Thermal Fluid System Design. Team Design #1

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1 Thermal Fluid System Design Team Design #1

2 Table of Contents Nomenclature Listing.3 Executive Summary.6 Introduction.7 Analysis.8 Results/Discussion..18 Conclusion..29 References..29 Appendix A: Detailed Calculations..30 Appendix B: Excel Data Tables..43 Appendix C: Graphs..46 2

3 Nomenclature Listing : Surface area of specified geometry; ft 2 ACH: Air change per hour; 1/hr; Equation (9) : Inner area of main; ft 2 ; Equation (10) : Specific heat of air; Btu/lb- F; Equation (7) CFM: Volumetric flow rate of ventilation; ft 3 /min; Equation (8) : Buried depth to center of tunnel; ft; Equation (2) : Diameter of tunnel; 10ft; Equation (18) : Inner diameter of main; ft; Equation (10) : Power supplied by boiler or fan; Btu/hr; Equation (18) : Power required by boiler; Btu/hr; Equation (22) : Power required by fan; Btu/hr; Equation (19) : Friction factor; Equation (10) : Gravity; 32.2 ft/s 2 ; Equation (18) : Gravitational constant; 32.2 lb m -ft/lb f -s 2 ; Equation (10) h: Heat transfer coefficient; Btu/ft 2 -hr- F : Enthalpy at state i or j; Btu/lb; Equation (14) : Enthalpy at saturated liquid and vapor, respectively; Btu/lb; Equation (15) : Difference in enthalpy between water entering boiler and steam leaving boiler; Btu/lb; Equation (21) : Heat transfer coefficient due to radiation; Btu/ft 2 - R : Thermal conductivity of specified material; Btu/h-ft- F; Equation (1) : Thermal conductivity of soil; Btu/h-ft- F; Equation (2) 3

4 : Length of system; ft; Equation (1) : Production of condensate; lb/hr; Equation (16) : Mass flow rate of fuel; lb/hr; Equation (24) : Mass flow rate over entire section; lb/hr; Equation (10) : New mass flow rate of steam after condensate loss; lb/hr; Equation (17) : Mass flow rate of air ventilation; lb/hr; Equation (7) : Boiler efficiency; %; Equation (22) : Fan efficiency; %; Equation (19) : Density of air in tunnel; ft 3 /lb; Equation (8) : Average density of fuels; ft 3 /lb; Equation (25) : Absolute pressure at state i or j; psia; Equation (10) : Heat boiler must supply to make up for condensate loss; Btu/hr; Equation (21) : Total heat transfer through network; Btu/hr; Equation (3) : Heat transfer from state i to j; Btu/hr; Equation (13) : Heat transfer due to radiation; Btu/hr; Equation (3) : Heat that must be removed by ventilation; Btu/hr; Equation (6) : Sum of air resistance and insulation resistance; hr-ft- F/Btu; Equation (1) : Resistance due to air; hr-ft- F/Btu; Equation (1) : Resistance due to conduction; hr-ft- F/Btu : Resistance due to convection; hr-ft- F/Btu : Resistance due to insulation; hr-ft- F/Btu; Equation (1) : Resistance due to radiation; hr-ft- F/Btu 4

5 : Resistance due to soil; hr-ft- F/Btu; Equation (2) : Radius of tunnel; ft; Equation (2) : Ratio of radii for conduction through cylinders (r o = outer radius, r i = inner radius); ft; Equation (1) : Air space temperature; F; Equation (4) : Steam temperature; 475 F; Equation (3) : Soil temperature; 66 F; Equation (3) : Velocity in access shaft; ft/s; Equation (18) : Volume of tunnel; ft 3 ; Equation (9) : Specific volume at state i or j; lb m /ft 3 ; Equation (10) : Quality of mixture; %; Equation (15) 5

6 Executive Summary This project entails the optimization of a steam main system. This system is buried underground in a 10 ft diameter tunnel. Insulation may be used to limit the heat transfer to the tunnel air space (as it is necessary to keep the temperature in the tunnel between 95 F and 120 F) since workers must be able to access the mains. Keeping in mind that condensation formation can impact the system, care must be taken to find the optimal insulation thickness as well as optimal flow rate. To do so, a mathematical layout is applied to the project. This allows the team to work through different permutations of insulation thickness and mass flow rate to achieve a range of results. With the help of Microsoft Excel, the job is simplified, as input boxes can be altered which instantly changes the results due to that given parameter. Evaluating the data in this manner led the team to decide that 2 of insulation, a mass flow rate of 50 lb/s, and 11,647 CFM of ventilation for the tunnel would optimize the system with respect to cost. 6

