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Flux.cpp
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Flux.cpp
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/*******************************************************************************************************
* Copyright 2017 Alliance for Sustainable Energy, LLC
*
* NOTICE: This software was developed at least in part by Alliance for Sustainable Energy, LLC
* (“Alliance”) under Contract No. DE-AC36-08GO28308 with the U.S. Department of Energy and the U.S.
* The Government retains for itself and others acting on its behalf a nonexclusive, paid-up,
* irrevocable worldwide license in the software to reproduce, prepare derivative works, distribute
* copies to the public, perform publicly and display publicly, and to permit others to do so.
*
* Redistribution and use in source and binary forms, with or without modification, are permitted
* provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, the above government
* rights notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice, the above government
* rights notice, this list of conditions and the following disclaimer in the documentation and/or
* other materials provided with the distribution.
*
* 3. The entire corresponding source code of any redistribution, with or without modification, by a
* research entity, including but not limited to any contracting manager/operator of a United States
* National Laboratory, any institution of higher learning, and any non-profit organization, must be
* made publicly available under this license for as long as the redistribution is made available by
* the research entity.
*
* 4. Redistribution of this software, without modification, must refer to the software by the same
* designation. Redistribution of a modified version of this software (i) may not refer to the modified
* version by the same designation, or by any confusingly similar designation, and (ii) must refer to
* the underlying software originally provided by Alliance as “System Advisor Model” or “SAM”. Except
* to comply with the foregoing, the terms “System Advisor Model”, “SAM”, or any confusingly similar
* designation may not be used to refer to any modified version of this software or any modified
* version of the underlying software originally provided by Alliance without the prior written consent
* of Alliance.
*
* 5. The name of the copyright holder, contributors, the United States Government, the United States
* Department of Energy, or any of their employees may not be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
* FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER,
* CONTRIBUTORS, UNITED STATES GOVERNMENT OR UNITED STATES DEPARTMENT OF ENERGY, NOR ANY OF THEIR
* EMPLOYEES, BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER
* IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
* THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*******************************************************************************************************/
#include "Flux.h"
#include "math.h"
#include "Toolbox.h"
#include "Heliostat.h"
#include "Ambient.h"
#include "Receiver.h"
#include "SolarField.h"
#include "Land.h"
//#include <vector>
#include <iostream>
#include <algorithm>
#include <iostream>
#include <fstream>
using namespace std;
using namespace Toolbox;
/*
Note:
Several algorithms in this class are based on the Hermite expansion technique for characterizing
Gaussian flux distributions which was developed by Dellin, Walzel, Lipps, et al, and implemented
in DELSOL3. These algorithms are publicly available through the following publications:
[1] T. A. Dellin, “An improved Hermite expansion calculation of the flux distribution from
heliostats,” Sandia National Laboratory, Livermore, CA, 1979. SAND79-8619.
[2] M. D. Walzel, F. W. Lipps, and Vant-Hull, “A solar flux density calculation for a solar
tower concentrator using a two-dimensional Hermite function expansion,” Solar Energy,
vol. 19, pp. 239–256, 1977.
[3] B. L. Kistler, “A user’s manual for DELSOL3: A computer code for calculating the optical
performance and optimal system design for solar thermal central receiver plants,” Sandia
National Laboratory, Albuquerque, NM, 1986. SAND86-8018.
*/
// ----------------- random class -------------
Random::Random()
{
srand( (unsigned int)time( (time_t*)NULL) ); //Seed with time on init
rmax = RAND_MAX;
}
double Random::uniform()
{
return double( rand() )/double(rmax);
}
double Random::triangular()
