 3.1 329 1.38 1.51 -9.6

586 1.22 1.25 -2.7

Multiple Screen Pressure Results Since a combination of two screens were used in

multiple screen tests, the pressure drop between the screens was expected to vary as a function of their spacing. As a result of plotting the pressure values versus relative locations, it was observed that a wave was formed immediately behind the first screen and behind the second screen (Fig. 7). T h e presence of these waves has not been explained, but the repeatable pattern

Figure 7. Multiple Screen Static Pressure Loss

The pressure loss coefficient (Kj values for both screens were calculated using EQ. (1) where P,, for the first screen calculations was used as PSI in the second screen calculations. Also for both K1 and K2, the free stream dynamic pressure upstream from the first screen was used.

DISCUSS10

In order to determine the turbulence reduction capability of a screen, the energy loss was evaluated in terms of the pressure loss coefficient (K). Based on the generated data from this experiment and data collected from other references, mathematical models for evaluating K were generated.

Single Screen Pressure Loss Coefficient In gencral, pressure loss depends on two

paramctcrs, the physical properties of the screen wires and the viscous effects of the fluid. Davis7 was the first to identify the significance of these factors as shown in EQ. (10) & (11). Davis considered screcns with very

8

small porosity, 0.340 - 0.402, operated over a very low range of Reynolds numbers, 50-300. Screens with such low porosity values behave erratically, especially a t the low Re range considered. In this paper, screen solidities and R, were chosen based on practical conditions in settling chambers of subsonic wind tunnels.

Effect of Solidity o n K To describe the physical characteristics of the

screens, the term solidity (S) was used. Solidity represents the amount of obstruction presented by the screen and is directly related to its drag.

The analysis was first started by calculating the K values for the tested screens and collecting sufficient data from References 3, 5 and 6. Reference screens are described in Table 4. Only screens with solidity values between 0.19 and 0.55 were considered. Solidities above 0.6 were not considered useful because of their erratic performance.

Table 4. Reference Screen Characteristics

Screen d M S Reference Number inches mm inches rnrn

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

20 21 22 ’)?

0.039 0.0i5 0.009 0.015 0.030 0.020 0.040 0.012 0.023 0.009 0.039 0.007 0.009 0.009 0.014 0.008 0.038 0.009 0.026

0.025 0.008 0.006

1.000 0.390 0.240 0.390 0.770 0.500 1.010 0.3 10 0.580 0.240 1.000 0.190 0.240 0.240 0.360 0.200 0.970 0.230 0.670

0.315 8.000 0.230 0.095 2.410 0.300 0.048 1.210 0.350 0.079 2.000 0.350 0.158 4.010 0.350 0.097 2.460 0.360 0.195 4.960 0.370 0.055 1.400 0.390 0.104 2.650 0.390 0.041 1.050 0.410 0.157 4.000 0.440 0.029 0.740 0.450 0.036 0.920 0.450 0.035 0.890 0.460 0.052 1.330 0.470 0.027 0.690 0.490 0.130 3.290 0.500 0.030 0.760 0.520 0.081 2.060 0.540

0.635 0.250 6.350 0.190 0.191 0.042 1.059 0.327 0.140 0.020 0.508 0.473

5

3

0.007 0.178 0.025 0.635 0.482

A plot of the measured pressure loss coefficients (K,) versus solidity (S) was generated as shown in Figure 8. The data was observed to have remarkably little scatter. A common problem in comparing and evaluating

data from published material is the absence of numerical values (frequently data is shown only o n graphs) also the definitions of parameters a re not always consistent. The data presented in Table 5 and Figure 8 were taken from plots in Reference 3 and from tabular numerical data from References 5 and 9. A n equation was derived based o n Davis’ work (Eq. 10) to fit the data in Figure 8.

K o = \ r 2 ( 1 - c + s ) 2 1 - s

Table 5. Reference Data

Screen Rw Km Kp % Error Reference

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

20

21

22

23

400 0.42 0.38 8.8 175 0.62 0.61 1.1 103 1.01 0.93 8.1 171 0.85 0.76 10.6 357 0.74 0.77 -4.0 233 0.85 0.88 -3.5 471 0.75 0.62 17.8 160 1.24 1.00 19.6

119 1.20 1.15 4.5

99 1.97 1.52 22.7 134 1.60 1.48 7.4 145 1.72 1.58 8.2 212 1.68 1.61 3.9 108 1.93 1.98 -2.6

294 1.00 1.00 -0.1

547 1.03 1.06 -3.3

580 1.67 1.72 -2.7 165 2.42 2.09 13.6 450 2.24 2.35 -5.0

195 245 390 50 75 100 150 50 75 100 150 175 200 225 25 50 75 100

0.35 0.32 7.4 0.35 0.31 10.9 0.35 0.29 18.5

0.80 0.92 -15.1 0.79 0.81 -2.0 0.63 0.68 -8.7 2.00 2.11 -5.3 1.80 1.88 -4.7 1.70 1.77 -4.1 1.50 1.65 -9.9

1.45 1.68 -15.9

0.90 1.14 -26.9

1.47 1.61 -9.6

1.40 1.67 -19.6 2.30 2.82 -22.5 1.85 2.18 -17.9 1.65 1.96 -18.8 1.55 1.85 -19.1

5

4

150 1.35 1.72 -27.7 -.

