Measurements of the Influence of Integral Length Scale on Stagnation Region Heat Transfer

G. James Van Fossen National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44135


INTRODUCTION
Heat transfer to a stagnation region is important in many engineering applications; none, however, is more critical than in the gas turbine where combustor exit temperatures often exceed the melting point of superalloy turbine airfoil materials.In most cases the highest heat transfer rate on a turbine airfoil occurs in the stagnation region thus making it critical for the design of cooling schemes to obtain an accurate pre-higher levels.
Stagnation region heat transfer augmentation in the presence of free stream turbulence is believed to be caused by vorticity amplification (see Morkovin  [1979] for a review).Free stream turbulence can be viewed as a continuum of tangled, vortical filaments; those filaments with components normal to the stag- nation line and normal to the free stream flow are convected into the stagnation region where they are stretched and tilted by the divergence of streamlines and acceleration around the bluff body.This stretch- ing causes the vorticity to be intensified through con- servation of angular momentum.It has been shown both experimentally and numerically (Hanarp and  Suden, 1982; VanFossen and Simoneau, 1987; Rigby  and VanFossen, 1991) that vorticity in the stagnation region causes heat transfer to be increased while the boundary layer remains laminar.Turbulent eddies that are very large relative to the size of the bluff body are not stretched and thus act only as mean flow variations while eddies that are very small are de- stroyed by viscous dissipation before they can inter- act with the boundary layer.This leads to the hypothesis that somewhere between these two extremes there must be an optimum eddy size that causes the highest heat transfer augmentation.Two goals of this research were to determine this optimum eddy size and to develop a more accurate correlation that could be used by designers to predict heat transfer.
It has been known for many years that free stream turbulence can augment stagnation region heat trans- fer (Giedt, 1951 Seban, 1960); however, results of ex- periments are inconsistent and attempts to correlate heat transfer augmentation as a function of turbulence intensity and Reynolds number while ignoring the length scale (Zapp, 1950; Schnautz, 1958; Smith and  Kuethe, 1966; Kestin and Wood, 1971; Mehendale et   al., 199t) have not been entirely successful.Any re- sulting correlations usually predict the author's data but not data from other researchers.Lowery and Va- chon [1975] measured lateral length scale in their study of the effect of grid generated turbulence on stagnation region heat transfer but they did not have a sufficient variety of grids to deduce an effect of scale.
Their resulting correlation has been used as a standard against which subsequent data sets have been com- pared, sometimes with large discrepancies; see for ex- ample O'Brien and VanFossen [1985].There have been several attempts to isolate the effect of turbulence length scale; Yardi and Sukhatme [1978] used four dif- ferent grids to generate a range of length scales.The four grids were all of different geometry; i.e. two were screens and two were biplane grids, all had different rod spacing to rod diameter ratios.They showed a trend of increasing heat transfer with decreasing length scale; however, there is so much scatter in the data that their claim of ten boundary layer thicknesses for an optimum length scale is questionable.Dyban et al [1975] used perforated plates as well as a fully de- veloped turbulent pipe flow to investigate the effect of intensity and scale on stagnation region heat transfer.
Their results showed increasing augmentation with decreasing scale but they did not attempt to correlate the data based .onthis finding.
More recently, Ames [19901 used simulated com-  bustor segments to generate turbulence and measure its effect on heat transfer to a fiat plate and a stagnation region.Ames concentrated on relatively large scale turbulence where the length scale to leading edge di- ameter ratio was greater than 1.0.He used the rapid distortion theory of Hunt [19731 and the measure- ments of Hunt and Graham 1978] near a plane surface to develop a model for the spectrum of turbulence near stagnation.He integrated his model spectrum to esti- mate the eddy viscosity in the stagnation region.The viscosity was then used in a phenomenological model after Smith and Kuethe [1966] to develop a new cor- relating parameter involving Reynolds number, turbu- lence intensity, and what Ames calls an energy scale (the average size of the energy containing eddies).
Ames used three different diameter cylinders to inves- tigate stagnation region heat transfer; his data were well correlated using his new parameter.The data of several other researchers (Lowery and Vachon, 1975;  Dyban et al., 1975) were also correlated by his parameter but with more scatter.
For the present work, a model with a circular lead- ing edge was fabricated with heat transfer gages in the stagnation region.The model was qualified in a low turbulence flow by comparing measurements with Frossling's solution for stagnation region heat transfer.Five turbulence generating grids were fabri- cated; tour were square mesh, biplane grids made from square bars with different bar widths.Each of the four had identical mesh to bar width ratio.The fifth grid was an array of fine parallel wires that were perpendicular to the axis of the cylindrical leading edge.Turbulence intensity and integral length scale were measured as a function of distance from the grids.Stagnation region heat transfer was measured with each grid at various distances upstream of the model.Data were taken at cylinder Reynolds numbets ranging from 42,000 to 193,000.Turbulence in- tensities were in the range 1.1 to 15.9 percent while the ratio of integral length scale to cylinder diameter ranged from 0.05 to 0.3.
Measurements of length scale and intensity are presented as well as the stagnation region heat trans- fer results.A correlation involving the turbulence pa- rameters and Reynolds number is presented that fits the heat transfer data for the square bar grids to within +_4%.The data of other researchers will also be compared with the correlation.Heat transfer data from the array of parallel wires will also be dis- cussed.Finally, a method for determining the heat transfer distribution downstream of the stagnation point will be presented.

