Tagliatela College of EngineeringEASC1112 – Methods of Engineeri.docx
- 1. Tagliatela College of Engineering EASC1112 – Methods of Engineering Analysis TO: EASC 1112 Students FROM: EASC1112 Instructor Subject: Project 2, Optimum Pipe Insulation A long pipe is to be installed to transport steam from a boiler to another part of the plant. Insulation is needed on the pipe for both safety and economic reasons. You are to develop a spreadsheet to calculate the surface temperature of the insulated pipe and to model the heat loss to the surrounding air as a function of the thickness of insulation on the outside of the pipe. Your model should allow for variation in the key parameters to explore the effect of various changes. Using data generated by your model, select the best insulation thickness to maximize the present value of net savings in comparison to an un-insulated pipe. Provide appropriate plots and data tables to support your decision and to show the financial penalty for using a different insulation thickness. Heat Loss Calculation The steam pipe is to be made from schedule 40 steel with a diameter in the range of 2 to 3.5 inches (nominal pipe size). The pipe will be encased in fiberglass insulation with an aluminum sheet cladding to protect from weather. Heat loss for this case can be modeled using a combination of convection and conduction heat transfer rate equations. Heat from the steam is transferred to the inside wall of the pipe by forced convection, then through each of three layers by conduction (pipe wall, insulation, cladding) and finally from the outside of the cladding to the surrounding air by natural convection. The governing equations are shown below to calculate heat transferred per unit length of pipe:
- 2. View of pipe looking along axis QS = rate of heat lost by steam to inside pipe wall Aluminum Cladding Q1, Q2, Q3 = rates of heat transferred through pipe wall, insulation, aluminum cladding, respectively r2 r1 r4 r3 Fiberglass Insulation Steel Pipe STEAM QA=rate of heat lost to air The heat transfer rate equations include constants for the thermal conductivity of the materials and heat transfer coefficients for the convective situations. Values for these will be fixed for the analysis. The temperatures of the steam and the air will be fixed values, but the temperatures at each surface will be dependent on the thickness of insulation and size of the pipe. The subscripts used for the temperatures correspond to radial distances from the center of the pipe. The radii values will be fixed for a particular case of pipe size and insulation thickness, but will be varied as part of the optimization work. The intermediate temperatures, to be found by simultaneous solution of the
- 3. equation set, are: T1 = temperature of the inside wall of the pipe, at distance r1 from the pipe center axis T2 = temperature of the outside pipe wall and the inside of the insulation, distance r2 T3=temperature of the outside of the insulation and inside of the aluminum cladding, distance r3 T4 = temperature of the outside surface of the cladding, exposed to the air, at distance r4 Average steady-state conditions will be used for the analysis of each case, thus the rate of heat lost from the steam must equal the rate of heat transferred through each layer and ultimately the rate of heat lost from the outside cladding to the air. Thus four linear equations can be obtained by setting QA = Q1, Q1=Q2, etc. The resulting equations can be solved using matrix techniques to find the unknown temperatures. Any one of the heat rate equations can then be used to find the heat loss rate. The constants (h's , k's, π and numbers) and the parameters (radii values) become the coefficients, and are shown in the equations above as C1 through C4. For a given case, these will be easily calculated. Terms containing the steam and air temperature are also constants (shift to the right side of equation). For example, setting QS = Q1 and Q1 = Q2 results in the following: Similar equations result from setting Q2 = Q3 and Q3 = QA. Your spreadsheet should have a data section for setting the pipe diameter and insulation thickness along with values for the constants, such as steam and air temperatures, thermal conductivity values, cost information, etc. Develop the model such that entry of a pipe diameter and an insulation thickness
