Abstract:
Pulse detonation combustors of valveless construction. One valveless pulse detonation combustor, having a tube with a closed end and an open end, is constructed with a flame accelerator within the tube, adjacent the open end. A valveless, apertured flow restrictor is positioned between the flame accelerator and the closed end of the tube. A sparking device is positioned within the tube, between the flow restrictor and the flame accelerator. Valveless fuel and air ports are positioned between the flow restrictor and the closed end of the tube. Substantially right-angle manifold passageways are in communication with each of the ports.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This application claims the benefit of U.S. Provisional Patent Application Ser. No. 60/786,462, filed Mar. 28, 2006, which application is hereby incorporated by reference. 

   TECHNICAL FIELD OF THE INVENTION 
   The present invention relates generally to power generation and, more particularly, to pulsed detonation combustors. 
   BACKGROUND OF THE INVENTION 
   A detonation is a supersonic combustion wave associated with a shock wave propagating through a reactive mixture. The self-sustained detonation wave has a particular pressure and propagation velocity described as the Chapman-Jouget detonation. The Chapman-Jouget detonation shows a similar thermodynamic behavior to a constant volume combustion process which provides higher thermodynamic performance than constant pressure combustion. A pulsed detonation combustor (PDC) is a device which creates the self-sustained detonation waves in a cyclic fashion in order to convert their thermal energy to kinetic energy. Potential applications include engines in subsonic and supersonic flight, vehicles, and industrial power generators. 
   One of the technical challenges in pulsed detonation combustor is a valving scheme. Because of the unsteady nature of the wave, the combustor needs to provide combustible mixture in a cyclic fashion.  FIG. 1  shows a schematic chronology of a cyclic ideal operation for a valved pulsed detonation combustor. Once the fill valve is closed, after the combustion mixture filling process, ignition is provided by a spark plug and deflagration to detonation transition process is initiated by a flame accelerator. After a short period of time, the purge valve starts to open to exhaust combustion products and to prepare the tube for the next filling process. A valved structure is able to realize a cyclic unsteady detonation initiation but it requires an additional mechanical complexity and poses mechanical/thermal fatigue issues for its long service. 
   SUMMARY OF THE INVENTION 
   The present invention involves aspects of valveless pulse detonation combustors. One valveless pulse detonation combustor, having a tube with a closed end and an open end, is constructed with a flame accelerator within the tube, adjacent the open end. A valveless, apertured flow restrictor is positioned between the flame accelerator and the closed end of the tube. A sparking device is positioned within the tube, between the flow restrictor and the flame accelerator. Valveless fuel and air ports are positioned between the flow restrictor and the closed end of the tube. Substantially right-angle manifold passageways are in communication with each of the ports. 
   The objects and advantages of the present invention will be more apparent upon reading the following detailed description in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic of the ideal cyclic operation of a valved PDC. 
       FIG. 2  is a side view of a first embodiment of a valveless PDC according to one aspect of the present invention. 
       FIG. 3  is a perspective view of the valveless PDC of  FIG. 2 . 
       FIG. 4  shows three variants of the inlet face used in the valveless PDC of  FIG. 2 . 
       FIG. 5  is a diagram of the valveless PDC of  FIG. 2 , showing placement of pressure sensors. 
       FIG. 6  is a space-time diagram of the detonation wave and transmitted shock propagations inside the valveless PDC of  FIG. 2 . 
       FIG. 7  is a timing diagram of a cycle of the valveless PDC. 
       FIG. 8  shows pressure-time histories recorded for C 2 H 4 — air mixture with ø=1.1, a fill fraction of 1.7 and an operating frequency of 5.26 Hz. 
       FIG. 9  shows pressure-time histories recorded for C 2 H 4 — air mixture with ø=1.1, a fill fraction of 1.7 and an operating frequency of 5.26 Hz; a single pulse extracted from the multi-cyclic pressure history. 
       FIG. 10  Pressure-time histories recorded for C 2 H 4 — air mixture with ø=1.1, a fill fraction of 1.1 and an operating frequency of 5.26 Hz; typical pressure histories in multi-cyclic operation of the valveless PDC. 
       FIG. 11  Pressure-time histories recorded for C 2 H 4 — air mixture with ø=1.1, a fill fraction of 1.1 and an operating frequency of 5.26 Hz; a single pulse extracted from the multi-cyclic pressure history. 
       FIG. 12  Pressure-time histories recorded for C 3 H 8 — air mixture with ø=1.1, a fill fraction of 2.3 and an operating frequency of 1.54 Hz 
       FIG. 13  Pressure histories recorded at the inlet and vortex generator sections for C 2 H 4 — air mixture with ø=1.1, a fill fraction of 1.7 and an operating frequency of 5.26 Hz. 
       FIG. 14  Pressure histories recorded at the inlet and vortex generator sections for C 2 H 4 — air mixture with ▭=1.1, a fill fraction of 1.1 and an operating frequency of 5.26 Hz. 
       FIG. 15  Idealized model of pressure history at the thrust surface. 
       FIG. 16  Pressure histories at fuel and air manifold recorded for C 2 H 4 — air mixture with ø=1.1, a fill fraction of 1.7 and an operating frequency of 5.26 Hz. 
       FIG. 17  Pressure histories at fuel and air manifold recorded for C 2 H 4 — air mixture with ø=1.1, a fill fraction of 1.1 and an operating frequency of 5.26 Hz. 
       FIG. 18  Relation between the spark interval and the gasdynamic valve cycle time to describe a possible operational region with the valveless PDC. 
       FIG. 19  shows a perspective view of a second embodiment of a valveless PDC according to another aspect of the present invention. 
       FIG. 20  is a cross-sectional diagram of the valveless PDC shown in  FIG. 19 . 
   

