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theory_vc.m
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function ustar = theory_vc(model,mode,parameters)
ustar = -1;
k = 1;
pass = 0;
% ustep = .0001;
% us = -ustep;
tolerance = 1e-15;
us = 1;
ustep = 1;
% if ~isfield(parameters,'assumption')
% parameters.assumption.nldrag = 0;
% parameters.assumption.liftforce = 0;
% parameters.assumption.gravityforce = 0;
% else
% if ~isfield(parameters.assumption,'nldrag')
% parameters.assumption.nldrag = 0;
% end %if
% if ~isfield(parameters.assumption,'liftforce')
% parameters.assumption.liftforce = 0;
% end %if
% if ~isfield(parameters.assumption,'gravityforce')
% parameters.assumption.gravityforce = 0;
% end %if
% end %if
switch model
% -------------------------------------------------------------------------
% ******************************** Rolling ********************************
% -------------------------------------------------------------------------
% *********** Rolling - Smooth - Sublayer ***************
case 'TPL-Rolling-Sublayer-Smooth'
switch mode
case 'Detached moment'
parameters.a = theory_cradius('TPL',parameters);
parameters.Fpo = theory_pulloff('TPL',parameters);
Mr = theory_rmoment('Detached moment-Smooth',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Sublayer-Smooth',parameters);
parameters.Fl = theory_lift('Saffman-Sublayer-Smooth',parameters);
parameters.M = theory_momentp('Sublayer-Smooth',parameters);
Mh = theory_hmoment('Smooth',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
% if (Mh >= Mr)
% k = 0;
% ustar = us;
% return
% end %if
end %while
end %switch mode
case 'JKR-Rolling-Sublayer-Smooth'
switch mode
case 'Detached moment'
parameters.a = theory_cradius('JKR',parameters);
parameters.Fpo = theory_pulloff('JKR',parameters);
Mr = theory_rmoment('Detached moment-Smooth',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Sublayer-Smooth',parameters);
if (parameters.assumption.nldrag == 1)
parameters.Fd = theory_drag('Nonlinear-Sublayer',parameters);
end %if
if (parameters.assumption.liftforce == 1)
parameters.Fl = theory_lift('Saffman-Sublayer-Smooth',parameters);
else
parameters.Fl = 0;
end %if
parameters.M = theory_momentp('Sublayer-Smooth',parameters);
Mh = theory_hmoment('Smooth',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
% if (Mh >= Mr)
% k = 0;
% ustar = us;
% return
% end %if
end %while
case 'Max moment'
parameters.a = theory_cradius('JKR-Mmax',parameters);
Mr = theory_rmoment('MmaxJKR-Smooth',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Sublayer-Smooth',parameters);
if (parameters.assumption.nldrag == 1)
parameters.Fd = theory_drag('Nonlinear-Sublayer',parameters);
end %if
if (parameters.assumption.liftforce == 1)
parameters.Fl = theory_lift('Saffman-Sublayer-Smooth',parameters);
else
parameters.Fl = 0;
end %if
parameters.M = theory_momentp('Sublayer-Smooth',parameters);
Mh = theory_hmoment('Smooth',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
% if (Mh >= Mr)
% k = 0;
% ustar = us;
% return
% end %if
end %while
end %switch mode
case 'DMT-Rolling-Sublayer-Smooth'
switch mode
case 'Max moment'
parameters.a = theory_cradius('DMT-Mmax',parameters);
Mr = theory_rmoment('MmaxDMT-Smooth',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Sublayer-Smooth',parameters);
if (parameters.assumption.nldrag == 1)
parameters.Fd = theory_drag('Nonlinear-Sublayer',parameters);
end %if
if (parameters.assumption.liftforce == 1)
parameters.Fl = theory_lift('Saffman-Sublayer-Smooth',parameters);
else
parameters.Fl = 0;
end %if
parameters.M = theory_momentp('Sublayer-Smooth',parameters);
Mh = theory_hmoment('Smooth',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
% if (Mh >= Mr)
% k = 0;
% ustar = us;
% return
% end %if
end %while
end %switch
%*********** Rolling - Smooth - Burst/Inrush ***********
case 'TPL-Rolling-Burst-Smooth'
parameters.a = theory_cradius('TPL',parameters);
parameters.Fpo = theory_pulloff('TPL',parameters);
switch mode
case 'Detached moment'
Mr = theory_rmoment('Detached moment-Smooth',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Burst-Smooth',parameters);
if (parameters.assumption.nldrag == 1)
parameters.Fd = theory_drag('Nonlinear-Burst',parameters);
end %if
parameters.Fl = theory_lift('Saffman-Burst-Smooth',parameters);
parameters.M = theory_momentp('Burst-Smooth',parameters);
