RHEOLOGICAL, OPTICAL, AND BALLISTIC INVESTIGATIONS OF PARAFFIN-BASED FUELS FOR HYBRID ROCKET PROPULSION USING A TWO-DIMENSIONAL SLAB-BURNER

This paper describes combined rheological, ballistic, and optical analyses performed on para©n-based mixtures that can be used as high regression rate hybrid rocket fuels. Experimental activities have been done at the DLR Institute of Space Propulsion in Lampoldshausen and at SPLab of Politecnico di Milano [1]. Herein, the experiments that were performed at the DLR are described in detail. Viscosity, surface tension, and regression rate of the fuels have been determined. Furthermore, the combustion was evaluated by optical measurements. Data collected so far indicate an increasing regression rate for decreasing viscosity of the liquid para©n which is in accordance with the current theories. Droplet entrainment, which is related to high regression rates, is only visible for the low-viscosity para©n-based fuels.


INTRODUCTION AND THEORY
Hybrid rocket engines are said to combine the advantages of solid and liquid propulsion systems: simple and safe storability due to separately stored oxidizer and fuel, straightforward control of mixture ratio by variation of the oxidizer mass §ow, and the possibility for immediate shutdown by closing the oxidizer£s main valve.Compared to solids, they o¨er a higher speci¦c impulse and thus more payload capability.Applications of hybrid rocket engines can be in small and medium sized sounding rockets or also as upper stages.Such programs

PROGRESS IN PROPULSION PHYSICS
exist in a large variety at di¨erent universities and companies worldwide.The inherent safety of hybrids makes them also attractive for manned §ights.The most well-known example clearly shows the advantages and possibilities of hybrid rocket engines: Space Ship One by Scaled Composites achieved the ¦rst privately funded manned suborbital §ight in 2004.
In the past, hybrid rocket engines have been blamed for their relatively low regression rate compared to solid rocket engines.For high thrust levels, long fuel grains with multiple ports are necessary which results in a low volumetric e©ciency [2].Carrick and Larson with colleagues evaluated cryogenic solid hybrid rocket fuels [35].They used cryogenic solid n-pentane and measured regression rates 510 times higher than polymeric hybrid fuels.Following these studies, the tests have been done at Stanford University with hydrocarbons with longer chains that are solid at ambient temperature [6].These fuels are para©n-based hydrocarbons and show a regression rate 3 to 5 times higher than that obtained with conventional fuels.These high values are achieved by entrainment mass transfer.Normal polymeric fuels need to be fully vaporized or pyrolysed before being burned.Para©n-based hydrocarbons form a melt layer on the surface on the fuel.From that layer, liquid droplets are entrained by liquid layer instabilities.Those are caused by the interaction of the high-velocity gas §ow in the combustion chamber and the liquid melt layer [7].For liquefying hybrids, the regression rate ' r is composed of two parts, namely, the classical regression rate ' r vap consisting of the vaporizing fuel and an additional term ' r ent which accounts for the mass transfer by entrainment: ' r = ' r vap + ' r ent ≈ 3 : 5 ' r HTPB .
To account for the increased regression rate by entrainment, the classical hybrid combustion theory needs to be modi¦ed to consider the reduced heating of the entrained fuel, the reduced blocking e¨ect due to two-phase §ow, and the increased heat transfer due to the increased surface roughness.Through the entrainment, much more fuel can be transported into the §ame zone before being totally vaporized.Scale-up tests have been done con¦rming that the theory is applicable also for large engines [8].
To quantify the value of the entrainment mass §ow ' m ent , Karabeyoglu et al. [6] assume an empirical formula adapted from ¦lm cooling experiments with entrainment.It includes the dynamic pressure p dyn , the thickness of the melt layer h, the surface tension σ, and the melt layer viscosity η l : The upper part of Eq. ( 1) contains the operational parameter of the combustion, p dyn , and indirectly the oxidizer mass §ux.The lower part of Eq. ( 1) contains the material properties σ and η l of the fuel.Literature values for the exponents 11.5 ¡ > π < γ of Eq. ( 1) are given in Table 1.The advantage of the entrainment mass §ow is that it is not limited by the heat transfer to the fuel.The exponents α and β are believed to be between 1 and 2 whereas γ and π should be almost 1.They also state that the melt layer viscosity should have a greater in §uence on the regression rate than the surface tension, meaning γ > π.The melt layer thickness h can be solved explicitly according to Karabeyoglu et al. [6].Assuming a black propellant that is absorbing all radiative heat transfer on the surface of the liquid melt layer, the melt layer thickness can be calculated as The characteristic thermal thickness δ l of the liquid layer is de¦ned by the density of the liquid ρ l and solid para©n ρ s , the regression rate ' r and the thermal di¨usivity of the liquid layer κ l as Karabeyoglu et al. compare the burning rate of their baseline mixture Paraf-¦n Wax FR 5560 (SP-1a) with the burning rate of high-density polyethylene (HDPE) and two PE Waxes samples [11].SP-1a achieves a 5 times higher regression rate than HDPE.The PE Waxes burn 23 times faster than HDPE.The viscosity data are not reported for all samples.

Optical Investigations
Nakagawa and Hikone did an investigation on the dependence of the regression rate on the fuel viscosity [12].They investigated para©n and oxygen as propellants in a two-dimensional (2D) slab burner with windows in the side for optical access [13].They used pure para©n and the same para©n blended with different viscosities by adding 10% and 20% of ethylene-vinyl acetate.Tests were run at atmospheric pressure where they could show that droplets are generated during combustion and entrain in the §ow.They assume the heat transfer coef-¦cient h as Here, k is the thermal conductivity; u ∞ is the melted fuel general velocity; η is the kinetic viscosity of the fuel, and c pl is the speci¦c heat capacity of the liquid layer.This gives a relation of the heat transfer and regression rate to be proportional to η −1/6 .This would be a very weak dependence on the viscosity of ' r ent .Additionally, the mass §ux of the tests was very low.The viscosities which were compared with the tests have been measured only at one temperature of 120 • C.But the average melt layer temperature is expected to be much higher [14].Also, the temperature during combustion might be di¨erent and the viscosity depends on the temperature of the fuel.
Chandler et al. could also show droplet entrainment [15,16].They used a 2D chamber with two windows at the side and one on top.Tests have been done with pure and blackened para©n as well as with HDPE and hydroxyl-terminated polybutadiene (HTPB).For para©n-based grains, small droplet entrainment was visible but no ¦ne details with good resolution could be measured.For HDPE, they report that only little droplet entrainment was visible.They expected this due to the high viscosity of the liquid HDPE.For HTPB, no droplet entrainment could be measured.
DeLuca et al. also did an optical investigation of the hybrid combustion process with a novel technique.They look inside a pressurized chamber over a mirror setup inside the burning fuel grain and thereby measured the instantaneous regression rate [17].

Para©n Fuels
Four di¨erent waxes are being researched as fuels.They are used in pure form as well as with di¨erent additives to modify mechanical and rheological properties.Their properties given from the manufacturer can be seen in Table 2. Type 6003 is a pure para©n wax while type 0907 is a microcrystalline wax which is used, for example, in hot glues.Type 6805 has the same application but it is a para©n wax.The last type 1276 is used for coatings, gloss, and sealing.Coatings manufactured with these waxes exhibit higher strength and, hence, abrasion resistance as well as an improved gloss impression.Its special formulation is based on waxes and a variety of di¨erent additives according to the manufacturer Sasol Wax.These para©n waxes have been tested in pure form and also mixed with 2% carbon black (CB) and 10% stearic acide (SA).

Experimental Setup and Data Acquisition
The burning rate tests of wax-based fuel formulations were evaluated in terms of regression rate values.Gaseous oxygen was used as the oxidizer.The experimental tests have been performed at the Institute of Space Propulsion at the DLR Lampoldshausen at test complex M11.An already existing modular combustion chamber was adjusted and used for the test campaigns [18,19].This chamber has been designed and used in the past to investigate the combustion behavior of solid fuel ramjets.A rearward facing step before the fuel grain was used to provide adequate §ame holding and assure combustion stability.A side view of the whole combustion chamber setup can be seen in Fig. 1.The oxidizer main §ow is entering the combustion chamber from the left after having passed two §ow straighteners.Ignition is done via an oxygen/hydrogen torch igniter from the bottom of the chamber.Two windows at each side enable several di¨erent optical diagnostic tools, which have already been performed successfully in the past during ramjet experiments.Previous test campaigns with this chamber have used the following methods to investigate the combustion behavior in solid fuel ramjets [18,19]: a color schlieren setup was used to visualize the refractive index gradients in the chamber.These can be related in pure §ows without combustion to the density gradients or species gradients.Particle image velocimetry (PIV) was used to get information about the §ow ¦eld and velocity magnitudes.A coherent antistokes Raman spectroscopy (CARS) was applied there to get information about the temperature distribution.A gas sampling probe system was used to collect condensed combustion products and analyze them subsequently.A test sequence is programmed before the test and is run automatically by the test bench control system.All tests have been done with the same settings shown in Table 3.Each test duration is 5 s.For redundancy, a separate measurement system is used for data acquisition during the tests.For this purpose, an ADwin measurement system by J ager Messtechnik is used.Data acquisition on this measurement system was programmed by the proprietary software named ADbasic.All raw data are low-pass ¦ltered via Dewetron signal ampli¦ers before the data acquisition.Depending on the sensor type that is used, a gain and additional ¦lters can be set to the

