40 Rules of Thumb for Mechanical Engineers and, for no change of phase flow, of shell diameter. If there is no change of phase in the shell-side fluid, the baf- fle pitch should not exceed the shell inside diameter. Other- wise, the fluid would tend to flow parallel with the tubes, rather than perpendicular to them, resulting in a poorer heat transfer coefficient. Impingement bafles are requjred on shell-side inlet noz- zles to protect the bundle against impingement by the in- coming fluid when the fluid 1. is condensing 2. is a liquid vapor mixture 3. contains abrasive material 4. is entering at high velocity In addition, TEMA requires bundle impingement protec- tion when nozzle values of pu2 (fluid density, kg/m3, times velocity squared m2/s2) exceed: 1. 2,230 kg/m-s2 for noncorrosive, nonabrasive, single- 2.744 kg/m-s2 for all other liquids Also, the minimum bundle enu-ance area should equal or exceed the inlet nozzle area and should not produce a value of pu2 greater than 5,950 kg/m-s2, per TEMA. Impingement baffles can be either flat or curved. In order to maintain a maximum tube count, the impingement plate is sometimes located in a conical nozzle opening or in a dome cap above the shell. The impingement plate material should be at least as good as that of the tubes. phase fluids Sources 1. Standards of Tubular Manufactiners Association, 7th Ed, 2. Cheremisinoff, N. P., Heat Transfer Pocket Handbook. TEMA, Tarrytown, NY, 1988. Houston: Gulf Publishing Co., 1984. The following notes summarize design features of shells for shell-and-tube heat exchangers. The single-pass shell is the most common shell con- struction used. The shell-side inlet and outlet nozzles are located at opposite ends of the shell. The nozzles can be placed on opposite or adjacent sides of the shell, depend- ing on the number and type of baffles used. A typical one- shell pass exchanger with horizontal segmental baffles is illustrated in Figure 23 [A] (TEMA E). A two-pass shell uses a longitudinal baffle to direct the shell-side flow. An exchanger with two shell passes is shown in Figure 23 [B]. Note that both the shell inlet and outlet nozzles are adjacent to the stationary tube sheets. A shell-side temperature range exceeding 195°C should be avoided, since greater temperature ranges result in exces- sive heat leakage through the baffle, as well as thermal stresses in the baffle, shell, and tube sheet. The longitudinal baffle can be either welded or remov- able. Since there are severe design and cost penalties as- sociated with the use of welded baffles in floating head ex- changers, this type of design should be used only with fixed-tube sheet units that do not require expansion joints. Removable longitudinal baffles require the use of flexible light gauge sealing strips or a packing device between the baffle and the shell, to reduce fluid leakage from one side to the other (TEMA F). A dividedflow shell has a central inlet nozzle and two outlet nozzles, or vice-versa. A divided flow exchanger is illustrated in Figure 23 [C]. This type is generally used to reduce pressure drop in a condensing service. In minimiz- ing pressure drop the shell fits in as follows: . E shell with segmental baffles E shell with double segmental baffles Heat Transfer 41 SINGLE PASS SHELL (4 TWO PASS SHELL (B) h DIVIDED FLOW SHELL (C) Figure 23. (A) Single-pass shell; (B) two-pass shell; (C) divided flow shell [2]. J shell with segmental baffles J shell with double segmental baffles E shells in parallel with segmental baffles E shells in parallel with double segmental baffles J shells in parallel with segmental baffles J shells in parallel with double segmental baffles Generally, for most designs, double segmental baffles are used with J shells. Double segmental baffles in a divided-flow exchanger nor- mally have a vertical cut. This