Analysis of Surface Temperature Fluctuations Induced by Slot Jet Impingement

Vinod Narayanan1 and Vishal A. Patil.2

Oregon State University, Corvallis, OR 97331, USA

Data of transient surface temperature are analyzed for an impinging slot jet at nozzle spacings of 0.5, 1.0, 2.0, 4.5, and 5 nozzle hydraulic diameters from the impingement surface at a fixed turbulent exit Reynolds number of 22,500. Spanwise time-traces of temperature at specific streamwise locations of interest identified from mean temperature maps are analyzed. At a larger nozzle spacing of 5 hydraulic diameters, periodically repeating hot and cold temperature streaks are observed suggesting the presence of near-wall streamwise counter-rotating vortex pairs along the impingement line. For a near-wall nozzle spacing of 0.5 hydraulic diameter, temperature streaks at the impingement line are not detected; however, distinct thermal streaks are observed at locations corresponding to the local minimum and secondary peak, in heat transfer. For the analysis of transient thermal structures induced by jet impingement, a proper orthogonal decomposition (POD) algorithm is employed on a time series of 1656 datapoints. Results indicate that approximately 80 percent of the thermal fluctuations of the filtered data at the impingement line can be reconstructed from five modes for a transitional and developed jet impinging on the surface. When the nozzle to surface spacing is small, POD performed at the two off-centerline locations indicates that two modes could describe approximately 80 percent of thermal fluctuations in the filtered data.

Nomenclature ak = expansion coefficient or amplitude F = matrix of time series fluctuating temperature data (oC) Dh = hydraulic diameter of the nozzle (m) r = radial coordinate (m) R = covariance matrix

Re = Reynolds number, Re = VmoDhν

T = temperature (oC) Tf,ij = fluctuating temperature at location j at time instant i (oC) Tm = time and spatially averaged image temperature (oC)

Tm, j = time-averaged temperature at location j along the z axis (oC); Tm, j = Ti, ji∑ n

Vmo = mean velocity at nozzle exit (m/s) x = streamwise coordinate along the minor axis of the nozzle; x = 0.0 corresponds to the projected nozzle

centerline on the impingement surface (m) Xws = width of the slot jet (m) y = normal (vertical) co-ordinate, y = 0.0 location corresponds to the impingement surface, unless

otherwise mentioned (m) Y = nozzle-to-surface spacing along the y axis (m) z = spanwise coordinate along the major axis of the nozzle, z = 0.0 location corresponds to minor axis of

the projected nozzle centerline on the impingement surface (m) Greek symbols Δ = differential

1 Assistant Professor, Department of Mechanical Engineering, 204 Rogers Hall, Corvallis, OR 97331-6001. 2 Graduate Student, Department of Mechanical Engineering, 204 Rogers Hall, Corvallis, OR 97331-6001.

1 American Institute of Aeronautics and Astronautics

9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference5 - 8 June 2006, San Francisco, California

AIAA 2006-3267

Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

λ = spacing between thermal streaks (m) or eigenvalue ν = fluid kinematic viscosity (m2/s) θ j = non-dimensional RMS temperature fluctuations at location j along the z axis ψk = eigenfunction Subscript ad = adiabatic h = heated m = mean value max = maximum i = time index j = index for spatial location along the z axis t = time x = x direction y = y direction z = z direction

I. Introduction Jet impingement heat transfer and fluid mechanics has been studied extensively for the past five decades due to

its importance in convective cooling applications. Both experimental and numerical studies on jet impingement have been well documented in literature1,2. A brief overview of relevant studies in stagnation region flow structure and heat transfer, and those related to impingement at close nozzle spacing is provided below; a more detailed account has been presented in a previous paper3. a) Heat transfer and near-wall flow structure resulting from transitional jet impingement (Y/Dh>3)

Several prior studies have studied the flow and heat transfer at the impingement line for a slot jet, or the impingement point for a circular jet. VanFossen and Simoneau4 determined the presence of pairs of counter-rotating streamwise vortices at the forward stagnation point of a cylinder when an array of parallel wires was placed perpendicular to the stagnation line and located upstream of the cylinder. They found regions of high heat transfer corresponded to locations in between the vortices, where the flow directly impinged on the surface. At these locations, the turbulence intensity just prior to impingement was a minimum. They also determined that regions of high near-wall turbulence corresponding to these vortices were well outside the theoretical laminar boundary layer.

