[abiy]

Hello Guys,

Does anybody know the meaning of "prime2Mean" option that's specified when we want to calculate average of the a field. Please look the following code. Thank you very much!

functions
{
    fieldAverage1
    {
        type            fieldAverage;
        libs            ("libfieldFunctionObjects.so");
        writeControl    writeTime;

        fields
        (
            U
            {
                mean        on;
                prime2Mean  on;
                base        time;
            }
        );
    }
}

[agustinvo]

Hello

it means that you get the average of the product of the fluctuations of the variable. For instances, in your case you have U. It means that you get UPrime2Mean, it is
, so you get the symmTensor where you have the Reynolds stresses.

For a scalar T, you get , the time average of the squared fluctuations.

[atulkjoy]

Hi ,
If I use Umean = U - squrt(Uprime2mean) will it be the right thing to find mean value. As mean is instantaneous - fluctuating field.

[winsway]

I don't think so. I have caculated it. the equation is not correct. you can see the case /tutorials/incompressible/pimpleFoam/LES/channel395; And you remove the functions{...} ，then get the result to compare with the result without remove the functions. you can find the U and U_0 are same. but you cann't connect the relationship between U and UMeasure and UPrime2Mean. I'm confused with it too!

[Santiago]

Originally Posted by abiy

Hello Guys,

Does anybody know the meaning of "prime2Mean" option that's specified when we want to calculate average of the a field. Please look the following code. Thank you very much!

functions
{
    fieldAverage1
    {
        type            fieldAverage;
        libs            ("libfieldFunctionObjects.so");
        writeControl    writeTime;

        fields
        (
            U
            {
                mean        on;
                prime2Mean  on;
                base        time;
            }
        );
    }
}

Is the second order moment, or square root of the variance, of the quantity of interest. In the case of the velocity, is equivalent to the square root of the trace elements of the R. Stress tensor.

[winsway]

Originally Posted by Santiago

Is the second order moment, or square root of the variance, of the quantity of interest. In the case of the velocity, is equivalent to the square root of the trace elements of the R. Stress tensor.

thank you for you reply.
I'am caculating the result.the case 40s, first point.
U_0=(0.00631659 -9.16861e-07 -0.0020712);//i don't understand the varible's mean...
U=(0.00625804 4.31012e-06 -0.00207582);
UMean=(0.00956163 5.37524e-05 -0.00152819);
UX=0.00625804;UMeanx=0.00956163;
Uprime2Mean=(6.34187e-06 2.28789e-08 -1.65954e-07 1.92607e-08 1.25591e-07 1.12799e-05);
U'=UX-UMean;
but the equation Uprime2Mean !=sqrt(U'*U');
this is my confused!

[Santiago]

Because thats not how you calculate the standard deviation!
You calculate it like follows:

// variance
S = mean(U U) - mean(U)mean(U)
// std. Dev
S = sqrt(S)

[winsway]

Originally Posted by Santiago

Because thats not how you calculate the standard deviation!
You calculate it like follows:

// variance
S = mean(U U) - mean(U)mean(U)
// std. Dev
S = sqrt(S)

I understand your means.
mean(UxUx)=UMeanx*UMeanx+Uprime2Mean(1,1);
mean(UyUy)=UMeany*UMeany+Uprime2Mean(2,2);
mean(UzUz)=UMeanz*UMeanz+Uprime2Mean(3,3);
For instance :
mean(uxux)=0.00956163^2+6.34187e-06=0.0000977666382569;
mean(uyuy)=5.37524e-05^2+1.92607e-08=2.215002050576E-08
mean(uzuz)=-0.00152819^2+1.12799e-05=0.0000136152646761
mean(uxux)=1/t*integral（uxux）dt;y and z are same.
but how to calculate the ux ， uy , uz ?

[makaveli_lcf]

hi!
which mean do you mean? you are mixing Ux and ux so it is hard to understand what are you looking for. Time averaged mean velocity one already have in UMean array.

[makaveli_lcf]

the only official description I found is here:
https://cpp.openfoam.org/v3/a00751.html#details


But I found it is confusing as most of OpenFOAM documentations.
Instead of




I would raver write






Otherwise you cannot get a tensor for a vector field for example. Or at least some special multiplication operator should be used instead of power 2.

[Santiago]

Originally Posted by makaveli_lcf

the only official description I found is here:
https://cpp.openfoam.org/v3/a00751.html#details


But I found it is confusing as most of OpenFOAM documentations.
Instead of




I would raver write






Otherwise you cannot get a tensor for a vector field for example. Or at least some special multiplication operator should be used instead of power 2.

Both forms are correct, it's just a matter of taste! The first form (vector notation) assumes x to be a vector, and as such, the outer product can be perfectly written as

[makaveli_lcf]

wouldn't it give a scalar for the vector? outer product is actually (a*a^T) to give a tensor, for example in N-S the convective term is not U^2 but U U^T

Originally Posted by Santiago

Both forms are correct, it's just a matter of taste! The first form (vector notation) assumes x to be a vector, and as such, the outer product can be perfectly written as

[agustinvo]

Hi,


if you look into the programmers' guide (link), there you can see in Section 1.3.4 how OpenFOAM deals with the outer product.


Then, in Section 1.3.6:

Square of a tensor is defined as the outer product of the tensor with itself,e.g.for a vectora, the square a^2=aa

I hope it helps to answer your question.

[Santiago]

Originally Posted by makaveli_lcf

wouldn't it give a scalar for the vector? outer product is actually (a*a^T) to give a tensor, for example in N-S the convective term is not U^2 but U U^T

an outer product is an outer product, irrespective of notation! Meaning that an outer product between two euclidean vectors return a tensor. The definition given by you is more natural in Linear Algebra, and real analysis, whereas the tensor algebra intended in OF follows more the notation common in some books of functional analysis

[makaveli_lcf]

Thank you Agustin! if that means the outer product, it is fine)))


Cheers!

Originally Posted by agustinvo

Hi,


if you look into the programmers' guide (link), there you can see in Section 1.3.4 how OpenFOAM deals with the outer product.


Then, in Section 1.3.6:



I hope it helps to answer your question.

[makaveli_lcf]

Dear Santiago, for me aa or a^2 is a dot product, that is why I find it confusing. But if they accept it as an outer product I agree

Originally Posted by Santiago

an outer product is an outer product, irrespective of notation! Meaning that an outer product between two euclidean vectors return a tensor. The definition given by you is more natural in Linear Algebra, and real analysis, whereas the tensor algebra intended in OF follows more the notation common in some books of functional analysis

[makaveli_lcf]

the last thing I dont like at


https://cpp.openfoam.org/v3/a00751.html#details


is that the ^2 operator is out of the averaging since to find Reynolds-like stress we average the product of the fluctuating part, but not multiply the the average of the fluctuations, which are actually zero in the ideal case. So it should be: