Heat transfer due to impinging co-axial jets and the jets’ fluid flow characteristics

Experimental Thermal and Fluid Science 33 (2009) 715–727

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Heat transfer due to impinging co-axial jets and the jets’ fluid flow characteristics Nevin Celik a,*, Haydar Eren b a b

Department of Mechanical Engineering, University of Minnesota, 111 Church Street SE, Minneapolis, MN 55455, USA Department of Mechanical Engineering, University of Firat, Elazig 23279, Turkey

a r t i c l e

i n f o

Article history: Received 6 May 2008 Received in revised form 8 January 2009 Accepted 22 January 2009

Keywords: Co-axial jet Impingement heat transfer Flow dynamics of jets Turbulence intensity

a b s t r a c t This investigation had multiple goals. One goal was to obtain definitive information about the heat transfer characteristics of co-axial impinging jets, and this was achieved by measurements of the stagnationpoint, surface-distribution and average heat transfer coefficients. These results are parameterized by the Reynolds number Re which ranged from 5000 to 25,000, the dimensionless separation distance between the jet exit and the impingement plate H/D (4–12), and the ratio of the inner diameters of the inner and outer pipes d/D (0–0.55). The d/D = 0 case corresponds to a single circular jet. The other major goal of this work was to quantify the velocity field of co-axial free jets (impingement plate removed). The velocityfield study included both measurements of the mean velocity and the turbulence intensity. It was found that the variation of the stagnation-point heat transfer coefficient with d/D attained a maximum at d/D = 0.55. Furthermore, the variation of the local heat transfer coefficient across the impingement surface was more peaked for d/D = 0 and became flatter with decreasing d/D. This suggests that for cooling a broad expanse of surface, co-axial jets of high d/D are preferable. On the other hand, for localized cooling, the single jet (d/D = 0) performed the best. In general, for a given Reynolds number, a co-axial jet yields higher heat transfer coefficients than a single jet. Off-axis velocity peaks were encountered for the jets with d/D = 0.105. The measurements of turbulence intensity yielded values as high as 18%. Ó 2009 Elsevier Inc. All rights reserved.

1. Introduction Co-axial jets play an important role in the mechanical and aeronautical engineering; for example, in combustion, aerodynamics, and air conditioning systems. The main factor that affects co-axial jet flow is the velocity ratio k (k = Ui/Uo, where Ui is the mean axial velocity at the exit of the inner pipe, and Uo is the mean axial velocity at the exit of annular section). The case k ? 0 means there is only annular flow, while k ? 1 is the case of a central round jet. Prior researchers have experimented with many geometrical configurations in order to obtain the optimum value in the range 0 6 k 6 1. Obviously, the variable parameters are the inner and outer diameter of the co-axial pipes. A review of the literature showed that the first study of co-axial jet fluid mechanics is that of Forstall and Shapiro [1]. These authors were primarily concerned with the jet-mixing problem. In this study, it was shown that the ratio of the mean velocities in the central jet to that in the annulus jet at the jet origin was the most important independent variable in determining the flow configuration and velocity profiles. Durao and Whitelaw [2] performed their experiments to explore the development of the interacting jets in the region downstream of the jet origin, and at the result showed * Corresponding author. Tel.: +1 651 354 2968. E-mail address: [email protected] (N. Celik). 0894-1777/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2009.01.007

