COOLING SYSTEM AND METHOD FOR COMBUSTORS

Abstract

The cooling system includes a jacket disposed at least partially around a combustor having a combustor channel opening. The jacket includes a slot having an opening oriented towards a downstream end of the combustor. The slot may include a width ranging from around 0.5% to around 100% of a width of the combustor channel opening. The slot accepts a coolant through the opening of the slot.

Claims

1. A cooling system comprising: a combustor having a central axis; a jacket disposed at least partially around the combustor, wherein the jacket includes a slot having an opening oriented towards a downstream end of the combustor.

2. The cooling system of claim 1, wherein the slot includes a width ranging from around 0.5% to around 100% of a width of a channel opening of the combustor.

3. The cooling system of claim 1, wherein the slot is substantially parallel with the central axis.

4. The cooling system of claim 1, wherein the slot is angled in comparison to the central axis.

5. The cooling system of claim 1, wherein the opening of the slot includes a tapered surface.

6. The cooling system of claim 1, wherein an interior wall of the slot includes a wavy surface.

7. The cooling system of claim 1, wherein the slot accepts a coolant through the opening of the slot.

8. The cooling system of claim 7, wherein the coolant includes at least one of a fuel and an oxidizer.

9. The cooling system of claim 7, wherein the coolant is injected in at least one of subsonic and supersonic core flow.

10. The cooling system of claim 7, wherein a flow of the coolant is at a lower pressure than a pressure in the combustor.

11. The cooling system of claim 1, wherein the slot further includes a stator vane to change directionality of the coolant flow.

12. The cooling system of claim 1, wherein the jacket has discrete cooling holes to enable additional film cooling.

13. The cooling system of claim 1; wherein a wall of the jacket includes a porous material to enable transpiration cooling.

14. The cooling system of claim 1; wherein a wall of the jacket is coated with a thermal barrier coating.

15. The cooling system of claim 1, further including a downstream nozzle.

16. The cooling system of claim 1, wherein the combustor includes at least one of a hollow cylinder and a concentric cylinder.

17. The cooling system of claim 19, wherein the concentric cylinder includes a coolant slot.

18. The cooling system of claim 19, wherein the cylinder of the combustor includes at least one of a diverging wall and a converging wall.

19. A method of using a cooling system configured to cool an end wall or lower an operating temperature of a combustor having a combustor channel opening around a central axis, the method comprising the steps of: providing the cooling system having a jacket disposed at least partially around the combustor, wherein the jacket includes a slot having an opening oriented towards a downstream end of the combustor; injecting a coolant into the opening of the slot; and cooling the combustor.

20. The method of claim 22, wherein the injected coolant has a coolant flow ranging from around 10% to around 200% of a main inlet air flow of the combustor.

21. The method of claim 22, wherein the cooling system accepts oblique shock waves.

Description

DRAWINGS

[0011] The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations and are not intended to limit the scope of the present disclosure.

[0012] FIG. 1 is a front perspective view of a cooling system, according to one embodiment of the present disclosure;

[0013] FIG. 2A is a cross sectional left side elevational view of the cooling system, taken at B-B in FIG. 1, according to one embodiment of the present disclosure;

[0014] FIG. 2B is an enlarged view of the cooling system shown in FIG. 2A, further depicting a plurality of slots, according to one embodiment of the present disclosure;

[0015] FIG. 3 is a front perspective cross-sectioned view of the cooling system, as shown in FIGS. 2A-2B, according to one embodiment of the present disclosure;

[0016] FIG. 4 is a front perspective view of the jacket of the cooling system, according to one embodiment of the present disclosure;

[0017] FIG. 5A is a left side elevational view of the cooling system having a three-slot design;

[0018] FIG. 5B is a left side elevational view of the cooling system, further depicted as a computational mesh, according to one embodiment of the present disclosure;

[0019] FIG. 6A is a front perspective view of the cooling capabilities of the system over time at T= Tdetonation, according to one embodiment of the present disclosure;