Yokobori et al.5 studied similar vortical structures that formed above the impingement line of a two-dimensional turbulent slot jet. The vortex formation frequency was a maximum for the nozzle spacing, Y/Dh= 3.5, and the average value of the spacing between the vortex pairs was found to be equal to the slot nozzle width. This spacing was found to be insensitive to Reynolds number variations in the range of their experiments. Counter-rotating vortex pairs were seldom observed for nozzle spacings of Y/Dh ≤ 2. Based on flow visualization observations, they conjectured that counter-rotating vortices at the impingement plane were a result of periodic distortions of primary shear vortices generated in the mixing layers on both sides of a plane free jet prior to impingement.

Kataoka et al.6 confirmed the observations of Yokobori et al.5 and Yokobori et al.7 in their flow and heat transfer experiments and extracted surface renewal frequencies from the data. Based on an analysis of time averaged velocity gradients in the streamwise and spanwise directions, they concluded that for spacings larger than Y/Dh=2, streamwise gradients were high in the inner impingement region, while spanwise gradients dominated in the outer impingement region, indicating a surface renewal by streamwise vortex stretching in the inner impingement region, and by impingement of large-scale eddies in the outer impingement region.

Sakakibara et al.8 measured, simultaneously, the near-wall vortex structure and temperature distribution in the impingement region. They observed counter-rotating vortices sweeping cold fluid toward the wall, and ejecting high-temperature fluid toward the outer region. The wall temperature in the ejection region under the vortex pair was higher than in the region between the vortex pairs, where the cold fluid directly impinged on the surface. Amplification of vorticity due to stretching by the accelerating mean flow in the streamwise direction was indicated as the cause for enhanced heat transfer in the stagnation region.

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b) Heat transfer and near-wall flow structure resulting from near-wall jet impingement (Y/Dh <2.5) A non-monotonic trend in local heat transfer coefficient distribution in both axisymmetric and two-dimensional jets has been observed in several studies2 when the potential core of the jet is present on impingement. The non-monotonic trend in radial distribution of heat transfer coefficients in circular jet impingement at close nozzle-to-surface spacing was attributed to local thinning of the laminar boundary layer caused by flow acceleration in the vicinity of the impingement point (primary peak), the interaction of the large-scale turbulence generated in the mixing layer, and transition to developed turbulent radial wall jet (secondary peak). Gardon and Akfirat9 observed a secondary peak in heat transfer distribution for slot jet with nozzle-to-surface spacings between 1 and 3 hydraulic diameters, and attributed it to a transition from laminar to turbulent boundary layer. They also reported a local minimum at the stagnation line, surrounded by primary peaks on either side for a very close spacing, Y/Dh = 0.33. A transition to turbulent flow, they conjectured, was triggered by the disappearance of the favorable pressure gradient which existed in the accelerating flow past impingement, which manifested as the rise in local heat transfer coefficients at x/Dh = 2. This trend continued until the boundary layer thickened accompanied with a decrease in mean flow velocity due to jet spread. These two opposing effects, they speculated, resulted in a secondary peak in heat transfer at a x/Dh = 3.5, beyond which heat transfer decreased monotonically.

II. Background and Objectives Narayanan et al.10 compared the mean flow field, turbulent intensities, and heat transfer coefficients at spacings

corresponding to transitional jet (Y/Dh = 3.5) and near-wall (Y/Dh = 0.5) impingement on a flat surface. For the transitional jet, turbulence was high close to the surface prior to impingement. The peak values of mean and rms-averaged fluctuating surface pressure, and local heat transfer occurred in the impingement region and decreased monotonically in the wall bounded flow past impingement. At the lower spacing, the primary peak in heat transfer, which occurred in the impingement region, was followed by a region of local minimum and a secondary peak that occurred at x/Dh= 1.5 and 3.2, respectively. The peak mean surface pressure occurred in the impingement region; however, the RMS-averaged surface pressure fluctuation profile exhibited a peak at the location of minimum heat transfer. There was a good correlation between the locations of the secondary peak in heat transfer and peak near-wall streamwise turbulence. However, local heat transfer coefficient could not be related solely to the near-wall streamwise turbulence, and was strongly dependent on the relation between outer shear layer and near-wall turbulence. This relation was deduced from data of RMS pressure fluctuations. The high RMS pressure fluctuations for transitional jet impingement was attributed to the high turbulence above the impingement line, while for the near-wall jet impingement, it resulted from correlated turbulent motion in the outer region of the wall-bounded flow past impingement. Flow visualization revealed the presence of coherent structures in the outer region at low nozzle-to-surface spacing.