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
   For the purpose of promoting an understanding of the principles of the invention, reference will now be made to the embodiments illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended, such alterations and further modifications in the illustrated device and such further applications of the principles of the invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the invention relates. 
   One embodiment of a valveless pulse detonation combustor ( 10 ) according to the present invention is shown in  FIGS. 2 and 3 , comprising three major sections: inlet section  12 , vortex generator  14 , and detonation tube  16 . The detonation tube  16  contains a Shchelkin spiral  18  ( FIG. 5 ) as a flame accelerator. In one example combustor, the selection of blockage ratio, designed as the blocked area divided by the detonation tube cross-sectional area, is 0.44. The detonation tube shown is made of 2 inch I.D. stainless steel pipe. 
   An acceptable pitch size for single-head spin detonation is related to its spinning pitch size of the marginal detonation. It has been found that the detonability limit for spin pitch size is based on the acoustic theories. Theory predicts the ratio of spin pitch to the critical tube diameter, d c , and its pitch size is estimated on the order of the cell size, λ, for d c ˜λ/1.7 
   The vortex generator  14  is constructed to provide sufficient flow recirculation zones for flame stabilization and mitigation of flame blowout under high speed filling without a large pressure loss across a step. The vortex generator shown steps down from an 8 inch internal diameter carbon steel tube to a 2 inch internal diameter carbon steel tube. As shown in  FIGS. 2 and 3 , spark plugs  20  and associated voltage discharge modules (not shown) are used to ignite the combustible mixture upstream of the contracting section  22  so as to create a quasi-stable recirculation zone of unsteady flow. Multiple spark plugs are mounted radially in order to assure ignition of the combustible mixture. (The number of spark plugs may vary depending upon the particular application.) The total energy provided by the forced ignition is a minuscule amount compared with the critical energy required for direct initiation with stoichiometric ethylene-air (56 kJ) and stoichiometric propane-air combustible mixtures (215 kJ). 
   The inlet face  24  is positioned approximately at the middle of the vortex generator  14  (downstream of the inlet section  12 ) as a stationary flow restrictor. The inlet face generally comprises a perforated plate with one or more apertures therethrough. The plate may be circular (as shown in  FIG. 4 ), or generally square or rectangular in design, depending upon the particular valveless PDC application. The apertures through the inlet faces may be cut straight through the discs, as shown, or may be tapered or angled inwardly or outwardly in certain applications. Inlet face  24  provides valveless operation, and acts as a fluid diode, providing the lowest possible resistance to inflow and the highest possible resistance to backflow. Inlet face  24  also serves as a mixing device during filling processes and as a thrust surface during the backflow phase of operation. The inlet face, with its multiple holes, promotes free shear flows within the vortex generator  14  thereby developing mixing layers that reduce mixing time and permit a higher operating frequency. 
     FIG. 4  shows three different 8 inch I.D. circular inlet faces  24   a ,  24   b ,  24   c , and  24   d  made of ⅛ inch thick stainless steel, which may be used in the valveless PDC shown in  FIGS. 2 and 3 . Inlet face  24   b , for example, has five 1 inch diameter apertures  26  therethrough, with the four outer apertures spaced ½ the radius away from the center aperture. The five apertures occupy approximately 3.9 square inches of the approximately 50.2 square inch inlet face, resulting in about 8 percent open space. 
   The inlet section  12  is preferably made of carbon steel pipe (3 inch inner diameter pipe is shown in  FIGS. 2 and 3 . Other sizes may be used depending upon the application.) and has an instantaneous expanded section  28  connected to inlet face  24 . The longer inlet section effectively serves as a buffer zone to restrain backflow from reaching inlet ports  30 . A longer inlet provides a greater buffer zone at the expense of a longer flow time and reduced operating frequency. One of the technical issues in a valveless combustor is a backflow of hot combustion products which is generated during the closing phase of a gas dynamic valve. This is a part of the loss associated with a valveless configuration, and the amount of loss can be decreased by reducing inlet sizes avoiding flashback to the fuel manifold or the buffer zone. However, reduction of inlet size decreases its flow coefficient causing an undesirable increase of manifold pressure. Heat transfer on the inlet wall can be increased by various cooling schemes in order to increase inlet port diameter impeding flashback with an optimized manifold pressure and a flow coefficient. 
   The instantaneous expanded section  28  behind the inlet face  24  also serves to enhance a preconditioning of combustible mixture through a mixing process with remaining combustion products from a previous cycle. 
   Inlet ports  30  for fuel and air supply are constructed of 90 degree elbows and may contain solenoid valves for emergency shutoff. There are four inlet ports for air supply and one inlet port for fuel supply separately connected to the inlet section  12  in order to impede flame propagation to manifolds during the backflow phase. This configuration, also called a 180 degree return bend (substantially 180 degrees), serves as a thrust generator during the backflow in order to minimize backflow-induced pressure losses. The number of inlet ports may vary, depending upon the estimated range of valveless operating frequency and fill fraction. Air and fuel manifold pressures, which are estimated by their flow coefficients and expected mass flow rates in quasi-steady operation, set the aerodynamic valve operating times. 
