Material Properties and Regolith Layering

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Revision as of 16:10, 25 January 2019

Contents

Regolith Layering

No Layering (Default)

IC2 = 999

No need to specify IC2 =999 (or thick, see below), 

out = krc(lat = 0., lon = 0.)
out = krc(lat = 0., lon = 0., IC2 = 999)
out = krc(lat = 0., lon = 0., thick = 0.)

...give identical results.


Two Layers

The DaVinci Interface automatically determines the parameters to adjust from a thickness value (thick, in meters). The user can provide either an upper layer thickness (in m) or the layer index where the material properties change occurs. 

out = krc(lat = 0., thick = 0.03)

Here, the property change occurs at a depth of 3 cm below the surface. 

out = krc(lat=23., IC2 = 4)

Here, the property change occurs abetween the 3rd and the 4th mesh element.


H Parameter

A "H" parameter can describe the exponential variation of regolith properties with depth (density and conductivity). See Hayne et al. 2016. For this configuration, thick < 0, with abs(thick) = H 

out = krc(lat = 0., lon = 0., thick = -0.3 )

In this case, H = 30 cm, and the material properties are taken from the default input file values. 

out = krc(lat = 0., lon = 0., thick = -0.3, INERTIA = 200., INERTIA2 = 1200., LKofT = "F" )

In this case, H = 30 cm, and the material inertias are defined by the user.


Alternatively, all the parameters can be explicitely provided: 

out = krc(lat = 0., lon = 0., thick = -0.3, COND = 0.1, DENSITY = 1800., SPEC_HEAT = 600., COND2 = 0.1, DENS2 = 1800., SpHeat2 = 600., LKofT = "F" )

out = krc(lat = 0., lon = 0., thick = -0.3, INERTIA = 200., INERTIA2 = 1200. )

In this case, H = 30 cm, and the material properties are defined by the user, with temperature dependence.

LIMITATION: Only top 2 elements have temperature-dependent properties


N Layers or Tables

Table Zone


Material Properties

Material properties are defined by (no temperature dependence): 

INERTIA
DENSITY
SPEC_HEAT

INERTIA2
DENS2
SpHeat2

KRC doesn't explicitly require a conductivity, it derives it from INERTIA, DENSITY, and SPEC_HEAT. But the interface can ingest a conductivity, as well as a combo of other parameters. 

COND

COND2

Density, conductivity, and specific heat can be calculated from standard materials behaviors ("basalt", and "H2O") assuming they form continuous media. To assign material properties, indicate Mat1 and and Mat2 if necessary. 

Mat1 = "basalt"

...assigns bulk basalt properties to the upper material. 

Mat2 = "H2O"

...assigns water ice properties to the lower material.


Density

Doesn't vary with temperature, and is defined by: 

DENS

and 

DENS2

Variations with depth can be defined with an H parameter, or a Table.

When TI < TI_CO, the interface assumes a density associated with a porosity of 0.4, and a bulk density associated with basalt. The porosity can be changed by setting: 

 Por1 = [0. - 1.]

And if needed: 

Por2 = [0. - 1.]

Alternatively, the density can be set directly.

For water ice, the density is set to = 924.148 kg/m^3 (220 K). [Rottger et al. (2011): Lattice constants and thermal expansion of H2O and D2O Ice Ih between 10 and 265 K. Addendum], but depending on the temperature (body), this value might need to be changed. See plot below:

PLOT HERE DENSITY VS TEMPERATURE.

More details in the tab "Density(T) H2O" in this document for the derivation density versus temperature: File:Material KRC.xlsx

For basalt, the density is set to = 3100. kg/m^3. [J. MORE 2001, DENS. OF BASALT CORE FROM HILO DRILL HOLE, HAWAII]. For the absolute density value. For trend with temperature: [F.E. Heuze. High temperature mechanical, physical and thermal properties of granitic rocks: A review. Int. J. Rock Mech. Mining Sci., 20:3–10, 1983.].

PLOT HERE DENSITY VS TEMPERATURE.

More details in the tab "Density(T) Basalt" in this document for the derivation density versus temperature: File:Material KRC.xlsx

NOT IMPLEMENTED YET

For CO2, the density is set to = 1621. kg/m^3. [1], but depending on the temperature (body), this value might need to be changed. See plot below:

PLOT HERE DENSITY VS TEMPERATURE.

