* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download module 7
Survey
Document related concepts
Hypothermia wikipedia , lookup
Building insulation materials wikipedia , lookup
Cutting fluid wikipedia , lookup
Radiator (engine cooling) wikipedia , lookup
Thermal conductivity wikipedia , lookup
Underfloor heating wikipedia , lookup
Solar air conditioning wikipedia , lookup
Solar water heating wikipedia , lookup
Cogeneration wikipedia , lookup
Reynolds number wikipedia , lookup
Intercooler wikipedia , lookup
Dynamic insulation wikipedia , lookup
R-value (insulation) wikipedia , lookup
Heat equation wikipedia , lookup
Thermoregulation wikipedia , lookup
Copper in heat exchangers wikipedia , lookup
Heat exchanger wikipedia , lookup
Transcript
MODULE 7 HEAT EXCHANGERS 7.1 What are heat exchangers? Heat exchangers are devices used to transfer heat energy from one fluid to another. Typical heat exchangers experienced by us in our daily lives include condensers and evaporators used in air conditioning units and refrigerators. Boilers and condensers in thermal power plants are examples of large industrial heat exchangers. There are heat exchangers in our automobiles in the form of radiators and oil coolers. Heat exchangers are also abundant in chemical and process industries. There is a wide variety of heat exchangers for diverse kinds of uses, hence the construction also would differ widely. However, in spite of the variety, most heat exchangers can be classified into some common types based on some fundamental design concepts. We will consider only the more common types here for discussing some analysis and design methodologies. 7.2 Heat Transfer Considerations The energy flow between hot and cold streams, with hot stream in the bigger diameter tube, is as shown in Figure 7.1. Heat transfer mode is by convection on the inside as well as outside of the inner tube and by conduction across the tube. Since the heat transfer occurs across the smaller tube, it is this internal surface which controls the heat transfer process. By convention, it is the outer surface, termed Ao, of this central tube which is referred to in describing heat exchanger area. Applying the principles of thermal resistance, t T di do Figure 7.1: End view of a tubular heat exchanger r ln o r i 1 1 R ho Ao 2 kl hi Ai If we define overall the heat transfer coefficient, Uc, as: Uc 1 RAo Substituting the value of the thermal resistance R yields: 1 1 U c ho r ro ln o r i A o k hi Ai Standard convective correlations are available in text books and handbooks for the convective coefficients, ho and hi. The thermal conductivity, k, corresponds to that for the material of the internal tube. To evaluate the thermal resistances, geometrical quantities (areas and radii) are determined from the internal tube dimensions available. 7.3 Fouling Material deposits on the surfaces of the heat exchanger tubes may add more thermal resistances to heat transfer. Such deposits, which are detrimental to the heat exchange process, are known as fouling. Fouling can be caused by a variety of reasons and may significantly affect heat exchanger performance. With the addition of fouling resistance, the overall heat transfer coefficient, Uc, may be modified as: 1 1 R" Ud Uc where R” is the fouling resistance. Fouling can be caused by the following sources: 1) Scaling is the most common form of fouling and is associated with inverse solubility salts. Examples of such salts are CaCO3, CaSO4, Ca3(PO4)2, CaSiO3, Ca(OH)2, Mg(OH)2, MgSiO3, Na2SO4, LiSO4, and Li2CO3. 2) Corrosion fouling is caused by chemical reaction of some fluid constituents with the heat exchanger tube material. 3) Chemical reaction fouling involves chemical reactions in the process stream which results in deposition of material on the heat exchanger tubes. This commonly occurs in food processing industries. 4) Freezing fouling is occurs when a portion of the hot stream is cooled to near the freezing point for one of its components. This commonly occurs in refineries where paraffin frequently solidifies from petroleum products at various stages in the refining process. , obstructing both flow and heat transfer. 5) Biological fouling is common where untreated water from natural resources such as rivers and lakes is used as a coolant. Biological microorganisms such as algae or other microbes can grow inside the heat exchanger and hinder heat transfer. 6) Particulate fouling results from the presence of microscale sized particles in solution. When such particles accumulate on a heat exchanger surface they sometimes fuse and harden. Like scale these deposits are difficult to remove. With fouling, the expression for overall heat transfer coefficient becomes: 1 Ud r ln( o r ) 1 1 i R" k ho r hi i r o 7.4 Basic Heat Exchanger Flow Arrangements Two basic flow arrangements are as shown in Figure 7.2. Parallel and counter flow provide alternative arrangements for certain specialized applications. In parallel flow both the hot and cold streams enter the heat exchanger at the same end and travel to the opposite end in parallel streams. Energy is transferred along the length from the hot to the cold fluid so the outlet temperatures asymptotically approach each other. In a counter flow arrangement, the two streams enter at opposite ends of the heat exchanger and flow in parallel but opposite directions. Temperatures within the two streams tend to approach one another in a nearly linearly fashion resulting in a much more uniform heating pattern. Shown below the heat exchangers are representations of the axial temperature profiles for each. Parallel flow results in rapid initial rates of heat exchange near the entrance, but heat transfer rates rapidly decrease as the temperatures of the two streams approach one another. This leads to higher exergy loss during heat exchange. Counter flow provides for relatively uniform temperature differences and, consequently, lead toward relatively uniform heat rates throughout the length of the unit. t1 t2 t2 T1 T1 T1 T2 Parallel Flow t1 T1 Temperature T2 t1 t2 T2 Counter Flow Temperature T2 t2 t1 Position Position Fig. 7.2 Basic Flow Arrangements for Tube in Tube Heat Exchangers. 7.5 Log Mean Temperature Differences Heat flows between the hot and cold streams due to the temperature difference across the tube acting as a driving force. As seen in the Figure below, the difference will vary with axial position within the HX so that one must speak in terms of the effective or integrated average temperature differences. Counter Flow T1 Parallel Flow 1 T1 t1 t2 2 t1 2 t2 T2 1 T2 Position Position Temperature Differences Between Hot and Cold Process Streams Working from the three heat exchanger equations shown above, after some development it if found that the integrated average temperature difference for either parallel or counter flow may be written as: LMTD 1 2 ln 1 2 The effective temperature difference calculated from this equation is known as the log mean temperature difference, frequently abbreviated as LMTD, based on the type of mathematical average that it describes. While the equation applies to either parallel or counter flow, it can be shown that eff will always be greater in the counter flow arrangement. This can be shown theoretically from Second Law considerations but, for the undergraduate student, it is generally more satisfying to arbitrarily choose a set of temperatures and check the results from the two equations. The only restrictions that we place on the case is that it be physically possible for parallel flow, i.e. 1 and 2 must both be positive. Another interesting observation from the above Figure is that counter flow is more appropriate for maximum energy recovery. In a number of industrial applications there will be considerable energy available within a hot waste stream which may be recovered before the stream is discharged. This is done by recovering energy into a fresh cold stream. Note in the Figures shown above that the hot stream may be cooled to t1 for counter flow, but may only be cooled to t2 for parallel flow. Counter flow allows for a greater degree of energy recovery. Similar arguments may be made to show the advantage of counter flow for energy recovery from refrigerated cold streams. 7.6 Applications for Counter and Parallel Flows We have seen two advantages for counter flow, (a) larger effective LMTD and (b) greater potential energy recovery. The advantage of the larger LMTD, as seen from the heat exchanger equation, is that a larger LMTD permits a smaller heat exchanger area, Ao, for a given thermal duty, Q. This would normally be expected to result in smaller, less expensive equipment for a given application. This should not lead to the assumption that counter flow is always a superior. Parallel flows are advantageous (a) where the high initial heating rate may be used to advantage and (b) where the more moderate temperatures developed at the tube walls are required. In heating very viscous fluids, parallel flow provides for rapid initial heating. The quick decrease in viscosity which results may significantly reduce pumping requirements through the heat exchanger. The decrease in viscosity also serves to shorten the distance required for flow to transition from laminar to turbulent, enhancing heat transfer rates. Where the improvements in heat transfer rates compensate for the lower LMTD parallel flow may be used to advantage. A second feature of parallel flow may occur due to the moderation of tube wall temperatures. As an example, consider a case where convective coefficients are approximately equal on both sides of the heat exchanger tube. This will result in the tube wall temperatures being about the average of the two stream temperatures. In the case of counter flow the two extreme hot temperatures are at one end, the two extreme cold temperatures at the other. This produces relatively hot tube wall temperatures at one end and relatively cold temperatures at the other. Temperature sensitive fluids, notably food products, pharmaceuticals and biological products, are less likely to be “scorched” or “thermally damaged” in a parallel flow heat exchanger. Chemical reaction fouling may be considered as leading to a thermally damaged process stream. In such cases, counter flow may result in greater fouling rates and, ultimately, lower thermal performance. Other types of fouling are also thermally sensitive. Most notable are scaling, corrosion fouling and freezing fouling. Where control of temperature sensitive fouling is a major concern, parallel flow may be used to advantage. 