Mh = theory_hmoment('Smooth',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
% if (Mh >= Mr)
% k = 0;
% ustar = us;
% return
% end %if
end %while
end %switch
case 'JKR-Rolling-Burst-Smooth'
switch mode
case 'Detached moment'
parameters.a = theory_cradius('JKR',parameters);
parameters.Fpo = theory_pulloff('JKR',parameters);
Mr = theory_rmoment('Detached moment-Smooth',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Burst-Smooth',parameters);
if (parameters.assumption.nldrag == 1)
% disp ('nonlinear')
parameters.Fd = theory_drag('Nonlinear-Burst',parameters);
end %if
if (parameters.assumption.liftforce == 1)
parameters.Fl = theory_lift('Saffman-Burst-Smooth',parameters);
else
parameters.Fl = 0;
end %if
parameters.M = theory_momentp('Burst-Smooth',parameters);
Mh = theory_hmoment('Smooth',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
% if (Mh >= Mr)
% k = 0;
% ustar = us;
% return
% end %if
end %while
case 'Max moment'
parameters.a = theory_cradius('JKR-Mmax',parameters);
Mr = theory_rmoment('MmaxJKR-Smooth',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Burst-Smooth',parameters);
if (parameters.assumption.nldrag == 1)
parameters.Fd = theory_drag('Nonlinear-Burst',parameters);
end %if
if (parameters.assumption.liftforce == 1)
parameters.Fl = theory_lift('Saffman-Burst-Smooth',parameters);
else
parameters.Fl = 0;
end %if
parameters.M = theory_momentp('Burst-Smooth',parameters);
Mh = theory_hmoment('Smooth',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
% if (Mh >= Mr)
% k = 0;
% ustar = us;
% return
% end %if
end %while
end %switch
case 'DMT-Rolling-Burst-Smooth'
switch mode
case 'Max moment'
parameters.a = theory_cradius('DMT-Mmax',parameters);
Mr = theory_rmoment('MmaxDMT-Smooth',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Burst-Smooth',parameters);
if (parameters.assumption.nldrag == 1)
parameters.Fd = theory_drag('Nonlinear-Burst',parameters);
end %if
if (parameters.assumption.liftforce == 1)
parameters.Fl = theory_lift('Saffman-Burst-Smooth',parameters);
else
parameters.Fl = 0;
end %if
parameters.M = theory_momentp('Burst-Smooth',parameters);
Mh = theory_hmoment('Smooth',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
% if (Mh >= Mr)
% k = 0;
% ustar = us;
% return
% end %if
end %while
end %switch
% ______________________________________
% ------------ Rolling - Rough --------
% ______________________________________
%********* Rolling - Rough - Sublayer ********
case 'JKR-Rolling-Sublayer-Rough'
Dp = parameters.Dp;
beta = parameters.betap * Dp;
Deltac = parameters.Deltac;
switch mode
case 'Detached moment'
parameters.fpo = theory_pulloff('JKR-asperity',parameters);
deltac = ((parameters.fpo)^2/(3*(parameters.K)^2*beta))^(1/3);
sigma = deltac/Deltac;
parameters.sigma = sigma;
parameters.H0 = 0;
parameters.L = theory_rough_L(0,parameters);
N = .1/(sigma*beta);
parameters.N = N;
parameters.a = theory_cradius('JKR-Rough',parameters);
parameters.FM = theory_pulloff('JKR-Rough',parameters);
Mr = theory_rmoment('Detached moment-Rough',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Sublayer-Rough',parameters);
if (parameters.assumption.nldrag == 1)
parameters.Fd = theory_drag('Nonlinear-Sublayer',parameters);
end %if
parameters.Fl = theory_lift('Saffman-Sublayer-Rough',parameters);
parameters.M = theory_momentp('Sublayer-Rough',parameters);
Mh = theory_hmoment('Rough',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
% if (Mh >= Mr)
% k = 0;
% ustar = us;
% return
% end %if
end %while
end %switch
%*********** Rolling - Rough - Burst ************
case 'JKR-Rolling-Burst-Rough'
Dp = parameters.Dp;
beta = parameters.betap * Dp;
Deltac = parameters.Deltac;
switch mode
case 'Detached moment'
parameters.fpo = theory_pulloff('JKR-asperity',parameters);
deltac = ((parameters.fpo)^2/(3*(parameters.K)^2*beta))^(1/3);
sigma = deltac/Deltac;
parameters.sigma = sigma;
parameters.H0 = 0;
parameters.L = theory_rough_L(0,parameters);
N = .1/(sigma*beta);
parameters.N = N;
parameters.a = theory_cradius('JKR-Rough',parameters);
parameters.FM = theory_pulloff('JKR-Rough',parameters);
Mr = theory_rmoment('Detached moment-Rough',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Burst-Rough',parameters);
if (parameters.assumption.nldrag == 1)
parameters.Fd = theory_drag('Nonlinear-Burst',parameters);
end %if
parameters.Fl = theory_lift('Saffman-Burst-Rough',parameters);
