[ekha]

Hi,

I am simulating a simple natural convection problem in a 2D rectangular cavity with the following boundary conditions: adiabatic top layer, periodic side walls and rigid non-slip bottom with random heat flux boundary condition applied over the faces of the layer using a UDF following this equation: Q= k*T*(-exp(-h)+ epsilon*[rand(x)-0.5])/h , where rand is a one dimensional array of random numbers uniformly distributed in the range of [0,1], k,T and h are the thermal conductivity, fluid temperature and vertical hight of the cavity respectively.

When using the UDF as heat flux boundary condition at the bottom layer, I supposed to see plumes or vortex on the temperature contour profile, similar to Figure 6 in the Journal article (Hattori et. at, 2015) https://doi.org/10.1016/j.ijheatmass...er.2015.03.060

Please advice me with the correct setup for the heat flux boundary condition, do I need to specify heat transfer coeff manually in the convection tap?
whats the proper methods of discretisation should I use?
any other advices please?

Many thanks,

Esra'a

[AlexanderZ]

what is your problem?
show your udf

best regards

[ekha]

Hi,

Thnks for your reply.

Following the udf I used, the returned values of my UDF were correct, attached the bottom layer profile with the applied heat flux using the UDF.

#include "udf.h"

#include "stdlib.h"            
/* srand and rand */

#include "random.h"

#include "time.h"

/*#define RAND_MAX 32767*/

#define k 0.6                
/* thermal conductivity */

#define T 300               
/* Temp in Kelvin */

DEFINE_PROFILE(rand_pertubation,thread,index)

{

real x[ND_ND]; 
/* this will hold the position vector */

face_t f;

real time = CURRENT_TIME;

float h = 0.5;
float E = 0.01;


begin_f_loop(f,thread)

{


F_CENTROID (x,f,thread);

F_PROFILE(f,thread,index) = k*T*(- exp(-h)+E*(uniform_random()-0.5))/h;         
/* apply random perturbation */

}

end_f_loop(f,thread);



}

My problem is that I am not getting plumes emitted back from the bottom layer !
I didn't get the expected results. The author in the journal article I mentioned before used SNS code generated in Fortran. However, what I am aiming to as a PhD student is to use Fluent to build a similar model and compare the results with the output of SNS code.

I have tried the following options as a thermal boundary condition for the bottom layer:

*Constant heat flux ,
*Variable heat flux (random perturbation equation through a UDF),
*Added heat flux coefficient of 10 W/m3-k to the variable heat flux perturbation
*Used a temperature difference with heat flux perturbation,
*Constant temp diff of 5 deg,
*Temp diff of 5 deg with random Temp perturbation
*Temp diff of 10 deg with random perturbation

For each run I used a time step size of 0.0001 and converged each time step, waited to t=0.06 BUT didn't get plumes rising up, what happen is that the domain is heated up to the temp of bottom layer.

[AlexanderZ]

what is it?

uniform_random()

show your case settings, models you are using, material properties for air (fluid)

best regards

[ekha]

I am aiming to apply a random heat flux boundary condition over the faces of the bottom layer using a UDF following this equation: Q= k*T*(-exp(-h)+ epsilon*[rand(x)-0.5])/h, where rand is a random number between 0 and 1.

Water is the fluid in the domain with Boussinesq approximation being used with a constant thermal expansion coefficient.

I am using a transient laminar model with the following discretisation methods:
Coupled for the pressure velocity coupling scheme, PRESTO! for pressure, Second order Upwind for Momentum and Energy, along with first order implicit for transient.


For each run I used a time step size of 0.0001 and converged each time step, waited till t=0.01 sec BUT didn't get plumes rising up, what happen is that the domain is heated up to the temp of bottom layer.

Do I need to wait for longer time more that t= 0.01 to see plumes ? using SNS code the onset of instability for the same problem has been captured at earlier time of t= 0.001 sec !

I have tried before a transient 3D problem with the same setups and discretisation methods, where delta T was 180 deg and a dimensions of (0.3, 0.15, 0.15)m .. and it works vey well !!

Is this a limitation in Fluent that it can't run 2D DNS problems?

[AlexanderZ]

all seems correct from my point of view...
as far as I know DNS is 3D from its nature, however, you still should get non uniform temperature distribution

best regards

[ekha]

Yes, you are right.

According to Tennekes & Lumley in their book "The first course in turbulence", The basic characteristics of turbulence are irregularity, diffusivity, large Reynolds numbers, three-dimensional vorticity fluctuations and dissipation. They also stated in chapter2 that the interaction between eddies and the mean flow require three-dimensional flow. In chapter3, Tennekes & Lumley explained that vorticity doesn't occur in two-dimensional flow.

I'll expand the geometry to 3D and let you know if it works fine.
Many thanks

[ekha]

hi,

I run the simulation with a boundary condition of random heat flux at the bottom layer. I used the simple pressure-velocity coupling method and reduced the under relaxation factor to half their values.
time step size of 0.005, number of steps of 200.

the results I get at t=1.45 attached here, I didn't get plumes rising up as expected.



For the coupled method what should be the value of CFL? its 200 by default, in my case it must be lower than 5.
However, in the user guide they mentioned that reducing the CFL number below 10 is not recommended. In most transient cases, the CFL number should be set to 10^7 with an explicit relaxation of 1.0. Please see:https://www.sharcnet.ca/Software/Ans...olve_pvel.html

Please let me know what modification should I do?

[ekha]

Sorry, I don't have permission to attach pictures, so I can share my results.

However, what I get is simply diffusion problem, the bottom layer start heating up the fluid in the domain by constant temp.

[AlexanderZ]

CFL is not the Courant number as far as I know.

may be the problem comes from your boundary condition -> UDF

use F_UDMI(c,t,0) to monitor your boundary condition (you can plot it)
may be the amplitude is not enough....
make some artificial case, where hot and cold place are explicitly designed

best regards