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Module 1: Introduction to Experimental Techniques
Lecture 5: Design of experiments
The Lecture Contains:
Design of Experiments
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Design of Experiments: Determining the Best Experimental Plan and Optimal Duration, Slides of Mechanical Engineering
The importance of designing experiments effectively to determine the best experimental plan and optimal duration. It covers two examples: one for determining the constant 'k' in a decaying system and another for estimating the cooling rates of a heated circular cylinder. How to find the optimum time duration using the variance criterion and compares the transient and steady state methods for obtaining the heat transfer coefficient.
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Module 1: Introduction to Experimental Techniques
Lecture 5: Design of experiments
The Lecture Contains:
Design of Experiments
Module 1: Introduction to Experimental Techniques
Lecture 5: Design of experiments
Design of Experiments
Even after the objectives of an experiment are laid out, various possibilites for the route to be adopted can emerge. Thus, two main questions that arise during experimentation are: (1) Among the various options, find the one that is the best, subject to constraints of accuracy and cost; (2) For a given experiment, what is the best action plan, in terms of spacing between data points, duration of the experiment and other such decision variables. These questions are addressed in the theory of design of experiments. The subject is illustrated below through examples.
Example 1: The response of a system is expected to vary as
An experiment is designed to determine the constant by a least squares procedure. It is required that data be collected at equal time intervals with a total of points.What should be the duration of the test? Let be the total time needed for the experiment. If is very small, the decaying feature of the function is lost. If is very large, the time step also becomes large and results in large resolution errors.
Module 1: Introduction to Experimental Techniques
Lecture 5: Design of experiments
Example 2: It is required to determine the cooling rates of a heated circular cylinder exposed to an air stream in terms of the heat transfer coefficient. This coefficient is defined as the energy lost per unit area per unit temperature difference between the cylinder and the air stream. Two experiments are proposed for estimating. In the first, the cylinder is heated to a temperature and suddenly placed in the air stream at a temperature. The heat transfer coefficient is then obtained from the cooling curve of the cylinder. In functional form, the cooling curve is given as
where is the cylinder temperature at any time , is the surface area, is the mass of the cylinder and is its specific heat. The experiment is stopped when the left side of the above equation is for which and
Module 1: Introduction to Experimental Techniques
Lecture 5: Design of experiments
In the second experiment, the measurements are carried out at steady state by continuously heating the cylinder. This can be accomplished by directly passing current through the cylinder, or by using electric rod heaters, held concentrically within the cylinder. Depending on the air velocity the cylinder will attain a temperature. From energy balance, one can write
where is the electrical heater input to the cylinder.
The question here is: Of the transient and steady state experiments identify the method to be preferred for obtaining the heat transfer coefficient. To answer this question, one needs to realize that the transient method relies on measurement of time while the steady state method relies on the measurement of electrical power. Assuming fixed uncertainties in time and electrical power ( and respectively), it is clear that the transient method is preferable if
and the steady state method should be adopted if