[0020] FIG. 6B is a front perspective view of the cooling capabilities of the system over time at T= Tdetonation, according to one embodiment of the present disclosure;

[0021] FIG. 6C is a front perspective view of the cooling capabilities of the system over time at T= Tdetonation, according to one embodiment of the present disclosure;

[0022] FIG. 6D is a front perspective view of the cooling capabilities of the system over time at T= Tdetonation, according to one embodiment of the present disclosure;

[0023] FIG. 7A is a front elevational view of a stator that may be utilized with in the cooling system, according to one embodiment of the present disclosure;

[0024] FIG. 7B is a front elevational cross-sectioned view of the stator, as shown in FIG. 7A, according to one embodiment of the present disclosure;

[0025] FIG. 8 is a front perspective view of the cooling system, further depicting the opening of the slots, according to one embodiment of the present disclosure;

[0026] FIG. 9 is a top perspective view of the cooling system, further depicting the inlet feed tubes of the cooling as well as measurement ports, according to one embodiment of the present disclosure;

[0027] FIG. 10 is a cross sectional left side elevational view of the slot having a tapered end wall near the opening of the slot, according to one embodiment of the present disclosure;

[0028] FIG. 11 is a cross sectional left side elevational view of an angled slot, according to one embodiment of the present disclosure;

[0029] FIG. 12 is a line graph illustrating a four-fold reduction in heat flux reduction of the cooling system compared to non-cooled combustors, according to one embodiment of the present disclosure;

[0030] FIG. 13A-B are line graphs illustrating how the exhaust profile can be altered, further depicting the uncooled combustor providing an exit temperature of 2000K, whereas the cooling jacket lowered the exit temperatures to around 1500K while keeping a transonic-supersonic exhaust, according to one embodiment of the present disclosure;

[0031] FIG. 14 is a flowchart of a method for using the cooling system, according to one embodiment of the present disclosure;

[0032] FIG. 15 is a series of rear elevational views of the combustor, further depicting the progression of a detonation wave over time, according to one embodiment of the present disclosure;

[0033] FIG. 16 is a pair of line graphs comparing the temperature profile of the cooling system compared to an uncooled system over time, further depicting the cooling system illustrating no significant increase in slot temperature, according to one embodiment of the present disclosure;

[0034] FIG. 17 is a line graph illustrating load cell data utilized for determining the start and end points for the test data in FIG. 18, according to one embodiment of the present disclosure;

[0035] FIG. 18 is a list of test duration results, according to one embodiment of the present disclosure;

[0036] FIG. 19 is a scatter plot diagram depicting a correlation between cooling mass-flow and slot temperature increase rate, according to one embodiment of the present disclosure;

[0037] FIG. 20 is the scatter plot diagram, as shown in FIG. 19, having the slapping mode tests removed;

[0038] FIG. 21 is a line graph illustrating slot pressures compared between the cooling system and uncooled systems, according to one embodiment of the present disclosure; and

[0039] FIG. 22 is a scatter plot diagram of the slot pressure ratios compared the blowing ratio, according to one embodiment of the present disclosure.

DETAILED DESCRIPTION

[0040] The following description of technology is merely exemplary in nature of the subject matter, manufacture, and use of one or more inventions, and is not intended to limit the scope, application, or uses of any specific invention claimed in this application or in such other applications as may be filed claiming priority to this application, or patents issuing therefrom. Regarding methods disclosed, the order of the steps presented is exemplary in nature, and thus, the order of the steps can be different in various embodiments, including where certain steps can be simultaneously performed. A and an as used herein indicate at least one of the item is present; a plurality of such items may be present, when possible. Except where otherwise expressly indicated, all numerical quantities in this description are to be understood as modified by the word about and all geometric and spatial descriptors are to be understood as modified by the word substantially in describing the broadest scope of the technology. About when applied to numerical values indicates that the calculation or the measurement allows some slight imprecision in the value (with some approach to exactness in the value; approximately or reasonably close to the value; nearly). If, for some reason, the imprecision provided by about and/or substantially is not otherwise understood in the art with this ordinary meaning, then about and/or substantially as used herein indicates at least variations that may arise from ordinary methods of measuring or using such parameters.

