HEAT TRANSFER IN FALLING FILMS

Transcription

1 REA T TRANSFER - LAB LESSON NO.5 HEAT TRANSFER IN FALLING FILMS Before die start of die lab lesson you should be able to explain / answer die following points or questions regarding heat transfer in falling films: 1. What simplified assumptions have been made (in the theory for falling films on a vertical plate) with regard to the temperature? 2. What is here meant with r? 3. Defme Reynolds number for falling films. When (at what Re-number) does the change between laminar and turbulent flow take place? 4. Defme the Nusselt number. Express also Graetz number in other non-dimensional numbers. 5. What thermal property affects the heat transfer most with varying temperature? 1

2 REA T TRANSFER LAB LESSON NO.5 HEAT TRANSFER IN FALLING FILMS INTRODUCTION: Heat transfer in falling films takes place between a thin liquid film and a surface that emits or absorbs heat: The liquid flows or falls over this surface because of gravity. With falling films one can obtain comparatively very high coefficient of heat transfer and this method is often used at cooling and heating processes in such industries as breweries, dairy factories, chemical industries, etc. These traditional applications nonnally operates with low Reynolds number and laminar flow. Falling films have lately found a new area of application as evaporators in large heat pumps using water as heat source. A high mass flow rate is normally used giving turbulent flow that in falling films usually is obtained when Reynolds number is > 16, while Re < 16 usually gives laminar flow. OBJECT: The purpose of the lab lesson is to determine the coefficient of heat transfer and Reynolds number as well as the Nusselt number as a function of the mass flow rate at a vertical falling film and turbulent flow. Water is flowing on the outside of a vertical tube that is heated by a water circuit in the tube. The coefficient of heat transfer shall be determined for a number of measuring points where the mass flow rate of the falling film varies. The results of the experiment are then compared with an empiric equation by McAdams for falling films with turbulent flow. 2

3 THEORY: "Heat transfer in falling films" is summarized in the 1996 edition of "Heat Transfer - Collection of formulas and Tables of Thermal Properties" by Eric Granryd. Simplifying assumptions made in the theory of falling films: The flow velocity of the falling film along the vertical tube wall is assumed to be constant. This would mean that no acceleration takes place as there is balance between liquid friction and the weight of the liquid. Any effect of the curving of the liquid fllm on the tube wall is disregarded. The heat transfer in the direction of the liquid flow is small in comparison can thereby be regarded as constant. - The curves of temperature. The whole tube wall surface is assumed to have the same temperature, tv, while the temperature of the falling medium at the inlet is to and its mean temperature at the outlet is tmh. In the picture the falling medium is heated by the tube wall, but it can be either heated or cooled. 1mH t ~ 1: Temperature profile where falling f11m is heated by the tube wall 3

4 For falling films on vertical walls and with the above given temperature conditions we can arrive at an equation for the coefficient of heat transfer related to the logaritrnic mean temperature difference, hln, for a wall with the height, H. The heat flux divided by the breadth of the wall, q', can with symbols according to the Table of symbols (p.9) be expressed as: q' = r.cp.(~o-~h) = hb1.h.(~o-~h)/(ln(~o/~h) This equation can be changed to the following form: hjn.hjk = r'(cp/k).ln(~o/~) When the non-dimensional Nusselt and Graetz numbers (see p.9) are introduced the equation can be written in the following non-dimensional form: Nuln = Gz.ln( ~o/~) Experimental correlations for heat transfer at turbulent flow. Heat transfer in falling films with turbulent flow has experimentally been examined among others by McAdams, Drew and Bays. At these experiments water was heated by flowing inside vertical tubes while water steam of 1 bar was condensing on me outside of me tubes. Wim support from experimental data McAdams states generally that the following non-dimensional equation can be used to determine the coefficient of heat transfer at turbulent flow and a vertical falling film: hln/(k3.p2.g/~11/3 = O.Ol.(~.cP/k)I/3.(4.r/~)I/3 (4) By introducing non-dimensional numbers the equation can be written as: NUIn = O.O159'(g'H 3 Iv) 2 1/3.(r'cp/k) 1/3 = O.Ol59.(G.Gz) 1/3 (5) All the property constants in this equation shall be related to the so called film temperature, tf = (tv+tb)/2. 4