baffle arrangement also re- quires that there be an odd number of total baffles, but there must also be an odd number of baffles in each end of the shell. The center baffle for this arrangement is normally similar to the center baffle used with segmental cut. The baffles on each side of the central baffle and the last baffle toward the ends of the shell have solid centers with cutaway edges. The choice of whether to stack shells depends on main- tenance considerations, as well as on the amount of plot am available. Stacking shells requires less area and frequent- ly less piping. Normally, shells are not stacked more than two high. However, stacked heat exchangers are more costly to maintain, because of accessibility. If sufficient plot area is available, the following guide- lines apply: 1. If the fluids are known to be clean and noncorrosive, 2. If the fluids are moderately clean or slightly corrosive, 3. If the fluids are very dmy or corrosive, the shells should the shells should usually be stacked. the shells may be stacked. not be stacked, to allow for ease of maintenance. Sources 1. Standards of Tubular Exchanger Manufacturer’s As- 2. Cheremisinoff, N. P., Heat Transfer Pocket Handbook. sociation, 7th Ed., TEMA, Tarrytown, NY, 1988. Houston: Gulf Publishing Co., 1984. 42 Rules of Thumb for Mechanical Engineers Miscellaneous Data Design-related data are given in Tables 8 through 10. Table 8 provides typical tube dimensions and tube surface areas per unit length. Table 9 gives thermal conductivities of materials commonly used for exchanger construction. Table 10 gives recommended maximum number of tube passes as a function of tube size. Source Cheremisinoff, N. P., Heat Transfer Pocket Handbook. Houston: Gulf Publishing Co., 1984. Table 8 Tube Dimensions and Surface Areas Per Unit Length $= O.D. of =w (-1 19.05 19.05 19.05 19.05 25.40 25.40 25.40 25.40 38.10 38.10 38.10 2.77 2.11 1.65 1.24 3.40 2.77 2.11 1.65 3.40 2.77 2.11 I.D. of 13.51 14.83 15.75 16.56 18.59 19.86 21 18 22.10 31.29 32.56 33.88 nm (m) Internal Area 143.8 172.9 194.8 215.5 271.6 309.0 352.3 383.2 769.0 832.9 901.3 (-3 Ex&rnal surface WRLength (4 0.0598 0.0598 0.0598 0.0598 0.0798 0.0798 0.0798 0.0798 0.1197 0.1197 0.1197 Table 9 Thermal Conductivities of Materials of Construction Thermal Cmductivity, k, Material (hlpO&ition Wt/m-"C 71 Cu-28 Zn-1 Sn 111 16 Admiralty Type 316 stainless steel 17 Cr-12 Ni-2 Mo Type 304 stainless steel 18 Cr-8 Ni 16 BrasS 70 Cu-30 Zn 99 Redbrass 85 Cu-15 Zn 159 Alumimlmbraps 76 Cu-22 Zn-2 Al 10 Cup-nickel 90 Cu-10 Ni 71 CupnicM 70 Cu-30 Ni 29 Mod 67 Ni-30 Cu-1.4 Fe 26 Inconel 19 Aluminum 202 Carbonsteel 45 Carbon-moly 0.5 Mo 43 386 35 copper Lead Nickel 62 Titanium 19 Chrome-moly steel 1 Cr-0.5 Mo 42 2'/4 Cr-0.5 Mo 38 5 Cr4.5 Mo 35 12 Cr-1 MO 28 Table 10 Maximum Number of Tube Passes RecommendedMaximum Shell I.D. (mm) NWllb6XOfltlllePaSSeS e250 4 250- e510 6 510- e760 8 760- <1,020 10 1,020- <1,270 12 1,270- <1,5u) 14 FLOW REGIMES AND PRESSURE DROP IN TWO-PHASE HEAT TRANSFER Flow Regimes Standard practice for heat exchanger analysis is to first identify the flow regimes and then employ the appropriate correlations. Bubbly flow. In this type, the gas or vapor phase is dis- tributed as discrete bubbles in a continuous liquid phase. At one extreme, the bubbles may be small and spherical, and at the other extreme, the bubbles may be large with a spherical cap and a flat tail. Slug flow. The gas or vapor bubbles are approximately the diameter of the pipe. The nose of the bubble has a charac- Vertical Upward Concumnt Flow Flows of this type are shown in Figure 24. Heat Transfer 43 WISPY- ANNULAR BUBBLY FLOW SLUQ FLOW CHURN FLOW ANNULAR FLOW Figure 24. Flow patterns in vertical concurrent flow [l]. teristic spherical cap, and the gas in the bubble is separat- ed from the pipe wall by a