[0041] Although the open-ended term comprising, as a synonym of non-restrictive terms such as including, containing, or having, is used herein to describe and claim embodiments of the present technology, embodiments may alternatively be described using more limiting terms such as consisting of or consisting essentially of. Thus, for any given embodiment reciting materials, components, or process steps, the present technology also specifically includes embodiments consisting of, or consisting essentially of, such materials, components, or process steps excluding additional materials, components or processes (for consisting of) and excluding additional materials, components or processes affecting the significant properties of the embodiment (for consisting essentially of), even though such additional materials, components or processes are not explicitly recited in this application. For example, recitation of a composition or process reciting elements A, B and C specifically envisions embodiments consisting of, and consisting essentially of, A, B and C, excluding an element D that may be recited in the art, even though element D is not explicitly described as being excluded herein.

[0042] As referred to herein, disclosures of ranges are, unless specified otherwise, inclusive of endpoints and include all distinct values and further divided ranges within the entire range. Thus, for example, a range of from A to B or from about A to about B is inclusive of A and of B. Disclosure of values and ranges of values for specific parameters (such as amounts, weight percentages, etc.) are not exclusive of other values and ranges of values useful herein. It is envisioned that two or more specific exemplified values for a given parameter may define endpoints for a range of values that may be claimed for the parameter. For example, if Parameter X is exemplified herein to have value A and also exemplified to have value Z, it is envisioned that Parameter X may have a range of values from about A to about Z. Similarly, it is envisioned that disclosure of two or more ranges of values for a parameter (whether such ranges are nested, overlapping, or distinct) subsume all possible combination of ranges for the value that might be claimed using endpoints of the disclosed ranges. For example, if Parameter X is exemplified herein to have values in the range of 1-10, or 2-9, or 3-8, it is also envisioned that Parameter X may have other ranges of values including 1-9, 1-8, 1-3, 1-2, 2-10, 2-8, 2-3, 3-10, 3-9, and so on.

[0043] When an element or layer is referred to as being on, engaged to, connected to, or coupled to another element or layer, it may be directly on, engaged, connected, or coupled to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being directly on, directly engaged to, directly connected to or directly coupled to another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., between versus directly between, adjacent versus directly adjacent, etc.). As used herein, the term and/or includes any and all combinations of one or more of the associated listed items.

[0044] Although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms may be only used to distinguish one element, component, region, layer or section from another region, layer, or section. Terms such as first, second, and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer, or section discussed below could be termed a second element, component, region, layer, or section without departing from the teachings of the example embodiments.

[0045] Spatially relative terms, such as inner, outer, beneath, below, lower, above, upper, and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially relative terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the FIG. is turned over, elements described as below, or beneath other elements or features would then be oriented above the other elements or features. Thus, the example term below can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.

[0046] A cooling system 100 of the present disclosure may be configured to lower an operating temperature of a combustor 102 and/or reduce the temperature near a wall of the combustor 102 without lowering the core temperature of the combustor 102. As shown in FIGS. 1-2A, the combustor 102 may include a combustor channel opening 104 around a central axis A. The cooling system 100 includes a jacket 106 disposed at least partially around the combustor 102. As shown in FIGS. 2B and 5A-5B, the jacket 106 includes a slot S1, S2, S3 having an opening oriented towards a downstream end DE of the combustor 102. The slot S1, S2, S3 may include a width W1 ranging from around 0.5% to around 100% of a width W2 of the combustor channel opening 104, as shown in FIGS. 5A and 8. In a specific example, the slot S1, S2, S3 may accept a coolant through the opening of the slot S1, S2, S3. The coolant may enhance the cooling capabilities of the cooling system 100.