Wind Tunnel
The experiments were carried out in the wind tunnel shown in figure l, which is described in detail by "\,.Probe "k__.\.... Access VanFossen and Simoneau [1987].Air flow drawn from the test cell passes through a flow conditioning section and a 4.85:1 contraction before entering the 15.2.cm wide by 68.6 cm high test section.The max- imum velocity attainable was about 46 m/sec.Clear tunnel turbulence levels were less than 0.5 percent for all flow rates.After leaving the test section, the flow passed through a transition section into a 10-inch pipe in which a flow measuring orifice plate was lo- cated.Air then passed through a butterfly valve which was used to control the tunnel flow rate and then to the Laboratory exhaust system.The readings from four exposed-ball Chromel-Constantan thermocou- ples located around the perimeter of the inlet were averaged to yield the stagnation temperature.An ac- tuator system with four degrees of freedom was used to position a hot wire probe at any desired measure- ment location within the rectangle shown on figure 1.

Turbulence Grids
Turbulence generating grids were installed at any one of several axial locations upstream of the model.For the present tests, five turbulence generating grids were used.Four were square bar, square mesh, bi- plane grids.The fifth grid consisted of an array of parallel wires oriented perpendicular to the stream- wise and spanwise directions.Grid parameters are de- fined in figure 2 and dimensions of the grids are given in Table I.Henceforth grids will be referred to by the number given in the table.Grids G1 to G4 were fabricated keeping the ratio of mesh spacing to INTEGRAL LENGTH SCALE AND HEAT TRANSFER size, different length scales could be produced at fixed intensity by varying the distance from the grid.

