User talk:Sidharth

FPROPS uses function pointers from the underlying correlation (helmholtz or Pengrob) to calculate fundamental quantities with Temperature and rho as the input. Following are those functions of fprops :-

1. fprops_p
2. fprops_u
3. fprops_h
4. fprops_s
5. fprops_a
6. fprops_g
7. fprops_P
8. fprops_dpdrho_T
9. fprops_alphap
10. fprops_betaP
11. fprops_cp
12. fprops_cv
13. fprops_w

Both the underlying correlations provide these 13 functions calculated from first principles, with T and <math>\rho</math> as inputs. So the TTSE implementation for a specific liquid and a specific correlation (H or P) should eventually generate tables for each of the above 13 entries. For the saturation function fprops_sat(), takes only 1 input (temperature) and returns saturated liquid density, saturated vapour density and the saturation pressure. This function involves solving equations iteratively and tabulation should speed up calculation on saturation curve.

To begin with we can tabulate the following functions:

1. helmholtz_p
2. helmholtz_s
3. helmholtz_u
4. helmholtz_g
5. helmholtz_h

In order to tabulate these routines we need new routines which complete the set of all partial derivatives we need:

For each of the above variable X (where X is either of P,s,u,g and h) we need <math> \frac{\partial X}{\partial T}\bigg|_{\rho} ,

\frac{\partial^2 X}{\partial T^2}\bigg|_{\rho} ,
   \frac{\partial X}{\partial \rho}\bigg|_{T} , 
\frac{\partial^2 X}{\partial \rho^2}\bigg|_{T}</math>   and <math>
  \frac{\partial^2 X}{\partial \rho \partial T} </math>

Many of the partial derivatives are already listed in helmholtz.c. Specifically the new ones we need to implement are:

Partial second derivatives of Pressure p

1. helmholtz_d2pdT2_rho() -- <math>\frac{\partial^2 p}{\partial T ^2}\bigg|_{\rho}</math>
2. helmholtz_d2pdrhodT() -- <math>\frac{\partial^2 p}{\partial (T \rho)} </math>

Partial second derivatives of enthalpy h

1. helmholtz_d2hdrho2_T() -- <math>\frac{\partial^2 h}{\partial \rho^2}\bigg|_{T}</math>
2. helmholtz_d2hdT2_rho() -- <math>\frac{\partial^2 h}{\partial T ^2}\bigg|_{\rho}</math>
3. helmholtz_d2hdrhodT() -- <math>\frac{\partial^2 h}{\partial (T \rho)} </math>

Partial second derivatives of internal energy u

1. helmholtz_d2udrho2_T() -- <math>\frac{\partial^2 u}{\partial \rho^2}\bigg|_{T}</math>
2. helmholtz_d2udT2_rho() -- <math>\frac{\partial^2 u}{\partial T^2}\bigg|_{\rho }</math>
3. helmholtz_d2udrhodT() -- <math>\frac{\partial^2 u}{\partial (T \rho)}</math>

Partial first and second derivatives of entropy s

1. helmholtz_dsdT_rho() -- <math>\frac{\partial s}{\partial T}\bigg|_{\rho}</math>
2. helmholtz_dsdrho_T() -- <math>\frac{\partial s}{\partial \rho}\bigg|_{T}</math>
3. helmholtz_d2sdrho2_T() -- <math>\frac{\partial^2 s}{\partial \rho^2}\bigg|_{T}</math>
4. helmholtz_d2sdT2_rho() -- <math>\frac{\partial^2 s}{\partial T^2}\bigg|_{\rho}</math>
5. helmholtz_d2sdrhodT() -- <math>\frac{\partial^2 s}{\partial (T \rho)}</math>

Partial first and second derivatives of gibbs energy g

1. helmholtz_dgdT_rho() -- <math>\frac{\partial g}{\partial T}\bigg|_{\rho}</math>
2. helmholtz_dgdrho_T() -- <math>\frac{\partial g}{\partial \rho}\bigg|_{T}</math>
3. helmholtz_d2gdrho2_T() -- <math>\frac{\partial^2 g}{\partial \rho^2}\bigg|_{T}</math>
4. helmholtz_d2gdT2_rho() -- <math>\frac{\partial^2 g}{\partial T^2}\bigg|_{\rho}</math>
5. helmholtz_d2gdrhodT() -- <math>\frac{\partial^2 g}{\partial (T \rho)}</math>