slowly descending liquid film. The liquid flow is contained in liquid slugs that separate suc- cessive gas bubbles. Slugs may or may not contain small- er entrained gas bubbles carried in the wake of the large bub- ble. The length of the main gas bubble varies. Churn flow. Formed by the breakdown of the large vapor bubbles in slug flow. The gas or vapor flows chaotically through the liquid that is mainly displaced to the channel wall. The flow has a time-varying character and hence is called "churn flow." This region is also sometimes re- ferred to as semi-annular or slug-annular flow. Wispy-annular flow. The flow takes the form of a relatively thick liquid film on the walls of the pipe together with a con- siderable amount of liquid entrained in a central gas or vapor core. The liquid in the film is aerated by small gas bubbles and the entrained liquid phase appears as large droplets which have agglomerated into long irregular filaments or wisps. This generally occurs at high mass velocities. Annular flow. A liquid film forms at the pipe wall with a continuous central gas or vapor core. Large amplitude co- herent waves are usually present on the surface of the film, and the continuous break up of these waves forms a source for droplet entrainment, which occurs in varying amounts in the central gas core. Vertical Heated Channel Upward Flow Heat flux through the channel wall alters the flow pat- tern from that which would have occurred in a long unheated channel at the same local flow conditions. These changes occur due to: 1. The departure from thermodynamic equilibrium cou- pled with the presence of radial temperature profiles in the channel. 2. The departure from local hydrodynamic equilibrium throughout the channel. Figure 25 shows a vertical tubular channel heated by a uniform low heat flux and fed with liquid just below the sat- uration temperature. BOILING REGIME Y . *. . .:>'. E: : ,. :.e ::':: :. ,. . .A .::I f FLOW Figure 25. Flow patterns in a vertical evaporator tube [2]. In the initial single-phase region, the liquid is heated to the saturation temperature. A thermal boundary layer forms at the wall, and a radial temperature profile forms. At some distance from the inlet, the wall temperature and the con- ditions for the formation of vapor (nucleation) at the wall are satisfied. Vapor forms at preferred positions on the tube surface. Vapor bubbles grow from these sites finally de- taching to form a bubbly flow. With the production of more vapor, the bubble population increases with length and co- alescence occurs, forming slug flow, which in turn gives way to annular flow further along the channel. Close to this 44 Rules of Thumb for Mechanical Engineers point the formation of vapor at sites on the wall may cease and further vapor formation will result from evaporation at the liquid-film vapor-core interface. Increasing velocities in the vapor core cause entrainment of liquid in the form of droplets. The depletion of the liquid from the film by this entrainment and by evaporation finally causes the film to dry out completely. Droplets continue to exist and are slowly evaporated until only single-phase vapor is present. Figure 26 shows the flow patterns of liquid-vapor flow in a heated pipe as a function of wall heat flux. Liquid en- ters the pipe at a constant flow rate and at a temperature lower than the saturation temperature. As the heat flux in- creases, the vapor appears closer and closer to the pipe inlet. The local boiling length is the extent of pipe where bubbles form at the wall and condense in the liquid core where the liquid temperature is still lower than the saturation tem- perature. Vapor forms by: 1. Wall nucleation 2. Direct vaporization on the interfaces located in the flow itself I?GREASINO HEAT FLUX w SUPERWUTLD VAPOR REOlON OPlsCT OF ((UCLCATE BOKINO