7 Introduction This project examines the effects that insulation thickness and mass flow rate have on a steam distribution system. While steam distribution is a very important process in everyday life, most are unaware of how intricate the system is. Such a system includes a boiler, which supplies steam at a certain temperature and pressure from a sendout station, steam mains, and a distribution port some length from the sendout station. Figure 1 is a basic diagram showing the path the steam travels once leaving the sendout station. 66 F Soil Temperature 10 ft Diameter Concrete Tunnel 5 ft Diameter Ventilation Shaft 95 F Ambient Temperature Inside Tunnel 50 ft 5000 ft Nominal 24" Schedule 20 Steel Pipe 2" Thick Calcium Silicate Insulation Figure 1: Schematic As Figure 1 suggests, the tunnel is 10 ft in diameter, constructed of concrete, and buried at a depth of 50 ft. For the project at hand, steam leaves the sendout station at 475 F and 200 psig, travelling through two 24 steel mains to a distribution port 5000 ft away. Because condensation is a major issue in steam distribution, calcium silicate insulation will be wrapped around the mains to prevent steam loss. This insulation may vary in thickness, as shown in the Results 7

8 section. The tunnel that contains the two mains must be accessible by workers and thus, must be maintained at a temperature of 95 F to 120 F. Due to fittings, bends, and valves, the associated friction loss is 10% of the total friction loss in the mains. To be able to optimize this system with respect to cost, it is necessary to figure out a feasible insulation thickness, yet keeping condensation to a minimum. Also, by varying the flow rate of steam the system will behave differently. With this exposition for the project done, it is appropriate to look at the mathematical analysis of the system, as well as the assumptions made. Analysis This project can be broken into two main sections. That associated with heat transfer, and that of fluid mechanics. Heat transfer plays a factor in that a resistance network can be drawn starting from the fluid and finishing at the soil. Figure 2 displays this network. Resistance Through Soil 50 ft below ground level Resistance Through Concrete 10 ft Diameter Concrete Tunnel Resistance Through Tunnel Air Resistance Through 2" Calcium Silicate Insulation Nominal 24" Schedule 20 Steel Pipe Figure 2: Resistance Network 8

9 As Figure 2 depicts, there is a convection resistance from the steam to the pipe wall. This can be neglected as the heat transfer coefficient, h, is very high for steam (approximately Btu / ft 2 -hr- F). The resistance due to convection is computed by: Where A is the surface area of the inner pipe. Due to the fact that R conv. is quite small, this affirms that the convection resistance due to steam doesn t contribute a major factor to the total resistance and is appropriate to neglect. Furthermore, conduction through the pipe wall contributes a nominal resistance as well. This is affirmed by: Where r 2 is the outer radius of the pipe while r 1 is the inner radius, k = 25, and L = 1 ft, as this resistance is also per unit length. 9

10 Lastly, it is important to look at the effect radiation has. While it can be assumed that because the temperature difference between the insulation surface and tunnel shouldn t be very much, allowing radiation to be neglected, it is good engineering practice to ensure that this is actually the case. The resistance due to radiation is as follows: With the resistance due to the steam convection, and resistance due to the pipe wall neglected, the resistance due to radiation must be incorporated into the mathematical mode. It is now appropriate to move onto the analysis of the entire network. Starting at the pipe, there are two resistances present: the resistance of the insulation and the resistance of the air space. This is expressed in Equation (1). Where And (1) With R i being the conduction resistance through the insulation and R a the resistance due to the air space. Referencing Appendix A, r 3 is the outer radius of insulation whereas r 2 is the outer pipe radius. With respect to the air resistance,.053 comes from the fact that an average heat transfer 10