Viscosity Measurements
The viscosity of a §uid de¦nes its resistance to deformation by external forces like shear stress or tensile stress.The viscosity in Eq. ( 1) is expected to have the greatest in §uence on ' m ent .For this reason, the viscosity of fuels in these tests is evaluated in detail and will be compared with the regression rate results from the burning rate tests.The relation between the viscosity η( ' γ), the shear rate ' γ, and the shear stress τ ( ' γ) is described by The viscosity measurements have been done with a Haake RheoStress 6000 rotational rheometer with a plateplate and coneplate geometry.The measurement range is between 10 −7 and A measurement of the viscosity of the pure waxes at di¨erent shear rates was done before each test and can be seen in Fig. 3.Then, a shear rate for the temperature ramp measurement was chosen where the waxes are still in the linear viscoelastic range.In Fig. 4, the measurement of viscosity depending on the temperature is shown.Tests have been done starting from 200 • C down to the solidi¦cation point of the para©n samples.The viscosities of each type seem to reach asymptotic values at higher temperatures but the exact value cannot be clearly determined [20].Thus, it is di©cult to choose the viscosity at an average temperature between the melting and boiling temperature which could be used for Eq. ( 1).The boiling and average temperature can be calculated, for example, with equations from Marano and Holder [21].
The pure para©n samples investigated here show a Newtonian behavior, which means that the measured viscosity is independent of the applied shear rate.For the mixtures with CB and SA, a non-Newtonian behavior is measured for percentages of CB greater than 1.5%.This can be seen in Fig. 5.The in §uence of the CB percentage to the viscosity is shown in Fig. 6.Viscosity is increasing with increasing CB percentage.The in §uence of the 10% SA addition on the viscosity in the mixed para©n samples has also been measured.The change in viscosity compared to the pure para©n samples was negligible.

Surface Tension Measurements
Surface tension is the property of a liquid to resist against an external force applied to it.It is caused by the cohesion force of similar molecules.Surface tension depends strongly on the temperature with a linear relation.Empirical correlations like the E otv os rule use the critical temperature, the molar volume, and the molar surface tension to cal- Another relation that can be used is from GuggenheimKatayama.For the present experiments, a Kr uss EasyDyne tensiometer was used to measure the surface tension σ of the waxes.The measurement range is from 1 to 999 mN/m with an accuracy of ±0.1 mN/m.Figure 7 shows the measured surface tension values of Sasol 6003 as an example at different temperatures.About 3540 measurements for each sample have been taken at decreasing temperature.The starting temperature of the para©n samples was approximately 130 • C.Then, the measurements have been taken while the sample was cooling down until it started to solidify.A best-¦t line   6 and 7 (T av is the average temperature between the melting temperature (≈ 6094 • C, see Table 2) and boiling temperature (≈ 450 • C) of the individual para©n type).Table 6 shows a comparison of the surface tension values of the pure substances.The change -σ is calculated by comparison with the value from type 6003.Figure 8 shows the best-¦t lines of all pure Sasol waxes.It can be seen that type 6003 and 6805 have about the same negative slope of the curve and also approximately the same value of surface tension with only 2.08 percent di¨erence (see also Table 6).Type 0907 has a smaller negative slope as 6003 and, therefore, the value of surface tension at T av in Table 6 is −31.89%lower than that of 6003.At 100 • C, the increase in surface tension is about 6.9% compared to 6003.In contrast, type 1276 has a slightly bigger negative slope which results in a 28.18 percent increase in surface tension at T av , compared to a 9.5 percent increase at 100 • C. Looking back at Eq. ( 1), it should be reminded that an increase in surface tension would result in a decrease in ' r ent .
An overview about the meas- ured surface tensions of the paraf-¦n waxes with di¨erent additives at 100 • C is shown in Table 7 [22].
The surface tension at the average temperature T av between the melting and boiling temperature of par-af¦n is also extrapolated from the measured data and the deviation from the pure formulation is calculated.
Comparing the surface tension in Table 7, one can see that the di¨erences are smaller than 3% between the pure formulations and those with additives at 100 • C. At T av , the di¨erences are bigger.Stearic acide decreases the surface tension for 6003, 6805 and 1276 while an increase of 16.42% is measured for 0907.For CB, one has small changes in surface tension with 6003, 6805, and 1276 while 0907 has a 19.51 percent increase in surface tension.Addition of 10% Al gives only a 2.84 percent increase for 6003 while one gets 7.17 percent increase for 0907.One can see that for some additives, the surface tension at extrapolated temperature is changed up to 20%.This would also result in a change in ' r ent assuming that Eq. ( 1) and its exponents from Table 1 are valid.