Narayanan3 presented low-frequency time traces and RMS-averaged data of the impingement surface temperature at the two spacings, Y/Dh = 5.0 and Y/Dh = 0.5. Time traces of surface temperature at locations downstream of the impingement line for near-wall jet impingement revealed flow structures that had not been reported previously.

This paper presents an analysis of time series data of fluctuating surface temperatures using a Proper Orthogonal Decomposition (POD) method to identify the dominant modes in surface heat transfer for slot jet impingement from different nozzle-to-surface spacings. Nozzle-to-surface spacings of 0.5, 1.0, 2.0, 4.5 and 5.0 hydraulic diameters are analyzed. The jet exit Reynolds number was maintained constant at 22,500 based on the nozzle hydraulic diameter.

Lumley11 was the first to apply POD in turbulence analysis. Also known as Karhunen-Loeve decomposition, principal component analysis and empirical orthogonal function analysis, POD is a method for analyzing the variability of a data set. When applied to a scalar field such as temperature map, dominant thermal structures and their trends can be extracted. This technique decomposes variability in data along an orthogonal eigenvector basis with associated eigenvalue giving measure of variability contained in that mode.

III. Experimental Facility and Procedure A detailed description of the experimental set-up and test section are provided elsewhere10. Briefly, compressed

air, supplied by two dedicated screw compressors was dried, filtered, and directed into a plenum through two settling tanks and pressure regulators. The mass flow rate was measured with a sonic nozzle at the exit of the last settling tank. The plenum consisted of a series of screens and a honeycomb, followed by a convergent section. The flow exited the plenum through an end plate consisting of seven contoured slots of aspect ratio 20:1. For this experiment, the nozzle was attached to the central slot, and all other slots were sealed. A schematic of the heat transfer test section is shown in Fig. 1. The impingement surface consisted of a central constant heat flux surface

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Inconel 600 foil, 0.0254 mm thick

38.1 mm

38.1

mm

63.5

mmcopper bus bars

infrared camera

foil tensioning screwPlexiglas side plates

38.1 cm63.5 cm

38.1 cm

63.5 mm

+ve -veto dc power supply to dc power supply

63.5 cm

Figure 1. Schematic of heat transfer test section.

surrounded by Plexiglas end plates on all sides. The entire test section was 63.5 cm long and 63.5 cm wide. The central heat transfer test section consisted of a 0.0254 mm thick inconel 600 foil 38.1 cm long and 38.1 cm wide, stretched tightly between two solid copper bus bars. The foil was electrically heated by means of a high current DC power supply and represents a near-constant heat flux surface. The nozzle had an aspect ratio 20:1, with a slot width, Xws=12.7 mm with semi-circular ends. The jet flow was unconfined at the radial ends.

Local surface temperatures were measured non-intrusively with a 8-13 μm wavelength infrared (IR) camera (Mikron Inc., model 6T62 thermotracer). The imager was operated in a time trace mode in which the imaging optics scanned across a single horizontal line encompassing 256 spatial locations over 206 equal time intervals for each frame recorded. In this mode, temperatures could be recorded at a frame rate (or an equivalent line scan rate) ranging from 1/60 frames per second (3.45 Hz) to 1 frame per second (207 Hz). For transient temperature measurements at a user-specified location on the surface, once steady state conditions were reached, the camera was operated in the time trace mode to obtain temporal variations in surface temperature along the chosen x = constant line. In each case, 8 frames of data were collected and stored in the imager memory before being transferred to the computer through a GPIB interface. A total of 8 frames at each frame rate provided 1656 temperature values at discrete time intervals at each of the 256 locations along the horizontal line.

IV. Data Analysis A POD analysis was performed on discrete temperature data obtained from IR images. For the analysis, only the

central 106 locations along the z-axis are chosen because they represent the planar region of the jet. Recall that the ends of the nozzle were circular and the jet was unconfined at its ends. The analysis technique outlined by Bjornsson and Venegas12 was applied in Matlab®. The fluctuating component of temperature at each location was found using

x

z

Tf ,ij =Tij −Tm, j (1)

The time series fluctuating data at each location was arranged as a column vector in a matrix F. The covariance matrix, R, of F was calculated as

R=F t × F (2)

Solving the eigenvalue problem for this matrix gives POD eigenfunctions ( ) and its associated eigenvalue

(ψ k

λk ). The eigenfuctions are ordered in decreasing order of their eigenvalues. The fraction of the total variance in R as explained by that mode can be determined by dividing its eigenvalue by sum of all the eigenvalues. Hence, the first modes represent the largest or the most dominant fluctuating thermal features in the temperature field. The expansion coefficients or the amplitudes ( ) of the kak th mode can be found by projecting F onto the kth eigenfunction,

ak =F ×ψ k (3)

The expansion coefficients provide the variation of that POD mode with time. The original data can be

constructed from the modes using

F = ak (ψ k )j= 1

n∑ (4)

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Figure 2 shows temporal distribution of instantaneous differential temperature, Figure 2 shows temporal distribution of instantaneous differential temperature, ΔTij recorded at a minor axis location x/Dh= 0 (the centerline) for Y/Dh= 0.5, where ΔTij is defined as

ΔTij = Tij − Tm (5) No distinct thermal streaks can be observed from the figure, and hence the observed temperature fluctuations

observed were attributed to random noise. Because the temperature fluctuations for all time traces were less than 1oC and because the data in the time trace mode was collected at a low signal-to-noise ratio, the fluctuating temperature data was quite noisy. In order to distinguish clearly the thermal structures from the background noise, a filtering scheme was adopted. In each time trace, the POD modes with lower eigenvalues were attributed to this noise. Thus, in this filtering process, the lower energy modes were chosen such that the data reconstructed from these modes had standard deviation averaged over all z equal to the z-averaged standard deviation for x/Dh = 0 and Y/Dh = 0.5 case. The remaining modes were used to reconstruct the filtered data. The percent contribution of each

z/Dh

θ j

-2 -1 0 1 2 30.0x10+00

1.0x10-04

2.0x10-04

3.0x10-04

4.0x10-04

5.0x10-04

x a= 0.00D dat= 1.19D dat= 1.19D iltered= 1.19D deleted

x ax fx

x/Dh = 0.00 original x/Dh = 1.67 original x/Dh = 1.67 filtered x/Dh = 1.67 deleted

Figure 3. RMS temperature fluctuations at two streamwise locations, x/D

Figure 2. Temporal variation of temperature fluctuation along the centerline, z/Dh=0.00 for slot jet impingement; Y/D

h = 0.00 and 1.67 for near-wall slot jet impingement, Y/Dh=0.5. h = 0.5. Also shown are the filtered and deleted RMS profiles at x/Dh = 1.67

(a) (b)

Figure 4. Time traces of fluctuating wall temperature by slot jet impingement at Y/Dh = 0.50 at x/Dh = 1.67 downstream of impingement corresponding to RMS data in Fig. 3. The fluctuations are estimated based on the spatial and temporal average temperature, Tm, given by Eq. 5. (a) original data; (b) filtered data

ta; (b) filtered data

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mode toward the total thermal fluctuation was calculated based on the filtered dataset. Figure 3 shows the non-dimensional RMS temperature for Y/Dh= 0.5 and x/Dh= 0 and filtered and unfiltered

non-dimensional RMS temperature for Y/Dh= 0.5 and x/Dh= 1.19. The non-dimensional RMS temperature is defined as

θ j =1

Tm, j

(Tij − Tm, j )2

i=1

i=n

∑n −1

(6)

Also shown in Fig. 3 is the filtered (subtracted) portion of the fluctuations at this location x/Dh = 1.67. As mentioned in the previous section, the standard deviation of the filtered data, averaged over all z locations, is equal to that of the base case of Y/Dh= 0.5 and z/Dh = 0.00. Figures 4a &b represent the time traces of the original data and the filtered data at x/Dh = 1.67 for the near-wall spacing for which the corresponding RMS profile of this case was presented in Fig. 3. Comparing the two time traces, it can be seen that the main features are preserved in the filtered data, while the background noise has been removed.