11 coefficient due to an air space is 3, thus simplifying, and leaves the air resistance as a function of insulation thickness. Keeping in mind that this is assuming free convection, it is important to see the effect ventilation has on this heat transfer coefficient. This will be assessed later in the report. Since the tunnel containing the steam mains is buried, it is necessary to take the resistance of the soil into account. Thus, Equation (2) is formulated. (2) Where d is the buried depth to the center of the tunnel in feet, r o is the radius of the tunnel in feet, and k s is the conductivity of the soil (taken as 1 ) 1. With these three resistances, it is possible to compute the total heat flow from the steam main to the ground surface. This is portrayed in Equation (3). (3) Where T i is the steam temperature, T s is the soil temperature (taken as 66 F), q rad.is the heat transfer due to radiation, and R is computed in Equation (1). With the total heat flow known, it is possible to break up the resistance network and calculate the temperature of the air space, as shown in Equation (4). (4) 11

12 With T a being the air space temperature. Also of interest is the temperature on the surface of the insulation. This is displayed by Equation (5) 1. (5) Next it is appropriate to look at the ventilation needed if the air space is to be maintained at a temperature of 95 F. By using Equation 4, and setting T a as 95 F, the amount of heat that must be removed can be computed. Equation (6) calculates this. (6) Where 62.8 is the ideal amount of heat transfer if the air space is to be 95 F. With q vent. calculated, Equation (7) solves for the mass flow rate associated with the ventilation heat transfer rate. (7) With c p =.24, ΔT is the difference in temperature between the outside air, which will be assumed to 95 F (the worst case scenario average temperature for a New York summer), and the previously calculated air space temperature. Now that the mass flow rate of ventilation is computed, Equation (8) obtains the associated amount of CFM for such a flow and Equation (9) allows the air change per hour to be computed for the tunnel. (8) 12

13 Where ρ is the density of air at 95 F. (9) With ACH as air change per hour and is the volume of the tunnel in ft 3. Now that the heat transfer aspect of the problem is done, it is appropriate to look at the fluid mechanics aspect of the project, primarily the pressure drop along the mains and the associated condensate formation. With respect to fluid mechanics, the steam is a compressible fluid. Thus, compressible flow formulas must be used as opposed to regular analysis, such as the Moody Chart and Bernoulli equation. Splitting the main into 500 ft sections will allow the temperature to be considered constant 2. By assuming this, the pressure at the end of this section along with the enthalpy, will satisfy the requirement of two independent intensive properties to fix a state. Appendix A portrays the section of pipe and the associated properties at state i as well as state j. To start these calculations, the pressure at state j will be computed by Equation (10). (10) Where p j is the pressure at state j in psia, p i is the pressure at state i, v i is the specific volume at state i in lb m /ft 3, f is the friction factor (noting it is multiplied by 1.1 as 10% of the friction losses are due to minor losses such as fittings), L is the length of the section in feet, is the mass flow rate from state i (assumed to be constant from i to j), g c is the gravitational constant in lb m -ft / lb f -s 2, D inner is the inner diameter of the main in feet and A inner is the inner area in square feet. Equation (10) allows the friction factor to be calculated with the use of the Weymouth Equation 3. (11) 13

14 With d the diameter of the main in inches. Knowing the pressure at state j, it is possible to compute the pressure drop across a unit length of the mains, as shown in Equation (12). (12) Note that these pressures are absolute. Now it is necessary to use the heat loss in this 500 ft section to ultimately calculate the enthalpy at state j. Equation (13) allows the heat loss to be evaluated. (13) Where ΔT is the difference in temperature between the steam and air space and R is the same resistance computed in Equation (1). Finally, Equation (14) allows the enthalpy at state j to be calculated. (14) This equation doesn t take into account kinetic or potential energies, as they can be neglected over the 500 ft section, and no work is done by/on the system. With p j and h j, state j is now fixed. Having the enthalpy at state j, the quality of the mixture (if the steam falls below superheated vapor) can be determined, as shown by Equation (15). While quality isn t a problem at high mass flow rates, at lower mass flow rates condensation will have a much greater chance to form. (15) 14