that co-axial jets tended to reach a self-preserving state much more rapidly than asymmetric single jets. In contrast, Champagne and Wygnanski [3] investigated the velocity profiles in the fully developed jet region. Measurements of velocity and air concentration in co-axial jets, confined by a cylindrical duct, were performed by Lima and Palma [4]. They tested the mixing region for two different velocity ratios k = 0.3125 and 0.158. Ko and Kwan [5], and Ko and Au[6] experimentally investigated a large range of velocity ratios from low k < 1 to high k > 1. Warda et al. [7] investigated two limiting cases of co-axial jets; round central jet (k ? 1) and annular jet (k ? 0). The variations along the jets centerline and the radial profiles for mean and fluctuating longitudinal velocities were presented. Mostafa et al. [8] performed both numerical and experimental work for three rectangular jets of which arrangements were made so that the outer jets have equal centerline velocities of Uo = 20 m/s, while the central jet has centerline velocity of Ui = 2 m/s at the exit plane. It was claimed that a good agreement was achieved between experimental and numerical results of the mean velocity, turbulence kinetic energy and shear stress. In order to understand the effects of an elliptic co-flow on a circular inner jet flow-field, the near-field flow characteristics of a turbulent elliptical co-axial jet with velocity ratios k = 1.81 and 0.68 were numerically computed and experimentally measured by Vargas and Choudhuri [9]. The flow characteristics were com-

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Nomenclature A c d D g H hfg h  h Ja k L Nu Nu Q r Re T u u0 U t Tu V_ z

heat transfer area (m2) specific heat (J/kg °C) inner diameter of inner pipe (m) inner diameter of outer pipe (m) gravitational acceleration (m/s2) jet-to-plate separation distance (m) latent heat of vaporization (J/kg) local heat transfer coefficient (W/m2 °C) average heat transfer coefficient, (W/m2 °C) Jakob number thermal conductivity (W/m °C) height of the vertical plate (m) Nusselt number average Nusselt number rate of heat transfer (W) radial coordinate (m) Reynolds number temperature (°C) time-averaged velocity (m/s) fluctuating velocity (m/s) mean velocity (m/s) time (s) turbulence intensity (%) volumetric flow rate of air (m3/s) axial distance between the jet exit and probe (m)

pared with a circular co-flow. As a result, dependence on the outer structures with different velocity ratios was observed in the elliptical co-flow jet. Fan et al. [10] presented a numerical study including co-axial jet with secondary parallel moving stream. They found that, radial profiles of the mean velocity component u depending on the velocity ratio k show good similarity in the fully developed zone. Kriaa et al. [11] also prepared a numerical work in order to show the mean axial velocity profiles of non-isothermal co-axial jets for a constant diameter ratio d/D = 0.35. Different aspects of co-axial free jet flows have been studied by many investigators, as mentioned above. The significant progress, especially in the recent decade, has been made to understand jet exit effects on nonlinear flow dynamics. There is a common agreement that using co-axial jets enhances potential core region and turbulence intensity at the nozzle exit due to presence of mixing of primary and secondary flows. Although the effects of nozzle shape on heat transfer have been studied extensively by many researchers [12–15], the effects of the co-axial shape is still remained a raw subject, and more research on this subject is needed. To the best of authors’ knowledge, the co-axial jet flow case, in which there is both annular and central flow, has not been previously studied in detail yet. In the present study, the heat transfer and flow characteristics of a co-axial turbulent impinging jet are experimentally searched for various diameter ratios (d/D = 0, 0.105, 0.35 and 0.55).

2. Experimental study 2.1. Setup A schematic diagram of the experimental apparatus is presented in Fig. 1a. The air flow which is supplied by a compressor is dried, filtered, and regulated before entering the jet pipe. The compressor has a 500-liter calming chamber. Two rotameters are used for measuring the volumetric flow rate of the air, depending on the magnitude of the flow rate.