Regression Rate
The reason to use a 2D fuel slab was primarily to get an insight into the combustion process above the fuel surface.The regression rates with this setup have also been measured but they should not be compared directly with data from cylindrical fuel grains.With the 2D slab, the convective and radiative heat §uxes are di¨erent.Much more heat is lost to the surroundings like the Quartz glass windows and the upper metallic surface of the combustion chamber.Thus, less heat is transferred to the fuel and the regression rates measured are lower than with cylindrical fuel grains.
The fuel mass §ow ' m f from the solid fuel into the combustion zone is de¦ned by the heat of vaporization of the fuel and the total heat transfer by convection and radiation into the fuel.It is proportional to fuel£s density ρ f , its surface area A S , and the regression rate ' r: The regression rate ' r in a hybrid rocket engine is described with the oxidizer mass §ux G ox by ' r = aG n ox .The fuel slabs being used have a length of about 180 mm, width of 90 mm, and height of 18 mm.The leading edge upstream has an angle of about 20 • with a length of 50 mm.The tests have also been done with smaller slabs with dimensions of length of about 100 mm, width of 70 mm, and height of 14 mm.The regression rate values shown are space-and time-averaged.A measurement uncertainty during the tests is that some para©n is §owing down beneath the fuel slab in the chamber.This fuel is not burning and remains in the chamber.Thus, this residual is collected after the test and is considered for the mass loss.For Para©n 0907 and 6805, di¨erent tests with both fuel slab sizes can be seen in Fig. 9.For 0907, the big fuel slabs show about twice the regression rate of the small slabs at similar oxidizer mass §ux.For 6805, the di¨erence is almost 34 times.The reason for this lies in the di¨erent oxidizer mass §ow to fuel mass §ow ratios (ROF) during the tests with the small and the big slabs.For the big slab, the ROF is between 515 whereas for the small slabs, the ROF is much higher, up to 70.When the combustion temperature is computed for 0907 with CEA for di¨erent ROF, one gets a graph like in Fig. 10.There one can see that the maximum temperature is at the stoichiometric ratio between 2 and 3 and the temperature is decreasing rapidly for higher ROF.Thus, for higher ROF, less heat can be transferred to the solid fuel and the regression rate decreases.Therefore, care must be taken to compare regression rates of the fuels at similar ROF.Karabeyoglu et al. propose a correction for this e¨ect based on the regression rate constants and the ROF [8,23].The e¨ect of increasing ROF can also be seen in Fig. 9b  ROF of 0907 other using the same slab.The highest regression rate 0.24 mm/s corresponds to an ROF of about 7.Then, the regression rate decreases as ROF increases.At 0.23 mm/s, one has an ROF of 8.2.The smallest value 0.19 mm/s had an ROF of 13.2.