7.7 Multipass Flow Arrangements In order to increase the surface area for convection relative to the fluid volume, it is common to design for multiple tubes within a single heat exchanger. With multiple tubes it is possible to arrange to flow so that one region will be in parallel and another portion in counter flow. An arrangement where the tube side fluid passes through once in parallel and once in counter flow is shown in the Figure below. Normal terminology would refer to this arrangement as a 1-2 pass heat exchanger, indicating that the shell side fluid passes through the unit once, the tube side twice. By convention the number of shell side passes is always listed first. The primary reason for using multipass designs is to increase the average tube side fluid velocity in a given arrangement. In a two pass arrangement the fluid flows through only half the tubes and any one point, so that the Reynold’s number is effectively doubled. Increasing the Reynolds’s number results in increased turbulence, increased Nusselt numbers and, finally, in increased convection coefficients. Even though the parallel portion of the flow results in a lower effective T, the increase in overall heat transfer coefficient will frequently compensate so that the overall heat exchanger size will be smaller for a specific service. The improvements achievable with multipass heat exchangers is sufficiently large that they have become much more common in industry than the true parallel or counter flow designs. The LMTD formulas developed earlier are no longer adequate for multipass heat exchangers. Normal practice is to calculate the LMTD for counter flow, LMTDcf, and to apply a correction factor, FT, such that eff FT LMTDCF The correction factors, FT, can be found theoretically and presented in analytical form. The equation given below has been shown to be accurate for any arrangement having 2, 4, 6, .....,2n tube passes per shell pass to within 2%. 1 P R 2 1 ln 1 R P FT 2 P R 1 R2 1 R 1 ln 2 2 P R 1 R 1 where the capacity ratio, R, is defined as: T1 T2 t 2 t1 R The effectiveness may be given by the equation: P 1 X 1/ N shell R X 1/ N shell provided that R1. In the case that R=1, the effectiveness is given by: P N shell Po Po N shell 1 where Po and X t2 t1 T1 t1 Po R 1 Po 1 As an alternative to using the formulas for the correction factors, which can become tedious for non-computerized calculations, charts are available. Several are included in standard texts. Experience has shown that, due to variability in reading charts, considerable error can be introduced into the calculations and the equations are recommended. When charts are used, they should be reproduced at a sufficiently large scale, and considerable care should be used in making interpolations. 7.8 Limitations of Multipass Arrangements Since the 1-2 heat exchanger uses one parallel pass and one counter current, it follows that the maximum heat recovery for these units should be between that of parallel and counter flow. As a practical limit it is important that nowhere Figure . Temperature Profiles for a 1-2 HX with a in the unit should the cold fluid Temperature Cross. temperature exceed that of the hot fluid. If so, then heat transfer is obviously in the wrong direction. Such a situation can arise in a multipass heat exchanger as seen in Figure 6. This unit represents a cold fluid, located on the tube side of the heat exchanger, making two passes through the unit, the hot fluid, on the shell side, traveling across the unit only once. Here the cold fluid is heated to a temperature slightly above that of the hot fluid near the exit for the two streams. At this axial location, near the left end of the unit, the temperature of the cold fluid in the first pass remains well below that of the hot fluid so that considerable heat transfer occurs. The cold fluid in the second pass is slightly above that of the hot fluid at the same location. The small temperature difference between the second pass cold fluid and the hot stream, indicates that only a small amount of heat will be transferred between these streams. Overall heat will flow from hot to cold fluid, but a portion of the heat transfer surface is being used in a counter productive way. This condition is termed as a temperature cross. In the limit the hot fluid exit temperature could be cooled to the average of the cold fluid inlet and exit temperature. This would, however, be highly inefficient and would require an excessively large surface area. Some engineers advocate that good design should not permit a temperature cross, indicating that the 1-2 should operate with the same heat recovery limit as a true parallel flow. The preferred method of attaining additional heat recovery is to stage heat exchangers in series so that no temperature cross occurs in any unit. An equivalent solution