[0047] In certain circumstances, the slot S1, S2, S3 may be provided in various ways. For instance, the slot S1, S2, S3 may be substantially parallel with the central axis A. In another example, as shown in FIG. 11, the slot S1, S2, S3 may be angled in comparison to the central axis A. As shown in FIG. 10, the opening of the slot S1, S2, S3 may include a tapered surface 108 to reduce the size of the region of recirculating flow at the tip of the slot S1, S2, S3 which increases cooling effectiveness. The combustor end wall can be configured with other contouring to reduce pressure losses. An interior wall of the slot S1, S2, S3 may further include a wavy surface 110 which may locally add acceleration and/or compression regions. In a specific example, the stator 112 may measure stagnation pressure. Provided as a non-limiting example, the slot S1, S2, S3 may include a plurality of slots. The plurality of slots S1, S2, S3 may be disposed substantially adjacent to, yet separated from each other, as shown in FIGS. 2A-3, 5A-6, and 8. Advantageously, by adding more slots, there are more injection points for coolant, ensuring that if the passing detonation disrupts the coolant layer, more coolant will be injected downstream. As a non-limiting example, FIGS. 2A-3 and 5A-6D illustrate the cooling system 100 having a three-slotted design. With further reference to FIG. 5B, a computational mesh was made of a structured mesh in ICEM. The total mesh size was around 50 million cells, in which care was taken to resolve the viscous sublayer in the main combustion chamber. To simplify the geometry, a premixed simulation was performed, in which hydrogen-air was imposed at the inlet of the domain. The first two slots S1, S2 require higher feed pressures than the third slot S3 which lies in the transonic/supersonic exhaust of the combustor 102. Additionally, downstream of the slots S1, S2, S3, a diverging section DS may allow the flow coming out of the combustor 102 to fully expand to supersonic conditions. It is also contemplated the combustor 102 may instead utilize a converging section for certain applications. After reaching steady state, FIGS. 6A-6D shows a snapshot of unsteady interaction of the jets with the main detonation wave. At T= Tdetonation, the cooling slots S1, S2, S3 do not have enough pressure to push cooling into the combustion chamber, but at T= Tdetonation, cooling starts to flow into the main combustion chamber all the way until T= Tdetonation. One skilled in the art may select other suitable ways to provide the slot S1, S2, S3, within the scope of the present disclosure.

[0048] In certain circumstances, as shown in FIGS. 3 and 7A-B, the cooling system 100 may further include a stator 112 disposed downstream from the combustor 102. The stator 112 may straighten a combustor exit flow before it enters a turbine, thus enhancing power extraction. In certain circumstances, the stator 112 may include a plurality of stators. In a specific example, the stator 112 may measure stagnation pressure. In yet another specific example, the slot S1, S2, S3 may further includes a stator vane to change directionality of the coolant flow. One skilled in the art may select other suitable ways for providing the stator 112 with the cooling system 100, within the scope of the present disclosure.

[0049] In certain circumstances, the coolant may be provided in various ways. For instance, the coolant may be provided in a gaseous state. The coolant may include nitrogen. In a more specific example, the coolant may include air. In another non-limiting example, the coolant may include a fuel and/or an oxidizer. The coolant may be injected in a subsonic and/or supersonic core flow. A flow of the coolant may be provided at a lower static pressure than the static pressure in the combustor 102 if injected in a high-speed region. A skilled artisan may select other suitable ways to provide the coolant, within the scope of the present disclosure.

[0050] The pressures in the rotating detonation combustor 102 vary cyclically, which means that during a certain period of time the combustor pressure might be too high to inject cooling into the combustor 102, and flow reversal can happen or the cooling slots S1, S2, S3 are blocked off. Whereas when the pressure is sufficiently low within the combustion chamber, the cooling slots S1, S2, S3 are activated and cooling may be provided to the combustor walls.

[0051] In certain circumstances, the jacket 106 may be provided in various ways. For instance, the jacket 106 may be constructed from a metal, a ceramic, a composite material, and/or a plastic. In a specific example, the jacket 106 may be constructed from milling and/or additive manufacturing. In another specific example, the jacket 106 may be made of a porous material to allow transpiration cooling to further enhance its cooling capabilities. As shown in FIGS. 4 and 9, further film cooling may also be further added through discrete holes 114 and/or the inclusion of a thermal barrier coating could aid in reducing wall heat flux. Provided as a non-limiting example, the jacket 106 may be constructed on a direct metal laser sinter 3D printer. Provided as another non-limiting example, the jacket 106 may be specifically made with SAE 316L stainless steel which offers fair corrosion resistance at high temperatures while also minimizing costs. In another specific example, the cooling system 100 may also include a downstream nozzle and/or ejector that may be utilized to provide a secondary air stream. One skilled in the art may select other suitable ways to provide the jacket 106, within the scope of the present disclosure.

[0052] The cooling system 100 may be provided in various ways. For instance, as shown in FIG. 14, the cooling system 100 may be used according to a method 200 to lower an operating temperature of a combustor 102 having a combustor channel opening 104 around a central axis A. The method 200 may include a step 202 of providing the cooling system 100 having a jacket 106 disposed at least partially around the combustor 102. The jacket 106 may include a slot S1, S2, S3 having an opening oriented towards a downstream end DE of the combustor 102. A coolant may be injected into the opening of the slot S1, S2, S3. Afterwards, the combustor 102 may be cooled. In a specific example, the injected coolant may have a coolant flow ranging from around 10% to around 200% of a main inlet air flow of the combustor 102. Advantageously, the cooling system 100 may accept oblique shock waves. A skilled artisan may select other suitable methodologies for using the cooling system 100, within the scope of the present disclosure.

[0053] In certain circumstances, the cooling system 100 may include a combustor 102 having a central axis A and a jacket 106 disposed at least partially around the combustor 102. The jacket 106 may include a slot S1, S2, S3 having an opening oriented towards a downstream end DE of the combustor 102. In a specific example, the combustor 102 may include a hollow cylinder and/or a concentric cylinder. In a more specific example, the cylinder of the combustor 102 may include a diverging wall and/or a converging wall. In another specific example, the inner cylinder may also contain a slot or a plurality of slots to provide cooling to protect this surface. It is also contemplated that the cooling system 100 may include a combustor 102 that does not utilize a center body, such as a cylinder. One skilled in the art may select other suitable ways to provide the cooling system 100, within the scope of the present disclosure.

[0054] Advantageously, as shown in FIG. 12, the cooling system 100 may provide a multi-fold heat flux reduction when compared to a non-cooled combustor and keep the walls below melting temperature through a thin layer of cooling flow. The cooling mass flow may constitute around 30% of the core mass flow. Additionally, as shown in FIGS. 13A-13B, the exhaust profile may be altered when utilizing the cooling system 100. For instance, an uncooled combustor may provide an exit temperature of 2000K, whereas the cooling system 100 may lower the exit temperatures to around 1500K while keeping a transonic-supersonic exhaust.

EXAMPLE

[0055] Provided as a specific, non-limiting example, one embodiment of the cooling system 100 was experimentally tested. Thermocouples were affixed to the rear-side of all three film-cooling slots S1, S2, S3 to determine surface temperature of each cooling slot S1, S2, S3. Additionally, pressure taps were integrated into the film-cooling apparatus such that static pressures were also available for each slot S1, S2, S3.

[0056] For each test, a Phantom high-speed camera operating at 100 khz was used in conjunction with a mirror to visualize the detonation waves from the aft of the combustor 102, looking forward. Due to heat distortion from the combustor exhaust during firing, the resulting high-speed footage exhibits noticeable distortion. Nevertheless, detonation waves are still visible, as shown in FIG. 15. A still image taken before the test starts is shown on the left, and then the following sequence depicts a single detonation wave propagation in a clockwise direction. For clarity, the detonation wave is highlighted by the circle in the lower sequence.