9

The essential modification to Davis' equation was the addition of the bias term, S, the solidity. Also, Davis used a value of 0.95 for C whereas the present curve fit uses C = 1.

E x 3

. 20

d 28

'p 2 4

C U * 0 2

u r n

j 14

ui ui 18

B 12

? I : aa E aa a a 4

';j 02 r 0 0.1 0.15 02 025 0.3 0.35 0.4 0.45 0.5 0.55 0.8

0 B

Solidity, S

2 - EClnI: t Ref.9kAlj:lb:iri 0 R c r . 3 a 111.1.5

Figure 8. Effect of Solidity on K

This modification provided a better curve fit as shown in Fig.8. Ea. 19 only considered the physical characteristics of the screen. Although the equation provided a very good fit to the measured data, more accurate results could be achieved by considering the viscous effects which a re related to R,.

Effect of Revnolds Number on K In order to determine the R, effect on the

screen's K, a graph of K, versus R, was generated as shown in Fig. 9.

E x 20

d = 2 2 .ii 10

. 2 4 d

*I 18

0 14

12

: I

j 0.0

~ 0.0

L a4 : 02

B O L

d -a4 4 . 8

a -02

o m i r n m m o 2 s o 3 a o m m ~ s o m ~ 0 8 0 0 1

i:

id B

Rirc Reynolds Number, Rn

,,t Ref. 9 k Aljahari 4 Ref. 3 X Rer. 5

Figure 9. 'K, vs. R ,

It can be seen that there was a large scatter in the data.

Values of KO determined by EQ. 17 were subtracted from the raw values of K,. T h e differences, K, values, were then plotted against wire Reynolds number in Figure 10. This step resulted in less scattered data. Analysis was partially based o n the work of Davis in which h e estimated that K, = C/Rc. The analysis also used second degree equation terms in Reynolds number to improve the fit. T h e second degree equation was based o n the work of Von Karman and Rubach6 and Strouha19 (pg. 31).

I

Figure 10. K, vs. R,

Since some of the energy loss across the screen was related to the formation of the vortex streets behind its wires, the analysis was focused o n the wires and their drag. Von Karman and Rubach8 showed that a stable vortex system exists for flow downstream of a cylinder with a longitudinal to cross-flow vortex stream spacing ratio:

h = 0.283

Assuming a stable vortex system and no viscous effects, Von Karman dcrived a n equation to estimate the cylinder's drag based on the vortex street velocity and the cylinder vclocity.

But.

U 1 _ - v - 1 -- 10

Where lo = V T

Experiments conductcd by Prand tl and Tietjens revealed the flow pattern behind a cylinder. A photograph of that experiment has bccn reproduced by Schlichting9 (figures 2.6 and 2.9). From this and other flow visualization

10

experiments, reference 14, the cross flow vortex spacing, h, can be estimated to be about 0.4d in the region close behind the cylinder.

(K) based on the empirical relationships, Eqs. 17 and 25. The predicted values, K,, are listed in Tables 3 and 5. Also listed in the tables are the percentage errors. The average error for all data was 0.1% with standard

For h = 0.4 d, l = f i deviation of 13%.

d d2 V T V2 T2 c d = 1.338 - 0.584 ~ - 1.85 ~

Strouhal in 1878 found a linear variation in the frequency of the flow disturbances, Strouhal number, behind a cylinder when plotted against the logarithm of the Reynolds number. This linear variation continued for Reynolds numbers up to 400. T h e Strouhal number reached a constant value, 0.21, for Re above 400 (reference 9, Fig. 2.9) as shown in the equations below:

St = 0.0964 logRe - 0.03 12 50< Re <400 (22)

st = 0.21 400< Re <3000 (23)

Substituting EQ. 22 into EQ. 21, the drag coefficient for a cylinder as a function of Reynolds number was found to be:

Cd =1.354 - .04521og Re - .0172(1og Re)2 Re> 50 (24)