parameters.M = theory_momentp('Burst-Rough',parameters);
Mh = theory_hmoment('Rough',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
% if (Mh >= Mr)
% k = 0;
% ustar = us;
% return
% end %if
end %while
case 'Burst-(Iman)'
parameters.L = theory_rough_L(0,parameters);
parameters.a = theory_cradius('JKR-Rough-Iman',parameters);
parameters.FM = theory_pulloff('JKR-Rough-Iman',parameters);
Mr = theory_rmoment('Detached moment-Rough',parameters);
while (k == 1)
us = us + ustep;
parameters.ustar = us;
parameters.Fd = theory_drag('Stokes-Burst-Rough',parameters);
if (parameters.assumption.nldrag == 1)
parameters.Fd = theory_drag('Nonlinear-Burst',parameters);
end %if
parameters.Fl = theory_lift('Saffman-Burst-Rough',parameters);
parameters.M = theory_momentp('Burst-Rough',parameters);
Mh = theory_hmoment('Rough',parameters);
if ((Mh > Mr) && (ustep > 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if ((Mh < Mr) && (ustep < 0))
ustep = -ustep / 2;
pass = pass + 1;
end %if
if (abs((Mr-Mh)/Mr) <= tolerance)
ustar = us;
k = 0;
return
end %if
end %while
end %switch
% -------------------------------------------------------------------------
% ******************************** Sliding ********************************
% -------------------------------------------------------------------------
% ______________________________________
% -------------Sliding - Smooth --------
% ______________________________________
%********* Sliding - Smooth - Sublayer **********
case 'TPL-Sliding-Sublayer-Smooth'
parameters.Fpo = theory_pulloff('TPL',parameters);
mus = parameters.mus;
switch mode
case 'With lift/gravitational forces'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fd = theory_drag('Stokes-Sublayer-Smooth',parameters);
Fl = theory_lift('Saffman-Sublayer-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('With lift/gravitational forces',parameters);
if (Fd >= mus*Fn)
k = 0;
ustar = us;
return
end %if
end %while
end %switch
case 'JKR-Sliding-Sublayer-Smooth'
parameters.Fpo = theory_pulloff('JKR',parameters);
mus = parameters.mus;
switch mode
case 'With lift/gravitational forces'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fd = theory_drag('Stokes-Sublayer-Smooth',parameters);
Fl = theory_lift('Saffman-Sublayer-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('With lift/gravitational forces',parameters);
if (Fd >= mus*Fn)
k = 0;
ustar = us;
return
end %if
end %while
case 'No gravitational force'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fd = theory_drag('Stokes-Sublayer-Smooth',parameters);
Fl = theory_lift('Saffman-Sublayer-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('No gravitational force',parameters);
if (Fd >= mus*Fn)
k = 0;
ustar = us;
return
end %if
end %while
case 'No lift/gravitational forces'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fd = theory_drag('Stokes-Sublayer-Smooth',parameters);
Fl = theory_lift('Saffman-Sublayer-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('No lift/gravitational forces',parameters);
if (Fd >= mus*Fn)
k = 0;
ustar = us;
return
end %if
end %while
end %switch
%************ Sliding - Smooth - Burst/Inrush **********
case 'TPL-Sliding-Burst-Smooth'
parameters.Fpo = theory_pulloff('TPL',parameters);
mus = parameters.mus;
switch mode
case 'With lift/gravitational forces'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fd = theory_drag('Stokes-Burst-Smooth',parameters);
Fl = theory_lift('Saffman-Burst-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('With lift/gravitational forces',parameters);
if (Fd >= mus*Fn)
k = 0;
ustar = us;
return
end %if
end %while
end %switch
case 'JKR-Sliding-Burst-Smooth'
parameters.Fpo = theory_pulloff('JKR',parameters);
mus = parameters.mus;
switch mode
case 'With lift/gravitational forces'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fd = theory_drag('Stokes-Burst-Smooth',parameters);
Fl = theory_lift('Saffman-Burst-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('With lift/gravitational forces',parameters);
if (Fd >= mus*Fn)
k = 0;
ustar = us;
return
end %if
end %while
case 'No gravitational force'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fd = theory_drag('Stokes-Burst-Smooth',parameters);
Fl = theory_lift('Saffman-Burst-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('No gravitational force',parameters);
if (Fd >= mus*Fn)
k = 0;
ustar = us;
return