t COWSTANT LlOUlD PLOWRATS Figure 26. Convective boiling in a heated channel [3]. (With permission of Elsevier Science Ltd.) There is progressively less liquid between the wall and the interfaces. Consequently, the thermal resistance de- creases along with the wall temperature, resulting in an end to wall nucleation. In annular flow, the liquid film flow rate decreases through evaporation and entrainment of droplets, although some droplets are redeposited. In heat flux con- trolled systems, when the film is completely dried out, the wall temperature rises very quickly and can exceed the melting temperature of the wall (called dryout). Flow pat- terns are shown in Figure 27. In upward bubbly flow, bubbles are spread over the en- tire pipe cross-section whereas in the downward flow bub- bles gather near the pipe axis. Figure 27. Air-water flow patterns in a downward con- current flow in a vertical pipe: (1) bubbly, (2) slug, (3) falling film, (4) bubbly falling film, (5) churn, and (6) dispersed annular flow [4]. At higher gas flow rates (but a constant liquid flow rate) the bubbles agglomerate into large gas pockets. The tops of these gas plugs are dome-shaped whereas the lower ex- tremity is flat with a bubbly zone underneath. This slugflow is generally more stable than in the upward case. With annular flow, at small liquid and gas flow rates, a liquid film flows down the wall (falling film flow). If the liquid flow rate is higher, the bubbles are entrained with- in the film (bubbZyfaZZingJiZm). At greater liquid and gas flow rates chumflow exists, which can evolve into dispersed annular flow for very high gas flow rates. Horizontal Concurrent Flow The flow patterns for this type of flow are shown in Figure 28. Bubbly flow (froth flow). This resembles the case in ver- tical flow except that the vapor bubbles tend to travel in the upper half of the pipe. At moderate gas and liquid veloci- ties, the entire pipe cross-section contains bubbles. At higher velocities, a flow pattern equivalent to the wispy-an- nular pattern exists. Plug flow. This is similar to slug flow in the vertical di- rection. Again, the gas bubbles tend to travel in the upper half of the pipe Stratified flow. This pattern only occurs at very low liq- uid and vapor velocities. The two phases flow separately with a relatively smooth interface. Wavy flow. As the vapor velocity is increased, the inter- face becomes disturbed by waves traveling in the direction of flow. Slug flow. At higher vapor velocities the waves at the in- terface break up to form a frothy slug which is propagat- Heat Transfer 45 b - Stratified wavy Annular Flow - Figure 28. Flow patterns in horizontal flow [l]. ed along the channel at a high velocity. The upper surface of the tube behind the wave is wetted by a residual film, which drains into the bulk of the liquid. Annular flow. At higher vapor velocities a gas core forms with a liquid film around the periphery of the pipe. The film may or may not be continuous around the entire circum- ference but it will be thicker at the base of the pipe. Flow patterns formed during the generation of vapor in hor- izontal tubular channels are influenced by departures from thermodynamic and hydrodynamic equilibrium. Figure 29 shows a horizontal tubular channel heated by a uniform low heat flux and fed with liquid just below the saturation tem- perature. The sequence of flow patterns corresponds to a rel- atively low inlet velocity (<I ds). Note the intermittent dyng and rewetting of the upper surfaces of the tube in wavy flow and progressive drying out over long tube lengths of the upper circumference of the tube wall in annular flow. At high- er inlet liquid velocities, the influence of gravity is less ob- vious, the phase distribution becomes more symmetrical, and the flow patterns become closer to those