{
return pow(uniform(), .5); //1.0 is more likely, 0.0 is less likely
}
double Random::normal(double stddev)
{
//Sample from normal distribution - recursive call
//Distribution mean is 0., half-tail is positive
double
u = uniform()*2. - 1.,
v = uniform()*2. - 1.,
r = u*u + v*v;
if(r == 0 || r > 1) return normal(stddev);
double c = sqrt(-2 * log(r)/r);
return u*c*stddev;
}
double Random::sign()
{
return uniform()<.5 ? -1. : 1.;
}
int Random::integer(int min, int max)
{
return int(floor(uniform()*(max-min)));
}
//--------------------------------------------
Random *Flux::getRandomObject(){return _random; }
//Constructor
Flux::Flux(){
_random = new Random();
_jmin = 0;
_jmax = 0;
};
Flux::~Flux(){
delete _random;
if( _jmin != 0 ) delete[] _jmin;
if( _jmax != 0 ) delete[] _jmax;
};
//Copy constructor
Flux::Flux(Flux &f) :
_hermitePoly(f._hermitePoly),
_fact_odds(f._fact_odds),
_fact_d(f._fact_d),
_binomials(f._binomials),
_binomials_hxn(f._binomials_hxn),
_mu_SN(f._mu_SN),
_mu_GN(f._mu_GN),
_n_order(f._n_order),
_n_terms(f._n_terms),
pi(f.pi),
Pi(f.Pi)
{
//Create a new random object
//if(_random != (Random*)NULL) delete _random;
_random = new Random();
for(int i=0; i<4; i++)
_ci[i] = f._ci[i];
for(int i=0; i<16; i++){
_ag[i] = f._ag[i];
_xg[i] = f._xg[i];
_jmax = new int[_n_terms];
_jmin = new int[_n_terms];
for(int i=0; i<_n_terms; i++){
_jmax[i] = f._jmax[i];
_jmin[i] = f._jmin[i];
}
}
};
void Flux::Setup()
{
_n_order = 6;
_n_terms = 7;
//Pi
pi = 4.*atan(1.); Pi = pi;
//Calculate the array of factorial terms in the Hermite expansion
factOdds();
_fact_d.resize(_n_terms*2);
for(int i=0;i<_n_terms*2; i++){_fact_d.at(i) = factorial_d(i);}
Binomials();
Binomials_hxn();
//set up coefficient weighting arrays for Hermite integral
double cit[] = {.196584,.115194,.000344,.019527};
double agt[] = {.02715246, .06225352, .09515851, .12462897,
.14959599, .16915652, .18260341, .18945061,
.14959599, .16915652, .18260341, .18945061,
.02715246, .06225352, .09515851, .12462897};
double xgt[] = {.98940093, .94457502, .86563120, .75540441,
.61787624, .45801678, .28160355, .09501251,
-.61787624,-.45801678,-.28160355,-.09501251,
-.98940093,-.94457502,-.86563120,-.75540441};
for(int i=0; i<4; i++)
_ci[i] = cit[i];
for(int i=0; i<16; i++){
_ag[i] = agt[i];
_xg[i] = xgt[i];
}
//Create jmin and jmax arrays
_jmin = new int[_n_terms];
_jmax = new int[_n_terms];
for(int i=0; i<_n_terms; i++){
_jmin[i] = i%2+1;
_jmax[i] = _n_terms - i;
}
}
void Flux::factOdds(){
//Calculate the factorial values for the odd terms in the hermite expansion
int i;
//factorial of odds.. 1*3*5... etc
_fact_odds.resize_fill(_n_terms*2, 0.0);
_fact_odds[1] = 1.; //first value is 1
i=0;
for (i=3; i<_n_terms*2; i=i+2) {
_fact_odds[i] = _fact_odds[i-2]*double(i);
}
//Return
return;
}
int Flux::JMN(int i){
//Frequently used bounds calculation
//Treat as an array, should return [1,2,1,2,1,2]...
//return i%2+1;
return _jmin[i];
}
int Flux::JMX(int i){
//Frequently used bounds calculation
//Treat JMX like an array for conventions to match DELSOL. i.e. where in DELSOL we would call JMX(1) and
//expect to get back 7, here we call JMX(0) and get back 7.
//return _n_terms - i;
return _jmax[i];
}
int Flux::IMN(int i){
//Frequently used bounds calculation
//return JMN(i);
return _jmin[i];
}
void Flux::Binomials(){
_binomials.resize_fill(_n_terms,_n_terms,0.0);
//Calculate the binomial coefficients
for(int i=1; i<_n_terms+1; i++){
for(int j=1; j<i+1; j++){
_binomials.at(i-1,j-1) = _fact_d.at(i-1)/_fact_d.at(j-1)/_fact_d.at(i-j);
}
}
}
void Flux::Binomials_hxn(){
/*
Calculation of "binomial coefficients" (different from previously calculated array) assigned
to the array HXN, DELSOL lines 741-754.
I don't know where this comes from mathematically.
*/
_binomials_hxn.resize_fill(_n_terms,_n_terms,0.0);
_binomials_hxn.at(0,0) = 1.;
_binomials_hxn.at(1,1) = 1.;
int i,j;
double fi;
for(i=3;i<_n_terms+1;i++){
fi = float(i-2);
_binomials_hxn.at(i-1,0) = -fi*_binomials_hxn.at(i-3,0);
for(j=2; j<_n_terms+1; j++){
_binomials_hxn.at(i-1,j-1) = _binomials_hxn.at(i-2,j-2) - fi*_binomials_hxn.at(i-3,j-1);
}
}
}
matrix_t<double> Flux::hermitePoly( double x) {
//THIS ISN"T USED
/*Evaluate the set of Hermite polynomials described by
H_n(x)=SUM_(p=0)^(n){h_p^n*x^n}
Where the only non-zero h_p^n are those for which p+n=even
This method is used to calculate the polynomial coefficients for the Hermite series, given a slant range
'x' and desired order of the equation. DELSOL3 recommends N_order=6 (or 7 polynomial terms).
*/
//Evaluate the polynomial equations
matrix_t<double> hermitePoly(1,_n_terms+1,0.0);
//for (int i=0; i<N_order+1; i+=1) {_hermitePoly.push_back(0.); }
hermitePoly[0] = 1.;
hermitePoly[1] = x; //Need to set H0 and H1
for(int n=1; n<_n_terms+1; n++) {
hermitePoly[n+1] = x*hermitePoly[n] - double(n)*hermitePoly[n-1];
}
/*
Equations:
H[0]=1.
H[1]=x
H[2]=x**2-1.
H[3]=x**3-3*x
H[4]=x**4-6*x**2+3
H[5]=x**5-10*x**3+15*x
H[6]=x**6-15*x**4+45*x**2-15.
*/
return hermitePoly;
}
void Flux::initHermiteCoefs(var_map &V){
/*
Fills out the constant coefficients that don't change during the simulation
*/
//Sun shape
hermiteSunCoefs(V, _mu_SN);
//Error distribution coefficients
hermiteErrDistCoefs(_mu_GN);
return;
}
void Flux::hermiteSunCoefs(var_map &V, matrix_t<double> &mSun) {
/*
###############################################################################################
-------WHEN TO CALL------
Call this subroutine once to determine the sunshape coefficients. The coefficients do not
currently depend on solar position, time of day, weather, etc. These coefficients will be used
in the subroutine "imagePlaneIntercept" to determine the moments of sunshape.
---INFORMATION REQUIRED--
* Requires the sunshape model type -> Ambient
* the _fact_odds array must have been calculated
* for a user-specified sunshape, the sunshape array must be filled out -> Ambient.getUserSun()
---------OUTPUT----------
Fills out the "mSun" (NxN) array
###############################################################################################
This function calculates the coefficients of sunshape distribution. The moments are used
in the analytical Hermite polynomial formulation. Each sunshape moment
is of form [Dellin, 1979]:
mu_S_(i,j) = (1/(i+j+2) - 0.5138/(i+j+6))/(1/2 - .5138/6) * (i!!*j!!/((i+j)/2)!)*2^((i+j)/2)r_0^(i+j)
where r_0 = (4.65e-3 mrad) * (slant range)
The sun-shape can take one of several forms. The limb-darkening expres-
sion is given by [Dellin, 1979]:
S(r) = 1 - .5138 * (r/r_0)^4
where 'r' is the radius about the aim poing in the image plane,
and r_0 is given above. The r_0 value is not actually applied in this
algorithm.
Other options for sunshape include point-source (model=0), square-wave
sun (model=2), or user-defined sunshape (model=3).
For the user-defined sunshape, the user must provide a 2-D array of
sun intensity and corresponding angular deviation from the center of the
solar disc.
suntype = [[angle0, intens0], [angle1, intens1] ...]
Otherwise, sunshape can be declared using:
suntype = <option number>
Default sunshape is limb-darkened (option 1)
*/
double factdum1, factdum2, dfact;
//--Arrays and values used later
if(mSun.ncols() != static_cast<size_t>(_n_terms) ||
mSun.nrows() != static_cast<size_t>(_n_terms)) {
mSun.resize_fill(_n_terms, _n_terms, 0.0);
}
//Get the sun type from the ambient settings
int suntype = V.amb.sun_type.mapval(); //A.getSunType();
double sun_rad_limit = V.amb.sun_rad_limit.val; //A.getSunRadLimit();
//Select a suntype case here
switch(suntype) {
//case 0:
case var_ambient::SUN_TYPE::POINT_SUN:
//---Point of sun unit intensity---
for (int i=1; i<_n_terms+1; i+=2) { //iterate 'i' from 1 to N_order by 2
int jmax = _n_terms-i+1; //Set the upper bound on the iteration limit for j
for (int j=1; j<jmax+1; j+=2) {
mSun.at(i-1,j-1) = 0.;
}
}
mSun.at(0,0) = 1.;
break;
//case 1:
case var_ambient::SUN_TYPE::LIMBDARKENED_SUN:
//---Limb-darkened sunshape--- see DELSOL3 lines 6399-6414
for (int i=1; i<_n_terms+1; i+=2){ //iterate 'i' from 1 to N_order by 2
int jmax = _n_terms-i+1; //Set the upper bound on the iteration limit for j
factdum1 = 1.;
if (i>1) { factdum1 = _fact_odds[i-2]; } //Hold on to the factorial i-1 value to avoid constant recalculation. If i==1, set to 1.
for (int j=1; j<jmax+1; j+=2){
factdum2 = 1.;
if (j>1) { factdum2 = _fact_odds[j-2]; } //Hold on to the factorial j-1 value to avoid recalc. if j==1, set to 1.