15 With h f, in Btu/lb, as the saturated liquid enthalpy and h fg, in Btu/lb, is the difference in saturated liquid enthalpy and saturated vapor enthalpy. If the system has a quality value, then condensate has formed and it is of interest to determine the flow rate of this condensate loss. Equation (16) computes this. (16) Where Equation (17) allows the new mass flow rate, section., to be found that continues to the next (17) This process can be repeated for the other nine sections, yielding the pressure and temperature at the distribution point. Although the problem appears solved, it is of good engineering practice to include a cost analysis, whether it is for ventilation, or the boiler. With respect to the ventilation cost, Equation (18) allows the power that the fan supplies to the air to be calculated. (18) Where 1.1f is the friction factor for laminar flow, taking into account minor losses which contribute approximately 10%, L is the length of the entire main (5000 ft), D is the diameter of the tunnel (10 ft), and V is the velocity of the air moving through the access shaft in ft/s. Equation (19) uses the power the fan supplies to the air, to ultimately compute the power supplied to the fan 4. 15

16 (19) Assuming that the fan has an efficiency of 80%. Knowing the power that the fan consumes to supply the ventilation flow, it is possible to compute the associated cost, as shown in Equation (20). (20) With $ per Btu being the cost of power. Another point of interest with respect to cost of the system is the boiler. As the system loses steam due to condensate along the 5000 ft main length, the boiler has to work that extra amount to supply the necessary amount of steam. This cost is then charged to a customer. Equation (21) allows the extra heat the boiler must supply to be computed. (21) Where is the mass flow rate of condensation and Δh is the difference in enthalpy from the water entering the boiler, to the steam exiting. It is fair to assume that the temperature entering the boiler is at 55 F. Equation (22) allows the power supplied to the boiler to be computed. (22) 16

17 Where is the power put into the boiler. Equation (23) allows the cost associated with the boiler to be computed. (23) Also important is the heating value for fuel being burned, as when different fuels combust, different amounts of usable energy are released. Knowing the amount of energy the boiler requires in making up for the losses due to condensate, and that an average heating value (whether it be a natural gas, gasoline, or diesel powered boiler) is 14,660 Btu/lb, Equation (24) allows the flow rate of fuel supplied by the boiler ( ) to be computed 5. (24) Knowing how much fuel the boiler requires to make up for the condensate loss, it would be possible to find an associated cost of combustion, depending on the cost of the fuel used. Equation (25) utilizes an average density (in order to obtain volumetric flow rate) and an average fuel cost to ultimately find the cost of combustion. (25) Where converts ft 3 /hr to gal/hr and $2.87 is the average fuel cost 6. These equations and assumptions encompass the mathematical analysis for the entire project. It is now appropriate to look at the Results. Keeping in mind that there a plethora of 17

18 combinations that this system can be subject to, different cases will be looked at to gain knowledge about the system and ultimately optimize it with respect to cost. Results/Discussion Due to the fact that this project has a multitude of solutions, depending on a chosen insulation thickness and mass flow rate, this section will present data in the form of charts and graphs in an effort to keep the results organized. Cases will be evaluated and interpreted when new parameters are defined for the system. With this being said, it is appropriate to observe the system s behavior. Firstly, it is important to note the fact that the maximum mass flow rate ( lb/hr) isn t synonymous with that given in the problem statement. As shown in Appendix A, when using a mass flow of lb/hr (per pipe), the pressure drop is so great in the main that no steam would actually reach the distribution port! This is discovered as Equation (10) yields a negative number under the radical. Thus, it is apparent that a maximum flow rate must be solved for by either fixing the end pressure, increasing the pressure of the steam from the sendout station, or changing the pipe size to one that can accommodate the lb/hr rate. The team chose to fix the end pressure at 100 psia and 14.7 psia to obtain proper mass flow rates. Choosing these pressures isn t arbitrary but takes data from systems, much like Con Edison s, and the associated pressure at the distribution port 2, which is close to 100 psia. Also, by choosing 14.7psia as an exit pressure, the maximum flow rate to get steam to the distribution port for the given pipe size can be computed. This is helpful as perhaps the distribution port has a pressurizing system to bring the pressure back up to feasible distribution levels. Nevertheless, the aim of the team is to focus on the 100 psia pressure, since it doesn t assume specifications regarding the distribution port. Another important fact regarding flow rates is that between the given ranges of lb/hr to lb/hr, no condensate forms. This is due to the fact that the saturation temperature associated with 200 psig is roughly 100 F less than the initial steam temperature, and with that range of flow rates, the steam temperature would never drop quick enough to produce condensate. While this is actually a good thing, it is impractical to solely look at these cases as a good indication of how the system will function. Thus, in an 18

