Question

Which of these represent time averaging?

(a) \(\frac{1}{V}\int_V \phi dV\)

(b) \(lim_{V→∞}\frac{⁡1}{V}\int_V \phi dV\)

(c) \(\frac{1}{T}\int_t^{t+T}\phi dt\)

(d) \(lim_{T→∞}⁡\frac{1}{T}\int_t^{t+T}\phi dt\)

This question was posed to me in homework.

Enquiry is from Turbulence Modelling in portion Turbulence Modelling of Computational Fluid Dynamics

Answer 1

The correct answer is (d) \(lim_{T→∞}⁡\frac{1}{T}\int_t^{t+T}\phi dt\)

Best explanation: Time averaging represents the average of the flow variable based on a time interval ‘T’. It uses integration to sum up the flow variables at different times and then divides by the time interval \(lim_{T→∞}⁡\frac{1}{T}\int_t^{t+T}\phi dt\).