int ij = i+j; //Hold on to the i+j value to avoid multiple recalculations
//Calculate the moment for this i-j combination. Algorithm taken from DELSOL3, lines 6399-6414
dfact = double(factorial((ij)/2-1));
mSun.at(i-1,j-1) = ((1./double(ij)-.5138/double(ij+4))/(.5-.5138/6.) * factdum1 * factdum2 / dfact /pow(2.,(ij-2)/2)) * pow(4.65e-3, ij-2) ;
}
}
break;
//case 2:
case var_ambient::SUN_TYPE::PILLBOX_SUN:
//---Square-wave sunshape--- see DELSOL3 lines 6416-6425
for (int i=1; i<_n_terms+1; i+=2) { //Iterate 'i' from 1 to N_order by 2
factdum1 = 1.;
if (i>1) { factdum1 = _fact_odds[i-2]; } //Hold on to the factorial i-1 value to avoid constant recalculation. If i==1, set to 1.
for (int j=1; j<_n_terms+1; j+=2) {
factdum2 = 1.;
if (j>1) {factdum2 = _fact_odds[j-2]; } //Hold on to the factorial j-1 value to avoid recalc. if j==1, set to 1.
int ij = i+j; //Hold on to the i+j value to avoid multiple recalculations
mSun.at(i-1,j-1) = (2.*factdum1*factdum2/factorial(ij/2-1)/pow(2.,(ij-2)/2)/double(ij))*pow(sun_rad_limit/1000., ij-2); //pow(4.645e-3,ij-2);
}
}
break;
//case 4: //Gaussian
//case 5: //Buie model
//case 3:
case var_ambient::SUN_TYPE::GAUSSIAN_SUN:
case var_ambient::SUN_TYPE::BUIE_CSR:
case var_ambient::SUN_TYPE::USER_SUN:
//---user-defined sunshape --- see DELSOL3 lines 6432-6454
//User provides array of angle (radians) and intensity
matrix_t<double> *user_sun;
matrix_t<double> temp_sun;
if(suntype == 4){ //Create a gaussian distribution
int npt = 50;
temp_sun.resize(npt,2);
double ffact = 1./sqrt(2.*pi*sun_rad_limit);
for(int i=0; i<npt; i++){
double theta = (double)i*25./(double)npt; //25 mrad is the limit of most pyroheliometers
temp_sun.at(i, 0) = theta; //mrad -> later converted to rad
temp_sun.at(i, 1) = ffact * exp(-0.5 * pow(theta/sun_rad_limit, 2)); //Gaussian with standard deviation of sun_rad_limit
}
user_sun = &temp_sun; //Assign
}
else if(suntype == 5){ //Create the Buie (2003) sun shape based on CSR
//[1] Buie, D., Dey, C., & Bosi, S. (2003). The effective size of the solar cone for solar concentrating systems. Solar energy, 74(2003), 417–427.
//[2] Buie, D., Monger, A., & Dey, C. (2003). Sunshape distributions for terrestrial solar simulations. Solar Energy, 74(March 2003), 113–122.
double
kappa, gamma, theta, chi;
//calculate coefficients
chi = V.amb.sun_csr.val; //A.getSunCSR();
kappa = 0.9*log(13.5 * chi)*pow(chi, -0.3);
gamma = 2.2*log(0.52 * chi)*pow(chi, 0.43) - 0.1; //0.43 exponent is positive. See reference [2] above.
int npt = 50;
temp_sun.resize(npt, 2);
for(int i=0; i<npt; i++){
theta = (double)i*25./(double)npt;
temp_sun.at(i, 0) = theta;
if(theta > 4.65){
temp_sun.at(i,1) = exp(kappa)*pow(theta, gamma)*.1;
}
else
{
temp_sun.at(i,1) = cos(0.326 * theta)/cos(0.308 * theta)*.1;
}
}
user_sun = &temp_sun;
}
else //Use the user-defined distribution
{
user_sun = &V.amb.user_sun.val; //A.getUserSun();
}
std::vector<double> azmin;
azmin.resize(12,0.);
//for(int i=0; i<8; i++) azmin[i] = 0.0;; //Set up an array
int nn = (int)user_sun->nrows()-1;
for (int n=1; n<nn+1; n+=1) { //DELSOL goes 1..nn
//The disc angle and corresponding intensity
double disc_angle, intens;
disc_angle = user_sun->at(n-1,0)/1000.;
intens = user_sun->at(n-1,1);
//The next disc angle and intensity pair in the array
double disc_angle_next, intens_next;
disc_angle_next = user_sun->at(n,0)/1000.;
intens_next = user_sun->at(n,1);
//fractional step size
double rel_step = 1./(disc_angle_next - disc_angle);
//Relative to the step size, how far away are we from the centroid?