[0057] A full test matrix for this campaign is shown below in Table 1. Of note, despite 33 tests having been run, only 23 of the tests had successful ignition. The remaining were either cold-flows or failed-ignitions. For this data analysis, only the ignited tests have been considered. Test #32 is an uncooled control case.

TABLE-US-00001 TABLE 1 Air + H2 Air H2 Chamber 1 Chamber 2 Duration Mass Flow Pressure Pressure Mass Flow Pressure Mass Flow Pressure Test # (sec) Type (lb/s) (psi) (psi) Rate (lb/s) (psi) Rate (lb/s) (psi) 1 0.3 Cold 1 334 N/A 0.1 365 0 0 2 0.3 Cold 1 334 N/A 0 0 0.09 370 3 0.3 Cold 1 334 N/A 0.38 365 0.22 370 4 0.3 Cold 1 334 N/A 0.29 365 0.19 370 5 0.3 Ignition 1 334 525 0.1 365 0.09 370 6 1 No ignition 1 334 525 0.1 365 0.09 370 7 1 Ignition 1 334 525 0.1 365 0.07 370 8 1.5 No ignition 1 334 525 0.1 365 0.1 370 9 2 Partial ignition 1 334 525 0.1 365 0.1 370 10 2 Ignition 1.39 473 691 0.1 365 0.1 370 11 2.5 No ignition 1 333 527 0.1 365 0.1 370 12 2.5 No ignition 1 333 527 0.1 365 0.1 370 13 1 Ignition 1 341 499 0.1 365 0.1 380 14 2 Ignition 1 343 546 0.1 365 0.1 380 16 2 Ignition 1 340 540 0.1 364 0.1 369 17 2 Ignition 1 340 540 0.2 780 0.2 770 18 2 Ignition 1 340 540 0.2 730 0.2 745 19 2 Ignition 1 343 537 0.2 730 0.2 740 20 2 Ignition 1 342 532 0.3 1128 0.2 745 21 2 Ignition 1 341 642 0.3 1150 0.2 742 22 2 Ignition 1 343 643 0.3 1108 0.2 742 23 2 Ignition 1.5 490 756 0.3 1108 0.2 744 24 2.5 Ignition 1.5 490 823 0.3 1108 0.2 744 25 2.5 No ignition 1.5 506 805 0.3 1106 0.2 743 26 2.5 Ignition 1.5 504 806 0.3 1106 0.2 743 27 2.5 Ignition 2 655 1068 0.3 1110 0.2 739 28 3 Ignition 2 668 1070 0.3 1099 0.2 747 29 3 Ignition 2 666 1070 0.2 730 0.2 742 30 3 Ignition 2 671 1066 0.3 1096 0.3 1137 31 3 Ignition 2 669 1063 0.4 1458 0.3 1107 32 0.5 Ignition 1 344 539 0 0 0 0 33 5 Ignition 1 340 548 0.3 1106 0.2 738

[0058] As an initial demonstration of the cooling-slot effectiveness, the temperature profile of the uncooled control case (Test #32) is plotted alongside that of Test #33, the longest duration cooled test and is depicted in FIG. 16. The vertical dashed lines denote the start and end times of each test. As can be seen, the uncooled test experiences a rapid increase in slot temperature over the short test duration, whereas the cooled test experiences no significant increase in slot temperature, enabling a much longer duration test.

[0059] The start and end times used here are derived from thrust measurements by virtue of a load-cell integrated into the RDC frame. Due to installation, an absolute value of the RDC thrust was not measured, however the load-cell data provides a relative comparison that enables the determination of the test window, as shown in FIG. 17. A rolling-average is applied to smooth the noisy thrust data, and a threshold value is set halfway between the initial sensor value and the maximum recorded value. The test duration is then simply found by counting the time spent above the threshold.