19 Temperature (F) Pressure (psi) attempt to get realistic trends regarding mass flow rate, insulation, and condensate formation, a new range of mass flow rates will be defined. This range is lb/hr to lb/hr. Two of the parameters that are greatly affected by the mass flow rate and insulation thickness are the steam exit pressure and temperature at the distribution port, as well as the heat loss and pressure drop per unit length of the mains. Figure 3 shows how the end conditions vary with the system s parameters, while Figure 4 corresponds to the heat loss and pressure drop Outlet Conditions with Varying Mass Flow Rates and 2" Insulation Mass Flow Rate (lb/s) Temperature Pressure Figure 3: End Conditions at Distribution Port 19

20 Heat Loss (Btu/ hr) Pressure Drop (psi/ft) 600 Heat Loss and Pressure Drop per Unit Length at Mass Flow of 4.5 lb/s Heat Loss Pressure Drop Insulation Thickness (in) 0 Figure 4: Heat Loss and Pressure Drop per Unit Length Figure 3 is an important display of how larger mass flow rates increase pressure drop but reduce condensate loss, while lower mass flow rates allow condensate to form. Larger mass flow rates allow a higher end temperature as the steam loses less heat while travelling through the main. Conversely, lower mass flow rates allow more heat to transfer through the main, ultimately causing a lower end temperature. It is interesting to note that the highest mass flow rate evaluated actually results in a lower final temperature then some of the lower flow rates. This is due to an increase in pressure drop over the last 500 foot section of pipe. The pressure drop is about one and a half times larger than it is in the previous 500 foot section while heat transfer remains virtually constant. This causes a large increase in specific volume that affects the properties of the steam and subsequently creates a lower end temperature. Figure 4 shows that heat loss decreases as the insulation thickness increases while the pressure drop remains the same. This makes sense as the more insulation, the more heat that stays in the steam main. The reason that the 4.5 lb/s ( lb/hr) is only used as the mass flow rate is because this mass flow rate was analyzed and created the greatest formation of condensate, as pressure drop is constant for each case. These results can be applied to other mass flow rates but similar trends will be displayed for heat loss, while pressure drop will 20

21 Heat Transfer (Btu/s) increase as flow rate increases (as depicted in Figure 3). The important aspects of Figures 3 and 4 are the effects that mass flow rate and insulation thickness have on the system. Using the new range of workable mass flow rates, Figure 5 shows various heat transfer rates for both pipes with insulation thickness ranging from 2 to 6 inches Heat Transfer Over Tunnel Insulation Thickness (in) Figure 5: Heat Transfer Rate as Function of Insulation Thickness This data is affirming in that one would assume as insulation thickness increases, the heat transfer to the air space decreases. Due to the fact that the insulation cost is denoted by $( d)/ft, this cost adds up to be very substantial for the system. Table 1 shows the associated cost for the given insulation thicknesses. Insulation Thickness (in) Installation Cost ($) 2 $3,000, $3,250, $3,500, $3,750, $4,000, Table 1: Insulation Cost Due to Insulation Thickness 21

22 Percent Condensate Loss (%) Thus, in an effort to optimize the cost, 2 of insulation will be wrapped around the two mains at a minimum cost of $3,000,000. Because the smallest insulation thickness is being used, condensate formation could become an issue. Figure 6 shows the percent of steam loss with respect to the steam leaving the boiler at various insulation thicknesses, while Figure 7 shows the percent steam loss with respect to steam leaving the boiler at various mass flow rates. 2.5 Steam Loss at Varying Insulation Thickness Insulation Thickness (in) Figure 6: Percent Condensate Loss Relative to Insulation Thickness at 4.5 lb/s Mass Flow 22

23 Percent Steam Loss (%) Steam Loss at Varying Mass Flow Rates with 2" Insulation Initial Mass Flow Rate (lb/s) Figure 7: Percent Condensate Loss Relative to Mass Flow Rate These Figures are indicative of the effect that mass flow rate and insulation thickness have on the system. As shown in Figure 6, by increasing the amount of insulation the percent condensate relative to the sendout station is less. This is due to the fact that more heat stays in the pipe. On the other hand, by having a higher mass flow rate, condensate loss isn t even an issue, which is depicted in Figure 7. As discussed later in this section, to optimize the system, both of these parameters must be taken into account. ` Temperature of the steam is also important with respect to the saturation temperature over the length of the mains. Figures 8 and 9 show this for the maximum flow rate of lb/s lb/hr) as well as the minimum flow rate of 4.5 lb/s lb/hr), while Appendix C contains graphs at other insulation thicknesses and flow rates. 23