Preliminary POD analysis was performed for time traces with different recording scan rates of the IR camera; Both the RMS temperature and the POD modes were largely unaltered with scan rate; hence, time traces recorded with a frequency of 3.45 Hz were used for subsequent POD analysis.

V. Results and Discussion Figures 5a shows the distribution of the time-mean, spatially-local impingement surface temperature differential, (Tm,h-Tm,ad), between the hot surface and the unheated surface. An x/Dh = 0.0 corresponded to the nozzle centerline along the minor axis. The extent of the nozzle in the x-direction was between

At steady state, the time-averaged temperature distribution was uniform along the centerline, to within −0.25 ≤ x / Dh ≤ 0.25.

+0.1 oC. Isotherms developed parallel to the impingement line along the x-direction, with increasing deviation from x = constant lines at larger distances (x/Dh > 3.5). These deviations can be attributed to the interaction of the flow from the circular ends of the jet, which caused radial temperature isotherms at the ends. The temperature differential increased monotonically from the impingement line outward which corresponded to a decrease in the heat transfer coefficient.

Figure 5b presents (Tm, h-Tm,ad) for the slot jet at a spacing of Y/Dh = 0.5 from the centerline. The differential mean temperature distribution at this spacing was very different from that for the transitional jet impingement. The lowest temperature occurred at the impingement location. Surrounding the impingement region were regions of high temperature around x/Dh = 1.6 corresponding to a local minimum in heat transfer coefficient, followed by regions of

(a) (b)

Figure 5. Time-mean, spatially local surface temperature differential data for slot jet impingement at a nozzle-to-surface spacing of (a) Y/Dh = 5.0, and (b) Y/Dh = 0.50

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lower temperatures around x/Dh = 3.2, corresponding to a secondary peak in heat transfer. Past x/Dh = 3.2, the temperature decays with increasing distance downstream.

Time traces were recorded at locations denoted by the dotted lines in Figures 5a & b. For the Y/Dh = 5. 0 nozzle spacing, this corresponded to the impingement line, x/Dh = 0.00 and a downstream location of x/Dh = 1.19. For the near-wall spacing of Y/Dh = 0.5, time traces were recorded at the impingement line, in the vicinity of the local minimum in heat transfer, x/Dh = 1.67, and at the location of the secondary peak in heat transfer, x/Dh = 3.2. Time traces for the rest of the nozzle spacings have similar trends to either one of the above two cases. Figures 6-9 represent reconstructions of the fluctuating temperature data for jet impingement for the above two spacings at the specified x/Dh locations. Note that x/Dh = 0.00 for the near-wall spacing of Y/Dh = 0.50 was presented in Fig. 2, and is used for filtering data of all other nozzle spacings and locations. Table 1 summarizes the percentage of temperature fluctuation that is accounted by each mode for various nozzle to surface spacings and streamwise locations.

Analysis of the time traces at a location of x/Dh = 1.67 for the near-wall nozzle spacing of x/Dh = 0.50 is presented in Figure 6. Figure 6a shows the filtered temperature fluctuations at this location. Note that the filtered data in this and the remaining plots are presented with respect to the local time-mean data that is determined using Eq. 1. This is in contrast to the representation in Fig. 4b of the same data, where the temperature fluctuation at each location is determined with respect to the spatial and time mean temperature, given by Eq. 5. Use of Eq. 1 to represent temperature fluctuations is preferred because the true temperature fluctuations at each location are clearly identified. Figures 6b -6f represent the reconstructed data using modes 1-5, respectively. From the figures, it is clear that the first two modes represent most of the temperature fluctuations; Table 1 indicates this value to be 79 percent. Note that this percentage is calculated with respect to the filtered dataset. The cumulative reconstruction using the first five modes is presented in Fig. 6g; table 1 indicates this percent of temperature fluctuations to be 99 percent of the filtered dataset.

Figure 7 presents the analysis of time traces at the location of the secondary peak in heat transfer, x/Dh = 3.2 for the near-wall spacing of x/Dh = 0.5. Figure 7a indicates the time trace obtained after the filtering procedure. Figures 7 b-d represent reconstructions of the data using the first three modes. As seen from the figures, the temperature fluctuations of the filtered data set at this location are almost completely explained by the first two modes alone. Table 1 indicated that the first two modes account for 92 percent of the fluctuations of the filtered data set.

