Quantitative Analysis of Francis Turbine: Questions & Confusions

In summary, The speaker is confused about the quantitative analysis of Francis turbine and wrote a small program to calculate the results. The results matched the normal circumstances but there were some peculiarities, such as negative and over 1 values for the degree of reaction at certain speeds, and a different shape for the relation between discharge and speed compared to what is described in the textbook. The speaker also mentions a peculiar finding where they did not have to input discharge in order for the program to calculate successfully. They also ask about the procedure for regulating flow in a Francis turbine and question whether variations in blade inlet angle with rpm are neglected in the design process.
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so I am still very much confused about the quantitative analysis of Francis turbine, so i wrote a small program. I have attached a copy of the results.

Everything is fine, the results do match the normal circumstances. But upto speed 110, degree of reaction(R in the table) is negative, and over 440, it is over 1. I cross checked all the calculations by hand, and various values seemed to be OK. Is it really so practically?? I had the impression, it is always between 0 and 1(from its definition). And if it really is so, how can it be put forth qualitatively??

Second the relation between discharge and speed is sort of hyperbolic shape, whereas it is of drooping shape in the textbook. I am confused about this. One more peculiar thing, I didn't have to feed anything to calculate discharge, when i did, program said the code is over specified, so i deleted the discharge as input and it calculated successfully! Only input i entered is head and rpm!
Qualitatively, in a pelton wheel, a spear is pulled back & forth to regulate the flow. What is the procedure for the Francis turbine?,is it guide blade angle?

The angle which Vr1 makes with horizontal(also called the blade inlet angle), changes continuously as the rpm increases, so there is nothing as shock less entry, therefore the tip of the blade is always airfoil like(round). Am I correct??(I also noticed this in my fluid lab).

Or is it that a turbine is designed to serve only at the optimum efficiency and these variations with rpm are neglected??
 

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velocity diagram
 

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1. What is the purpose of quantitative analysis in studying Francis turbines?

The purpose of quantitative analysis in studying Francis turbines is to obtain numerical data and measurements that can be used to evaluate the performance of the turbine. This analysis helps in understanding the efficiency, power output, and other important parameters of the turbine.

2. How is the efficiency of a Francis turbine calculated?

The efficiency of a Francis turbine is calculated by dividing the actual power output by the theoretical power output. The theoretical power output is calculated by multiplying the flow rate, head, and density of the fluid. The efficiency of the turbine is typically expressed as a percentage.

3. What factors can affect the performance of a Francis turbine?

There are several factors that can affect the performance of a Francis turbine, including the design of the turbine, the operating conditions, and the condition of the turbine components. Changes in any of these factors can impact the efficiency and power output of the turbine.

4. What are some common sources of confusion when analyzing Francis turbines quantitatively?

Some common sources of confusion when analyzing Francis turbines quantitatively include incorrect measurements, lack of understanding of the underlying principles, and incorrect assumptions about the operating conditions. It is important to carefully check and validate all data and calculations to avoid these confusions.

5. How can quantitative analysis of Francis turbines be used in the design process?

Quantitative analysis of Francis turbines can be used in the design process to optimize the performance of the turbine. The data obtained from this analysis can be used to make informed decisions about the design parameters, such as blade shape, runner diameter, and number of blades. This helps in creating more efficient and powerful turbines.

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