This equation could be used directly to evaluate K,. By examining the data in Fig. 10 and considering the findings of Strouhal and Derbunovich, some modifications to the first term in equation 24 had to be considered to achieve a better fit to the data. According to D e r b u n o ~ i c h ~ , for Reynolds numbers below 175, the turbulence varied linearly with R , . Above that Reynolds number, the screen generated turbulence level became constant. Also according to Strouhal, for Reynolds numbers below 400, the Strouhal number varied linearly with Reynolds number and above that number, S, became constant. Based o n these findings, three flow regions were considered. The first region was for Reynolds numbers below 175, the second region was for R, between 175 and 400, the third region was for R, above 400. For each region the first term in equation 24 was modified to provide a better fit within the data with the exception of the first region where the term was based on Davis' findings. This derived relationship is plotted in Fig. 11. and shown below:

30.3 K, = R, - .04521og R, - .0172(log R,)2 R, 4 7 5 (25a)

K, =.25 - .045210g R, - .0172(bg Rw)2 175<Rw<400 (25b)

K, =.024 - ,045210g R, - .0172(10g Rw)2 40O<RW<600 (25C)

Predictions were made for screen pressure loss

28

j 2 4

22

'; 2

c 10

u 14

VI 12

i u 10 0

VI

3 0.;

0.6

3 L14 VI VI 02 0 l . 0 a 4 2

; 4.4 ; -0.0

D 50 im r n z m 2 5 O m 3 5 0 4 0 0 4 5 0 9 W 5 5 0 B W c h Wire Reynolds Nriniber, Rw

; 4 1 1 . 2 5 0 K ~ l l - K u

Figure 11. Effect of Reynolds Number on K

Multiple Screen Pressure Loss Coefficient The mechanism of pressure loss in the case of

multiple screens is very similar to that of single screens. The only exception being the presence of a second screen downstream of the first one.

The subject of optimal screen spacing has been addressed with little success. T h e data acquired in Reference 6 indicated that there was little if any effect on K for screens spaced a t distances when x/M > 200. That corresponds to distances between screens from eight to twenty inches (200 to 500 mm) for commonly used screens. The results of single screen analysis could be applied to multiple screen systems with large spacing.

The second part of this experiment was conducted to gain better understandingof the mechanism of pressure loss across two screens closely spaced (1 to 8 inches). Based on the collected pressure data, values of K, were plotted against the screen spacing. Plots for Reynolds numbers near and below critical showed large variations. Due to these high variations, no clear conclusions could be drawn from those graphs.

Effect of Screen Spacing on K Plots of K, verses screen spacing for Reynolds

numbers above critical were compared. First, i t was observed that as the two screens were brought closer, the pressure loss coefficients of the first screen were increased in value while the second screen experienced reduction in K values. This observation could be seen in Figs. 12 - 14 for the different screen combinations. This behavior was partially explained by Reference 15.

13

S 1 =0.3 13, S2=0.46 Re1 265, R u Z = 850

SPACING UFI'REE;': SCREENS ( i l l )

@ litiil t K i n ? .? l i l p A K Z p

Figure 14. K vs. Screen Spacing For S1=.313 SC S2=.46

As the distance between the two screens was reduced, the boundary laycr of the downstream screen was made turbulent by the broad wake created by the upstream screen, thus producing a supercritical flow pattern with a correspondingly smaller pressure loss (drag). At the same time, the obstruction presentcd by the closeness of the second screen caused the vortex system generated by the upstream screen to have a wider longitudinal, h, vortex spacing. This divergence in the longitudinal vortex spacing increased the pressure loss (drag) of the first screcn. It is believed that the same phenomenon exists even for Reynolds numbers near and below critical.

Equations 17 and 25 were used to evaluate the pressure loss coefficicnt of each screen in the multiple screen arrangcment. T h c results were interestingly accurate when considering the average pressure loss coefficients a t all spacings. No direct mathematical relationship could be derived to take into account the spacing cffcct. Further analysis and study need to be conducted to better understand multiple screen behavior a t close arrangements.

Error Analysis Clearly the drag of cylindcrs is different from the

complex mixing flow behind a screen. However, the dominant flow characteristic is expected to be that of the cylinderical wires from which the screen was constructed. Von Karman's solution applied to the stability of a vortex stream and ignored thc viscous cffccts which created the stream. The creation and distribution of vortices was primarily a viscous effect below Rcr.

Scrcen drag was most directly related to screen solidity, the measure of the physical obstruction of the flow. Screen drag was also related to the viscous effects, vortices generated by the cylindrical cornponcnts. Wire intcrscctions and flow mixing which were not considered in the analysis, also contribute to the pressure loss.

Further, screen flow distortions were affected by the angle of the upstream flow caused by cither sag in the screen o r placement angle.