double r_steps = disc_angle*rel_step;
for (int m=1; m<8; m+=2) {
double fm = double(m+1);
int L = m+1;
double temp1 = (pow(disc_angle_next,L) - pow(disc_angle,L))/fm;
double temp2 = (pow(disc_angle_next,m+2) - pow(disc_angle,m+2))/(fm+1.);
azmin.at(m-1) += intens*(temp1*(1.+r_steps) - temp2*rel_step)+intens_next*(-temp1*r_steps + temp2*rel_step);
}
}
double xnorm = 1.; //Initialize the normalizing variable.. it will be reset once the new value is calculated below
//Also initialize an array that's needed for this calculation - see DELSOL3 lines 6238-6244
double RSPA[7][7] = {{2.,0.,1.,0.,.75,0.,.625},
{0.,0.,0.,0.,0.,0.,0.},
{1.,0.,.25,0.,.125,0.,0.},
{0.,0.,0.,0.,0.,0.,0.},
{.75,0.,.125,0.,0.,0.,0.},
{0.,0.,0.,0.,0.,0.,0.},
{.625,0.,0.,0.,0.,0.,0.}};
for(int i=1; i<_n_terms+1; i+=2){
int jmax = _n_terms - i+1;
for (int j=1; j<jmax+1; j+=2) {
int ij = i+j;
mSun.at(i-1,j-1) = azmin.at(ij-2)*RSPA[i-1][j-1]/xnorm*pi;
xnorm = mSun.at(0,0);
}
}
mSun.at(0,0) = 1.;
break;
//default:
// ;
}
return;
}
void Flux::hermiteErrDistCoefs(block_t<double> &errDM)
{
/*
###############################################################################################
-------WHEN TO CALL------
Call once. Coefficients will be used to calculate the moments of the error distribution in the
subroutine "imagePlaneIntercept" below.
---INFORMATION REQUIRED--
No dependencies.
---------OUTPUT----------
Fills in the "errDM" (N x N x 4) array for the coefficients of the error distribution moments.
###############################################################################################
This method calculates the moments of error distribution "G".
The array is N_terms x N_terms x 4 (3D array)
From Dellin (1979), pp14:
G represents the normalized probability distribution that the reflected
vector t_hat will be displaced from its nominal value by and amount dt in the image
plane (i_hat_t, j_hat_t) due to errors in the system. These displacements result
from the cumulative effect of many individual error sources and the magnitude
depends on the detailed design of the system.
DELSOL3 lines 6461-6483
*/
int i, ii, j, k, jmax, jmin;
double temp1;
//resize
errDM.resize(_n_terms, _n_terms, 4);
//zeros
errDM.fill(0.0);
//Calculate each moment
temp1 = 1.;
for (i=1; i<_n_terms+1; i+=2) {
if(i>1) { temp1 = _fact_odds[i]; }
}
for (i=1; i<_n_terms+1; i++) {
jmax = JMX(i-1);
jmin = JMN(i-1);
for (j=jmin; j<jmax+1; j+=2) {
ii = (i-1)/2+1;
for (k=1; k<ii+1; k++) {
temp1 = 1.;
if(i+j > 2*k) {temp1 = _fact_odds[i+j-2*k-1]; }
errDM.at(i-1,j-1,k-1) = temp1 * _fact_d.at(i-1)/(_fact_d.at(i-2*k+1)*_fact_d.at(k-1));
}
}
}
return;
}
void Flux::hermiteMirrorCoefs(Heliostat &H, double tht) {
/*
###############################################################################################
-------WHEN TO CALL------
This method should be called once for each heliostat template (NOT for each heliostat!).
---INFORMATION REQUIRED--
Heliostat geometry, tower height (to normalize information). The heliostat templates should be
previously initialized, then when flux initialization occurs, set the mirror coefficients
---------OUTPUT----------
Fills out the mirror moment coefficient array "errMM", which is normalized by the tower height
and applies to each unique heliostat geometry.
###############################################################################################
This method calculates the moments of mirror shape, 'M'. Moments are based on heliostat
dimensions that are normalized by the tower height.
This method references an established heliostat geometry and requires a receiver
object with an associated tower height.
-> Heliostat
-> Receiver
From Dellin (1979), pp 17:
M represents the flux produced by a perfect heliostat reflecting a point sun.
For a flat heliostat M is given by the geometrical projection of all point
on the mirror that are neither shaded nor blocked. WLV showed that the moments
of a flat rectangular heliostat (including the effects of shading and blocking)
can be evaluated analytically.