Heat Transfer Model
The heat transfer model used in this study was a 6.60 cm thick flat plate that was 15.2 cm wide; the leading edge of the plate was a semi-circular cylinder.The fiat plate extended 26.4 cm downstream from the tan- gent point to the cylinder and a 6.2 wedge then ex- tended downstream and ended in a cylindrical trailing edge 0.635 cm in diameter.A photograph of the heat transfer model is shown in figure 3. Nineteen heat ttux gages were embedded symmetrically around the stagnation line at 8.7 intervals so as to obtain heat transfer coefficients up to _78 on either side of the stagnation line.Each heat flux gage consisted of an aluminum strip 6.60 cm long by 0.476 cm wide and 0.32 cm deep.A Kapton(R) encapsulated, foil, electric heater was fastened to the back of each aluminum strip with pressure-sensitive adhesive.Gage tempera- FIGURE3 Heat transfer model.
ture was measured by a Chromel-Alumel thermocou- ple embedded in a groove in each aluminum strip.A guard heater behind the heat flux gages prevented heat conduction to the interior of the model.The av- erage gap between the aluminum strips was 0.025 cm and was filled with epoxy.The aluminum strips were maintained at a uniform constant temperature by a specially designed control circuit (see VanFossen et al. 119841 for details).Steady state, spanwise-aver- aged heat transfer coefficients were calculated for each aluminum strip basett on the power supplied to the strip and the wall-to-fluid temperature difference.Instrumentation and Data Acquisition Turbulence measurements were obtained using a two channel, constant temperature, linearized, hot wire anemometer system.Turbulence intensities, and au- tocorrelations were measured using a standard, 5 lm, single, hot-wire oriented perpendicular to the flow direction.A cross-flow type X-wire probe was used for the two component measurements.The hotwire signals were linearized with analog linearizers.
For addition and subtraction of the signals from the X-wire, a signal conditioner was used.A program- mable digital multimeter was used to calculate the root mean square (rms) velocity fl'om the wires us- ing 100-averages for each reading.Mean voltages were read on an integrating digital voltmeter with an adjustable time constant.
A dual channel spectrum analyzer was used to obtain autocorrelation data.The analyzer featured a 12-bit analog to digital conversion rate of 2.56 times the selected frequency and an anti-aliasing filter with a rollofl" of 120 dB/octave.The selectable frequency range was from 10 Hz to 100 kHz.A personal com- puter was interfaced to the spectrum analyzer for data storage and processing.Steady-state operating conditions (temperature, pressures, voltage and cur- rent to gages, etc.) were recorded on the Laboratory data acquisition system called ESCORT (see Miller, 1978).For every heat transfer data point, twenty readings of each data channel were recorded.These twenty readings were averaged to give a single value for each channel.To eliminate any off'set between data channels caused by the solid state multiplexers, a reading was obtained by shorting all the inputs to ESCORT and subtracting this "zero" from each sub- sequent reading.
tions were carried out using a two point, iteration method in conjunction with the signal linearizers (see Anon).The frequency response of the hot-wire ane- mometer system was estimated to be around 30 kHz using the standard square wave test.For the two com- ponent velocity measurements, the correction factor in Champagne's equation (Champagne et al., 1967)   which accounted for the cooling due to the tangential velocity component along the wire was determined experimentally by varying the angle between the Xwire bisector and the jet between 35 and 55 at jet velocities of 23 and 46 m/sec.A least squares curve fit of Champagne's equation was then used to find the correction factor.Complete details of the hot wire calibration procedure are given in VanFossen et al. [1994].

Heat Flux Measurements
For the heat transfer measurements, all 19 heat flux gages were heated to temperatures of either 46 or 54C; the average recovery temperature of the air was about 27C giving wall to air temperature ratios of approximately 1.06 or 1.1.All of the heat flux gages were maintained at the same temperature within _0.2C.Heat flux measurement were carried out with each grid in at least 7 axial locations from the stagnation line of the leading edge.For each grid position, tests were performed at 5 Reynolds numbers ranging from 42,000 to 193,000.

DATA REDUCTION AND UNCERTAINTY ANALYSIS EXPERIMENTAL PROCEDURE Hot Wire Calibration
The hot-wires used for the turbulence measurements were calibrated in an open air jet at nearly the same temperature as the wind tunnel flow.Velocity calibra- Turbulence Intensity Turbulence intensities were calculated from the sin- gle hot-wire and the X-wire.The local turbulence in- tensity for the single wire was calculated as the ratio of the rms to mean linearized, bridge voltage.Two component turbulence intensities were calculated from the linearized signals of the X-wire using the method of Champagne [1967].

Integral Length Scale
The integral length scale describes the average eddy size associated with the turbulence.There are at least three practical ways to obtain the integral-length scale (see VanFossen et al. [1994]); however, the availability of a spectrum analyzer that could com- pute the autocorrelation and average any number of them together made this method the natural choice.With this method, Taylor's hypothesis that time and streamwise distance are related by the mean velocity is invoked.A single point autocorrelation is thus equivalent to a two point space correlation separated by streamwise distance.The area under the normal- ized autocorrelation function gives a time scale, for the average eddy which when multiplied by the mean velocity yields the longitudinal integral length scale,

A x
The autocorrelation method suffers from a problem with low frequency noise, i.e. low frequency noise keeps the autocorrelation from approaching zero in a consistent manner.Many investigators have used the first zero crossing as the upper limit of integration (Ames, 1990;Wiegland, 1978;Tan-Atichat, 1980).
The dashed lines on figure 4 are a typical pair of autocorrelations taken behind grid G1; examination of this figure makes it clear that integrating until the first zero crossing will give very different results for the length scale.
To eliminate the low frequency noise problem, it was decided to use a least squares fit of the autocor- relation by the exponential function, i.e.