24 Temperature (F) Temperature (F) Steam Temperature Along Tunnel with Mass Flow lb/s and 2" Insulation Tunnel Distance (ft) Actual Temperature Saturation Temperature Figure 8: Steam Temperature and Saturated Temperature vs. Tunnel Distance ( lb/hr) Steam Temperature Along Tunnel with Mass Flow 4.5 lb/s and 2" Insulation Tunnel Distance (ft) Actual Temperature Saturation Temperature Figure 9: Steam Temperature and Saturated Temperature vs. Tunnel Distance ( lb/hr) 24

25 Figures 8 and 9 compare steam temperature to saturation temperature to show the effect that flow rate has on condensate formation. This is apparent in Figure 8, since the saturation temperature drops at a similar rate as the steam temperature along the pipe as well, never allowing the steam temperature to fall below the saturation temperature. This is due to the fact that pressure drop is very high with a high mass flow rate (up to 114 psi over the entire main). Conversely, Figure 9 shows the temperature of steam is dipping below the saturation temperature. The condensation formation is due to the lack of pressure drop along the main (.1 psia over the entire main). When condensation occurs, the steam moves out of the superheated vapor region and into the mixture region. The temperature then levels off because the steam is going through a phase change (vapor to liquid). While referencing Appendix C for the graphs at other insulation thicknesses and flow rates, it is interesting to note how condensate formation is controlled solely by mass flow rate. While thicker insulation does keep more heat in the steam main, all of the low mass flow rates ( lb/hr to lb/hr) have condensate formation regardless of insulation thickness. After inspection, it is apparent that this is caused by the low pressure drop throughout the main that associated with a low flow rate. Because the pressure drop is so low, the associated saturation temperature is almost constant, ultimately allowing the steam temperature to fall below this saturation temperature. Another factor to be taken into account is the specific volume at each section. Specific volume plays a big role as it increases for higher mass flow rates, while decreasing for lower mass flow rates. This affects the pressure drop, as shown in Equation (10), since the specific volume is in the numerator of the equation. The larger specific volume contributes to the smaller pressure drop seen in low mass flow rate systems and conversely, a smaller specific volume contributes to the larger pressure drop seen in high mass flow rates. This data can be seen in Appendix B. While using a higher flow rate will hinder condensation, the cost associated to have the boiler supply this larger rate is initially higher (bigger pump need), but the heat loss over the entire length would be less, meaning less insulation is needed. Conversely, a lower flow rate will appear more inexpensive initially (smaller pump need) but in reality the extra work done by the boiler to make up for condensate loss may be more costly. This cost due to loss of condensation is evaluated by Equations (21)-(23) and displayed in Figure 10. The cost of condensation associated with 2 of insulation corresponds to a cost of $987 per hour. This cost 25

26 Cost per Second ($/hr) is indicative of the extra work the boiler must do to make up for the steam loss due to condensate. Extrapolating this value, if the boiler were to run for 12 hours per day, 365 days per year and for 15 years, the cost is $64,845,800. These values show that due to the amount of condensation produced at low flow rates (nearly 50% of the initial steam), thicker insulation would be beneficial to keep operating costs down. Evaluating the results for the selected range of mass flow rates from lb/hr to lb/hr, a flow rate in this range such as lb/hr would provide a nice balance between pumping cost (as it isn t an exceptionally high flow rate) while equally hindering condensation formation. Furthermore, the reason Figure 10 pertains to a single flow rate of lb/hr, with only insulation thickness varying, is due to the fact that at the slightly higher flow rate of lb/hr, less condensate forms. The data is identical to that of the lower flow rate, with the cost simply being shifted down on the graph, making it a null factor in analyzing the cost due to condensation. The worst case scenario is only of interest. 1, Cost of Condensate Loss At Varying Insulation Thickness with Mass Flow 4.5 lb/s Insulation Thickness (in) Figure 10: Boiler Cost Due to Condensate Lost 26

