BACKGROUND 
   The present disclosure generally relates to cyclic pulsed detonation combustors (PDCs) and more particularly, the enhanced mixing and turbulence levels of the fuel-air mixture and flame kernel in order to promote the deflagration-to-detonation transition process. 
   In a generalized pulse detonation combustor, fuel and oxidizer (e.g., oxygen-containing gas such as air) are admitted to an elongated combustion chamber at an upstream inlet end. An igniter is used to initiate this combustion process. Following a successful transition to detonation, a detonation wave propagates toward the outlet at supersonic speed causing substantial combustion of the fuel/air mixture before the mixture can be substantially driven from the outlet. The result of the combustion is to rapidly elevate pressure within the combustor before substantial gas can escape through the combustor exit. The effect of this inertial confinement is to produce near constant volume combustion. Such devices can be used to produce pure thrust or can be integrated in a gas-turbine engine. The former is generally termed a pure thrust-producing device and the latter is termed a hybrid engine device. A pure thrust-producing device is often used in a subsonic or supersonic propulsion vehicle system such as rockets, missiles and afterburner of a turbojet engine. Industrial gas turbines are often used to provide output power to drive an electrical generator or motor. Other types of gas turbines may be used as aircraft engines, on-site and supplemental power generators, and for other applications. 
   The deflagration-to-detonation process begins when a fuel-air mixture in a chamber is ignited via a spark or other source. The subsonic flame generated from the spark accelerates as it travels along the length of the chamber due to various chemical and flow mechanics. As the flame reaches critical speeds, “hot spots” are created that create localized explosions, eventually transitioning the flame to a super sonic detonation wave. The DDT process can take up to several meters of the length of the chamber, and efforts have been made to reduce the distance required for DDT by using internal obstacles in the flow. The problem with obstacles for cyclic detonation devices is that they have relatively high pressure drop, and require cooling. Shaped-wall features, which reduce run-up to detonation that are integrated with the wall for cooling and have low pressure drop are desirable. Shaped walls will herein include, but not be limited to, geometric features including dimples, protrusions, local recesses, cross-hatching, depressions, and ridges. 
   As used herein, a “pulse detonation combustor” is understood to mean any device or system that produces pressure rise, temperature rise and velocity increase from a series of repeating detonations or quasi-detonations within the device. A “quasi-detonation” is a supersonic turbulent combustion process that produces pressure rise, temperature rise and velocity increase higher than pressure rise, temperature rise and velocity increase produced by a deflagration wave. Embodiments of pulse detonation combustors include a fuel injection system, an oxidizer flow system, a means of igniting a fuel/oxidizer mixture, and a detonation chamber, in which pressure wave fronts initiated by the ignition process coalesce to produce a detonation wave. Each detonation or quasi-detonation is initiated either by external ignition, such as spark discharge or laser pulse, or by gas dynamic processes, such as shock focusing, autoignition or by another detonation (cross-fire). The geometry of the detonation combustor is such that the pressure rise of the detonation wave expels combustion products out the pulse detonation combustor exhaust to produce a thrust force. Pulse detonation combustion can be accomplished in a number of types of detonation chambers, including shock tubes, resonating detonation cavities and tubular/tuboannular/annular combustors. As used herein, the term “chamber” includes pipes having circular or non-circular cross-sections with constant or varying cross sectional. Exemplary chambers include cylindrical tubes, as well as tubes having polygonal cross-sections, for example hexagonal tubes. 
   BRIEF SUMMARY 
   Exemplary embodiments of shaped walls include a detonation chamber for a pulse detonation combustor including: a plurality of dimples disposed on at least a portion of an inner surface of the detonation chamber wherein the plurality of dimples enhance a turbulence of a fluid flow through the detonation chamber 
   Exemplary embodiments also include a pulse detonation engine including: a pulse detonation combustor; a gas supply section for feeding a gas into the detonation chamber; a fuel supply section for feeding a fuel into the detonation chamber; an igniter for igniting a mixture of the gas and the fuel in the detonation chamber, wherein the pulse detonation combustor comprises a plurality of dimples disposed on an inner surface of the detonation chamber and a protrusion which is integral to the inner surface of the detonation chamber, extending into the detonation chamber; and wherein the plurality of dimples enhance a turbulence of a fluid flow through the detonation chamber. 
   Further exemplary embodiments include a deflagration-to-detonation transition method including: drawing an air-fuel mixture into a detonation chamber comprising a plurality of dimples disposed on an inner surface of the detonation chamber and a plurality protrusions disposed on the inner surface of the detonation chamber extending into the pulse detonation combustor; igniting the air-fuel mixture; tripping a flame resulting from igniting the air-fuel mixture; increasing the turbulent kinetic energy in the flame with the plurality of dimples; and obstructing the flame with at least a first portion of the protrusions effective to initiate detonation. 
