American Institute of Mathematics, San Jose, California
Ellis Cumberbatch and Wei Kang
Each problem will be described by an engineer or scientist who represents the industry or public agency and who is well versed in the problem area. Teams of mathematicians and graduate students will work intensively on problem formulation, analysis, and implementation. The style of the workshop will be a blend of the format of the Math-in-Industry Study Group introduced in Oxford and the focused, collaborative style of AIM workshops
The Pajaro Valley farming area of the Monterey Bay is one of the world's largest producers of berries and vegetables. The water supply to thousands of farmed acres is from an underground aquifer that is slowly being depleted. The estimates for the overdraft of the water vary, with some ranging up to a 50% overdraft (or around 25,000 acre feet) per year. This overdraft also creates a significant problem of salt water intrusion along the coast, making many coastal wells unusable.
The sustainability problem will focus on helping one particular berry company evaluate how various water and land management techniques could be utilized by landowners and farmers to work towards balancing aquifer levels. The goal of this evaluation would be to help landowners choose water and land management techniques based on the possible hydrological benefits and the costs associated with each technique. Techniques that will be evaluated include: retiring certain portions of land, crop rotations, fallowing land (3 year rotations), creating small scale catchment basins for recharge, collecting storm water and runoff, conservation (irrigation efficiency), and other means to get to a reasonable water usage and still stay profitable.
This industry problem will focus on a method to determine reserve requirements for large-scale renewable energy integration, in particular, there will be a focus on increasing penetration of intermittent generation.
Since 2007, the Electric Power Research Institute (EPRI) has conducted research on reserve determination using stochastic optimal power flow methods. These studies demonstrated the successful application of this technology to small- and medium-size cases. Computational efficiency is the biggest challenge for implementing the stochastic models that properly handle the uncertainties in forecasts of output from many intermittent resources. The main research question now is whether there are scalable methods that efficiently handle the expanded problem size. Realistic systems have tens of thousands of busses and uncountable numbers of scenarios representing the full uncertainties of system outages, intermittent generation, demand response, and the forecasting errors for intermittent generation and demand. The current stage of research focuses on increasing the size and complexity of the stochastic dispatch model to realistic proportions, creating a platform for experimentation and analysis.
The main question is: What is the most computationally efficient method to represent the variability and uncertainty of a multitude of smaller and more diverse set of distributed renewable resources within a dispatch model?
Power output of such systems can sometimes be boosted by using multiple transducer patches and channeling energy generated by some of the patches into other patches for the purpose of exciting additional vibrational modes. A general approach to this problem is suggested by J. T. Scruggs in his paper "An optimal stochastic control theory for distributed energy harvesting techniques," published in the Journal of Sound and Vibration 320 (2009), pp. 707-725. This approach uses H2 optimal control theory for the design of feedback controllers for energy harvesting systems for maximal power generation. However, the analysis performed in that paper suffers from some limitations. These include failure to account for bandwidth restrictions and controller order limitations and the power needed to operate the control intelligence and the drive circuitry.
Making this technology practical requires addressing these limitations, extending the geometry of the structure beyond simple cantilevered beams to realistic structural elements, and allowing the shapes of the piezoelectric transducer patches to vary. Moreover, the engineering of the structure and the energy harvesting system should be accomplished simultaneously, i.e. the design problem should be reposed as the problem of maximizing power production subject to constraints on the structure, namely that it meet structural integrity, weight, and load requirements. A complete solution to this problem would include not only a proper problem formulation, but also viable approaches for performing both the structural and geometric modeling required, adding the needed enhancements to Scruggs' models, and demonstrating the feasibility on a realistic test problem.
A novel device which promises to significantly enhance waste heat recovery efficiencies from a large variety of heat sources consists of a two-phase thermal system combining a Loop Heat Pipe with a Tesla turbine operating in a thermodynamic two-phase regime. A similar concept using Loop Heat Pipe and a generic turbine operating in the superheated regime has been patented. However, in the proposed approach, by effective use of a Tesla turbine to operate within the saturated region, near-Carnot efficiencies can be achieved by harvesting a significant portion of the fluid enthalpy. The loop heat pipe's efficiency in transferring low-level heat and the Tesla turbine's capability of operating in the saturated liquid-vapor region offer a unique ability to harvest low-level heat at a very high efficiency, doubling what can be achieved by state of the art solid state thermoelectric devices. With modeling as a two phase Rankine Cycle system, the expected efficiency of operation is in the range of 17% assuming a very conservative 60% turbine efficiency; Carnot efficiency at these temperatures is 28%. A state of the art thermoelectric device, such as a superlattice thermoelectric converter can achieve only about 8% efficiency in this temperature range.
Successful demonstration of such a device can have a significant impact on the carbon footprint globally by harvesting heat from a huge variety of low-level waste heat sources which normally cannot be achieved efficiently or cost-effectively.
Traditional impeller steam turbines can only tolerate superheated vapor and little to no liquid condensation. However, Tesla turbines, because they don't have impeller blades, can operate in mixed flow conditions handling both vapor and liquid condensation. We are expecting that the heat of condensation will heat up the gas passing through the turbine and cause it to spin faster; and it is this additional amount of energy that we expect to harness. This technology is being patented by NASA's Jet Propulsion Laboratory (JPL) under its Global Change and Energy initiative.
The workshop problem will be to model the flow through a Tesla turbine of a liquid-vapor fluid.
The workshop schedule.
A report on the workshop activities.