end %if
end %while
case 'No lift/gravitational forces'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fd = theory_drag('Stokes-Burst-Smooth',parameters);
Fl = theory_lift('Saffman-Burst-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('No lift/gravitational forces',parameters);
if (Fd >= mus*Fn)
k = 0;
ustar = us;
return
end %if
end %while
end %switch
% ______________________________________
% ----------- Sliding - Rough ----------
% ______________________________________
%********* Sliding - Rough - Sublayer *********
case 'JKR-Sliding-Sublayer-Rough'
Dp = parameters.Dp;
beta = parameters.betap * Dp;
Deltac = parameters.Deltac;
parameters.fpo = theory_pulloff('JKR-asperity',parameters);
deltac = ((parameters.fpo)^2/(3*(parameters.K)^2*beta))^(1/3);
sigma = deltac/Deltac;
parameters.sigma = sigma;
parameters.H0 = 0;
parameters.L = theory_rough_L(0,parameters);
N = .1/(sigma*beta);
parameters.N = N;
parameters.a = theory_cradius('JKR-Rough',parameters);
parameters.FM = theory_pulloff('JKR-Rough',parameters);
parameters.Fpo = parameters.FM;
mus = parameters.mus;
switch mode
case 'With lift/gravitational forces'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fd = theory_drag('Stokes-Sublayer-Rough',parameters);
Fl = theory_lift('Saffman-Sublayer-Rough',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('With lift/gravitational forces',parameters);
if (Fd >= mus*Fn)
k = 0;
ustar = us;
return
end %if
end %while
end %switch
%********* Sliding - Rough - Burst ***************
case 'JKR-Sliding-Burst-Rough'
Dp = parameters.Dp;
beta = parameters.betap * Dp;
Deltac = parameters.Deltac;
parameters.fpo = theory_pulloff('JKR-asperity',parameters);
deltac = ((parameters.fpo)^2/(3*(parameters.K)^2*beta))^(1/3);
sigma = deltac/Deltac;
parameters.sigma = sigma;
parameters.H0 = 0;
parameters.L = theory_rough_L(0,parameters);
N = .1/(sigma*beta);
parameters.N = N;
parameters.a = theory_cradius('JKR-Rough',parameters);
parameters.FM = theory_pulloff('JKR-Rough',parameters);
parameters.Fpo = parameters.FM;
mus = parameters.mus;
switch mode
case 'With lift/gravitational forces'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fd = theory_drag('Stokes-Burst-Rough',parameters);
Fl = theory_lift('Saffman-Burst-Rough',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('With lift/gravitational forces',parameters);
if (Fd >= mus*Fn)
k = 0;
ustar = us;
return
end %if
end %while
end %switch
% -------------------------------------------------------------------------
% ******************************** Lifting ********************************
% -------------------------------------------------------------------------
%********** Lifting - Smooth - Sublayer ********
case 'TPL-Lifting-Sublayer-Smooth'
parameters.Fpo = theory_pulloff('TPL',parameters);
switch mode
case 'With gravitational force'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fl = theory_lift('Saffman-Sublayer-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('With lift/gravitational forces',parameters);
if (Fn <= 0)
k = 0;
ustar = us;
return
end %if
end %while
end %switch
case 'JKR-Lifting-Sublayer-Smooth'
parameters.Fpo = theory_pulloff('JKR',parameters);
switch mode
case 'With gravitational force'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fl = theory_lift('Saffman-Sublayer-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('With lift/gravitational forces',parameters);
if (Fn <= 0)
k = 0;
ustar = us;
return
end %if
end %while
end %switch
%*********** Lifting - Smooth - Burst/Inrush *********
case 'TPL-Lifting-Burst-Smooth'
parameters.Fpo = theory_pulloff('TPL',parameters);
switch mode
case 'With gravitational force'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fl = theory_lift('Saffman-Burst-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('With lift/gravitational forces',parameters);
if (Fn <= 0)
k = 0;
ustar = us;
return
end %if
end %while
end %switch
case 'JKR-Lifting-Burst-Smooth'
parameters.Fpo = theory_pulloff('JKR',parameters);
switch mode
case 'With gravitational force'
while (k == 1)
us = us + ustep;
parameters.ustar = us;
Fl = theory_lift('Saffman-Burst-Smooth',parameters);
parameters.Fl = Fl;
Fn = theory_normalforce('With lift/gravitational forces',parameters);
if (Fn <= 0)
k = 0;
ustar = us;
return
end %if
end %while
end %switch
%********** Lifting - Rough - Burst ************
end %switch model