   The valveless PDC is preferably filled in a cyclic fashion with an air-fuel mixture, such as ethylene-air or propane-air mixtures, near stoichiometric conditions at various fill fractions and operating frequencies. Mass flow rates for fuel and air are preferably controlled through critical flow measurements with sonic orifice plates. Averaged mass flow rates may be controlled based on a volumetric fill fraction, an equivalence ratio, and an operating frequency of the valveless PDC. The operating frequency of the PDC may be controlled by an ignition control system (not shown) arranged with automobile ignition modules and digital timer/counter boards. One such ignition control system has been designed to provide digital pattern outputs to the ignition modules in 20 MHz external handshaking mode. The system was also capable of accepting 80 MHz digital output frequency to decide a certain event timing to control  32  ignition modules. 
   There were seven piezoelectric pressure transducers and two low-natural frequency pressure transducers mounted in locations as indicated in  FIG. 5  during experimental testing (described below) of the valveless PDC  10 : the thrust surface (P 1 ), the inlet section (P 2 ), the vortex generator (P 3 ), fuel and air manifolds (P 8  and P 9 ) and along the detonation tube (P 4 -P 7 ). The article “Multicyclic Detonation Initiation Studies in Valveless Pulsed Detonation Combustors,” by M. Shimo and S. Hester, 42 nd  AIAA/ASME/SAE/ASEE Joint Propulsion Conference &amp; Exhibit, Jul. 9-12, 2006, Sacramento, Calif., AIAA 2006-4308, and “Multicyclic Detonation Initiation Studies in Valveless Pulsed Detonation Combustors,” Ph.D. Thesis, Purdue University, West Lafayette, Ind., December 2006, are expressly incorporated by reference herein, along with all references cited therein. 
   Details of various wave propagations after a direct initiation of detonation are illustrated by a space-time wave diagram in  FIG. 6 , showing essential features of wave dynamics in an ideal situation. The reactant state is labeled on  FIG. 6  as State  1  where there is non-stagnant flow present initially in filling the entire tube with u=u fill . State  2  represents the Chapman-Jouguet state followed by the self-similar expansion wave called the Taylor wave, just behind the detonation wave. The flow behind the Chapman-Jouguet detonation wave (State  2 ) is subsonic relative to the tube for typical hydrocarbon fuel-air mixtures. The first reflected characteristic Ĉ −  appears after the detonation wave front reaches the interface between combustion mixture and air at the open end of tube. The slope of this characteristic is specified by interaction with the Taylor wave. The transmitted shock and contact surface propagate outside the detonation tube making the flow expand radially in three dimensions. The region behind the first reflected characteristic is a non-simple region caused by interactions between the reflected expansion wave and the Taylor wave. 
   The Taylor wave makes the flow expand and decrease in pressure, but because of the porous surface of inlet face  24 , the Taylor wave needs to further expand the flow from u 2  to a negative flow speed of u 3  in State  3 . The first reflected characteristic Ĉ −  propagates at speed u 3 +u 3  after passing through the Taylor wave due to this non-stagnant region, State  3 . This characteristic continues to propagate through variable cross sectional area to reduce pressure at the thrust surface  32 . A compression wave propagates toward the inlet section  12  as a transmitted shock due to this converging configuration of the vortex generator  14 . The transmitted shock brings the reactant flow to rest at the inlet section  12  and increases the pressure at the inlet section as a consequence of the backflow process. Fuel and airflows may be metered upstream such that the respective flow rates are insensitive to changes in manifold pressure, i.e. upstream orifices remained choked throughout the process. 
   A gasdynamic valve cycle time of the valveless PDC is dependent on the detonation wave dynamics in the rig configuration. In general, a PDC cycle consists of four distinct processes occurring sequentially. The processes and associated time duration are defined as (i) detonation initiation and DDT process, τ DDT , (ii) blowdown process, τ BD , (iii) purge process, τ purge  and (iv) fill process, τ fill , which are illustrated in detail in  FIG. 7 . The purging and filling processes occur when the gasdynamic valve is open (τ open ). The gasdynamic cycle time, τ, of the valveless PDC  10  is obtained via summation of gasdynamic valve open and close times, the former including actual fill and purge processes 
                       τ   =       ⁢       τ   DDT     +     τ   BD     +     τ   purge     +     τ   fill                   =       ⁢       τ   close     +         τ   open     ⁡     (       τ   open     =       τ   purge     +     τ   fill         )       .                           (   1   )               (   2   )                     
The gasdynamic valve cycle time of the valveless PDC is required to be less than the spark interval time which controls the operating frequency of the valveless PDC. The gasdynamic valve opening duration, τ open , consists of the purge and the fill process and the time required for the fill process, τ fill , can be approximately estimated by a one-dimensional uniform flow at ambient condition as follows
 