[0060] This method was found to be robust enough to determine test start and end points for all ignited tests. As shown in FIG. 18, the test duration for each test depicts the measured test-time from this method, which can be compared to the target times in the test matrix shown in Table 1.

[0061] To determine the impact of the coolant mass-flow on the cooling performance, the blowing ratio (BR) is defined as follows:

[00001]$\begin{array}{cc}\mathrm{BR}=\frac{m_{\mathrm{co}\stackrel{.}{o}\mathrm{lant}}}{m_{\mathrm{fuel}+\stackrel{.}{o}\mathrm{xidizer}}}=\frac{m_{\stackrel{.}{N}2}}{m_{\stackrel{.}{a}\mathrm{ir}}+{\stackrel{.}{m}}_{H2}}& \mathrm{Eq}.1\end{array}$

[0062] A higher value of BR indicates more cooling, for instance a value of 1 indicates cooling mass-flow is equal to propellant mass flow, whereas a value of 0 indicates an uncooled test. For these experiments, blowing ratio never exceeds 0.5, as a measure to avoid ignition/detonation difficulty due to excessive nitrogen dilution.

[0063] The slot temperature increase can be shown by the average rate of slot temperature change, expressed as the following ratio:

[00002]$\begin{array}{cc}\frac{\left(T_{\mathrm{final}}-T_{\mathrm{initial}}\right)}{t_{\mathrm{test}}}& \mathrm{Eq}.2\end{array}$

[0064] Where T.sub.max and T.sub.initial are the temperatures recorded at the end and at the start of the test respectively, and t.sub.test is the test duration. The decision to use this rate instead of a direct temperature delta (T.sub.finalT.sub.inital) or ratio (T.sub.final/T.sub.inital) was made to remove the dependence on test duration.

[0065] By plotting this rate against the previously defined blowing ratio, a correlation between cooling mass-flow and slot temperature increase rate can be observed in FIG. 19, colored by the total mass flow rate (coolant and propellant). During the testing, high-speed camera footage revealed that in many tests, a single detonation wave was not observed. Rather, two or more counter-rotating waves were seen, in a slapping mode. To indicate these other modes, the unfilled points in FIG. 19 correspond to multi-wave solutions, whereas the single-wave solutions are shown as filled in.

[0066] As can be seen, the uncooled test has the highest slot temperature change, but as cooling increases, the slot temperature change is less pronounced. For a clearer view, the slapping-mode tests have been omitted in FIG. 20. Uncertainty bands are based on a thermocouple uncertainty of +3 degrees Kelvin, however conduction and velocity errors are unaccounted for in this analysis.

[0067] As shown in FIG. 21. slot pressures were also plotted for comparison between the cooled and uncooled tests, during actual combustion, the feed slots undergo a higher-pressure during combustion, as part of the slot undergoes back flow from the RDE.

[0068] With reference to FIG. 22, slot pressure ratios (final vs. initial) are plotted against the blowing ratio. Once again, single wave solutions are marked with solid points, and hollow points indicate multi-wave solutions. These results are shown, colored by the slot temperature change, in FIG. 22.

[0069] As shown through the experimental testing, the temperature readings of the cooling system 100 show the successful cooling of the hardware throughout the test matrix, also at lower blowing ratios.

[0070] Example embodiments are provided so that this disclosure will be thorough and will fully convey the scope to those who are skilled in the art. Numerous specific details are set forth such as examples of specific components, devices, and methods, to provide a thorough understanding of embodiments of the present disclosure. It will be apparent to those skilled in the art that specific details need not be employed, that example embodiments may be embodied in many different forms, and that neither should be construed to limit the scope of the disclosure. In some example embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail. Equivalent changes, modifications and variations of some embodiments, materials, compositions, and methods can be made within the scope of the present technology, with substantially similar results.