# DNS, RANS & Turbulent Modeling In CFD

Posted October 29, 2015 at 00:41 by adarsh tiwari

Tags dns, k-epsilon, k-omega, k-omegasst, rans

Hi, Guys! My last blog “2 Funny Cases In CFD” was to chill you up, as mechanics is not only about serious topics and discussion. Mechanical people can also have fun while they work (for professionals ) and learn and study (for students ). Today’s topic is very interesting as I am going to discuss Turbulence Modelling.

Though I will keep on talking and you will keep on reading, as we proceed 😀 😀 , I will try not to bore you, and keep you engaged. At any point if you feel you have some thoughts you would like to share or discuss with me I’d be very happy to take it up in the comment box below or you can always reach me out at learn@mycadcfd.com and I will try to revert back ASAP.

So Guys, Let’s Start…!!!

As we know, turbulent flow is 3-D in nature and the fluctuations are very rapid in space and time. Hence, it is required to keep the time step low as well as equally small grid spacing is required. But the problem comes into picture when, we have to simulate it. Low time steps and finer grid leads to exponentially increased computational time. However, there are attempts where, finer grids with small time steps are simulated without any numerical approximations. This approach is called DNS.

DNS stands for Direct Numerical Simulation. In DNS the N-S equations are directly solved, without further approximations, except the one, the fluid is Newtonian in nature. As we discussed earlier, this is computationally expensive and most of the time we do not need much-detailed results. Hence, there is a requirement of sufficiently less detailed results with lesser calculation. Lesser calculations mean lesser time and lower computational power requirements. Reynolds Averaging is one of the alternatives for this.

Another simulation techniques evolved from Reynolds’s averaging, known as RANS. RANS stands for Reynolds Averaged Navier-Stokes equation. RANS forms the basis of simulation of turbulent flow in CFD. All the equations are time-averaged.

Suppose we want to estimate the climatic condition of any place, say Pune. Now, we need a recording device for recording the temperature, humidity and solar radiation fluctuations. It is not very difficult to say that every minute there is a variation in these parameters.

Now, we have to analyse the climatic condition of Pune and mention the detail of every minute. We have to average the data with certain approximations and present it in a most logical way.

For example, If we want to give a weather data for today, by averaging, we can say that today the temperature would be 27℃ with 60% RH. Here the fluctuation happening every minute is of least importance.

Further, if somebody asks for the month’s climatic condition of Pune, we can say that it will be (or was) slightly colder in Pune with the temperature of 21℃. Here, the fluctuation happening every hour is safely neglected.

Again, if we want to yearly specify the temperature, we again approximate the temperature on a weekly basis and will not give much importance to changes happening on a daily or hourly basis.

The point which I am trying to make here is there are levels of detail required in each analysis. Hence for solving the purpose we need to approximate/average the parameters.

Now, again coming back to RANS, it assumes that every parameter is divided into parts viz., the average part and the fluctuating part. These fluctuations are with respect to time. Hence, the equations are time averaged. Let us consider we want to average the velocity with respect to time at point Xo, mathematically, RANS will be given as:

Here, this time window ‘T’ is sufficiently large enough to smooth out the fluctuations, but is not so wide that we will suppress the inherent time dependence of the equations. Hence, as explained the analogy above, the time step must be chosen wisely.

Other models evolved are basically described as one-equation model and two-equation model. Examples being Spallart-Allmaras, K-Epsilon, K-Omega, K-OmegaSST etc.

In my training session at MYCADCFD, I give more attention towards the modeling and applications. Remember, for a wise person nothing is difficult. A Wise person is well experienced because he learns from his own mistakes and failure.

Though I will keep on talking and you will keep on reading, as we proceed 😀 😀 , I will try not to bore you, and keep you engaged. At any point if you feel you have some thoughts you would like to share or discuss with me I’d be very happy to take it up in the comment box below or you can always reach me out at learn@mycadcfd.com and I will try to revert back ASAP.

So Guys, Let’s Start…!!!

**The DNS Approach**As we know, turbulent flow is 3-D in nature and the fluctuations are very rapid in space and time. Hence, it is required to keep the time step low as well as equally small grid spacing is required. But the problem comes into picture when, we have to simulate it. Low time steps and finer grid leads to exponentially increased computational time. However, there are attempts where, finer grids with small time steps are simulated without any numerical approximations. This approach is called DNS.

DNS stands for Direct Numerical Simulation. In DNS the N-S equations are directly solved, without further approximations, except the one, the fluid is Newtonian in nature. As we discussed earlier, this is computationally expensive and most of the time we do not need much-detailed results. Hence, there is a requirement of sufficiently less detailed results with lesser calculation. Lesser calculations mean lesser time and lower computational power requirements. Reynolds Averaging is one of the alternatives for this.

**RANS**Another simulation techniques evolved from Reynolds’s averaging, known as RANS. RANS stands for Reynolds Averaged Navier-Stokes equation. RANS forms the basis of simulation of turbulent flow in CFD. All the equations are time-averaged.

*Best analogy I can give for Reynolds averaging as:*Suppose we want to estimate the climatic condition of any place, say Pune. Now, we need a recording device for recording the temperature, humidity and solar radiation fluctuations. It is not very difficult to say that every minute there is a variation in these parameters.

Now, we have to analyse the climatic condition of Pune and mention the detail of every minute. We have to average the data with certain approximations and present it in a most logical way.

For example, If we want to give a weather data for today, by averaging, we can say that today the temperature would be 27℃ with 60% RH. Here the fluctuation happening every minute is of least importance.

Further, if somebody asks for the month’s climatic condition of Pune, we can say that it will be (or was) slightly colder in Pune with the temperature of 21℃. Here, the fluctuation happening every hour is safely neglected.

Again, if we want to yearly specify the temperature, we again approximate the temperature on a weekly basis and will not give much importance to changes happening on a daily or hourly basis.

The point which I am trying to make here is there are levels of detail required in each analysis. Hence for solving the purpose we need to approximate/average the parameters.

Now, again coming back to RANS, it assumes that every parameter is divided into parts viz., the average part and the fluctuating part. These fluctuations are with respect to time. Hence, the equations are time averaged. Let us consider we want to average the velocity with respect to time at point Xo, mathematically, RANS will be given as:

Here, this time window ‘T’ is sufficiently large enough to smooth out the fluctuations, but is not so wide that we will suppress the inherent time dependence of the equations. Hence, as explained the analogy above, the time step must be chosen wisely.

Other models evolved are basically described as one-equation model and two-equation model. Examples being Spallart-Allmaras, K-Epsilon, K-Omega, K-OmegaSST etc.

In my training session at MYCADCFD, I give more attention towards the modeling and applications. Remember, for a wise person nothing is difficult. A Wise person is well experienced because he learns from his own mistakes and failure.

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