                   τ   fill     =           ρ   mix     ⁢     V   pdc           m   .     mix       .             (   3   )               
where ρ mix  and {dot over (m)} mix  are suitable average values for a given cycle. The combustible mixture density, ρ mix  was approximated to be an ambient condition due to its low fill speed and no significant ram pressure decrease can be expected. The time required for the purge process, τ purge , can be approximately estimated by the time between when self-aspiration of air starts and when self-aspiration of fuel starts but the purge time, τ purge , may be significantly lower than the fill time, τ fill . The purge process creates a small buffer zone between reactants and products in order to avoid an autoignition of reactants during the fill process. The timing and duration of the purge process are dependent on the configuration of the valveless PDC and respective manifold pressures.
 
   The gasdynamic valve closing duration, τ close , consists of the detonation initiation and DDT process and the blowdown process. The gasdynamic valve closing duration is also related to the characteristic time, τ Ĉ     −   . The pressure at the thrust surface remains constant until the first reflected characteristic from the tube&#39;s open end reaches the thrust surface at time, τ Ĉ     −   . When the thrust surface is pressurized in addition to the inlet section, fuel and air mass fluxes from their inlet ports are decelerated by a compression wave which is described by the following relation based on the method of characteristics 
                         J   +     =       ⁢         u   1     +       2     γ   -   1       ⁢     c   1         =       u   +       2     γ   -   1       ⁢   c       =     (   const   )                       ⇒     u     c   1         =       ⁢         J   +       c   1       -       2     γ   -   1       ⁢     c     c   1                       =       ⁢         J   +       c   1       -       2     γ   -   1       ⁢       (     P     P   1       )         γ   -   1       2   ⁢   γ         ⁢     (     &lt;       u   1       c   1         )                                                     (   4   )                                     (   5   )                                           (   6   )                                           
assuming that a transmitted compression wave propagating to upstream of the manifolds is weak enough to maintain isentropic conditions. The gasdynamic valve continues to be closed until the thrust surface is depressurized. When the inlet section is depressurized, an expansion wave is initiated and propagates into manifolds causing acceleration of fuel and air masses. The gasdynamic valve closing duration is a design parameter constrained by the size of the valveless PDC including the manifold arrangement which regulates arrival of reflected characteristics, and the minimum manifold pressure which regulates onset of closing and opening time of the gasdynamic valve.
 