27 Heat Loss (Btu/s) Mass Flow (lb/s) The most important factor is that insulation thickness varies the cost by nearly $600/hr. Using this value, it is interesting to see how much fuel the boiler would have to consume to make up for the potential condensate loss. Equations (24) and (25) compute this. Once again, using the flow rate of lb/hr, the cost of fuel is approximately $188/hr. If the same assumptions are made regarding the running time and life expectancy of the system, this corresponds to $12,351,600 over the 15 years. These values show that compared to the initial cost of insulation, the running cost of the boiler cannot be neglected, if condensation is present. Thus, if a low flow rate is used thicker insulation could be justified as a means to keep costs to a minimum. Nevertheless, it is important to note that most of the flow rates don t even fall below superheated vapor which means condensation will not be an issue. Due to the fact that the tunnel must be accessible by workers, it is crucial to keep the temperature at a reasonable value. Knowing the temperature in the air space, as calculated by Equation (4), and the amount of heat that must be removed to keep the tunnel between 95 F and 120 F, as calculated by Equation (6), it is possible to size the ventilation system. Shown in Figure 11, the amount of ventilation needed to keep the tunnel air at 95 F is a constant value Ventilation Heat Loss and Mass Flow Rate for Varying Insulation Thickness Ventilation Heat Loss Mass Flow of Air Insulation Thickness (in) 0 Figure 11: Insulation Thickness vs. Ventilation Flow Rate Required 27

28 This is due to the fact that while the increased insulation thickness removes more heat, the temperature difference between the ambient air and the tunnel air space also differs. As previously discussed, while the thinner insulation provides a very high ambient temperature in the tunnel, the thicker insulation provides a lower ambient temperature. The larger temperature difference between the tunnel and the outside allows the mass flow rate of air to be constant with respect to insulation thickness. This is due to thicker insulation having a smaller temperature difference while requiring less heat to be removed, while less insulation has a larger temperature difference and requires more heat to be removed. Because this ratio remains constant, the ventilation required will be constant at a value of 11,674 CFM for the 5000 ft tunnel length. This corresponds to approximately 1.9 ACH. Stated in the Analysis section is an assumption that considered the tunnel subject to free convection. This is an adequate statement as the flow velocity of the ventilation air is ft/s. This velocity isn t nearly enough to create a draft in the tunnel making forced convection analysis necessary. With this being said, it is appropriate to evaluate the cost associated with the ventilation system. Using Equations (18)-(20) it is possible to compute the cost associated for a fan to supply this air change. These calculations yield a cost of $.11 per hour, extrapolating to $7,227 over the estimated 15 year time period (running 12 hours per day, 365 days per year). Having this data and the presented evaluation, it is possible to summarize the specifications of the system as the team sees fit. The basis for these specifications is to optimize cost, yet remain a realistic outlook on the system (with respect to construction and feasibility). Summary of Specifications Insulation Thickness: 2 Required CFM of Ventilation: 11,674 for entire tunnel Ideal Mass Flow Rate: lb/hr Steam Exit Pressure and Temperature: 444 F, psia Heat Loss and Pressure Drop per Unit Length: 650 Btu/hr-ft, psia/ft 28

29 Conclusion The following conclusions are supported by the results of this study: That the correlation between mass flow rate and pressure drop are inversely related. That a high pressure drop will hinder condensate formation while a low flow rate will cater to condensation. By using thicker insulation, the heat loss through the pipe will be less while also decreasing the amount of condensate formation. When optimizing with respect to cost, the cost of insulation is much greater due to condensation when using a reasonable (higher) mass flow rate. By evaluating this project with these varying parameters, the team was able to gain much knowledge regarding the system s behavior, while allowing proper engineering theories to be affirmed. References 1) 1995 ASHRAE Handbook : Heating, Ventilating, and Air-conditioning Applications. I-P ed. Atlanta: ASHRAE, Print. 2) Dr. Litkouhi. "Team Design Problem #1." Personal interview. 9 th,17 th, 19 th, 24 th, 26th March ) Crane handout 4) Design of Fluid Thermal Systems. 3rd ed. Stamford, CT: Cengage Learning, Print. 5) Wikipedia. 9 Mar Web. 27 Mar < 6) US Energy Information Administration. 29 Mar Web. 29 Mar < 29

