For a non-isothermal compressible flow (highly viscous fluid) through a channel, I am getting spatial temperature values almost up to 10% elevated from the maximum value of temperature which has been set in the domain at the initial stage as boundary condition. Is this because of viscous dissipation which adds to the temperature or is this simply a wrong result? I am not using Boussinesq approximation in the code.
#Convection
#Thermal_Convection
#Heat_Transfer
#Viscous_Disspation
#Numerical_Methods
#Computational Fluid Dynamics
As a first approximation the power dissipated is equal to P=dP*Q with P the dissipated power, dP the pressure drop between inlet and outlet and Q the volumetric flow rate.
If one ignores heat exchange with the surroundings, then the amount of temperature increase due to viscous dissipation should be equal to dT=P/(m*Cp). Here dT is the flow averaged temperature increase between the inlet and the outlet, m the mass flow rate and Cp the specific heat.
You can check if this estimation gives the same order of magnitude of heating as your simulation and draw conclusions from there.
Leander Boer your explanation is precisely correct. However, I am dealing with a case where the flow is taking place inside a pipeline and because of its complex rheology, the temperature at certain parts of the domain seems to be going around 5% higher than the range set at the initial condition. I am trying to transport a complex fluid - kind of gel from inside the pipeline. Definitely, viscous dissipation will be an issue but I am not sure regarding its proportionate contribution in the elevation of temperature. I am not aware of any experimental study which actually has shown this kind of elevation. I am not sure if I am missing out on any other fundamentals. Till now what I could figure out is that my simulations are correct and this is the effect of viscous dissipation.
What about the BC.s? Then, you should supply some figures to understand your temperature profiles along the axis and check if there is presence of numerical wiggles.
But one more thing to take into account is that you are considering non-newtonian fluid and the chosen model can have influence.
Prof. Filippo Maria Denaro , can you elaborate on your statement, " But one more thing to take into account is that you are considering non-newtonian fluid and the chosen model can have influence."? Actually, I am using an Arrhenius type model to account for viscosity as a function of temperature and pressure. Otherwise, the numerical methodology is correct- I have validated my results with analytical/previous near-about numerical results with a thorough grid independence test.
I would ask if you consider the non-newtonian model. Could you plot viscosity and temperature along the direction normal to the wall for some stations?
However, you did not answer to my previous question, what about the BCs?
Prof. Filippo Maria Denaro , I am using an isothermal and no-slip condition at the cylindrical wall, Neumann's BC at the outlet and uniform flow and a uniform temperature (equivalent to the temperature at wall) at the inlet. I am using a time-dependent Non-Newtonian constitutive model to express gel degradation. I have noted the rise in temperature from the isothermal contours and that is where I noted a rise in temperature at the inlet. The viscosity for my work, is a function of temperature and shearing history.
Aniruddha Sanyal
In practice, you are using BCs that does not control the resulting heat flux. To get a solution having anergy equilibrium, the resulting heat flux (inflow + walls) must be in equilibrium with the Neumann condition for the temperature at the outlet.
The increasing of the temperature could be justified by this fact. Did you reach a steady solution? Have you tried to set adiabatic conditions at the walls?
Prof. Filippo Maria Denaro , yes, I could reach the steady-state solution. I did not try for adiabatic conditions. In fact, in the staggered grid, I have used the concept of "fictitious cells" or "ghost cells" at the boundaries in the finite-volume-based methodology used. However, I have taken care of the fact that " To get a solution having energy equilibrium, the resulting heat flux (inflow + walls) must be in equilibrium with the Neumann condition for the temperature at the outlet". I think the shearing action during the breakage of a gel (the non-Newtonian fluid) is responsible for the elevation of temperature- a kind of entropy (as a heat-generating source) may be due to viscous effects.
Good discussion and analysis. Did you check your grid (grid refinement study) and the fluid properties?
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