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 Rafal November 27, 2006 07:41

continuity equation

The problem to solve is temperature and gas composition which flows through porous solid phase. As the solid phase heats up it becomes a source of gaseous substances which pass to gas phase, and there chemical reaction occurs. The task is one dimensional.

I have formulated a set of equation which consists of energy ones (for solid and gas phase) and conservation of chemical species (for gas composition).

The problem is how to calculate gas velocity. In my case I assume constant pressure (it plays no important role) and gas velocity depends on gas sources (which cause growth of mass of gas, i.e. stream in kg/m2s) and temperature.

To solve my set of equation I use method described by S.V Patankar in "Numerical Heat Transfer And Fluid Flow". To obtain gas velocity I should use continuity equation (mass conservation equation). The problem is that this equation (2.14 p. 16 in this book) does not fit to the standard form (2.15), because the first term does not contain dependent variable Fi.

The problems are:

1. What stands for Fi in this equation (2.16), and can it be solved using the same algorithm as in case of the standard equation?

2. Maybe this mass conservation equation is a sum of all equations of conservation of chemical species, like Eq. 2.2, thus Fi is sum of all mass parts (so Fi0 = 1), Gamma = 0 (since assumption is made that velocity does not depend on gas viscosity, or Gamma is gas viscosity if it does), and S is sum of all sources of chemical substances which evolves from solid fraction. In this approach Fi is dimensionless, and gas stream is multiplied by Fi resulting from this equation.

3. If point 2 is right, then new gas stream might be obtained, and then velocity may be calculated using gas density, which include gas temperature, as it should be.

4. Or maybe I should use momentum equation (2.11), but in this case what denotes u (in italics) and u (in bold). Is it dimensionless velocity component, and velocity respectively. And then how include mass source in this equation? (Mass source is in kg/m3s, and all terms in this equation are in kg/m2s2)

Any comments would be very useful for me.

 F.B.Tian November 28, 2006 21:00

Re: continuity equation

I just ask u a question:if the pressure is const,how can u driven the flow?

 Rafal November 29, 2006 03:58

Re: continuity equation

I define gas stream as an initial condition (inflow to porous solid phase), and because its amount grows (by gas evolving from solid phase) I need to calculate gas velocity (it also changes with gas temperature).

Flow is driven by gas stream, and influence of pressure in this case may be neglected. I do not use SIMPLE algorithm, but I treat all my equations as an unsteady convection-diffusion ones with source, and I solve them using method described by Patankar up to chapter 5 in his book.

At the beginning of section 6.4 he writes, that when pressure field is given (in my case it is constant, so dp/dx = 0 in momentum equation 2.11), then momentum equation may be solved using method completed in chapter 5.

 F.B.Tian November 29, 2006 09:46

Re: continuity equation

1.Fi in this equation (2.16) or Fi in this equation (2.15)?equation (2.13) may help u. "can it be solved using the same algorithm as in case of the standard equation? ",my answer is yes. 2. 3. 4.

 Rafal November 29, 2006 10:27

Re: continuity equation

I have procedure for solving this kind of equation, so what should I substitute for Fi and S in continuity eq. 2.16?

I suppose, that the right side of this equation is not equals 0, because new gas is generated, so this right side equals S.

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