   Other exemplary embodiments include a method for forming a detonation chamber including: manipulating a textured sheet to form a chamber including an inlet, an outlet, a selective combination of a plurality of dimples and a plurality of protrusions. 


   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Referring to the exemplary drawings wherein like elements are numbered alike in the several Figures: 
       FIG. 1  is a schematic view illustrating a structure of a pulse detonation engine system for a hybrid engine; 
       FIG. 2  is a schematic view illustrating a structure of a detonation chamber section of  FIG. 1 ; 
       FIG. 3(   a )-( b ) is a diagram illustrating an improved pulse detonation combustor with shaped walls for deflagration-to-detonation transition enhancement in accordance with exemplary embodiments; 
       FIG. 4  is a cross section of an improved pulse detonation combustor with shaped walls for deflagration-to-detonation transition enhancement as depicted in  FIG. 3 ; and 
       FIGS. 5(   a )-( d ) is a diagram illustrating various shapes of the shaped walls of the improved pulse detonation combustor for deflagration-to-detonation transition enhancement in accordance with exemplary embodiments. 
   


   DETAILED DESCRIPTION 
   Referring now to  FIGS. 1 and 2 , various pulse detonation engine systems  10  convert kinetic and thermal energy of the exhausting combustion products into motive power necessary for propulsion and/or generating electric power.  FIG. 2  shows a pulse detonation combustor in a pure supersonic propulsion vehicle. The pulse detonation combustor in a hybrid engine concept  10 , shown in  FIG. 1 , or a pure pulse detonation engine shown in  FIG. 2 , includes a detonation chamber  16  having a gas supply section (e.g., an air valve)  26  for feeding a gas (e.g., oxidant such as air) into the detonation chamber  16 , a fuel supply section (e.g., a fuel valve)  28  for feeding a fuel into the detonation chamber  16 , and an igniter (for instance, a spark plug)  26  by which a mixture of gas combined with the fuel and air in the detonation chamber  16  is ignited. 
   In exemplary embodiments, air supplied from an inlet fan  20  and/or a compressor  12 , which is driven by a turbine  18 , is fed into the gas supply section  26  through an intake  30 . Fresh air is filled in the detonation chamber  16 , after purging combustion gases remaining in the detonation chamber  16  due to detonation of the fuel-air mixture from the previous cycle. After the purging the pulse detonation combustor  16 , fresh fuel is injected into pulse detonation combustor  16 . Then, the igniter  26  ignites the fuel-air mixture forming a flame, which accelerates down the pulse detonation combustor, finally transitioning to a detonation wave or a quasi-detonation wave. Due to the detonation combustion heat release, the gases exiting the pulse detonation combustor are at high temperature, high pressure and high velocity conditions, which expand across the turbine  18 , located at the downstream of the pulse detonation combustor  16 , thus generating positive work. For a hybrid engine application with the purpose of generation of power, the pulse detonation driven turbine  18  is mechanically coupled to a generator (e.g., a power generator)  22  for generating power output. For a hybrid engine application with the purpose of propulsion (such as the present aircraft engines), the turbine shaft is coupled to the inlet fan  20  and the compressor  12 . In a pure pulse detonation engine application of the pulse detonation combustor shown in  FIG. 2 , which does not contain any rotating parts such as a fan or compressor/turbine/generator, the kinetic energy of the combustion products and the pressure forces acting on the walls of the propulsion system, generate the propulsion force to propel the system. 
   Turning now to  FIG. 3   a  which shows an external view of the detonation chamber with shaped walls namely dimples and  FIG. 3   b  which shows a view of the inside of the detonation tube with shaped walls namely dimples by removing the top 50% of the tube surface, an improved detonation chamber with shaped walls for deflagration-to-detonation transition enhancement is generally depicted as  32 . The improved pulse detonation combustor  32  includes an inlet  40  and an outlet  42 . The improved pulse detonation combustor  32  also includes shaped walls  34  having a plurality of dimples  36  and one or more protrusions  38 ( a )-( c ). The protrusions  38 ( a )-( c ) may be disposed on either or both ends of the improved detonation chamber  32  and extend into the detonation chamber. The inlet  40  includes both an air intake  44  and a fuel intake  46 . 
   The plurality of dimples  36  on the inner surface of the improved detonation chamber  32  enhance the turbulent flame speed, and accelerate the turbulent flame, while limiting the total pressure loss in the pulse detonation combustor. The plurality of dimples  36  also enhance turbulence flame surface area by providing more volume, into which the flame can expand, compared to the flame surface area in a combustor with smooth walls. Contrary to the protrusions that constrict the flow, the plurality of dimples  36  can potentially result in a smaller pressure loss while generating the same levels of flame acceleration. However, a couple of protrusions were found to be necessary to affect the transition of the accelerating turbulent flame into a detonation wave. In addition, the pressure drop in the improved pulse detonation combustor was found to be considerably small when compared to the pressure drop in a pulse detonation combustor with only protrusions present (which is the current practice in achieving detonations in a pulse detonation combustor). 
