Fluid Mechanics In Renewable Energy - Report Example

FLUID MECHANICS IN RENEWABLE ENERGY Student Name Course Name Date Table of Contents Table of Contents 1 Introduction 2 Fluid Mechanics in Renewable Energy 2 Hydroelectric Energy 2 Ocean Energy 6 Wind Energy 9 Conclusion 11 Bibliography 12 Introduction Fluid mechanics has a large scope of applications in the day to day undertakings that affect human life. A study into the flow of fluids in pipes and channels for example has been used in understanding the flow of blood and air in the human body for the purpose of disease diagnostics. On an artificial level, dam spillways meant for the purpose of hydroelectric generation are entirely dependent on the understanding of fluid mechanics’ principles of flow, fluid turbulence and laminar flow among others. The combination of these principles usually aid in coming up with effective engineering designs for the sake of improving the achievable standards in renewable energy. On the other side, the on-going debates on climate due to emissions caused by burning of fossil fuels has led to in-depth researches on how to maximise the output from the renewable potential in order to act as a future replacement for the “dirty energy”. This discussion shall focus on the application of fluid mechanics in the renewable field with a bias to hydroelectric energy, ocean energy and wind energy. Fluid Mechanics in Renewable Energy Hydroelectric Energy Hydroelectric energy is one of the greatest beneficiaries of fluid mechanics’ applications in real life. The historic utilization of power from moving water Agricultural purposes such as wheat grinding during the agrarian revolution saw the emergency of hydro-generated power in middle of the 19th century. Generation of hydroelectric power is therefore entirely dependent on the thoughtfulness achieved from the characteristics of water in motion. The basic layout of a hydroelectric power generation plant is illustrated in diagram 1 below. The power house consists of the turbine, power control mechanisms and the stator (Bandyopadhyay 2006). Figure 1: An illustration of a high head power plant (Bandyopadhyay 2006). The flow of fluid is normally analysed in both two and three dimensions against other parameters like time where need arises with the main focus on water. The data obtained is used for the analysis of the power derivable for the sake of feasibility studies from the flow of water through the tunnel to when it hits the turbine which in turn runs the stator for the sake of electric power production (Teklemariam, et al. 2002). The basic power equation utilized for this purpose is shown in (i) below. ------------------------------- (i) Where: P = Power output Q = Discharge (m3/s) H = Head of water (m) η = Efficiency g = Specific gravity of water (N/m3) The choice of equipment and design to be applied in the generation of the energy entirely depends on the designer's keenness to follow the rules attached to the fluid mechanics field. The designs of tunnels utilized in electric energy generation are checked for the purpose of determining the friction that might occur in order to avoid damages on the pipes during the process of running the machinery. The turbulent flow is checked by use of the Darcy-Weisbach formula which is stated as follows (Hicks and Max 1987). ------------------------------------------------- (ii) Where: h = Friction of water f = Friction factor L = Length of the tunnel V = Maximum achievable velocity g = gravity D = Diameter tunnel During the design phase it is also necessary that the velocity in the tunnel be known to the engineers before commencement of work for the purpose of solving equation (ii) above. Therefore in order to calculate velocity in closed tunnel the Manning formula stated below becomes handy (Hicks and Max 1987). ----------------------------------------- (iii) Where: V = Velocity of water in tunnel R = Hydraulic radius S = Hydraulic gradient calculated as Whether the generation plant is meant for micro hydroelectric generation or large scale purposes, the choice of the equipment to be used entirely depends on fluid mechanics initiated by the above equations for this purpose. Water turbines are designed to meet a diversity of specifications depending on the nature of flow and power requirements. The Pelton turbine is meant for low head water and may generate a maximum of up to 35 rotations per minute (rpm) for a fast runner. For the Francis turbine, an rpm of up to 300 may be generated in an environment with a medium head. Kaplan is the most used turbine in high head water – generates up to 1000rpm. These turbines are designed in accordance to the laws of fluid mechanics in order to facilitate take over for the electrical engineers with ease when it comes to their choice of the stator size to be used. Without this information, the design failure is highly expected as the activity may not be well coordinated. For the purpose of illustration a single jet Pelton turbine consists of a nozzle with a control mechanism, a casing, hydraulic brake and buckets or runners as shown in diagram 2 below (Bandyopadhyay 2006). Figure 2: An illustration of the Kaplan turbine (Bandyopadhyay 2006). Ocean Energy The strategy behind ocean energy is the utilization of water to tap energy from the strong waves generated due to tidal differences. Although the technology behind the generation of tidal energy still remains as a major challenge, major advances have been made due to the mechanics of fluids leading to the production of a whopping 254 MW by Sihwa Lake Tidal Power project in South Korea. Tidal barrages containing turbines connected to generators are built across estuaries to utilize the motion emanating from the potential energy difference between the two water levels. The conversion of potential energy to kinetic energy is then transferred from the turbines to turbines to the generator through a rotational kinetic energy resulting from the turbines. The highest output in this case is only achievable when the water head is at its highest while the vice versa is true for the contrary (Fan 2004). Figure 3: An illustration of a power generation cycle of a tidal plant (Fan 2004). A tidal turbine is designed to take the shape of a