R('r) e -G,
(1) Data between 0.33 -< R(-) --< 1.0 were used for the curve fit; the resulting fit is also seen on figure 4. The exponential function does not reproduce the autocor- relation for very small values of "r but the fit is satis- factory over the main range of interest and the prob- lem of determining the upper limit of integration is solved.Integrating between 0 and o and multiplying by the mean velocity, the longitudinal length scale then becomes, U A x (2)

C
If the hot wire is long compared to the length scale of the flow, errors in intensity and scale can result due to averaging of flow variations over the wire length.Correction for the hot wire length was not made for the present tests; the smallest integral scale measured was 2.6 times the active length of the hot wire.

Heat Transfer
Power from the electric heaters is removed from the aluminum strips by convection to the air, radiation to the surroundings, and conduction to the epoxy gap between the gages where it is convected to the air.An energy balance was solved for the Frossling number for each gage (qE1-qr,,d- where ql; is the heat added by the heater (voltage x current), q,.,,d is the heat lost by radiation, and qgw, is  loss can be obtained from an exact solution for two- dimensional heat conduction in a rectangle half the epoxy gap width wide and the aluminum gage depth deep.Two adjacent sides are assumed insulated, one side held at the constant temperature of the aluminum strip and the final side convecting to the air at a known temperature.Details of this analysis are given by VanFossen et al. [1984].Corrections for radiation heat losses were also made assuming gray body radi- ation to black surroundings and an emissivity of 0.05 for the aluminum gage.Heat lost through the sides of the strips was on the order of 10 percent of the total heat flow, while the radiation heat losses were on the order of 0.2 percent.A is the exposed heat transfer gage surface area, T w is the gage temperature, and T,.
is the recovery temperature at the gage location cal- culated from T,. T.,.,.. + r (T-T,,.) T.,., is the static temperature upstream of the model.
The recovery factor, r, was calculated as U(s)] ,U)/ (1 ) (5) the mass flow ratio, pU(s)/(pU) was found from a numerical solution of flow over the plate that in- cluded the tunnel walls (Rigby and VanFossen,  1992).
The thermal conductivity and viscosity were eval- uated at the free stream total temperature from equations given by Hillsenrath et al. [1955].Total temper- ature was used to evaluate the thermal properties be- cause Rigby and VanFossen [1992] showed that if the thermal properties were based on a reference temper- ature that involved the wall temperature, reversing the direction of heat flux (cooling the wall) caused an undesirable change in the Frossling number.
The Reynolds number, Re,i, was based on the di- ameter of the leading edge and the mass-velocity av- eraged between the flow area with maximum model blockage and the unblocked flow area, i.e.

Uncertainty Analysis
Twenty samples were obtained for each steady-state measurement and averaged to minimize random er- rors.Standard deviations were also obtained from the twenty samples and used as an estimate of random error.Estimates of the accuracy of each measuring instrument were then made, added to the random component, and combined by the method of Kline &   McClintock [1953].Results of the uncertainty analy- sis indicated an average uncertainty (95% confi- dence) of ___6.6% for the Frossling number.The level of uncertainty introduced by the corrections made for the conduction heat losses from the sides and un- guarded ends of the aluminum strips accounted for about 44 percent of the total uncertainty; percentages attributed to other variables were: recovery tempera- ture--20, gage temperature--11, heater voltage--8, heater current--8, flow rate--7, and thermocouple reference temperature--2.The uncertainty in turbu- lence intensity and length scale was estimated with the method suggested by Yavuzkurt [1984] and is presented in table Ill.

RESULTS AND DISCUSSION
Turbulence Intensity Variation of turbulence intensity without the model in the test section is shown versus dimensionless dis- tance downstream of each grid in figure 5.All five grids were run at velocities of 11, 23, and 46 m/sec.The decay of the intensity is in qualitative agreement with the correlation of Baines and Peterson [1951] INTEGRAL LENGTH SCALE AND HEAT TRANSFER . [ . G1 R3 B&P [31]   iy.\k 'L--LLL-f f i : GGRR e.) Grid 5 200 400 600 800 x/b FIGURE 5 Turbulence intensity data and curve fit compared to data of Baines and Person [1951].
which is also shown on the figure for reference.Each grid and Reynolds number had slightly different char- acteristics so intensity data for each case were fit with a power law of the form Tu-at-} Coefficients for each of the fits appear in Table II and the curve for each case is shown on figure 5. Several spanwise traverses were made downstream of the grids; typically, the variation of turbulence intensity was around 5%.

