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1 1. Introduction As the price of energy in the world continues to rise more technology is being de- veloped to increase energy savings. Examples of this include the use of solar panels as well as wind turbine farms. Alternative and green methods are not the only area of interest for cost savings. The aspect of monetary savings may also be represented in existing energy sources such as boiler technology by more efficient operation. Boilers operate in a variety of applications and locations. This can include marine boilers in commercial ships such as liquid natural gas (LNG) tankers. Boilers also operate in commercial nuclear and conventional power stations. No matter what application and location boilers have one common need. The need to maintain clean heat transfer surfaces so that the most efficient heat transfer can occur. With proper heat transfer the cost incurred by the operating company can be reduced. There are a few basic parts of a conventional boiler. These parts are the tubes, steam drum, and water drum. Heat is transferred to the water flowing through the tubes and collects at the steam drum. The steam drum allows the water to boil and a dry pipe inside of the boiler carries the steam to perform whatever application the boiler is operating for. The steam that leaves the boiler is a vapor. The steam vapor is not able to carry any kind of solid material that may be dissolved in the boiler water. This can result in a concentration of impurities in the boiler steam drum. Depending on how long the boiler operates the concentration of these impurities can become quite large. This could cause boiler heat transfer surfaces to become coated with hard scale that would reduce heat transfer capability. To maintain the required amount of heat transfer with a scale layer on the heat transfer area increased energy consumption would be required. There is a simple way to prevent the hard scale build up problem. Typically a cer- tain amount of boiler water is drained and then fresh water is used to refill the boiler. This operation reduces the concentration of the impurities in the boiler. An unfortunate result of this operation is that it reduces the amount of heat and pressure inside the boiler as the fresh water mixes with the hot water in the steam drum. The freshwater must be heated to saturation temperature and this causes additional fuel consumption. This method of impurity reduction is known as boiler blow-down. Another method of boiler blow-down is a continuous boiler blow-down. A certain amount of water is drained from 2 the boiler steam drum as the boiler operates. To maintain a constant level in the boiler the loss in boiler water level is offset by the continuous addition of feed water by the boiler water feed system. This method of impurity level reduction has the benefit of not causing a significant reduction in boiler temperature and pressure. The water that is continuously removed however is thrown away as waste. It may be possible for the impurities to be removed from some of the high temperature water by evaporation. The water evaporated could then be condensed and stored to be reused as boiler makeup water. This could provide additional savings to the managing company. 3 2. Theory Methodology 2.1 Evaporator In able to reuse the boiler water from the steam drum the impurities within the water must be removed. Boilers operate at high temperature and pressure. The use of filters or resin beds with fine elements or resins could prove impractical and expensive. A method to remove salt and other impurities from sea water for consumption by people and commercial use is to boil the sea water in a reduced pressure. This method is known as distillation. The heating medium for this evaporator could be low pressure steam. Once the sea water is boiled off it can be condensed in another portion of the evaporator chamber where cooling coils are located. The condensed distillate then is collected on pans and pumped to tanks for use. A similar approach may be used for the removal of impurities in boiler water. Since the water being removed is already a heat saturated liquid only the necessary amount of enthalpy to boil the water would be required. The heating medium for this evaporator could come from a stage of one of the propulsion turbines. Once the boiler water is evaporated the impurities could collect in the bottom of the tank and be removed as waste. This process would help save at least some of the water that would normally be thrown away as waste. A complete vaporization of the entire amount of boiler blow down water into dry saturated steam is not the intent. If this occurred, then the collection tank would just be completely covered by hard scale from the impurities in the boiler water as these impuri- ties precipitated out of the steam. For this project a quality of 50% vapor was chosen for the steam water mixture. This would allow the possible saving of 50% of the boiler blow down water while concentrating the other 50% of the water containing the impuri- ties to collect at the bottom of the tank for removal. It is assumed that the lower density water vapor will rise in the chamber while the more dense water will collect at the bottom. A steam ship was based as the platform for this project. The operating boiler pres- sure is 600 psig. The steam turbines of this ship use superheated steam for propulsion. 