Jtam.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 45, 3, pp. 505-511, Warsaw 2007 ESTIMATION OF THE INFLUENCE OF INFLOW TURBULENCE ON HEAT CONVECTION FROM A SPHERE SURFACE Leon Bogusławski Poznań University of Technology, Chair of Thermal Engineering, Poland e-mail: leon.boguslawski@put.poznan.pl In the paper, results of an experimental investigation of a heat transfer coefficient on a sphere for different inflow turbulence levels have been presented. The average heat transfer coefficient on the sphere surface appear tobedependenton the turbulence level of flowaroundthe sphere. This effectof influenceof theflowstructurenear the sphere surfaceonthe heat transfer process have been presented. Distributions of heat transfer on spheres of different diameters for different turbulence levels of the inflow have been analyzed. It has been shown that an increase of the inflow turbulence level caused an increase of the average heat transfer coefficient on the sphere surface. The maximum increase of the heat transfer due to growing turbulence has been found to be about 30%. Key words: convective heat transfer, turbulence, sphere 1. Introduction The heat transfer process from a surface to flow is a function of many para- meters. For forced convection of heat from the surface, the main parameter which stimulates this process is the average flow velocity. Muchmore difficult is the problemwith description of the flow structure. A flowgenerated by different flow sources can be characterised by different flow structures for turbulent flows. The average velocity can be the some, but the level of turbulence, as the simplest parameter of the turbulent flow structure, can be different. Very often, the average flow velocity is not good enough to describe turbulent flow structureswhen they influence heat transfer processes on surfaces. Many literaturedata indicate thatan increase of the turbulence level causes an increase of the heat transfer coefficient evenwhen the average velocity does not change. Next, problems of the vortex structure of turbulent flows still 506 L. Bogusławski remain. Influence of the flow turbulence level on average heat transfer on spheres of different diameters is tested. To estimate the influence of the turbulence level of flowon the average heat transfer coefficient, experimental testswereperformed.Theflowwasgenerated by a nozzle. For different distances from the nozzle, the outlet turbulence level in free jet was varied from about 0.5% to about 25% with no change of the average flow velocity. A constant temperature anemometer was used to measure the level of flow turbulence. The average heat transfer coefficient on spheres was measured in steady state thermal conditions by means of an electrical heating system. 2. Measurement technique and apparatus Heat transfer convection from spheres diameters of 0.01m, 0.02m and 0.03m weremeasured for different turbulence levels of inflow.Theaverage heat trans- fer from spheres made of copper to ambient flow was measured by the use of a DC power supply. The electrical power was recorded in steady-state con- ditions. The difference between temperature of the isothermal sphere surface and ambient flow of about 60◦C was measured by making use of a thermo- couple with accuracy of 0.1◦C and then recorded. The information was used for calculations of the average heat transfer. The tested spheresweremounted on round, long supports. The support cross-section covered less than 0.5% of the sphere surface. Heat losses by supports was neglected because they were of the order of heat convection from free sphere surfaces. The influence of ra- diation was corrected using the radiation transfer equation from the surface to surroundings. The copper surface emissivity of 0.6 was taken into account. An openwind tunnel was used to perform the experimental test. The flow was generated by a free round jet outflow from nozzles of different diameters. The level of turbulence, in the jet axis, changed from about 0.5% near the nozzle outlet to about 20% far away from the nozzle. By changing the average flow velocity at the nozzle outlet it was possible to keep a constant value of velocity at different distances from the nozzle outlet where the tested spheres were located. Distribution of the average flowvelocity andflowvelocity turbu- lent fluctuations were measured by means of a TSI hot wire probe connected to a Constant Temperature Anemometer (CTA) bridge TSI 1050. The influ- ence of average velocity profile irregularity was tested by nozzles of different diameters. The nozzles of diameters D> 2dwere used. The reference flow velocity and turbulent level of jet flowwasmeasured at adistance x fromthenozzle outlet of diameter D,where the sphere stagnation pointwas located. TheReynolds number of average flowdefined on the sphere Estimation of the influence of inflow turbulence... 507 diameter was 32000 for all presentedmeasurements. As the reference value of heat transfermeasurements, the values obtained for the lowest level of external flow turbulence (∼ 0.5%) was taken into account. A diagram of the experimental setup and apparatus is shown in Figure 1. Fig. 1. Experimental setup and apparatus 3. Results of experimental investigations A turbulent flow generated by different flow sources can be characterised by different turbulent flow structures. The average velocity can be the some, but the level of turbulence, as the simplest parameter of the turbulent flow struc- ture, can be different. So, the average flow velocity in the Reynolds number is not good enough to describe turbulent flow structures when they influence heat transport processes from surfaces. Many literaturedata indicate thatan increase of the turbulence level causes an increase of the heat transfer coefficient evenwhen the average velocity does not change (Bogusławski, 1996; Incropera andWitt, 2001; Whitaker, 1972). As the reference heat transfer coefficient to indicate the influence of tur- bulence, the value of heat transfer obtained for a low turbulence level of about 0.5% was taken into account. This flow conditions occurs when the spheres were located at the half distance of the nozzle outlet diameter. The relations between experimental data obtained for spheres diameters of 0.01m, 0.02m and 0.03m and literature data are presented in Fig.2. For comparison, the following equations were taken into account. 