Length Scale
Figure 6 shows the variation of the integral length scale in the streamwise direction behind grids G1- G5.Increase in the integral length scale with distance from the grid is apparent in all cases.This is ex- pected, since the smaller eddies dissipate faster than the larger eddies.Also shown on the figure is a cor- relation due to Roach [1987].Roach developed a the- ory to correlate the variation of micro-scale with dis- tance from the grid.He states that it is not possible to develop a theory for the variation of integral scale with distance.He therefore assumed that the integral scale should follow the decay of micro-scale in the downstream direction but removed the Reynolds number dependence.His correlation has the form A X He determined from his data that I 0.2.The present data for the square bar, square mesh grids tend to be independent of Reynolds number and follow the square root of distance dependence as in Roach's cor- relation but the constant is larger.The data for the wire array do not follow the same square root of dis- tance dependence and are dependent on Reynolds number.Therefore, data for the wire array for each Reynolds number was fit with a power law curve.
The resulting constants for the curve fits for the length scale data for all the grids are given in Table lI.Curve fits of the integral scale versus distance from the grid are compared to the data in figure 6.
These curvefits were used to determine the value of length scale when evaluating the heat transfer dependence.

Isotropy
Figure 7 shows u'/v' versus x/b for grids G3 through G5; the ratio u'/v' is a measure of isotropy for the turbulence, a value of 1.0 would indicate isotropic flow in the plane of the stagnation stream sheet.Turbulence for the square-bar, square-mesh grids (G3 and G4) seems to be nearly isotropic while that for grid G5 shows highly non-isotropic behavior with u'/v' values depending on Reynolds number.The Xwire results for the streamwise turbulence component are in close agreement with those obtained using the single hot-wire.For example, values of the turbu- lence intensity with grid G3 calculated from the sin- gle hot-wire and the X-wire are within 8 percent of each other at all Reynolds numbers.

Verification
Heat transfer results in the leading edge region with no turbulence grid in the tunnel are shown in figure 8. Measured freestream turbulence intensity in this case was less than 0.5 percent.The ordinate for the heat transfer plots is the Frossling number plotted against surface distance from stagnation made dimensionless by the leading edge radius.Results are presented for four levels of Reynolds number and two levels of gage temperature; in all cases the data agree to within the estimated experimental error with the solution of Frossling [1958] and a 2-dimensional numerical so- lution from the PARC code (Rigby and VanFossen, 1992) thus confirming the accuracy of the experimen- tal technique.

Stagnation Region Augmentation
Figure 9 shows the Frossling number at stagnation plotted against the correlating parameter, TuRe,! /2, developed by Smith and Kuethe [1966].Turbulence intensity and length scale correspond to those mea- sured in the wind tunnel downstream of the grid at the axial location of the stagnation line of the cylinder without the model present and were calculated from the correlations in Table II.By moving a grid closer to the cylinder, turbulence intensity is in- creased while the length scale is decreased.The range of longitudinal length scale to leading edge diameter ratio varied from 0.05 to 0.30.The range of turbu- lence intensity varied from 1.1 to 15.9%.The range of length scale for each grid is indicated on the legend in the figure.Also shown on the figure is the correlation developed by Lowery and Vachon [1975].The Lowery and Vachon correlation predicts the heat transfer data only in a narrow range of scales and as the parameter TuRe, /2 increases beyond about 40, the correlation turns downward instead of continuing up as the data indicate.It is notable that there is no optimum length scale in the.range tested here; rather, the heat transfer augmentation continues to increase as scale decreases.
The stagnation heat transfer data for the square bar grids was fit with a function of the form Fr(O) Arm Tu Re, --d-/ + C (9) The constant, C, was set at the zero turbulence Frossling number of 0.939 calculated by the  Length scale versus distance from grid compared to curve fit and theory of Roach [1987].
INTEGRAL LENGTH SCALE AND HEAT TRANSFER Distance from grid, cm 0 ' 1 1 FIGURE 7 lsotropy of turbulence from grids 3, 4 and 5.
PARC-2D code, the constants A;:,., and [3 were de-  termined from a least square fit of the data.The curve fit and the data are compared on figure 10; the func- tion correlates the data to within +4% as shown by the bands drawn on either side of the correlation.Recall, that the turbulence for grids G1-G4 was shown to be isotropic; that for grid G5 (the array of parallel wires) was not.The stagnation heat transfer results tbr grid G5 are compared to the stagnation region heat transfer correlation in figure 11.It is ob- vious from this figure that anisotropic turbulence with  the majority of its vorticity oriented normal to the axis of the leading edge causes increased augmenta- tion over isotropic turbulence.As discussed in the INTRODUCTION, Ames [1990]  scale he called an energy-scale.An attempt was made to correlate our data using his parameter, however, results were not satisfactory.Figure 12 is a comparison of the stagnation heat transfer data of other authors with the present corre- lation.For cases where the authors did not measure length scale, it was estimated using the correlations given in Table II.The data of Zapp [1950] and Ames   [1990] fall well above of the ___8% band shown about the correlation.The turbulence generator of Ames was a simulated combustor segment and produced anisotropic turbulence.The turbulence generators of Zapp were not conventional grids; they consisted of 0.5" dowels (orientation not given) and "two screens next to each other."Not enough information is given about the generators to speculate on the cause of the discrepancy.The data of the other authors are in good agreement with the present correlation.
Distribution of Heat Transfer Around Leading Edge Figure 13 is a plot of the Frossling number normal- ized by the stagnation value versus dimensionless surface distance from the stagnation point.The symbols represent the average of the present data for all grids, Reynolds numbers, and grid positions.The dot- ted lines represent the standard deviation of the nor- malized data and the solid line is the PARC solution for a laminar free stream which has been similarly normalized.The conclusion to be drawn from this figure is that a good prediction of the heat transfer at a given surface distance from the stagnation point can FIGURE 13 Distribution of averaged, normalized Frossling num- ber downstream of stagnation point.