- 4. results in determination of the 4 temperatures and the rate of heat loss for the full pipe length. Analysis of Insulation Thickness Using your model, determine the optimum insulation thickness for different pipe diameters to achieve a maximum net present value of savings. Savings here is defined as the dollar value of energy NOT lost as a result of the insulation. To calculate this you must first determine the heat that would be lost if the pipe was not insulated. Simply subtract the heat loss for a particular insulation thickness from the bare pipe heat loss to determine the energy savings. The cost to insulate the pipe includes both the material cost and the installation labor. A net installed cost is found by multiplying the material cost by an installation factor to account for labor and other installation expenses. Data is provided at the end of this memo for physical properties, cost information etc. Optimization work requires an objective to be maximized or minimized. In this project the "objective function" is the present value of savings over a 5 year period using a specific interest rate with monthly compounding. The installed cost of insulating the pipe occurs at time zero (present) and is negative, so this is subtracted from the present value of 5 years of savings. Varying the insulation thickness will affect this value, so you can determine if there is an optimum which maximizes the present value. You should also be aware of safety concerns associated with a long run of steam pipe. In particular you should assure that the outside surface temperature is no higher than 50oC. Report Requirements At present, the diameter of the steam pipe has not determined, but it will be between 2 and 3 ½ inch schedule 40 steel pipe. Dimensions for standard steel pipe are available in the literature and should be used in this project. After creating the spreadsheet model, you should run simulations for cases in which you vary the insulation thickness from 0.1 to 6.0 cm. Prepare plots showing surface temperature, installed cost,
- 5. annual savings and net present value as a function of insulation thickness. Create other plots as you deem necessary to justify your design decisions regarding the insulation thickness. A full analysis of this type should be performed for one pipe diameter. In addition, you should determine the optimum thickness and required thickness to achieve an acceptable surface temperature for all pipe sizes in the range given above. Note that nominal pipe sizes in this range are incremented in ½ inch steps. For each pipe size, recommend an insulation thickness. Your memo should give an overview of the project, discuss your approach, present results and discuss methods used and assumptions made. Tables and plots should appear in the memo to with explanation to make your points. Your concluding paragraph should include a discussion of what you learned in doing the project. Your spreadsheet should, of course, be well- documented and well-organized to show clearly how the work was done. The spreadsheet should include the following features: · List of pipe diameters using the data validation methods · Retrieval of dimensions for pipes from a table keyed to the selected pipe size (use Vlookup) · Scroll bar to set the insulation thickness · Key results copied to tables, with accompanying graphs for key results · Use Solver to vary thickness to maximize present value of net savings · Any additional functional features you wish to include to make the simulation tool more useful The project is due per your instructors directions, with a paper submission of the memo and attached printout of the spreadsheet. The spreadsheet should also be submitted via Blackboard. Required data is found on the next page. Input data for use in project Properties of pipe, insulation and outer cladding material
- 6. Financial Analysis Parameters Item Material k, thermal conductivity density cost *Install Factor Energy cost Annual Interest Rate Period of analysis W/m-C kg/m3 $/kg $/$ $/kWh percent years Pipe steel 43 7800 NA 5 $0.04 3.0% 5 insulation fiber glass 0.055 64.1 30
- 7. Per month months Outer Layer aluminum 206 2700 40 0.25% 60 0.5 mm thick * Installed cost = (total material cost) x installation factor Heat Transfer Coefficients W m2-oC Other Parameters From steam to inside pipe wall From outside pipe cladding to air Steam Temperature Air Temperature Pipe Length hS hA
- 8. C C Meter 50 5 150 10 50 Properties of Standard Steel Pipe Schedule 40 Pipe Diameters Wall thickness Pipe OD, cm ID, cm cm 2 6.033 5.25 o.39 2.5 7.303 6.271 0.52 3 8.89 7.792 0.55 3.5 10.16 9.012 0.57
- 20. - Layer Each for Rate Transfer Heat p p p p p Alaboudi 1 UNIVERSITY OF NEW HAVEN Tagliatela College of Engineering TO: Professor FROM: Abdullah Alaboudi November 10, 2016 EASC 1112 Project 2: Optimum Pipe Insulation