4 Due to piping flow reductions from the steam drum to the proposed system a pressure of 514 psig was chosen as the heat saturated boiler water at 472 F. This correlates to 244 C. All aspects of the heat exchanger are unknown so dimensions, material, as well as operating pressure and temperature of the heating steam need to be determined. The heat exchanger chosen to be used as an evaporator is a parallel flow annulus type heat exchanger see [Figure 1]. This was chosen for the simplicity in design and construction. An inner tube diameter of 1 cm was chosen. A flow rate of 1 gallon per minute was chosen as the blow down capacity. This flow rate was chosen because it is low enough to not affect boiler water levels and confuse operators when the ship is maneuvering. A second reason this flow rate was chosen is that this level reduction should be easily maintained continuously with a conventional boiler feed system. Once the application was determined a method was needed to solve the heat bal- ance. Dimensions were unknown as previously stated. Many heat exchangers require the use of an overall heat transfer coefficient [2]. This was chosen as the starting point for the analysis. The overall heat transfer coefficient provides the ability to combine the two methods of heat transfer occurring between the steam and water in the annulus type heat exchanger as well as account for their material differences [3, page 180]. The two methods of heat transfer occurring in the evaporator are conduction and convection. The heat transfer mechanism between the steam and the outer surface area of the inner tube of the annulus type heat exchanger is convection. Conduction occurs within the steel pipe. Lastly convection occurs between the steel pipe inner surface area and the boiler water [see figure 3]. The overall heat transfer coefficient for an annulus type heat exchanger can be calculated using the following equation [1, page 508]. The terms in the equation relate to the forced convection on the inner and out- er portions of the inner pipe of the annulus heat exchanger. The outer convection heat transfer coefficient is and is the inner heat transfer coefficient. The convection 5 heat transfer coefficients are dependent on many parameters of their fluid flow. These parameters include viscosity, temperature, and velocity [4]. To calculate the Chen correlation was used [1, page 675]. The boiler water that has been removed from the steam drum is heat saturated water close to boiling. Since the boiler water is a heat saturated liquid carrying a significant amount of heat the transition from bubble and slug flow in flow regimes of boiling quickly turns into the annular flow regime. For this project it is assumed that the boiling within the evaporator occurs in the annular flow regime. Chen has suggested that there is a two part correlation to the boiling heat transfer coefficient in the annular flow region. The two parts consist of a convection heat transfer coefficient as well as a nucleate boiling heat transfer coefficient. The two coefficients are calculated separately and then their affects are additive to create a singular heat transfer coefficient. The Chen correlation of the annular flow region was chosen because this correlation has been tested and the results proven. This specific correlation has provided satisfacto- ry data for water, methanol, cyclohexane, pentane, heptane, and benzene for different pressures. The pressure ranges evaluated were between 0.5 and 35 atm and the quality of vapors produced was between 1 and 71% [1, page 675]. Numerous experiments have been conducted on the area of forced convection boil- ing however at this time it is not yet possible to understand all of the characteristics of forced convection boiling due to the significant number of variables the process depends upon as well as the two-phase flow patterns that occur. These two phase flow patterns occur as the quality of the vapor-liquid mixture increase during vaporization [1, page 667-668]. Most of the data used for the correlations of forced convection represented in this project are based upon photographs taken by high speed cameras. These photo- graphs are then used to obtain a qualitative description of the process’ [1, page 668]. Chen is one of the first people to suggest a forced convention boiling correlation. This proposal has proven very useful and is used widespread [5]. Chen proposed a 6 major difference between conventional nucleate pool boiling and nucleate boiling in forced convention. Chen proposed that the large temperature difference of the hot inside surface of the pipe compared to the temperature of the fluid moving through the pipe causes a partial suppression of nucleation in boiling sites. This results in a partial reduction in heat transfer due to nucleate boiling [5]. Chen also noticed that as evapora- tion took place the vapor voids formed had the effect of increasing the velocity of the fluid through the pipe which created an increase in the heat transfer coefficient of convection as would be compared to a regular single phase flow of the fluid [5]. These effects can be summarized by saying that the higher flow rate caused by the formation of vapor spaces in the flow channel suppresses bubble growth and increases the convective heat transfer by increasing turbulence of the fluid flowing through the pipe [6, page 123]. Chen found two dimensionless functions that can be calculated empirically. These values are S and F. The value of