Greek symbols k inner-to-outer jet velocity ratio l dynamic viscosity (kg/ms) m kinematic viscosity (m2/s) q density (kg/m3) Subscripts cond condensation FC forced convection i inner impinged after impingement j jet l liquid local local losses losses (heat) MIXED mixed convection NC natural convection o outer surf surface sat saturation state w wall v vapor

The co-axial jets are generated by means of two co-axial cylindrical pipes configured in a concentric orientation. This arrangement is shown in Fig. 1b. As can be seen from the figure, the flow coming from the compressor enters the outer of two pipes. After a pre-selected flow length, the air encounters the inner of the two pipes, at which point it splits, with one portion entering the inner pipe and the remainder flowing in the annular space between the two pipes. These two parallel flows automatically become jets at the downstream end of the pipes. Of particular note are the adjustments incorporated into the apparatus to facilitate the maintenance of concentricity. At each of two axial stations, small-diameter adjustment screws were positioned 120° apart around the circumference. A special tool in the shape of a washer was put in place to establish concentricity before the adjustment screws were tightened. Fig. 1b consists of four diagrams which illustrate the geometric configurations which were studied during the course of this investigation. These diagrams show a sequence of configurations in which the diameter and the length of the inner pipe is progressively decreased. The geometric information describing these different situations is listed in the figure. The variations in the cross-sectional areas associated with each of the configurations enabled the ratio of the velocity of the inner jet to the velocity of the outer jet to be varied from <1, =1 and >1. The research to be described here has two foci. The first is the determination of the heat transfer characteristics of impinging co-axial jets. The second focus is to characterize the velocity field and turbulence intensity in the free jet. The impingement surface for the heat transfer studies was oriented vertically for these experiments. In the experimental setup, the ambient-temperature co-axial jet impinged on a heated isothermal surface. The heated surface was one face of a stainless steel plate of planform 590 by 530 mm and of thickness 0.5 mm. The heating of the plate was accomplished by the condensation of a stream of flowing water vapor on the other principal face of the plate. The use of condensing steam as a means of deducing heat transfer coefficients is well established in the archival literature.

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Fig. 1. Properties of experimental setup. (a) Front view of whole setup and (b) jet pipes configurations.

However, in previous applications, it was necessary to use somewhat questionable assumptions to extract information that would enable the determination of local results. Here, a logic-tight approach was used with the aid of numerical simulation. As will be discussed shortly, ANSYS software was used to connect conduction in the plate on which condensation took place with convective

heat transfer on the surface of the plate that was exposed to the air flow. The stream of water vapor that passed over the condensation surface was contained in a stainless steel rectangular duct. After passing the condensing surface, the residual water vapor was discharged to the ambient. In order to avoid the issue of

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Fig. 2. Velocity and turbulence intensities along the centerline for single circular jet (d/D = 0).

non-condensable gasses, the steam generator was operated for a considerable period of time prior to its use as a heating medium. Two methods were used to determine the heat transfer to the plate due to condensation. One of the methods was to measure the rate of accumulation of the condensate. The other approach was to use the Nusselt correlation for condensation heat transfer on a vertical isothermal surface. The two methods proved to be in very good agreement (±4.3%), so that for all subsequent data runs, only the Nusselt method was employed. The temperature of the impingement surface was measured by a total of 33 type-T thermocouples. The diameter of each of the thermocouple wires was 0.3 mm. The thermocouple placement reflected the focus of the work on a square sub-area of dimensions 160 by 160 mm laid-out symmetrically on the impingement surface proper. Twenty-five of the aforementioned thermocouples were positioned at the intersections of network of gridlines which defined a mesh of 25 squares. The other eight thermocouples were deployed in a tight ring around the stagnation-point of the impinged jet. A detailed picture of the locations of thermocouples is previously presented by the co-authors [16]. The thermocouples were glued on the rear side of the plate surface through drilled holes, and the void space between the wire and the hole was completely filled with thermal epoxy. Sufficient precaution was taken when drilling and gluing the thermocouples. So the temperature measured on the whole surface was in fact the rear surface wall temperature. However the depth of the hole on the plate was nearly 0.4 mm, and the distance between the touching point of thermocouple and front surface was 0.1 mm. The conduction heat transfer along the 0.1 mm-distance was neglected, and this neglecting was taken into consideration when the uncertainties of Nusselt number were estimated. Velocity and turbulence intensity distributions of the co-axial free jets formed as discussed in the foregoing were measured by means of a hot-wire anemometer. To accommodate the range of velocities encountered, it was necessary to use two anemometers, respectively, for the higher and lower velocity ranges (Models: TSI 8475-075-1 and TSI 8455-075-1). The preliminary velocity measurements were focused on establishing the axisymmetric nature of the flow field. To this end, traverses were made along two perpendicular directions with respect to the jet axis. The result of these measurements confirmed that the flow field was truly axisymmetric (i.e., two-dimensional). Therefore, with the estab-