wind turbine and planted in water to resemble the wind farms that exist on the surface. A tidal barrage is designed to take the shape of a bulb turbine illustrated in figure 4 below. Figure 4: A Bulb Turbine The timing of water available is important for the determination of head available for the sake of power generation. In some cases it is important to consider the mode of power generation ranging from Ebb generation, two-way generation, flood generation or pumping generation. In a hypothetical setup, the sluicing of barrage gates is realized by the sluice flow equation (iv) based on the fluid mechanics model (Fan 2004). -------------------------------------------- (iv) Where: Q = Sluice flow C = Gate or turbine sluicing coefficient A = Gate or turbine sluicing area H = Head above the sluice g = Gravity The maximum achievable energy generated by a sluice gate turbine is shown in (v) below: --------------------- (v) Where: E = Energy generated in kWh. Q = Flow across the turbine. H = Turbine head Et = Efficiency of the respective turbine. Eg = Efficiency of the generator place. Etr = the efficiency of the transformer. Lt = Factor of loss in line. Lsu = the station’s loss factor. Lo = Outage loss factor T = Time between increment. The power conversion model takes that of the wind since moving water can only be intercepted at the frontal area. Therefore the energy equation used in determining this is as follows: ----------------------------- (vi) The mechanical form which can also be said as the usable energy form can be determined by the fluid equation: ------------------------- (vii) Since the turbine is exposed to incompressible flowing fluid, the maximum theoretical value is set at 0.593. This is in accordance to Betz law which states that the device’s power coefficient should be proportional to the tip speed ratio. Since the energy captured is determined by the quasi-steady flow of the tides the estimation should involve the velocity (Fan 2004). The velocity is determined by the following equation: ------------------------------------------- (viii) The final power equation for the ocean energy is calculated by solving the equation (ix) below on a given function: ---------- (ix) Wind Energy Wind energy like any other renewable sources uses the phenomenon of fluid transfer to generate electricity. This mode of electricity generation uses air under accelerated motion (wind) to transfer energy to the turbines which are connected to the generators for this purpose. The working principle of the wind turbine was drawn from the draconian windmills which have been used since time immemorial for grinding corn and other cereals (clara.net 2012). Figure 5: Pictorial view of a wind turbine (clara.net 2012). Fluid mechanics models have been designed by engineers to come up with the correct wind turbines for the purpose of maximizing this natural resource. The implementation of mathematical simulations drawn from laboratories and field are all achievable through the applications that are contributed by fluid mechanics. The performance of a wind turbine is determined by a multitude of factors which add towards the final effective power coefficient (Lanzafame and Messina 2007). Equation (x) below show the power coefficient Cp of a wind turbine: ----------------------------------------- (x) Where: P = Power. ρ = density of air. V = Velocity of air. R = Radius of rotor. Wind energy of a turbine is also affected by factors worth discussing such as the boundary layer effects. The frictional resistance that results from the earth surface thus the wind velocity is expected to differ at all levels. The height at which the turbine is installed thus cannot correct the speed gained but shall be corrected by the boundary layer phenomenon. The wind data available at a height (Z) at a set roughness of Z0 is determined by the equation (xi) below (Mathew 2011). ------------------------------ (xi) Where: V = velocity of wind. The energy equation that is used to determine the final effective power of a turbine is the normal kinetic energy equation. However due to the adjustments made from the rate of energy change, the following equation is derived for this sake. --------------------------------------------- (xii) The fact that no wind turbine can convert more than 59.3% of the energy gained from the wind velocity was established by Albert Betz in 1919. Further, the wind turbine cannot achieve the absolute coefficient by Betz, therefore it is maintained between 0.35 – 0.45 depending on the type of gearboxes used to convert this important natural resource into a usable commodity (Mathew 2011). The power conversion equation becomes: -------------------------------------- (xiii) Conclusion The laws of fluid mechanics are highly called for in the day to day life of man. The applications further indicate that the discoveries made regarding fluids cannot do without these important facts. In the renewable energy field it has been established that the field of fluid mechanics is not only a subsidiary to such power generators as wind, ocean, geothermal and hydroelectric. This begins right from the design stage to the production stage in which equations derived to deal with matters pertaining to fluids are used. Bibliography Bandyopadhyay, M. N. Electrical Power Systems: Theory and Practice. Delhi: PHI Learning Pvt. Ltd., 2006. clara.net. Energy Resources: Wind power. July 25, 2012. http://home.clara.net/darvill/altenerg/wind.htm (accessed June 3, 2013). Fan, Zou. Tidal Power Energy: Renewable Energy in Future. Gävle: University of Gävle: Department of Technology and Built Environment, 2004. Hicks, Tyler Gregory, and Kurtz Max. Civil engineering calculations reference guide. New York: McGraw-Hill, 1987. Lanzafame, R., and M. Messina. "Fluid dynamics wind turbine design:Critical analysis, o ptimization and application of BEM theory." Renewable Energy 32, 2007: pp 2291–2305. Mathew, Sathyajith. Advances in Wind Energy and Conversion Technology. Heidelberg: Springer, 2011. Teklemariam, Efrem , Brian W. Korbaylo, Joe L. Groeneveld, and David M. Fuchs. "Computational Fluid Mechanics: Diverse Applications in Hydropower Project's Design and Analysis." Water Management in a Changing "Climate"”, 2002: pp 1-20. Read More