S relates the suppression of the nucleation sites to the Forster and Zuber micro convective heat transfer relation for boiling [6, page 123]. The value of F applies to the Dittus-Boelter macro convective heat transfer relation for forced convection [6, page 123]. The Dittus-Boelter correlation is: And the Nusselt number is calculated from: Therefore the heat transfer coefficient can be calculated by solving for it on one side of the equation: This causes the heat transfer coefficient to change to The value of F is calculated based upon the following equation [1, page 675]: 7 The use of the Martinelli parameter for the calculation of is required [5]. The value of F applies the contribution of the convection heat transfer coefficient on the convection coefficient [1, page 675]: The nucleate pool boiling correlation of Forster and Zuber is indicted below [5]. This correlation is corrected for forced convection by the parameter S. The value of S is known as the nucleate boiling suppression factor [5]. This value is calculated from: For For For The value of is calculated as follows: 8 This value is similar to the conventional Reynolds number that is calculated as fol- lows [7, page 88]: The value of F is used to correct the Reynolds number using the Martinelli parame- ter for the calculation of [5]. After the value of S has been calculated it is used to correct the nucleate pool boiling correlation as follows: Once these values are obtained the heat transfer coefficients are added to create the forced convection boiling heat transfer coefficient. The heat transfer coefficient on the exterior of the inner pipe of the annulus heat ex- changer does not have as many terms as the inner heat transfer coefficient. This is due to no phase change occurring on the exterior surface of the inner pipe. The empirical correlation chosen for this parameter is an empirical correlation for heat transfer in a non-circular duct with turbulent flow [8, page 114]. The dimension is the exterior diameter formed between the outer surface of the inner tube of the heat exchanger and the dimension is the outer diameter of the inner tube. This correlation was chosen based upon the physical properties of the steam being used as the heat source. The Pr number was calculated to be greater than 0.6 and the Re number was calculated to be greater than 7,000. The Pr number of the heating steam was calculated by the following equation [7, page88]. 9 The Reynolds number was calculated based upon the equivalent hydraulic diameter for an annulus. The hydraulic diameter of the annulus was calculated based upon the following equation [1, page 376]: The flow of the steam is assumed to be fully developed so the Reynolds number was calculated using the hydraulic diameter from the following equation. To complete the calculation of the overall heat transfer coefficient a rough estimate was needed for the length of the evaporator heat exchanger. Initially, to obtain a rough estimate of length it was assumed that the exterior surface of the heat exchanger was maintained at a constant temperature. This would be true if the steam used as the heat source was condensing on the outer surface of the inner tube. With the assumption of phase change occurring on both sides of the heat exchanger calculation of the temper- ature difference would become simplified. This was performed based upon the fact that at this time a mean temperature difference had not yet been calculated. Using this approach the Chen correlation was used in an iterative process to calculate the required length of the heat exchanger inner tube. The mass flow velocity of the flow internal to the pipe was calculated using the equation: This provided the mass flow rate of the fluid flowing through the tube per second. The Reynolds number was calculated using the equation for flow through a pipe: 10 The iterative process resulted in a table of variable length and qualities of vapor generat- ed [Table 1]. The column on the left hand side of the table is the quality parameter (x). This is the quality of the vapor and water mixture exiting the evaporator. The step increase in the quality parameter is the column labeled ( . The column located on the right hand side of the table is the length column (l). This is the length of the annulus heat exchanger required to obtain the indicated quality of that row. Initially values of 0 were used as quality and length. The values of (x) were changed from 0 all the way up to the required value of 0.5. This resulted in an increased length of the heat exchanger as the quality grew. A final value of approximately 0.5 meters was obtained to provide the required heat input to obtain a 0.5 quality vapor. The values of , were updated in each row as the quality of the steam and water mixture ( values changed. Since the values of and change in each row the combined heat transfer coefficient for forced convection boiling changes as well. This iterative method was used based upon the heat flux over a length being directly linked to the increase in quality of the steam and water mixture at its saturation tempera- ture illustrated by the following [1, page 677]. This equation can be rearranged with the values of and on either side. The last row of [table 1] is the most important. As stated above the very last row of [table 1] indicates the 0.5 meter length required to obtain the 0.5 quality exit quality. It is important to state that this method was chosen to obtain a