We provide an artificial temperature floor of 20 Kelvin to prevent DELTAE from trying to use negative temperatures when it is really lost. Consequently, no temperature below 20 Kelvin can be used. In any case, most of the equations for the fluids are inaccurate when this limit is reached.
In what follows, ta is temperature in Kelvin, t1 is temperature in Celsius.
Unless otherwise specified, properties are computed using fits to the data compiled in Touloukian's TPRC series.
DELTAE looks for a 10-character field to determine fluid type. Be sure to use plenty of trailing spaces after short fluid names like ``air" to get comments like ``gas-type" out of the field.
Ideal gas approximation for equation of state (including sound speed and expansion coefficient) and specific heat. Transport from Touloukian:
k0=0.0025672*ta**0.716 mu=0.412e-6*ta**0.68014
Number in the fluid name is helium fraction. Ideal gas approximation for equation of state and specific heat. Transport from Touloukian.
k0he=0.0025672*ta**0.716 amuhe=0.412e-6*ta**0.68014 k0ar=(1.39e-4*ta**0.852-1.5e-8*(ta-300.)*(ta-300.))*(1.+2.e-8*pm) amuar=(1.77e-7*ta**0.852-25.e-12*(ta-300.)*(ta-300.))*(1.+2.e-8*pm) k0=x1*k0ar+x2*k0he-(k0ar+k0he)*x1*x2**1.5 mu=x1*amuar+x2*amuhe+0.2*(amuar+amuhe)*x1*x2
Number in the fluid name is helium fraction. Ideal gas approximation for equation of state and specific heat. Our fits to Touloukian's transport data are only accurate for frxe <0.5 or for frxe =1.000:
k0he=0.0025672*ta**0.716 amuhe=0.412e-6*ta**0.68014 k0xe=4.75e-5*ta**0.84*(1.+1.e-7*pm) amuxe=0.187e-6*ta**0.85*(1.+25.e-9*pm) frxe=1.-fhe k0=k0he*fhe+k0xe*frxe-2.*(k0he+k0xe)*frxe*fhe*fhe mu=amuhe*fhe+amuxe*frxe+(amuhe+amuxe)*frxe*fhe*fhe*(0.8+3.7*fhe*fhe*(0.25-frxe))
Ideal gas approximation for equation of state (including sound speed and expansion coefficient) and specific heat. Transport from Touloukian:
k0=0.001149*ta**0.65907 mu=0.735e-6*ta**0.66065
Ideal gas approximation for equation of state and specific heat. Transport from Pierce, Acoustics:
parameter (tps=110.4,tpa=245.4,tpb=27.6,tp0=300.,tpexp=223.8306) k0=2.624e-2*(ta/tp0)**1.5*(tp0+tpexp)/(ta+tpa*\exp (-tpb/ta)) mu=1.846e-5*(ta/tp0)**1.5*(tp0+tps)/(ta+tps)
Ideal gas approximation for equation of state (including sound speed and expansion coefficient) and specific heat. Transport from Touloukian:
k0=0.0003609*ta**0.7512 mu=0.3577e-6*ta**0.6885
Ideal gas approximation for equation of state (including sound speed and expansion coefficient) and specific heat. Transport from Touloukian:
k0=0.002627*ta**0.744 mu=0.19361e-6*ta**0.6723
Ideal gas approximation for equation of state (including sound speed and expansion coefficient) and specific heat. Transport from Touloukian:
k0=0.002795*ta**0.686 mu=0.2726e-6*ta**0.6721
Ideal gas approximation for equation of state (including sound speed and expansion coefficient) and specific heat. Transport from Touloukian:
k10=2.8646E-5*ta**1.1318 k20=3.692E-5*ta**1.0940 k0=k10+(pm-1.01e6)/(1.01e6)*(k20-k10) u10=1.4187E-7*ta**.8216 u20=1.5416E-7*ta**.8094 mu=u10+(pm-1.01e6)/(1.01e6)*(u20-u10)
Data for sodium from Foust, Sodium-NaK Engineering Handbook.