508 L. Bogusławski The Ranz andMarshall equation (Ranz andMarshall, 1952) Nu=2+0.6Re0.5Pr0.33 (3.1) TheWhitaker equation (Whitaker, 1972) Nu=2+(0.4Re0.5+0.06Re0.666)Pr0.4 (µf µw ) (3.2) TheKancnelsonandTimofiejewa equation (Wiśniewski andWiśniewski, 2000) Nu=2+0.03Pr0.33Re0.54+0.35Pr0.356Re0.58 (3.3) Theobtaineddata are in goodagreementwithRanzandMarshall equation (3.1).Twoother equations give resultswhichareabove ownexperimental data. Fig. 2. Distribution of experimental data of the heat transfer coefficient on spheres in comparison with literature data For the sphere, an increase of the turbulence level of flowcauses an increase of the average heat transfer from the isothermal surface of the sphere to am- bient air as shown in Fig.3. This figure illustrates the process of heat transfer intensification for the sphere diameter of 0.03m in a turbulent flow generated by nozzles of diameters D = 0.06m, 0.12m and 0.15m. An increass of the flow turbulence by 22% causes an increase of the heat transfer by about 30%. The average flow velocity around the sphere does not change. The observed increase of average heat transfer can be interpreted as a result of the increase of flow turbulence. In this case (i.e. d=0.03m), the plot of experimental data looks to be independent of the nozzle diameter. This suggests that the scale of turbulent flow structures generated by nozzles of different diameters does not influence heat transfer processes. For the spherediameter of 0.02m, theplot of experimental data is shown in Fig.4.Again, the increase offlowturbulence increases theheat transferprocess from the isothermal sphere surface. The plot of data indicates, a nearly linear trend. Intensification of the heat transfer is smaller because for the turbulence of about 15%, the increase of heat transfer reaches 20%. Estimation of the influence of inflow turbulence... 509 Fig. 3. Distribution of the average heat transfer coefficient on the sphere surface diameter of 0.03m for different inflow turbulence levels Fig. 4. Distribution of the average heat transfer coefficient on the sphere surface diameter of 0.02m for different inflow turbulence level For a smaller sphere with the diameter of 0.01m, the plot of experimen- tal data gets more complicated as shown in Fig.5. For the nozzle diameter of 0.01m, the influence of flow turbulence on heat transfer is much lower. For turbulence below 10%, the heat transfer increase is rather weakly visible. For the turbulence level beyond 15%, the heat transfer increases and reaches about 18% above the reference value at the turbulence level equal 20%. The Reynolds numbers of average flow over spheres is the some for all spheres and nozzles. The trend lines of increasing heat transfer coefficients for the tested sphe- res are presented in Fig.6. A comparison between the trend lines for different diameters of spheres indicates that for smaller spheres the influence of in- tensity of turbulence is lower. There is no clear evidence that the scale of turbulent structures generated by nozzles of different diameters effects heat transfer phenomena in the tested range of the nozzle-to-sphere diameter ratio. Nevertheless, the diameter of spheres and its interaction with the flow struc- ture cause that the influence of turbulent flow intensity on heat convection is lower when the diameter becomes smaller. 510 L. Bogusławski Fig. 5. Distribution of the average heat transfer coefficient on the sphere surface diameter of 0.01m for different inflow turbulence level Fig. 6. Trend lines of increasing average heat transfer coefficient on spheres with the surface diameter of 0.01m, 0.02m and 0.03m for different inflow turbulence levels We can initially assume that turbulent vortexes are not able to effectively influence the increase of transport phenomena in the boundary layer on small diameter spheres. In this case, the boundary layer is thin. Because of this, the boundary layer is not so sensitive to turbulent perturbations. When the size of spheres grows, the possibility of affecting the heat transfer process by increasing flow turbulence grows essentially as well. 4. Conclusions The increase of turbulence of the external inflow intensifies heat transfer phe- nomena on the sphere in an essential way. This effect is more visible when the diameter of spheres grows in the tested range. The boundary layer on sphe- res of smaller diameters is less sensitive to intensification of the heat transfer by external flow turbulence. Local heat transfer distributions indicate that Estimation of the influence of inflow turbulence... 511 for spheres of large diameters the external flow turbulent vortex is able to influence the boundary layer transport phenomenamore intensively. References 1. Bogusławski L., 1996, Losses of heat from sphere surface at different inflow conditions [in polish],XVIThermodinamics Conference, Kołobrzeg,1, 135-140 2. Incropera F.P., De Witt D.P., 2001, Fundamentals of Heat and Mass Transfer, JohnWiley and Sons, NewYork 3. Ranz W., Marshall W., 1952,Chem. Eng. Prog., 48, 141 4. Whitaker S., 1972, Forced convection heat transfer correlation for flow in pipes, past flat plates, single cylinders, single spheres and flow in packed beds and tube bundles, J. of AICHE, 18, 361-371 5. Wiśniewski S., Wiśniewski T., 2000,Heat Transfer [in polish],WNT,War- szawa Oszacowanie wpływu turbulencji napływu na konwekcję ciepła z powierzchni kuli Streszczenie W pracy przedstawiono wyniki badań eksperymentalnychwspółczynników przej- mowaniaciepłanakuli przy różnychstopniach turbulencji napływającej strugi. Średni współczynnik przejmowania ciepła na powierzchni kuli jest zależny od stopnia turbu- lencji przepływu wokół kuli. Jest to rezultat zmiany struktury przepływu w pobliżu ścianki kuli wpływającej na procesy transportu ciepła. Przeprowadzonoanalizę zmian wymiany ciepła na kulach o różnych średnicach przy zmianie stopnia turbulencji na- pływającej strugi. Wzrost stopnia turbulencji napływu powoduje wzrost średniego współczynnika przejmowania ciepła na powierzchni kuli.Maksymalnywzrost wymia- ny ciepła spowodowanywzrostem turbulencji przepływu był rzędu 30%. Manuscript received February 21, 2007; accepted for print April 13, 2007