Time traces of fluctuating temperature data of transitional jet impingement at the impingement line for a nozzle-to-surface spacing, Y/Dh = 5.0, is presented in Figures 8. Figure 8a shows the filtered data, and Figs. 8b-f represent reconstructions of temperature fluctuations using modes 1-5, respectively. The first two modes account for 54 percent of the filtered temperature fluctuations. At this nozzle-to-surface spacing, hot and cold thermal streaks are observed at the stagnation line and parallel the observations made in other studies of the fluid flow near the surface at impingement. Recall that for jet impingement at such spacings, prior studies 4,5,6,8 indicated the presence of pairs of counter-rotating vortices at the stagnation line, aligned with the streamwise direction. The thermal streaks indicated in Fig. 8a could be regarded as thermal “imprints” of these near-wall flow structures. The modal reconstructions indicate that approximately 54 percent of the thermal fluctuations at the impingement line can be reconstructed from the first two modes. Analysis of temperature fluctuations at a further downstream location of

Table 1: Distribution of the temperature fluctuations among the dominant modes during slot jet impingement

Mod1 Mod2 Mod3 Mod4 Mod5 Mode 6 H/d=0.5; x/d=1.67 0.54 0.25 0.09 0.06 0.05 H/d=0.5; x/d=3.2 0.52 0.40 0.08 _ _ H/d=1; x/d=1.67 0.60 0.19 0.13 0.07 _ H/d=1; x/d=3.2 0.60 0.22 0.1 0.05 0.02

H/d=2; x/d=1.67 0.61 0.22 0.09 0.07 _ H/d=2; x/d=3.2 0.58 0.17 0.11 0.07 0.06

H/D = 4.5; x/D = 0 0.28 0.22 0.20 0.16 0.14 - H/D =4.5; x/D = 1.19 0.30 0.24 0.19 0.14 0.13 -

H/D = 5; x/D = 0 0.30 0.24 0.20 0.14 0.12 - H/D = 5; x/D = 1.19 0.30 0.21 0.17 0.11 0.11 0.10

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x/Dh = 1.19 is presented in Figs. 9. The thermal streaks are observed to persist at this location, and are more intense than at the stagnation line. The first two modes account for 51 percent of the filtered temperature fluctuation data shown in Fig. 9a.

Table 1 documents the results from the POD analysis of all nozzle-to-surface spacings, including Y/Dh = 1.0, 2.0 and 4.5. The former two cases follow on the lines of the Y/Dh = 0.50 case because the potential core is present in both these cases on impingement. The latter case pf Y/Dh = 4.5 follows the Y/Dh = 5.0 case, because they both represent transitional jet impingement.

VI. Conclusions A proper orthogonal decomposition analysis was performed on the transient surface temperature data obtained during slot jet impingement. Two distinctly different trends are observed with variation of nozzle to surface spacing. For a low nozzle spacing of Y/Dh = 0.5, centerline fluctuations were negligible. This is attributed to the impingement of the low turbulence intensity jet potential core. However, distinct thermal streaks are observed at downstream locations of x/Dh = 1.67 and 3.2. The latter location corresponds to the secondary peak in heat transfer that is observed for low nozzle to surface spacing jet impingement. Approximately 80 percent of the fluctuations are captured by the first two modes at these locations for the near-wall nozzle spacing. For a larger nozzle spacing of Y/Dh = 5.0, distinct hot and cold thermal streaks are observed at the centerline. These streaks are observed to persist at a downstream location of x/Dh = 1.19. The first five modes explain a majority of the fluctuations for jet impingement at this spacing.

References 1Martin, H., “Heat and Mass Transfer between Impinging Gas Jets and Solid Surfaces,” Advances in Heat Transfer, Vol. 13,

1977, pp. 1-60. 2Viskanta, R., “Heat Transfer to Impinging Isothermal Gas and Flame Jets,” Experimental Thermal and Fluid Science, Vol.