   In order to estimate the gasdynamic valve closing duration, τ close : fuel and air manifold pressures were measured. The gasdynamic valve closing duration is approximately estimated by measuring time between spark initiation, t DDT , and peak pressure detected at each manifold, t peak . As a result, the gasdynamic valve cycle time of the valveless PDC has the following relation:
 
τ=τ close +τ open ≈( t   peak   −t   DDT )+τ fill .  (7)
 
assuming that τ purge &lt;&lt;τ fill  and t peak ≈t open . A reciprocal of the spark initiation frequency requires to be greater than the gasdynamic cycle time, t, which controls an operating frequency of the valveless PDC.
 
   Pressure data is presented in this here to illustrate the internal flowfield in the detonation tube  16  of the valveless PDC  10 . The experiments described were carried out at atmospheric initial pressure with an averaged equivalence ratio of 1.1 for ethylene-air combustion mixture and an operating frequency of 5.26 Hz. Pressure data for the same averaged equivalence ratio of 1.1 for propane-air combustion mixture under an operating frequency of 1.54 Hz are also presented in  FIG. 12  in order to show initiation of the DDT process with a heavier hydrocarbon fuel. Typical time histories of multi-cyclic pressure pulses measured along the detonation tube are presented in  FIGS. 8 and 10  in order to show repeatability of combustion waves. (The downward slope in pressure in  FIG. 8  is due to transducer drift due to heating.)  FIGS. 9 and 11  represent a single pulse history obtained from the multi-cyclic operation with a specified fill fraction. There are variations of pressure magnitude for each wave as shown in  FIGS. 8 and 10  but  FIGS. 9 and 11  represent general trends for their specific conditions. In order to clarify a wave propagation process, time axis is taken on the abscissa, where zero corresponds to the time of spark ignition. Pressure magnitude is taken on the ordinate, where zero corresponds to the reference pressure. Tracking each peak of a pressure history permits construction of the pressure wave trajectory down the tube and the deflagration to detonation transition (DDT) process. Data in  FIG. 9  indicate acceleration to peak detonation conditions by the time the wave reaches the location of transducer P 5  with peak pressures in excess of 4 MPa at this locale. 
   Data for fill fraction of approximately 1.7 and 1.1 appear in  FIGS. 9 and 11 , respectively. Note that the fill fractions were estimated by the following equation: 
                       FF   =       ⁢         V   .     ⁡     (       1     f   ap       -     τ   close       )         V   pdc                   ≈       ⁢           V   .     ⁢     {       1     f   ap       -     (       t   peak     -     t   DDT       )       }         V   pdc       .                                     (   8   )                                                           (   9   )                     
At 1.7 fill fraction ( FIG. 9 ), the maximum peak pressure is 4.18 MPa, which is greater than the Chapman-Jouguet detonation pressure of 1.89 MPa, indicating possible presence of a overdriven detonation. The wave speed is 1917 m/s measured between P 5  and P 7 , which is greater than the Chapman-Jouguet detonation speed of 1846 m/s. At a 1.1 fill fraction ( FIG. 11 ), the maximum peak pressure is 2.04 MPa, which is close to the Chapman-Jouguet detonation pressure of 1.89 MPa but the wave speed is 1104 m/s measured between P 5  and P 7  indicating that it resides in a choked flame regime or a pressure wave decoupled from a reaction zone. At 2.3 fill fraction with propane-air mixture ( FIG. 12 ), the maximum peak pressure is 4.93 MPa and the wave speed is 2116 m/s, which are greater than the Chapman-Jouguet detonation pressure of 1.88 MPa and the Chapman-Jouguet detonation speed of 1819 m/s indicating presence of a overdriven detonation. The large fill fractions required to attain maximum performance are indicative of poor mixing of the fuel and air streams. Optimization of the mixing process was not objective of the present study.
 