lishment of this feature, the main body of the velocity measurements was performed as 30-point radial traverses at five axial stations. The measurements were performed for five different jet Reynolds numbers in the range from 5000 to 25,000. In this con_ pDm, where nection, the Reynolds number is defined as Re ¼ 4V= V_ is the volumetric flow in the co-axial jet system at the origin of the free jet, and D is the inner diameter of the outer pipe. The traversing mechanism was controlled automatically from the keyboard of a personal computer. Details of the velocity measurement apparatus may be found in the thesis book of Celik [17] and the article of Eren et al. [18]. The data were recorded by using a multichannel data logger (Campbell CR10X). 2.2. Validation of the experimental method As a preliminary to the evaluation of the impingement heat transfer coefficients, numerical simulation was performed to evaluate the temperature distribution on the impingement surface. For this purpose, ANSYS finite-element software was used. The solution domain selected for study was the impingement plate, with boundary conditions which encompassed a prescribed uniform temperature at the surface on which steam condensed, convective heat transfer on the impingement surface, and adiabatic edges. Tentative values of the heat transfer coefficients on the impingement surface, needed as input to the simulation model, were taken from the experimental data. It was realized that these tentative values could be revised depending on the outcome of the simulation. A mesh-independence study was performed to validate the numerical results, with the final computer runs being made with 22,022 nodes. The results of the simulation runs indicated that the surfaceto-freestream temperature difference varied, at most, by about ±2% over the entire thermally active portion of the impingement surface. This finding establishes, for all practical purposes, the isothermal nature of the surface. As a corollary of this finding, it was deemed unnecessary to revise the values of the heat transfer coefficients that were used as input to the numerical simulation. 2.3. Post-processing method of experimental data Attention will now be turned to the determination of the heat transfer coefficient by means of post-processing of the experimen-

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Fig. 3. Variation of mean velocities at Re = 5000, for: (a) d/D = 0.105; (b) d/D = 0.35 and (c) d/D = 0.55.

tal data. The first step is to evaluate the rate of condensation heat transfer on the rear-facing surface of the impingement plate. As has already been discussed, it was found suitable to evaluate the

overall rate at which heat is delivered to the impingement plate from the well-known modified Nusselt condensation formula, which is

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Fig. 4. Variation of turbulence intensities, at Re = 5000, for: (a) d/D = 0.105; (b) d/D = 0.35 and (c) d/D = 0.55.

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Fig. 5. Comparisons of the jets behavior, at the jet exit (z/D = 0.23) for Re = 25,000, with respect to their: (a) mean velocities and (b) turbulence intensities.

" #1=4 3 0   g ql ðql  qv Þkl hfg hcond Nusselt ¼ 0:943 ll ðT sat  T s ÞL

ð1Þ

presence of natural convection. A well-established approach to mixed convection is

 ðQ cond ÞNusselt ¼ h cond Asurf ðT sat  T surf Þ

ð2Þ

 n n 1=n n  n 1=n hMIXED ¼ hFC þ hNC ¼ hFC 1 þ ðhNC =hFC Þ

In this equation, the subscripts l, v, sat and surf refer, respectively, to the liquid, vapor, saturation state and surface. The quan0 tity hfg includes both the latent heat of condensation and the heat liberated by subcooling of the condensed liquid and is given by (1 + 0.68Ja). In the latter expression, the symbol Ja denotes the Jakob number defined as Ja = cl(Tsat  Tsurf)/hfg. The rate of heat transfer delivered to the plate by condensation must be corrected for whatever losses which may occur. These may include natural convection and radiation at the impingement surface and edge losses. With regard to natural convection, it is fruitful to consider the possible mixed convection outcome in the