5 EXPERIMENTAL APPARATUS: The experimental apparatus is built as a simple heat exchanger. An inner water circuit heats up a vertical brass tube (H = 1. m; dy =.65 rn). Cold water from a water pipe is flowing outside the tube. At the bottom of the tube the water runs to the bottom container and is then led out through the drain. (See Figure 2). 1. Flow meter for falling water r11m Control and cut-off valve Falling film distributor Brass tube for falling film Circulation pump, inner circuit Electric water heater, - " - Electric kwh-meter, - " - Temperature recorder (thermo couples are marked as arrows) Figure 2: Outline diagram of experimental apparatus The inner heat emitting water circuit is heated up by an electric heater. Water is pumped through the circuit with high speed with the aid of a circulation pump. The high water velocity contributes to an almost constant tube wall temperature as the temperature difference between the incoming and outgoing water outside the tube wall is small. This gives a rather good agreement with the theory where constant tube wall temperature is assumed. Falling film distributor The.water that is to flow outside the tube is taken fro~ a water pipe and enters at the lower edge of the upper receptacle (See Figure 3). In the receptacle the water level raises until it reaches the upper end of the middle tube. The water then flows into this tube and passes two centering plates with many holes. These plates even the falling film flow and prevent whirls. 5

6 In the bottom of the receptacle there are a number of plates by which the width of the gap can be regulated in a number of steps. When the water has passed these plates it falls as an even film down the outside of the vertical brass tube over which the heat transfer takes place. 1. Glass gauge showing apparent pressure level 2. Glass g~uge showing actual pressure level 3. Inlet, falling water film 4. Middle tube 5. Thermo couple for measuring tube wall temperature 6. Thermo couple pocket 7. Blind pipe 8. Brass tube for falling film 9. Plates for plate regulating => Path of falling water > Path of inner medium Figure 3: Falling film distributor Measuring devices Thermo couple threads of copper - konstantan connected to a temperature registrator are used for temperature measurements. Some threads are soldered to the measuring objects and some are inserted into thermo couple pockets. A volume flow meter is used to measure the incoming cold water volume flow. Incoming electric power to the pump and heater for the inner circuit is measured with a normal kwh-meter. (Measure the time for several revolutions.) This measurement is made as a control of the energy balance.

7 TEST PROCEDURE: Start of lab lesson A control should first be made that there is water in the inner circuit. This is done by observing the glass gauge at the top of the expansion vessel. Water has to be added if no water level is visible. To start the water flow on the outside of the brass tube you first have to fully open the water tap at the wall (green pipe) and thereafter fully open the red tap situated after the volume flow meter. This red tap is also used to regulate the water flow for the five measuring points. Your laboratory assistant will show you the switch used to start the pump and electric heater for the inner circuit. Measuring and guiding values Wait for steady conditions, reasonable thermal balance, which can be observed on the registrator, for each of the measuring points. Measurements are then made of temperatures, volume (mass) flow and electric power. The five measuring points should be made at decreasing and evenly spread water flows between max flow (appr.5 1/s) and =::.1 1/s (kg/s). (The left small red indicator at the flow meter makes one revolution/liter. Measure the time for a suitable number of revolutions.) Enter the measured values in Table 1. The values listed under Calculated values in Table 1 are easily calculated with the help of the Table of symbols (p.9) and Appendix (p.14) with property constants for water. These property constant should be taken at the so called film-temperature, tf = (tv + tb)/2. 7