30 Appendix A: Detailed Calculations (see attached) 30

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43 Appendix B: Excel Data Tables Distance (ft) Temperature (F) Pressure (psi) Enthalpy (Btu/hr) Specific Volume (ft 3 /lb) m steam (lb/s) Figure B-1: Steam Properties Along Tunnel at Mass Flow lb/s and 2 Insulation Distance (ft) Temperature (F) Pressure (psi) Enthalpy (Btu/hr) Specific Volume (ft 3 /lb) m steam (lb/s) Figure B-2: Steam Properties Along Tunnel at Mass Flow 250 lb/s and 2 Insulation 43

44 Distance (ft) Temperature (F) Pressure (psi) Enthalpy (Btu/hr) Specific Volume (ft 3 /lb) m steam (lb/s) Figure B-3: Steam Properties Along Tunnel at Mass Flow 50 lb/s and 2 Insulation Distance (ft) Temperature (F) Pressure (psi) Enthalpy (Btu/hr) Specific Volume (ft 3 /lb) m steam (lb/s) Figure B-4: Steam Properties Along Tunnel at Mass Flow 7.5 lb/s and 2 Insulation 44

45 Distance (ft) Temperature (F) Pressure (psi) Enthalpy (Btu/hr) Specific Volume (ft 3 /lb) m steam (lb/s) Figure B-5: Steam Properties Along Tunnel at Mass Flow 4.5 lb/s and 2 Insulation Distance (ft) Temperature (F) Pressure (psi) Enthalpy (Btu/hr) Specific Volume (ft 3 /lb) m steam (lb/s) Figure B-6: Steam Properties Along Tunnel at Mass Flow 4.5 lb/s and 3 Insulation 45

46 Distance (ft) Temperature (F) Pressure (psi) Enthalpy (Btu/hr) Specific Volume (ft 3 /lb) m steam (lb/s) Figure B-7: Steam Properties Along Tunnel at Mass Flow 4.5 lb/s and 4 Insulation Distance (ft) Temperature (F) Pressure (psi) Enthalpy (Btu/hr) Specific Volume (ft 3 /lb) m steam (lb/s) Figure B-8: Steam Properties Along Tunnel at Mass Flow 4.5 lb/s and 5 Insulation 46

47 Distance (ft) Temperature (F) Pressure (psi) Enthalpy (Btu/hr) Specific Volume (ft 3 /lb) m steam (lb/s) Figure B-9: Steam Properties Along Tunnel at Mass Flow 4.5 lb/s and 6 Insulation 47

48 Temperature (F) Appendix C: Graphs Figure C-1: Steam Temperature Along Tunnel at Mass Flow 250 lb/s and 2 Insulation Steam Temperature Along Tunnel With Mass Flow 200 lb/s and 2" Insulation Tunnel Distance (ft) Actual Temperature Saturation Temperature C-2: Steam Temperature Along Tunnel at Mass Flow 200 lb/s and 2 Insulation 48

49 Temperature (F) Temperature (F) Steam Temperature Along Tunnel with Mass Flow 4.5 lb/s and 2" Insulation Tunnel Distance (ft) Actual Temperature Saturation Temperature C-3: Steam Temperature Along Tunnel at Mass Flow 4.5 lb/s and 2 Insulation Steam Temperature Along Tunnel with Mass Flow 4.5 lb/s and 3" Insulation Actual Temperature Saturation Temperature Tunnel Distance (ft) C-4: Steam Temperature Along Tunnel at Mass Flow 4.5 lb/s and 3 Insulation 49

50 Temperature (F) Temperature (F) Steam Temperature Along Tunnel with Mass Flow 4.5 lb/s and 4" Insulation Actual Temperature Saturation Temperature Tunnel Distance (ft) C-5: Steam Temperature Along Tunnel at Mass Flow 4.5 lb/s and 4 Insulation Steam Temperature Along Tunnel with Mass Flow 4.5 lb/s and 5" Insulation Actual Temperature Saturation Temperature Tunnel Distance (ft) C-6: Steam Temperature Along Tunnel at Mass Flow 4.5 lb/s and 5 Insulation 50

51 Temperature (F) Steam Temperature Along Tunnel with Mass Flow 4.5 lb/s and 6" Insulation Tunnel Distance (ft) Actual Temperature Saturation Temperature C-7: Steam Temperature Along Tunnel at Mass Flow 4.5 lb/s and 6 Insulation 51

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