Material Properties and Regolith Layering

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,INERTIA=200.,INERTIA2=1200.)

Here, the property change from INERTIA to INERTIA2 occurs at a depth of 3 cm below the surface.

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

Here, the property change occurs between 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 explicitly 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

If LZONE = "T", regolith properties profiles with depth can be specified in the form of 4 x n x 1 array defined by "thick".

Column 1: Mesh (or Zone) Element Thickness [m]

Column 2: Mesh (or Zone) Element Density [kg/m^3]

Column 3: Pointer for Column 4, or conductivity [J/kg/K/s]

Column 4: Conductivity and Specific heat from Materials 1 and 2

Make sure to define the first column as the zone thickness, not the depth.

OUT = krc(lat=0.,LZONE="T",thick=TABLE)

Material Properties

DaVinci function Mat_Prop() distributed with the krc interface .dvrc calculates density, conductivity, and Cp (krc-ready) for volatiles (H2O, CO2, N2, CH4, SO2) as a function of temperature.

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.

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.].

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

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:

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

Cp is defined by SPEC_HEAT if LKofT = "F", or the 4 SphUpx (or SphLox) parameters if LKofT = "T":

SphUp0 = SPEC_HEAT = SpHeat2
SphUp1
SphUp2
SphUp3

Cp = SphUp0 + SphUp1 x + SphUp2 x^2 + SphUp3 x^3

where x = ( T - 220 ) * 0.01

See [2] for trends and coefficients of a variety of materials.

Parameter	Basalt[1]	H2O[2]	CO2[3]	N2[3]	SO2[3]	CH4[3]
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

[1] 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

[2] W. F. Giauque and J. W. Stout (1936)]

[3] [3]

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

Thermal Conductivity

The thermal conductivity is defined by COND if LKofT = "F", or the 4 ConUpx (or ConLox) parameters if LKofT = "T":

ConUp0 = COND = COND2
ConUp1
ConUp2
ConUp3

k = ConUp0 + ConUp1 x + ConUp2 x^2 + ConUp3 x^3

where x = ( T - 220 ) * 0.01

Fines in Vacuum

In a vacuum, if INERTIA is provided (at T_user) and INERTIA < TI_CO, the interface assumes a T^3 trend for the conductivity. First, the interface derives the thermal conductivity at T_user:

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

...using parameters provided by the user, or default material properties based on the planetary body.

Then the thermal conductivity coefficients are derived from a polynomial fit between 10 and 500K and follows a trend described in [Hayne REF]:

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

In this case, the user should specify:

LKofT = "T"

T_user

INERTIA

Mat1 / DENS / Por1

In the one point mode, this temperature-dependence trend can be indicated with k_style = "Moon". Note that this is a risky behavior, because high thermal inertia typically doesn't follow this trend.

Fines with an Atmosphere

With an atmosphere (PTOTAL > 0.1), if INERTIA < TI_CO and LKofT = "T", the interface assumes a sqrt(T) trend for the conductivity (INERTIA set at T_user). First, the interface derives the thermal conductivity at T_user:

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

...using parameters provided by the user, or default material properties based on the planetary body.

Then the thermal conductivity coefficients are derived from a polynomial fit between 10 and 500K and follows a trend described in [4]:

k = COND*sqrt(T/T_user)

Note: T_user (vs 220 K) might be hardcoded as 220K in interface. This will need to be verified by the user. In this case, the user should specify:

LKofT = "T"

T_user

INERTIA

Mat1 / DENS / Por1

In the one point mode, this temperature-dependence trend can be indicated with k_style = "Mars". Note that this is a risky behavior, because high thermal inertia typically doesn't follow this trend.

Massive Basalt and Ices

If INERTIA > TI_CO, the conductivity trend is driven by the bulk solid properties:

Parameter	Basalt [1]	H2O [2]	CO2 [3]	N2 [4]	SO2 [5]	CH4 [6]
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

[Slack, G.A. (1980), Thermal conductivity of ice. Physical Review , B22, 3065-71]