ð3Þ

For the present experiments, it was estimated that the ratio of the natural convection to the forced convection heat transfer coefficients is about 1%. To exaggerate the effect of natural convection, it is suitable to take n = 2. With this, the result

hMIXED ¼ 1:00005hFC

ð4Þ

This result indicates that natural convection is insignificant in the present situation. With regard to radiation, for the case of the surface emissivity of 0.25, the radiation loss was found to be approximately 0.3% of the impingement heat transfer rate. The possible edge losses were made negligible by the use of suitable insulation.

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Fig. 6. Stagnation-point Nusselt number variations with respect to Reynolds number for: (a) d/D = 0.55, (b) d/D = 0.35, (c) d/D = 0.105, and (d) d/D = 0.

In view of the foregoing,

Q impinged ¼ Q cond  Q losses

ð5Þ

Then, for the average heat transfer coefficient,

 h impinged ¼

Q impinged Asurf ðT w  T j Þ

ð6Þ

the dimensionless form of which is

 Nu ¼ h impinged D=k

ð7Þ

For the determination of the local heat transfer coefficient, as a first approximation it was assumed that the heat transfer rate Qimpinged is uniformly distributed over the impingement surface. Therefore, (Qimpinged/Asurf) is taken to be a constant. With this, it follows that

 himpinged;local ¼

Q impinged =Asurf ðT w  T j Þ

 ð8Þ

and

Nu ¼ himpinged;local D=k

dimensionless representation, these coordinates become z/D and r/D. The local time-averaged velocity (denoted as the mean velocity) is defined as u. It was obtained by averaging the instantaneous local velocities listed in a spread sheet. A dimensionless form was obtained by using the jet exit velocity Uj as the normalizing quantity, resulting in the ratio u/Uj. The fluctuating part of the instantaneous local velocity is termed u0 . It is defined as:

u0 ðz; r; tÞ ¼ uðz; r; tÞ  uðz; rÞ

ð10Þ

In this equation, u(z, r, t) is the instantaneous velocity at a location (z, r) and u(z, r) is the time-averaged velocity at that same location. The values of u0 obtained in this way are normalized in the form of the turbulence intensity Tu, defined as:

Dimensionless turbulence intensity : Tu ¼

pffiffiffiffiffiffi u02 =U j

ð11Þ

2.4. Uncertainty analysis

ð9Þ

As was noted earlier, a second focus of this work is the fluid dynamics of the free jet flow of the co-axial system. It has already been pointed out that the free jet flow is axisymmetric. Therefore, the location of the velocity-field measurements can be described in terms of the axial coordinate z and the radial coordinate r. for a

The Nusselt number Nu uncertainty analysis on the basis of 95% confidence level of errors has been carried out using the method by Kline and McClintock [19]. The maximum uncertainty in the Nusselt number Nu is estimated to be 8%, while the uncertainties for Reynolds number Re and the turbulence intensity Tu are 4.89% and 4.84%, respectively.

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Fig. 7. Average Nusselt number variations with respect to Reynolds number for: (a) d/D = 0.55, (b) d/D = 0.35, (c) d/D = 0.105, and (d) d/D = 0.