   Although the equivalence ratios of these fill fraction conditions are the same, different attributes of combustion waves were observed in the detonation tube. This observation is associated with the fact that an actual filling time is regulated by filling/mixing process in a certain configuration of PDC. The time required to get a sufficient fill of PDC for DDT initiation is reduced by a higher set fill fraction (i.e. mass flow rate) and lower set fill fraction may not provide enough fill of combustible mixture within a spark interval time to initiate a DDT. Note that a higher set fill fraction increases a fill speed but simultaneously it causes flame stabilization issues in this head-end filling scheme configuration. 
   Pressure data at the inlet and vortex generator sections appear in  FIGS. 13 and 14  illustrating the case of ethylene-air mixture with equivalence ratio of 1.1 and operating frequency of 5.26 Hz but different fill fractions of 1.7 and 1.1, respectively. In order to clarify a wave propagation process, the time axis is taken on the abscissa, where zero corresponds to the time of spark ignition, and pressure magnitude along the valveless PDC is taken on the ordinate. The ignition sources were located at the vortex generator section ( FIG. 5 ) so that the first pressure rise was detected by the pressure transducer located at P 3 . A transmitted compression wave propagating toward the thrust surface is observed in the pressure histories as described in  FIG. 6 . 
   A significant pressure rise is detected at the thrust surface (P 1 ) for the fill fraction of 1.7 as shown in  FIG. 13  due to a transmitted shock propagation on area convergence which is stronger than the incident shock. There are two peak pressure spikes over 4 MPa detected at P 1  within 1 ms and are greater than the Chapman-Jouguet detonation pressure of 1.89 MPa ( FIG. 13 ). A plateau pressure region including these two pressure spikes appears for about 7 ms (6 ms˜13 ms) at P 1  which is followed by a region of decreasing pressure caused by numerous reflected characteristics as shown in  FIG. 13 . The other plateau regions detected at P 2  and P 3  also appear for about 7 ms (5 ms˜12 ms for both P 2  and P 3 ) which are also followed by a region of decreasing pressure caused by numerous reflected characteristics as shown in  FIG. 13 . A reflected shock at the thrust surface is observed as a weak pressure spike at the pressure transducers located at P 2  and P 3  around 7 ms in  FIG. 13 . Onset of pressure decrease due to arrival of the first reflected characteristic: C— is started from the transducer close to the exit end of detonation tube (P 3 ). 
   A similar pressure-time trace is also measured at the thrust surface (P 1 ) for the fill fraction of 1.1 as shown in  FIG. 14  due to a transmitted shock propagation on area convergence which is stronger than the incident shock. However, the magnitude of the transmitted shock is much smaller than for the fill fraction of 1.7 due to its failure to initiate a successful DDT as shown in  FIG. 11 . There are two peak pressure spikes over 2 MPa detected at P 1  within 1 ms ( 14 ). A plateau pressure region including these two pressure spikes appears for about 6 ms (7 ms˜13 ms) at P 1  which is followed by a region of decreasing pressure caused by numerous reflected characteristics as shown in  FIG. 14 . The other plateau regions detected at P 2  and P 3  also appear for about 6 ms (7 ms˜13 ms for both P 2  and P 3 ) which are also followed by a region of decreasing pressure caused by numerous reflected characteristics as shown in  FIG. 14 . A reflected shock at the thrust surface is observed as a weak pressure spike at the pressure transducers located at P 2  and P 3  around 9 ms in  FIG. 14 . 
   The pressure-time traces detected at P 1  for both 1.7 and 1.1 of the fill fractions were compared with the idealized pressure-time trace model at the thrust surface for a straight detonation tube proposed by Wintenberger et al., which are given in Table 1 and its schematic of the pressure-time trace is presented in  FIG. 15 . Both of the pressure spikes detected at the thrust surface are higher than the pressure spike estimated as the Chapman-Jouguet detonation for a straight detonation tube partly due to the contracting configuration of the inlet section  12 . Successful DDT initiation for the fill fraction of 1.7 creates a higher magnitude of pressure waves than for the fill fraction of 1.1, which may be caused by three dimensional effects of filling/mixing process associated with filling time of the combustor. In addition, there is ignition delay observed in  FIG. 14  compared with  FIG. 13 , which may be caused by the same reason. Note that the gasdynamic valve was functioned for both fill fractions of 1.1 and 1.7 as long as magnitude of the transmitted shock has a certain value associated with manifold pressure. 
   