DELSOL3 lines 6494-6525
Round heliostats:
DELSOL3 lines 6529-6540
*/
double wm2s, hm2s, wm, hm;
int kl, k, l, ncantx, ncanty;
var_heliostat *V = H.getVarMap();
//Assign some values from the heliostat instance
wm = V->width.val;
hm = V->height.val;
ncantx = V->n_cant_x.val;
ncanty = V->n_cant_y.val;
//Calculate the effective mirror width to use for
if(V->is_faceted.val){
//Use the smaller cant panel dimensions for image calculations
wm2s = 0.; hm2s = 0.;
//Use average panel width/height
wm2s = 0.; hm2s = 0.;
double ff = 1./((double)(ncantx*ncanty)*2.*tht);
for(int r=0; r<ncanty; r++){
for(int c=0; c<ncantx; c++){
wm2s += H.getPanel(r,c)->getWidth()*ff;
hm2s += H.getPanel(r,c)->getHeight()*ff;
}
}
}
else
{
//Use the large structure width (or no canting is specified) for image calculations
wm2s = wm/(tht * 2.);
hm2s = hm/(tht * 2.);
}
matrix_t<double> *errMM = H.getMirrorShapeNormCoefObject();
errMM->resize(_n_terms, _n_terms);
errMM->fill(0.0);
//Calculate the moments depending on whether the heliostats are circular or rectangular
if (V->is_round.mapval() == var_heliostat::IS_ROUND::ROUND) {
//----Round heliostats----
double temp1=1.;
for (k=1; k<_n_terms+1; k+=2) {
for (l=1; l<_n_terms+1; l+=2) {
if(k > 1) {temp1 = _fact_odds[k-2];}
if(l > 1) {temp1 = temp1 * _fact_odds[l-2];}
kl = k+l;
//Calculate the moments
errMM->at(k-1,l-1) = pow(wm2s, kl)*pi/double(kl)*temp1/_fact_d.at(kl/2-1)*pow(2., 1-(kl-2)/2);
}
}
}
else {
//----Rectangular heliostats ----
double wm2sk = wm2s; //is pow(wm2s,k)
double wm2s2 = wm2s*wm2s;
for(k=1; k<_n_terms+1; k+=2)
{
wm2sk *= wm2s2;
double hm2sl = hm2s; //is pos(hm2s,l)
double hm2s2 = hm2s*hm2s;
for(l=1; l<_n_terms+1; l+=2){
kl = k*l;
//Calculate the moments
hm2sl *= hm2s2;
errMM->at(k-1,l-1) = 4./double(kl)*wm2sk*hm2sl;
}
}
//Potentially add other geometries here. No other geometries are defined in DELSOL3.
}
return;
}
double Flux::imagePlaneIntercept(var_map &V, Heliostat &H, Receiver *Rec, Vect *Sun) {
/*
###############################################################################################
-------WHEN TO CALL------
Call this method to evaluate the sunshape, heliostat error distribution, and heliostat mirror
shape distribution for EACH HELIOSTAT IN THE FIELD. Output will change when any input except
tower height changes.
*This is the main optical intercept algorithm that should be called during simulation. This
calls the other Hermite flux characterization algorithms.*
---INFORMATION REQUIRED--
* Heliostat geometry
* Tower height
* Receiver geometry
* Sun position
* Evaluated Hermite flux coefficients (mirror geometry, error distribution, sunshape)
---------OUTPUT----------
Calculates:
* moments of sunshape "_mu_S"
* moments of mirror shape "_mu_M"
* moments of error distribution "_mu_G"
* convolved moments "_mu_F"
--> All of these are normalized by the tower height
Calls the subroutine chain:
hermiteIntEval() -> hermiteIntegralSetup() -> hermiteIntegral()
...and returns the result (double) of the chain.
###############################################################################################
This subroutine calculates the moments of the sunshape, heliostat error
distribution, and heliostat shape on the image plane and then convolves
these to find the moments of the heliostat image.
This method is derived from the DELSOL3 subroutine "MOMENT", beginning on
line 8249.
*/
//First check to make sure the heliostat can see the aperture plane. If not, don't bother.
PointVect NV;
Rec->CalculateNormalVector(*H.getLocation(), NV);
bool view_ok = false;
double h_rad = H.getRadialPos(); //[m] Get the heliostat radius from the tower
/*if(Rec->getReceiverType() == Receiver::REC_TYPE::CYLINDRICAL
&& h_rad < Rec->getReceiverWidth()/2.)
return 0.0;
*/
Vect rnorm;
rnorm.Set(NV.i, NV.j, NV.k);
if(Toolbox::dotprod(rnorm, *H.getTowerVector()) < 0.) view_ok = true; //We actually want the opposite of the tower vector, so take negative dot products to be ok.