INTEGRAL LENGTH SCALE AND HEAT TRANSFER
be obtained by first using equation ( 9) to predict the stagnation heat transfer and then multiplying by the ratio of local to stagnation heat transfer from a solu- tion for a laminar free stream.
7. Frossling number downstream of stagnation nor- malized by the stagnation value can be repre- sented by a universal curve for both laminar and turbulent flow.

SUMMARY OF CONCLUSIONS NOMENCLATURE
Spanwise average stagnation region heat transfer measurements have been made on a model with a circular leading edge downstream of five turbulence generators.Four of the turbulence generators were square mesh, square bar, biplane grids with identical mesh spacing to bar width ratios and bar widths rang- ing from 0.16 to 1.27 cm.The fifth turbulence generator was an array of fine, parallel wires with the wires oriented normal to the axis of the cylindrical leading edge.Cylinder Reynolds numbers ranged from 42,000 to 193,000, turbulence intensities ranged from I. to 15.9%, and the ratio of integral length scale to cylinder diameter ranged from 0.05 to 0.30.Conclu- sions are summarized as follows: 1. Low turbulence heat transfer results agree with both the Frossling solution and a numerical solu- tion to within estimated experimental accuracy validating the experimental method. 2. Augmentation of stagnation region heat transfer by turbulence increases as integral length scale de- creases.
3. No optimum length scale was found for the turbu- lence generating grids used in the present test (Ax/d >-0.05).
4. A correlation for stagnation heat transfer for the four square bar grids was developed which re- duced data scatter to ___4%. 5.The stagnation heat transfer data of other authors with similar turbulence generators was predicted to within _+8% by the correlation. 6.The correlation did not predict the heat transfer for the array of parallel wires indicating that augmen- tation must also be a function of isotropy of the turbulent flow field.This was also true for the data of other authors who generated anisotropic turbu- lence. A surface area of gage, m 2 constant in equation ( 9) constant in fit of intensity, eqn.( 7) tunnel blockage turbulence grid bar width, cm constant in equation ( 9) parameter in equation ( 1) diameter of leading edge (=2R), cm mean hot wire voltage, V rms of linearized bridge voltage, V Frossling number constant in eqn.( 8) thermal conductivity of air, W/mK turbulence grid mesh spacing, cm exponent in fit of intensity, eqn.(7) exponent in fit of length scale, Tbl.II FIGURE

FIGURE 4
FIGURE 4 Typical autocorrelation for successive readings. 123 FIGURE 6 Length scale versus distance from grid compared to curve fit and theory ofRoach [1987].

FIGURE 8
FIGURE 8Frossling number distribution compared toPARC and  Frossling solutions.

FIGURE 9
FIGURE 9 Stagnation point Frossling number vs TuRe '/2 show- ing the effect of length scale.
FIGURE 12 StagnationFrossling number data of other authors compared to correlation.
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TABLE Turbulence
*Grid G5--array of parallel wires

TABLE II Power
Law Curve Fits of Turbulence Intensity and Integral Length Scale Data