Often in oil reservoirs a layer of water lies under the layer of oil. The suction pressure due to a distribution of oil wells will cause the oil-water interface to rise up towards the wells. A three-dimensional boundary integral formulation is presented for calculating the steady interface shape when the oil wells are represented by point sinks. Sophisticated integration techniques are implemented in an effort to obtain accurate results. In particular, the efficiency of various integration methods are compared for this problem, including QUADPACK routines, adaptive methods based on the IMT rule, the Kronrod rule, the method of degenerate quadrilaterals, and the Gauss-Rational rule for infinite integrals. Numerical results for various general multi-sink distributions are discussed, as are some further results for the axisymmetric single well problem.

Electrical insulation failure is the most common failure mechanism in electrical machines (motors and generators). High temperatures and/or temperature gradients (HTTG) are the main drivers of insulation failure in electrical machines. HTTG combine with and augment other destructive effects from over-voltage, to voltage transients, overload and load variations, poor construction techniques, and thermal cycling. These operating conditions cause insulation damage that leads to electrical insulation failure. The insulation failure process is greatly accelerated by pollutants and moisture absorption. A simple and robust way to reduce HTTG and moisture adsorption is by maintaining constant internal temperatures. The current method to maintain elevated internal temperatures and reduce condensation issues is by internal electrical heating elements. This paper examines the effectiveness of applying thermoelectric coolers (TECs), solid-state heat pumps (Peltier devices), as heaters to raise a motor’s internal temperature by pumping heat into the motor core rather than heating the internal air. TEC technology is relatively new, and the application of TECs to heat a motor’s internal volume has not previously been explored. In this paper, we explore the hypothesis that TECs can pump heat into a motor when out of service, reducing the HTTG by maintaining high winding slot temperatures and eliminating condensation issues. This paper describes a test motor setup with simple resistive heating (traditional method), compared with the application of TECs with heat sinks, heat pipes, and a water circulation heat exchanger, to gauge the capability of TECs to heat the inner core or winding area. In this paper, we demonstrate the full integration of TECs into a motor. The results show that each of the systems incorporating the TECs would effectively pump heat into the core and keep the winding hot, eliminating condensation issues and water ingress due to thermal cycling.

This paper explores the application of thermoelectric cooler/heater (TEC) modules (Peltier heat pumps devices) to control core and winding temperatures, aiming to reduce the effects of thermal cycling and moisture issues that affect the life of electrical machines. Electrical windings in a motor will fail for a variety of reasons, and a major contributor to adverse effects of a motor’s life is humidity. Due to thermal cycling, air containing moisture is drawn into a motor through a variety of access points such as terminal boxes, bearings, end covers and mounting systems. Even spare or replacement motors specially stored in heated spare equipment stores suffer from moisture ingress because of normal daily temperature changes. The better a machine can be kept warm, the less it is affected by moisture and the effects of mechanical stresses from cycling temperatures. A series of experiments were conducted, whereby a TEC was attached to a section of motor core and was set up to pump heat into the core segment. The thermal properties of the core material and the capacity to control winding temperatures along the core in specific locations and over time was measured. The results of this research demonstrate that the temperature of the motor can be tightly controlled, thus enabling the reduction of the effects of moisture, and reducing core and winding temperature differences. This has a positive influence in reducing the thermal stresses, which will result in improved insulation life and machine reliability.

Electric motors and generators underpin life in today’s world. They are numerous and widespread and consume approximately 45% of the world’s energy. Any improvements in efficiency or reductions in their whole-of-life costs are actively and continually being sought. While designs accommodate the removal of heat caused by internal losses because of inefficiencies, temperature variations due to load changes and environmental temperature fluctuations, and system harmonic content still stresses electrical insulation systems. This causes the fretting of insulation, combined with moisture ingress, which leads to leakage currents and, consequently, the early failure of the electrical insulation. This paper explores the addition of thermoelectric coolers/heaters (TECs) or Peltier effect devices. We show that these solid-state devices can actively support the thermal management of a motor by keeping its internals hot, reducing moisture ingress when off, and assisting in heat removal when under load, resulting in a more thermally stable internal environment. A thermally stable environment inside the electrical machine reduces the mechanical stresses on the electrical insulation, resulting in a longer operational life and reducing the whole-of-life costs.

Internal losses in motor windings and cores result in unwanted heat. According to International Energy Agency, majority of motors in service today are AC induction motors between 0.75 and 375 kW. For these motors, internal losses (heat) are conducted to the surrounding environment by internal conduction to the casing and then to the surrounding environment by convection. For small motors of up to 5 kW, the cores are mounted in a simple round housing and as they get larger the housings are ribbed and external fans are installed. Motors are designed assuming an environmental maximum temperature of 40 °C and with a hot spot allowance of 10 °C can withstand up to 155 °C (class F) at the winding position. However, due to changes in environmental temperatures, system voltage variations and harmonics, winding temperatures often exceed this limit. Consequently, this range of motors last only approximately 3 years. This paper investigates the possible application of thermoelectric cooler (TEC) to increase the heat flow from the core to reduce the temperature at the winding position, potentially providing longer insulation and motor life. For small motors, they can be simply attached to the outer surface. For larger motors with frames incorporating cooling ribs, they could be installed between the cores and the frames. The experimental results found that the application of TEC reduces the winding temperatures by 25.4%. Ability to incorporate this technology allows the opportunity to add a controlled device that can reduce temperatures at the windings when the temperatures exceed normal ratings.

This chapter introduces the Zeckendorf representation of a Fibonacci sequence, a form of a natural number which can be easily found using a greedy algorithm: given a number, subtract the largest Fibonacci number less than or equal to it, and repeat until the entire number is used up. This chapter first compares the efficiency of representing numbers using Zeckendorf form versus traditional binary with a fixed number of digits and shows when Zeckendorf form is to be preferred. It also shows what happens when variants of Zeckendorf form are used. Not only can natural numbers as be presented sums of Fibonacci numbers, but arithmetic can also be done with them directly in Zeckendorf form. The chapter includes a survey of past approaches to Zeckendorf representation arithmetic, as well as some improvements.