   The plurality of dimples  36  may be arranged as depicted in  FIGS. 4 , and  5 ( a ) through  5 ( d ). In exemplary embodiments, the plurality of dimples  36  may be disposed in a number of rows and columns as depicted in  FIG. 3(   a ) and  3 ( b ), circumferentially spaced as depicted in  FIG. 4  with the columns being spaced axially along the improved pulse detonation combustor  32 , and the rows being spaced circumferentially along the improved pulse detonation combustor. Additionally, the number of rows and columns and the spacing between each may be varied to achieve detonations or quasi-detonations in varying fuel-air systems. In other exemplary embodiments, the plurality of dimples  36  may be disposed in a number of rows and columns with the dimples having staggered or inline arrangement along the axial direction. In further exemplary embodiments, the plurality of dimples  36  may have varying density of dimples on the walls of the pulse detonation combustor. In general, higher density of dimples which are closely spaced are found to be more effective in achieving successful detonations or quasi-detonations. 
   Turning now to  FIG. 4 , a cross section of an improved pulse detonation combustor is depicted generally as  48 . The improved pulse detonation combustor  48  includes inner chamber  50  that has a plurality of dimples  52 . The plurality of dimples  52  may be disposed in a wide variety of arrangements. In exemplary embodiments, the plurality of dimples  52  has a range of axial spacing of 0.375-0.75 inches. The circumferential spacing of the plurality of dimples  52  can vary from 25-50°. In an exemplary embodiment the plurality of dimples  52  are spaced circumferentially, by approximately 30 degrees ( FIG. 4 ). In exemplary embodiments, the improved detonation chamber  48  includes a cooling system disposed inside of the outer chamber  54 . The plurality of dimples  52  increases the surface area of the inner chamber  50  and therefore increases the cooling of the improved pulse detonation combustor wall, thereby ensuing the integrity of the pulse detonation combustor walls. 
   Further, the plurality of dimples may have varying diameters and depths. In exemplary embodiments the arrangement, diameter, depth of the plurality of dimples, the density of the dimples and the type of packing of the dimples (staggered vs inline arrangement and densely packed vs loosely packed depending on axial and radial spacing dimensions) may all be adjusted to achieve the desired turbulent flame acceleration in the improved pulse detonation combustor. In further exemplary embodiments, the shaped walls do not necessarily be confined to be of spherical features but can range from fractionally-spherical, conical frustrum, cubic or rectangular features, as shown in  FIGS. 5(   a ) through  5 ( d ). While one embodiment of size/spacing/orientation is provided, it will be understood that many relative scales can be used depending on the overall size of the tube. 
   As illustrated in  FIGS. 3   a  and  3   b , a set of protrusions  38 ( a )- 38 ( c ) can be disposed in the improved pulse detonation combustor  32  between the inlet  40  and the plurality of dimples  36 . Stable flame ignition is promoted by the use of the 1 st  protrusion,  38 ( a ). The second and third protrusions  38 ( b ) and  38 ( c ) facilitate transition of an accelerated turbulent flame into a detonation wave. The protrusions  38 ( a )-( c ) may be orifice plates, rearward-facing steps or any other suitable obstruction which are integral parts of the inner surface of the pulse detonation combustor. The protrusions  38 ( a )-( c ) enhance mixing between the fuel and the air and enhance spark initiation in the improved detonation chamber  32 . Additionally, the protrusions  38 ( a )-( c ) help create ‘hot spots’ during shock-to-flame interactions regime corresponding to the sonic/choked flow conditions of gases behind the leading combustion wave. 
   The improved detonation chamber  32  may be constructed in a variety of ways. In exemplary embodiments, a piece of sheet metal is shaped to include the plurality of dimples  36  and the protrusions  38 . For example, a ball hammer may be used to create the plurality of dimples  36 . The piece of sheet metal may then be rolled into form the improved detonation chamber  32 . The improved detonation chamber  32  may also be formed through several other methods including, but not limited to, casting or molding. In exemplary embodiment, protrusions  38  are orifice plates that are welded into the improved detonation chamber  32 . 
   While the disclosure has been described with reference to an exemplary embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the disclosure. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the disclosure without departing from the essential scope thereof. Therefore, it is intended that the disclosure not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this disclosure, but that the disclosure will include all embodiments falling within the scope of the appended claims.
A detonation chamber for a pulse detonation combustor including: a plurality of dimples disposed on at least a portion of an inner surface of the detonation chamber wherein the plurality of dimples enhance a turbulence of a fluid flow through the detonation chamber.