6, 1993, pp. 111-134. 3Narayanan, V., “Time-Resolved Thermal Flow Structures in Impinging Slot Jet Flows,” Proceedings of the 2003 Summer

Heat Transfer Conference, Las Vegas, Nevada, 2003, HT2003-47493. 4VanFossen, G. J., and Simoneau, R. J., “A Study of the Relationship Between Free-Stream Turbulence and Stagnation

Region Heat Transfer,” Journal of Heat Transfer, Vol. 109, 1987, pp. 10-15. 5Yokobori, S., Kasagi, N., Hirata, M., Nishiwaki, N., “Role of Large-Scale Eddy Structure on Enhancement of Heat Transfer

in Stagnation Region of Two-Dimensional, Submerged, Impinging Jet,” Sixth International Heat Transfer Conference, Vol. 5, Toronto, Canada, 1978, pp. 305-310.

6Kataoka, K., Kawasaki, H., Tsujimoto, M., and Ohmura, N., “Effect of Longitudinal Vortices on Heat Transfer Surfaces a Two-Dimensional Jet Strikes Against,” Proceedings of the tenth International Heat Transfer Conference, Vol. 3, 4EC-8, Brighton, U.K., 1994, pp. 31-36.

7Yokobori, S., Kasagi, N., Hirata, M., Nakamura, M., and Haramura, Y., “Characteristic Behaviour of Turbulence and Transport Phenomena at the Stagnation Region of an Axi-Symmetrical Impinging Jet,” Second Symposium on Turbulent Shear Flows-International Symposium on Turbulent Shear Flows, Imperial College, London, 1979, pp. 4.12-4.17.

8Sakakibara, J., Hishida, K., Maeda, M., “Vortex Structure and Heat Transfer in the Stagnation Region of an Impinging Plane Jet (Simultaneous Measurements of Velocity and Temperature Fields by Digital Particle Image Velocimetry and Laser-Induced Fluorescence),” International Journal of Heat and Mass Transfer, Vol. 40 (13), 1997, pp. 3163-3176.

9Gardon, R., Akfirat, J. C., “Heat Transfer Characteristics of Impinging Two-Dimensional Air Jets,” Journal of Heat Transfer, Vol. 86, 1966, pp. 101-108.

10V. Narayanan, J. Seyed-Yagoobi, and R.H. Page, “Combined Fluid Mechanics and Heat Transfer Measurements in Normally Impinging Slot Jet Flows," International Journal of Heat and Mass Transfer, Vol. 47, 2004, pp. 1827-1845.

11Lumley L.J., 1970, “Stochastic Tools in Turbulence”, Academic Press, New York. 12Bjornsson H. and Venegas S.A., “A Manual for EOF and SVD Analyses of Climatic Data”, Feb. 1997, CCGCR

Report 97-1.

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(a) (b)

(c) (d)

(e) (f)

(g)

Figure 6. Time traces of fluctuating wall temperature at x/Dh = 1.67 downstream of impingement, produced by near-wall slot jet impingement; nozzle-to-surfac e spacing, Y/Dh = 0.50. The fluctuations are estimated based on the temporally averaged temperature, Tm,j at each spatial location, j, given by Eq. 1. (a) filtered data; data reconstruction using (b) mode 1; (c) mode 2; (d) mode 3; (e) mode 4; (f) mode 5; (g) modes 1-5

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(a) (b)

(c) (d)

Figure 7. Time traces of fluctuating wall temperature at x/Dh = 3.20 downstream of impingement; nozzle-to-surface spacing, Y/Dh = 0.50. The fluctuations are estimated based on the temporally averaged temperature, Tm,j at each spatial location, j, given by Eq. 1. (a) filtered data; data reconstruction using (b) mode 1; (c) mode 2; (d) mode 3

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(a) (b)

(c) (d)

(e) (f)

Figure 8. Time traces of fluctuating wall temperature at the impingement line, x/Dh = 0.00; nozzle-to-surface spacing, Y/Dh = 5.0. The fluctuations are estimated based on the spatial and temporal average temperature, Tm, given by Eq. 5. (a) filtered data; data reconstruction using (b) mode 1, (c) mode 2, (d) mode 3, (e) mode 4, and (f) mode 5

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(a) (b)

(c) (d)

(e) (f)

(g)

Figure 9. Time traces of fluctuating wall temperature, x/Dh = 1.19 downstream of the impingement line; nozzle-to-surface spacing, Y/Dh = 5.0. The fluctuations are estimated based on the spatial and temporal average temperature, Tm, given by Eq. 5. (a) filtered data; data reconstruction using (b) mode 1, (c) mode 2, (d) mode 3, (e) mode 4, and (f) mode 5, and (g) mode 6.

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