Much of the variation in reported data and predictions were due to difficulties inherent in the experiment. Further, data used in some analyses were taken from graphs. Often the experimental conditions were not fully dcscribcd. Dcrbunovich', et al. was belicvcd to have presented the best experimcntal data available. In their work, the widest range of screen designs over the largest Rcynolds number range werc used with the best of experimental techniques. The Kpavg for the Rcfcrcnce 5 data based on Eqs. 17 and 25 was 5% with a standard deviation of 896, the lowest for any data set.

If the data considered were restricted to Reynolds numbers above critical, thc I(pavg was zero with

12

a standard deviation of less than 10%. That was not unexpected since the main characteristic of flow below R,,, = 175 is its irregularity. It was noted that better turbulence reduction can be expected if the screen could be operated above the critical range.

In addition, an error of 1% in the measurement or manufacture of screen mesh or wire diameter could result in a 2% error in K,.

Derbunovich', et. al. showed that turbulence could be reduced by the factor F as shown in EQ. 12, The upstream turbulence level, To, could be measured and screen turbulence, T,,, could be predicted from physical properties of the screen. The remaining unknown would be the pressure loss coefficient, K. If the pressure loss coefficient were in error by 1%, there would be errors of 0.25 to 0.3% in estimating the turbulence rcduction factor of a screen.

Conclusions and Recommendations A study of a variety of measurements of wind

Tunnel turbulence reduction screens has resulted in empirical equations which could predict single as well as multiple screen pressure loss coefficients with reasonable accuracy. These values could be used with other relationships to accurately evaluate screen turbulence reduction effectiveness. For multiple screen systems, it was noted that as the spacing of the screens became less than 8 inches, the drag of the upstream screen was increased while the drag of the downstream screen was decreased. The sccond screen drag was dccrcased due to its presence in the turbulent flow region generated by the first screen. The second screen drag was increased due to the presence of the obstruction downstream which caused an increase in the longitudinal spacing of the vortex system generated by the first screen, thus resulting in higher drag.

Further analysis and investigation of different combinations of screens would be necessary to arrive at more accurate and detailed conclusions in the case of multiple screens.

NCES

'Prandtl, L., "Attaining a Steady Airstream in Wind Tunnels," NACA TM 726, 1933.

Dryden, H. L.; and Schubauer, G. B., "The Use of Damping Screens for the Reduction of Wind Tunnel Turbulence," J. Aeronaut. Sci., Vol. 14, no. 4, Apr. 1947, pp. 221-228.

4Tan-Atichat, J., H. M. Nagib and R. I. Loehrke, "Interaction of Free Strcam Turbulence with Screens and Grids: A Balance betwccn Turbulence Scales," Journal of Fluid Mechanics, Vol. 114, pp. 501-538, 1982.

SDerbunovich, G.I.; Zcmskaya, A.S.; Repik, Ye.U. and Sosedko, Yu.P., Optimum Wire Screens for Control of Turbulence in Wind Tunnels," Fluid Mechanics-Soviet Research, Vol. 10, no. 5 , Sept-Oct 1981.

%almirs, S. and Herrick, P., "Measurement of Turbulence Decay Between Wind Tunnel Turbulence Reducing Screens," AIAA 22-90, January 1990.

'Davis, G. De Vahl, "The Flow of Air Through Wire Screens," Hydraulics and Fluid Mechanics, Richard Sylvester, ed., Macmillan Co., 1964, pp. 191-212.

V o n Karman and Rubach, H., "The Mechanism of Fluid Resistance," Classical Aerodynamic Theory, NASA Reference Publication 1050, Compiled by Jones, R.,Dec. 1979.

'Schlichting, H., "Boundary Layer Theory," 7th. Edition, McGraw-Hill, 1979.

'OCollar,R. A., "The Effect of a Gauze on the Velocity Distribution in a Uniform Duct," R.& M. No.1867, Feb. 1939.

"Annand, W.J.D., "The Resistance to Air Flow of Wire Gauzes," Journal of the Royal Aeronautical Society. Vol. 57, March, 1953 pp 141..146.

12Weighardt, K.E.G., "On the Resistance of Screens," Aeronaut. Q. Vol4, 1953 pp 186-192.

'?Scheiman, James, "Comparison of Experimental and Theoretical Turbulence Reduction Characteristics for Screens, Honeycomb, and Honeycomb-Screen Combinations," NASA TP 1958, 1981.

14Van Dyke, M., " An Album of Fluid Motion," The parabolic Press, Stanford, Ca, 1982.

15Hoerner, S. F., "Fluid-Dynamic Drag," Hoerner, S. F., 1965.

3Schubauer, G. B., Spangenberg, W.G. and Klebanoff, P.S., "Aerodynamic Characteristics of Damping Screens," NACA TN 2001, January 1949.

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