- 21. Summery: A team contains three students were tasked to design and develop a spreadsheet to calculate the surface temperature of the installed pipe. The team needs to concern the heat loss from the steam transported through a pipe from a boiler to another part of the plant. The team’s aim was to determined the best insulation thickness and pipe size to maximized the value of net saving and camper with the un-insulated pipe to find the financial penalty by using different insulation thickness. The present value cost was to be operated for five years. The team decided to pick the 2.5 pipe size as the best choice economically, and it terms of energy loss. Challenges: 1. Set up the equations. 2. Conflict schedules between team members. 3. Excel deleted some of the work, and it cost more time to re-do it. Discussion: The issue was to figure the heat loss (Q), the radius in each layer, (R), temperatures (T), and the (C’s). The first thing the team has done was rearranging the given equations to solve by using matrix. After that, the team solves for the heat loss since the team found the temperatures by the inverse of the coefficient. To begin, the properties of pipe and the material
- 22. were sorted out, including the thickness of each layer. In this data chart, the costs of every material, steel, protection, and aluminum, were set by taking the mass, material cost, and establishment expense (Appendix I). The following step was to focus on the different parameters and the inverse of coefficients. For instance, the temperature of the air, steam, and the length of the funnel (Appendix II). The budgetary parameters and the financial analysis were sorted to be the vitality expense and the interest rate from month to month or year to year. (Appendix III). Moreover, the properties of a standard steel pipe including the pipe size, outside, inside dimeter and well thickness, which involve finding the different temperature (Appendix IV). After solving for the various temperatures by using taking the coefficient and solve using matrix (Appendix V) and (Appendix VI). The team had to do the same method to solve with out insulation by doing the same methods (Appendix VII). The Q’s comparisons for networks were utilized to find the temperature for each thickness forms the protected pipe. To calculate the radiuses and convert to be cm by using offset equation (Appendix VIII) The team used the annual saving, cost, heat loss, and the present value of a Y and the insulation thickness as an X to show the changes as the insulation thickness changes (Appendix XI) (Appendix XII) (Appendix XIII) (Appendix XIV). By using Solver, the team was able to identify the best insulation thickness in each pipe
- 23. (Appendix XV). Conclusion: Project 2 in EASC 1112 course, was a very enjoyable project, and made the team think in terms of saving energy and money as well by using the given methods. Each member of the team contributed and did their best to get the work done nicely and accurately. For the final result, the team identified that pipe 2.5 with 3.57 insulation thickness was the best choice for the pipe to be installed. Appendices:
- 24. Appendix I: Properties of pipe, insulation and outer cladding material Appendix II: Heat Transfer Coefficients and Other Parameters Chart. Appendix III: Financial Analysis Parameters Chart Appendix IV: properties of stander steel Pipe. Appendix V: Matrix of Temperatures Chart Appendix VI: Matrix Q with Insulation Chart Appendix VII: Matrix Q without Insulation Chart Appendix VIII: Pipe size and the radius Appendix IX: Off sit equation for Pipe size Appendix X: Off sit equation for insulation thickness Appendix XI: Surface Temperature versus Insulation Thickness Graph Appendix XII: Annual Savings versus Insulation Thickness Graph Appendix XIII: Installed Cost versus Insulation Thickness Graph Appendix XIV: Present Value versus Insulation Thickness Graph Appendix XV: Best insulation thickness of each pipe.
- 25. Appendix I: Properties of pipe, insulation and outer cladding material Appendix II: Heat Transfer Coefficients and Other Parameters Chart. Appendix III: Financial Analysis Parameters Chart Appendix IV: properties of stander steel Pipe Appendix V: Matrix of Temperatures Chart Appendix VI: Matrix Q with Insulation Chart Appendix VII: Matrix Q without Insulation Chart. Appendix VIII: Pipe size and the radius.
- 26. The team uses the Offset equation to make the pipe size and insulation thickness changeable as a shortcut. Offset equation is shown in the pictures shown below. Appendix IX: Off sit equation for Pipe size Appendix X: Off sit equation for insulation thickness Appendix XI: Surface Temperature versus Insulation Thickness Graph Appendix XII: Annual Savings versus Insulation Thickness Graph Appendix XIII: Installed Cost versus Insulation Thickness Graph Appendix XIV: Present Value versus Insulation Thickness Graph Appendix XV: Best insulation thickness of each pipe. The picture displayed below shows a chart with calculation.
- 27. The picture displayed below shows the 5 years’ payment.