Transactions on Engineering Sciences vol 18, 1998 WIT Press, ISSN

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1 Mixed convection in a horizontal circular channel in high pressure conditions A. Maj, W. Nowak, A. Stachel Technical University of Szczecin, department of Heat Engineering, al Piastow 19, Szczecin, Poland ktc@safona. tuniv.szczecin.pl Abstract The main aim of the research is to determine the range of mixed convection and setting the limits of its occurrence. The laboratory tests are conducted at the Technical University of Szczecin in the Department of Heat Transfer with the use of the horizontal circular heat exchanger. The measurements are made with the pressures from 0,1 to 10,0 [MPa] and different heating powers. In order to carry out the planned research and analyse its results, a criterion of mixed and free convection occurrence by Metais and Eckert [4] stating that the boundary between the free and mixed convection results from the comparison of convectional heat flux values resulting only from displacement forces (free convection) and the sum of displacement forces together with body forces (mixed convection) was applied. It was assumed that if the relative difference between the convectional heat flow occurring together with the existing combination of displacement forces, and body forces as well as the heat flux resulting from the influence on air molecules exceeded 10%, mixed convection took place. On the basis of such analysis it is possible to allot a boundary line between the area of occurrence of mixed and free convection (when the influence of the factor flow caused by body forces on the heat penetration is negligible).

2 150 Advances in Fluid Mechanics II Nomenclature d inside diameter of the exchanger Gr Grashof number 1 measurement length of the exchanger Nu Nusselt number Nuf Nusselt number for the factor average temperature Pr Prandtl number Prf Prandtl number for the factor average temperature Pr* Prandtl number for the wall average temperature Q^ heat flux transmitted in the experimental exchanger to the flowing factor Re Reynolds number Ref Reynolds number for the factor average temperature AT* 1^ average logarithmic difference of the factor temperature Apj thermal conductivity of the factor Introduction The range of the examined phenomenon includes the laminar flow in Reynolds' numbers range 15<Re<1800. The measurements were carried out in a pressure chamber in the absolute pressure range from 0,1 to 10,0 [MPa]. This produced high values of Grashof numbers without the necessity of changing the factor flowing through the chamber. One of the aims of the planned research was to show the quality difference between the heat transfer process taking place together with pure convection, for example forced convection, and heat transfer occurring in the mixed convection conditions. If this was to be true, the influence of free convection on the intensity of the heat penetration, taking place simultaneously with the forced laminar flow, in certain geometrical conditions is so big, that the traditional criteria! equations characterising the heat transfer in the range of this flow do not reflect the physical character of changes which resulted from the mixed flow, and must be replaced with other forms of criterial equations.

3 Advances in Fluid Mechanics II 151 Figure 1 shows the state of the free, forced and mixed convection for horizontal tubes, with the factor flowing in the conditions of constant temperature of the wall along the tube. Re FORCED CONVECTION TURBULENT -TRANSITION LAMINAR-TURBULENT ic? null FORCED FLOW LAMINAR MIXED CONVECTION LAMINAR MIXED CONVECTION TURBULENT 10 10= ICf It 10* 10* 10 GrPr Figure 1: Regimes of free, forced, and mixed convection for flow trough horizontal tube for 10 XPr--(l [4] The occurrence of the combination of forced laminar flow with the spontaneously induced free factor flow creates a difficult to analyse case - a case of overlapping of heat penetration processes. Research results concerning free and forced convection process elaborated for the laminar motion range obtained by various scientists are shown in figure 2. In order to create a comparison, these dependencies have been transformed to form Nu-/(Pr, Gr,...) = C Re* The comparison of dependencies points to noticeable discrepancies between the results obtained on the basis of formulas elaborated by different research workers.