     
       
             
           
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Comparisons between pressure at the thrust surface for a straight 
             
             
               tube configuration estimated by Wintenberger and pressure measured 
             
             
               at the thrust surface in the valveless PDC; C 2 H 4  - air mixture 
             
             
               with an operating frequency of 5.26 Hz. 
             
           
        
         
             
                 
                 
               Fill 
               P 1 , 
               T 1 , 
               P spike , 
               P 3 , 
               t spike , 
             
             
               Data source 
               φ 
               fraction 
               MPa 
               K 
               MPa 
               MPa 
               ms 
             
             
                 
             
           
        
         
             
               Wintenberger 30   
               1.0 
               1.0 
               0.1 
               300 
               1.825 
               0.684 
               — 
             
             
               Present work 
               1.1 
               1.7 
               0.1 
               298 
               &gt;4.46 
               &gt;0.67 
               &gt;0.5 
             
             
               Present work 
               1.1 
               1.1 
               0.1 
               298 
               &gt;2.56 
               &gt;0.34 
               &gt;0.5 
             
             
                 
             
           
        
       
     
   
   Typical pressure data for the fuel and air manifolds (P 8  and P 9  in  FIG. 5 ) are depicted in  FIGS. 16 and 17  for the case of ethylene-air mixture with equivalence ratio of 1.1 and operating frequency of 5.26 Hz but with different fill fractions of 1.7 and 1.1, respectively. The time of spark ignition corresponds to 0 ms in  FIGS. 16 and 17 . A pressure rise caused by a pressure build-up at the inlet section is observed with a pressure transducer at both fuel and air manifold in  FIGS. 16 and 17 . There are pressure oscillations detected at a rising edge at the fuel manifold (P 8 ) for both the fill fractions cases probably because of structural response of the flex lines. The pressure difference at the inlet port allows a transmitted compression wave to propagate toward both fuel and air manifolds which consequently causes the entire reactant flow flux to decelerate. 
     FIG. 16  shows that minimum manifold pressures for the air and fuel systems are approximately 0.78 MPa and 0.29 MPa, respectively. A combination of fuel and air minimum manifold pressures regulates timing of purging and filling processes in the valveless PDC. The manifold pressure for the air system is higher than the manifold pressure for the fuel system enabling the gasdynamic valve for the air system to open itself prior to the one for the fuel system in order to initiate a purging process of combustion products. The purging process creates a buffer zone between combustion products and newly charged reactants, which impedes pre-ignition of the fresh reactants. Fuel is not supplied until pressure at the inlet section is low enough to generate an expansion wave transmitted to the fuel manifold having adequate pressure drop across the manifold. By the use of method of characteristics, time which is required for the head of a compression wave to reach the manifold can be computed. Assuming that mass flow in a reactant supply line is subsonic, a negative sound speed of the first characteristic propagating upstream to the manifold is 
                           C   -     :       ⅆ   x       ⅆ   t         =       ⁢     u   -   c                 =       ⁢         m   .       ρ   ⁢           ⁢   A       -         γ   ⁢           ⁢   RT       .                                                                       (   10   )                     
The time when the pressure transducer at the manifold detects the head of compression wave can be computed as
 
                   t   delay     =       l          u   -   c            =       l              m   .       ρ   ⁢           ⁢   A       -       γ   ⁢           ⁢   RT                .               (   11   )               
The pressure transducers at the fuel manifold (P 8 ) and at the air manifold (P 9 ) detected their pressure rises at 11 ms (estimated time: 13.0 ms) and 25 ms (estimated time: 28.9 ms) as shown in  FIG. 16  having a reasonable agreement with estimated times. A pressure peak detected at the fuel manifold appears approximately within 40 ms from a spark initiation, which is relatively consistent in every cycle.  FIG. 17  also shows that a pressure detected at the fuel manifold appears approximately within 40 ms from a spark initiation, but the magnitude of pressure rise is less than the other due to the magnitude of plateau pressure at the inlet section.
 
