# Design Steam Turbine for Solar Energy: Math Help Needed

• pixelpuffin
In summary, the conversation discusses designing a steam turbine and boiler for a solar energy project, with a goal of achieving 60% efficiency at average operating conditions and >20% efficiency at the high and low ends of its operation. The speaker is struggling with determining the inlet and outlet area, steam velocity, pressure, and temperature, as well as calculating the ratio between thermal and pressure drop off. They mention using the ideal gas law and their coding knowledge, and suggest researching the Rankine cycle for help with making estimations.
pixelpuffin
im designing a steam turbine and boiler for a solar energy project but i can't figure out the math and have had trouble looking it up
the only thing that is definite about the turbine (other than that its a tesla turbine) is that the thermal wattage is 5,855 watts or 1,434.72 calories per second (because its solar its actually a range but i plan to optimize the system for the average and later install a thermal buffer)
i need to determine
inlet and outlet area
inlet and outlet steam velocity
inlet and outlet steam pressure
inlet and outlet steam temperature

my goal is to get ~ 60% efficiency at average operating conditions and >20% efficiency at the high and low ends of its operation
it would be nice if it operated at 60 hertz or 3,600 rpm though that's not important

using the ideal gas law i get P*1/T*2.16*1/1,000=p so i can calculate the density with pressure and temperature

from there I am pretty much lost, mainly because i can't find any way to calculate the ratio between thermal drop off and pressure drop off

does anybody know how to at least estimate this
i have some coding knowledge so if there's a differential equation i have no trouble solving it

The steam turbines are dictated by the Rankine cycle (they are 12 pages for that lesson in the previous link). To help you familiarize with the concept, there are plenty of examples on the web to help you understand how to make the estimation you are looking for.

Keywords: Rankine cycle.

## 1. What is a steam turbine and how does it work?

A steam turbine is a device that converts the thermal energy from pressurized steam into mechanical energy, which can then be used to generate electricity. The steam enters the turbine at high pressure and high temperature, causing the turbine blades to rotate. The rotating motion is then used to turn a generator, producing electricity.

## 2. How can solar energy be used to power a steam turbine?

Solar energy can be used to power a steam turbine through the use of concentrated solar power (CSP) systems. These systems use mirrors or lenses to focus sunlight onto a receiver, which heats up a fluid to create steam. The steam is then used to power a steam turbine, producing electricity.

## 3. What factors need to be considered when designing a steam turbine for solar energy?

Some important factors to consider when designing a steam turbine for solar energy include the type of CSP system being used, the size and efficiency of the turbine, the operating temperature and pressure of the steam, and the materials used to withstand high temperatures and corrosive environments.

## 4. How is mathematics used in the design of a steam turbine for solar energy?

Mathematics plays a crucial role in the design of a steam turbine for solar energy. Calculations are needed to determine the size and shape of the turbine blades, the optimal operating conditions for maximum efficiency, and the amount of energy that can be generated. Additionally, mathematical models can be used to simulate and optimize the performance of the turbine.

## 5. What are the potential advantages and challenges of using a steam turbine for solar energy?

The main advantage of using a steam turbine for solar energy is that it can provide a reliable and consistent source of electricity, even when the sun is not shining. This is because the steam can be stored and used to power the turbine at a later time. However, challenges include high upfront costs, the need for large land areas for CSP systems, and the potential for water usage and environmental impacts in the steam generation process.

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