a0=2578. at1=-.52 ap=6.1e-7 r0=950.1 rt1=-2.2976e-1 rt2=-1.46e-5 rt3=5.638e-9 c0=1.4361e3 ct1=-5.8024e-1 ct2=4.6208e-4 k0=.918e2-4.9e-2*t1 if(t1.le.500.) then e1=.697 e2=1.235e-5 else e1=1.04 e2=8.51e-6 endif a=a0+at1*t1 rho=r0+rt1*t1+rt2*t1**2+rt3*t1**3 beta=(-rt1-2.*rt2*t1-3.*rt3*t1**2)/rho bt=beta**2-(2.*rt2+6.*rt3*t1)/rho cp=c0+ct1*t1+ct2*t1**2 rp=1./a/a+ta*beta**2/cp bp=-beta/(rho*a**2)+2.*at1/(rho*a**3)-beta**2/rho/cp bp=bp-2.*ta*beta*bt/rho/cp-ta*beta**3/rho/cp bp=bp+ta*beta**2*(ct1+2.*ct2*t1)/rho/cp/cp cpp=-ta*(beta**2+bt)/rho c So far, everything is evaluated at p=0. a=a+ap*pm rho=rho+rp*pm beta=beta+bp*pm cp=cp+cpp*pm gamma=1.+ta*beta**2*a**2/cp mu=e2*rho**(1./3.)*\exp (e1*rho/ta)
This is for eutectic NaK-78. Data for sodium-potassium from Foust, Sodium-NaK Engineering Handbook.
a0=2051. at1=-.53 ap=0. r0=876.4 rt1=-2.183e-1 rt2=-2.982e-5 rt3=0. c0=970.69 ct1=-.36903 ct2=3.4309e-4 k0=21.4+2.07e-2*t1-2.2e-5*t1**2 if(t1.le.400.) then e1=.688 e2=1.16e-5 else e1=.979 e2=8.2e-6 endif a=a0+at1*t1 rho=r0+rt1*t1+rt2*t1**2+rt3*t1**3 beta=(-rt1-2.*rt2*t1-3.*rt3*t1**2)/rho bt=beta**2-(2.*rt2+6.*rt3*t1)/rho cp=c0+ct1*t1+ct2*t1**2 rp=1./a/a+ta*beta**2/cp bp=-beta/(rho*a**2)+2.*at1/(rho*a**3)-beta**2/rho/cp bp=bp-2.*ta*beta*bt/rho/cp-ta*beta**3/rho/cp bp=bp+ta*beta**2*(ct1+2.*ct2*t1)/rho/cp/cp cpp=-ta*(beta**2+bt)/rho c So far, everything is evaluated at p=0. a=a+ap*pm rho=rho+rp*pm beta=beta+bp*pm cp=cp+cpp*pm gamma=1.+ta*beta**2*a**2/cp mu=e2*rho**(1./3.)*\exp (e1*rho/ta)
Files can have any name valid under the operating system under which DELTAE is running, and should end with the extension .tpf. If the root filename is the same as any pre-defined fluids, DELTAE will replace it's internal calculations for that fluid with those given in the user file. To request a user-defined fluid, simply use the root file name as you would any other fluid. The .tpf file should be in the same directory or folder as the model file. The name of the fluid is set to the root filename of the external fluid file. Up to five distinct external fluids can be used at one time.
Each property is specified by a line containing
1-10 real coefficients to be read in as C_0-9, where unused parameters are
set to zero. The order of the property lines is
. Comment lines can be added with an
initial `!', and blank lines are ignored.
Each of the five properties is derived from its 10 coefficients using the following equation:
where T and p_m are the absolute temperature (K) and mean pressure (Pa) for each point at which a segment using the fluid is evaluated.