3. Results and discussions 3.1. Mean velocity and turbulence intensity results The local velocities are determined quantitatively by averaging the instantaneous velocity measurements for the specified flow rate (or Re) at selected locations characterized by z/D and by r/D. The data for each location were taken over a time duration of 60 s at 2 s intervals. The instantaneous velocity data in the potential core region confirmed that steady flow is attained. The local mean velocities (u) are scaled with the jet exit velocity at the axis (Uj) to obtain the dimensionless values. Attention will first be focused on the validity of the results. For this aim the velocity and turbulence intensity results of the single circular jet (d/D = 0) was compared to those obtained from a similar jet (see Lee et al. [20]), and the comparison was presented in Fig. 2. As seen from the figure, the velocity profile along the centerline (z/D) for present study has an agreeable curve, comparing to the results of Lee et al. The deviation percentages between the present work and the reference cited work are 3% and 30% for mean velocities and turbulence intensities, respectively. The axial mean velocities presented in Fig. 3. The figure consists of three graphs which correspond, respectively, to d/D = 0.105, 0.35 and 0.55. In each graph, the dimensionless velocity u/Uj is plotted as a function of the dimensionless radial distance r/D from the axis for parametric values of the axial distance z/D from the jet exit. For the data reported in this figure as well as in Figs. 4 and 5, the

impingement plate was removed from the experimental setup. Therefore, the data correspond to a free jet. All of Figs. 3–5 are enhanced by color bands adjacent to the vertical axis. The leftmost color band spans the inner radius of the central jet of the system, while the rightmost band extends to the inner radius of the annular jet of the system. It can be seen from these color bands that the central jet radius is varied throughout the investigated range, but the outer radius of the annulus is held fixed. Attention now be focused on radial positions r/D 6 0.5 on the plane z/D = 0.23. This plane lies just below the exit of the co-axial jets, while the radial position of the velocity probe is, for this discussion, confined to the initial jet width. Inspection of the data that correspond to the aforementioned region indicates an evolving variation in the velocity field with increasing d/D. In Fig. 3a, while the velocity is more or less uniform across the central jet, it rises significantly in the annular jet, creating an off-axis peak. This trend is the result of the presence of higher exit velocities in the annulus relative to those in the central jet. Again, the results for z/D = 2 mirror those for z/D = 0.23. Next, it is seen in Fig. 3b that the velocity is rather flat across the central jet and at the inner fringe of the annulus, whereafter it decreases moderately across the remainder of the annulus; a similar behavior is evidenced by the results for z/D = 2. A rather different behavior is in evidence in Fig. 3c, the velocity distribution displays a maximum at the axis (r/D = 0) and decreases rapidly with increasing r/D. Further study of Fig. 3 indicates that beyond r/D  0.5, the jet velocity profiles for the three d/D cases are very similar to one

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Fig. 8. Local Nusselt number distribution of tested jets, at H/D = 4, for: (a) Re = 5000 and (b) Re = 25,000.

another. For instance, the nominal jet width, defined as the radial distance where u/Uj = 0.5, is approximately one diameter of the co-axial jet. Furthermore, an overlay of the a, b and c parts of Fig. 3 shows near congruence of the velocity profiles beyond r/D  0.5. A display of turbulence intensity results, similar in format to that of the mean velocity results of Fig. 3, is provided in Fig. 4. For d/D = 0.105 (k = 0.93), the turbulence intensity is maximum at the annular jet exit. In the exit plane of the co-axial jet (z/

D = 0.23), the dimensionless radial distance r/D = 0.36 approximately corresponds to a point centered in the cross-section of the annular jet. At this point, the turbulence is higher than that at the axis (r/D = 0). With increasing axial distance, especially after z/D = 4 and 6, the turbulence profile broadens. It can be seen from Fig. 4 that the turbulence intensity for locations r/D P 0.5, the profiles for z/D = 6 and 8 tend to coalesce. In Fig. 5, the mean velocities and turbulence intensities for d/ D = 0, 0.105, 0.35 and 0.55 are plotted with respect to r/D for

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Fig. 9. Local Nusselt number distribution of tested jets, at H/D = 12, for: (a) Re = 5000 and (b) Re = 25,000.