is to put multiple 1–n arrangements within a single shell. A 2–4 unit is the equivalent of 2 1–2 units provided that the total heat transfer area is equal. Similarly a 3–6 unit is the equivalent of 3 1–2 units with equal overall area. Other engineers suggest that a small temperature cross may be acceptable and may provide a less expensive design than the more complex alternatives. If one were to plot the locus of points where the temperature cross occurs for the 1-2 heat exchanger on the temperature correction chart, it would be found to correspond to a relatively narrow range of FT values ranging from about 0.78 to 0.82. Lower values of FT may be taken as an indication that a temperature cross will occur. A second consideration is that at lower FT values the slope, dFT/dP, becomes extremely steep. This is an indication that the temperature efficiency, P, is asymptotically approaching its upper limit and the design has no margin to accommodate uncertainties. A good rule of thumb is that the minimum slope of dFT/dP, which is negative, should not fall below -1.5. Instead a 2-4 or even a 36 should be selected to provide the needed operational design margin.. Similar restrictions exist for these designs as well. In the limit a counter flow design may be the only suitable selection for high heat recovery applications. 7.9 Effectiveness-NTU Method: In our previous discussions, we have been looking at practical HX designs using the LMTDCF with a Ft correction factor to account for the mixed flow conditions. Now we wish to consider an alternate, more recent approach that is in common use today. This is the effectiveness-NTU method. Effectiveness, Consider two counter-flow heat exchangers, one in which the cold fluid has the larger T (smaller mcp) and a second in which the cold fluid has the smaller T (larger mcp): t > T MCp > mcp T2 T1 T > t mcp > MCp t2 T2 t1 T1 t2 t1 We may see in the first case that, because the cold fluid heat capacity is small, its temperature changes rapidly. If we seek efficient energy recovery, we see that in the limit a HX could be designed in which the cold fluid exit temperature would reach that of the hot fluid inlet. In the second case, the hot fluid temperature changes more rapidly, so that in the limit the hot fluid exit temperature would reach that of the cold fluid inlet. The effectiveness is the ratio of the energy recovered in a HX to that recoverable in an ideal HX. cp t2 t1 m cp T1 t1 m C T T M p 1 2 C T t M t > T p 1 T > t 1 Canceling identical terms from the numerator and denominator of both terms: t t T t 2 1 1 1 t > T T T T t 1 2 1 1 T > t We see that the numerator, in the two cases, is the temperature change for the stream having the larger temperature change. The denominator is the same in either case: Tmax In the LMTD-Ft method an effectiveness was defined: T t 1 1 P t 2 t1 T1 t1 Note that the use of the upper case T in the numerator, in contrast to our normal terminology, does not indicate that the hot fluid temperature change is used here. The max subscript over-rides the normal terminology and indicates that this refers to the side having the larger temperature change. Number of Transfer Units (NTU) Recall that the energy flow in any HX is described by three equations: Q = UAeff Q = -MCpT Q = mcpt HX equation 1st Law Equation 1st Law Equation We may generalize the latter two expressions, using -NTU terminology as follows: Q = (MCp)minTmax Q = (MCp)maxTmin Again the use of the upper case letters is over-ridden by the use of the subscripts. If we eliminate Q between the HX equation and one of the 1 st Law equations, UAeff = (MCp)minTmax This expression may be made non-dimensional by taking the temperatures to one side and the other terms to the other side: NTU UA C M p Tmax eff min Physically we see that a HX with a large product UA and a small (MCp)min should result in a high degree of energy recovery, i.e. should result in a large effectiveness, . Capacity Ratio, CR The final non-dimensional ratio needed here is the capacity ratio, defined as follows: CR ( M Cp ) min ( M Cp ) max Tmin Tmax In the LMTD-Ft method a capacity ratio was defined: R T1 T2 t 2 t1 -NTU Relationships In the LMTD-Ft method, we found a general equation which described Ft for all 1-2N, 2-4N, 3-6N, etc. heat exchangers. Another relationship, not given here, is required for cross flow arrangements. In a similar fashion, we may develop a number of functional relationships showing = (NTU, CR) or, alternatively: NTU = NTU(,CR) These relationships are shown in tables in standard text books. For example, we find that the relationship for a parallel flow exchanger is: 1 e 1 CR e NTU (1 CR ) NTU (1 CR ) Note: These correlations are not general. Specific correlations will be given for different kind of HX. The -NTU method offers a number of advantages to the designer over the traditional LMTD-Ft method. One type of calculation where the -NTU method may be used to clear advantage would be cases in which neither fluid outlet temperature is known. Th1 Hot fluid ∆T1 Cold fluid Th1 Th2 ∆T2 Tc2 Hot fluid ∆T1 dTh Tc1 dQ Cold fluid Tc1 Th2 ∆T2 dTc Tc2 End 1 End 2 End 1 End 2