More details in the tab "Density(T) C2O" in this document for the derivation density versus temperature: File:Material KRC.xlsx


N2 Not formalized yet.

Specific Heat

SphUp0 = SPEC_HEAT = SpHeat2
SphUp1
SphUp2
SphUp3

Cp = SphUp0 + SphUp x + SphUp2 x^2 + SphUp3 x^3

where x = ( T - 220 ) * 0.01

See [REF VU] for trends and coefficients of a variety of materials.

Parameter Basalt H2O CO2 N2 SO2 CH4
SphUp0 609.906 1704.57 1399.88 6137.28 1132.09 18356.1
SphUp1 214.231 713.339 652.64 4082.15 364.914 29096.3
SphUp2 -40.9437 110.694 432.015 789.538 127.915 18515.3
SphUp3 11.2575 75.7506 192.398 -0.109612 77.4213 4143.07


Basalt: Hemingway, Robie, Wilson, http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1973LPSC....4.2481H&db_key=AST&page_ind=0&data_type=GIF&type=SCREEN_VIEW&classic=YES

H2O: W. F. Giauque and J. W. Stout (1936)]

CO2: REF HERE

N2: REF HERE

SO2: REF HERE

CH4: REF HERE

More details on the fits here: File:Material KRC.xlsx

Thermal Conductivity

For material properties temperature dependence: 

ConUp0 = COND = COND2
ConUp1
ConUp2
ConUp3

k = ConUp0 + ConUp x + ConUp2 x^2 + ConUp3 x^3

where x = ( T - 220 ) * 0.01


Fines in Vacuum

In a vacuum, if INERTIA < TI_CO, the interface assumes a T^3 trend for the conductivity (INERTIA/COND set at T_user) from a polynomial fit between 10 and 500K yat follows the REF equation: 

COND = INERTIA^2/(SPEC_HEAT*(1.-Por1)*Density_bulk)

k = COND*(1+2.7*((T-T_user)/350.)^3)

PLOT k HERE FOR A COUPLE OF EXAMPLES


Fines with an Atmosphere

With an atmosphere, if INERTIA < TI_CO, the interface assumes a sqrt(T) trend for the conductivity (INERTIA/COND set at T_user) from a polynomial fit between 10 and 500K yat follows the REF equation: 

COND=INERTIA^2/(SPEC_HEAT*(1-Por1)*Density_bulk)

COND*sqrt(T/T_user)

HERE CHECK T_user vs 220 K in interface (interface seems to be stuck at 220k)

PLOT k HERE FOR A COUPLE OF EXAMPLES


Bulky Water Ice

If INERTIA > TI_CO, the conductivity trend is driven by bulk water ice properties [Slack, G.A. (1980), Thermal conductivity of ice. Physical Review , B22, 3065-71]:

ConUp0=INERTIA^2/(SPEC_HEAT*(1.-Por1)*Density_bulk) ConUp0=3.06 SI from Ref at 220K

ConUp1=-1.08693

ConUp2=-0.334381

ConUp3=-1.60453

More details in the tab "k(T) H2O bulk" in this document for the derivation density versus temperature: File:Material KRC.xlsx

PLOT HERE

Bulky Basalt

If INERTIA > TI_CO, the conductivity trend is driven by bulk water ice properties [REF UNKNOWN]:

ConUp0 = INERTIA^2/(SPEC_HEAT*(1-Por1)*Density_bulk) ConUp0 = 5.32202 SI from Ref at 220K.

ConUp1=-1.51737

ConUp2=0.587176

ConUp3=-0.126695

More details in the tab "basalt(T) H2O bulk" in this document for the derivation density versus temperature: File:Material KRC.xlsx

PLOT HERE

Bulky CO2 Ice

Text here

Bulky N2 Ice

tetx here


Parameter Basalt H2O CO2 N2 SO2 CH4
ConUp0 5.32202 3.06445 0.441346 0.07 N/A 0.0308666
ConUp1 -1.51737 -1.08693 -0.0686357 0. N/A 0.071247
ConUp2 0.587176 -0.334381 0.425127 0. N/A 0.289212
ConUp3 -0.126695 -1.60453 0.233004 0. N/A 0.0617607