Re = 25,000, respectively, in the a and b parts. In these figures, a different shading format is used in order to enable a more compact presentation in which all of the various d/D cases are exhibited in a single graph. Note that there are four vertical lines to the right of the vertical axis. These vertical lines, counting from left to right, will be designated as 1, 2, 3 and 4. If lines 1 and 4 are taken together, the corresponding representation is that for d/D = 0.105. Similarly, lines 2 and 4, when taken together represent d/D = 0.35 and the lines 3 and 4 represent d/D = 0.55. Finally, the line 4 alone corresponds to single jet d/D = 0.

In Fig. 5a and b, it is seen that the main differences between the jet configurations defined by the different values of d/D are most marked in the range of r/D = 0–0.5. Aside from the case where d/D = 0.105 the peak values of the mean velocities are observed to be at the axis. For d/D = 0.105 the peak occurs in the annular portion of the co-axial jet. Beyond r/D = 0.5, the trends exhibited by the mean velocity profiles and the turbulence profiles are more or less the same. By checking Fig. 5b some quantities may be presented. For example, for the case d/D = 0.105, on the plane z/D = 0.23, the

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turbulence intensity at the axis is approximately 5%, while at r/ D = 0.362 (approximately in the center of the annular jet) it is 10%, and at r/D = 0.5 it is 11%. For larger r/D the turbulent intensity rapidly decreases and goes to zero at r/D = 6.5. For d/D = 0.35, the corresponding percentages are 7%, 10% and 9%, while they are 7%, 9% and 10% for d/D = 0.55, meaning not a quite change between the values for each jet types. However, for d/D = 0 the corresponding values are, respectively, 5%, 6% and %5 which are lower than all of the values for the other co-axial types. Also it should be noticed that for a pipe flow the turbulence intensity is nearly 6% in literature. 3.2. Heat transfer In this section, surface heat transfer characteristics of a co-axial jet impinging on a flat surface will be presented. These results include graphs of the stagnation-point and surface-average values, and contour diagrams of the local heat transfer coefficients. These graphs and diagrams extend over a Reynolds number Re range from 5000 to 25,000, dimensionless jet origin to impingement plate separation distances H/D from 4 to 12, and dimensionless co-axial jet inner-to-outer diameter ratios d/D = 0 (single jet), 0.105, 0.35 and 0.55. The presentation begins with a display of the stagnation-point Nusselt numbers in Fig. 6. Fig. 6 consists of four parts, with each part corresponding to a specific value of the inner-to-outer jet diameters d/D. In each part, the Nusselt number is plotted as a function of the Reynolds number for parametric values of the dimensionless jet origin to impingement plate separation distance H/D. As expected, the stagnation-point Nusselt number increases monotonically with the Reynolds number. Careful inspection of the curves indicates that the rate of increase of Nu with Re is more or less the same for the various d/D ratios. On the other hand, it appears that the rate of increase is slightly greater at the lower H/D than at the higher H/D. This behavior is manifested by the slight spreading of the curves with increasing Reynolds number. Cross plots of the results of Fig. 6 were made to reveal additional trendwise behaviors. At given values of the Reynolds number and of the separation distance, the Nusselt number variation with the d/D displayed a minimum for the single jet (d/D = 0). An apparent maximum occurred at the d/D = 0.55, followed by a monotonic decrease. From a second cross plot, it was noted that the Nusselt number decreased monotonically as a function of H/ D. This finding reinforces the experience of other investigators of single jets who found a local maximum of Nu at a value of H/D in the range from 1 to 2 and a monotonic decrease thereafter. Attention will next be focused on the results for the surfaceaverage Nusselt number. It is important to note that the averaging was performed over a square area on the impingement surface, the side S of which, relative to the outer jet diameter, is S/D = 11.6. The results for the average Nu are presented in Fig. 7. In common with Fig. 6, this figure is subdivided into four parts, each corresponding to a different value of d/D. From an overall inspection of Figs. 6 and 7, the trends that were identified in the former appear to hold for the latter. Careful inspection of the values of the stagnation-point and average Nusselt numbers reveals that the stagnation values are generally higher than the average values. The relationship between these two Nusselt numbers depends on d/D and to a lesser extent on H/D. For example, for d/D = 0.105, the largest deviation between the stagnation and average values was approximately 10% for H/D = 12 and 8% for H/D = 4. These largest deviations occurred at Re = 25,000, while for Re = 5000, the deviations were no more than a few percent. For the single jet case, d/D = 0, the largest deviations were on the order of 4%. The third type of heat transfer result is the local Nusselt number distribution over the instrumented portion of the impingement