in vertical flow. STRATIFIED- SPRAY FLOW STRATIFIED FLOW VERTICAL a HORIZONTAL FLOWS SPRAY FLOW INTERNITTENT Fl VERTICAL FLOW .ow BUBBLY FLOW Figure 30. Shell-side two-phase flow patterns [5]. (With permission of ASME.) Spray flow. This occurs at high mass flow qualities with liquid carried along by the gas as a spray. Bubbly flow. This occurs at low mass flow qualities with the gas distributed as discrete bubbles in the liquid. Intermittent flow. Intermittent slugs of liquid are pro- pelled cyclically by the gas. Stratified-spray flow. The liquid and gas tend to separate with liquid flowing along the bottom. The gas-phase is en- trained as bubbles in the liquid layer and liquid droplets are carried along by the gas as a spray. Stratified flow. The liquid and gas are completely separated. Spray and bubbly flows occur for either vertical up-and- down flow or horizontal side-to-side flow. Intermittent flow only occurs with vertical up-and-down flow and stratified- spray and stratified flow with horizontal side-to-side flow. Flow Normal to Tube Banks Sources The flow patterns in the crossflow zones are shown in Figure 30. Figum 29. Flow patterns in a horizontal tube evaporator [2]. 1. Cheremisinoff, N. P., Heat Transfer Pocket Handbook, 2. Collier, J. G., Convective Boiling and Condensation. 3. Hewitt, G. F. and Hall-Taylor, N. S., Annular Two-Phase 4. Oshinowo, T. and Charles, M. E., in Can. Journ. of 5. Grant, I. D. R. and Chisholm, D. in Trans ASME, Jour- Houston: Gulf Publishing Co., 1984. New York: McGraw-Hill, 1972. Flow. London: Pergamon Press, 1970. Chem. Engrg., 52: 25-35, 1974. nal ofHeat Transfel; 101 (Series C): 3842, 1979. 46 Rules of Thumb for Mechanical Engineers A flow pattern map is a two-dimensional representation of the flow pattern existence domains. The respective pat- terns may be represented as areas on a graph, the coordi- nates of which are the actual superficial-phase velocities (il or jJ. The coordinate systems are different according to var- ious authors, and so far there is no agreement on the best coordinate system. Vertical Upward Flow Figure 3 1 shows a flow pattern map based on observa- tions on low-pressure air-water and high-pressure steam- water flow in small diameter (1-3 cm) vertical tubes [4]. The axes are the superficial momentum fluxes of the liq- uid (pi1) and vapor (pi,') phases, respectively. These su- perficial momentum fluxes can also be expressed in terms of mass velocity G and the vapor quality x: Figure 3 1 should be considered as a rough guide only. Vertical Downward Flow Figure 32 shows one investigator's chart [2]. Data are based on two-component mixtures of air and different liq- uids flowing in a pipe 25.4 mm in diameter at a pressure of around 1.7 bar. The abscissa and ordinate are the quan- tities Fr/a and m) (where p is the liquid holdup fraction) which are calculated at the test section pressure and temperature. The Froude number, Fr, is defined by: Fr = (ig + jlI2/gdi where g = acceleration due to the gravity di = pipe diameter A = a coefficient that accounts for the liquid phys- ical properties where p = liquid viscosity p = liquid density o = liquid surface tension Subscript w refers to water at 20°C and 1 bar. (3) I '8 0- 8 8 '. -Y -Jug 8 # 8 'sue Lghh (0 ddddo' c .I I I 1 1 3 LA Ib ' rddddo' ' 46 Figure 31. Flow pattern map for vertical upward flow [4]. (With permission of AEA Technology plc.) .1oIql .lo 1 10 100 1000 10000 cr/ a Figure 32. Flow pattern map for vertical downward flow: (1) bubbly, (2) slug falling film, (3) falling film, (4) bubbly falling film, (5) churn, and (6) dispersed annular flow [a. Heat Transfer 47 Horizontal Flow Flow Normal to Tube Banks The well-known Baker plot consists of a plot of GJh and G,hv/G,, where G, and GI are the superficial mass veloc- ities of the vapor and liquid phases, respectively [5]. The factors h and y~ are: and v=(%) (4) (5) Baker's map has been modified by many investigators. Mandhane et al. [6] based a map upon 5,935 data points, 1,178 of which concern air-water flows. Its coordinates are the superficial velocities j, and j, calculated at the test sec- tion pressure and temperature. The map is shown in Figure 33 and is valid for the parameter ranges given in Table 11. I 10-3 10 lo2 103 jg m/s 10-2 10-1 Figure 33. Flow map proposed by Mandhane et al. [SI. (With permission of Elsevier Science Ltd.) Flow pattern maps for both vertical and horizontal flow normal to the tube banks are given in Figure 34. The para- meters of these maps are those of Baker [5], modified ac- cording to Bell, et al. [7]. It is a plot of superficial gas ve- Table 11 Parameter Ranges for the Flow Map Proposed by Mandhane et al. Conditions Range of Values Liquid density 705 - 1,009 kg-~n-~ Gas density 0.80 - 50.5 kg-x~-~ Liquid viscosity 3 x - 9 x Pa Gas viscosity 10-5 - 2.2 x Pa Surface tension 24 - 103 mN-m-' Liquid superficial velocity Gas superficial velocity Source: Mandhane [6]. Pipe inner diameter 12.7 - 165.1 IIIRI cm-s-' m-s-' 0.09 - 731 0.04 - 171 .1 .o 1 rn \ ti N > 'm -4 Q Q Y rn *n .* .o 1 \ INrrOMlTlENT FLOW YEIlTKM FLOW SmAY FLW / IiORlZONTAL FLOW 1 I 0.1 1 10 j, (pRI-r,)1/3/a (s2/*s) 'I3 Figure 34. Shell-side flow pattern maps [3]. (With per- mission of ASME.) 48 Rules of Thumb for Mechanical Engineers locity vs. superficial liquid velocity with physical property terns attached. Superficial is used in the sense that the total flow area and not the actual phase flow area is used to eval- uate the phase velocity. The flow area referred to is the min- imum cross-sectional area for flow through the tube bank. Sources 1. Cheremisinoff, N. P., Heat Transfer Pocket Handbook. 2. Oshinowo, T. and Charles, M. E., in Can. Journ. of Houston: Gulf Publishing Co., 1984. Chem. Engrg., 52: 25-35,1974. 3. Grant, I. D. R. and Chisholm, D. in Transactions ASME, Jozimal of Heat Transfer; 101 (Series C): 3842, 1979. 4. Hewitt, G. E and D. N. Roberts, “Studies of Two-Phase Flow Patterns by Simultaneous X-Ray and Flash Pho- tography,” AERE-M2159, H.M.S.O., 1969. Copyright AEA Technology plc. 5. Baker, 0. in Oil &Gas Journ., 53 (12): 185-190,1954. 6. Mandhane, J. M., Gregory, G. A., and Aziz, K. in Intl. Joum. of Multi Flow, 1: 533-537, 1974. 7. Bell, K. J., Taborek, J., and Fenoglio, E, Chem. Engrg. Progress, Symposium Series (Heat Transfer-Min- neapolis), 66 (102): 150-165, 1970. Estimating Pressure Drop Two-phase drop in a shell-and-tube heat exchanger con- sists of friction, momentum change, and gravity: AP = APf + APm + APg (6) The entrance and exit pressure losses, usually considered in a compact heat exchanger application, are neglected because of 1. The lack of two-phase data for these pressure losses 2. Their small contribution to the total pressure drop for tubular exchangers The evaluation of AP due to momentum and gravity effects is generally based on a homogeneous model. Homogeneous Flow Model This is the simplest two-phase flow model. The basic premise is that a real two-phase flow can be replaced by a singlephase flow with the density of the homogeneous mix- ture defined by: 1 l-x x +- Phorn PI Pg -=- where v is the specific volume. Subscripts 1 and g denote liquid and gas phases and x is the quality (the ratio of gas mass flow rate to total [gas + liquid] mass flow rate). The pressure droplrise due to an elevation change is: Angle 9 is measured from the horizontal. The + sign stands for a downflow, and the - sign stands for an upflow. Grav- ity pressure drop predictions from this theory are good for high quality and high pressure applications. When APg is predominant (one half to two thirds of the AP), such as for low velocities and low pressure applications, the following