In the numerical simulation of a hydrocyclone (which consists of two parts: cylindrical and conical), using FORTRAN programm, without commercial software.

I am a tenderfoot, so at the beginning I choose a simple model: single, laminar-phase flow (without particles), in a axis equilibrium cylinder coordinate (using two-dimension to solve three-dimension-velocity: u, v, w). When I draw the streamline through Tecplot (Version 7.5). I find that the value of "f" (here "f" refers to the flux) near the inlet is negative.

I have taken boundary conditions, flux equilibrium, inlet and outlet conditions, etc into account, but in this model, I have not considered air column. And the calculation has reached to its convergence.

How can I explain it?

send me books on cfd

i m new student of cfd thanks

For clarification, I thought that TechPlot draws streaklines (traces of virtual particles) rather than streamlines. Check the TechPlot documentation to see if this is true in your version. Streamlines and streaklines should be very similar in shape for steady state flows if you have a mesh that resolves the flow well. To calculate streamlines in TechPlot, I used to evaluate the stream function on the computational mesh, then plotted contours of the stream function.

I don't understand the 'air column' comment, probably because I don't know a lot about cyclones. Just what 'flux' is negative and why is that not good?

Could explain the difference between "streamline" and "streekline" in detail? In terms of "air column", it is a special part of a hydrocyclone.

For a lot of detail, you'll need to consult a book on fluid mechanics with the emphasis on vector notation. This explanation will be illustrative but can be made mathematically rigorous.

This is limited to a two-dimensional cartesian coordinate system, although it carries easily into a two-dimensional axisymmetrical cylindrical system including rotating flows. Models cannot include sources or sinks of mass.

The incompressible stream function Q is a two-dimensional function [Q(x,y) or Q(r,z)] that satisfies the continuity equation identically for incompressible two-dimensional flows. The incompressible velocity field (u, v) is defined by u = Q_y and v = - Q_x, where Q_x is the partial derivitive of Q with respect to x.

For compressible STEADY STATE flows, the mass flux components rho*u = Q_y and rho*v = - Q_x satisfy the continuity equation identically where rho is the fluid density.

The velocity (or mass flux) vectors are everywhere tangent to lines of constant Q, making contour level plots of the stream function useful for visualizing a two-dimension flow field; the flow is between the lines of constant value of stream function.

If your flow is 3-dimensional, the two-dimensional function Q no longer exists. If a compressible 2-d flow field is not at steady state, Q does not exist.

Streak lines are generated by intregrating the velocity field to show the path that a massless particle would take through your flow field,

u = dx/dt --> x(t+dt) = x(t) + u*dt

v = dy/dt --> y(t+dt) = y(t) + v*dt

w = dw/dt --> w(t+dt) = w(t) + w*dt

Plotting x, y, z vs t shows the flow path of that 'particle', again aiding in visualizing the flow. Note that the streak lines can be generated from any velocity field, one, two or three-dimensional, transient or steady state. This is the calculation I think Tecplot performs.