define ice_prop(composition,T) {

if($ARGC == 0){ 

   printf (" Returns a structure containing physical properties of ices:  \n")
   printf (" density, specific heat, conductivity, vapor pressure \n")
   printf (" Source is Solar System Ices book \n")
   printf (" $1 = ice composition, between double quotes \n") 
   printf (" Supported ices CO2, H2O, SO2, N2, CH4 \n")
   printf (" $2 = Temperature in K \n")
             }

if($ARGC !=0){

composition = $1 T = $2

ice=struct()

if (composition == "CO2") { 

 a_dens = 32.939*44.0095
 b_dens = 0.06842*44.0095 
 c_dens = -0.0002847*44.0095 
 d_dens = 0.0
 e_dens = 0.0

 a_spht = -18282.0/44.0095 
 b_spht = 1360.3/44.0095 
 c_spht = -12.152/44.0095 
 d_spht = 0.05158/44.0095 
 e_spht = -0.00007699/44.0095 

 buffer = -5.39941 + 5.45894*log10(T) - 1.41326*(log10(T))^2
 k = 10^buffer

 a_p = 25.784
 b_p = -3258.2
 c_p = 0.77194
 d_p = -0.0081188
 e_p = 1
                           }

if (composition == "H2O") { 

 a_dens = 53.03*18.01528
 b_dens = -0.0078409*18.01528
 c_dens = 0
 d_dens = 0
 e_dens = 0

 a_spht = -262.49/18.01528
 b_spht = 140.52/18.01528
 c_spht = 0
 d_spht = 0
 e_spht = 0

 buffer = -8.98536+103.12814*log10(T)-413.60906*(log10(T))^2+909.93398*(log10(T))^3-1197.181581*(log10(T))^4
 buffer = buffer+979.4272418*(log10(T))^5-502.5613545*(log10(T))^6+157.3223437*(log10(T))^7
 buffer = buffer-27.46439969*(log10(T))^8+2.049301625*(log10(T))^9
 k = 10^buffer

 a_p = 28.766
 b_p = -6109.19
 c_p = 0.0
 d_p = 0.0
 e_p = 0.0
                       }

if (composition == "SO2") { 

 a_dens = 32.3811*64.0638 
 b_dens = -0.0204768*64.0638 
 c_dens = 0
 d_dens = 0
 e_dens = 0

 a_spht = -22900/64.0638
 b_spht = 1723.6/64.0638
 c_spht = -16.519/64.0638
 d_spht = 0.076593/64.0638
 e_spht = -0.00012792/64.0638

 k = 0.0

 a_p = 95.972
 b_p = -6426.94
 c_p = -10.6005
 d_p = 0.0
 e_p = 0.0

                         }

if (composition == "N2") { 

 a_dens = 37.87*28.0134 
 b_dens = -0.060272*28.0134 
 c_dens = 0
 d_dens = 0
 e_dens = 0

 a_spht = 27420/28.0134
 b_spht = 170.1/28.0134
 c_spht = 2.2125/28.0134
 d_spht = 0
 e_spht = 0

 a_k = 1.3081 
 b_k = -0.085791 
 c_k = 0.0027961 
 d_k = -0.000044695 
 e_k = 0.00000027819

 k = a_k+b_k*T+c_k*T^2+d_k*T^3+e_k*T^4

 a_p = 28.766
 b_p = -6109.19
 c_p = 0.0
 d_p = 0.0
 e_p = 0.0

                       }

if (composition == "CH4") { 

 a_dens = 33.022*16.04246
 b_dens = -0.01587*16.04246
 c_dens = -0.000155*16.04246
 d_dens = 0
 e_dens = 0

 a_spht = -2550/16.04246
 b_spht = 1249.9/16.04246
 c_spht = -14.17/16.04246
 d_spht = 0.06648/16.04246
 e_spht = 0

 buffer = 5.679842 - 13.421524*log10(T) + 9.534462*(log10(T))^2 - 2.196201*(log10(T))^3
 k = 10^buffer

 a_p = 22.1398
 b_p = -1159.3
 c_p = 0.0
 d_p = 0.0
 e_p = 0.0

  }

ice.dens = a_dens+b_dens*T+c_dens*T^2+d_dens*T^3+e_dens*T^4 ice.spht = a_spht+b_spht*T+c_spht*T^2+d_spht*T^3+e_spht*T^4 ice.k = k ice.TI = sqrt(ice.k*ice.dens*ice.spht) ice.pressure = exp(a_p+b_p/T+c_p*ln(T)+d_p*T^e_p)

return(ice)

} } 

----
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