PROGRESS IN PROPULSION PHYSICS
An overview about the averaged regression rates of all tests with big fuel slabs and similar ROF can be seen in Fig. 11.Here, one can see that para©n 6003 with the lowest viscosity shows the highest regression rate.This is valid for the pure sample and, also, for the mixture with CB and SA, where the mixtures have a higher viscosity.Furthermore, the regression rates are decreasing as the viscosity values of the para©n samples are increasing (see also Tables 4 and 5).Type 1276 with its very high viscosity shows regression rate values as low as HTPB values measured at SPLab at similar mass §ux [1].When looking at Table 6, one sees that the di¨erence in surface tension compared to the fastest burning para©n type 6003 is only 9.5%.Thus, one can conclude that a low viscosity has a much higher in §uence on the entrainment mass §ow than a low surface tension.
The importance of the viscosity gets more clear if, one looks at Table 8.There, the average of all regression rate values from Fig. 11 is computed.One can see that type 6003 with the lowest viscosity achieves the highest regression   rates.The di¨erence -' r pure in regression rate uses the value of pure 6003 for the pure para©ns.Concerning the mixtures, the formulation of 6003 + CB + SA is chosen as reference.The same applies for the change in viscosity -η.The change in viscosity and regression rate of the para©n samples due to the addition of CB and SA is shown in Table 9.

Ignition delay
From the video data, the ignition behavior has also been analyzed.The tests with 5000 FPS recording rate and similar shutter settings have been chosen (Table 10).The appearance of the ¦rst §ame corresponds to the ignition of the oxygen/hydrogen torch igniter.Then, the time of the ¦rst §ame on top of the fuel slab is considered as time when the fuel slab starts to ignite.The time di¨erence between these two is listed as the ignition delay.Finding the ignition time of the fuel is sometimes di©cult because the igniter also illuminates the picture and the §ame of the para©n is not very bright initially.Generally, it seems that the pure para©n samples ignite faster than the mixtures, after about 0.1 to 0.2 s.For the mixtures, the ignition delay is higher, between 0.22 and about 0.5 s.Only the samples 1276 in pure and mixed form seem to ignite after the same delay of only 0.1 s.Additionally, the §ame of type 1276 appeared brighter and thicker compared to the other samples.This might also lead to an earlier visibility of the ¦rst §ame and, thus, apparently a shorter ignition delay.

Combustion behavior
The burning rate tests have been recorded with a high-speed camera to get more knowledge about the combustion process.All images are recorded with the oxidizer §ow direction from left to right.Figure 12 shows the entrainment process in good detail.The image is taken during the ignition phase of test 169 at T = 0.424 s.In the video, a lot of very ¦ne droplets can be seen which are released from all along the surface of the fuel.Droplets are released also from the waves rolling over the fuel surface.This is in accordance with the theory of the liquid layer KelvinHelmholtz instability [7].The droplet entrainment is not stationary, but appears rather periodically.A huge burst of droplets entraining is followed by a slight decrease and then again a burst of more droplets.For all tests, a wave like §ame structure can be seen in the high-speed video data.Figure 13 shows an image of test 096 during combustion.The §ame is turbulent and not stationary.One can see a roll up of the §ame at start of the fuel grain and then the §ame is moving along on top of the fuel.About 2 4 single large-scale waves can be seen on top of the fuel at one frame during steady state.The rotation of a vortex after the §ame-holding step can also be seen.The step generates a small §ame in front of the fuel which is burning continuously.The appearance of the long wave like structures on top of the fuel seems related with the vortex shedding after the step.The in §uence of the rearward facing step in the precombustion chamber is currently in progress.More results are shown in [24].The lines in Fig. 13 in the middle of the image are cracks in the glass due to a hard ignition in a previous test.Waves during the combustion of para©n have also been seen by Kim et al. [25].But they were able to measure strong droplet entrainment only during nonreacting hotgas injection.Optical experiments by Nakagawa and Hikone could also only show minor droplet entrainment but no details on the roll wave instabilities [12].
Due to the high shutter settings, droplet formation seems only visible during the ignition transients.When the igniter starts burning and the para©n is not yet fully ignited, many droplets can be seen being released mainly from the area of the fuel where the igniter hits the fuel slab.When the para©n is fully burning, the §ame is too bright.Thus, only some thicker droplets can be seen which are released from near the burning surface but no ¦ne droplets and structures like during ignition.
As a reference, HDPE has also been used in a further test campaign [24].An example is shown in Fig. 14.Here, almost no droplet entrainment was visible during the tests.The §ames also show wave behavior.Also, HDPE is expected to form a liquid layer, but high viscosity prevents entrainment.
Figure 15 shows an image of a fuel sample after the combustion test.Here, one can also see some residual wave like structure on the surface.These structures appeared on most of the recovered fuel samples, for the mixtures and, also, the pure samples.It is likely that this structure can be linked to the combustion behavior of the para©n samples and the wave like §ame structure.But one should also consider that N 2 purge §ow was initiated at the end of the test to end the combustion and purge the pipes.This might have also in §uenced the surface of the para©n.
The pressure of 1 bar in the current combustion chamber is still subcritical for the para©ns which are used [21].Thus, a liquid melt layer is expected.This is in agreement with the huge droplet entrainment which was measured optically in the tests.At higher pressures, the para©n would be in supercritical conditions and a pyrolysis layer is expected on top of the liquid layer [11].This could change the liquid layer instabilities and also the entrainment process.But according to Karabeyoglu et al. [8], no pressure e¨ects on the regression rate are expected for typical operating pressures.This has been stated due to measured regression rate data during tests, but no clear optical investigations at higher pressure have been made until now.

