<HTML> <HEAD><TITLE>Richard Nakka's Experimental Rocketry Site </TITLE> </HEAD> <BODY bgcolor="99cccc"><H2><A NAME="DC"></A></H2> <HR SIZE=5><H2><CENTER>Richard Nakka's <EM>Experimental Rocketry</EM> Web Site</CENTER></H2> <HR WIDTH=50% ALIGN=center SIZE=2> <CENTER><H3><FONT COLOR="brown">Technical Notepad #8 -- RNX-57 Ideal Performance Calculations</FONT></H3></CENTER> <A NAME="note1"> <FONT FACE="Arial" SIZE=2 COLOR="#ff0000"><P>Note 1 </P> </FONT><FONT FACE="Arial" SIZE=2> <P>RNX-57 @ 1000 psia chamber pressure</P> <P>From PROPEP results, for 100 grams mixture: </P> <CENTER><IMG SRC="techpix/propep_chem_RNX-57.gif" ALT="GUIPEP results for RNX-57" WIDTH=600 HEIGHT=358 ALIGN="middle"></CENTER> <P>&nbsp;</P> </FONT><FONT FACE="Arial" SIZE=2><P>The effective Molecular Weight is given by dividing the number GAS moles into the system mass. Since the system mass is 100 grams:</P> </FONT><FONT FACE="Arial" SIZE=1> </FONT><FONT FACE="Courier New" SIZE=1><P><IMG SRC="techpix/mw_eqn_57.gif" WIDTH=282 HEIGHT=39 ALIGN="middle"> </FONT><FONT FACE="Arial" SIZE=2>g/mole</P> </FONT><FONT FACE="Arial" SIZE=2> Note that this is the proper molecular weight to use in the thermodynamic equations.<P> <P>The mass fraction of condensed phase is given by the mass of the condensed phase (K<SUB>2</SUB>CO<SUB>3</SUB>, Fe and FeO) divided by the system mass</P> <P>The MW of K<SUB>2</SUB>CO<SUB>3</SUB> = 138.21 g/mole and the MW of FeO = 71.844 g/mole. Thus<BR> </FONT><BR><IMG SRC="techpix/x_eqn_57.gif" WIDTH=311 HEIGHT=40 ALIGN="middle"></P> </FONT><FONT FACE="Arial" SIZE=1> </FONT><FONT FACE="Arial" SIZE=2 COLOR="#ff0000"><P>Note 2</FONT><FONT FACE="Arial" SIZE=2> <A NAME="note2"> <P> <P>Mole fractions and mass fractions for each combustion product are calculated in the table below: </P> <CENTER><IMG SRC="techpix/RNX-57_table2.gif" WIDTH=407 HEIGHT=250 ALIGN="middle" ALT="Nf chart"></CENTER><P><HR WIDTH=30%> <CENTER><IMG SRC="techpix/RNX-57_table3.gif" WIDTH=859 HEIGHT=82 ALIGN="middle" ALT="Cp chart"></CENTER><P> The values for Cp and Cs are obtained from NIST Chemistry WebBook. Units of Cp and Cs are J/mol-K.<P>The Cp for the gas only products and mixture (gas+condensed) is given by<BR> <IMG SRC="techpix/techeq1.gif"><BR><IMG SRC="techpix/techeq2.gif" ALIGN="middle"><P> where <EM>n</EM><SUB><EM>i</EM> </SUB>is the number of moles of gas component <EM> i </EM>, <EM>n</EM><SUB><EM>s</EM></SUB> the number of moles of condensed component, <EM>n</EM> the total number of gas moles. The ratio of specific heats for the mixture, for the gas-only, and for two-phase flow is given by<P> <IMG SRC="techpix/techeq3.gif" ALIGN="middle">&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; where <IMG SRC="techpix/run.gif" ALIGN="middle"> = 8.314 J/mol-K (universal gas constant).<BR><IMG SRC="techpix/techeq4.gif" ALIGN="middle"><P> <IMG SRC="techpix/techeq5.gif" ALIGN="middle">&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;<P> where <FONT FACE="Symbol" SIZE=2>y</FONT> = X /(1-X).<BR> Note that <EM>k</EM> for two-phase (gas+condensed) flow is a modified form of the gas-only <EM>k'. </EM>This is the correct form of k to use in the thermodynamic equations involving products with a significant fraction of condensed-phase particles. The value of<EM> k</EM> given in the PROPEP output (Cp/Cv) is for the mixture.<P> <A NAME="note3"> <FONT FACE="Arial" SIZE=2 COLOR="#ff0000"><P>Note 3 </FONT></P> Characteristic exhaust velocity is given by<P> <IMG SRC="techpix/techeq6.gif"><P>with<BR> To = 1644 K<BR> M = 45.54 kg/kmol<BR> k = 1.159&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Note: k for the <EM>mixture </EM>is the proper value to use, as c* represents a static condition<BR> <IMG SRC="techpix/run.gif" ALIGN="middle"> = 8314 J/kmol-K <BR> this gives c* = 855.5 m/s (2807 ft/s).<P> <A NAME="note4"> <FONT FACE="Arial" SIZE=2 COLOR="#ff0000"><P>Note 4 </FONT></P><P>The propellant specific impulse is given by the effective exhaust velocity divided by g.<P> <IMG SRC="techpix/techeq7.gif"><P>with<BR> To = 1644 K<BR> M = 45.54 kg/kmol<BR> k = 1.026&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Note: k for <EM>2-phase flow</EM> is the proper value to use, as Isp represents a dynamic condition<BR> <P>Thus, ideal Isp = 158.1 sec.<BR> for standard conditions of Po = 68 atm. (1000 psia) and Pe = 1 atm., and g = 9.806 m/s<BR> (maximum theoretical, assumes frozen equilibrium, and no particle velocity lag or thermal lag).<P> <A NAME="note5"> <FONT FACE="Arial" SIZE=2 COLOR="#ff0000"><P>Note 5 </FONT></P><P>The propellant ideal mass density is 1.869 grams/cm<SUP>3</SUP>.<P> <HR WIDTH=50% ALIGN=center SIZE=2></FONT> <CENTER><H4>Last updated&nbsp;July 5, 2018</H4></CENTER> <HR SIZE=5 NOSHADE> </BODY> </HTML>