surface. It may be recalled that the instrumented part of the surface is a square having a side dimension of 160 mm, while the inner diameter of the co-axial jet at exit is D = 13.8 mm. The method of conveying the local results is by means of contour diagrams which are presented in Figs. 8 and 9, respectively, for H/D = 4 and 12. In each figure, graphs are displayed for Reynolds numbers of 5000 and 25,000. The upper and lower halves of each figure, respectively, encompass four graphs, conveying information for d/D = 0, 0.105, 0.35, and 0.55. Each individual graph represents a quadrant of the instrumented section of the impingement surface. An overall view of Figs. 8 and 9 indicates a regular pattern in which the highest values of the local Nusselt number occur in the stagnation region with an orderly drop off with increasing distance from the stagnation-point. In recognition of the fact that only a quadrant of the surface of interest is shown, it may be imagined that a display of the entire instrumented surface would be characterized by a set of square contour lines with rounded corners. For a given spacing ratio H/D, the gradient of the Nu across the surface is larger at the higher of the two Re. Furthermore, at a fixed value of the Re, the surface gradients of the Nu are smaller the larger the value of H/D. A further trend that can be identified is the dependence of the gradient on d/D for fixed values of H/D and Re. The smallest surface gradient corresponds to the single jet d/D = 0, while the largest gradient is for d/D = 0.55. For the other d/D values, the gradients lie between those for d/D = 0 and d/D = 0.55.

4. Concluding remarks This investigation has encompassed both fluid flow and heat transfer experiments. For the fluid flow studies, the impingement surface was removed and measurements were made of both the mean and turbulent velocity fields of the resulting free jet. The heat transfer experiments were focused on the determination of the local and average heat transfer coefficients resulting from the impingement of a co-axial jet on a heated surface. With regard to the mean velocity measurements, it was found that for the smallest investigated value of d/D (=0.105), off-axis peaks in the radial velocity profile immediately adjacent to the jet exit plane were encountered. These peaks decayed with increasing distance from the exit plane. At the radial distances beyond the outer boundary of the co-axial system, the jet velocity profiles for the three d/D > 0 cases are very similar to one another. The turbulence intensity measurements disclosed values as high as 18%. For the heat transfer studies, parametric variations were made of the ratio d/D of the inner and outer diameters that bound the co-axial jets, the dimensionless separation distance H/D between the jet exit and impingement surface, and the Reynolds number Re. All the experiments were performed in turbulent flow regime. The results for the stagnation-point heat transfer coefficient, unique dependence of the results on the diameter ratio d/D was observed. For the d/D = 0, which corresponds to a single jet, the heat transfer coefficient is least. With increasing values of d/D, the heat transfer coefficient increases and achieves a maximum at d/D = 0.55. For further increases of d/D, the coefficient was found to decrease. The dimensionless separation distance H/D ranged from 4 to 12. In this range, the stagnation-point heat transfer coefficient decreased monotonically with increasing H/D. The variation of the local heat transfer coefficients across the impingement surface tended to be more gradual at the higher values of d/D. This characteristic suggests that if it is desired to have more or less uniform cooling of a wide expanse of surface, a co-axial jet with high d/D should be used. On the other hand, if the desired cooling effect is to be highly localized, a low value of d/D is preferred.

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