rough estimate of the length of the heat exchanger to obtain the overall heat transfer coefficient. This table 11 is updated to reflect a more accurate temperature difference between the steam and water vapor mixtures once a mean temperature difference is obtained. After the internal, external, and overall heat transfer coefficients as well as a rough estimation of size of the heat exchanger were generated the question of what the outlet temperature of the steam still remained. When calculating the heat transfer coefficient the appropriate reference temperature of the fluid bulk temperature is re- quired. The water flowing through the internal pipe is boiling so only the necessary latent heat of vaporization needs to be added. This does not result in a sensible heat change or in other words, the temperature of the boiling water within the heat exchanger does not change. However, as the steam flows over the heat exchanger the temperature of the heating steam does not remain the same. The steam temperature changes along the flow path as well as in the direction of heat flow [see figure 4]. A certain cross section of the heat exchanger needs be chosen to determine the reference point for the following equation: As stated above an accurate representation of the steam temperature requires calculation. The calculated temperature is typically an average temperature chosen as a reference temperature. This is commonly known as average fluid bulk or average mixing cup temperature [1, page 377]. Prior to obtaining this temperature difference an outlet temperature of the steam was required. This resulted in use of the heat exchanger effectiveness method. The heat transfer capabilities of a heat exchanger can be evaluated by a method called the heat exchanger effectiveness method [1, page 519]. This method compares the ratio of the actual rate of heat transfer in a heat exchanger to the maximum heat exchange rate possible. One of the assumptions in the design of the evaporator heat exchanger is that the annulus heat exchanger exterior is completely and perfectly insu- lated [1, page 519]. Assuming that the outer body is completely insulated, then the heat provided from the steam flows only into the boiler water and no heat escapes to the environment. The equation for the effectiveness is: 12 This equation requires calculation of the heat capacity rate ratio of the hot and cold fluids. This value is determined from the equation: Normally, the values of and are calculated by multiplying the mass flow rates and specific heats of the fluids and evaluating which one is the smaller and which one is the larger. In other words the mass flow rate of the steam is multiplied by the specific heat of the steam. The value calculated is specific heat rate of the hot fluid. The value of is 0 for an evaporator or condenser. This value is zero be- cause if one of the fluids temperatures remains zero throughout the streams specific heat and heat capacity are equal to infinity [1, page 520]. Once the effectiveness is calculated it can be used in the following equation to cal- culate the exit temperature of the steam. = = A little rearranging of the above equation provides: = The effectiveness calculated for this heat exchanger was approximately 0.544 which correlates with [figure 2] quite well for a parallel flow type heat exchanger with equal to 0. Once the outlet temperature of the steam was calculated the reference tempera- ture difference of the steam and steam/water mixture could be determined. The log mean temperature difference was used. Due to this fact a reference temperature known as the mean temperature difference must be calculated to be used in the calculation below. 13 To use the log mean temperature difference method it is assumed that the overall heat transfer coefficient is constant along the length of the heat exchanger, the kinetic energy changes of the fluid are neglected, and the heat exchanger is perfectly insulated [1, page 512]. The equation for the log mean temperature difference is illustrated below. The value of is the difference in temperature of the inlet fluids and the value of is the difference in temperature of the outlet fluids. Once the reference temperature difference was obtained the iterative process of cal- culating the required length of the annulus heat exchanger could be reperformed. The same process was performed as [table 1] resulting in [table 2]. Observing [table 2] the values of , h, and q were all updated to reflect the temper- ature difference term or the term in the equation below. The value of q is an important parameter to be observed due to its value being the required amount of heat being added to the boiler water to create the 50% quality vapor. This value will be used to ensure the condenser has the required capacity to remove this amount of heat. 2.2 Condenser 14 3. References [1] Principles of Heat Transfer-fifth edition [2] http://www.engineersedge.com/heat_transfer/overall_heat_transfer_coef.htm (7-30-11) [3]Engineering Formulas Conversions and Tables, Frank Sims [4] http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html (7-30-11) [5] http://www.wlv.com/products/databook/db3/data/db3ch10.pdf (7-30-11) [6] Boiling Heat Transfer and Two-Phase Flow, Tong [7]Convective Heat and Mass Transfer, Wiliam Kays, Michael Crawford, Bernhard Weigand. [8]A Concise Encyclopedia of Heat Transfer, Kutateladze, and Borishanskii 15

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