8 The mass flow rate divided by the breadth of the plate, r, is calculated from r = fn/(n.dy) where m is mass flow of the falling water film. The transferred heat flow is calculated from q = ffi'cp.j1.t, where J1.t = tmh - to. The coefficient of heat transfer hln, related to the logaritmic mean temperature difference is calculated from the equation: q = hin.ar'(~~h)/ln(&/~) (6) where At = n.dy. H (m2) is the outside area of the brass tube. Corresponding Nusselt number is calculated from NUIn = hln. H/k. Reynolds number is here easiest calculated fron Re = 4. r/j!. The heat losses can be estimated from qr = qel - q. All the calculated values are entered into Table 1. Mark in DIAGRAM 1 measured temperatures (tin, tout, tvo, tvh, to, tmh) at the top or bottom of the brass tube. Connect appropriately with (straight) lines. Mark in DIAGRAM 2 calculated hbl-values as a function of r1f3. Draw also lines for ~~ (McAdams equation) in the same diagram for tf = 1, 2 and 3 C. First you can trim ~~ to the form hbl = O.1.( )I/3.rl/3 outlined in ~ 1: and then calculate hbl for the given r1/3-values. Mark in DIAGRAM Draw also lines for ~~ 3 calculated Nuln-values as a function of Reynolds number. in the same diagram for tf = 1 and 3 C. These lines can also be obtained by trimming ~~, but now to calculate NUIn = 1/3 1/3..1.( ).Re and then calculate Nuln for the given Re-values. How do the marked values from the measuring points in Diagrams 2 and 3 compare with the lines based on McAdams equation? - Can we give any explanation for possible deviations from these lines? 8

9 TABLE OF SYMBOLS: A (m1 cross section area of water film At (m1 outside area of brass tube (= n.dy.h) de (m) hydraulic diameter of water film dy (m) outer diameter of brass tube wall H (m) height of brass tube wall g (m/s1 acceleration due to gravity (:== 9.81) qel (W) electric power to inner circuit m ~:W/m) mass flow of falling medium r (kg/m,s) mass flow rate divided by breadth of plate wall (= in/n.dy) q (W) heat flow q' (W 1m) heat flow per length of plate wall qr (W) heat losses (= qel - q) to (oc) temperature of flowing medium at inlet tmh (oc) temperature of flowing medium at outlet tvo (oc) temperature of tube ~all at inlet tvh ( C) temperature of tube ~all at outlet tin (oc) temperature of inner circuit at illiet toot (oc) temperature of inner circuit at Q!!!let tb (oc) mean temperature of flowing medium (= (to+tmh)/2) tv ( C) mean temperature of tube ~all (= (tvo+tvh)/2) tr ( C) [1lm temperature (= (tv+tb)/2) L\t (K) temperature difference of flowing medium (= tmh-to) ~O (K) temperature difference at inlet of tube (= tvo-to) ~ (K) temperature difference at outlet of tube (= tvh-tmh) cp (J/kg,K) specific heat (at tr) k (W Im,K) thermal conductivity (at tr) J.l (Ns/m1 dynamic viscosity (at tr) V (m2/s) kinematic viscosity (at tr) p (kg/m3) density (at tr) hjn (W/m2,K) coefficient of heat transfer (see defmition at equation 6) Nuln (-) corresponding Nusselt number (= hjn.hjk) G ( - ) gravity number (= g. H3/V1 Gz ( - ) Graetz number (= r.cp/k) Pr ( - ) Prandtl number (= J.l'Cp/k) Re ( - ) Reynolds number (= wm.de/v = ffi.de/(a.j.l) = 4.r/J.l) <)

10 TABLE 1: MEASURED AND CALCULATED VALUES 1

11 TABLE 2: CALCULATIONS FOR McADAMS EQUATION 11

12 DIAGRAM 1 and DIAGRAM ~ ~ 1:... t+..- o C.- - c c2 = t/j = ~.c NI I" Q) s e.8 Co,a ~ t <U > 8. e 5 ~ E-o <U.:.:, ;a s +J +J.J:I I u u ("'I N (:> - 12

13 DIAGRAM.;1: Nusseltsnumber as a function of Reynolds number (NUIn f(re) ~..- Ln (f') 11'1 13

14 APPENDIX: PROPERTY CONSTANTS FOR WATER p Cp k J.1 density (kg/m3) specific heat (J/kg,K) thermal conductivity (W /m,k) dynamic viscosity (Ns/m , ) 2 4 5C 14