   The performance of the device has been assessed over a wide range of spark intervals.  FIG. 18  illustrates the effect of the gasdynamic valve cycle time on spark interval which controls operating frequency of the valveless PDC. The cycle time is approximately estimated using Eq. 7 assuming that the purge process, τ purge , is negligible compared with the fill process, τ fill , and the gasdynamic valve closing duration, τ close , is approximated to be the duration between time of the spark initiation and of the peak pressure detected at the fuel manifold, t peak −t DDT . The fill duration, τ fill , is estimated by Eq. 3. Reference for the cycle time corresponds to the spark initiation, t DDT . This plot includes all data points describing pulsed combustion modes regardless of their DDT accomplishments. Successful mode designates that a spark frequency corresponds with an actual operating frequency. Failed mode designates that a spark frequency doesn&#39;t correspond with an actual operating frequency. Experimental conditions used to generate the plot are listed on Table 2. The gasdynamic valve cycle time is required to be less than the spark interval in order to synchronize spark initiation frequency. Reduction of fill time can be achieved by increasing a fill fraction, reducing a combustor size or optimizing a filling scheme. 
   
     
       
             
           
             
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE 2 
             
           
           
             
                 
             
             
               Experimental conditions of the valveless PDC operation; 
             
             
               averaged fill fraction and equivalence ratio based on 
             
             
               actual frequency, and approximate gasdynamic valve cycle 
             
             
               time estimated by Eq. 7 are listed in this table. 
             
           
        
         
             
                 
               Spark 
               Actual 
               Fill 
                 
                 
             
             
               Reactant 
               frequency, Hz 
               frequency, Hz 
               fraction 
               φ 
               τ, ms 
             
             
                 
             
           
        
         
             
               C 2 H 4 -air 
               5.3 
               5.3 
               1.7 
               1.1 
               128 
             
             
               C 2 H 4 -air 
               5.3 
               5.3 
               1.7 
               1.1 
               130 
             
             
               C 2 H 4 -air 
               5.3 
               5.3 
               1.1 
               1.1 
               178 
             
             
               C 2 H 4 -air 
               8.3 
               8.3 
               1.1 
               0.8 
               120 
             
             
               C 2 H 4 -air 
               11.1 
               5.6 
               2.0 
               0.7 
               108 
             
             
               C 3 H 8 -air 
               1.5 
               1.5 
               2.3 
               1.0 
               313 
             
             
               C 3 H 8 -air 
               1.5 
               1.5 
               2.3 
               1.2 
               310 
             
             
               C 3 H 8 -air 
               1.5 
               1.5 
               2.3 
               1.1 
               309 
             
             
               C 3 H 8 -air 
               4.0 
               4.0 
               1.8 
               0.9 
               140 
             
             
               C 3 H 8 -air 
               4.0 
               4.0 
               1.9 
               1.0 
               158 
             
             
               C 3 H 8 -air 
               4.0 
               4.0 
               1.8 
               0.9 
               159 
             
             
               C 3 H 8 -air 
               4.0 
               4.0 
               1.2 
               0.9 
               213 
             
             
               C 3 H 8 -air 
               4.0 
               4.0 
               0.9 
               1.1 
               255 
             
             
               C 3 H 8 -air 
               6.7 
               3.3 
               2.4 
               0.9 
               151 
             
             
               C 3 H 8 -air 
               8.3 
               4.1 
               2.1 
               1.0 
               141 
             
             
               C 3 H 8 -air 
               8.3 
               4.2 
               2.6 
               0.8 
               120 
             
             
               C 3 H 8 -air 
               8.3 
               4.3 
               1.9 
               1.1 
               146 
             
             
               C 3 H 8 -air 
               12.5 
               6.2 
               2.0 
               0.9 
               103 
             
             
               C 3 H 8 -air 
               12.5 
               6.2 
               1.9 
               0.8 
               102 
             
             
               C 3 H 8 -air 
               12.5 
               5.7 
               2.0 
               1.0 
               113 
             
             
               C 3 H 8 -air 
               12.5 
               6.0 
               1.9 
               1.0 
               113 
             
             
               C 3 H 8 -air 
               12.5 
               6.3 
               1.7 
               1.0 
               110 
             
             
               C 3 H 8 -air 
               12.5 
               6.2 
               1.2 
               0.0 
               143 
             
             
                 
             
           
        
       
     
   
   While the invention has been illustrated and described in detail in the drawings and foregoing description, the same is to be considered as illustrative and not restrictive in character, it being understood that only the preferred embodiment has been shown and described and that all changes and modifications that come within the spirit of the invention, such as placing a diffuser downstream from the buffer section to feed two detonation tubes, for example, are desired to be protected.