if(! view_ok) return 0.;
//Otherwise, there's a satisfactory option so continue
//Variable declarations
int i, j, jmax, jmin;
double slant, tht;
//--------Calculate the moments of the sun-----------
tht = V.sf.tht.val;
//vector to store calculated sun moments
matrix_t<double> *mu_S = H.getSunShapeCoefObject();
mu_S->resize_fill(_n_terms, _n_terms, 0.0);
//Pointer to the relevant receiver
//Receiver *Rec = SF.getReceivers()->at(rec);
var_receiver* Rv = Rec->getVarMap();
int rec_type = Rv->rec_type.mapval();
//Calculate the range-dependent expansion coefficients
//Calculate the slant range
if(rec_type == var_receiver::REC_TYPE::EXTERNAL_CYLINDRICAL ){ //External cylindrical
double rec_width = Receiver::getReceiverWidth( *Rv );;
double rec_opt_ht = Rv->optical_height.Val();
double hmr = h_rad - rec_width*0.5;
slant = sqrt( hmr*hmr + rec_opt_ht*rec_opt_ht ) / tht; //[tht] the distance to the receiver
}
else{
double rec_opt_ht = Rv->optical_height.Val();
slant = sqrt( h_rad*h_rad + rec_opt_ht*rec_opt_ht )/tht; //normalized. This is the default for all cavity/flat-plate type receivers
}
matrix_t<double> srange; srange.resize_fill(1, _n_terms, 0.);
srange[0] = 1.;
//..and the actual array (DELSOL line 7349):
for(i=1; i<_n_terms; i++) { srange[i] = srange[i-1]*slant; }
for(i=1; i<_n_terms+1; i+=2) {
jmax = JMX(i-1);
jmin = 2-i+2*(i/2);
for(j=jmin; j<jmax+1; j+=2) {
//RUS -> hmSun
mu_S->at(i-1,j-1) = srange[i+j-2] * _mu_SN.at(i-1,j-1); //The sun moments, DELSOL 8299
}
}
//---------Calculate moments of the error distribution -------------
//DELSOL 8304-8339
/*
The error distribution moments are evaluated using the formulation from Dellin (1979)
equations 3-6 and 3-7 on page 16. The angles for this equation are defined according
to the figures on page 38-39 of Dellin, and also on page 26-27 of the DELSOL manual.
Equation 3-6 contains terms for sigma_x^2, sigma_y^2, and rho, each of which are evaluated
by their formulations described in Eq. 3-7 of Dellin. These three relationships contain
several phrases that are identical, so to save computational effort, they are assigned
unique variable names.
The expansion coefficients are calculated in the "B(:,:)" array.
Description of variables and angles from DELSOL:
---Nomenclature system ---
-Char 1
C Cosine
S Sine
-Char 2
S Sun vector
T Helio-to-receiver vector
N Heliostat tracking vector
-Char 3
P with reference to zenith (polar)
A with reference to azimuth
Suffix
ANG Array
Variable Primary description---
AZMANG Heliostat aiming azimuth angle
CBNS CSA*CNA+SNA*SSA
CBNT j_hat component of the normal tracking vector
CDEC Cosine of the declination angle
CLAT cosine of latitude
CNA check CTA
CNP Cosine of the tracking normal zenith angle
CSA Equals CSAANG(I,J)
CSAANG Cosine of solar azimuth angle
CSP Equals CSPANG(I,J)
CSPANG Cosine of solar zenith angle
CT Cosine of hour angle
CTA Equals CTAANG(L)
CTAANG cosine of heliostat location azimuth angle
CTP Equals CTPANG(K)
CTPANG cosine of TPANG
ELVANG Heliostat aiming elevation (?) angle
HCOS Heliostat cosine loss
HINSOL
I Iterator, 1 -> Number of azimuth angles in table
J Iterator, 1-> Number of zenith angles in table
K Iterator, 1-> Number of azimuthal zones
L Iterator, 1-> Number of radial zones
SBNS SNA*CSA-CNA*SSA
SBNT i_hat component of the normal tracking vector
SDEC Sine of the declination angle
SLAT sine of latitude
SNA Sine of the tracking azimuth angle
SNP Sine of the tracking zenith angle
SSA Equals SSAANG(I,J)
SSAANG Sine of solar azimuth angle
SSP Equals SSPANG(I,J)
SSPANG Sine of solar zenith angle
STA Equals STAANG(L)
STAANG sine of heliostat location azimuth angle
STP Equals STPANG(K)
STPANG sin of TPANG
T Hour angle
TPANG Heliostat to receiver zenith angle
UAZ Array of user-defined solar azimuth angles
UEL Array of user-defined solar ZENITH angles
*/
//calculate relevant angles
Vect
n_hat, //tracking vector
t_hat, //heliostat to tower vector
z_hat, //zenith unit vector - values are 0,0,1 by default
s_hat; //Solar position vector
z_hat.Set(0.,0.,1.);
n_hat = *H.getTrackVector(); //heliostat tracking vector
t_hat = *H.getTowerVector(); //heliostat-to-receiver vector
s_hat = *Sun; //Sun position vector