equation, which takes into account the velocity slip between two phases via the void fraction a (the ratio of gas volume to total volume), should be used: APg = f (p, (1 - a) + pga) (gig,) L sin 8; for APg > 0.5 APtod (9) The momentum pressure drop/rise from the homogeneous model is: p2 and p1 are the densities of homogeneous mixtures at the exchanger (tube) outlet and inlet, respectively. They are individually evaluated using Equation 7. G is the mass velocity. Heat Transfer 49 Separated Flow Model Here, the two phases are artificially segregated into two streams. Each stream (vapor and liquid) is under the same pressure gradient but not necessarily with the same veloc- ity. The separated flow model reduces to the homogeneous flow model if the mean velocities of the two streams are the same. The best known separated flow model is the Lock- hart and Martinelli correlation [2]. In the Lockhart-Martinelli method, the two fluid streams are considered segregated. The conventional pressure-drop friction-factor relation- ship is applicable to individual streams. The liquid- and gas- phase pressure drops are considered equal irrespective of the flow patterns. $:denotes the ratio of a two-phase fric- tional pressure drop to a single-phase frictional pressure drop for the liquid flowing alone in the tube: And for vapor: where AP, is the single-phase frictional pressure drop for the gas flowing alone in the tube. x2 is the ratio of a single-phase pressure drop for the liq- uid phase flowing alone in the tube to that for the gas phase flowing alone in the tube. 2 - Dl AP?2 x The correlation is shown in Figure 35 and the curves can be represented in equation form as: c1 xx $?=I+ +, or where the value of C is dependent upon the four possible single-phase flow regimes. (1- 01 Q) XI 1 01 1 PARAMETER X Figure 35. Lockhart-Martinelli correlation [2]. (With permission of ASME.) Liquid Gas C Turbulent - Turbulent (W 20 Viscous - Turbulent (vt) 12 Turbulent - (tv) 10 Viscous - Viscous (w) 5 (1 6) Viscous The two-phase frictional pressure drop by the Lock- hart-Martinelli method is determined as follows. First, from the amount of liquid and gas flow rates, and using cor- responding friction factors or appropriate correlations, AP, and AP, are calculated. The liquid flow is considered to oc- cupy the entire cross-section for the A€’, evaluation, and the gas flow occupies the whole cross-section for the APg eval- uation. The parameter x is then calculated from Equation 13. The value of C is determined from Equation 16 and @, or are computed from Equations 14 and 15. The two- phase frictional pressure drop is then calculated from the definition of $. The Lockhart-Martinelli method was developed for two component adiabatic flows at a pressure close to atmospheric. Martinelli and Nelson [3] extended this method for forced convection boiling for all pressures up to the critical point. The mixture of steam and water was considered “turbulent- turbulent.” They presented (& graphically as a function of the quality x and the system pressure as shown in Figure 36. [...]... sziblimation Fusion and vaf porization values for water at 14.7 psi are 1 43. 4 and 970 .3 Btdlbm, respectively Table 1 Gas Properties Mol W t Gas C P c , k R 2.0 60 030 5 0.240 0 53 2 025 0 0.2 43 01 15 0.422 120 5 34 0 2 0.5 93 0 23 77 01 7 4 1 0.4064 01 599 012 71 5 94 5 33 9 10 3 51 5 52 027 4 02 7 1 01 7 1 6 01 549 0 .38 00 13 0 14 0 13 2 12 8 14 0 13 9 11 8 16 6 1.41 13 2 14 0 14 0 11 2 12 8 12 6 ~ AS=-Q T... 57 58 Work 58 Heat 58 First Law of Thermodynamicsfor Closed Systems 58 First Law of Thermodynamicsfor Open Systems 58 Second Law of Thermodynamics Reversible Processes and Cycles 59 59 51 59 59 60 60 60 61 61 62 63 63 64 52 Rules of Thumb for Mechanical Engineers THERMODYNAMIC ESSENTIALS Thermodynamicsis the subject of engineering that predicts how much energy can be... T2) The thermal efficiency of the cycle is: 64 Rules of Thumb for Mechanical Engineers r 3 1 I V S Figure 9 Diesel cycle 6as Power Cycles with Regeneration Use of regeneration is an effective way of increasing the thermal efficiency of the cycle, particularly at low compressor pressure ratios The Stirling and Ericsson cycles are such attempts to get efficiencies close to that of the ideal Camot cycle... 