4 152 Advances in Fluid Mechanics II Re Figure 2: The comparison of the generalized dependencies describing the heat transfer process in a circular channel for the laminar flow range according to: 1. Kraussold, 2. Sieder & Tate, 3. Eisner, 4. Cholette, 5. Colburn, 6. Michiejew The conducted research results were compared with the generalised dependencies to Nusselt number by: - Michiejew: «,=o,i5-: Pr 0,25 (1) The correction factor e for 1/d > 50 is 1. - Cholette: 0,4 (2)

5 Advances in Fluid Mechanics II 153 Description of the test stand and the measurement methodology Scientific research on heat transfer with a factor flowing in the circular channel was carried out at a test stand for heat measurements in hyperbaric conditions. The schema of the test stand is shown in figure 3. Its main element was a measuring chamber (1), which was fed from Figure 3: Schematic diagram of the experimental system designed for investigation of convective heat transfer in high pressure environment 1. pressure chamber, 2. support, 3. absorption vessels, 4. inlet into the chamber, 5. electric pressure terminal, 6. pressure tank, 7. compressor, 8. drain pipe, 9. rotameters, 10. valves, 11. control input valves, 12. drying valve, 13. release valve, 14 manometers a compressor (7), through a pressure tank (6) (accumulating the factor) and a set of three equalising tanks (3). The measuring chamber was made of a tube closed (from both sides) with covers. The right cover was equipped with an inlet into the chamber (4) enabling the connection of the chamber containing a test heat exchanger with pressure installation of the stand. The left cover of the measuring chamber was equipped with an electric pressure terminal (5). The pressure tank for the compressed air with 0,39 [m*] capacity could work by the maximum pressure of 16 [MPa]. Inside the measuring chamber was a circular heat exchanger. The exchanger was made of a copper tube with an inside diameter of 12 millimetres and the overall length of 1050 millimetres. On the exterior surface of the exchanger an electrical heating element

6 154 Advances in Fluid Mechanics II (functioning as the source of heat conveyed to the gas factor flowing inside the exchanger) was placed The whole device was insulated and equipped with a set of indispensable sensors as well as connected to a controlling and measuring apparatus. The air forced from the compressor to the pressure equalising tank reached the horizontal circular channel Having got heated there it left the measuring chamber in the drain-pipe The test stand was working in an open system, with the air flowing out into the surroundings. The regulation of the volume of the air flow was conducted with the help of a pressure reducing valve, a set of control valves and precise throttle valves. The measurement of the flowing factor quantity was held with the help of three rotameters placed inside the drain-pipe On the basis of the values obtained during the measurements, individual result quantities were calculated The readings of the pressure value in the measuring chamber were taken from the manometer installed in that chamber. The readings of the heat power, however, were taken from the supervisory-measuring apparatus. The analytical method The heat transfer effect observed during the forced flux of factor in the circular channels at the steady heat flux state can be described by means of a general dimensionless equation form, taking the following: (3) What results from the analysis of the phenomenon is the meaning of the individual dimensionless numbers and their usefulness to the descriptions of detailed, individual occurrences of heat transfer processes. Depending on the character of the factor flux in channel, in the established thermal stabilization conditions of the process and moderate speeds in the turbulent flow area, as well as with steady channel geometry, for which the simplex 1 = 85 -d, the equation [3] resolves itself to detailed forms. Hence, for the area in question, i.e. for the laminar and transitory flow, we get a dependence: -_) (4) Pr,

7 Advances in Fluid Mechanics II 155 On the grounds of calculating such prime quantities, as heat flux transmitted in the experimental exchanger to the flowing factor, air temperature at the inflow and the outflow of the channel, temperature of the exchanger wall surface as well as the insulation layer etc., the quantities constituting the dimensionless equation were defined. For example, the Nusselt number was defined according to the following dependence: Nu = ^' (5) where: (L the heat flux transmitted in the experimental exchanger to the flowing factor, / the measurement length of the exchanger, Ar,,,g the average logarithmic difference of factor temperatures, A pj the thermal conductivity of the factor. On the basis of the data obtained from the measurements the values of Nusselt, Reynolds, Prandtl and Grashof numbers for the tested cases were calculated. The results of the measurements On the grounds of conducted preliminary measurements a series of results showing the convectional heat transfer processes in the concerned flow range was obtained. For the purpose of simplifying the analysis and interpretation, the results of conducted tests are presented in a graphic form. In the enclosed figure number 4 the results of measurements obtained with the pressure of 0,1 [MPa] and different heat powers are shown, as compared with the results obtained by Michiejew. In figure number 5 exemplary Nusselt number values were obtained with 10 [W] heat power and pressure of 4,0[MPa] and the flow in the range of Reynolds number < 1000 have been presented.