double cos_s_zen = s_hat.k; //cos(theta_s_zen), //Cosine of the solar zenith angle (CSP)
double sin_s_zen = sqrt(1.-s_hat.k*s_hat.k); //sin(theta_s_zen), //Sine of the solar zenith angle (SSP)
sin_s_zen = sin_s_zen == 0. ? 1.e-6 : sin_s_zen;
double cos_s_az = s_hat.j/sin_s_zen; //cos(theta_s_az), //Cosine of the solar azimuth angle (CSA)
double sin_s_az = s_hat.i/sin_s_zen; //sin(theta_s_az); //Sine of the solar azimuth angle (SSA)
////double theta_n_zen= acos(n_hat.k); //zenith angle of the tracking vector
//double cos_n_zen = n_hat.k; //cos of the zenith angle of tracking vector (CNP)
//double sin_n_zen = sqrt(1.-n_hat.k*n_hat.k); //sin(theta_n_zen); //sine of the zenith angle of the tracking vector (SNP)
// sin_n_zen = sin_n_zen == 0. ? 1.e-6 : sin_n_zen;
////theta_n_az = atan2(n_hat.i;n_hat.j); //Azimuth angle of the tracking vector (0..360)
//double sin_n_az = n_hat.i/sin_n_zen; //sin(theta_n_az);
//double cos_n_az = n_hat.j/sin_n_zen; //cos(theta_n_az);
////double theta_t_zen = acos(dotprod(t_hat, z_hat));
//double cos_t_zen = dotprod(t_hat, z_hat); //cos of zenith of helio-tower vector
//double sin_t_zen = sqrt(1.-cos_t_zen*cos_t_zen); //sin(theta_t_zen);
// sin_t_zen = sin_t_zen == 0. ? 1.e-6 : sin_t_zen;
////double theta_t_az = atan2(t_hat.i,t_hat.j); //azimuth angle of the heliostat-to-receiver vector
//double sin_t_az = t_hat.i/sin_t_zen; //(theta_t_az);
//double cos_t_az = t_hat.j/sin_t_zen; //cos(theta_t_az);
//-----------------------------------------------------------------------------
double theta_n_zen= acos(n_hat.k); //zenith angle of the tracking vector
double cos_n_zen = n_hat.k; //cos of the zenith angle of tracking vector (CNP)
double sin_n_zen = sin(theta_n_zen); //sine of the zenith angle of the tracking vector (SNP)
sin_n_zen = sin_n_zen == 0. ? 1.e-6 : sin_n_zen;
double theta_n_az = atan2(n_hat.i,n_hat.j); //Azimuth angle of the tracking vector (0..360)
double sin_n_az = sin(theta_n_az);
double cos_n_az = cos(theta_n_az);
double theta_t_zen = acos(dotprod(t_hat, z_hat));
double cos_t_zen = dotprod(t_hat, z_hat); //cos of zenith of helio-tower vector
double sin_t_zen = sin(theta_t_zen);
sin_t_zen = sin_t_zen == 0. ? 1.e-6 : sin_t_zen;
double theta_t_az = atan2(t_hat.i,t_hat.j); //azimuth angle of the heliostat-to-receiver vector
double sin_t_az = sin(theta_t_az);
double cos_t_az = cos(theta_t_az);
//---------------------------------------------------
//Calculate the heliostat cosine loss
double // sqrt(2)/2
eta_cosine = 0.7071067811865*sqrt(1.+cos_s_zen*cos_t_zen+sin_s_zen*sin_t_zen*(cos_t_az*cos_s_az + sin_t_az*sin_s_az));
//double eta_test = dotprod(s_hat, n_hat);
//get heliostat inputs
var_heliostat *Hv = H.getVarMap();
//get error terms - See Kistler pp. 184 for definition
double err_angular[2], err_surface[2], err_reflected[2];
err_angular[0] = Hv->err_azimuth.val;
err_angular[1] = Hv->err_elevation.val;
err_surface[0] = Hv->err_surface_x.val;
err_surface[1] = Hv->err_surface_y.val;
err_reflected[0] = Hv->err_reflect_x.val;
err_reflected[1] = Hv->err_reflect_y.val;
//Depending on the canting method, calculate the A[], B[] arrays differently.
double A11, A12, A21, A22, B11, B12, B21, B22;
//---Are the heliostats canted?
int cant_method = Hv->cant_method.mapval(); //{0=none, -1=on-axis at slant, 1=on-axis at user def., 3=off-axis at hour-day}
//reused terms:
//SAVE=SIGAZ2*SNP**2+SIGSX2 | 8304
double term1 = err_angular[0] * sin_n_zen; //first reused term
term1 *= term1;
term1 += err_surface[0]*err_surface[0];
//SAVE2=SIGEL2+SIGSY2
double term2 = err_angular[1]*err_angular[1] + err_surface[1] * err_surface[1]; //second reused term
switch (cant_method)
{
//case Heliostat::CANT_TYPE::FLAT:
//case Heliostat::CANT_TYPE::AT_SLANT:
//case Heliostat::CANT_TYPE::ON_AXIS_USER:
case var_heliostat::CANT_METHOD::NO_CANTING:
case var_heliostat::CANT_METHOD::ONAXIS_AT_SLANT:
case var_heliostat::CANT_METHOD::ONAXIS_USERDEFINED:
{
//Everything except individual off-axis canting and vector canting
//A(1,1)=CBNT
A11 = cos_t_az * cos_n_az + sin_n_az * sin_t_az;
//A(1,2)=CNP*SBNT
A12 = cos_n_zen * (sin_n_az * cos_t_az - cos_n_az * sin_t_az);
//A(2,1)=-CTP*SBNT
A21 = -cos_t_zen * A12/cos_n_zen;