44.00 2.0 80 7.0 09 3. 7 00 40 0 20 0 1.0 60 28.00 3. 0 20 4.9 40 18.00 6 0 41 044 0 040 6 0154 0.0885 037 50 0.7540 245 30 0.4692 0 .36 00 01 230 21.8 5 13 3 63 8 766.8 9 64 5 52 4 83 3 50 85.8 2 40 Thennodynamics 55 ~~ DeterminingProperties Ideal Gas A gas is considered ideal when it obeys certain laws Usually, the gas at very low pressurehigh temperature will fall into this state One of the laws is Boyle’s... n- 1 The Zeroth law of Thermodynamics The Zeroth Law of Thermodynamics defines temperature This law states that heat flows from one source to another only if there is a temperature difference between the two Therefore, two systems are in thermal equilibrium if they are at the same temperature 58 Rules of Thumb for Mechanical Engineers FIRST LAW OF THERMODYNAMICS The first law of thermodynamicsestablishes...50 Rules of Thumb for Mechanical Engineers where B = (CI' - 22- +2)/(r2- 1) r = AP,JAP,, 2 + C = (PI/P~)'/~/KK (p$pI)'" K = velocity ratio = jg/jl Figure 36 Martinelli-Nelson correlation [ ] 3 (19) (20) (21) (22) n is the exponent in the Blasius relation for friction factor f = CI/Ren,with n = 0.25 for the turbulent flow These discussions are inclusive of tube flow only Two-phase... states that “equal volumes of different gases with the same temperature and pressure contain the same number of molecules,” we arrive at the general law for the ideal gas (equation of state): where ah’ accounts for the intermolecularattraction forces and b accounts for the finite size of the gas molecules In theory, equations of state may be developed that relate any properzy of a system to any two other... der Waals Equatlon The ideal gas equation may be corrected for its two worst assumptions,i.e., infinitesimal molecular size and no intermolecular forces, by the following equation: I S Figure 2 The T-s diagram 56 Rules of Thumb for Mechanical Engineers Fisobars (psi) std atmosphere (14.7 psi) moisture content) are shown Above it are the lines of constant superheat and constant temperature Isobars are... Values of exponent n for the crossflow zone are: n = 0.46 for horizontal side-to-side flow, and n = 0 .37 for vertical up-and-down flow Table 12 Values of B for Two-Phase Frictional Pressure-Drop Evaluation in Crossflow and Window-Flow Zones by Equation 18 where API0is the frictional pressure drop for the liquid flow alone, in the same tube, with a mass flow rate equal to the total mass flow rate of the... accounted for This also means that heat entering a closed system must either increase the temperature (in the form of u> and/or be used to perform useful work W W J Q = *U + Note that the Joule’s constant was used to convert work to its heat equivalent (ft.lbf to Btu) First Law of Thermodynamics for Open Systems The law for open systems is basically Bernoulli’s equation extended for nonadiabatic processes For . 16.56 18.59 19.86 21 18 22.10 31 .29 32 .56 33 .88 nm (m) Internal Area 1 43. 8 172.9 194.8 215.5 271.6 30 9.0 35 2 .3 38 3.2 769.0 832 .9 901 .3 ( -3 Ex&rnal surface WRLength. 0.1 230 k R 1 .30 59.4 1.40 53. 3 1 .32 91.0 1.28 35 .1 1.40 55.2 1 .39 21.8 1.18 51 .3 1.41 766.8 1.40 48 .3 1.28 85.8 1.66 38 6 .3 1 .32 96.4 1.40 55.2 1.12 35 .0 1.26 24.0 Thennodynamics. 0.1 1 10 j, (pRI-r,)1 /3/ a (s2/*s) 'I3 Figure 34 . Shell-side flow pattern maps [3] . (With per- mission of ASME.) 48 Rules of Thumb for Mechanical Engineers locity vs. superficial