8 156 Advances in Fluid Mechanics II 51, f\ Q 1 A 71 A C -1C o 1 c 1 -IE n QA n 7A MM**. j_ i _. ''' $ i : 2? I i i \ H. 9 : i ; ; ;*;, M i j j...! j i ' ^ ' r o -8 opf) <'.'. j ^ _ i : o a o :<y x> i o I...-..?. 1 *%=* O "<y : "" : O j i. v j.! I o o 0 : :"" 1 o " 1 c 0 ; : : :» : : : jo A : : o! 0 j j i : 6 : : : i o ace. to Michiejew : A heat power 25[W] '--.. * heat power 40[W].'-.. 0! : i i i : i : : Figure 4: The results of measurements obtained with the pressure of 0,1 [MPa] and different heat powers as compared to the results obtained by Michiejew from laminar to turbulent flow Re... i ] 9 i O; i O ; o o i o : i i : D i : Q; : : A A heat power 10[W] : A: o ace. to Michiejew D i A : o ace. to Cholote A ^ i I Re Figure 5: The results of measurements obtained with the pressure of 4,0[MPa] and 10[W] heat power as compared to the results obtained by Michiejew and Cholette

Advances in Fluid Mechanics II 157 Conclusions The preliminary research into the processes of heat transfer conducted with the circular heat exchanger has proved to be compatible with the results

9 Advances in Fluid Mechanics II 157 Conclusions The preliminary research into the processes of heat transfer conducted with the circular heat exchanger has proved to be compatible with the results determined on the basis of Michiejew's dependencies. It is particularly visible with the transient and turbulent flow area. In the turbulent flow area the influence of heat power on the convective heat-transfer coefficient slowly disappears. In the laminar flow area there are departures from the results obtained on the basis of the dimensionless equation elaborated by Michiejew. The results obtained with the 4,0 [MPa] pressure and the 10 [W] heat power show the existence of divergence with Michiejew's results and are close to those obtained by Cholette. For now the measurements for pressure range from 0,1 to 4,0 [MPa] and for the concerned heat power have ended. At this point, dimensionless equations and mixed convection area cannot be defined yet At present, it may be noted that the heat transfer rate in the circular channel in the hyperbaric conditions is connected with the pressure value and the heat transfer flux density. The pressure increase with the same Reynolds' number values causes the increase in Nusselts' number values. This is the reason why the research should be continued References [1] Bergles, A E & Simonds, R.R.,,Combined forced andfreeconvection for laminar flow in horizontal tubes with uniform heat flux", Heat Mass Transfer, Vol. 14, pp , [2] Ghajar, A J & Tarn, L.M.,,Flow regime map for a horizontal pipe with uniform wall heat flux and three different inlet configurations", ASME, HTD-Vol.247, pp , [3] Ghajar, A J & Tarn, L.M. ^Correlations for forced and mixed convection in straight duct flows with three different inlet configurations", ASME, HTD-vol.204, [4] Metais, B. & Eckert, ERG,,Forced, Mixed and Free Convection Regimes", ASME J. Heat Transfer, Vol.10, pp , 1964.

HEAT TRANSFER IN THE LAMINAR AND TRANSITIONAL FLOW REGIMES OF SMOOTH VERTICAL TUBE FOR UPFLOW DIRECTION

HEAT TRANSFER IN THE LAMINAR AND TRANSITIONAL FLOW REGIMES OF SMOOTH VERTICAL TUBE FOR UPFLOW DIRECTION Bashir A.I. and Meyer J.P.* *Author for correspondence Department of Mechanical and Aeronautical