CONCLUDING REMARKS
Experimental characterization has been done with para©n fuels that can be used for high regression rate applications.Optical investigations of the entrainment process have been done with high quality.The entrainment process for lowviscosity fuels shows a huge amount of very ¦ne droplets being released from the surface and, thereby, enabling high regression rates.A wide database concerning viscosity, surface tension, burning rate data, and optical measurements has been established.The regression rate data collected so far indicate an increasing regression rate for decreasing viscosity of the liquid para©n.These results show the same qualitative trend as with 2D radial burning rate tests done at SPLab with the same fuels [1].Viscosity data show big di¨erences depending on the para©n type and type and amount of additives.At higher CB percentages, the mixtures show non-Newtonian behavior where the viscosity of the mixture depends also on the applied shear rates.The di¨erences in surface tension between di¨erent para©n samples are smaller and, thus, are less in §uencing on the regression rate.

Figure 1
Figure 1 Sideview of combustion chamber setup

Figure 3
Figure 3 Comparison viscosity vs. shear rate of pure para©n at T = 120 • C: 1 ¡ Sasol wax 0907; 2 ¡ Sasol wax 1276; 3 ¡ Sasol wax 6003; and 4 ¡ Sasol wax 6805 1500 min −1 at constant shear or at constant rotation.The frequency range is between 10 −5 and 100 Hz.A measurement of the viscosity of the pure waxes at di¨erent shear rates was done before each test and can be seen in Fig.3.Then, a shear rate for the temperature ramp measurement was chosen where the waxes are still in the linear viscoelastic range.In Fig.4, the measurement of viscosity depending on the temperature is shown.Tests have been done starting from 200 • C down to the solidi¦cation point of the para©n samples.

Figure 7
Figure 7 All measurements (signs) of Sasol 6003 surface tension; line ¡ linear regression culate the surface tension of pure liquids at a certain temperature.Another relation that can be used is from GuggenheimKatayama.For the present experiments, a Kr uss EasyDyne tensiometer was used to measure the surface tension σ of the waxes.The measurement range is from 1 to 999 mN/m with an accuracy of ±0.1 mN/m.Figure7shows the measured surface tension values of Sasol 6003 as an example at different temperatures.About 3540 measurements for each sample have been taken at decreasing temperature.The starting temperature of the para©n samples was approximately 130 • C.Then, the measurements have been taken while the sample was cooling down until it started to solidify.A best-¦t line

Figure 9
Figure 9 Comparison between regression rates of big (1) and small (2) fuel slabs of 0907 (a) and 6805 (b)

Table 1
Entrainment exponent values

Table 2
Wax properties given by manufacturer

Table 3
Automatic test sequence 2% of the §ow rate.A mass §ow rate measurement of the oxidizer can be seen in Fig.2.A steady-state mass §ow rate of about 53 g/s is set for all tests.Mass §ow rate data are acquired in Labview via a digital protocol.The tests are done at atmospheric pressure.

Table 5
Average di¨erence between measured viscos-

Table 6
Comparison surface tension of pure para©n at 100 • C

Table 7
Measured surface tension values at 100 • C was calculated to get a linear relation and extrapolate the surface tension values at T av in Tables

Table 8
Comparison average regression rates of pure para©n and para©n with CB and SA

Table 9
Comparison average regression rates be-

Table 10
Ignition delay of the di¨erent para©n samples